%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SCT170^2 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n183.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 300.06s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SCT170^2 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n183.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 08:26:41 CDT 2014
% % CPUTime  : 300.06 
% 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 0x1210518>, <kernel.Type object at 0x1210c20>) of role type named ty_ty_tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring arrow_475358991le_alt:Type
% FOF formula (<kernel.Constant object at 0x15eb908>, <kernel.Type object at 0x12105f0>) of role type named ty_ty_tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring arrow_1429601828e_indi:Type
% FOF formula (<kernel.Constant object at 0x1210b90>, <kernel.Type object at 0x12107e8>) of role type named ty_ty_tc__List__Olist_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv
% Using role type
% Declaring list_A518015091_alt_o:Type
% FOF formula (<kernel.Constant object at 0x1210c20>, <kernel.Type object at 0x12104d0>) of role type named ty_ty_tc__List__Olist_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oind
% Using role type
% Declaring list_A524553945_alt_o:Type
% FOF formula (<kernel.Constant object at 0x12105f0>, <kernel.Type object at 0x1210560>) of role type named ty_ty_tc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvl
% Using role type
% Declaring list_P1178103901_alt_o:Type
% FOF formula (<kernel.Constant object at 0x1210cb0>, <kernel.Type object at 0x12104d0>) of role type named ty_ty_tc__List__Olist_I_Eo_J
% Using role type
% Declaring list_o:Type
% FOF formula (<kernel.Constant object at 0x1210488>, <kernel.Type object at 0x1210c20>) of role type named ty_ty_tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_J
% Using role type
% Declaring list_A2115238852le_alt:Type
% FOF formula (<kernel.Constant object at 0x1210dd0>, <kernel.Type object at 0x1210440>) of role type named ty_ty_tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_J
% Using role type
% Declaring list_A1484739013e_indi:Type
% FOF formula (<kernel.Constant object at 0x12104d0>, <kernel.Type object at 0x1210560>) of role type named ty_ty_tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilv
% Using role type
% Declaring list_l1475218533le_alt:Type
% FOF formula (<kernel.Constant object at 0x1210c20>, <kernel.Type object at 0x1210368>) of role type named ty_ty_tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring list_P736798472le_alt:Type
% FOF formula (<kernel.Constant object at 0x1210440>, <kernel.Type object at 0x1210758>) of role type named ty_ty_tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell
% Using role type
% Declaring list_P1295265784le_alt:Type
% FOF formula (<kernel.Constant object at 0x1210560>, <kernel.Type object at 0x12107a0>) of role type named ty_ty_tc__Nat__Onat
% Using role type
% Declaring nat:Type
% FOF formula (<kernel.Constant object at 0x1667290>, <kernel.Type object at 0x1210758>) of role type named ty_ty_tc__prod_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring produc344885491_alt_o:Type
% FOF formula (<kernel.Constant object at 0x1210368>, <kernel.Type object at 0x10f5f80>) of role type named ty_ty_tc__prod_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_062
% Using role type
% Declaring produc634020647_alt_o:Type
% FOF formula (<kernel.Constant object at 0x12107e8>, <kernel.Type object at 0x10f5f80>) of role type named ty_ty_tc__prod_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O
% Using role type
% Declaring produc603869735_alt_o:Type
% FOF formula (<kernel.Constant object at 0x1210758>, <kernel.Type object at 0x10f5ef0>) of role type named ty_ty_tc__prod_I_Eo_M_Eo_J
% Using role type
% Declaring product_prod_o_o:Type
% FOF formula (<kernel.Constant object at 0x12106c8>, <kernel.Type object at 0x10f5b90>) of role type named ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_Mtc__Arrow__
% Using role type
% Declaring produc1501160679le_alt:Type
% FOF formula (<kernel.Constant object at 0x1210758>, <kernel.Type object at 0x10f5ef0>) of role type named ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_Mtc__Arrow_
% Using role type
% Declaring produc1091721111e_indi:Type
% FOF formula (<kernel.Constant object at 0x12107e8>, <kernel.Type object at 0x160a518>) of role type named ty_ty_tc__prod_Itc__List__Olist_I_062_I_062_Itc__Arrow____Order____Mirabelle____
% Using role type
% Declaring produc1362754407_alt_o:Type
% FOF formula (<kernel.Constant object at 0x1210758>, <kernel.Type object at 0x160a518>) of role type named ty_ty_tc__prod_Itc__List__Olist_I_062_Itc__Arrow____Order____Mirabelle____lcilvl
% Using role type
% Declaring produc2070394625_alt_o:Type
% FOF formula (<kernel.Constant object at 0x1210758>, <kernel.Type object at 0x160a5a8>) of role type named ty_ty_tc__prod_Itc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle
% Using role type
% Declaring produc1361459593_alt_o:Type
% FOF formula (<kernel.Constant object at 0x10f53b0>, <kernel.Type object at 0x160a368>) of role type named ty_ty_tc__prod_Itc__List__Olist_I_Eo_J_Mtc__List__Olist_I_Eo_J_J
% Using role type
% Declaring produc1191881495list_o:Type
% FOF formula (<kernel.Constant object at 0x10f5ef0>, <kernel.Type object at 0x160a560>) of role type named ty_ty_tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring produc1362454231le_alt:Type
% FOF formula (<kernel.Constant object at 0x10f5680>, <kernel.Type object at 0x160a200>) of role type named ty_ty_tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv___001
% Using role type
% Declaring produc343559527e_indi:Type
% FOF formula (<kernel.Constant object at 0x10f5ef0>, <kernel.Type object at 0x160a488>) of role type named ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabell
% Using role type
% Declaring produc938956263le_alt:Type
% FOF formula (<kernel.Constant object at 0x10f5ef0>, <kernel.Type object at 0x160a098>) of role type named ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____lc
% Using role type
% Declaring produc347927591le_alt:Type
% FOF formula (<kernel.Constant object at 0x160a200>, <kernel.Type object at 0x160a170>) of role type named ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order__
% Using role type
% Declaring produc1884787239le_alt:Type
% FOF formula (<kernel.Constant object at 0x160a488>, <kernel.Type object at 0x160af80>) of role type named ty_ty_tc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_Mt
% Using role type
% Declaring produc1076844957le_alt:Type
% FOF formula (<kernel.Constant object at 0x160a098>, <kernel.Type object at 0x160aea8>) of role type named ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lc
% Using role type
% Declaring produc1787997437le_alt:Type
% FOF formula (<kernel.Constant object at 0x160a5a8>, <kernel.DependentProduct object at 0x160af38>) of role type named sy_c_All2
% Using role type
% Declaring all2:((produc1501160679le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x160a290>, <kernel.DependentProduct object at 0x160a128>) of role type named sy_c_All1
% Using role type
% Declaring all1:((produc1362454231le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x160a7a0>, <kernel.DependentProduct object at 0x10f9cf8>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_OIIA
% Using role type
% Declaring arrow_797024463le_IIA:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x160a710>, <kernel.DependentProduct object at 0x160af38>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_OLin
% Using role type
% Declaring arrow_823908191le_Lin:((produc1501160679le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x160a098>, <kernel.DependentProduct object at 0x122bfc8>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_OProf
% Using role type
% Declaring arrow_734252939e_Prof:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x160a7a0>, <kernel.DependentProduct object at 0x122bef0>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Oabove
% Using role type
% Declaring arrow_789600939_above:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->(produc1501160679le_alt->Prop))))
% FOF formula (<kernel.Constant object at 0x160a710>, <kernel.DependentProduct object at 0x122bd40>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Obelow
% Using role type
% Declaring arrow_2098199487_below:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->(produc1501160679le_alt->Prop))))
% FOF formula (<kernel.Constant object at 0x160a098>, <kernel.DependentProduct object at 0x122bfc8>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Odictator
% Using role type
% Declaring arrow_1212662430ctator:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))
% FOF formula (<kernel.Constant object at 0x160a710>, <kernel.DependentProduct object at 0x122bc20>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Omkbot
% Using role type
% Declaring arrow_2054445623_mkbot:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(produc1501160679le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x160a098>, <kernel.DependentProduct object at 0x122bdd0>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Omktop
% Using role type
% Declaring arrow_55669061_mktop:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(produc1501160679le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x160a7a0>, <kernel.DependentProduct object at 0x122bcb0>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Ounanimity
% Using role type
% Declaring arrow_1706409458nimity:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x160a7a0>, <kernel.DependentProduct object at 0x122bc20>) of role type named sy_c_Ex2
% Using role type
% Declaring ex2:((produc1501160679le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x122be60>, <kernel.DependentProduct object at 0x122bcb0>) of role type named sy_c_Ex1
% Using role type
% Declaring ex1:((produc1362454231le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x122bd40>, <kernel.DependentProduct object at 0x122bef0>) of role type named sy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000t
% Using role type
% Declaring in_rel1252994498le_alt:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x122bb00>, <kernel.DependentProduct object at 0x122b950>) of role type named sy_c_FunDef_Oin__rel_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcil
% Using role type
% Declaring in_rel1156631736le_alt:((produc1362454231le_alt->Prop)->(list_A2115238852le_alt->(list_A2115238852le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x122b9e0>, <kernel.DependentProduct object at 0x122b680>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O
% Using role type
% Declaring pi_Arr195212324lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x122b8c0>, <kernel.DependentProduct object at 0x122b680>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O_002
% Using role type
% Declaring pi_Arr1005837828le_alt:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x122bcb0>, <kernel.DependentProduct object at 0x122b680>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O_003
% Using role type
% Declaring pi_Arr338314351e_indi:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x122bd40>, <kernel.DependentProduct object at 0x122b680>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O_004
% Using role type
% Declaring pi_Arr2076738722le_alt:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x122b6c8>, <kernel.DependentProduct object at 0x122b3b0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M
% Using role type
% Declaring pi_Arr1304755663_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x122b440>, <kernel.DependentProduct object at 0x122b9e0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_005
% Using role type
% Declaring pi_Arr952516694lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x122bcb0>, <kernel.DependentProduct object at 0x122b4d0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_006
% Using role type
% Declaring pi_Arr1483346486le_alt:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x122bd40>, <kernel.DependentProduct object at 0x122bef0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_007
% Using role type
% Declaring pi_Arr1232280765e_indi:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x122b6c8>, <kernel.DependentProduct object at 0x122b5f0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_008
% Using role type
% Declaring pi_Arr1957214192le_alt:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x122b440>, <kernel.DependentProduct object at 0x122bb00>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz
% Using role type
% Declaring pi_Pro422690258lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(Prop->Prop))->(((produc1501160679le_alt->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x122bcb0>, <kernel.DependentProduct object at 0x122b8c0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz_009
% Using role type
% Declaring pi_Pro1868152754le_alt:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))->(((produc1501160679le_alt->Prop)->arrow_475358991le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x122b560>, <kernel.DependentProduct object at 0x122b440>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz_010
% Using role type
% Declaring pi_Pro468373057e_indi:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))->(((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x122bd40>, <kernel.DependentProduct object at 0x122bcb0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz_011
% Using role type
% Declaring pi_Pro1678345076le_alt:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))->(((produc1501160679le_alt->Prop)->produc1362454231le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x122b6c8>, <kernel.DependentProduct object at 0x160b0e0>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvl
% Using role type
% Declaring pi_o_A1186128886_alt_o:((Prop->Prop)->((Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x122b560>, <kernel.DependentProduct object at 0x160b1b8>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring pi_o_A1182933120_alt_o:((Prop->Prop)->((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x122bcb0>, <kernel.DependentProduct object at 0x160b050>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lc
% Using role type
% Declaring pi_o_P553196292_alt_o:((Prop->Prop)->((Prop->((produc1501160679le_alt->Prop)->Prop))->((Prop->(produc1501160679le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x122b560>, <kernel.DependentProduct object at 0x160b0e0>) of role type named sy_c_FuncSet_OPi_000_Eo_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring pi_o_P657324555le_alt:((Prop->Prop)->((Prop->(produc1501160679le_alt->Prop))->((Prop->produc1501160679le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x122bcb0>, <kernel.DependentProduct object at 0x160b170>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000_062_
% Using role type
% Declaring pi_Arr515871190_alt_o:((arrow_475358991le_alt->Prop)->((arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x122b6c8>, <kernel.DependentProduct object at 0x160b320>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000_062__012
% Using role type
% Declaring pi_Arr578767520_alt_o:((arrow_475358991le_alt->Prop)->((arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x122b6c8>, <kernel.DependentProduct object at 0x160ba70>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000_062__013
% Using role type
% Declaring pi_Arr1520776484_alt_o:((arrow_475358991le_alt->Prop)->((arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))->((arrow_475358991le_alt->(produc1501160679le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x160b1b8>, <kernel.DependentProduct object at 0x160ba70>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000tc__p
% Using role type
% Declaring pi_Arr1786181611le_alt:((arrow_475358991le_alt->Prop)->((arrow_475358991le_alt->(produc1501160679le_alt->Prop))->((arrow_475358991le_alt->produc1501160679le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x160b170>, <kernel.DependentProduct object at 0x1221830>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000_062
% Using role type
% Declaring pi_Arr1564509167_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x160b290>, <kernel.DependentProduct object at 0x1221908>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000_062_014
% Using role type
% Declaring pi_Arr1060328391_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x160ba70>, <kernel.DependentProduct object at 0x1221830>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000_062_015
% Using role type
% Declaring pi_Arr1929480907_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x160b170>, <kernel.DependentProduct object at 0x1221830>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000tc__
% Using role type
% Declaring pi_Arr329216900le_alt:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((arrow_1429601828e_indi->produc1501160679le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x160b290>, <kernel.DependentProduct object at 0x1221758>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oal
% Using role type
% Declaring pi_Pro1701359055_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(Prop->Prop))->((produc1501160679le_alt->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x160b170>, <kernel.DependentProduct object at 0x1221758>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oal_016
% Using role type
% Declaring pi_Pro315446191le_alt:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(arrow_475358991le_alt->Prop))->((produc1501160679le_alt->arrow_475358991le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x160b290>, <kernel.DependentProduct object at 0x1221758>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oal_017
% Using role type
% Declaring pi_Pro1767455108e_indi:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(arrow_1429601828e_indi->Prop))->((produc1501160679le_alt->arrow_1429601828e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x160ba70>, <kernel.DependentProduct object at 0x1221950>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oal_018
% Using role type
% Declaring pi_Pro666407479le_alt:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(produc1362454231le_alt->Prop))->((produc1501160679le_alt->produc1362454231le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x160ba70>, <kernel.DependentProduct object at 0x1221680>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__
% Using role type
% Declaring pi_Pro441468706_alt_o:((produc1362454231le_alt->Prop)->((produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x12217a0>, <kernel.DependentProduct object at 0x1221680>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___019
% Using role type
% Declaring pi_Pro121963604_alt_o:((produc1362454231le_alt->Prop)->((produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x12217e8>, <kernel.DependentProduct object at 0x1221710>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___020
% Using role type
% Declaring pi_Pro589599960_alt_o:((produc1362454231le_alt->Prop)->((produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))->((produc1362454231le_alt->(produc1501160679le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x12216c8>, <kernel.DependentProduct object at 0x12217a0>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___021
% Using role type
% Declaring pi_Pro1708969783le_alt:((produc1362454231le_alt->Prop)->((produc1362454231le_alt->(produc1501160679le_alt->Prop))->((produc1362454231le_alt->produc1501160679le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x12215a8>, <kernel.DependentProduct object at 0x1221710>) of role type named sy_c_HOL_Oequal__class_Oequal_000tc__List__Olist_Itc__Arrow____Order____Mirabell
% Using role type
% Declaring equal_484611810le_alt:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1221560>, <kernel.DependentProduct object at 0x1221710>) of role type named sy_c_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlk
% Using role type
% Declaring if_Pro314693991le_alt:(Prop->(produc1362454231le_alt->(produc1362454231le_alt->produc1362454231le_alt)))
% FOF formula (<kernel.Constant object at 0x12216c8>, <kernel.DependentProduct object at 0x12218c0>) of role type named sy_c_List_Oappend_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring append326058957_alt_o:(list_A518015091_alt_o->(list_A518015091_alt_o->list_A518015091_alt_o))
% FOF formula (<kernel.Constant object at 0x12215f0>, <kernel.DependentProduct object at 0x1221488>) of role type named sy_c_List_Oappend_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_
% Using role type
% Declaring append295924073_alt_o:(list_A524553945_alt_o->(list_A524553945_alt_o->list_A524553945_alt_o))
% FOF formula (<kernel.Constant object at 0x1221710>, <kernel.DependentProduct object at 0x1221638>) of role type named sy_c_List_Oappend_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring append612833133_alt_o:(list_P1178103901_alt_o->(list_P1178103901_alt_o->list_P1178103901_alt_o))
% FOF formula (<kernel.Constant object at 0x12218c0>, <kernel.DependentProduct object at 0x12215a8>) of role type named sy_c_List_Oappend_000_Eo
% Using role type
% Declaring append_o:(list_o->(list_o->list_o))
% FOF formula (<kernel.Constant object at 0x1221488>, <kernel.DependentProduct object at 0x1221560>) of role type named sy_c_List_Oappend_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring append179082452le_alt:(list_A2115238852le_alt->(list_A2115238852le_alt->list_A2115238852le_alt))
% FOF formula (<kernel.Constant object at 0x1221638>, <kernel.DependentProduct object at 0x12216c8>) of role type named sy_c_List_Oappend_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring append711934367e_indi:(list_A1484739013e_indi->(list_A1484739013e_indi->list_A1484739013e_indi))
% FOF formula (<kernel.Constant object at 0x12215a8>, <kernel.DependentProduct object at 0x12215f0>) of role type named sy_c_List_Oappend_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlk
% Using role type
% Declaring append1166001599le_alt:(list_l1475218533le_alt->(list_l1475218533le_alt->list_l1475218533le_alt))
% FOF formula (<kernel.Constant object at 0x1221560>, <kernel.DependentProduct object at 0x1221710>) of role type named sy_c_List_Oappend_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa
% Using role type
% Declaring append1229289570le_alt:(list_P736798472le_alt->(list_P736798472le_alt->list_P736798472le_alt))
% FOF formula (<kernel.Constant object at 0x12216c8>, <kernel.DependentProduct object at 0x12218c0>) of role type named sy_c_List_Oappend_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_
% Using role type
% Declaring append423770578le_alt:(list_P1295265784le_alt->(list_P1295265784le_alt->list_P1295265784le_alt))
% FOF formula (<kernel.Constant object at 0x12215f0>, <kernel.DependentProduct object at 0x1221638>) of role type named sy_c_List_Obutlast_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_
% Using role type
% Declaring butlas1138247126_alt_o:(list_A518015091_alt_o->list_A518015091_alt_o)
% FOF formula (<kernel.Constant object at 0x1221710>, <kernel.DependentProduct object at 0x12215a8>) of role type named sy_c_List_Obutlast_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring butlas813143712_alt_o:(list_A524553945_alt_o->list_A524553945_alt_o)
% FOF formula (<kernel.Constant object at 0x12218c0>, <kernel.DependentProduct object at 0x1221128>) of role type named sy_c_List_Obutlast_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlk
% Using role type
% Declaring butlas368541988_alt_o:(list_P1178103901_alt_o->list_P1178103901_alt_o)
% FOF formula (<kernel.Constant object at 0x1221638>, <kernel.DependentProduct object at 0x1221170>) of role type named sy_c_List_Obutlast_000_Eo
% Using role type
% Declaring butlast_o:(list_o->list_o)
% FOF formula (<kernel.Constant object at 0x12215a8>, <kernel.DependentProduct object at 0x1221098>) of role type named sy_c_List_Obutlast_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring butlas274947851le_alt:(list_A2115238852le_alt->list_A2115238852le_alt)
% FOF formula (<kernel.Constant object at 0x1221128>, <kernel.DependentProduct object at 0x12210e0>) of role type named sy_c_List_Obutlast_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring butlas1554122024e_indi:(list_A1484739013e_indi->list_A1484739013e_indi)
% FOF formula (<kernel.Constant object at 0x1221170>, <kernel.DependentProduct object at 0x1221050>) of role type named sy_c_List_Obutlast_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O
% Using role type
% Declaring butlas661498859le_alt:(list_P736798472le_alt->list_P736798472le_alt)
% FOF formula (<kernel.Constant object at 0x1221098>, <kernel.DependentProduct object at 0x12219e0>) of role type named sy_c_List_Obutlast_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle
% Using role type
% Declaring butlas464406491le_alt:(list_P1295265784le_alt->list_P1295265784le_alt)
% FOF formula (<kernel.Constant object at 0x12210e0>, <kernel.DependentProduct object at 0x12215a8>) of role type named sy_c_List_Odistinct_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv
% Using role type
% Declaring distin1908010863_alt_o:(list_A518015091_alt_o->Prop)
% FOF formula (<kernel.Constant object at 0x1221050>, <kernel.DependentProduct object at 0x1221a28>) of role type named sy_c_List_Odistinct_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oind
% Using role type
% Declaring distin1869760583_alt_o:(list_A524553945_alt_o->Prop)
% FOF formula (<kernel.Constant object at 0x12219e0>, <kernel.DependentProduct object at 0x1221a70>) of role type named sy_c_List_Odistinct_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvl
% Using role type
% Declaring distin1582710603_alt_o:(list_P1178103901_alt_o->Prop)
% FOF formula (<kernel.Constant object at 0x12215a8>, <kernel.DependentProduct object at 0x1221ab8>) of role type named sy_c_List_Odistinct_000_Eo
% Using role type
% Declaring distinct_o:(list_o->Prop)
% FOF formula (<kernel.Constant object at 0x1221a28>, <kernel.DependentProduct object at 0x1221b00>) of role type named sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring distin236324274le_alt:(list_A2115238852le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x1221a70>, <kernel.DependentProduct object at 0x1221b48>) of role type named sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring distin1916799041e_indi:(list_A1484739013e_indi->Prop)
% FOF formula (<kernel.Constant object at 0x1221ab8>, <kernel.DependentProduct object at 0x1221b90>) of role type named sy_c_List_Odistinct_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring distin1776819972le_alt:(list_P736798472le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x1221b00>, <kernel.DependentProduct object at 0x1221bd8>) of role type named sy_c_List_Odistinct_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell
% Using role type
% Declaring distin561495412le_alt:(list_P1295265784le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x1221b48>, <kernel.DependentProduct object at 0x1221bd8>) of role type named sy_c_List_OdropWhile_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkz
% Using role type
% Declaring dropWh583351873_alt_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(list_A518015091_alt_o->list_A518015091_alt_o))
% FOF formula (<kernel.Constant object at 0x1221b90>, <kernel.DependentProduct object at 0x1221cb0>) of role type named sy_c_List_OdropWhile_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oin
% Using role type
% Declaring dropWh73644021_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(list_A524553945_alt_o->list_A524553945_alt_o))
% FOF formula (<kernel.Constant object at 0x1221c20>, <kernel.DependentProduct object at 0x1221ab8>) of role type named sy_c_List_OdropWhile_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilv
% Using role type
% Declaring dropWh1049991161_alt_o:(((produc1501160679le_alt->Prop)->Prop)->(list_P1178103901_alt_o->list_P1178103901_alt_o))
% FOF formula (<kernel.Constant object at 0x1221b00>, <kernel.DependentProduct object at 0x1221ab8>) of role type named sy_c_List_OdropWhile_000_Eo
% Using role type
% Declaring dropWhile_o:((Prop->Prop)->(list_o->list_o))
% FOF formula (<kernel.Constant object at 0x1221b90>, <kernel.DependentProduct object at 0x1221638>) of role type named sy_c_List_OdropWhile_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring dropWh1316781920le_alt:((arrow_475358991le_alt->Prop)->(list_A2115238852le_alt->list_A2115238852le_alt))
% FOF formula (<kernel.Constant object at 0x1221c68>, <kernel.DependentProduct object at 0x1221b48>) of role type named sy_c_List_OdropWhile_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring dropWh1160116755e_indi:((arrow_1429601828e_indi->Prop)->(list_A1484739013e_indi->list_A1484739013e_indi))
% FOF formula (<kernel.Constant object at 0x1221dd0>, <kernel.DependentProduct object at 0x1221cf8>) of role type named sy_c_List_OdropWhile_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_
% Using role type
% Declaring dropWh680325334le_alt:((produc1501160679le_alt->Prop)->(list_P736798472le_alt->list_P736798472le_alt))
% FOF formula (<kernel.Constant object at 0x1221e18>, <kernel.DependentProduct object at 0x1221c20>) of role type named sy_c_List_OdropWhile_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel
% Using role type
% Declaring dropWh612508742le_alt:((produc1362454231le_alt->Prop)->(list_P1295265784le_alt->list_P1295265784le_alt))
% FOF formula (<kernel.Constant object at 0x1221e60>, <kernel.DependentProduct object at 0x1221b00>) of role type named sy_c_List_Odrop_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oi
% Using role type
% Declaring drop_A1326872290_alt_o:(nat->(list_A518015091_alt_o->list_A518015091_alt_o))
% FOF formula (<kernel.Constant object at 0x1221ea8>, <kernel.DependentProduct object at 0x1221b90>) of role type named sy_c_List_Odrop_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_
% Using role type
% Declaring drop_A776701076_alt_o:(nat->(list_A524553945_alt_o->list_A524553945_alt_o))
% FOF formula (<kernel.Constant object at 0x1221c20>, <kernel.DependentProduct object at 0x1221c68>) of role type named sy_c_List_Odrop_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv
% Using role type
% Declaring drop_P619902232_alt_o:(nat->(list_P1178103901_alt_o->list_P1178103901_alt_o))
% FOF formula (<kernel.Constant object at 0x1221b00>, <kernel.DependentProduct object at 0x1221dd0>) of role type named sy_c_List_Odrop_000_Eo
% Using role type
% Declaring drop_o:(nat->(list_o->list_o))
% FOF formula (<kernel.Constant object at 0x1221b90>, <kernel.DependentProduct object at 0x1221e18>) of role type named sy_c_List_Odrop_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring drop_A1346709759le_alt:(nat->(list_A2115238852le_alt->list_A2115238852le_alt))
% FOF formula (<kernel.Constant object at 0x1221c68>, <kernel.DependentProduct object at 0x1221ea8>) of role type named sy_c_List_Odrop_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring drop_A1596373044e_indi:(nat->(list_A1484739013e_indi->list_A1484739013e_indi))
% FOF formula (<kernel.Constant object at 0x1221dd0>, <kernel.DependentProduct object at 0x1221b90>) of role type named sy_c_List_Odrop_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring drop_P933863159le_alt:(nat->(list_P736798472le_alt->list_P736798472le_alt))
% FOF formula (<kernel.Constant object at 0x1221cf8>, <kernel.DependentProduct object at 0x1221c68>) of role type named sy_c_List_Odrop_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___
% Using role type
% Declaring drop_P1438419175le_alt:(nat->(list_P1295265784le_alt->list_P1295265784le_alt))
% FOF formula (<kernel.Constant object at 0x1221b00>, <kernel.DependentProduct object at 0x1603128>) of role type named sy_c_List_Ofoldl_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring foldl_296410428le_alt:((list_A2115238852le_alt->(arrow_475358991le_alt->list_A2115238852le_alt))->(list_A2115238852le_alt->(list_A2115238852le_alt->list_A2115238852le_alt)))
% FOF formula (<kernel.Constant object at 0x1221c68>, <kernel.DependentProduct object at 0x1603128>) of role type named sy_c_List_Ohd_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oind
% Using role type
% Declaring hd_Arr1786382991_alt_o:(list_A518015091_alt_o->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x1221cf8>, <kernel.DependentProduct object at 0x1603170>) of role type named sy_c_List_Ohd_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_06
% Using role type
% Declaring hd_Arr574592295_alt_o:(list_A524553945_alt_o->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x1221c68>, <kernel.DependentProduct object at 0x1603128>) of role type named sy_c_List_Ohd_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring hd_Pro622402603_alt_o:(list_P1178103901_alt_o->(produc1501160679le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1221cf8>, <kernel.DependentProduct object at 0x1603290>) of role type named sy_c_List_Ohd_000_Eo
% Using role type
% Declaring hd_o:(list_o->Prop)
% FOF formula (<kernel.Constant object at 0x1221b00>, <kernel.DependentProduct object at 0x1603098>) of role type named sy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring hd_Arr1965683346le_alt:(list_A2115238852le_alt->arrow_475358991le_alt)
% FOF formula (<kernel.Constant object at 0x1221b00>, <kernel.DependentProduct object at 0x16032d8>) of role type named sy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring hd_Arr1023890273e_indi:(list_A1484739013e_indi->arrow_1429601828e_indi)
% FOF formula (<kernel.Constant object at 0x1603290>, <kernel.DependentProduct object at 0x1603320>) of role type named sy_c_List_Ohd_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_M
% Using role type
% Declaring hd_Pro297626148le_alt:(list_P736798472le_alt->produc1501160679le_alt)
% FOF formula (<kernel.Constant object at 0x1603098>, <kernel.DependentProduct object at 0x1603368>) of role type named sy_c_List_Ohd_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____l
% Using role type
% Declaring hd_Pro856774804le_alt:(list_P1295265784le_alt->produc1362454231le_alt)
% FOF formula (<kernel.Constant object at 0x16032d8>, <kernel.DependentProduct object at 0x1603368>) of role type named sy_c_List_Oinsert_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring insert81217164_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(list_A518015091_alt_o->list_A518015091_alt_o))
% FOF formula (<kernel.Constant object at 0x1603320>, <kernel.DependentProduct object at 0x1603050>) of role type named sy_c_List_Oinsert_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_
% Using role type
% Declaring insert128393578_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(list_A524553945_alt_o->list_A524553945_alt_o))
% FOF formula (<kernel.Constant object at 0x1603440>, <kernel.DependentProduct object at 0x1603290>) of role type named sy_c_List_Oinsert_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring insert451602158_alt_o:((produc1501160679le_alt->Prop)->(list_P1178103901_alt_o->list_P1178103901_alt_o))
% FOF formula (<kernel.Constant object at 0x1603368>, <kernel.DependentProduct object at 0x1603290>) of role type named sy_c_List_Oinsert_000_Eo
% Using role type
% Declaring insert_o:(Prop->(list_o->list_o))
% FOF formula (<kernel.Constant object at 0x1603320>, <kernel.DependentProduct object at 0x16034d0>) of role type named sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring insert2120566741le_alt:(arrow_475358991le_alt->(list_A2115238852le_alt->list_A2115238852le_alt))
% FOF formula (<kernel.Constant object at 0x1603488>, <kernel.DependentProduct object at 0x16033f8>) of role type named sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring insert1474580190e_indi:(arrow_1429601828e_indi->(list_A1484739013e_indi->list_A1484739013e_indi))
% FOF formula (<kernel.Constant object at 0x1603290>, <kernel.DependentProduct object at 0x1603518>) of role type named sy_c_List_Oinsert_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa
% Using role type
% Declaring insert1177064865le_alt:(produc1501160679le_alt->(list_P736798472le_alt->list_P736798472le_alt))
% FOF formula (<kernel.Constant object at 0x16034d0>, <kernel.DependentProduct object at 0x1603440>) of role type named sy_c_List_Oinsert_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_
% Using role type
% Declaring insert1334153361le_alt:(produc1362454231le_alt->(list_P1295265784le_alt->list_P1295265784le_alt))
% FOF formula (<kernel.Constant object at 0x16033f8>, <kernel.DependentProduct object at 0x1603290>) of role type named sy_c_List_Olast_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oi
% Using role type
% Declaring last_A1273867721_alt_o:(list_A518015091_alt_o->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x1603518>, <kernel.DependentProduct object at 0x16032d8>) of role type named sy_c_List_Olast_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_
% Using role type
% Declaring last_A1049530989_alt_o:(list_A524553945_alt_o->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x1603320>, <kernel.DependentProduct object at 0x1603680>) of role type named sy_c_List_Olast_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv
% Using role type
% Declaring last_P685913713_alt_o:(list_P1178103901_alt_o->(produc1501160679le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1603488>, <kernel.DependentProduct object at 0x1603710>) of role type named sy_c_List_Olast_000_Eo
% Using role type
% Declaring last_o:(list_o->Prop)
% FOF formula (<kernel.Constant object at 0x16034d0>, <kernel.DependentProduct object at 0x16036c8>) of role type named sy_c_List_Olast_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring last_A1217315288le_alt:(list_A2115238852le_alt->arrow_475358991le_alt)
% FOF formula (<kernel.Constant object at 0x1603680>, <kernel.DependentProduct object at 0x1603758>) of role type named sy_c_List_Olast_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring last_A303846811e_indi:(list_A1484739013e_indi->arrow_1429601828e_indi)
% FOF formula (<kernel.Constant object at 0x1603710>, <kernel.DependentProduct object at 0x16037a0>) of role type named sy_c_List_Olast_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring last_P1656409182le_alt:(list_P736798472le_alt->produc1501160679le_alt)
% FOF formula (<kernel.Constant object at 0x16036c8>, <kernel.DependentProduct object at 0x16037e8>) of role type named sy_c_List_Olast_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___
% Using role type
% Declaring last_P1879176142le_alt:(list_P1295265784le_alt->produc1362454231le_alt)
% FOF formula (<kernel.Constant object at 0x1603758>, <kernel.DependentProduct object at 0x1603680>) of role type named sy_c_List_Olex_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring lex_Ar1415517219le_alt:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x16037a0>, <kernel.DependentProduct object at 0x16037e8>) of role type named sy_c_List_Olex_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv
% Using role type
% Declaring lex_li663137712le_alt:((produc1362454231le_alt->Prop)->(produc938956263le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1603488>, <kernel.DependentProduct object at 0x1603680>) of role type named sy_c_List_Olexn_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring lexn_A170361439le_alt:((produc1501160679le_alt->Prop)->(nat->(produc1362454231le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x16034d0>, <kernel.DependentProduct object at 0x1603908>) of role type named sy_c_List_Olexord_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring lexord1104163445_alt_o:((produc344885491_alt_o->Prop)->(produc1362754407_alt_o->Prop))
% FOF formula (<kernel.Constant object at 0x16038c0>, <kernel.DependentProduct object at 0x1603680>) of role type named sy_c_List_Olexord_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_
% Using role type
% Declaring lexord1645229249_alt_o:((produc634020647_alt_o->Prop)->(produc2070394625_alt_o->Prop))
% FOF formula (<kernel.Constant object at 0x1603758>, <kernel.DependentProduct object at 0x1603908>) of role type named sy_c_List_Olexord_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring lexord842870469_alt_o:((produc603869735_alt_o->Prop)->(produc1361459593_alt_o->Prop))
% FOF formula (<kernel.Constant object at 0x1603830>, <kernel.DependentProduct object at 0x1603680>) of role type named sy_c_List_Olexord_000_Eo
% Using role type
% Declaring lexord_o:((product_prod_o_o->Prop)->(produc1191881495list_o->Prop))
% FOF formula (<kernel.Constant object at 0x1603998>, <kernel.DependentProduct object at 0x1603908>) of role type named sy_c_List_Olexord_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring lexord958095404le_alt:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1603950>, <kernel.DependentProduct object at 0x1603680>) of role type named sy_c_List_Olexord_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring lexord1661684807e_indi:((produc1091721111e_indi->Prop)->(produc343559527e_indi->Prop))
% FOF formula (<kernel.Constant object at 0x16038c0>, <kernel.DependentProduct object at 0x1603908>) of role type named sy_c_List_Olexord_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlk
% Using role type
% Declaring lexord469916775le_alt:((produc1362454231le_alt->Prop)->(produc938956263le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1603a28>, <kernel.DependentProduct object at 0x1603680>) of role type named sy_c_List_Olexord_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa
% Using role type
% Declaring lexord501678858le_alt:((produc1076844957le_alt->Prop)->(produc347927591le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1603a70>, <kernel.DependentProduct object at 0x1603908>) of role type named sy_c_List_Olexord_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_
% Using role type
% Declaring lexord973342842le_alt:((produc1787997437le_alt->Prop)->(produc1884787239le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1603ab8>, <kernel.DependentProduct object at 0x1603908>) of role type named sy_c_List_Olist_OCons_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring cons_A279268466_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(list_A518015091_alt_o->list_A518015091_alt_o))
% FOF formula (<kernel.Constant object at 0x1603b00>, <kernel.DependentProduct object at 0x1603b48>) of role type named sy_c_List_Olist_OCons_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oi
% Using role type
% Declaring cons_A2010997508_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(list_A524553945_alt_o->list_A524553945_alt_o))
% FOF formula (<kernel.Constant object at 0x1603c20>, <kernel.DependentProduct object at 0x1603a28>) of role type named sy_c_List_Olist_OCons_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcil
% Using role type
% Declaring cons_P1239653256_alt_o:((produc1501160679le_alt->Prop)->(list_P1178103901_alt_o->list_P1178103901_alt_o))
% FOF formula (<kernel.Constant object at 0x1603170>, <kernel.DependentProduct object at 0x1603b00>) of role type named sy_c_List_Olist_OCons_000_Eo
% Using role type
% Declaring cons_o:(Prop->(list_o->list_o))
% FOF formula (<kernel.Constant object at 0x1603c68>, <kernel.DependentProduct object at 0x1603bd8>) of role type named sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring cons_A228743023le_alt:(arrow_475358991le_alt->(list_A2115238852le_alt->list_A2115238852le_alt))
% FOF formula (<kernel.Constant object at 0x1603a28>, <kernel.DependentProduct object at 0x1603ab8>) of role type named sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring cons_A663037380e_indi:(arrow_1429601828e_indi->(list_A1484739013e_indi->list_A1484739013e_indi))
% FOF formula (<kernel.Constant object at 0x1603170>, <kernel.DependentProduct object at 0x1603c20>) of role type named sy_c_List_Olist_OCons_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lci
% Using role type
% Declaring cons_l635097956le_alt:(list_A2115238852le_alt->(list_l1475218533le_alt->list_l1475218533le_alt))
% FOF formula (<kernel.Constant object at 0x1603bd8>, <kernel.DependentProduct object at 0x1603b00>) of role type named sy_c_List_Olist_OCons_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv
% Using role type
% Declaring cons_P1913588871le_alt:(produc1501160679le_alt->(list_P736798472le_alt->list_P736798472le_alt))
% FOF formula (<kernel.Constant object at 0x1603ab8>, <kernel.DependentProduct object at 0x1603680>) of role type named sy_c_List_Olist_OCons_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabe
% Using role type
% Declaring cons_P2048401015le_alt:(produc1362454231le_alt->(list_P1295265784le_alt->list_P1295265784le_alt))
% FOF formula (<kernel.Constant object at 0x1603c20>, <kernel.Constant object at 0x1603680>) of role type named sy_c_List_Olist_ONil_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkz
% Using role type
% Declaring nil_Ar253733922_alt_o:list_A518015091_alt_o
% FOF formula (<kernel.Constant object at 0x1603bd8>, <kernel.Constant object at 0x1603680>) of role type named sy_c_List_Olist_ONil_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oin
% Using role type
% Declaring nil_Ar1876942676_alt_o:list_A524553945_alt_o
% FOF formula (<kernel.Constant object at 0x1603ab8>, <kernel.Constant object at 0x1603680>) of role type named sy_c_List_Olist_ONil_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilv
% Using role type
% Declaring nil_Pr28438488_alt_o:list_P1178103901_alt_o
% FOF formula (<kernel.Constant object at 0x1603c20>, <kernel.Constant object at 0x1603680>) of role type named sy_c_List_Olist_ONil_000_Eo
% Using role type
% Declaring nil_o:list_o
% FOF formula (<kernel.Constant object at 0x1603bd8>, <kernel.Constant object at 0x1603680>) of role type named sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring nil_Ar1286194111le_alt:list_A2115238852le_alt
% FOF formula (<kernel.Constant object at 0x1603ab8>, <kernel.Constant object at 0x1603680>) of role type named sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring nil_Ar380161396e_indi:list_A1484739013e_indi
% FOF formula (<kernel.Constant object at 0x1603c20>, <kernel.Constant object at 0x1603680>) of role type named sy_c_List_Olist_ONil_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcil
% Using role type
% Declaring nil_li1907286804le_alt:list_l1475218533le_alt
% FOF formula (<kernel.Constant object at 0x1603bd8>, <kernel.Constant object at 0x1603680>) of role type named sy_c_List_Olist_ONil_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_
% Using role type
% Declaring nil_Pr861385783le_alt:list_P736798472le_alt
% FOF formula (<kernel.Constant object at 0x1603ab8>, <kernel.Constant object at 0x1603680>) of role type named sy_c_List_Olist_ONil_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel
% Using role type
% Declaring nil_Pr365739559le_alt:list_P1295265784le_alt
% FOF formula (<kernel.Constant object at 0x1603c20>, <kernel.DependentProduct object at 0x1234128>) of role type named sy_c_List_Olist_Olist__case_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_
% Using role type
% Declaring list_c1623890103le_alt:(list_A2115238852le_alt->((arrow_475358991le_alt->(list_A2115238852le_alt->list_A2115238852le_alt))->(list_A2115238852le_alt->list_A2115238852le_alt)))
% FOF formula (<kernel.Constant object at 0x1603fc8>, <kernel.DependentProduct object at 0x1234200>) of role type named sy_c_List_Olistrel1_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring listre2064003096le_alt:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1603ab8>, <kernel.DependentProduct object at 0x1234128>) of role type named sy_c_List_Olistrel1_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilv
% Using role type
% Declaring listre620555643le_alt:((produc1362454231le_alt->Prop)->(produc938956263le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1603c20>, <kernel.DependentProduct object at 0x1234050>) of role type named sy_c_List_Olistrel_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring listre1920655591le_alt:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1603ab8>, <kernel.DependentProduct object at 0x1234170>) of role type named sy_c_List_Olistrel_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvl
% Using role type
% Declaring listre623166444le_alt:((produc1362454231le_alt->Prop)->(produc938956263le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1603c20>, <kernel.DependentProduct object at 0x12341b8>) of role type named sy_c_List_Olistrelp_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring listre1213162009le_alt:((arrow_475358991le_alt->(arrow_475358991le_alt->Prop))->(list_A2115238852le_alt->(list_A2115238852le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x1603fc8>, <kernel.DependentProduct object at 0x1234290>) of role type named sy_c_List_Olistrelp_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilv
% Using role type
% Declaring listre816681018le_alt:((list_A2115238852le_alt->(list_A2115238852le_alt->Prop))->(list_l1475218533le_alt->(list_l1475218533le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x1603fc8>, <kernel.DependentProduct object at 0x1234248>) of role type named sy_c_List_Onull_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring null_A1520965063le_alt:(list_A2115238852le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x1234128>, <kernel.DependentProduct object at 0x1234050>) of role type named sy_c_List_Opartition_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring partit1487577784le_alt:((arrow_475358991le_alt->Prop)->(list_A2115238852le_alt->produc1362454231le_alt))
% FOF formula (<kernel.Constant object at 0x1234290>, <kernel.DependentProduct object at 0x1234368>) of role type named sy_c_List_Oreplicate_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring replic1511538809le_alt:(nat->(arrow_475358991le_alt->list_A2115238852le_alt))
% FOF formula (<kernel.Constant object at 0x12341b8>, <kernel.DependentProduct object at 0x1234200>) of role type named sy_c_List_Orev_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oin
% Using role type
% Declaring rev_Ar5548482_alt_o:(list_A518015091_alt_o->list_A518015091_alt_o)
% FOF formula (<kernel.Constant object at 0x1234050>, <kernel.DependentProduct object at 0x1234170>) of role type named sy_c_List_Orev_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_0
% Using role type
% Declaring rev_Ar413755828_alt_o:(list_A524553945_alt_o->list_A524553945_alt_o)
% FOF formula (<kernel.Constant object at 0x1234368>, <kernel.DependentProduct object at 0x1234440>) of role type named sy_c_List_Orev_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_
% Using role type
% Declaring rev_Pr1006783032_alt_o:(list_P1178103901_alt_o->list_P1178103901_alt_o)
% FOF formula (<kernel.Constant object at 0x1234200>, <kernel.DependentProduct object at 0x1234488>) of role type named sy_c_List_Orev_000_Eo
% Using role type
% Declaring rev_o:(list_o->list_o)
% FOF formula (<kernel.Constant object at 0x1234170>, <kernel.DependentProduct object at 0x12344d0>) of role type named sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring rev_Ar1106406943le_alt:(list_A2115238852le_alt->list_A2115238852le_alt)
% FOF formula (<kernel.Constant object at 0x1234440>, <kernel.DependentProduct object at 0x1234518>) of role type named sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring rev_Ar501922580e_indi:(list_A1484739013e_indi->list_A1484739013e_indi)
% FOF formula (<kernel.Constant object at 0x1234488>, <kernel.DependentProduct object at 0x1234560>) of role type named sy_c_List_Orev_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_
% Using role type
% Declaring rev_Pr1216324055le_alt:(list_P736798472le_alt->list_P736798472le_alt)
% FOF formula (<kernel.Constant object at 0x12344d0>, <kernel.DependentProduct object at 0x12345a8>) of role type named sy_c_List_Orev_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____
% Using role type
% Declaring rev_Pr1619606471le_alt:(list_P1295265784le_alt->list_P1295265784le_alt)
% FOF formula (<kernel.Constant object at 0x1234518>, <kernel.DependentProduct object at 0x12345f0>) of role type named sy_c_List_Orotate1_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring rotate335349260le_alt:(list_A2115238852le_alt->list_A2115238852le_alt)
% FOF formula (<kernel.Constant object at 0x1234560>, <kernel.DependentProduct object at 0x1234638>) of role type named sy_c_List_Oset_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oin
% Using role type
% Declaring set_Ar1356274881_alt_o:(list_A518015091_alt_o->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x12345a8>, <kernel.DependentProduct object at 0x1234518>) of role type named sy_c_List_Oset_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_0
% Using role type
% Declaring set_Ar571341173_alt_o:(list_A524553945_alt_o->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x12345f0>, <kernel.DependentProduct object at 0x1234758>) of role type named sy_c_List_Oset_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_
% Using role type
% Declaring set_Pr592386425_alt_o:(list_P1178103901_alt_o->((produc1501160679le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1234638>, <kernel.DependentProduct object at 0x1234170>) of role type named sy_c_List_Oset_000_Eo
% Using role type
% Declaring set_o:(list_o->(Prop->Prop))
% FOF formula (<kernel.Constant object at 0x1234518>, <kernel.DependentProduct object at 0x12345a8>) of role type named sy_c_List_Oset_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring set_Ar577454304le_alt:(list_A2115238852le_alt->(arrow_475358991le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1234758>, <kernel.DependentProduct object at 0x12344d0>) of role type named sy_c_List_Oset_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring set_Ar778541203e_indi:(list_A1484739013e_indi->(arrow_1429601828e_indi->Prop))
% FOF formula (<kernel.Constant object at 0x12346c8>, <kernel.DependentProduct object at 0x12345f0>) of role type named sy_c_List_Oset_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv
% Using role type
% Declaring set_li1631982259le_alt:(list_l1475218533le_alt->(list_A2115238852le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x12347a0>, <kernel.DependentProduct object at 0x1234638>) of role type named sy_c_List_Oset_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_
% Using role type
% Declaring set_Pr1525059414le_alt:(list_P736798472le_alt->(produc1501160679le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x12347e8>, <kernel.DependentProduct object at 0x1234518>) of role type named sy_c_List_Oset_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____
% Using role type
% Declaring set_Pr412222150le_alt:(list_P1295265784le_alt->(produc1362454231le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1234830>, <kernel.DependentProduct object at 0x1234758>) of role type named sy_c_List_Osplice_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring splice1520898450le_alt:(list_A2115238852le_alt->(list_A2115238852le_alt->list_A2115238852le_alt))
% FOF formula (<kernel.Constant object at 0x1234878>, <kernel.DependentProduct object at 0x1234758>) of role type named sy_c_List_OtakeWhile_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkz
% Using role type
% Declaring takeWh877796585_alt_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(list_A518015091_alt_o->list_A518015091_alt_o))
% FOF formula (<kernel.Constant object at 0x1234518>, <kernel.DependentProduct object at 0x12347a0>) of role type named sy_c_List_OtakeWhile_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oin
% Using role type
% Declaring takeWh1825606477_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(list_A524553945_alt_o->list_A524553945_alt_o))
% FOF formula (<kernel.Constant object at 0x1234950>, <kernel.DependentProduct object at 0x12347e8>) of role type named sy_c_List_OtakeWhile_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilv
% Using role type
% Declaring takeWh1715715921_alt_o:(((produc1501160679le_alt->Prop)->Prop)->(list_P1178103901_alt_o->list_P1178103901_alt_o))
% FOF formula (<kernel.Constant object at 0x1234830>, <kernel.DependentProduct object at 0x12347e8>) of role type named sy_c_List_OtakeWhile_000_Eo
% Using role type
% Declaring takeWhile_o:((Prop->Prop)->(list_o->list_o))
% FOF formula (<kernel.Constant object at 0x1234518>, <kernel.DependentProduct object at 0x12346c8>) of role type named sy_c_List_OtakeWhile_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring takeWh1696291512le_alt:((arrow_475358991le_alt->Prop)->(list_A2115238852le_alt->list_A2115238852le_alt))
% FOF formula (<kernel.Constant object at 0x1234908>, <kernel.DependentProduct object at 0x1234878>) of role type named sy_c_List_OtakeWhile_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring takeWh831911099e_indi:((arrow_1429601828e_indi->Prop)->(list_A1484739013e_indi->list_A1484739013e_indi))
% FOF formula (<kernel.Constant object at 0x1234a70>, <kernel.DependentProduct object at 0x1234998>) of role type named sy_c_List_OtakeWhile_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_
% Using role type
% Declaring takeWh302148478le_alt:((produc1501160679le_alt->Prop)->(list_P736798472le_alt->list_P736798472le_alt))
% FOF formula (<kernel.Constant object at 0x1234ab8>, <kernel.DependentProduct object at 0x1234950>) of role type named sy_c_List_OtakeWhile_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel
% Using role type
% Declaring takeWh1571807982le_alt:((produc1362454231le_alt->Prop)->(list_P1295265784le_alt->list_P1295265784le_alt))
% FOF formula (<kernel.Constant object at 0x1234b00>, <kernel.DependentProduct object at 0x1234518>) of role type named sy_c_List_Otl_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oind
% Using role type
% Declaring tl_Arr2017860491_alt_o:(list_A518015091_alt_o->list_A518015091_alt_o)
% FOF formula (<kernel.Constant object at 0x1234b48>, <kernel.DependentProduct object at 0x1234908>) of role type named sy_c_List_Otl_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_06
% Using role type
% Declaring tl_Arr1704054571_alt_o:(list_A524553945_alt_o->list_A524553945_alt_o)
% FOF formula (<kernel.Constant object at 0x1234950>, <kernel.DependentProduct object at 0x1234bd8>) of role type named sy_c_List_Otl_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring tl_Pro1735316527_alt_o:(list_P1178103901_alt_o->list_P1178103901_alt_o)
% FOF formula (<kernel.Constant object at 0x1234518>, <kernel.DependentProduct object at 0x1234c20>) of role type named sy_c_List_Otl_000_Eo
% Using role type
% Declaring tl_o:(list_o->list_o)
% FOF formula (<kernel.Constant object at 0x1234908>, <kernel.DependentProduct object at 0x1234c68>) of role type named sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring tl_Arr465451158le_alt:(list_A2115238852le_alt->list_A2115238852le_alt)
% FOF formula (<kernel.Constant object at 0x1234bd8>, <kernel.DependentProduct object at 0x1234cb0>) of role type named sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring tl_Arr25726557e_indi:(list_A1484739013e_indi->list_A1484739013e_indi)
% FOF formula (<kernel.Constant object at 0x1234c20>, <kernel.DependentProduct object at 0x1234cf8>) of role type named sy_c_List_Otl_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_M
% Using role type
% Declaring tl_Pro932635936le_alt:(list_P736798472le_alt->list_P736798472le_alt)
% FOF formula (<kernel.Constant object at 0x1234c68>, <kernel.DependentProduct object at 0x1234d40>) of role type named sy_c_List_Otl_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____l
% Using role type
% Declaring tl_Pro1448262032le_alt:(list_P1295265784le_alt->list_P1295265784le_alt)
% FOF formula (<kernel.Constant object at 0x1234cb0>, <kernel.DependentProduct object at 0x1234d88>) of role type named sy_c_Nat_OSuc
% Using role type
% Declaring suc:(nat->nat)
% FOF formula (<kernel.Constant object at 0x1234cf8>, <kernel.DependentProduct object at 0x1234e60>) of role type named sy_c_Nat_Onat_Onat__case_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____
% Using role type
% Declaring nat_ca2147365008le_alt:(list_A2115238852le_alt->((nat->list_A2115238852le_alt)->(nat->list_A2115238852le_alt)))
% FOF formula (<kernel.Constant object at 0x1234d40>, <kernel.DependentProduct object at 0x1234c20>) of role type named sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_
% Using role type
% Declaring size_s1858781230le_alt:(list_A2115238852le_alt->nat)
% FOF formula (<kernel.Constant object at 0x1234908>, <kernel.DependentProduct object at 0x1234ef0>) of role type named sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Or
% Using role type
% Declaring size_s1911906171le_alt:(list_l1475218533le_alt->nat)
% FOF formula (<kernel.Constant object at 0x1234e60>, <kernel.DependentProduct object at 0x1234dd0>) of role type named sy_c_Order__Relation_Ostrict__linear__order__on_000tc__Arrow____Order____Mirabel
% Using role type
% Declaring order_1995917111le_alt:((arrow_475358991le_alt->Prop)->((produc1501160679le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1234c20>, <kernel.DependentProduct object at 0x1234ef0>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat
% Using role type
% Declaring ord_less_nat:(nat->(nat->Prop))
% FOF formula (<kernel.Constant object at 0x1234cb0>, <kernel.DependentProduct object at 0x1234d40>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat
% Using role type
% Declaring ord_less_eq_nat:(nat->(nat->Prop))
% FOF formula (<kernel.Constant object at 0x1234dd0>, <kernel.DependentProduct object at 0x1234f80>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_I_062_I_062_Itc__Arrow____Order____Mirab
% Using role type
% Declaring top_to1969627639lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x1234ef0>, <kernel.DependentProduct object at 0x1234cb0>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__Arrow____Order____Mirabelle__
% Using role type
% Declaring top_to2122763103lt_o_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x1234cf8>, <kernel.DependentProduct object at 0x1234d40>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__prod_Itc__Arrow____Order____M
% Using role type
% Declaring top_to1842727771lt_o_o:((produc1501160679le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1234f80>, <kernel.DependentProduct object at 0x1234cb0>) 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 0x1234ef0>, <kernel.DependentProduct object at 0x123b098>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____lcil
% Using role type
% Declaring top_to728987956_alt_o:(arrow_475358991le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x1234fc8>, <kernel.DependentProduct object at 0x123b0e0>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____lcil_022
% Using role type
% Declaring top_to988227749indi_o:(arrow_1429601828e_indi->Prop)
% FOF formula (<kernel.Constant object at 0x1234f80>, <kernel.DependentProduct object at 0x123b128>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__prod_Itc__Arrow____Order____Mirabel
% Using role type
% Declaring top_to1841428258_alt_o:(produc1501160679le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x1234ef0>, <kernel.DependentProduct object at 0x123b170>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow___
% Using role type
% Declaring top_to1039387826_alt_o:(produc1362454231le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x1234d40>, <kernel.Sort object at 0x10f1518>) 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 0x1234fc8>, <kernel.DependentProduct object at 0x123b248>) of role type named sy_c_Product__Type_OPair_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilv
% Using role type
% Declaring produc434968681_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc344885491_alt_o))
% FOF formula (<kernel.Constant object at 0x1234d40>, <kernel.DependentProduct object at 0x123b1b8>) of role type named sy_c_Product__Type_OPair_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_
% Using role type
% Declaring produc425112727_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc634020647_alt_o))
% FOF formula (<kernel.Constant object at 0x1234d40>, <kernel.DependentProduct object at 0x123b128>) of role type named sy_c_Product__Type_OPair_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____l
% Using role type
% Declaring produc548346135_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->Prop)->produc603869735_alt_o))
% FOF formula (<kernel.Constant object at 0x123b098>, <kernel.DependentProduct object at 0x123b320>) of role type named sy_c_Product__Type_OPair_000_Eo_000_Eo
% Using role type
% Declaring product_Pair_o_o:(Prop->(Prop->product_prod_o_o))
% FOF formula (<kernel.Constant object at 0x123b290>, <kernel.DependentProduct object at 0x123b1b8>) of role type named sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_
% Using role type
% Declaring produc1347929815le_alt:(arrow_475358991le_alt->(arrow_475358991le_alt->produc1501160679le_alt))
% FOF formula (<kernel.Constant object at 0x123b2d8>, <kernel.DependentProduct object at 0x123b0e0>) of role type named sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring produc1851452045e_indi:(arrow_1429601828e_indi->(arrow_1429601828e_indi->produc1091721111e_indi))
% FOF formula (<kernel.Constant object at 0x123b320>, <kernel.DependentProduct object at 0x123b3b0>) of role type named sy_c_Product__Type_OPair_000tc__List__Olist_I_062_I_062_Itc__Arrow____Order____M
% Using role type
% Declaring produc385333463_alt_o:(list_A518015091_alt_o->(list_A518015091_alt_o->produc1362754407_alt_o))
% FOF formula (<kernel.Constant object at 0x123b1b8>, <kernel.DependentProduct object at 0x123b200>) of role type named sy_c_Product__Type_OPair_000tc__List__Olist_I_062_Itc__Arrow____Order____Mirabel
% Using role type
% Declaring produc1301429239_alt_o:(list_A524553945_alt_o->(list_A524553945_alt_o->produc2070394625_alt_o))
% FOF formula (<kernel.Constant object at 0x123b0e0>, <kernel.DependentProduct object at 0x123b098>) of role type named sy_c_Product__Type_OPair_000tc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order_
% Using role type
% Declaring produc127168767_alt_o:(list_P1178103901_alt_o->(list_P1178103901_alt_o->produc1361459593_alt_o))
% FOF formula (<kernel.Constant object at 0x123b3b0>, <kernel.DependentProduct object at 0x123b290>) of role type named sy_c_Product__Type_OPair_000tc__List__Olist_I_Eo_J_000tc__List__Olist_I_Eo_J
% Using role type
% Declaring produc1835210381list_o:(list_o->(list_o->produc1191881495list_o))
% FOF formula (<kernel.Constant object at 0x123b200>, <kernel.DependentProduct object at 0x123b2d8>) of role type named sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____
% Using role type
% Declaring produc776457805le_alt:(list_A2115238852le_alt->(list_A2115238852le_alt->produc1362454231le_alt))
% FOF formula (<kernel.Constant object at 0x123b518>, <kernel.DependentProduct object at 0x123b320>) of role type named sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_____023
% Using role type
% Declaring produc1195920727e_indi:(list_A1484739013e_indi->(list_A1484739013e_indi->produc343559527e_indi))
% FOF formula (<kernel.Constant object at 0x123b290>, <kernel.DependentProduct object at 0x123b1b8>) of role type named sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order
% Using role type
% Declaring produc1317709143le_alt:(list_l1475218533le_alt->(list_l1475218533le_alt->produc938956263le_alt))
% FOF formula (<kernel.Constant object at 0x123b2d8>, <kernel.DependentProduct object at 0x123b0e0>) of role type named sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mir
% Using role type
% Declaring produc1573901719le_alt:(list_P736798472le_alt->(list_P736798472le_alt->produc347927591le_alt))
% FOF formula (<kernel.Constant object at 0x123b320>, <kernel.DependentProduct object at 0x123b3b0>) of role type named sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arro
% Using role type
% Declaring produc1065979415le_alt:(list_P1295265784le_alt->(list_P1295265784le_alt->produc1884787239le_alt))
% FOF formula (<kernel.Constant object at 0x123b1b8>, <kernel.DependentProduct object at 0x123b200>) of role type named sy_c_Product__Type_OPair_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlk
% Using role type
% Declaring produc1348021779le_alt:(produc1501160679le_alt->(produc1501160679le_alt->produc1076844957le_alt))
% FOF formula (<kernel.Constant object at 0x123b0e0>, <kernel.DependentProduct object at 0x123b518>) of role type named sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mir
% Using role type
% Declaring produc1443807987le_alt:(produc1362454231le_alt->(produc1362454231le_alt->produc1787997437le_alt))
% FOF formula (<kernel.Constant object at 0x123b3b0>, <kernel.DependentProduct object at 0x123b290>) of role type named sy_c_Product__Type_Ocurry_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring produc910278158_alt_o:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x123b200>, <kernel.DependentProduct object at 0x123b320>) of role type named sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Arrow____Order____Mirabelle___
% Using role type
% Declaring produc1739499928_alt_o:((produc1362454231le_alt->Prop)->(list_A2115238852le_alt->(list_A2115238852le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x123b758>, <kernel.DependentProduct object at 0x123b0e0>) of role type named sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____lcilv
% Using role type
% Declaring produc362454893_alt_o:((arrow_475358991le_alt->(arrow_475358991le_alt->Prop))->(produc1501160679le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x123b2d8>, <kernel.DependentProduct object at 0x123b7e8>) of role type named sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M
% Using role type
% Declaring produc1948161143_alt_o:((list_A2115238852le_alt->(list_A2115238852le_alt->Prop))->(produc1362454231le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x123b3b0>, <kernel.DependentProduct object at 0x123b7a0>) of role type named sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_024
% Using role type
% Declaring produc677212559le_alt:((list_A2115238852le_alt->(list_A2115238852le_alt->produc1362454231le_alt))->(produc1362454231le_alt->produc1362454231le_alt))
% FOF formula (<kernel.Constant object at 0x123b200>, <kernel.DependentProduct object at 0x123b878>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring collec2009291517_alt_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x123b0e0>, <kernel.DependentProduct object at 0x123b2d8>) of role type named sy_c_Set_OCollect_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_
% Using role type
% Declaring collec682858041_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x123b758>, <kernel.DependentProduct object at 0x123b998>) of role type named sy_c_Set_OCollect_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring collec94295101_alt_o:(((produc1501160679le_alt->Prop)->Prop)->((produc1501160679le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123b3b0>, <kernel.DependentProduct object at 0x123b7e8>) of role type named sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring collec742074788le_alt:((arrow_475358991le_alt->Prop)->(arrow_475358991le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x123b908>, <kernel.DependentProduct object at 0x123b998>) of role type named sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring collec22405327e_indi:((arrow_1429601828e_indi->Prop)->(arrow_1429601828e_indi->Prop))
% FOF formula (<kernel.Constant object at 0x123b200>, <kernel.DependentProduct object at 0x123b7e8>) of role type named sy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa
% Using role type
% Declaring collec869865362le_alt:((produc1501160679le_alt->Prop)->(produc1501160679le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x123b830>, <kernel.DependentProduct object at 0x123b998>) of role type named sy_c_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O
% Using role type
% Declaring fequal781288069le_alt:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x123b950>, <kernel.DependentProduct object at 0x123b200>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring member1823529808lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123ba28>, <kernel.DependentProduct object at 0x123b7a0>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv___025
% Using role type
% Declaring member474974512le_alt:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123ba70>, <kernel.DependentProduct object at 0x123b200>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv___026
% Using role type
% Declaring member1452482393e_indi:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bb48>, <kernel.DependentProduct object at 0x123b7a0>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv___027
% Using role type
% Declaring member845447052le_alt:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bb90>, <kernel.DependentProduct object at 0x123b200>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_
% Using role type
% Declaring member616898751_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bbd8>, <kernel.DependentProduct object at 0x123b950>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi__028
% Using role type
% Declaring member939334982lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123ba70>, <kernel.DependentProduct object at 0x123b7a0>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi__029
% Using role type
% Declaring member1596146470le_alt:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bb48>, <kernel.DependentProduct object at 0x123bc20>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi__030
% Using role type
% Declaring member44294883e_indi:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123b908>, <kernel.DependentProduct object at 0x123bcb0>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi__031
% Using role type
% Declaring member1849320470le_alt:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bcf8>, <kernel.DependentProduct object at 0x123ba28>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring member1961363906lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->((((produc1501160679le_alt->Prop)->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bd40>, <kernel.DependentProduct object at 0x123b950>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk_032
% Using role type
% Declaring member1524522914le_alt:(((produc1501160679le_alt->Prop)->arrow_475358991le_alt)->((((produc1501160679le_alt->Prop)->arrow_475358991le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bc20>, <kernel.DependentProduct object at 0x123b908>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk_033
% Using role type
% Declaring member304866663e_indi:(((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->((((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123b7a0>, <kernel.DependentProduct object at 0x123bcf8>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk_034
% Using role type
% Declaring member1099563162le_alt:(((produc1501160679le_alt->Prop)->produc1362454231le_alt)->((((produc1501160679le_alt->Prop)->produc1362454231le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bdd0>, <kernel.DependentProduct object at 0x123b908>) of role type named sy_c_member_000_062_I_Eo_M_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlk
% Using role type
% Declaring member1957863580_alt_o:((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bc20>, <kernel.DependentProduct object at 0x123ba28>) of role type named sy_c_member_000_062_I_Eo_M_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O
% Using role type
% Declaring member1394214384_alt_o:((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123b7a0>, <kernel.DependentProduct object at 0x123bf80>) of role type named sy_c_member_000_062_I_Eo_M_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lci
% Using role type
% Declaring member1862122484_alt_o:((Prop->(produc1501160679le_alt->Prop))->(((Prop->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bdd0>, <kernel.DependentProduct object at 0x123be18>) of role type named sy_c_member_000_062_I_Eo_Mtc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz
% Using role type
% Declaring member492167345le_alt:((Prop->produc1501160679le_alt)->(((Prop->produc1501160679le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bc20>, <kernel.DependentProduct object at 0x123bea8>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_M_062_I
% Using role type
% Declaring member89384572_alt_o:((arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123b908>, <kernel.DependentProduct object at 0x123bdd0>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_M_062_I_035
% Using role type
% Declaring member1876989968_alt_o:((arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123b7a0>, <kernel.DependentProduct object at 0x123bdd0>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_M_062_I_036
% Using role type
% Declaring member1908358676_alt_o:((arrow_475358991le_alt->(produc1501160679le_alt->Prop))->(((arrow_475358991le_alt->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bf38>, <kernel.DependentProduct object at 0x123be18>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_Mtc__pr
% Using role type
% Declaring member712472209le_alt:((arrow_475358991le_alt->produc1501160679le_alt)->(((arrow_475358991le_alt->produc1501160679le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bef0>, <kernel.DependentProduct object at 0x1240128>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_062_
% Using role type
% Declaring member811956313_alt_o:((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bdd0>, <kernel.DependentProduct object at 0x12401b8>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_062__037
% Using role type
% Declaring member1234151027_alt_o:((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123be18>, <kernel.DependentProduct object at 0x1240170>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_062__038
% Using role type
% Declaring member526088951_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bef0>, <kernel.DependentProduct object at 0x1240248>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_Mtc__p
% Using role type
% Declaring member351225838le_alt:((arrow_1429601828e_indi->produc1501160679le_alt)->(((arrow_1429601828e_indi->produc1501160679le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bdd0>, <kernel.DependentProduct object at 0x1240050>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa
% Using role type
% Declaring member377231867_alt_o:((produc1501160679le_alt->Prop)->(((produc1501160679le_alt->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bef0>, <kernel.DependentProduct object at 0x1240200>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa_039
% Using role type
% Declaring member1416774619le_alt:((produc1501160679le_alt->arrow_475358991le_alt)->(((produc1501160679le_alt->arrow_475358991le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123be18>, <kernel.DependentProduct object at 0x1240248>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa_040
% Using role type
% Declaring member1640632174e_indi:((produc1501160679le_alt->arrow_1429601828e_indi)->(((produc1501160679le_alt->arrow_1429601828e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bef0>, <kernel.DependentProduct object at 0x1240128>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa_041
% Using role type
% Declaring member220989473le_alt:((produc1501160679le_alt->produc1362454231le_alt)->(((produc1501160679le_alt->produc1362454231le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x123bef0>, <kernel.DependentProduct object at 0x1240170>) of role type named sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_
% Using role type
% Declaring member654997644_alt_o:((produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x12402d8>, <kernel.DependentProduct object at 0x12403f8>) of role type named sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__042
% Using role type
% Declaring member392452608_alt_o:((produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x12400e0>, <kernel.DependentProduct object at 0x12403f8>) of role type named sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__043
% Using role type
% Declaring member2082473988_alt_o:((produc1362454231le_alt->(produc1501160679le_alt->Prop))->(((produc1362454231le_alt->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240290>, <kernel.DependentProduct object at 0x1240488>) of role type named sy_c_member_000_062_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__044
% Using role type
% Declaring member428957857le_alt:((produc1362454231le_alt->produc1501160679le_alt)->(((produc1362454231le_alt->produc1501160679le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240320>, <kernel.DependentProduct object at 0x12402d8>) 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 0x12400e0>, <kernel.DependentProduct object at 0x1240440>) of role type named sy_c_member_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring member84363362le_alt:(arrow_475358991le_alt->((arrow_475358991le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240488>, <kernel.DependentProduct object at 0x12404d0>) of role type named sy_c_member_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring member2052026769e_indi:(arrow_1429601828e_indi->((arrow_1429601828e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x12402d8>, <kernel.DependentProduct object at 0x1240518>) of role type named sy_c_member_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O
% Using role type
% Declaring member998134961le_alt:(list_A2115238852le_alt->((list_A2115238852le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240440>, <kernel.DependentProduct object at 0x1240560>) of role type named sy_c_member_000tc__prod_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring member1909339872_alt_o:(produc344885491_alt_o->((produc344885491_alt_o->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x12404d0>, <kernel.DependentProduct object at 0x12405a8>) of role type named sy_c_member_000tc__prod_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oi
% Using role type
% Declaring member423327892_alt_o:(produc634020647_alt_o->((produc634020647_alt_o->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240518>, <kernel.DependentProduct object at 0x12405f0>) of role type named sy_c_member_000tc__prod_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcil
% Using role type
% Declaring member1998617236_alt_o:(produc603869735_alt_o->((produc603869735_alt_o->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x12401b8>, <kernel.DependentProduct object at 0x1240680>) of role type named sy_c_member_000tc__prod_I_Eo_M_Eo_J
% Using role type
% Declaring member1392690260od_o_o:(product_prod_o_o->((product_prod_o_o->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240440>, <kernel.DependentProduct object at 0x1240518>) of role type named sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_Mtc
% Using role type
% Declaring member214075476le_alt:(produc1501160679le_alt->((produc1501160679le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x12405f0>, <kernel.DependentProduct object at 0x12406c8>) of role type named sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_Mt
% Using role type
% Declaring member1239815300e_indi:(produc1091721111e_indi->((produc1091721111e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x12401b8>, <kernel.DependentProduct object at 0x1240710>) of role type named sy_c_member_000tc__prod_Itc__List__Olist_I_062_I_062_Itc__Arrow____Order____Mira
% Using role type
% Declaring member119836116_alt_o:(produc1362754407_alt_o->((produc1362754407_alt_o->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240518>, <kernel.DependentProduct object at 0x1240758>) of role type named sy_c_member_000tc__prod_Itc__List__Olist_I_062_Itc__Arrow____Order____Mirabelle_
% Using role type
% Declaring member1890873582_alt_o:(produc2070394625_alt_o->((produc2070394625_alt_o->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x12406c8>, <kernel.DependentProduct object at 0x12407a0>) of role type named sy_c_member_000tc__prod_Itc__List__Olist_I_062_Itc__prod_Itc__Arrow____Order____
% Using role type
% Declaring member79660662_alt_o:(produc1361459593_alt_o->((produc1361459593_alt_o->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240710>, <kernel.DependentProduct object at 0x12407e8>) of role type named sy_c_member_000tc__prod_Itc__List__Olist_I_Eo_J_Mtc__List__Olist_I_Eo_J_J
% Using role type
% Declaring member806300420list_o:(produc1191881495list_o->((produc1191881495list_o->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240758>, <kernel.DependentProduct object at 0x1240830>) of role type named sy_c_member_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lci
% Using role type
% Declaring member28618436le_alt:(produc1362454231le_alt->((produc1362454231le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x12407a0>, <kernel.DependentProduct object at 0x1240878>) of role type named sy_c_member_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____lci_045
% Using role type
% Declaring member1618636500e_indi:(produc343559527e_indi->((produc343559527e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x12407e8>, <kernel.DependentProduct object at 0x12408c0>) of role type named sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____Order___
% Using role type
% Declaring member1732936276le_alt:(produc938956263le_alt->((produc938956263le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240830>, <kernel.DependentProduct object at 0x1240908>) of role type named sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabe
% Using role type
% Declaring member475755924le_alt:(produc347927591le_alt->((produc347927591le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240878>, <kernel.DependentProduct object at 0x1240950>) of role type named sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow__
% Using role type
% Declaring member608607380le_alt:(produc1884787239le_alt->((produc1884787239le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x12408c0>, <kernel.DependentProduct object at 0x1240998>) of role type named sy_c_member_000tc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv
% Using role type
% Declaring member1664185994le_alt:(produc1076844957le_alt->((produc1076844957le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240908>, <kernel.DependentProduct object at 0x12409e0>) of role type named sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabe
% Using role type
% Declaring member902484714le_alt:(produc1787997437le_alt->((produc1787997437le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1240950>, <kernel.DependentProduct object at 0x1240878>) of role type named sy_v_F
% Using role type
% Declaring f:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1240998>, <kernel.DependentProduct object at 0x12409e0>) of role type named sy_v_P_H____
% Using role type
% Declaring p_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x12408c0>, <kernel.DependentProduct object at 0x1240830>) of role type named sy_v_P____
% Using role type
% Declaring p:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x12407e8>, <kernel.Constant object at 0x1240830>) of role type named sy_v_a____
% Using role type
% Declaring a:arrow_475358991le_alt
% FOF formula (<kernel.Constant object at 0x1240998>, <kernel.Constant object at 0x1240830>) of role type named sy_v_b____
% Using role type
% Declaring b:arrow_475358991le_alt
% FOF formula (<kernel.Constant object at 0x12408c0>, <kernel.Constant object at 0x1240830>) of role type named sy_v_c____
% Using role type
% Declaring c:arrow_475358991le_alt
% FOF formula ((member526088951_alt_o p) arrow_734252939e_Prof) of role axiom named fact_0__096P_A_058_AProf_096
% A new axiom: ((member526088951_alt_o p) arrow_734252939e_Prof)
% FOF formula (arrow_797024463le_IIA f) of role axiom named fact_1_assms_I3_J
% A new axiom: (arrow_797024463le_IIA f)
% FOF formula (arrow_1706409458nimity f) of role axiom named fact_2_u
% A new axiom: (arrow_1706409458nimity f)
% FOF formula (not (((eq arrow_475358991le_alt) a) b)) of role axiom named fact_3__096a_A_126_061_Ab_096
% A new axiom: (not (((eq arrow_475358991le_alt) a) b))
% FOF formula (distin236324274le_alt ((cons_A228743023le_alt a) ((cons_A228743023le_alt b) ((cons_A228743023le_alt c) nil_Ar1286194111le_alt)))) of role axiom named fact_4_dist
% A new axiom: (distin236324274le_alt ((cons_A228743023le_alt a) ((cons_A228743023le_alt b) ((cons_A228743023le_alt c) nil_Ar1286194111le_alt))))
% FOF formula (forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt a) b)) (p _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt b) a)) (p_1 _TPTP_I)))) of role axiom named fact_5_iff
% A new axiom: (forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt a) b)) (p _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt b) a)) (p_1 _TPTP_I))))
% FOF formula ((forall (C_2:arrow_475358991le_alt), ((distin236324274le_alt ((cons_A228743023le_alt a) ((cons_A228743023le_alt b) ((cons_A228743023le_alt C_2) nil_Ar1286194111le_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_2:arrow_475358991le_alt), ((distin236324274le_alt ((cons_A228743023le_alt a) ((cons_A228743023le_alt b) ((cons_A228743023le_alt C_2) nil_Ar1286194111le_alt))))->False))->False)
% FOF formula ((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> (((arrow_2098199487_below (((arrow_2098199487_below (p P_30)) c) b)) b) a))) arrow_734252939e_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: ((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> (((arrow_2098199487_below (((arrow_2098199487_below (p P_30)) c) b)) b) a))) arrow_734252939e_Prof)
% FOF formula ((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> (((arrow_2098199487_below (((arrow_2098199487_below (((arrow_2098199487_below (p P_30)) c) b)) b) a)) a) c))) arrow_734252939e_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: ((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> (((arrow_2098199487_below (((arrow_2098199487_below (((arrow_2098199487_below (p P_30)) c) b)) b) a)) a) c))) arrow_734252939e_Prof)
% FOF formula ((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> (((arrow_2098199487_below (p P_30)) c) b))) arrow_734252939e_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: ((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> (((arrow_2098199487_below (p P_30)) c) b))) arrow_734252939e_Prof)
% FOF formula (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (Z_1:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_2054445623_mkbot L_1) Z_1))) ((and ((and (not (((eq arrow_475358991le_alt) Y) Z_1))) ((((eq arrow_475358991le_alt) X) Z_1)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) X) Z_1))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1))))) of role axiom named fact_10_in__mkbot
% A new axiom: (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (Z_1:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_2054445623_mkbot L_1) Z_1))) ((and ((and (not (((eq arrow_475358991le_alt) Y) Z_1))) ((((eq arrow_475358991le_alt) X) Z_1)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) X) Z_1))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1)))))
% FOF formula (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (Z_1:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_55669061_mktop L_1) Z_1))) ((and ((and (not (((eq arrow_475358991le_alt) X) Z_1))) ((((eq arrow_475358991le_alt) Y) Z_1)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) Y) Z_1))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1))))) of role axiom named fact_11_in__mktop
% A new axiom: (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (Z_1:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_55669061_mktop L_1) Z_1))) ((and ((and (not (((eq arrow_475358991le_alt) X) Z_1))) ((((eq arrow_475358991le_alt) Y) Z_1)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) Y) Z_1))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1)))))
% FOF formula (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_2098199487_below L_1) A_24) B_17))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) Y) A_24)->((member214075476le_alt ((produc1347929815le_alt X) B_17)) L_1)))) ((not (((eq arrow_475358991le_alt) Y) A_24))->((and ((((eq arrow_475358991le_alt) X) A_24)->((or (((eq arrow_475358991le_alt) Y) B_17)) ((member214075476le_alt ((produc1347929815le_alt B_17) Y)) L_1)))) ((not (((eq arrow_475358991le_alt) X) A_24))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1))))))))) of role axiom named fact_12_in__below
% A new axiom: (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_2098199487_below L_1) A_24) B_17))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) Y) A_24)->((member214075476le_alt ((produc1347929815le_alt X) B_17)) L_1)))) ((not (((eq arrow_475358991le_alt) Y) A_24))->((and ((((eq arrow_475358991le_alt) X) A_24)->((or (((eq arrow_475358991le_alt) Y) B_17)) ((member214075476le_alt ((produc1347929815le_alt B_17) Y)) L_1)))) ((not (((eq arrow_475358991le_alt) X) A_24))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1)))))))))
% FOF formula (forall (P_33:(produc1362454231le_alt->Prop)), ((iff (all1 P_33)) (forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), (P_33 ((produc776457805le_alt A) B))))) of role axiom named fact_13_split__paired__All
% A new axiom: (forall (P_33:(produc1362454231le_alt->Prop)), ((iff (all1 P_33)) (forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), (P_33 ((produc776457805le_alt A) B)))))
% FOF formula (forall (P_33:(produc1501160679le_alt->Prop)), ((iff (all2 P_33)) (forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), (P_33 ((produc1347929815le_alt A) B))))) of role axiom named fact_14_split__paired__All
% A new axiom: (forall (P_33:(produc1501160679le_alt->Prop)), ((iff (all2 P_33)) (forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), (P_33 ((produc1347929815le_alt A) B)))))
% FOF formula (forall (A_30:list_A2115238852le_alt) (B_23:list_A2115238852le_alt) (A_29:list_A2115238852le_alt) (B_22:list_A2115238852le_alt), ((iff (((eq produc1362454231le_alt) ((produc776457805le_alt A_30) B_23)) ((produc776457805le_alt A_29) B_22))) ((and (((eq list_A2115238852le_alt) A_30) A_29)) (((eq list_A2115238852le_alt) B_23) B_22)))) of role axiom named fact_15_Pair__eq
% A new axiom: (forall (A_30:list_A2115238852le_alt) (B_23:list_A2115238852le_alt) (A_29:list_A2115238852le_alt) (B_22:list_A2115238852le_alt), ((iff (((eq produc1362454231le_alt) ((produc776457805le_alt A_30) B_23)) ((produc776457805le_alt A_29) B_22))) ((and (((eq list_A2115238852le_alt) A_30) A_29)) (((eq list_A2115238852le_alt) B_23) B_22))))
% FOF formula (forall (A_30:arrow_475358991le_alt) (B_23:arrow_475358991le_alt) (A_29:arrow_475358991le_alt) (B_22:arrow_475358991le_alt), ((iff (((eq produc1501160679le_alt) ((produc1347929815le_alt A_30) B_23)) ((produc1347929815le_alt A_29) B_22))) ((and (((eq arrow_475358991le_alt) A_30) A_29)) (((eq arrow_475358991le_alt) B_23) B_22)))) of role axiom named fact_16_Pair__eq
% A new axiom: (forall (A_30:arrow_475358991le_alt) (B_23:arrow_475358991le_alt) (A_29:arrow_475358991le_alt) (B_22:arrow_475358991le_alt), ((iff (((eq produc1501160679le_alt) ((produc1347929815le_alt A_30) B_23)) ((produc1347929815le_alt A_29) B_22))) ((and (((eq arrow_475358991le_alt) A_30) A_29)) (((eq arrow_475358991le_alt) B_23) B_22))))
% FOF formula (forall (A_28:list_A2115238852le_alt) (B_21:list_A2115238852le_alt) (A_27:list_A2115238852le_alt) (B_20:list_A2115238852le_alt), ((((eq produc1362454231le_alt) ((produc776457805le_alt A_28) B_21)) ((produc776457805le_alt A_27) B_20))->(((((eq list_A2115238852le_alt) A_28) A_27)->(not (((eq list_A2115238852le_alt) B_21) B_20)))->False))) of role axiom named fact_17_Pair__inject
% A new axiom: (forall (A_28:list_A2115238852le_alt) (B_21:list_A2115238852le_alt) (A_27:list_A2115238852le_alt) (B_20:list_A2115238852le_alt), ((((eq produc1362454231le_alt) ((produc776457805le_alt A_28) B_21)) ((produc776457805le_alt A_27) B_20))->(((((eq list_A2115238852le_alt) A_28) A_27)->(not (((eq list_A2115238852le_alt) B_21) B_20)))->False)))
% FOF formula (forall (A_28:arrow_475358991le_alt) (B_21:arrow_475358991le_alt) (A_27:arrow_475358991le_alt) (B_20:arrow_475358991le_alt), ((((eq produc1501160679le_alt) ((produc1347929815le_alt A_28) B_21)) ((produc1347929815le_alt A_27) B_20))->(((((eq arrow_475358991le_alt) A_28) A_27)->(not (((eq arrow_475358991le_alt) B_21) B_20)))->False))) of role axiom named fact_18_Pair__inject
% A new axiom: (forall (A_28:arrow_475358991le_alt) (B_21:arrow_475358991le_alt) (A_27:arrow_475358991le_alt) (B_20:arrow_475358991le_alt), ((((eq produc1501160679le_alt) ((produc1347929815le_alt A_28) B_21)) ((produc1347929815le_alt A_27) B_20))->(((((eq arrow_475358991le_alt) A_28) A_27)->(not (((eq arrow_475358991le_alt) B_21) B_20)))->False)))
% FOF formula (forall (R_40:(produc1362454231le_alt->Prop)) (X_75:list_A2115238852le_alt) (Y_27:list_A2115238852le_alt), ((iff (((in_rel1156631736le_alt R_40) X_75) Y_27)) ((member28618436le_alt ((produc776457805le_alt X_75) Y_27)) R_40))) of role axiom named fact_19_in__rel__def
% A new axiom: (forall (R_40:(produc1362454231le_alt->Prop)) (X_75:list_A2115238852le_alt) (Y_27:list_A2115238852le_alt), ((iff (((in_rel1156631736le_alt R_40) X_75) Y_27)) ((member28618436le_alt ((produc776457805le_alt X_75) Y_27)) R_40)))
% FOF formula (forall (R_40:(produc1501160679le_alt->Prop)) (X_75:arrow_475358991le_alt) (Y_27:arrow_475358991le_alt), ((iff (((in_rel1252994498le_alt R_40) X_75) Y_27)) ((member214075476le_alt ((produc1347929815le_alt X_75) Y_27)) R_40))) of role axiom named fact_20_in__rel__def
% A new axiom: (forall (R_40:(produc1501160679le_alt->Prop)) (X_75:arrow_475358991le_alt) (Y_27:arrow_475358991le_alt), ((iff (((in_rel1252994498le_alt R_40) X_75) Y_27)) ((member214075476le_alt ((produc1347929815le_alt X_75) Y_27)) R_40)))
% FOF formula (forall (L_1:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_2098199487_below L_1) X) Y)) arrow_823908191le_Lin)))) of role axiom named fact_21_below__Lin
% A new axiom: (forall (L_1:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_2098199487_below L_1) X) Y)) arrow_823908191le_Lin))))
% FOF formula ((member526088951_alt_o p_1) arrow_734252939e_Prof) of role axiom named fact_22__096P_H_A_058_AProf_096
% A new axiom: ((member526088951_alt_o p_1) arrow_734252939e_Prof)
% FOF formula (forall (P_32:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_31:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_26:arrow_475358991le_alt) (B_19:arrow_475358991le_alt) (A_25:arrow_475358991le_alt) (B_18:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_25) B_18))->((not (((eq arrow_475358991le_alt) A_26) B_19))->((not (((eq arrow_475358991le_alt) A_25) B_19))->((not (((eq arrow_475358991le_alt) B_18) A_26))->(((member526088951_alt_o P_31) arrow_734252939e_Prof)->(((member526088951_alt_o P_32) arrow_734252939e_Prof)->((forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (P_31 _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (P_32 _TPTP_I))))->(((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (f P_31))->((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (f P_32))))))))))) of role axiom named fact_23__C1_C
% A new axiom: (forall (P_32:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_31:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_26:arrow_475358991le_alt) (B_19:arrow_475358991le_alt) (A_25:arrow_475358991le_alt) (B_18:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_25) B_18))->((not (((eq arrow_475358991le_alt) A_26) B_19))->((not (((eq arrow_475358991le_alt) A_25) B_19))->((not (((eq arrow_475358991le_alt) B_18) A_26))->(((member526088951_alt_o P_31) arrow_734252939e_Prof)->(((member526088951_alt_o P_32) arrow_734252939e_Prof)->((forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (P_31 _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (P_32 _TPTP_I))))->(((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (f P_31))->((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (f P_32)))))))))))
% FOF formula (forall (P_32:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_31:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_26:arrow_475358991le_alt) (B_19:arrow_475358991le_alt) (A_25:arrow_475358991le_alt) (B_18:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_25) B_18))->((not (((eq arrow_475358991le_alt) A_26) B_19))->((not (((eq arrow_475358991le_alt) A_25) B_19))->((not (((eq arrow_475358991le_alt) B_18) A_26))->(((member526088951_alt_o P_31) arrow_734252939e_Prof)->(((member526088951_alt_o P_32) arrow_734252939e_Prof)->((forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (P_31 _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (P_32 _TPTP_I))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (f P_31))) ((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (f P_32))))))))))) of role axiom named fact_24__C2_C
% A new axiom: (forall (P_32:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_31:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_26:arrow_475358991le_alt) (B_19:arrow_475358991le_alt) (A_25:arrow_475358991le_alt) (B_18:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_25) B_18))->((not (((eq arrow_475358991le_alt) A_26) B_19))->((not (((eq arrow_475358991le_alt) A_25) B_19))->((not (((eq arrow_475358991le_alt) B_18) A_26))->(((member526088951_alt_o P_31) arrow_734252939e_Prof)->(((member526088951_alt_o P_32) arrow_734252939e_Prof)->((forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (P_31 _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (P_32 _TPTP_I))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (f P_31))) ((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (f P_32)))))))))))
% FOF formula ((member616898751_alt_o f) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin))) of role axiom named fact_25_assms_I1_J
% A new axiom: ((member616898751_alt_o f) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin)))
% FOF formula (forall (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> L_1)) arrow_734252939e_Prof))) of role axiom named fact_26_const__Lin__Prof
% A new axiom: (forall (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> L_1)) arrow_734252939e_Prof)))
% FOF formula (forall (X:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_2054445623_mkbot L_1) X)) arrow_823908191le_Lin))) of role axiom named fact_27_mkbot__Lin
% A new axiom: (forall (X:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_2054445623_mkbot L_1) X)) arrow_823908191le_Lin)))
% FOF formula (forall (X:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_55669061_mktop L_1) X)) arrow_823908191le_Lin))) of role axiom named fact_28_mktop__Lin
% A new axiom: (forall (X:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_55669061_mktop L_1) X)) arrow_823908191le_Lin)))
% FOF formula (forall (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->(((member214075476le_alt ((produc1347929815le_alt A_24) B_17)) L_1)->(((member214075476le_alt ((produc1347929815le_alt B_17) A_24)) L_1)->False)))) of role axiom named fact_29_Lin__irrefl
% A new axiom: (forall (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->(((member214075476le_alt ((produc1347929815le_alt A_24) B_17)) L_1)->(((member214075476le_alt ((produc1347929815le_alt B_17) A_24)) L_1)->False))))
% FOF formula (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((not (((eq arrow_475358991le_alt) X) Y))->((iff (((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1)->False)) ((member214075476le_alt ((produc1347929815le_alt Y) X)) L_1))))) of role axiom named fact_30_notin__Lin__iff
% A new axiom: (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((not (((eq arrow_475358991le_alt) X) Y))->((iff (((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1)->False)) ((member214075476le_alt ((produc1347929815le_alt Y) X)) L_1)))))
% FOF formula (forall (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->((ex arrow_475358991le_alt) (fun (C_2:arrow_475358991le_alt)=> (distin236324274le_alt ((cons_A228743023le_alt A_24) ((cons_A228743023le_alt B_17) ((cons_A228743023le_alt C_2) nil_Ar1286194111le_alt)))))))) of role axiom named fact_31_third__alt
% A new axiom: (forall (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->((ex arrow_475358991le_alt) (fun (C_2:arrow_475358991le_alt)=> (distin236324274le_alt ((cons_A228743023le_alt A_24) ((cons_A228743023le_alt B_17) ((cons_A228743023le_alt C_2) nil_Ar1286194111le_alt))))))))
% FOF formula (forall (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_797024463le_IIA F_14)) (forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(forall (Xa:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o Xa) arrow_734252939e_Prof)->(forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A) B)) (X_2 _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt A) B)) (Xa _TPTP_I))))->((iff ((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 X_2))) ((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 Xa))))))))))) of role axiom named fact_32_IIA__def
% A new axiom: (forall (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_797024463le_IIA F_14)) (forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(forall (Xa:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o Xa) arrow_734252939e_Prof)->(forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A) B)) (X_2 _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt A) B)) (Xa _TPTP_I))))->((iff ((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 X_2))) ((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 Xa)))))))))))
% FOF formula (forall (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_1706409458nimity F_14)) (forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((forall (_TPTP_I:arrow_1429601828e_indi), ((member214075476le_alt ((produc1347929815le_alt A) B)) (X_2 _TPTP_I)))->((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 X_2)))))))) of role axiom named fact_33_unanimity__def
% A new axiom: (forall (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_1706409458nimity F_14)) (forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((forall (_TPTP_I:arrow_1429601828e_indi), ((member214075476le_alt ((produc1347929815le_alt A) B)) (X_2 _TPTP_I)))->((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 X_2))))))))
% FOF formula (forall (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->((ex (produc1501160679le_alt->Prop)) (fun (X_2:(produc1501160679le_alt->Prop))=> ((and ((member377231867_alt_o X_2) arrow_823908191le_Lin)) ((member214075476le_alt ((produc1347929815le_alt A_24) B_17)) X_2)))))) of role axiom named fact_34_complete__Lin
% A new axiom: (forall (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->((ex (produc1501160679le_alt->Prop)) (fun (X_2:(produc1501160679le_alt->Prop))=> ((and ((member377231867_alt_o X_2) arrow_823908191le_Lin)) ((member214075476le_alt ((produc1347929815le_alt A_24) B_17)) X_2))))))
% FOF formula (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_789600939_above L_1) A_24) B_17))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) X) B_17)->((member214075476le_alt ((produc1347929815le_alt A_24) Y)) L_1)))) ((not (((eq arrow_475358991le_alt) X) B_17))->((and ((((eq arrow_475358991le_alt) Y) B_17)->((or (((eq arrow_475358991le_alt) X) A_24)) ((member214075476le_alt ((produc1347929815le_alt X) A_24)) L_1)))) ((not (((eq arrow_475358991le_alt) Y) B_17))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1))))))))) of role axiom named fact_35_in__above
% A new axiom: (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_789600939_above L_1) A_24) B_17))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) X) B_17)->((member214075476le_alt ((produc1347929815le_alt A_24) Y)) L_1)))) ((not (((eq arrow_475358991le_alt) X) B_17))->((and ((((eq arrow_475358991le_alt) Y) B_17)->((or (((eq arrow_475358991le_alt) X) A_24)) ((member214075476le_alt ((produc1347929815le_alt X) A_24)) L_1)))) ((not (((eq arrow_475358991le_alt) Y) B_17))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1)))))))))
% FOF formula (distin236324274le_alt nil_Ar1286194111le_alt) of role axiom named fact_36_distinct_Osimps_I1_J
% A new axiom: (distin236324274le_alt nil_Ar1286194111le_alt)
% FOF formula (forall (A_23:arrow_475358991le_alt) (List_4:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) nil_Ar1286194111le_alt) ((cons_A228743023le_alt A_23) List_4)))) of role axiom named fact_37_list_Osimps_I2_J
% A new axiom: (forall (A_23:arrow_475358991le_alt) (List_4:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) nil_Ar1286194111le_alt) ((cons_A228743023le_alt A_23) List_4))))
% FOF formula (forall (A_22:arrow_475358991le_alt) (List_3:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) ((cons_A228743023le_alt A_22) List_3)) nil_Ar1286194111le_alt))) of role axiom named fact_38_list_Osimps_I3_J
% A new axiom: (forall (A_22:arrow_475358991le_alt) (List_3:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) ((cons_A228743023le_alt A_22) List_3)) nil_Ar1286194111le_alt)))
% FOF formula ((ex arrow_475358991le_alt) (fun (A:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (B:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (C_2:arrow_475358991le_alt)=> (distin236324274le_alt ((cons_A228743023le_alt A) ((cons_A228743023le_alt B) ((cons_A228743023le_alt C_2) nil_Ar1286194111le_alt)))))))))) of role axiom named fact_39_alt3
% A new axiom: ((ex arrow_475358991le_alt) (fun (A:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (B:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (C_2:arrow_475358991le_alt)=> (distin236324274le_alt ((cons_A228743023le_alt A) ((cons_A228743023le_alt B) ((cons_A228743023le_alt C_2) nil_Ar1286194111le_alt))))))))))
% FOF formula ((ex (produc1501160679le_alt->Prop)) (fun (L_2:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o L_2) arrow_823908191le_Lin))) of role axiom named fact_40_linear__alt
% A new axiom: ((ex (produc1501160679le_alt->Prop)) (fun (L_2:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o L_2) arrow_823908191le_Lin)))
% FOF formula (forall (A_21:arrow_475358991le_alt) (List_2:list_A2115238852le_alt) (A_20:arrow_475358991le_alt) (List_1:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((cons_A228743023le_alt A_21) List_2)) ((cons_A228743023le_alt A_20) List_1))) ((and (((eq arrow_475358991le_alt) A_21) A_20)) (((eq list_A2115238852le_alt) List_2) List_1)))) of role axiom named fact_41_list_Oinject
% A new axiom: (forall (A_21:arrow_475358991le_alt) (List_2:list_A2115238852le_alt) (A_20:arrow_475358991le_alt) (List_1:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((cons_A228743023le_alt A_21) List_2)) ((cons_A228743023le_alt A_20) List_1))) ((and (((eq arrow_475358991le_alt) A_21) A_20)) (((eq list_A2115238852le_alt) List_2) List_1))))
% FOF formula (forall (X_74:arrow_475358991le_alt) (Xs_127:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_74) Xs_127)) Xs_127))) of role axiom named fact_42_not__Cons__self2
% A new axiom: (forall (X_74:arrow_475358991le_alt) (Xs_127:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_74) Xs_127)) Xs_127)))
% FOF formula (forall (Xs_126:list_A2115238852le_alt) (X_73:arrow_475358991le_alt), (not (((eq list_A2115238852le_alt) Xs_126) ((cons_A228743023le_alt X_73) Xs_126)))) of role axiom named fact_43_not__Cons__self
% A new axiom: (forall (Xs_126:list_A2115238852le_alt) (X_73:arrow_475358991le_alt), (not (((eq list_A2115238852le_alt) Xs_126) ((cons_A228743023le_alt X_73) Xs_126))))
% FOF formula (forall (L_1:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_789600939_above L_1) X) Y)) arrow_823908191le_Lin)))) of role axiom named fact_44_above__Lin
% A new axiom: (forall (L_1:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_789600939_above L_1) X) Y)) arrow_823908191le_Lin))))
% FOF formula (forall (I_1:arrow_1429601828e_indi) (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o F_14) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin)))->((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A) B))->(((member214075476le_alt ((produc1347929815le_alt A) B)) (X_2 I_1))->((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 X_2)))))))->((arrow_1212662430ctator F_14) I_1)))) of role axiom named fact_45_dictatorI
% A new axiom: (forall (I_1:arrow_1429601828e_indi) (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o F_14) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin)))->((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A) B))->(((member214075476le_alt ((produc1347929815le_alt A) B)) (X_2 I_1))->((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 X_2)))))))->((arrow_1212662430ctator F_14) I_1))))
% FOF formula (forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->Prop)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_15) ((pi_Pro1701359055_alt_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False)))) of role axiom named fact_46_PiE
% A new axiom: (forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->Prop)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_15) ((pi_Pro1701359055_alt_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->produc1501160679le_alt)) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))), (((member712472209le_alt F_15) ((pi_Arr1786181611le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False)))) of role axiom named fact_47_PiE
% A new axiom: (forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->produc1501160679le_alt)) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))), (((member712472209le_alt F_15) ((pi_Arr1786181611le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member351225838le_alt F_15) ((pi_Arr329216900le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False)))) of role axiom named fact_48_PiE
% A new axiom: (forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member351225838le_alt F_15) ((pi_Arr329216900le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False))))
% FOF formula (forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->produc1501160679le_alt)) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->(produc1501160679le_alt->Prop))), (((member428957857le_alt F_15) ((pi_Pro1708969783le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False)))) of role axiom named fact_49_PiE
% A new axiom: (forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->produc1501160679le_alt)) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->(produc1501160679le_alt->Prop))), (((member428957857le_alt F_15) ((pi_Pro1708969783le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:Prop) (F_15:(Prop->produc1501160679le_alt)) (A_19:(Prop->Prop)) (B_16:(Prop->(produc1501160679le_alt->Prop))), (((member492167345le_alt F_15) ((pi_o_P657324555le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False)))) of role axiom named fact_50_PiE
% A new axiom: (forall (X_72:Prop) (F_15:(Prop->produc1501160679le_alt)) (A_19:(Prop->Prop)) (B_16:(Prop->(produc1501160679le_alt->Prop))), (((member492167345le_alt F_15) ((pi_o_P657324555le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False))))
% FOF formula (forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1876989968_alt_o F_15) ((pi_Arr578767520_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False)))) of role axiom named fact_51_PiE
% A new axiom: (forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1876989968_alt_o F_15) ((pi_Arr578767520_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1234151027_alt_o F_15) ((pi_Arr1060328391_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False)))) of role axiom named fact_52_PiE
% A new axiom: (forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1234151027_alt_o F_15) ((pi_Arr1060328391_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False))))
% FOF formula (forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member392452608_alt_o F_15) ((pi_Pro121963604_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False)))) of role axiom named fact_53_PiE
% A new axiom: (forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member392452608_alt_o F_15) ((pi_Pro121963604_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:Prop) (F_15:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(Prop->Prop)) (B_16:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1394214384_alt_o F_15) ((pi_o_A1182933120_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False)))) of role axiom named fact_54_PiE
% A new axiom: (forall (X_72:Prop) (F_15:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(Prop->Prop)) (B_16:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1394214384_alt_o F_15) ((pi_o_A1182933120_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False))))
% FOF formula (forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member1908358676_alt_o F_15) ((pi_Arr1520776484_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False)))) of role axiom named fact_55_PiE
% A new axiom: (forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member1908358676_alt_o F_15) ((pi_Arr1520776484_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member2082473988_alt_o F_15) ((pi_Pro589599960_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False)))) of role axiom named fact_56_PiE
% A new axiom: (forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member2082473988_alt_o F_15) ((pi_Pro589599960_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:Prop) (F_15:(Prop->(produc1501160679le_alt->Prop))) (A_19:(Prop->Prop)) (B_16:(Prop->((produc1501160679le_alt->Prop)->Prop))), (((member1862122484_alt_o F_15) ((pi_o_P553196292_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False)))) of role axiom named fact_57_PiE
% A new axiom: (forall (X_72:Prop) (F_15:(Prop->(produc1501160679le_alt->Prop))) (A_19:(Prop->Prop)) (B_16:(Prop->((produc1501160679le_alt->Prop)->Prop))), (((member1862122484_alt_o F_15) ((pi_o_P553196292_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False))))
% FOF formula (forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member89384572_alt_o F_15) ((pi_Arr515871190_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False)))) of role axiom named fact_58_PiE
% A new axiom: (forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member89384572_alt_o F_15) ((pi_Arr515871190_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member811956313_alt_o F_15) ((pi_Arr1564509167_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False)))) of role axiom named fact_59_PiE
% A new axiom: (forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member811956313_alt_o F_15) ((pi_Arr1564509167_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False))))
% FOF formula (forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member654997644_alt_o F_15) ((pi_Pro441468706_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False)))) of role axiom named fact_60_PiE
% A new axiom: (forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member654997644_alt_o F_15) ((pi_Pro441468706_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:Prop) (F_15:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(Prop->Prop)) (B_16:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1957863580_alt_o F_15) ((pi_o_A1186128886_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False)))) of role axiom named fact_61_PiE
% A new axiom: (forall (X_72:Prop) (F_15:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(Prop->Prop)) (B_16:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1957863580_alt_o F_15) ((pi_o_A1186128886_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False))))
% FOF formula (forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->arrow_475358991le_alt)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))), (((member1416774619le_alt F_15) ((pi_Pro315446191le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False)))) of role axiom named fact_62_PiE
% A new axiom: (forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->arrow_475358991le_alt)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))), (((member1416774619le_alt F_15) ((pi_Pro315446191le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))), (((member1640632174e_indi F_15) ((pi_Pro1767455108e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False)))) of role axiom named fact_63_PiE
% A new axiom: (forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))), (((member1640632174e_indi F_15) ((pi_Pro1767455108e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->produc1362454231le_alt)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(produc1362454231le_alt->Prop))), (((member220989473le_alt F_15) ((pi_Pro666407479le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False)))) of role axiom named fact_64_PiE
% A new axiom: (forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->produc1362454231le_alt)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(produc1362454231le_alt->Prop))), (((member220989473le_alt F_15) ((pi_Pro666407479le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False))))
% FOF formula (forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member1596146470le_alt F_15) ((pi_Arr1483346486le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False)))) of role axiom named fact_65_PiE
% A new axiom: (forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member1596146470le_alt F_15) ((pi_Arr1483346486le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member44294883e_indi F_15) ((pi_Arr1232280765e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False)))) of role axiom named fact_66_PiE
% A new axiom: (forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member44294883e_indi F_15) ((pi_Arr1232280765e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member1849320470le_alt F_15) ((pi_Arr1957214192le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False)))) of role axiom named fact_67_PiE
% A new axiom: (forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member1849320470le_alt F_15) ((pi_Arr1957214192le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member939334982lt_o_o F_15) ((pi_Arr952516694lt_o_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False)))) of role axiom named fact_68_PiE
% A new axiom: (forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member939334982lt_o_o F_15) ((pi_Arr952516694lt_o_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))), (((member1524522914le_alt F_15) ((pi_Pro1868152754le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False)))) of role axiom named fact_69_PiE
% A new axiom: (forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))), (((member1524522914le_alt F_15) ((pi_Pro1868152754le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))), (((member304866663e_indi F_15) ((pi_Pro468373057e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False)))) of role axiom named fact_70_PiE
% A new axiom: (forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))), (((member304866663e_indi F_15) ((pi_Pro468373057e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))), (((member1099563162le_alt F_15) ((pi_Pro1678345076le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False)))) of role axiom named fact_71_PiE
% A new axiom: (forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))), (((member1099563162le_alt F_15) ((pi_Pro1678345076le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->Prop)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(Prop->Prop))), (((member1961363906lt_o_o F_15) ((pi_Pro422690258lt_o_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False)))) of role axiom named fact_72_PiE
% A new axiom: (forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->Prop)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(Prop->Prop))), (((member1961363906lt_o_o F_15) ((pi_Pro422690258lt_o_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member474974512le_alt F_15) ((pi_Arr1005837828le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False)))) of role axiom named fact_73_PiE
% A new axiom: (forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member474974512le_alt F_15) ((pi_Arr1005837828le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member1452482393e_indi F_15) ((pi_Arr338314351e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False)))) of role axiom named fact_74_PiE
% A new axiom: (forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member1452482393e_indi F_15) ((pi_Arr338314351e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member845447052le_alt F_15) ((pi_Arr2076738722le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False)))) of role axiom named fact_75_PiE
% A new axiom: (forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member845447052le_alt F_15) ((pi_Arr2076738722le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member1823529808lt_o_o F_15) ((pi_Arr195212324lt_o_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False)))) of role axiom named fact_76_PiE
% A new axiom: (forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member1823529808lt_o_o F_15) ((pi_Arr195212324lt_o_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_15) ((pi_Arr1304755663_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False)))) of role axiom named fact_77_PiE
% A new axiom: (forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_15) ((pi_Arr1304755663_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False))))
% FOF formula (forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_15) ((pi_Arr1929480907_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False)))) of role axiom named fact_78_PiE
% A new axiom: (forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_15) ((pi_Arr1929480907_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False))))
% FOF formula (forall (Y_26:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Y_26) nil_Ar1286194111le_alt))->((forall (A:arrow_475358991le_alt) (List:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) Y_26) ((cons_A228743023le_alt A) List))))->False))) of role axiom named fact_79_list_Oexhaust
% A new axiom: (forall (Y_26:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Y_26) nil_Ar1286194111le_alt))->((forall (A:arrow_475358991le_alt) (List:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) Y_26) ((cons_A228743023le_alt A) List))))->False)))
% FOF formula (forall (Xs_125:list_A2115238852le_alt), ((iff (not (((eq list_A2115238852le_alt) Xs_125) nil_Ar1286194111le_alt))) ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Xs_125) ((cons_A228743023le_alt Y_1) Ys)))))))) of role axiom named fact_80_neq__Nil__conv
% A new axiom: (forall (Xs_125:list_A2115238852le_alt), ((iff (not (((eq list_A2115238852le_alt) Xs_125) nil_Ar1286194111le_alt))) ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Xs_125) ((cons_A228743023le_alt Y_1) Ys))))))))
% FOF formula (forall (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (I_1:arrow_1429601828e_indi), ((iff ((arrow_1212662430ctator F_14) I_1)) (forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(((eq (produc1501160679le_alt->Prop)) (F_14 X_2)) (X_2 I_1)))))) of role axiom named fact_81_dictator__def
% A new axiom: (forall (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (I_1:arrow_1429601828e_indi), ((iff ((arrow_1212662430ctator F_14) I_1)) (forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(((eq (produc1501160679le_alt->Prop)) (F_14 X_2)) (X_2 I_1))))))
% FOF formula (forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->Prop)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(Prop->Prop)), (((member377231867_alt_o F_13) ((pi_Pro1701359055_alt_o A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member_o (F_13 X_71)) B_15)))) of role axiom named fact_82_funcset__mem
% A new axiom: (forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->Prop)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(Prop->Prop)), (((member377231867_alt_o F_13) ((pi_Pro1701359055_alt_o A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->arrow_475358991le_alt)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member1416774619le_alt F_13) ((pi_Pro315446191le_alt A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15)))) of role axiom named fact_83_funcset__mem
% A new axiom: (forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->arrow_475358991le_alt)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member1416774619le_alt F_13) ((pi_Pro315446191le_alt A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member1640632174e_indi F_13) ((pi_Pro1767455108e_indi A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15)))) of role axiom named fact_84_funcset__mem
% A new axiom: (forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member1640632174e_indi F_13) ((pi_Pro1767455108e_indi A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->produc1362454231le_alt)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member220989473le_alt F_13) ((pi_Pro666407479le_alt A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15)))) of role axiom named fact_85_funcset__mem
% A new axiom: (forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->produc1362454231le_alt)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member220989473le_alt F_13) ((pi_Pro666407479le_alt A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member1596146470le_alt F_13) ((pi_Arr1483346486le_alt A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15)))) of role axiom named fact_86_funcset__mem
% A new axiom: (forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member1596146470le_alt F_13) ((pi_Arr1483346486le_alt A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member44294883e_indi F_13) ((pi_Arr1232280765e_indi A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15)))) of role axiom named fact_87_funcset__mem
% A new axiom: (forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member44294883e_indi F_13) ((pi_Arr1232280765e_indi A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member1849320470le_alt F_13) ((pi_Arr1957214192le_alt A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15)))) of role axiom named fact_88_funcset__mem
% A new axiom: (forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member1849320470le_alt F_13) ((pi_Arr1957214192le_alt A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(Prop->Prop)), (((member939334982lt_o_o F_13) ((pi_Arr952516694lt_o_o A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member_o (F_13 X_71)) B_15)))) of role axiom named fact_89_funcset__mem
% A new axiom: (forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(Prop->Prop)), (((member939334982lt_o_o F_13) ((pi_Arr952516694lt_o_o A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member1524522914le_alt F_13) ((pi_Pro1868152754le_alt A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15)))) of role axiom named fact_90_funcset__mem
% A new axiom: (forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member1524522914le_alt F_13) ((pi_Pro1868152754le_alt A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member304866663e_indi F_13) ((pi_Pro468373057e_indi A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15)))) of role axiom named fact_91_funcset__mem
% A new axiom: (forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member304866663e_indi F_13) ((pi_Pro468373057e_indi A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member1099563162le_alt F_13) ((pi_Pro1678345076le_alt A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15)))) of role axiom named fact_92_funcset__mem
% A new axiom: (forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member1099563162le_alt F_13) ((pi_Pro1678345076le_alt A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->Prop)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(Prop->Prop)), (((member1961363906lt_o_o F_13) ((pi_Pro422690258lt_o_o A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member_o (F_13 X_71)) B_15)))) of role axiom named fact_93_funcset__mem
% A new axiom: (forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->Prop)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(Prop->Prop)), (((member1961363906lt_o_o F_13) ((pi_Pro422690258lt_o_o A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member474974512le_alt F_13) ((pi_Arr1005837828le_alt A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15)))) of role axiom named fact_94_funcset__mem
% A new axiom: (forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member474974512le_alt F_13) ((pi_Arr1005837828le_alt A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member1452482393e_indi F_13) ((pi_Arr338314351e_indi A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15)))) of role axiom named fact_95_funcset__mem
% A new axiom: (forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member1452482393e_indi F_13) ((pi_Arr338314351e_indi A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member845447052le_alt F_13) ((pi_Arr2076738722le_alt A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15)))) of role axiom named fact_96_funcset__mem
% A new axiom: (forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member845447052le_alt F_13) ((pi_Arr2076738722le_alt A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(Prop->Prop)), (((member1823529808lt_o_o F_13) ((pi_Arr195212324lt_o_o A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member_o (F_13 X_71)) B_15)))) of role axiom named fact_97_funcset__mem
% A new axiom: (forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(Prop->Prop)), (((member1823529808lt_o_o F_13) ((pi_Arr195212324lt_o_o A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->produc1501160679le_alt)) (A_18:(arrow_475358991le_alt->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member712472209le_alt F_13) ((pi_Arr1786181611le_alt A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15)))) of role axiom named fact_98_funcset__mem
% A new axiom: (forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->produc1501160679le_alt)) (A_18:(arrow_475358991le_alt->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member712472209le_alt F_13) ((pi_Arr1786181611le_alt A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member351225838le_alt F_13) ((pi_Arr329216900le_alt A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15)))) of role axiom named fact_99_funcset__mem
% A new axiom: (forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member351225838le_alt F_13) ((pi_Arr329216900le_alt A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->produc1501160679le_alt)) (A_18:(produc1362454231le_alt->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member428957857le_alt F_13) ((pi_Pro1708969783le_alt A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15)))) of role axiom named fact_100_funcset__mem
% A new axiom: (forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->produc1501160679le_alt)) (A_18:(produc1362454231le_alt->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member428957857le_alt F_13) ((pi_Pro1708969783le_alt A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:Prop) (F_13:(Prop->produc1501160679le_alt)) (A_18:(Prop->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member492167345le_alt F_13) ((pi_o_P657324555le_alt A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15)))) of role axiom named fact_101_funcset__mem
% A new axiom: (forall (X_71:Prop) (F_13:(Prop->produc1501160679le_alt)) (A_18:(Prop->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member492167345le_alt F_13) ((pi_o_P657324555le_alt A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(arrow_475358991le_alt->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member1876989968_alt_o F_13) ((pi_Arr578767520_alt_o A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_102_funcset__mem
% A new axiom: (forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(arrow_475358991le_alt->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member1876989968_alt_o F_13) ((pi_Arr578767520_alt_o A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member1234151027_alt_o F_13) ((pi_Arr1060328391_alt_o A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_103_funcset__mem
% A new axiom: (forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member1234151027_alt_o F_13) ((pi_Arr1060328391_alt_o A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(produc1362454231le_alt->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member392452608_alt_o F_13) ((pi_Pro121963604_alt_o A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_104_funcset__mem
% A new axiom: (forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(produc1362454231le_alt->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member392452608_alt_o F_13) ((pi_Pro121963604_alt_o A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:Prop) (F_13:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(Prop->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member1394214384_alt_o F_13) ((pi_o_A1182933120_alt_o A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_105_funcset__mem
% A new axiom: (forall (X_71:Prop) (F_13:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(Prop->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member1394214384_alt_o F_13) ((pi_o_A1182933120_alt_o A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_18:(arrow_475358991le_alt->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member1908358676_alt_o F_13) ((pi_Arr1520776484_alt_o A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_106_funcset__mem
% A new axiom: (forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_18:(arrow_475358991le_alt->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member1908358676_alt_o F_13) ((pi_Arr1520776484_alt_o A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_18:(produc1362454231le_alt->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member2082473988_alt_o F_13) ((pi_Pro589599960_alt_o A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_107_funcset__mem
% A new axiom: (forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_18:(produc1362454231le_alt->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member2082473988_alt_o F_13) ((pi_Pro589599960_alt_o A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:Prop) (F_13:(Prop->(produc1501160679le_alt->Prop))) (A_18:(Prop->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member1862122484_alt_o F_13) ((pi_o_P553196292_alt_o A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_108_funcset__mem
% A new axiom: (forall (X_71:Prop) (F_13:(Prop->(produc1501160679le_alt->Prop))) (A_18:(Prop->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member1862122484_alt_o F_13) ((pi_o_P553196292_alt_o A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(arrow_475358991le_alt->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member89384572_alt_o F_13) ((pi_Arr515871190_alt_o A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_109_funcset__mem
% A new axiom: (forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(arrow_475358991le_alt->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member89384572_alt_o F_13) ((pi_Arr515871190_alt_o A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member811956313_alt_o F_13) ((pi_Arr1564509167_alt_o A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_110_funcset__mem
% A new axiom: (forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member811956313_alt_o F_13) ((pi_Arr1564509167_alt_o A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(produc1362454231le_alt->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member654997644_alt_o F_13) ((pi_Pro441468706_alt_o A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_111_funcset__mem
% A new axiom: (forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(produc1362454231le_alt->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member654997644_alt_o F_13) ((pi_Pro441468706_alt_o A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:Prop) (F_13:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(Prop->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member1957863580_alt_o F_13) ((pi_o_A1186128886_alt_o A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_112_funcset__mem
% A new axiom: (forall (X_71:Prop) (F_13:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(Prop->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member1957863580_alt_o F_13) ((pi_o_A1186128886_alt_o A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_13) ((pi_Arr1304755663_alt_o A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_113_funcset__mem
% A new axiom: (forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_13) ((pi_Arr1304755663_alt_o A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_13) ((pi_Arr1929480907_alt_o A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15)))) of role axiom named fact_114_funcset__mem
% A new axiom: (forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_13) ((pi_Arr1929480907_alt_o A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15))))
% FOF formula (forall (V_2:arrow_475358991le_alt) (Va:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt ((cons_A228743023le_alt V_2) Va)) nil_Ar1286194111le_alt)) ((cons_A228743023le_alt V_2) Va))) of role axiom named fact_115_splice_Osimps_I2_J
% A new axiom: (forall (V_2:arrow_475358991le_alt) (Va:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt ((cons_A228743023le_alt V_2) Va)) nil_Ar1286194111le_alt)) ((cons_A228743023le_alt V_2) Va)))
% FOF formula (forall (X_70:arrow_475358991le_alt) (Xs_124:list_A2115238852le_alt) (Y_25:arrow_475358991le_alt) (Ys_56:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt ((cons_A228743023le_alt X_70) Xs_124)) ((cons_A228743023le_alt Y_25) Ys_56))) ((cons_A228743023le_alt X_70) ((cons_A228743023le_alt Y_25) ((splice1520898450le_alt Xs_124) Ys_56))))) of role axiom named fact_116_splice_Osimps_I3_J
% A new axiom: (forall (X_70:arrow_475358991le_alt) (Xs_124:list_A2115238852le_alt) (Y_25:arrow_475358991le_alt) (Ys_56:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt ((cons_A228743023le_alt X_70) Xs_124)) ((cons_A228743023le_alt Y_25) Ys_56))) ((cons_A228743023le_alt X_70) ((cons_A228743023le_alt Y_25) ((splice1520898450le_alt Xs_124) Ys_56)))))
% FOF formula (forall (Ys_55:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt nil_Ar1286194111le_alt) Ys_55)) Ys_55)) of role axiom named fact_117_splice_Osimps_I1_J
% A new axiom: (forall (Ys_55:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt nil_Ar1286194111le_alt) Ys_55)) Ys_55))
% FOF formula (forall (Xs_123:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt Xs_123) nil_Ar1286194111le_alt)) Xs_123)) of role axiom named fact_118_splice__Nil2
% A new axiom: (forall (Xs_123:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt Xs_123) nil_Ar1286194111le_alt)) Xs_123))
% FOF formula (forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->Prop)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_12) ((pi_Pro1701359055_alt_o A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_119_Pi__mem
% A new axiom: (forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->Prop)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_12) ((pi_Pro1701359055_alt_o A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->arrow_475358991le_alt)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))), (((member1416774619le_alt F_12) ((pi_Pro315446191le_alt A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_120_Pi__mem
% A new axiom: (forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->arrow_475358991le_alt)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))), (((member1416774619le_alt F_12) ((pi_Pro315446191le_alt A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))), (((member1640632174e_indi F_12) ((pi_Pro1767455108e_indi A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_121_Pi__mem
% A new axiom: (forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))), (((member1640632174e_indi F_12) ((pi_Pro1767455108e_indi A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->produc1362454231le_alt)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(produc1362454231le_alt->Prop))), (((member220989473le_alt F_12) ((pi_Pro666407479le_alt A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_122_Pi__mem
% A new axiom: (forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->produc1362454231le_alt)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(produc1362454231le_alt->Prop))), (((member220989473le_alt F_12) ((pi_Pro666407479le_alt A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member1596146470le_alt F_12) ((pi_Arr1483346486le_alt A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_123_Pi__mem
% A new axiom: (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member1596146470le_alt F_12) ((pi_Arr1483346486le_alt A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member44294883e_indi F_12) ((pi_Arr1232280765e_indi A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_124_Pi__mem
% A new axiom: (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member44294883e_indi F_12) ((pi_Arr1232280765e_indi A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member1849320470le_alt F_12) ((pi_Arr1957214192le_alt A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_125_Pi__mem
% A new axiom: (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member1849320470le_alt F_12) ((pi_Arr1957214192le_alt A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member939334982lt_o_o F_12) ((pi_Arr952516694lt_o_o A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_126_Pi__mem
% A new axiom: (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member939334982lt_o_o F_12) ((pi_Arr952516694lt_o_o A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))), (((member1524522914le_alt F_12) ((pi_Pro1868152754le_alt A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_127_Pi__mem
% A new axiom: (forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))), (((member1524522914le_alt F_12) ((pi_Pro1868152754le_alt A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))), (((member304866663e_indi F_12) ((pi_Pro468373057e_indi A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_128_Pi__mem
% A new axiom: (forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))), (((member304866663e_indi F_12) ((pi_Pro468373057e_indi A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))), (((member1099563162le_alt F_12) ((pi_Pro1678345076le_alt A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_129_Pi__mem
% A new axiom: (forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))), (((member1099563162le_alt F_12) ((pi_Pro1678345076le_alt A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->Prop)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(Prop->Prop))), (((member1961363906lt_o_o F_12) ((pi_Pro422690258lt_o_o A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_130_Pi__mem
% A new axiom: (forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->Prop)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(Prop->Prop))), (((member1961363906lt_o_o F_12) ((pi_Pro422690258lt_o_o A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member474974512le_alt F_12) ((pi_Arr1005837828le_alt A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_131_Pi__mem
% A new axiom: (forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member474974512le_alt F_12) ((pi_Arr1005837828le_alt A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member1452482393e_indi F_12) ((pi_Arr338314351e_indi A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_132_Pi__mem
% A new axiom: (forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member1452482393e_indi F_12) ((pi_Arr338314351e_indi A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member845447052le_alt F_12) ((pi_Arr2076738722le_alt A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_133_Pi__mem
% A new axiom: (forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member845447052le_alt F_12) ((pi_Arr2076738722le_alt A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member1823529808lt_o_o F_12) ((pi_Arr195212324lt_o_o A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_134_Pi__mem
% A new axiom: (forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member1823529808lt_o_o F_12) ((pi_Arr195212324lt_o_o A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->produc1501160679le_alt)) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))), (((member712472209le_alt F_12) ((pi_Arr1786181611le_alt A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_135_Pi__mem
% A new axiom: (forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->produc1501160679le_alt)) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))), (((member712472209le_alt F_12) ((pi_Arr1786181611le_alt A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member351225838le_alt F_12) ((pi_Arr329216900le_alt A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_136_Pi__mem
% A new axiom: (forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member351225838le_alt F_12) ((pi_Arr329216900le_alt A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->produc1501160679le_alt)) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->(produc1501160679le_alt->Prop))), (((member428957857le_alt F_12) ((pi_Pro1708969783le_alt A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_137_Pi__mem
% A new axiom: (forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->produc1501160679le_alt)) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->(produc1501160679le_alt->Prop))), (((member428957857le_alt F_12) ((pi_Pro1708969783le_alt A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:Prop) (F_12:(Prop->produc1501160679le_alt)) (A_17:(Prop->Prop)) (B_14:(Prop->(produc1501160679le_alt->Prop))), (((member492167345le_alt F_12) ((pi_o_P657324555le_alt A_17) B_14))->(((member_o X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_138_Pi__mem
% A new axiom: (forall (X_69:Prop) (F_12:(Prop->produc1501160679le_alt)) (A_17:(Prop->Prop)) (B_14:(Prop->(produc1501160679le_alt->Prop))), (((member492167345le_alt F_12) ((pi_o_P657324555le_alt A_17) B_14))->(((member_o X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1876989968_alt_o F_12) ((pi_Arr578767520_alt_o A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_139_Pi__mem
% A new axiom: (forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1876989968_alt_o F_12) ((pi_Arr578767520_alt_o A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1234151027_alt_o F_12) ((pi_Arr1060328391_alt_o A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_140_Pi__mem
% A new axiom: (forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1234151027_alt_o F_12) ((pi_Arr1060328391_alt_o A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member392452608_alt_o F_12) ((pi_Pro121963604_alt_o A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_141_Pi__mem
% A new axiom: (forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member392452608_alt_o F_12) ((pi_Pro121963604_alt_o A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:Prop) (F_12:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(Prop->Prop)) (B_14:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1394214384_alt_o F_12) ((pi_o_A1182933120_alt_o A_17) B_14))->(((member_o X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_142_Pi__mem
% A new axiom: (forall (X_69:Prop) (F_12:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(Prop->Prop)) (B_14:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1394214384_alt_o F_12) ((pi_o_A1182933120_alt_o A_17) B_14))->(((member_o X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member1908358676_alt_o F_12) ((pi_Arr1520776484_alt_o A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_143_Pi__mem
% A new axiom: (forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member1908358676_alt_o F_12) ((pi_Arr1520776484_alt_o A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member2082473988_alt_o F_12) ((pi_Pro589599960_alt_o A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_144_Pi__mem
% A new axiom: (forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member2082473988_alt_o F_12) ((pi_Pro589599960_alt_o A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:Prop) (F_12:(Prop->(produc1501160679le_alt->Prop))) (A_17:(Prop->Prop)) (B_14:(Prop->((produc1501160679le_alt->Prop)->Prop))), (((member1862122484_alt_o F_12) ((pi_o_P553196292_alt_o A_17) B_14))->(((member_o X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_145_Pi__mem
% A new axiom: (forall (X_69:Prop) (F_12:(Prop->(produc1501160679le_alt->Prop))) (A_17:(Prop->Prop)) (B_14:(Prop->((produc1501160679le_alt->Prop)->Prop))), (((member1862122484_alt_o F_12) ((pi_o_P553196292_alt_o A_17) B_14))->(((member_o X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member89384572_alt_o F_12) ((pi_Arr515871190_alt_o A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_146_Pi__mem
% A new axiom: (forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member89384572_alt_o F_12) ((pi_Arr515871190_alt_o A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member811956313_alt_o F_12) ((pi_Arr1564509167_alt_o A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_147_Pi__mem
% A new axiom: (forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member811956313_alt_o F_12) ((pi_Arr1564509167_alt_o A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member654997644_alt_o F_12) ((pi_Pro441468706_alt_o A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_148_Pi__mem
% A new axiom: (forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member654997644_alt_o F_12) ((pi_Pro441468706_alt_o A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:Prop) (F_12:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(Prop->Prop)) (B_14:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1957863580_alt_o F_12) ((pi_o_A1186128886_alt_o A_17) B_14))->(((member_o X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_149_Pi__mem
% A new axiom: (forall (X_69:Prop) (F_12:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(Prop->Prop)) (B_14:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1957863580_alt_o F_12) ((pi_o_A1186128886_alt_o A_17) B_14))->(((member_o X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_12) ((pi_Arr1304755663_alt_o A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_150_Pi__mem
% A new axiom: (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_12) ((pi_Arr1304755663_alt_o A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_12) ((pi_Arr1929480907_alt_o A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69))))) of role axiom named fact_151_Pi__mem
% A new axiom: (forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_12) ((pi_Arr1929480907_alt_o A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69)))))
% FOF formula (forall (F_11:(produc1501160679le_alt->arrow_475358991le_alt)) (B_13:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member1416774619le_alt F_11) ((pi_Pro315446191le_alt A_16) B_13)))) of role axiom named fact_152_Pi__I
% A new axiom: (forall (F_11:(produc1501160679le_alt->arrow_475358991le_alt)) (B_13:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member1416774619le_alt F_11) ((pi_Pro315446191le_alt A_16) B_13))))
% FOF formula (forall (F_11:(produc1501160679le_alt->arrow_1429601828e_indi)) (B_13:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member1640632174e_indi F_11) ((pi_Pro1767455108e_indi A_16) B_13)))) of role axiom named fact_153_Pi__I
% A new axiom: (forall (F_11:(produc1501160679le_alt->arrow_1429601828e_indi)) (B_13:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member1640632174e_indi F_11) ((pi_Pro1767455108e_indi A_16) B_13))))
% FOF formula (forall (F_11:(produc1501160679le_alt->produc1362454231le_alt)) (B_13:(produc1501160679le_alt->(produc1362454231le_alt->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member220989473le_alt F_11) ((pi_Pro666407479le_alt A_16) B_13)))) of role axiom named fact_154_Pi__I
% A new axiom: (forall (F_11:(produc1501160679le_alt->produc1362454231le_alt)) (B_13:(produc1501160679le_alt->(produc1362454231le_alt->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member220989473le_alt F_11) ((pi_Pro666407479le_alt A_16) B_13))))
% FOF formula (forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member1596146470le_alt F_11) ((pi_Arr1483346486le_alt A_16) B_13)))) of role axiom named fact_155_Pi__I
% A new axiom: (forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member1596146470le_alt F_11) ((pi_Arr1483346486le_alt A_16) B_13))))
% FOF formula (forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member44294883e_indi F_11) ((pi_Arr1232280765e_indi A_16) B_13)))) of role axiom named fact_156_Pi__I
% A new axiom: (forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member44294883e_indi F_11) ((pi_Arr1232280765e_indi A_16) B_13))))
% FOF formula (forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member1849320470le_alt F_11) ((pi_Arr1957214192le_alt A_16) B_13)))) of role axiom named fact_157_Pi__I
% A new axiom: (forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member1849320470le_alt F_11) ((pi_Arr1957214192le_alt A_16) B_13))))
% FOF formula (forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member939334982lt_o_o F_11) ((pi_Arr952516694lt_o_o A_16) B_13)))) of role axiom named fact_158_Pi__I
% A new axiom: (forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member939334982lt_o_o F_11) ((pi_Arr952516694lt_o_o A_16) B_13))))
% FOF formula (forall (F_11:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (B_13:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member1524522914le_alt F_11) ((pi_Pro1868152754le_alt A_16) B_13)))) of role axiom named fact_159_Pi__I
% A new axiom: (forall (F_11:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (B_13:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member1524522914le_alt F_11) ((pi_Pro1868152754le_alt A_16) B_13))))
% FOF formula (forall (F_11:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (B_13:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member304866663e_indi F_11) ((pi_Pro468373057e_indi A_16) B_13)))) of role axiom named fact_160_Pi__I
% A new axiom: (forall (F_11:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (B_13:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member304866663e_indi F_11) ((pi_Pro468373057e_indi A_16) B_13))))
% FOF formula (forall (F_11:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (B_13:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member1099563162le_alt F_11) ((pi_Pro1678345076le_alt A_16) B_13)))) of role axiom named fact_161_Pi__I
% A new axiom: (forall (F_11:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (B_13:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member1099563162le_alt F_11) ((pi_Pro1678345076le_alt A_16) B_13))))
% FOF formula (forall (F_11:((produc1501160679le_alt->Prop)->Prop)) (B_13:((produc1501160679le_alt->Prop)->(Prop->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member1961363906lt_o_o F_11) ((pi_Pro422690258lt_o_o A_16) B_13)))) of role axiom named fact_162_Pi__I
% A new axiom: (forall (F_11:((produc1501160679le_alt->Prop)->Prop)) (B_13:((produc1501160679le_alt->Prop)->(Prop->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member1961363906lt_o_o F_11) ((pi_Pro422690258lt_o_o A_16) B_13))))
% FOF formula (forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member474974512le_alt F_11) ((pi_Arr1005837828le_alt A_16) B_13)))) of role axiom named fact_163_Pi__I
% A new axiom: (forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member474974512le_alt F_11) ((pi_Arr1005837828le_alt A_16) B_13))))
% FOF formula (forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member1452482393e_indi F_11) ((pi_Arr338314351e_indi A_16) B_13)))) of role axiom named fact_164_Pi__I
% A new axiom: (forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member1452482393e_indi F_11) ((pi_Arr338314351e_indi A_16) B_13))))
% FOF formula (forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member845447052le_alt F_11) ((pi_Arr2076738722le_alt A_16) B_13)))) of role axiom named fact_165_Pi__I
% A new axiom: (forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member845447052le_alt F_11) ((pi_Arr2076738722le_alt A_16) B_13))))
% FOF formula (forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member1823529808lt_o_o F_11) ((pi_Arr195212324lt_o_o A_16) B_13)))) of role axiom named fact_166_Pi__I
% A new axiom: (forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member1823529808lt_o_o F_11) ((pi_Arr195212324lt_o_o A_16) B_13))))
% FOF formula (forall (F_11:(arrow_475358991le_alt->produc1501160679le_alt)) (B_13:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member712472209le_alt F_11) ((pi_Arr1786181611le_alt A_16) B_13)))) of role axiom named fact_167_Pi__I
% A new axiom: (forall (F_11:(arrow_475358991le_alt->produc1501160679le_alt)) (B_13:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member712472209le_alt F_11) ((pi_Arr1786181611le_alt A_16) B_13))))
% FOF formula (forall (F_11:(arrow_1429601828e_indi->produc1501160679le_alt)) (B_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member351225838le_alt F_11) ((pi_Arr329216900le_alt A_16) B_13)))) of role axiom named fact_168_Pi__I
% A new axiom: (forall (F_11:(arrow_1429601828e_indi->produc1501160679le_alt)) (B_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member351225838le_alt F_11) ((pi_Arr329216900le_alt A_16) B_13))))
% FOF formula (forall (F_11:(produc1362454231le_alt->produc1501160679le_alt)) (B_13:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member428957857le_alt F_11) ((pi_Pro1708969783le_alt A_16) B_13)))) of role axiom named fact_169_Pi__I
% A new axiom: (forall (F_11:(produc1362454231le_alt->produc1501160679le_alt)) (B_13:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member428957857le_alt F_11) ((pi_Pro1708969783le_alt A_16) B_13))))
% FOF formula (forall (F_11:(Prop->produc1501160679le_alt)) (B_13:(Prop->(produc1501160679le_alt->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member492167345le_alt F_11) ((pi_o_P657324555le_alt A_16) B_13)))) of role axiom named fact_170_Pi__I
% A new axiom: (forall (F_11:(Prop->produc1501160679le_alt)) (B_13:(Prop->(produc1501160679le_alt->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member492167345le_alt F_11) ((pi_o_P657324555le_alt A_16) B_13))))
% FOF formula (forall (F_11:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member1876989968_alt_o F_11) ((pi_Arr578767520_alt_o A_16) B_13)))) of role axiom named fact_171_Pi__I
% A new axiom: (forall (F_11:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member1876989968_alt_o F_11) ((pi_Arr578767520_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member1234151027_alt_o F_11) ((pi_Arr1060328391_alt_o A_16) B_13)))) of role axiom named fact_172_Pi__I
% A new axiom: (forall (F_11:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member1234151027_alt_o F_11) ((pi_Arr1060328391_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member392452608_alt_o F_11) ((pi_Pro121963604_alt_o A_16) B_13)))) of role axiom named fact_173_Pi__I
% A new axiom: (forall (F_11:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member392452608_alt_o F_11) ((pi_Pro121963604_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member1394214384_alt_o F_11) ((pi_o_A1182933120_alt_o A_16) B_13)))) of role axiom named fact_174_Pi__I
% A new axiom: (forall (F_11:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member1394214384_alt_o F_11) ((pi_o_A1182933120_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (B_13:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member1908358676_alt_o F_11) ((pi_Arr1520776484_alt_o A_16) B_13)))) of role axiom named fact_175_Pi__I
% A new axiom: (forall (F_11:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (B_13:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member1908358676_alt_o F_11) ((pi_Arr1520776484_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (B_13:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member2082473988_alt_o F_11) ((pi_Pro589599960_alt_o A_16) B_13)))) of role axiom named fact_176_Pi__I
% A new axiom: (forall (F_11:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (B_13:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member2082473988_alt_o F_11) ((pi_Pro589599960_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(Prop->(produc1501160679le_alt->Prop))) (B_13:(Prop->((produc1501160679le_alt->Prop)->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member1862122484_alt_o F_11) ((pi_o_P553196292_alt_o A_16) B_13)))) of role axiom named fact_177_Pi__I
% A new axiom: (forall (F_11:(Prop->(produc1501160679le_alt->Prop))) (B_13:(Prop->((produc1501160679le_alt->Prop)->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member1862122484_alt_o F_11) ((pi_o_P553196292_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member89384572_alt_o F_11) ((pi_Arr515871190_alt_o A_16) B_13)))) of role axiom named fact_178_Pi__I
% A new axiom: (forall (F_11:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member89384572_alt_o F_11) ((pi_Arr515871190_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member811956313_alt_o F_11) ((pi_Arr1564509167_alt_o A_16) B_13)))) of role axiom named fact_179_Pi__I
% A new axiom: (forall (F_11:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member811956313_alt_o F_11) ((pi_Arr1564509167_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member654997644_alt_o F_11) ((pi_Pro441468706_alt_o A_16) B_13)))) of role axiom named fact_180_Pi__I
% A new axiom: (forall (F_11:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member654997644_alt_o F_11) ((pi_Pro441468706_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member1957863580_alt_o F_11) ((pi_o_A1186128886_alt_o A_16) B_13)))) of role axiom named fact_181_Pi__I
% A new axiom: (forall (F_11:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member1957863580_alt_o F_11) ((pi_o_A1186128886_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(produc1501160679le_alt->Prop)) (B_13:(produc1501160679le_alt->(Prop->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member377231867_alt_o F_11) ((pi_Pro1701359055_alt_o A_16) B_13)))) of role axiom named fact_182_Pi__I
% A new axiom: (forall (F_11:(produc1501160679le_alt->Prop)) (B_13:(produc1501160679le_alt->(Prop->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member377231867_alt_o F_11) ((pi_Pro1701359055_alt_o A_16) B_13))))
% FOF formula (forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member616898751_alt_o F_11) ((pi_Arr1304755663_alt_o A_16) B_13)))) of role axiom named fact_183_Pi__I
% A new axiom: (forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member616898751_alt_o F_11) ((pi_Arr1304755663_alt_o A_16) B_13))))
% FOF formula (forall (F_11:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_13:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member526088951_alt_o F_11) ((pi_Arr1929480907_alt_o A_16) B_13)))) of role axiom named fact_184_Pi__I
% A new axiom: (forall (F_11:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_13:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member526088951_alt_o F_11) ((pi_Arr1929480907_alt_o A_16) B_13))))
% FOF formula (forall (F_10:(produc1501160679le_alt->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member1416774619le_alt F_10) ((pi_Pro315446191le_alt A_15) (fun (Uu:produc1501160679le_alt)=> B_12))))) of role axiom named fact_185_funcsetI
% A new axiom: (forall (F_10:(produc1501160679le_alt->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member1416774619le_alt F_10) ((pi_Pro315446191le_alt A_15) (fun (Uu:produc1501160679le_alt)=> B_12)))))
% FOF formula (forall (F_10:(produc1501160679le_alt->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member1640632174e_indi F_10) ((pi_Pro1767455108e_indi A_15) (fun (Uu:produc1501160679le_alt)=> B_12))))) of role axiom named fact_186_funcsetI
% A new axiom: (forall (F_10:(produc1501160679le_alt->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member1640632174e_indi F_10) ((pi_Pro1767455108e_indi A_15) (fun (Uu:produc1501160679le_alt)=> B_12)))))
% FOF formula (forall (F_10:(produc1501160679le_alt->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member220989473le_alt F_10) ((pi_Pro666407479le_alt A_15) (fun (Uu:produc1501160679le_alt)=> B_12))))) of role axiom named fact_187_funcsetI
% A new axiom: (forall (F_10:(produc1501160679le_alt->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member220989473le_alt F_10) ((pi_Pro666407479le_alt A_15) (fun (Uu:produc1501160679le_alt)=> B_12)))))
% FOF formula (forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member1596146470le_alt F_10) ((pi_Arr1483346486le_alt A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12))))) of role axiom named fact_188_funcsetI
% A new axiom: (forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member1596146470le_alt F_10) ((pi_Arr1483346486le_alt A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12)))))
% FOF formula (forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member44294883e_indi F_10) ((pi_Arr1232280765e_indi A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12))))) of role axiom named fact_189_funcsetI
% A new axiom: (forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member44294883e_indi F_10) ((pi_Arr1232280765e_indi A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12)))))
% FOF formula (forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member1849320470le_alt F_10) ((pi_Arr1957214192le_alt A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12))))) of role axiom named fact_190_funcsetI
% A new axiom: (forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member1849320470le_alt F_10) ((pi_Arr1957214192le_alt A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12)))))
% FOF formula (forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_12:(Prop->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member939334982lt_o_o F_10) ((pi_Arr952516694lt_o_o A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12))))) of role axiom named fact_191_funcsetI
% A new axiom: (forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_12:(Prop->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member939334982lt_o_o F_10) ((pi_Arr952516694lt_o_o A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12)))))
% FOF formula (forall (F_10:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member1524522914le_alt F_10) ((pi_Pro1868152754le_alt A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12))))) of role axiom named fact_192_funcsetI
% A new axiom: (forall (F_10:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member1524522914le_alt F_10) ((pi_Pro1868152754le_alt A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12)))))
% FOF formula (forall (F_10:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member304866663e_indi F_10) ((pi_Pro468373057e_indi A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12))))) of role axiom named fact_193_funcsetI
% A new axiom: (forall (F_10:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member304866663e_indi F_10) ((pi_Pro468373057e_indi A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12)))))
% FOF formula (forall (F_10:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member1099563162le_alt F_10) ((pi_Pro1678345076le_alt A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12))))) of role axiom named fact_194_funcsetI
% A new axiom: (forall (F_10:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member1099563162le_alt F_10) ((pi_Pro1678345076le_alt A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12)))))
% FOF formula (forall (F_10:((produc1501160679le_alt->Prop)->Prop)) (B_12:(Prop->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member1961363906lt_o_o F_10) ((pi_Pro422690258lt_o_o A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12))))) of role axiom named fact_195_funcsetI
% A new axiom: (forall (F_10:((produc1501160679le_alt->Prop)->Prop)) (B_12:(Prop->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member1961363906lt_o_o F_10) ((pi_Pro422690258lt_o_o A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12)))))
% FOF formula (forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member474974512le_alt F_10) ((pi_Arr1005837828le_alt A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12))))) of role axiom named fact_196_funcsetI
% A new axiom: (forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member474974512le_alt F_10) ((pi_Arr1005837828le_alt A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12)))))
% FOF formula (forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member1452482393e_indi F_10) ((pi_Arr338314351e_indi A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12))))) of role axiom named fact_197_funcsetI
% A new axiom: (forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member1452482393e_indi F_10) ((pi_Arr338314351e_indi A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12)))))
% FOF formula (forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member845447052le_alt F_10) ((pi_Arr2076738722le_alt A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12))))) of role axiom named fact_198_funcsetI
% A new axiom: (forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member845447052le_alt F_10) ((pi_Arr2076738722le_alt A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12)))))
% FOF formula (forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_12:(Prop->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member1823529808lt_o_o F_10) ((pi_Arr195212324lt_o_o A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12))))) of role axiom named fact_199_funcsetI
% A new axiom: (forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_12:(Prop->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member1823529808lt_o_o F_10) ((pi_Arr195212324lt_o_o A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12)))))
% FOF formula (forall (F_10:(arrow_475358991le_alt->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member712472209le_alt F_10) ((pi_Arr1786181611le_alt A_15) (fun (Uu:arrow_475358991le_alt)=> B_12))))) of role axiom named fact_200_funcsetI
% A new axiom: (forall (F_10:(arrow_475358991le_alt->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member712472209le_alt F_10) ((pi_Arr1786181611le_alt A_15) (fun (Uu:arrow_475358991le_alt)=> B_12)))))
% FOF formula (forall (F_10:(arrow_1429601828e_indi->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member351225838le_alt F_10) ((pi_Arr329216900le_alt A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12))))) of role axiom named fact_201_funcsetI
% A new axiom: (forall (F_10:(arrow_1429601828e_indi->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member351225838le_alt F_10) ((pi_Arr329216900le_alt A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12)))))
% FOF formula (forall (F_10:(produc1362454231le_alt->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member428957857le_alt F_10) ((pi_Pro1708969783le_alt A_15) (fun (Uu:produc1362454231le_alt)=> B_12))))) of role axiom named fact_202_funcsetI
% A new axiom: (forall (F_10:(produc1362454231le_alt->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member428957857le_alt F_10) ((pi_Pro1708969783le_alt A_15) (fun (Uu:produc1362454231le_alt)=> B_12)))))
% FOF formula (forall (F_10:(Prop->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member492167345le_alt F_10) ((pi_o_P657324555le_alt A_15) (fun (Uu:Prop)=> B_12))))) of role axiom named fact_203_funcsetI
% A new axiom: (forall (F_10:(Prop->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member492167345le_alt F_10) ((pi_o_P657324555le_alt A_15) (fun (Uu:Prop)=> B_12)))))
% FOF formula (forall (F_10:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member1876989968_alt_o F_10) ((pi_Arr578767520_alt_o A_15) (fun (Uu:arrow_475358991le_alt)=> B_12))))) of role axiom named fact_204_funcsetI
% A new axiom: (forall (F_10:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member1876989968_alt_o F_10) ((pi_Arr578767520_alt_o A_15) (fun (Uu:arrow_475358991le_alt)=> B_12)))))
% FOF formula (forall (F_10:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member1234151027_alt_o F_10) ((pi_Arr1060328391_alt_o A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12))))) of role axiom named fact_205_funcsetI
% A new axiom: (forall (F_10:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member1234151027_alt_o F_10) ((pi_Arr1060328391_alt_o A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12)))))
% FOF formula (forall (F_10:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member392452608_alt_o F_10) ((pi_Pro121963604_alt_o A_15) (fun (Uu:produc1362454231le_alt)=> B_12))))) of role axiom named fact_206_funcsetI
% A new axiom: (forall (F_10:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member392452608_alt_o F_10) ((pi_Pro121963604_alt_o A_15) (fun (Uu:produc1362454231le_alt)=> B_12)))))
% FOF formula (forall (F_10:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member1394214384_alt_o F_10) ((pi_o_A1182933120_alt_o A_15) (fun (Uu:Prop)=> B_12))))) of role axiom named fact_207_funcsetI
% A new axiom: (forall (F_10:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member1394214384_alt_o F_10) ((pi_o_A1182933120_alt_o A_15) (fun (Uu:Prop)=> B_12)))))
% FOF formula (forall (F_10:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member1908358676_alt_o F_10) ((pi_Arr1520776484_alt_o A_15) (fun (Uu:arrow_475358991le_alt)=> B_12))))) of role axiom named fact_208_funcsetI
% A new axiom: (forall (F_10:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member1908358676_alt_o F_10) ((pi_Arr1520776484_alt_o A_15) (fun (Uu:arrow_475358991le_alt)=> B_12)))))
% FOF formula (forall (F_10:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member2082473988_alt_o F_10) ((pi_Pro589599960_alt_o A_15) (fun (Uu:produc1362454231le_alt)=> B_12))))) of role axiom named fact_209_funcsetI
% A new axiom: (forall (F_10:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member2082473988_alt_o F_10) ((pi_Pro589599960_alt_o A_15) (fun (Uu:produc1362454231le_alt)=> B_12)))))
% FOF formula (forall (F_10:(Prop->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member1862122484_alt_o F_10) ((pi_o_P553196292_alt_o A_15) (fun (Uu:Prop)=> B_12))))) of role axiom named fact_210_funcsetI
% A new axiom: (forall (F_10:(Prop->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member1862122484_alt_o F_10) ((pi_o_P553196292_alt_o A_15) (fun (Uu:Prop)=> B_12)))))
% FOF formula (forall (F_10:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member89384572_alt_o F_10) ((pi_Arr515871190_alt_o A_15) (fun (Uu:arrow_475358991le_alt)=> B_12))))) of role axiom named fact_211_funcsetI
% A new axiom: (forall (F_10:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member89384572_alt_o F_10) ((pi_Arr515871190_alt_o A_15) (fun (Uu:arrow_475358991le_alt)=> B_12)))))
% FOF formula (forall (F_10:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member811956313_alt_o F_10) ((pi_Arr1564509167_alt_o A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12))))) of role axiom named fact_212_funcsetI
% A new axiom: (forall (F_10:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member811956313_alt_o F_10) ((pi_Arr1564509167_alt_o A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12)))))
% FOF formula (forall (F_10:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member654997644_alt_o F_10) ((pi_Pro441468706_alt_o A_15) (fun (Uu:produc1362454231le_alt)=> B_12))))) of role axiom named fact_213_funcsetI
% A new axiom: (forall (F_10:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member654997644_alt_o F_10) ((pi_Pro441468706_alt_o A_15) (fun (Uu:produc1362454231le_alt)=> B_12)))))
% FOF formula (forall (F_10:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member1957863580_alt_o F_10) ((pi_o_A1186128886_alt_o A_15) (fun (Uu:Prop)=> B_12))))) of role axiom named fact_214_funcsetI
% A new axiom: (forall (F_10:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member1957863580_alt_o F_10) ((pi_o_A1186128886_alt_o A_15) (fun (Uu:Prop)=> B_12)))))
% FOF formula (forall (F_10:(produc1501160679le_alt->Prop)) (B_12:(Prop->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member377231867_alt_o F_10) ((pi_Pro1701359055_alt_o A_15) (fun (Uu:produc1501160679le_alt)=> B_12))))) of role axiom named fact_215_funcsetI
% A new axiom: (forall (F_10:(produc1501160679le_alt->Prop)) (B_12:(Prop->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member377231867_alt_o F_10) ((pi_Pro1701359055_alt_o A_15) (fun (Uu:produc1501160679le_alt)=> B_12)))))
% FOF formula (forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member616898751_alt_o F_10) ((pi_Arr1304755663_alt_o A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12))))) of role axiom named fact_216_funcsetI
% A new axiom: (forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member616898751_alt_o F_10) ((pi_Arr1304755663_alt_o A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12)))))
% FOF formula (forall (F_10:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member526088951_alt_o F_10) ((pi_Arr1929480907_alt_o A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12))))) of role axiom named fact_217_funcsetI
% A new axiom: (forall (F_10:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member526088951_alt_o F_10) ((pi_Arr1929480907_alt_o A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12)))))
% FOF formula (forall (F_9:(produc1501160679le_alt->arrow_475358991le_alt)) (B_11:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member1416774619le_alt F_9) ((pi_Pro315446191le_alt A_14) B_11)))) of role axiom named fact_218_Pi__I_H
% A new axiom: (forall (F_9:(produc1501160679le_alt->arrow_475358991le_alt)) (B_11:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member1416774619le_alt F_9) ((pi_Pro315446191le_alt A_14) B_11))))
% FOF formula (forall (F_9:(produc1501160679le_alt->arrow_1429601828e_indi)) (B_11:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member1640632174e_indi F_9) ((pi_Pro1767455108e_indi A_14) B_11)))) of role axiom named fact_219_Pi__I_H
% A new axiom: (forall (F_9:(produc1501160679le_alt->arrow_1429601828e_indi)) (B_11:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member1640632174e_indi F_9) ((pi_Pro1767455108e_indi A_14) B_11))))
% FOF formula (forall (F_9:(produc1501160679le_alt->produc1362454231le_alt)) (B_11:(produc1501160679le_alt->(produc1362454231le_alt->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member220989473le_alt F_9) ((pi_Pro666407479le_alt A_14) B_11)))) of role axiom named fact_220_Pi__I_H
% A new axiom: (forall (F_9:(produc1501160679le_alt->produc1362454231le_alt)) (B_11:(produc1501160679le_alt->(produc1362454231le_alt->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member220989473le_alt F_9) ((pi_Pro666407479le_alt A_14) B_11))))
% FOF formula (forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member1596146470le_alt F_9) ((pi_Arr1483346486le_alt A_14) B_11)))) of role axiom named fact_221_Pi__I_H
% A new axiom: (forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member1596146470le_alt F_9) ((pi_Arr1483346486le_alt A_14) B_11))))
% FOF formula (forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member44294883e_indi F_9) ((pi_Arr1232280765e_indi A_14) B_11)))) of role axiom named fact_222_Pi__I_H
% A new axiom: (forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member44294883e_indi F_9) ((pi_Arr1232280765e_indi A_14) B_11))))
% FOF formula (forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member1849320470le_alt F_9) ((pi_Arr1957214192le_alt A_14) B_11)))) of role axiom named fact_223_Pi__I_H
% A new axiom: (forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member1849320470le_alt F_9) ((pi_Arr1957214192le_alt A_14) B_11))))
% FOF formula (forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member939334982lt_o_o F_9) ((pi_Arr952516694lt_o_o A_14) B_11)))) of role axiom named fact_224_Pi__I_H
% A new axiom: (forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member939334982lt_o_o F_9) ((pi_Arr952516694lt_o_o A_14) B_11))))
% FOF formula (forall (F_9:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (B_11:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member1524522914le_alt F_9) ((pi_Pro1868152754le_alt A_14) B_11)))) of role axiom named fact_225_Pi__I_H
% A new axiom: (forall (F_9:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (B_11:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member1524522914le_alt F_9) ((pi_Pro1868152754le_alt A_14) B_11))))
% FOF formula (forall (F_9:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (B_11:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member304866663e_indi F_9) ((pi_Pro468373057e_indi A_14) B_11)))) of role axiom named fact_226_Pi__I_H
% A new axiom: (forall (F_9:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (B_11:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member304866663e_indi F_9) ((pi_Pro468373057e_indi A_14) B_11))))
% FOF formula (forall (F_9:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (B_11:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member1099563162le_alt F_9) ((pi_Pro1678345076le_alt A_14) B_11)))) of role axiom named fact_227_Pi__I_H
% A new axiom: (forall (F_9:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (B_11:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member1099563162le_alt F_9) ((pi_Pro1678345076le_alt A_14) B_11))))
% FOF formula (forall (F_9:((produc1501160679le_alt->Prop)->Prop)) (B_11:((produc1501160679le_alt->Prop)->(Prop->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member1961363906lt_o_o F_9) ((pi_Pro422690258lt_o_o A_14) B_11)))) of role axiom named fact_228_Pi__I_H
% A new axiom: (forall (F_9:((produc1501160679le_alt->Prop)->Prop)) (B_11:((produc1501160679le_alt->Prop)->(Prop->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member1961363906lt_o_o F_9) ((pi_Pro422690258lt_o_o A_14) B_11))))
% FOF formula (forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member474974512le_alt F_9) ((pi_Arr1005837828le_alt A_14) B_11)))) of role axiom named fact_229_Pi__I_H
% A new axiom: (forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member474974512le_alt F_9) ((pi_Arr1005837828le_alt A_14) B_11))))
% FOF formula (forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member1452482393e_indi F_9) ((pi_Arr338314351e_indi A_14) B_11)))) of role axiom named fact_230_Pi__I_H
% A new axiom: (forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member1452482393e_indi F_9) ((pi_Arr338314351e_indi A_14) B_11))))
% FOF formula (forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member845447052le_alt F_9) ((pi_Arr2076738722le_alt A_14) B_11)))) of role axiom named fact_231_Pi__I_H
% A new axiom: (forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member845447052le_alt F_9) ((pi_Arr2076738722le_alt A_14) B_11))))
% FOF formula (forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member1823529808lt_o_o F_9) ((pi_Arr195212324lt_o_o A_14) B_11)))) of role axiom named fact_232_Pi__I_H
% A new axiom: (forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member1823529808lt_o_o F_9) ((pi_Arr195212324lt_o_o A_14) B_11))))
% FOF formula (forall (F_9:(arrow_475358991le_alt->produc1501160679le_alt)) (B_11:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member712472209le_alt F_9) ((pi_Arr1786181611le_alt A_14) B_11)))) of role axiom named fact_233_Pi__I_H
% A new axiom: (forall (F_9:(arrow_475358991le_alt->produc1501160679le_alt)) (B_11:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member712472209le_alt F_9) ((pi_Arr1786181611le_alt A_14) B_11))))
% FOF formula (forall (F_9:(arrow_1429601828e_indi->produc1501160679le_alt)) (B_11:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member351225838le_alt F_9) ((pi_Arr329216900le_alt A_14) B_11)))) of role axiom named fact_234_Pi__I_H
% A new axiom: (forall (F_9:(arrow_1429601828e_indi->produc1501160679le_alt)) (B_11:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member351225838le_alt F_9) ((pi_Arr329216900le_alt A_14) B_11))))
% FOF formula (forall (F_9:(produc1362454231le_alt->produc1501160679le_alt)) (B_11:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member428957857le_alt F_9) ((pi_Pro1708969783le_alt A_14) B_11)))) of role axiom named fact_235_Pi__I_H
% A new axiom: (forall (F_9:(produc1362454231le_alt->produc1501160679le_alt)) (B_11:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member428957857le_alt F_9) ((pi_Pro1708969783le_alt A_14) B_11))))
% FOF formula (forall (F_9:(Prop->produc1501160679le_alt)) (B_11:(Prop->(produc1501160679le_alt->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member492167345le_alt F_9) ((pi_o_P657324555le_alt A_14) B_11)))) of role axiom named fact_236_Pi__I_H
% A new axiom: (forall (F_9:(Prop->produc1501160679le_alt)) (B_11:(Prop->(produc1501160679le_alt->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member492167345le_alt F_9) ((pi_o_P657324555le_alt A_14) B_11))))
% FOF formula (forall (F_9:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member1876989968_alt_o F_9) ((pi_Arr578767520_alt_o A_14) B_11)))) of role axiom named fact_237_Pi__I_H
% A new axiom: (forall (F_9:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member1876989968_alt_o F_9) ((pi_Arr578767520_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member1234151027_alt_o F_9) ((pi_Arr1060328391_alt_o A_14) B_11)))) of role axiom named fact_238_Pi__I_H
% A new axiom: (forall (F_9:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member1234151027_alt_o F_9) ((pi_Arr1060328391_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member392452608_alt_o F_9) ((pi_Pro121963604_alt_o A_14) B_11)))) of role axiom named fact_239_Pi__I_H
% A new axiom: (forall (F_9:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member392452608_alt_o F_9) ((pi_Pro121963604_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member1394214384_alt_o F_9) ((pi_o_A1182933120_alt_o A_14) B_11)))) of role axiom named fact_240_Pi__I_H
% A new axiom: (forall (F_9:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member1394214384_alt_o F_9) ((pi_o_A1182933120_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (B_11:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member1908358676_alt_o F_9) ((pi_Arr1520776484_alt_o A_14) B_11)))) of role axiom named fact_241_Pi__I_H
% A new axiom: (forall (F_9:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (B_11:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member1908358676_alt_o F_9) ((pi_Arr1520776484_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (B_11:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member2082473988_alt_o F_9) ((pi_Pro589599960_alt_o A_14) B_11)))) of role axiom named fact_242_Pi__I_H
% A new axiom: (forall (F_9:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (B_11:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member2082473988_alt_o F_9) ((pi_Pro589599960_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(Prop->(produc1501160679le_alt->Prop))) (B_11:(Prop->((produc1501160679le_alt->Prop)->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member1862122484_alt_o F_9) ((pi_o_P553196292_alt_o A_14) B_11)))) of role axiom named fact_243_Pi__I_H
% A new axiom: (forall (F_9:(Prop->(produc1501160679le_alt->Prop))) (B_11:(Prop->((produc1501160679le_alt->Prop)->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member1862122484_alt_o F_9) ((pi_o_P553196292_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member89384572_alt_o F_9) ((pi_Arr515871190_alt_o A_14) B_11)))) of role axiom named fact_244_Pi__I_H
% A new axiom: (forall (F_9:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member89384572_alt_o F_9) ((pi_Arr515871190_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member811956313_alt_o F_9) ((pi_Arr1564509167_alt_o A_14) B_11)))) of role axiom named fact_245_Pi__I_H
% A new axiom: (forall (F_9:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member811956313_alt_o F_9) ((pi_Arr1564509167_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member654997644_alt_o F_9) ((pi_Pro441468706_alt_o A_14) B_11)))) of role axiom named fact_246_Pi__I_H
% A new axiom: (forall (F_9:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member654997644_alt_o F_9) ((pi_Pro441468706_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member1957863580_alt_o F_9) ((pi_o_A1186128886_alt_o A_14) B_11)))) of role axiom named fact_247_Pi__I_H
% A new axiom: (forall (F_9:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member1957863580_alt_o F_9) ((pi_o_A1186128886_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(produc1501160679le_alt->Prop)) (B_11:(produc1501160679le_alt->(Prop->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member377231867_alt_o F_9) ((pi_Pro1701359055_alt_o A_14) B_11)))) of role axiom named fact_248_Pi__I_H
% A new axiom: (forall (F_9:(produc1501160679le_alt->Prop)) (B_11:(produc1501160679le_alt->(Prop->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member377231867_alt_o F_9) ((pi_Pro1701359055_alt_o A_14) B_11))))
% FOF formula (forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member616898751_alt_o F_9) ((pi_Arr1304755663_alt_o A_14) B_11)))) of role axiom named fact_249_Pi__I_H
% A new axiom: (forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member616898751_alt_o F_9) ((pi_Arr1304755663_alt_o A_14) B_11))))
% FOF formula (forall (F_9:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_11:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member526088951_alt_o F_9) ((pi_Arr1929480907_alt_o A_14) B_11)))) of role axiom named fact_250_Pi__I_H
% A new axiom: (forall (F_9:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_11:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member526088951_alt_o F_9) ((pi_Arr1929480907_alt_o A_14) B_11))))
% FOF formula (forall (B_10:(produc1501160679le_alt->(Prop->Prop))) (G:(produc1501160679le_alt->Prop)) (F_8:(produc1501160679le_alt->Prop)) (A_13:(produc1501160679le_alt->Prop)), ((forall (W:produc1501160679le_alt), (((member214075476le_alt W) A_13)->((iff (F_8 W)) (G W))))->((iff ((member377231867_alt_o F_8) ((pi_Pro1701359055_alt_o A_13) B_10))) ((member377231867_alt_o G) ((pi_Pro1701359055_alt_o A_13) B_10))))) of role axiom named fact_251_Pi__cong
% A new axiom: (forall (B_10:(produc1501160679le_alt->(Prop->Prop))) (G:(produc1501160679le_alt->Prop)) (F_8:(produc1501160679le_alt->Prop)) (A_13:(produc1501160679le_alt->Prop)), ((forall (W:produc1501160679le_alt), (((member214075476le_alt W) A_13)->((iff (F_8 W)) (G W))))->((iff ((member377231867_alt_o F_8) ((pi_Pro1701359055_alt_o A_13) B_10))) ((member377231867_alt_o G) ((pi_Pro1701359055_alt_o A_13) B_10)))))
% FOF formula (forall (B_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (F_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (G:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (W:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o W) A_13)->(((eq (produc1501160679le_alt->Prop)) (F_8 W)) (G W))))->((iff ((member616898751_alt_o F_8) ((pi_Arr1304755663_alt_o A_13) B_10))) ((member616898751_alt_o G) ((pi_Arr1304755663_alt_o A_13) B_10))))) of role axiom named fact_252_Pi__cong
% A new axiom: (forall (B_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (F_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (G:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (W:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o W) A_13)->(((eq (produc1501160679le_alt->Prop)) (F_8 W)) (G W))))->((iff ((member616898751_alt_o F_8) ((pi_Arr1304755663_alt_o A_13) B_10))) ((member616898751_alt_o G) ((pi_Arr1304755663_alt_o A_13) B_10)))))
% FOF formula (forall (B_10:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (F_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (G:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_13:(arrow_1429601828e_indi->Prop)), ((forall (W:arrow_1429601828e_indi), (((member2052026769e_indi W) A_13)->(((eq (produc1501160679le_alt->Prop)) (F_8 W)) (G W))))->((iff ((member526088951_alt_o F_8) ((pi_Arr1929480907_alt_o A_13) B_10))) ((member526088951_alt_o G) ((pi_Arr1929480907_alt_o A_13) B_10))))) of role axiom named fact_253_Pi__cong
% A new axiom: (forall (B_10:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (F_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (G:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_13:(arrow_1429601828e_indi->Prop)), ((forall (W:arrow_1429601828e_indi), (((member2052026769e_indi W) A_13)->(((eq (produc1501160679le_alt->Prop)) (F_8 W)) (G W))))->((iff ((member526088951_alt_o F_8) ((pi_Arr1929480907_alt_o A_13) B_10))) ((member526088951_alt_o G) ((pi_Arr1929480907_alt_o A_13) B_10)))))
% FOF formula (forall (S_1:(produc1362454231le_alt->Prop)) (R_39:(produc1362454231le_alt->Prop)), ((iff (forall (X_2:list_A2115238852le_alt) (Xa:list_A2115238852le_alt), ((iff ((member28618436le_alt ((produc776457805le_alt X_2) Xa)) R_39)) ((member28618436le_alt ((produc776457805le_alt X_2) Xa)) S_1)))) (((eq (produc1362454231le_alt->Prop)) R_39) S_1))) of role axiom named fact_254_pred__equals__eq2
% A new axiom: (forall (S_1:(produc1362454231le_alt->Prop)) (R_39:(produc1362454231le_alt->Prop)), ((iff (forall (X_2:list_A2115238852le_alt) (Xa:list_A2115238852le_alt), ((iff ((member28618436le_alt ((produc776457805le_alt X_2) Xa)) R_39)) ((member28618436le_alt ((produc776457805le_alt X_2) Xa)) S_1)))) (((eq (produc1362454231le_alt->Prop)) R_39) S_1)))
% FOF formula (forall (S_1:(produc1501160679le_alt->Prop)) (R_39:(produc1501160679le_alt->Prop)), ((iff (forall (X_2:arrow_475358991le_alt) (Xa:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X_2) Xa)) R_39)) ((member214075476le_alt ((produc1347929815le_alt X_2) Xa)) S_1)))) (((eq (produc1501160679le_alt->Prop)) R_39) S_1))) of role axiom named fact_255_pred__equals__eq2
% A new axiom: (forall (S_1:(produc1501160679le_alt->Prop)) (R_39:(produc1501160679le_alt->Prop)), ((iff (forall (X_2:arrow_475358991le_alt) (Xa:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X_2) Xa)) R_39)) ((member214075476le_alt ((produc1347929815le_alt X_2) Xa)) S_1)))) (((eq (produc1501160679le_alt->Prop)) R_39) S_1)))
% FOF formula (forall (Y_24:produc1362454231le_alt), ((forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), (not (((eq produc1362454231le_alt) Y_24) ((produc776457805le_alt A) B))))->False)) of role axiom named fact_256_prod_Oexhaust
% A new axiom: (forall (Y_24:produc1362454231le_alt), ((forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), (not (((eq produc1362454231le_alt) Y_24) ((produc776457805le_alt A) B))))->False))
% FOF formula (forall (Y_24:produc1501160679le_alt), ((forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), (not (((eq produc1501160679le_alt) Y_24) ((produc1347929815le_alt A) B))))->False)) of role axiom named fact_257_prod_Oexhaust
% A new axiom: (forall (Y_24:produc1501160679le_alt), ((forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), (not (((eq produc1501160679le_alt) Y_24) ((produc1347929815le_alt A) B))))->False))
% FOF formula (forall (P_29:produc1362454231le_alt), ((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt), (not (((eq produc1362454231le_alt) P_29) ((produc776457805le_alt X_2) Y_1))))->False)) of role axiom named fact_258_PairE
% A new axiom: (forall (P_29:produc1362454231le_alt), ((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt), (not (((eq produc1362454231le_alt) P_29) ((produc776457805le_alt X_2) Y_1))))->False))
% FOF formula (forall (P_29:produc1501160679le_alt), ((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt), (not (((eq produc1501160679le_alt) P_29) ((produc1347929815le_alt X_2) Y_1))))->False)) of role axiom named fact_259_PairE
% A new axiom: (forall (P_29:produc1501160679le_alt), ((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt), (not (((eq produc1501160679le_alt) P_29) ((produc1347929815le_alt X_2) Y_1))))->False))
% FOF formula (forall (P_28:(produc1362454231le_alt->Prop)), ((iff (ex1 P_28)) ((ex list_A2115238852le_alt) (fun (A:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (B:list_A2115238852le_alt)=> (P_28 ((produc776457805le_alt A) B)))))))) of role axiom named fact_260_split__paired__Ex
% A new axiom: (forall (P_28:(produc1362454231le_alt->Prop)), ((iff (ex1 P_28)) ((ex list_A2115238852le_alt) (fun (A:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (B:list_A2115238852le_alt)=> (P_28 ((produc776457805le_alt A) B))))))))
% FOF formula (forall (P_28:(produc1501160679le_alt->Prop)), ((iff (ex2 P_28)) ((ex arrow_475358991le_alt) (fun (A:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (B:arrow_475358991le_alt)=> (P_28 ((produc1347929815le_alt A) B)))))))) of role axiom named fact_261_split__paired__Ex
% A new axiom: (forall (P_28:(produc1501160679le_alt->Prop)), ((iff (ex2 P_28)) ((ex arrow_475358991le_alt) (fun (A:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (B:arrow_475358991le_alt)=> (P_28 ((produc1347929815le_alt A) B))))))))
% FOF formula (forall (X_68:arrow_475358991le_alt), (((eq list_A2115238852le_alt) ((insert2120566741le_alt X_68) nil_Ar1286194111le_alt)) ((cons_A228743023le_alt X_68) nil_Ar1286194111le_alt))) of role axiom named fact_262_insert__Nil
% A new axiom: (forall (X_68:arrow_475358991le_alt), (((eq list_A2115238852le_alt) ((insert2120566741le_alt X_68) nil_Ar1286194111le_alt)) ((cons_A228743023le_alt X_68) nil_Ar1286194111le_alt)))
% FOF formula (forall (X_67:arrow_475358991le_alt) (Xs_122:list_A2115238852le_alt), ((distin236324274le_alt Xs_122)->(distin236324274le_alt ((insert2120566741le_alt X_67) Xs_122)))) of role axiom named fact_263_distinct__insert
% A new axiom: (forall (X_67:arrow_475358991le_alt) (Xs_122:list_A2115238852le_alt), ((distin236324274le_alt Xs_122)->(distin236324274le_alt ((insert2120566741le_alt X_67) Xs_122))))
% FOF formula (forall (X_66:arrow_475358991le_alt) (A_12:(arrow_475358991le_alt->Prop)), ((iff ((member84363362le_alt X_66) A_12)) (A_12 X_66))) of role axiom named fact_264_mem__def
% A new axiom: (forall (X_66:arrow_475358991le_alt) (A_12:(arrow_475358991le_alt->Prop)), ((iff ((member84363362le_alt X_66) A_12)) (A_12 X_66)))
% FOF formula (forall (X_66:arrow_1429601828e_indi) (A_12:(arrow_1429601828e_indi->Prop)), ((iff ((member2052026769e_indi X_66) A_12)) (A_12 X_66))) of role axiom named fact_265_mem__def
% A new axiom: (forall (X_66:arrow_1429601828e_indi) (A_12:(arrow_1429601828e_indi->Prop)), ((iff ((member2052026769e_indi X_66) A_12)) (A_12 X_66)))
% FOF formula (forall (X_66:produc1362454231le_alt) (A_12:(produc1362454231le_alt->Prop)), ((iff ((member28618436le_alt X_66) A_12)) (A_12 X_66))) of role axiom named fact_266_mem__def
% A new axiom: (forall (X_66:produc1362454231le_alt) (A_12:(produc1362454231le_alt->Prop)), ((iff ((member28618436le_alt X_66) A_12)) (A_12 X_66)))
% FOF formula (forall (X_66:Prop) (A_12:(Prop->Prop)), ((iff ((member_o X_66) A_12)) (A_12 X_66))) of role axiom named fact_267_mem__def
% A new axiom: (forall (X_66:Prop) (A_12:(Prop->Prop)), ((iff ((member_o X_66) A_12)) (A_12 X_66)))
% FOF formula (forall (X_66:produc1501160679le_alt) (A_12:(produc1501160679le_alt->Prop)), ((iff ((member214075476le_alt X_66) A_12)) (A_12 X_66))) of role axiom named fact_268_mem__def
% A new axiom: (forall (X_66:produc1501160679le_alt) (A_12:(produc1501160679le_alt->Prop)), ((iff ((member214075476le_alt X_66) A_12)) (A_12 X_66)))
% FOF formula (forall (X_66:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member526088951_alt_o X_66) A_12)) (A_12 X_66))) of role axiom named fact_269_mem__def
% A new axiom: (forall (X_66:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member526088951_alt_o X_66) A_12)) (A_12 X_66)))
% FOF formula (forall (X_66:(produc1501160679le_alt->Prop)) (A_12:((produc1501160679le_alt->Prop)->Prop)), ((iff ((member377231867_alt_o X_66) A_12)) (A_12 X_66))) of role axiom named fact_270_mem__def
% A new axiom: (forall (X_66:(produc1501160679le_alt->Prop)) (A_12:((produc1501160679le_alt->Prop)->Prop)), ((iff ((member377231867_alt_o X_66) A_12)) (A_12 X_66)))
% FOF formula (forall (X_66:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member616898751_alt_o X_66) A_12)) (A_12 X_66))) of role axiom named fact_271_mem__def
% A new axiom: (forall (X_66:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member616898751_alt_o X_66) A_12)) (A_12 X_66)))
% FOF formula (forall (P_27:(arrow_475358991le_alt->Prop)), (((eq (arrow_475358991le_alt->Prop)) (collec742074788le_alt P_27)) P_27)) of role axiom named fact_272_Collect__def
% A new axiom: (forall (P_27:(arrow_475358991le_alt->Prop)), (((eq (arrow_475358991le_alt->Prop)) (collec742074788le_alt P_27)) P_27))
% FOF formula (forall (P_27:(arrow_1429601828e_indi->Prop)), (((eq (arrow_1429601828e_indi->Prop)) (collec22405327e_indi P_27)) P_27)) of role axiom named fact_273_Collect__def
% A new axiom: (forall (P_27:(arrow_1429601828e_indi->Prop)), (((eq (arrow_1429601828e_indi->Prop)) (collec22405327e_indi P_27)) P_27))
% FOF formula (forall (P_27:((produc1501160679le_alt->Prop)->Prop)), (((eq ((produc1501160679le_alt->Prop)->Prop)) (collec94295101_alt_o P_27)) P_27)) of role axiom named fact_274_Collect__def
% A new axiom: (forall (P_27:((produc1501160679le_alt->Prop)->Prop)), (((eq ((produc1501160679le_alt->Prop)->Prop)) (collec94295101_alt_o P_27)) P_27))
% FOF formula (forall (P_26:(list_A2115238852le_alt->Prop)) (Xs_121:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_121) nil_Ar1286194111le_alt))->((forall (X_2:arrow_475358991le_alt), (P_26 ((cons_A228743023le_alt X_2) nil_Ar1286194111le_alt)))->((forall (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_21) nil_Ar1286194111le_alt))->((P_26 Xs_21)->(P_26 ((cons_A228743023le_alt X_2) Xs_21)))))->(P_26 Xs_121))))) of role axiom named fact_275_list__nonempty__induct
% A new axiom: (forall (P_26:(list_A2115238852le_alt->Prop)) (Xs_121:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_121) nil_Ar1286194111le_alt))->((forall (X_2:arrow_475358991le_alt), (P_26 ((cons_A228743023le_alt X_2) nil_Ar1286194111le_alt)))->((forall (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_21) nil_Ar1286194111le_alt))->((P_26 Xs_21)->(P_26 ((cons_A228743023le_alt X_2) Xs_21)))))->(P_26 Xs_121)))))
% FOF formula (forall (X_2:(produc1501160679le_alt->Prop)) (Xa:arrow_475358991le_alt) (Xb:arrow_475358991le_alt), ((iff (((produc910278158_alt_o X_2) Xa) Xb)) (X_2 ((produc1347929815le_alt Xa) Xb)))) of role axiom named fact_276_curry__def
% A new axiom: (forall (X_2:(produc1501160679le_alt->Prop)) (Xa:arrow_475358991le_alt) (Xb:arrow_475358991le_alt), ((iff (((produc910278158_alt_o X_2) Xa) Xb)) (X_2 ((produc1347929815le_alt Xa) Xb))))
% FOF formula (forall (F_7:(produc1362454231le_alt->Prop)) (A_11:list_A2115238852le_alt) (B_9:list_A2115238852le_alt), ((F_7 ((produc776457805le_alt A_11) B_9))->(((produc1739499928_alt_o F_7) A_11) B_9))) of role axiom named fact_277_curryI
% A new axiom: (forall (F_7:(produc1362454231le_alt->Prop)) (A_11:list_A2115238852le_alt) (B_9:list_A2115238852le_alt), ((F_7 ((produc776457805le_alt A_11) B_9))->(((produc1739499928_alt_o F_7) A_11) B_9)))
% FOF formula (forall (F_7:(produc1501160679le_alt->Prop)) (A_11:arrow_475358991le_alt) (B_9:arrow_475358991le_alt), ((F_7 ((produc1347929815le_alt A_11) B_9))->(((produc910278158_alt_o F_7) A_11) B_9))) of role axiom named fact_278_curryI
% A new axiom: (forall (F_7:(produc1501160679le_alt->Prop)) (A_11:arrow_475358991le_alt) (B_9:arrow_475358991le_alt), ((F_7 ((produc1347929815le_alt A_11) B_9))->(((produc910278158_alt_o F_7) A_11) B_9)))
% FOF formula (null_A1520965063le_alt nil_Ar1286194111le_alt) of role axiom named fact_279_null__rec_I2_J
% A new axiom: (null_A1520965063le_alt nil_Ar1286194111le_alt)
% FOF formula (forall (Xs_120:list_A2115238852le_alt), ((iff (null_A1520965063le_alt Xs_120)) (((eq list_A2115238852le_alt) Xs_120) nil_Ar1286194111le_alt))) of role axiom named fact_280_List_Onull__def
% A new axiom: (forall (Xs_120:list_A2115238852le_alt), ((iff (null_A1520965063le_alt Xs_120)) (((eq list_A2115238852le_alt) Xs_120) nil_Ar1286194111le_alt)))
% FOF formula (forall (Xs_119:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) Xs_119) nil_Ar1286194111le_alt)) (null_A1520965063le_alt Xs_119))) of role axiom named fact_281_eq__Nil__null
% A new axiom: (forall (Xs_119:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) Xs_119) nil_Ar1286194111le_alt)) (null_A1520965063le_alt Xs_119)))
% FOF formula (forall (X_65:arrow_475358991le_alt) (Xs_118:list_A2115238852le_alt), ((null_A1520965063le_alt ((cons_A228743023le_alt X_65) Xs_118))->False)) of role axiom named fact_282_null__rec_I1_J
% A new axiom: (forall (X_65:arrow_475358991le_alt) (Xs_118:list_A2115238852le_alt), ((null_A1520965063le_alt ((cons_A228743023le_alt X_65) Xs_118))->False))
% FOF formula (forall (F_6:(produc1362454231le_alt->Prop)) (A_10:list_A2115238852le_alt) (B_8:list_A2115238852le_alt), ((((produc1739499928_alt_o F_6) A_10) B_8)->(F_6 ((produc776457805le_alt A_10) B_8)))) of role axiom named fact_283_curryD
% A new axiom: (forall (F_6:(produc1362454231le_alt->Prop)) (A_10:list_A2115238852le_alt) (B_8:list_A2115238852le_alt), ((((produc1739499928_alt_o F_6) A_10) B_8)->(F_6 ((produc776457805le_alt A_10) B_8))))
% FOF formula (forall (F_6:(produc1501160679le_alt->Prop)) (A_10:arrow_475358991le_alt) (B_8:arrow_475358991le_alt), ((((produc910278158_alt_o F_6) A_10) B_8)->(F_6 ((produc1347929815le_alt A_10) B_8)))) of role axiom named fact_284_curryD
% A new axiom: (forall (F_6:(produc1501160679le_alt->Prop)) (A_10:arrow_475358991le_alt) (B_8:arrow_475358991le_alt), ((((produc910278158_alt_o F_6) A_10) B_8)->(F_6 ((produc1347929815le_alt A_10) B_8))))
% FOF formula (forall (F_5:(produc1362454231le_alt->Prop)) (A_9:list_A2115238852le_alt) (B_7:list_A2115238852le_alt), ((((produc1739499928_alt_o F_5) A_9) B_7)->(F_5 ((produc776457805le_alt A_9) B_7)))) of role axiom named fact_285_curryE
% A new axiom: (forall (F_5:(produc1362454231le_alt->Prop)) (A_9:list_A2115238852le_alt) (B_7:list_A2115238852le_alt), ((((produc1739499928_alt_o F_5) A_9) B_7)->(F_5 ((produc776457805le_alt A_9) B_7))))
% FOF formula (forall (F_5:(produc1501160679le_alt->Prop)) (A_9:arrow_475358991le_alt) (B_7:arrow_475358991le_alt), ((((produc910278158_alt_o F_5) A_9) B_7)->(F_5 ((produc1347929815le_alt A_9) B_7)))) of role axiom named fact_286_curryE
% A new axiom: (forall (F_5:(produc1501160679le_alt->Prop)) (A_9:arrow_475358991le_alt) (B_7:arrow_475358991le_alt), ((((produc910278158_alt_o F_5) A_9) B_7)->(F_5 ((produc1347929815le_alt A_9) B_7))))
% FOF formula (forall (F_4:(produc1501160679le_alt->Prop)) (A_8:arrow_475358991le_alt) (B_6:arrow_475358991le_alt), ((iff (((produc910278158_alt_o F_4) A_8) B_6)) (F_4 ((produc1347929815le_alt A_8) B_6)))) of role axiom named fact_287_curry__conv
% A new axiom: (forall (F_4:(produc1501160679le_alt->Prop)) (A_8:arrow_475358991le_alt) (B_6:arrow_475358991le_alt), ((iff (((produc910278158_alt_o F_4) A_8) B_6)) (F_4 ((produc1347929815le_alt A_8) B_6))))
% FOF formula (forall (Xs_117:list_A2115238852le_alt), ((iff ((equal_484611810le_alt Xs_117) nil_Ar1286194111le_alt)) (null_A1520965063le_alt Xs_117))) of role axiom named fact_288_equal__Nil__null
% A new axiom: (forall (Xs_117:list_A2115238852le_alt), ((iff ((equal_484611810le_alt Xs_117) nil_Ar1286194111le_alt)) (null_A1520965063le_alt Xs_117)))
% FOF formula (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) arrow_734252939e_Prof) ((pi_Arr1929480907_alt_o top_to988227749indi_o) (fun (Uu:arrow_1429601828e_indi)=> arrow_823908191le_Lin))) of role axiom named fact_289_Prof__def
% A new axiom: (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) arrow_734252939e_Prof) ((pi_Arr1929480907_alt_o top_to988227749indi_o) (fun (Uu:arrow_1429601828e_indi)=> arrow_823908191le_Lin)))
% FOF formula (forall (A_7:list_A2115238852le_alt) (X_64:list_l1475218533le_alt) (B_5:list_A2115238852le_alt) (Y_23:list_l1475218533le_alt) (R_38:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt A_7) X_64)) ((cons_l635097956le_alt B_5) Y_23))) (lexord469916775le_alt R_38))) ((or ((member28618436le_alt ((produc776457805le_alt A_7) B_5)) R_38)) ((and (((eq list_A2115238852le_alt) A_7) B_5)) ((member1732936276le_alt ((produc1317709143le_alt X_64) Y_23)) (lexord469916775le_alt R_38)))))) of role axiom named fact_290_lexord__cons__cons
% A new axiom: (forall (A_7:list_A2115238852le_alt) (X_64:list_l1475218533le_alt) (B_5:list_A2115238852le_alt) (Y_23:list_l1475218533le_alt) (R_38:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt A_7) X_64)) ((cons_l635097956le_alt B_5) Y_23))) (lexord469916775le_alt R_38))) ((or ((member28618436le_alt ((produc776457805le_alt A_7) B_5)) R_38)) ((and (((eq list_A2115238852le_alt) A_7) B_5)) ((member1732936276le_alt ((produc1317709143le_alt X_64) Y_23)) (lexord469916775le_alt R_38))))))
% FOF formula (forall (A_7:arrow_475358991le_alt) (X_64:list_A2115238852le_alt) (B_5:arrow_475358991le_alt) (Y_23:list_A2115238852le_alt) (R_38:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt A_7) X_64)) ((cons_A228743023le_alt B_5) Y_23))) (lexord958095404le_alt R_38))) ((or ((member214075476le_alt ((produc1347929815le_alt A_7) B_5)) R_38)) ((and (((eq arrow_475358991le_alt) A_7) B_5)) ((member28618436le_alt ((produc776457805le_alt X_64) Y_23)) (lexord958095404le_alt R_38)))))) of role axiom named fact_291_lexord__cons__cons
% A new axiom: (forall (A_7:arrow_475358991le_alt) (X_64:list_A2115238852le_alt) (B_5:arrow_475358991le_alt) (Y_23:list_A2115238852le_alt) (R_38:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt A_7) X_64)) ((cons_A228743023le_alt B_5) Y_23))) (lexord958095404le_alt R_38))) ((or ((member214075476le_alt ((produc1347929815le_alt A_7) B_5)) R_38)) ((and (((eq arrow_475358991le_alt) A_7) B_5)) ((member28618436le_alt ((produc776457805le_alt X_64) Y_23)) (lexord958095404le_alt R_38))))))
% FOF formula (forall (Xs_116:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_116) nil_Ar1286194111le_alt))->((distin236324274le_alt Xs_116)->(distin236324274le_alt (butlas274947851le_alt Xs_116))))) of role axiom named fact_292_distinct__butlast
% A new axiom: (forall (Xs_116:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_116) nil_Ar1286194111le_alt))->((distin236324274le_alt Xs_116)->(distin236324274le_alt (butlas274947851le_alt Xs_116)))))
% FOF formula (forall (X_63:arrow_475358991le_alt) (Xs_115:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_115) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_63) Xs_115))) X_63))) of role axiom named fact_293_last__ConsL
% A new axiom: (forall (X_63:arrow_475358991le_alt) (Xs_115:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_115) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_63) Xs_115))) X_63)))
% FOF formula (forall (X_62:arrow_475358991le_alt) (Xs_114:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_114) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_62) Xs_114))) (last_A1217315288le_alt Xs_114)))) of role axiom named fact_294_last__ConsR
% A new axiom: (forall (X_62:arrow_475358991le_alt) (Xs_114:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_114) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_62) Xs_114))) (last_A1217315288le_alt Xs_114))))
% FOF formula (forall (X_61:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (top_to1969627639lt_o_o X_61)) of role axiom named fact_295_top1I
% A new axiom: (forall (X_61:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (top_to1969627639lt_o_o X_61))
% FOF formula (forall (X_61:(produc1501160679le_alt->Prop)), (top_to1842727771lt_o_o X_61)) of role axiom named fact_296_top1I
% A new axiom: (forall (X_61:(produc1501160679le_alt->Prop)), (top_to1842727771lt_o_o X_61))
% FOF formula (forall (X_61:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (top_to2122763103lt_o_o X_61)) of role axiom named fact_297_top1I
% A new axiom: (forall (X_61:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (top_to2122763103lt_o_o X_61))
% FOF formula (forall (X_61:produc1501160679le_alt), (top_to1841428258_alt_o X_61)) of role axiom named fact_298_top1I
% A new axiom: (forall (X_61:produc1501160679le_alt), (top_to1841428258_alt_o X_61))
% FOF formula (forall (X_61:arrow_1429601828e_indi), (top_to988227749indi_o X_61)) of role axiom named fact_299_top1I
% A new axiom: (forall (X_61:arrow_1429601828e_indi), (top_to988227749indi_o X_61))
% FOF formula (forall (X_61:arrow_475358991le_alt), (top_to728987956_alt_o X_61)) of role axiom named fact_300_top1I
% A new axiom: (forall (X_61:arrow_475358991le_alt), (top_to728987956_alt_o X_61))
% FOF formula (forall (X_60:list_A2115238852le_alt) (Y_22:list_A2115238852le_alt), ((iff ((equal_484611810le_alt X_60) Y_22)) (((eq list_A2115238852le_alt) X_60) Y_22))) of role axiom named fact_301_equal__list__def
% A new axiom: (forall (X_60:list_A2115238852le_alt) (Y_22:list_A2115238852le_alt), ((iff ((equal_484611810le_alt X_60) Y_22)) (((eq list_A2115238852le_alt) X_60) Y_22)))
% FOF formula (forall (A_6:(produc1501160679le_alt->Prop)), (((eq ((produc1501160679le_alt->Prop)->Prop)) ((pi_Pro1701359055_alt_o A_6) (fun (Uu:produc1501160679le_alt)=> top_top_o_o))) top_to1842727771lt_o_o)) of role axiom named fact_302_Pi__UNIV
% A new axiom: (forall (A_6:(produc1501160679le_alt->Prop)), (((eq ((produc1501160679le_alt->Prop)->Prop)) ((pi_Pro1701359055_alt_o A_6) (fun (Uu:produc1501160679le_alt)=> top_top_o_o))) top_to1842727771lt_o_o))
% FOF formula (forall (A_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1304755663_alt_o A_6) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> top_to1842727771lt_o_o))) top_to1969627639lt_o_o)) of role axiom named fact_303_Pi__UNIV
% A new axiom: (forall (A_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1304755663_alt_o A_6) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> top_to1842727771lt_o_o))) top_to1969627639lt_o_o))
% FOF formula (forall (A_6:(arrow_1429601828e_indi->Prop)), (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1929480907_alt_o A_6) (fun (Uu:arrow_1429601828e_indi)=> top_to1842727771lt_o_o))) top_to2122763103lt_o_o)) of role axiom named fact_304_Pi__UNIV
% A new axiom: (forall (A_6:(arrow_1429601828e_indi->Prop)), (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1929480907_alt_o A_6) (fun (Uu:arrow_1429601828e_indi)=> top_to1842727771lt_o_o))) top_to2122763103lt_o_o))
% FOF formula (((eq list_A2115238852le_alt) (butlas274947851le_alt nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt) of role axiom named fact_305_butlast_Osimps_I1_J
% A new axiom: (((eq list_A2115238852le_alt) (butlas274947851le_alt nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt)
% FOF formula (forall (X_59:list_A2115238852le_alt) (R_37:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_59) nil_Ar1286194111le_alt)) (lexord958095404le_alt R_37))->False)) of role axiom named fact_306_lexord__Nil__right
% A new axiom: (forall (X_59:list_A2115238852le_alt) (R_37:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_59) nil_Ar1286194111le_alt)) (lexord958095404le_alt R_37))->False))
% FOF formula (forall (X_58:arrow_475358991le_alt) (Xs_113:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Xs_113) nil_Ar1286194111le_alt)->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((cons_A228743023le_alt X_58) Xs_113))) nil_Ar1286194111le_alt))) ((not (((eq list_A2115238852le_alt) Xs_113) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((cons_A228743023le_alt X_58) Xs_113))) ((cons_A228743023le_alt X_58) (butlas274947851le_alt Xs_113)))))) of role axiom named fact_307_butlast_Osimps_I2_J
% A new axiom: (forall (X_58:arrow_475358991le_alt) (Xs_113:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Xs_113) nil_Ar1286194111le_alt)->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((cons_A228743023le_alt X_58) Xs_113))) nil_Ar1286194111le_alt))) ((not (((eq list_A2115238852le_alt) Xs_113) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((cons_A228743023le_alt X_58) Xs_113))) ((cons_A228743023le_alt X_58) (butlas274947851le_alt Xs_113))))))
% FOF formula (forall (X_57:arrow_475358991le_alt) (Xs_112:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Xs_112) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_57) Xs_112))) X_57))) ((not (((eq list_A2115238852le_alt) Xs_112) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_57) Xs_112))) (last_A1217315288le_alt Xs_112))))) of role axiom named fact_308_last_Osimps
% A new axiom: (forall (X_57:arrow_475358991le_alt) (Xs_112:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Xs_112) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_57) Xs_112))) X_57))) ((not (((eq list_A2115238852le_alt) Xs_112) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_57) Xs_112))) (last_A1217315288le_alt Xs_112)))))
% FOF formula (forall (Y_21:list_A2115238852le_alt) (R_36:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Y_21)) (lexord958095404le_alt R_36))) ((ex arrow_475358991le_alt) (fun (A:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (X_2:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Y_21) ((cons_A228743023le_alt A) X_2)))))))) of role axiom named fact_309_lexord__Nil__left
% A new axiom: (forall (Y_21:list_A2115238852le_alt) (R_36:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Y_21)) (lexord958095404le_alt R_36))) ((ex arrow_475358991le_alt) (fun (A:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (X_2:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Y_21) ((cons_A228743023le_alt A) X_2))))))))
% FOF formula (forall (Xs_111:list_l1475218533le_alt) (R_35:(produc1362454231le_alt->Prop)), ((forall (X_2:list_A2115238852le_alt), (((member28618436le_alt ((produc776457805le_alt X_2) X_2)) R_35)->False))->(((member1732936276le_alt ((produc1317709143le_alt Xs_111) Xs_111)) (lexord469916775le_alt R_35))->False))) of role axiom named fact_310_lexord__irreflexive
% A new axiom: (forall (Xs_111:list_l1475218533le_alt) (R_35:(produc1362454231le_alt->Prop)), ((forall (X_2:list_A2115238852le_alt), (((member28618436le_alt ((produc776457805le_alt X_2) X_2)) R_35)->False))->(((member1732936276le_alt ((produc1317709143le_alt Xs_111) Xs_111)) (lexord469916775le_alt R_35))->False)))
% FOF formula (forall (Xs_111:list_A2115238852le_alt) (R_35:(produc1501160679le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member214075476le_alt ((produc1347929815le_alt X_2) X_2)) R_35)->False))->(((member28618436le_alt ((produc776457805le_alt Xs_111) Xs_111)) (lexord958095404le_alt R_35))->False))) of role axiom named fact_311_lexord__irreflexive
% A new axiom: (forall (Xs_111:list_A2115238852le_alt) (R_35:(produc1501160679le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member214075476le_alt ((produc1347929815le_alt X_2) X_2)) R_35)->False))->(((member28618436le_alt ((produc776457805le_alt Xs_111) Xs_111)) (lexord958095404le_alt R_35))->False)))
% FOF formula (forall (X_56:list_l1475218533le_alt) (Y_20:list_l1475218533le_alt) (R_34:(produc1362454231le_alt->Prop)), ((forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), ((or ((or ((member28618436le_alt ((produc776457805le_alt A) B)) R_34)) (((eq list_A2115238852le_alt) A) B))) ((member28618436le_alt ((produc776457805le_alt B) A)) R_34)))->((or ((or ((member1732936276le_alt ((produc1317709143le_alt X_56) Y_20)) (lexord469916775le_alt R_34))) (((eq list_l1475218533le_alt) X_56) Y_20))) ((member1732936276le_alt ((produc1317709143le_alt Y_20) X_56)) (lexord469916775le_alt R_34))))) of role axiom named fact_312_lexord__linear
% A new axiom: (forall (X_56:list_l1475218533le_alt) (Y_20:list_l1475218533le_alt) (R_34:(produc1362454231le_alt->Prop)), ((forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), ((or ((or ((member28618436le_alt ((produc776457805le_alt A) B)) R_34)) (((eq list_A2115238852le_alt) A) B))) ((member28618436le_alt ((produc776457805le_alt B) A)) R_34)))->((or ((or ((member1732936276le_alt ((produc1317709143le_alt X_56) Y_20)) (lexord469916775le_alt R_34))) (((eq list_l1475218533le_alt) X_56) Y_20))) ((member1732936276le_alt ((produc1317709143le_alt Y_20) X_56)) (lexord469916775le_alt R_34)))))
% FOF formula (forall (X_56:list_A2115238852le_alt) (Y_20:list_A2115238852le_alt) (R_34:(produc1501160679le_alt->Prop)), ((forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((or ((or ((member214075476le_alt ((produc1347929815le_alt A) B)) R_34)) (((eq arrow_475358991le_alt) A) B))) ((member214075476le_alt ((produc1347929815le_alt B) A)) R_34)))->((or ((or ((member28618436le_alt ((produc776457805le_alt X_56) Y_20)) (lexord958095404le_alt R_34))) (((eq list_A2115238852le_alt) X_56) Y_20))) ((member28618436le_alt ((produc776457805le_alt Y_20) X_56)) (lexord958095404le_alt R_34))))) of role axiom named fact_313_lexord__linear
% A new axiom: (forall (X_56:list_A2115238852le_alt) (Y_20:list_A2115238852le_alt) (R_34:(produc1501160679le_alt->Prop)), ((forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((or ((or ((member214075476le_alt ((produc1347929815le_alt A) B)) R_34)) (((eq arrow_475358991le_alt) A) B))) ((member214075476le_alt ((produc1347929815le_alt B) A)) R_34)))->((or ((or ((member28618436le_alt ((produc776457805le_alt X_56) Y_20)) (lexord958095404le_alt R_34))) (((eq list_A2115238852le_alt) X_56) Y_20))) ((member28618436le_alt ((produc776457805le_alt Y_20) X_56)) (lexord958095404le_alt R_34)))))
% FOF formula (forall (X_55:produc1362454231le_alt), ((member28618436le_alt X_55) top_to1039387826_alt_o)) of role axiom named fact_314_UNIV__I
% A new axiom: (forall (X_55:produc1362454231le_alt), ((member28618436le_alt X_55) top_to1039387826_alt_o))
% FOF formula (forall (X_55:Prop), ((member_o X_55) top_top_o_o)) of role axiom named fact_315_UNIV__I
% A new axiom: (forall (X_55:Prop), ((member_o X_55) top_top_o_o))
% FOF formula (forall (X_55:arrow_1429601828e_indi), ((member2052026769e_indi X_55) top_to988227749indi_o)) of role axiom named fact_316_UNIV__I
% A new axiom: (forall (X_55:arrow_1429601828e_indi), ((member2052026769e_indi X_55) top_to988227749indi_o))
% FOF formula (forall (X_55:arrow_475358991le_alt), ((member84363362le_alt X_55) top_to728987956_alt_o)) of role axiom named fact_317_UNIV__I
% A new axiom: (forall (X_55:arrow_475358991le_alt), ((member84363362le_alt X_55) top_to728987956_alt_o))
% FOF formula (forall (X_55:produc1501160679le_alt), ((member214075476le_alt X_55) top_to1841428258_alt_o)) of role axiom named fact_318_UNIV__I
% A new axiom: (forall (X_55:produc1501160679le_alt), ((member214075476le_alt X_55) top_to1841428258_alt_o))
% FOF formula (forall (X_55:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_55) top_to2122763103lt_o_o)) of role axiom named fact_319_UNIV__I
% A new axiom: (forall (X_55:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_55) top_to2122763103lt_o_o))
% FOF formula (forall (X_55:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_55) top_to1842727771lt_o_o)) of role axiom named fact_320_UNIV__I
% A new axiom: (forall (X_55:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_55) top_to1842727771lt_o_o))
% FOF formula (forall (X_55:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_55) top_to1969627639lt_o_o)) of role axiom named fact_321_UNIV__I
% A new axiom: (forall (X_55:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_55) top_to1969627639lt_o_o))
% FOF formula (forall (X_54:produc1362454231le_alt), ((member28618436le_alt X_54) top_to1039387826_alt_o)) of role axiom named fact_322_iso__tuple__UNIV__I
% A new axiom: (forall (X_54:produc1362454231le_alt), ((member28618436le_alt X_54) top_to1039387826_alt_o))
% FOF formula (forall (X_54:Prop), ((member_o X_54) top_top_o_o)) of role axiom named fact_323_iso__tuple__UNIV__I
% A new axiom: (forall (X_54:Prop), ((member_o X_54) top_top_o_o))
% FOF formula (forall (X_54:arrow_1429601828e_indi), ((member2052026769e_indi X_54) top_to988227749indi_o)) of role axiom named fact_324_iso__tuple__UNIV__I
% A new axiom: (forall (X_54:arrow_1429601828e_indi), ((member2052026769e_indi X_54) top_to988227749indi_o))
% FOF formula (forall (X_54:arrow_475358991le_alt), ((member84363362le_alt X_54) top_to728987956_alt_o)) of role axiom named fact_325_iso__tuple__UNIV__I
% A new axiom: (forall (X_54:arrow_475358991le_alt), ((member84363362le_alt X_54) top_to728987956_alt_o))
% FOF formula (forall (X_54:produc1501160679le_alt), ((member214075476le_alt X_54) top_to1841428258_alt_o)) of role axiom named fact_326_iso__tuple__UNIV__I
% A new axiom: (forall (X_54:produc1501160679le_alt), ((member214075476le_alt X_54) top_to1841428258_alt_o))
% FOF formula (forall (X_54:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_54) top_to2122763103lt_o_o)) of role axiom named fact_327_iso__tuple__UNIV__I
% A new axiom: (forall (X_54:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_54) top_to2122763103lt_o_o))
% FOF formula (forall (X_54:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_54) top_to1842727771lt_o_o)) of role axiom named fact_328_iso__tuple__UNIV__I
% A new axiom: (forall (X_54:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_54) top_to1842727771lt_o_o))
% FOF formula (forall (X_54:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_54) top_to1969627639lt_o_o)) of role axiom named fact_329_iso__tuple__UNIV__I
% A new axiom: (forall (X_54:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_54) top_to1969627639lt_o_o))
% FOF formula (forall (X_53:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (top_to1969627639lt_o_o X_53)) top_top_o)) of role axiom named fact_330_top__apply
% A new axiom: (forall (X_53:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (top_to1969627639lt_o_o X_53)) top_top_o))
% FOF formula (forall (X_53:(produc1501160679le_alt->Prop)), ((iff (top_to1842727771lt_o_o X_53)) top_top_o)) of role axiom named fact_331_top__apply
% A new axiom: (forall (X_53:(produc1501160679le_alt->Prop)), ((iff (top_to1842727771lt_o_o X_53)) top_top_o))
% FOF formula (forall (X_53:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((iff (top_to2122763103lt_o_o X_53)) top_top_o)) of role axiom named fact_332_top__apply
% A new axiom: (forall (X_53:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((iff (top_to2122763103lt_o_o X_53)) top_top_o))
% FOF formula (forall (X_53:produc1501160679le_alt), ((iff (top_to1841428258_alt_o X_53)) top_top_o)) of role axiom named fact_333_top__apply
% A new axiom: (forall (X_53:produc1501160679le_alt), ((iff (top_to1841428258_alt_o X_53)) top_top_o))
% FOF formula (forall (X_53:arrow_1429601828e_indi), ((iff (top_to988227749indi_o X_53)) top_top_o)) of role axiom named fact_334_top__apply
% A new axiom: (forall (X_53:arrow_1429601828e_indi), ((iff (top_to988227749indi_o X_53)) top_top_o))
% FOF formula (forall (X_53:arrow_475358991le_alt), ((iff (top_to728987956_alt_o X_53)) top_top_o)) of role axiom named fact_335_top__apply
% A new axiom: (forall (X_53:arrow_475358991le_alt), ((iff (top_to728987956_alt_o X_53)) top_top_o))
% FOF formula (forall (Xs_110:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_110) nil_Ar1286194111le_alt))->((distin236324274le_alt Xs_110)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) (last_A1217315288le_alt Xs_110))))) Xs_110)) (butlas274947851le_alt Xs_110))))) of role axiom named fact_336_takeWhile__not__last
% A new axiom: (forall (Xs_110:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_110) nil_Ar1286194111le_alt))->((distin236324274le_alt Xs_110)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) (last_A1217315288le_alt Xs_110))))) Xs_110)) (butlas274947851le_alt Xs_110)))))
% FOF formula (forall (P_25:(arrow_475358991le_alt->Prop)), (((eq produc1362454231le_alt) ((partit1487577784le_alt P_25) nil_Ar1286194111le_alt)) ((produc776457805le_alt nil_Ar1286194111le_alt) nil_Ar1286194111le_alt))) of role axiom named fact_337_partition_Osimps_I1_J
% A new axiom: (forall (P_25:(arrow_475358991le_alt->Prop)), (((eq produc1362454231le_alt) ((partit1487577784le_alt P_25) nil_Ar1286194111le_alt)) ((produc776457805le_alt nil_Ar1286194111le_alt) nil_Ar1286194111le_alt)))
% FOF formula (forall (P_24:(arrow_475358991le_alt->Prop)), (((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_24) nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt)) of role axiom named fact_338_takeWhile_Osimps_I1_J
% A new axiom: (forall (P_24:(arrow_475358991le_alt->Prop)), (((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_24) nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt))
% FOF formula (forall (P_23:(arrow_475358991le_alt->Prop)) (Xs_109:list_A2115238852le_alt), ((distin236324274le_alt Xs_109)->(distin236324274le_alt ((takeWh1696291512le_alt P_23) Xs_109)))) of role axiom named fact_339_distinct__takeWhile
% A new axiom: (forall (P_23:(arrow_475358991le_alt->Prop)) (Xs_109:list_A2115238852le_alt), ((distin236324274le_alt Xs_109)->(distin236324274le_alt ((takeWh1696291512le_alt P_23) Xs_109))))
% FOF formula (forall (Xs_108:list_A2115238852le_alt) (P_22:(arrow_475358991le_alt->Prop)) (X_52:arrow_475358991le_alt), ((and ((P_22 X_52)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_22) ((cons_A228743023le_alt X_52) Xs_108))) ((cons_A228743023le_alt X_52) ((takeWh1696291512le_alt P_22) Xs_108))))) (((P_22 X_52)->False)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_22) ((cons_A228743023le_alt X_52) Xs_108))) nil_Ar1286194111le_alt)))) of role axiom named fact_340_takeWhile_Osimps_I2_J
% A new axiom: (forall (Xs_108:list_A2115238852le_alt) (P_22:(arrow_475358991le_alt->Prop)) (X_52:arrow_475358991le_alt), ((and ((P_22 X_52)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_22) ((cons_A228743023le_alt X_52) Xs_108))) ((cons_A228743023le_alt X_52) ((takeWh1696291512le_alt P_22) Xs_108))))) (((P_22 X_52)->False)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_22) ((cons_A228743023le_alt X_52) Xs_108))) nil_Ar1286194111le_alt))))
% FOF formula (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) top_to1969627639lt_o_o) (collec2009291517_alt_o (fun (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> True))) of role axiom named fact_341_UNIV__def
% A new axiom: (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) top_to1969627639lt_o_o) (collec2009291517_alt_o (fun (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> True)))
% FOF formula (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) top_to2122763103lt_o_o) (collec682858041_alt_o (fun (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> True))) of role axiom named fact_342_UNIV__def
% A new axiom: (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) top_to2122763103lt_o_o) (collec682858041_alt_o (fun (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> True)))
% FOF formula (((eq (produc1501160679le_alt->Prop)) top_to1841428258_alt_o) (collec869865362le_alt (fun (X_2:produc1501160679le_alt)=> True))) of role axiom named fact_343_UNIV__def
% A new axiom: (((eq (produc1501160679le_alt->Prop)) top_to1841428258_alt_o) (collec869865362le_alt (fun (X_2:produc1501160679le_alt)=> True)))
% FOF formula (((eq (arrow_1429601828e_indi->Prop)) top_to988227749indi_o) (collec22405327e_indi (fun (X_2:arrow_1429601828e_indi)=> True))) of role axiom named fact_344_UNIV__def
% A new axiom: (((eq (arrow_1429601828e_indi->Prop)) top_to988227749indi_o) (collec22405327e_indi (fun (X_2:arrow_1429601828e_indi)=> True)))
% FOF formula (((eq (arrow_475358991le_alt->Prop)) top_to728987956_alt_o) (collec742074788le_alt (fun (X_2:arrow_475358991le_alt)=> True))) of role axiom named fact_345_UNIV__def
% A new axiom: (((eq (arrow_475358991le_alt->Prop)) top_to728987956_alt_o) (collec742074788le_alt (fun (X_2:arrow_475358991le_alt)=> True)))
% FOF formula (((eq ((produc1501160679le_alt->Prop)->Prop)) top_to1842727771lt_o_o) (collec94295101_alt_o (fun (X_2:(produc1501160679le_alt->Prop))=> True))) of role axiom named fact_346_UNIV__def
% A new axiom: (((eq ((produc1501160679le_alt->Prop)->Prop)) top_to1842727771lt_o_o) (collec94295101_alt_o (fun (X_2:(produc1501160679le_alt->Prop))=> True)))
% FOF formula (forall (A_5:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), ((member28618436le_alt X_2) A_5))->(((eq (produc1362454231le_alt->Prop)) top_to1039387826_alt_o) A_5))) of role axiom named fact_347_UNIV__eq__I
% A new axiom: (forall (A_5:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), ((member28618436le_alt X_2) A_5))->(((eq (produc1362454231le_alt->Prop)) top_to1039387826_alt_o) A_5)))
% FOF formula (forall (A_5:(Prop->Prop)), ((forall (X_2:Prop), ((member_o X_2) A_5))->(((eq (Prop->Prop)) top_top_o_o) A_5))) of role axiom named fact_348_UNIV__eq__I
% A new axiom: (forall (A_5:(Prop->Prop)), ((forall (X_2:Prop), ((member_o X_2) A_5))->(((eq (Prop->Prop)) top_top_o_o) A_5)))
% FOF formula (forall (A_5:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), ((member2052026769e_indi X_2) A_5))->(((eq (arrow_1429601828e_indi->Prop)) top_to988227749indi_o) A_5))) of role axiom named fact_349_UNIV__eq__I
% A new axiom: (forall (A_5:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), ((member2052026769e_indi X_2) A_5))->(((eq (arrow_1429601828e_indi->Prop)) top_to988227749indi_o) A_5)))
% FOF formula (forall (A_5:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), ((member84363362le_alt X_2) A_5))->(((eq (arrow_475358991le_alt->Prop)) top_to728987956_alt_o) A_5))) of role axiom named fact_350_UNIV__eq__I
% A new axiom: (forall (A_5:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), ((member84363362le_alt X_2) A_5))->(((eq (arrow_475358991le_alt->Prop)) top_to728987956_alt_o) A_5)))
% FOF formula (forall (A_5:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), ((member214075476le_alt X_2) A_5))->(((eq (produc1501160679le_alt->Prop)) top_to1841428258_alt_o) A_5))) of role axiom named fact_351_UNIV__eq__I
% A new axiom: (forall (A_5:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), ((member214075476le_alt X_2) A_5))->(((eq (produc1501160679le_alt->Prop)) top_to1841428258_alt_o) A_5)))
% FOF formula (forall (A_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_2) A_5))->(((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) top_to2122763103lt_o_o) A_5))) of role axiom named fact_352_UNIV__eq__I
% A new axiom: (forall (A_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_2) A_5))->(((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) top_to2122763103lt_o_o) A_5)))
% FOF formula (forall (A_5:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_2) A_5))->(((eq ((produc1501160679le_alt->Prop)->Prop)) top_to1842727771lt_o_o) A_5))) of role axiom named fact_353_UNIV__eq__I
% A new axiom: (forall (A_5:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_2) A_5))->(((eq ((produc1501160679le_alt->Prop)->Prop)) top_to1842727771lt_o_o) A_5)))
% FOF formula (forall (A_5:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_2) A_5))->(((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) top_to1969627639lt_o_o) A_5))) of role axiom named fact_354_UNIV__eq__I
% A new axiom: (forall (A_5:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_2) A_5))->(((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) top_to1969627639lt_o_o) A_5)))
% FOF formula ((ex produc1362454231le_alt) (fun (X_2:produc1362454231le_alt)=> ((member28618436le_alt X_2) top_to1039387826_alt_o))) of role axiom named fact_355_UNIV__witness
% A new axiom: ((ex produc1362454231le_alt) (fun (X_2:produc1362454231le_alt)=> ((member28618436le_alt X_2) top_to1039387826_alt_o)))
% FOF formula ((ex Prop) (fun (X_2:Prop)=> ((member_o X_2) top_top_o_o))) of role axiom named fact_356_UNIV__witness
% A new axiom: ((ex Prop) (fun (X_2:Prop)=> ((member_o X_2) top_top_o_o)))
% FOF formula ((ex arrow_1429601828e_indi) (fun (X_2:arrow_1429601828e_indi)=> ((member2052026769e_indi X_2) top_to988227749indi_o))) of role axiom named fact_357_UNIV__witness
% A new axiom: ((ex arrow_1429601828e_indi) (fun (X_2:arrow_1429601828e_indi)=> ((member2052026769e_indi X_2) top_to988227749indi_o)))
% FOF formula ((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((member84363362le_alt X_2) top_to728987956_alt_o))) of role axiom named fact_358_UNIV__witness
% A new axiom: ((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((member84363362le_alt X_2) top_to728987956_alt_o)))
% FOF formula ((ex produc1501160679le_alt) (fun (X_2:produc1501160679le_alt)=> ((member214075476le_alt X_2) top_to1841428258_alt_o))) of role axiom named fact_359_UNIV__witness
% A new axiom: ((ex produc1501160679le_alt) (fun (X_2:produc1501160679le_alt)=> ((member214075476le_alt X_2) top_to1841428258_alt_o)))
% FOF formula ((ex (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (fun (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> ((member526088951_alt_o X_2) top_to2122763103lt_o_o))) of role axiom named fact_360_UNIV__witness
% A new axiom: ((ex (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (fun (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> ((member526088951_alt_o X_2) top_to2122763103lt_o_o)))
% FOF formula ((ex (produc1501160679le_alt->Prop)) (fun (X_2:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o X_2) top_to1842727771lt_o_o))) of role axiom named fact_361_UNIV__witness
% A new axiom: ((ex (produc1501160679le_alt->Prop)) (fun (X_2:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o X_2) top_to1842727771lt_o_o)))
% FOF formula ((ex ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (fun (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> ((member616898751_alt_o X_2) top_to1969627639lt_o_o))) of role axiom named fact_362_UNIV__witness
% A new axiom: ((ex ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (fun (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> ((member616898751_alt_o X_2) top_to1969627639lt_o_o)))
% FOF formula (((eq ((produc1501160679le_alt->Prop)->Prop)) arrow_823908191le_Lin) (collec94295101_alt_o (order_1995917111le_alt top_to728987956_alt_o))) of role axiom named fact_363_Lin__def
% A new axiom: (((eq ((produc1501160679le_alt->Prop)->Prop)) arrow_823908191le_Lin) (collec94295101_alt_o (order_1995917111le_alt top_to728987956_alt_o)))
% FOF formula (forall (Xs_107:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_107) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) ((append179082452le_alt (butlas274947851le_alt Xs_107)) ((cons_A228743023le_alt (last_A1217315288le_alt Xs_107)) nil_Ar1286194111le_alt))) Xs_107))) of role axiom named fact_364_append__butlast__last__id
% A new axiom: (forall (Xs_107:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_107) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) ((append179082452le_alt (butlas274947851le_alt Xs_107)) ((cons_A228743023le_alt (last_A1217315288le_alt Xs_107)) nil_Ar1286194111le_alt))) Xs_107)))
% FOF formula (forall (Xs_106:list_A2115238852le_alt) (X_51:arrow_475358991le_alt) (Ys_54:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_106) ((cons_A228743023le_alt X_51) nil_Ar1286194111le_alt))) Ys_54)) ((and ((and (not (((eq list_A2115238852le_alt) Ys_54) nil_Ar1286194111le_alt))) (((eq list_A2115238852le_alt) (butlas274947851le_alt Ys_54)) Xs_106))) (((eq arrow_475358991le_alt) (last_A1217315288le_alt Ys_54)) X_51)))) of role axiom named fact_365_snoc__eq__iff__butlast
% A new axiom: (forall (Xs_106:list_A2115238852le_alt) (X_51:arrow_475358991le_alt) (Ys_54:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_106) ((cons_A228743023le_alt X_51) nil_Ar1286194111le_alt))) Ys_54)) ((and ((and (not (((eq list_A2115238852le_alt) Ys_54) nil_Ar1286194111le_alt))) (((eq list_A2115238852le_alt) (butlas274947851le_alt Ys_54)) Xs_106))) (((eq arrow_475358991le_alt) (last_A1217315288le_alt Ys_54)) X_51))))
% FOF formula (forall (Xs_105:list_A2115238852le_alt) (R_33:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_105) nil_Ar1286194111le_alt)) (lex_Ar1415517219le_alt R_33))->False)) of role axiom named fact_366_Nil2__notin__lex
% A new axiom: (forall (Xs_105:list_A2115238852le_alt) (R_33:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_105) nil_Ar1286194111le_alt)) (lex_Ar1415517219le_alt R_33))->False))
% FOF formula (forall (Ys_53:list_A2115238852le_alt) (R_32:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Ys_53)) (lex_Ar1415517219le_alt R_32))->False)) of role axiom named fact_367_Nil__notin__lex
% A new axiom: (forall (Ys_53:list_A2115238852le_alt) (R_32:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Ys_53)) (lex_Ar1415517219le_alt R_32))->False))
% FOF formula (forall (Ys_52:list_A2115238852le_alt) (Us_3:list_A2115238852le_alt) (Xs_104:list_A2115238852le_alt) (Xs1_1:list_A2115238852le_alt) (Zs_9:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) ((append179082452le_alt Xs_104) Xs1_1)) Zs_9)->((((eq list_A2115238852le_alt) Ys_52) ((append179082452le_alt Xs1_1) Us_3))->(((eq list_A2115238852le_alt) ((append179082452le_alt Xs_104) Ys_52)) ((append179082452le_alt Zs_9) Us_3))))) of role axiom named fact_368_append__eq__appendI
% A new axiom: (forall (Ys_52:list_A2115238852le_alt) (Us_3:list_A2115238852le_alt) (Xs_104:list_A2115238852le_alt) (Xs1_1:list_A2115238852le_alt) (Zs_9:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) ((append179082452le_alt Xs_104) Xs1_1)) Zs_9)->((((eq list_A2115238852le_alt) Ys_52) ((append179082452le_alt Xs1_1) Us_3))->(((eq list_A2115238852le_alt) ((append179082452le_alt Xs_104) Ys_52)) ((append179082452le_alt Zs_9) Us_3)))))
% FOF formula (forall (Ys_51:list_A2115238852le_alt) (Xs_103:list_A2115238852le_alt) (Zs_8:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Ys_51) Xs_103)) ((append179082452le_alt Zs_8) Xs_103))) (((eq list_A2115238852le_alt) Ys_51) Zs_8))) of role axiom named fact_369_append__same__eq
% A new axiom: (forall (Ys_51:list_A2115238852le_alt) (Xs_103:list_A2115238852le_alt) (Zs_8:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Ys_51) Xs_103)) ((append179082452le_alt Zs_8) Xs_103))) (((eq list_A2115238852le_alt) Ys_51) Zs_8)))
% FOF formula (forall (Xs_102:list_A2115238852le_alt) (Ys_50:list_A2115238852le_alt) (Zs_7:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_102) Ys_50)) ((append179082452le_alt Xs_102) Zs_7))) (((eq list_A2115238852le_alt) Ys_50) Zs_7))) of role axiom named fact_370_same__append__eq
% A new axiom: (forall (Xs_102:list_A2115238852le_alt) (Ys_50:list_A2115238852le_alt) (Zs_7:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_102) Ys_50)) ((append179082452le_alt Xs_102) Zs_7))) (((eq list_A2115238852le_alt) Ys_50) Zs_7)))
% FOF formula (forall (Xs_101:list_A2115238852le_alt) (Ys_49:list_A2115238852le_alt) (Zs_6:list_A2115238852le_alt) (Ts:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_101) Ys_49)) ((append179082452le_alt Zs_6) Ts))) ((ex list_A2115238852le_alt) (fun (Us:list_A2115238852le_alt)=> ((or ((and (((eq list_A2115238852le_alt) Xs_101) ((append179082452le_alt Zs_6) Us))) (((eq list_A2115238852le_alt) ((append179082452le_alt Us) Ys_49)) Ts))) ((and (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_101) Us)) Zs_6)) (((eq list_A2115238852le_alt) Ys_49) ((append179082452le_alt Us) Ts)))))))) of role axiom named fact_371_append__eq__append__conv2
% A new axiom: (forall (Xs_101:list_A2115238852le_alt) (Ys_49:list_A2115238852le_alt) (Zs_6:list_A2115238852le_alt) (Ts:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_101) Ys_49)) ((append179082452le_alt Zs_6) Ts))) ((ex list_A2115238852le_alt) (fun (Us:list_A2115238852le_alt)=> ((or ((and (((eq list_A2115238852le_alt) Xs_101) ((append179082452le_alt Zs_6) Us))) (((eq list_A2115238852le_alt) ((append179082452le_alt Us) Ys_49)) Ts))) ((and (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_101) Us)) Zs_6)) (((eq list_A2115238852le_alt) Ys_49) ((append179082452le_alt Us) Ts))))))))
% FOF formula (forall (Xs_100:list_A2115238852le_alt) (Ys_48:list_A2115238852le_alt) (Zs_5:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((append179082452le_alt Xs_100) Ys_48)) Zs_5)) ((append179082452le_alt Xs_100) ((append179082452le_alt Ys_48) Zs_5)))) of role axiom named fact_372_append__assoc
% A new axiom: (forall (Xs_100:list_A2115238852le_alt) (Ys_48:list_A2115238852le_alt) (Zs_5:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((append179082452le_alt Xs_100) Ys_48)) Zs_5)) ((append179082452le_alt Xs_100) ((append179082452le_alt Ys_48) Zs_5))))
% FOF formula (forall (X_50:arrow_475358991le_alt) (Xs_99:list_A2115238852le_alt) (Ys_47:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((cons_A228743023le_alt X_50) Xs_99)) Ys_47)) ((cons_A228743023le_alt X_50) ((append179082452le_alt Xs_99) Ys_47)))) of role axiom named fact_373_append__Cons
% A new axiom: (forall (X_50:arrow_475358991le_alt) (Xs_99:list_A2115238852le_alt) (Ys_47:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((cons_A228743023le_alt X_50) Xs_99)) Ys_47)) ((cons_A228743023le_alt X_50) ((append179082452le_alt Xs_99) Ys_47))))
% FOF formula (forall (Xs_98:list_A2115238852le_alt) (Zs_4:list_A2115238852le_alt) (X_49:arrow_475358991le_alt) (Xs1:list_A2115238852le_alt) (Ys_46:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_49) Xs1)) Ys_46)->((((eq list_A2115238852le_alt) Xs_98) ((append179082452le_alt Xs1) Zs_4))->(((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_49) Xs_98)) ((append179082452le_alt Ys_46) Zs_4))))) of role axiom named fact_374_Cons__eq__appendI
% A new axiom: (forall (Xs_98:list_A2115238852le_alt) (Zs_4:list_A2115238852le_alt) (X_49:arrow_475358991le_alt) (Xs1:list_A2115238852le_alt) (Ys_46:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_49) Xs1)) Ys_46)->((((eq list_A2115238852le_alt) Xs_98) ((append179082452le_alt Xs1) Zs_4))->(((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_49) Xs_98)) ((append179082452le_alt Ys_46) Zs_4)))))
% FOF formula (forall (Ys_45:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt nil_Ar1286194111le_alt) Ys_45)) Ys_45)) of role axiom named fact_375_append__Nil
% A new axiom: (forall (Ys_45:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt nil_Ar1286194111le_alt) Ys_45)) Ys_45))
% FOF formula (forall (Xs_97:list_A2115238852le_alt) (Ys_44:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) nil_Ar1286194111le_alt) ((append179082452le_alt Xs_97) Ys_44))) ((and (((eq list_A2115238852le_alt) Xs_97) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Ys_44) nil_Ar1286194111le_alt)))) of role axiom named fact_376_Nil__is__append__conv
% A new axiom: (forall (Xs_97:list_A2115238852le_alt) (Ys_44:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) nil_Ar1286194111le_alt) ((append179082452le_alt Xs_97) Ys_44))) ((and (((eq list_A2115238852le_alt) Xs_97) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Ys_44) nil_Ar1286194111le_alt))))
% FOF formula (forall (Xs_96:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_96) nil_Ar1286194111le_alt)) Xs_96)) of role axiom named fact_377_append__Nil2
% A new axiom: (forall (Xs_96:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_96) nil_Ar1286194111le_alt)) Xs_96))
% FOF formula (forall (Xs_95:list_A2115238852le_alt) (Ys_43:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) Xs_95) ((append179082452le_alt Xs_95) Ys_43))) (((eq list_A2115238852le_alt) Ys_43) nil_Ar1286194111le_alt))) of role axiom named fact_378_self__append__conv
% A new axiom: (forall (Xs_95:list_A2115238852le_alt) (Ys_43:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) Xs_95) ((append179082452le_alt Xs_95) Ys_43))) (((eq list_A2115238852le_alt) Ys_43) nil_Ar1286194111le_alt)))
% FOF formula (forall (Ys_42:list_A2115238852le_alt) (Xs_94:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) Ys_42) ((append179082452le_alt Xs_94) Ys_42))) (((eq list_A2115238852le_alt) Xs_94) nil_Ar1286194111le_alt))) of role axiom named fact_379_self__append__conv2
% A new axiom: (forall (Ys_42:list_A2115238852le_alt) (Xs_94:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) Ys_42) ((append179082452le_alt Xs_94) Ys_42))) (((eq list_A2115238852le_alt) Xs_94) nil_Ar1286194111le_alt)))
% FOF formula (forall (Xs_93:list_A2115238852le_alt) (Ys_41:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_93) Ys_41)) nil_Ar1286194111le_alt)) ((and (((eq list_A2115238852le_alt) Xs_93) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Ys_41) nil_Ar1286194111le_alt)))) of role axiom named fact_380_append__is__Nil__conv
% A new axiom: (forall (Xs_93:list_A2115238852le_alt) (Ys_41:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_93) Ys_41)) nil_Ar1286194111le_alt)) ((and (((eq list_A2115238852le_alt) Xs_93) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Ys_41) nil_Ar1286194111le_alt))))
% FOF formula (forall (Xs_92:list_A2115238852le_alt) (Ys_40:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_92) Ys_40)) Xs_92)) (((eq list_A2115238852le_alt) Ys_40) nil_Ar1286194111le_alt))) of role axiom named fact_381_append__self__conv
% A new axiom: (forall (Xs_92:list_A2115238852le_alt) (Ys_40:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_92) Ys_40)) Xs_92)) (((eq list_A2115238852le_alt) Ys_40) nil_Ar1286194111le_alt)))
% FOF formula (forall (Xs_91:list_A2115238852le_alt) (Ys_39:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_91) Ys_39)) Ys_39)) (((eq list_A2115238852le_alt) Xs_91) nil_Ar1286194111le_alt))) of role axiom named fact_382_append__self__conv2
% A new axiom: (forall (Xs_91:list_A2115238852le_alt) (Ys_39:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_91) Ys_39)) Ys_39)) (((eq list_A2115238852le_alt) Xs_91) nil_Ar1286194111le_alt)))
% FOF formula (forall (Xs_90:list_A2115238852le_alt) (Ys_38:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_90) Ys_38)->(((eq list_A2115238852le_alt) Xs_90) ((append179082452le_alt nil_Ar1286194111le_alt) Ys_38)))) of role axiom named fact_383_eq__Nil__appendI
% A new axiom: (forall (Xs_90:list_A2115238852le_alt) (Ys_38:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_90) Ys_38)->(((eq list_A2115238852le_alt) Xs_90) ((append179082452le_alt nil_Ar1286194111le_alt) Ys_38))))
% FOF formula (forall (Ys_37:list_A2115238852le_alt) (Zs_3:list_A2115238852le_alt) (X_48:arrow_475358991le_alt) (Xs_89:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Ys_37) Zs_3)) ((cons_A228743023le_alt X_48) Xs_89))) ((or ((and (((eq list_A2115238852le_alt) Ys_37) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Zs_3) ((cons_A228743023le_alt X_48) Xs_89)))) ((ex list_A2115238852le_alt) (fun (Ys_36:list_A2115238852le_alt)=> ((and (((eq list_A2115238852le_alt) Ys_37) ((cons_A228743023le_alt X_48) Ys_36))) (((eq list_A2115238852le_alt) ((append179082452le_alt Ys_36) Zs_3)) Xs_89))))))) of role axiom named fact_384_append__eq__Cons__conv
% A new axiom: (forall (Ys_37:list_A2115238852le_alt) (Zs_3:list_A2115238852le_alt) (X_48:arrow_475358991le_alt) (Xs_89:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Ys_37) Zs_3)) ((cons_A228743023le_alt X_48) Xs_89))) ((or ((and (((eq list_A2115238852le_alt) Ys_37) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Zs_3) ((cons_A228743023le_alt X_48) Xs_89)))) ((ex list_A2115238852le_alt) (fun (Ys_36:list_A2115238852le_alt)=> ((and (((eq list_A2115238852le_alt) Ys_37) ((cons_A228743023le_alt X_48) Ys_36))) (((eq list_A2115238852le_alt) ((append179082452le_alt Ys_36) Zs_3)) Xs_89)))))))
% FOF formula (forall (X_47:arrow_475358991le_alt) (Xs_88:list_A2115238852le_alt) (Ys_35:list_A2115238852le_alt) (Zs_2:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_47) Xs_88)) ((append179082452le_alt Ys_35) Zs_2))) ((or ((and (((eq list_A2115238852le_alt) Ys_35) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_47) Xs_88)) Zs_2))) ((ex list_A2115238852le_alt) (fun (Ys_36:list_A2115238852le_alt)=> ((and (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_47) Ys_36)) Ys_35)) (((eq list_A2115238852le_alt) Xs_88) ((append179082452le_alt Ys_36) Zs_2)))))))) of role axiom named fact_385_Cons__eq__append__conv
% A new axiom: (forall (X_47:arrow_475358991le_alt) (Xs_88:list_A2115238852le_alt) (Ys_35:list_A2115238852le_alt) (Zs_2:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_47) Xs_88)) ((append179082452le_alt Ys_35) Zs_2))) ((or ((and (((eq list_A2115238852le_alt) Ys_35) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_47) Xs_88)) Zs_2))) ((ex list_A2115238852le_alt) (fun (Ys_36:list_A2115238852le_alt)=> ((and (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_47) Ys_36)) Ys_35)) (((eq list_A2115238852le_alt) Xs_88) ((append179082452le_alt Ys_36) Zs_2))))))))
% FOF formula (forall (Xs_87:list_A2115238852le_alt) (X_46:arrow_475358991le_alt) (Ys_34:list_A2115238852le_alt) (Y_19:arrow_475358991le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_87) ((cons_A228743023le_alt X_46) nil_Ar1286194111le_alt))) ((append179082452le_alt Ys_34) ((cons_A228743023le_alt Y_19) nil_Ar1286194111le_alt)))) ((and (((eq list_A2115238852le_alt) Xs_87) Ys_34)) (((eq arrow_475358991le_alt) X_46) Y_19)))) of role axiom named fact_386_append1__eq__conv
% A new axiom: (forall (Xs_87:list_A2115238852le_alt) (X_46:arrow_475358991le_alt) (Ys_34:list_A2115238852le_alt) (Y_19:arrow_475358991le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_87) ((cons_A228743023le_alt X_46) nil_Ar1286194111le_alt))) ((append179082452le_alt Ys_34) ((cons_A228743023le_alt Y_19) nil_Ar1286194111le_alt)))) ((and (((eq list_A2115238852le_alt) Xs_87) Ys_34)) (((eq arrow_475358991le_alt) X_46) Y_19))))
% FOF formula (forall (Xs_86:list_A2115238852le_alt) (L:list_A2115238852le_alt) (P_21:(arrow_475358991le_alt->Prop)) (X_45:arrow_475358991le_alt), (((P_21 X_45)->False)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_21) ((append179082452le_alt Xs_86) ((cons_A228743023le_alt X_45) L)))) ((takeWh1696291512le_alt P_21) Xs_86)))) of role axiom named fact_387_takeWhile__tail
% A new axiom: (forall (Xs_86:list_A2115238852le_alt) (L:list_A2115238852le_alt) (P_21:(arrow_475358991le_alt->Prop)) (X_45:arrow_475358991le_alt), (((P_21 X_45)->False)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_21) ((append179082452le_alt Xs_86) ((cons_A228743023le_alt X_45) L)))) ((takeWh1696291512le_alt P_21) Xs_86))))
% FOF formula (forall (Xs_85:list_A2115238852le_alt) (Ys_33:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Ys_33) nil_Ar1286194111le_alt)->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((append179082452le_alt Xs_85) Ys_33))) (butlas274947851le_alt Xs_85)))) ((not (((eq list_A2115238852le_alt) Ys_33) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((append179082452le_alt Xs_85) Ys_33))) ((append179082452le_alt Xs_85) (butlas274947851le_alt Ys_33)))))) of role axiom named fact_388_butlast__append
% A new axiom: (forall (Xs_85:list_A2115238852le_alt) (Ys_33:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Ys_33) nil_Ar1286194111le_alt)->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((append179082452le_alt Xs_85) Ys_33))) (butlas274947851le_alt Xs_85)))) ((not (((eq list_A2115238852le_alt) Ys_33) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((append179082452le_alt Xs_85) Ys_33))) ((append179082452le_alt Xs_85) (butlas274947851le_alt Ys_33))))))
% FOF formula (forall (Xs_84:list_A2115238852le_alt) (Ys_32:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Ys_32) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_84) Ys_32))) (last_A1217315288le_alt Xs_84)))) ((not (((eq list_A2115238852le_alt) Ys_32) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_84) Ys_32))) (last_A1217315288le_alt Ys_32))))) of role axiom named fact_389_last__append
% A new axiom: (forall (Xs_84:list_A2115238852le_alt) (Ys_32:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Ys_32) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_84) Ys_32))) (last_A1217315288le_alt Xs_84)))) ((not (((eq list_A2115238852le_alt) Ys_32) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_84) Ys_32))) (last_A1217315288le_alt Ys_32)))))
% FOF formula (forall (Xs_83:list_A2115238852le_alt) (Ys_31:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Ys_31) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_83) Ys_31))) (last_A1217315288le_alt Ys_31)))) of role axiom named fact_390_last__appendR
% A new axiom: (forall (Xs_83:list_A2115238852le_alt) (Ys_31:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Ys_31) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_83) Ys_31))) (last_A1217315288le_alt Ys_31))))
% FOF formula (forall (Xs_82:list_A2115238852le_alt) (Ys_30:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Ys_30) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_82) Ys_30))) (last_A1217315288le_alt Xs_82)))) of role axiom named fact_391_last__appendL
% A new axiom: (forall (Xs_82:list_A2115238852le_alt) (Ys_30:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Ys_30) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_82) Ys_30))) (last_A1217315288le_alt Xs_82))))
% FOF formula (forall (X_44:list_A2115238852le_alt) (U_2:list_A2115238852le_alt) (V_1:list_A2115238852le_alt) (R_31:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt U_2) V_1)) (lexord958095404le_alt R_31))->((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt X_44) U_2)) ((append179082452le_alt X_44) V_1))) (lexord958095404le_alt R_31)))) of role axiom named fact_392_lexord__append__leftI
% A new axiom: (forall (X_44:list_A2115238852le_alt) (U_2:list_A2115238852le_alt) (V_1:list_A2115238852le_alt) (R_31:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt U_2) V_1)) (lexord958095404le_alt R_31))->((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt X_44) U_2)) ((append179082452le_alt X_44) V_1))) (lexord958095404le_alt R_31))))
% FOF formula (forall (Xs_81:list_A2115238852le_alt) (X_43:arrow_475358991le_alt), (((eq list_A2115238852le_alt) (butlas274947851le_alt ((append179082452le_alt Xs_81) ((cons_A228743023le_alt X_43) nil_Ar1286194111le_alt)))) Xs_81)) of role axiom named fact_393_butlast__snoc
% A new axiom: (forall (Xs_81:list_A2115238852le_alt) (X_43:arrow_475358991le_alt), (((eq list_A2115238852le_alt) (butlas274947851le_alt ((append179082452le_alt Xs_81) ((cons_A228743023le_alt X_43) nil_Ar1286194111le_alt)))) Xs_81))
% FOF formula (forall (Xs_80:list_A2115238852le_alt) (X_42:arrow_475358991le_alt), (((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_80) ((cons_A228743023le_alt X_42) nil_Ar1286194111le_alt)))) X_42)) of role axiom named fact_394_last__snoc
% A new axiom: (forall (Xs_80:list_A2115238852le_alt) (X_42:arrow_475358991le_alt), (((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_80) ((cons_A228743023le_alt X_42) nil_Ar1286194111le_alt)))) X_42))
% FOF formula (forall (U_1:list_A2115238852le_alt) (X_41:list_A2115238852le_alt) (Y_18:list_A2115238852le_alt) (A_4:arrow_475358991le_alt) (B_4:arrow_475358991le_alt) (R_30:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt A_4) B_4)) R_30)->((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt U_1) ((cons_A228743023le_alt A_4) X_41))) ((append179082452le_alt U_1) ((cons_A228743023le_alt B_4) Y_18)))) (lexord958095404le_alt R_30)))) of role axiom named fact_395_lexord__append__left__rightI
% A new axiom: (forall (U_1:list_A2115238852le_alt) (X_41:list_A2115238852le_alt) (Y_18:list_A2115238852le_alt) (A_4:arrow_475358991le_alt) (B_4:arrow_475358991le_alt) (R_30:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt A_4) B_4)) R_30)->((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt U_1) ((cons_A228743023le_alt A_4) X_41))) ((append179082452le_alt U_1) ((cons_A228743023le_alt B_4) Y_18)))) (lexord958095404le_alt R_30))))
% FOF formula (forall (U_1:list_l1475218533le_alt) (X_41:list_l1475218533le_alt) (Y_18:list_l1475218533le_alt) (A_4:list_A2115238852le_alt) (B_4:list_A2115238852le_alt) (R_30:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt A_4) B_4)) R_30)->((member1732936276le_alt ((produc1317709143le_alt ((append1166001599le_alt U_1) ((cons_l635097956le_alt A_4) X_41))) ((append1166001599le_alt U_1) ((cons_l635097956le_alt B_4) Y_18)))) (lexord469916775le_alt R_30)))) of role axiom named fact_396_lexord__append__left__rightI
% A new axiom: (forall (U_1:list_l1475218533le_alt) (X_41:list_l1475218533le_alt) (Y_18:list_l1475218533le_alt) (A_4:list_A2115238852le_alt) (B_4:list_A2115238852le_alt) (R_30:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt A_4) B_4)) R_30)->((member1732936276le_alt ((produc1317709143le_alt ((append1166001599le_alt U_1) ((cons_l635097956le_alt A_4) X_41))) ((append1166001599le_alt U_1) ((cons_l635097956le_alt B_4) Y_18)))) (lexord469916775le_alt R_30))))
% FOF formula (forall (X_40:list_A2115238852le_alt) (R_29:(produc1501160679le_alt->Prop)) (Y_17:list_A2115238852le_alt), (((ex arrow_475358991le_alt) (fun (B:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Z:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Y_17) ((cons_A228743023le_alt B) Z))))))->((member28618436le_alt ((produc776457805le_alt X_40) ((append179082452le_alt X_40) Y_17))) (lexord958095404le_alt R_29)))) of role axiom named fact_397_lexord__append__rightI
% A new axiom: (forall (X_40:list_A2115238852le_alt) (R_29:(produc1501160679le_alt->Prop)) (Y_17:list_A2115238852le_alt), (((ex arrow_475358991le_alt) (fun (B:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Z:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Y_17) ((cons_A228743023le_alt B) Z))))))->((member28618436le_alt ((produc776457805le_alt X_40) ((append179082452le_alt X_40) Y_17))) (lexord958095404le_alt R_29))))
% FOF formula (forall (X_39:list_l1475218533le_alt) (U:list_l1475218533le_alt) (V:list_l1475218533le_alt) (R_28:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt ((append1166001599le_alt X_39) U)) ((append1166001599le_alt X_39) V))) (lexord469916775le_alt R_28))->((forall (A:list_A2115238852le_alt), (((member28618436le_alt ((produc776457805le_alt A) A)) R_28)->False))->((member1732936276le_alt ((produc1317709143le_alt U) V)) (lexord469916775le_alt R_28))))) of role axiom named fact_398_lexord__append__leftD
% A new axiom: (forall (X_39:list_l1475218533le_alt) (U:list_l1475218533le_alt) (V:list_l1475218533le_alt) (R_28:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt ((append1166001599le_alt X_39) U)) ((append1166001599le_alt X_39) V))) (lexord469916775le_alt R_28))->((forall (A:list_A2115238852le_alt), (((member28618436le_alt ((produc776457805le_alt A) A)) R_28)->False))->((member1732936276le_alt ((produc1317709143le_alt U) V)) (lexord469916775le_alt R_28)))))
% FOF formula (forall (X_39:list_A2115238852le_alt) (U:list_A2115238852le_alt) (V:list_A2115238852le_alt) (R_28:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt X_39) U)) ((append179082452le_alt X_39) V))) (lexord958095404le_alt R_28))->((forall (A:arrow_475358991le_alt), (((member214075476le_alt ((produc1347929815le_alt A) A)) R_28)->False))->((member28618436le_alt ((produc776457805le_alt U) V)) (lexord958095404le_alt R_28))))) of role axiom named fact_399_lexord__append__leftD
% A new axiom: (forall (X_39:list_A2115238852le_alt) (U:list_A2115238852le_alt) (V:list_A2115238852le_alt) (R_28:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt X_39) U)) ((append179082452le_alt X_39) V))) (lexord958095404le_alt R_28))->((forall (A:arrow_475358991le_alt), (((member214075476le_alt ((produc1347929815le_alt A) A)) R_28)->False))->((member28618436le_alt ((produc776457805le_alt U) V)) (lexord958095404le_alt R_28)))))
% FOF formula (forall (Xs_79:list_A2115238852le_alt) (P_20:(list_A2115238852le_alt->Prop)), ((P_20 nil_Ar1286194111le_alt)->((forall (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt), ((P_20 Xs_21)->(P_20 ((append179082452le_alt Xs_21) ((cons_A228743023le_alt X_2) nil_Ar1286194111le_alt)))))->(P_20 Xs_79)))) of role axiom named fact_400_rev__induct
% A new axiom: (forall (Xs_79:list_A2115238852le_alt) (P_20:(list_A2115238852le_alt->Prop)), ((P_20 nil_Ar1286194111le_alt)->((forall (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt), ((P_20 Xs_21)->(P_20 ((append179082452le_alt Xs_21) ((cons_A228743023le_alt X_2) nil_Ar1286194111le_alt)))))->(P_20 Xs_79))))
% FOF formula (forall (Xs_78:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_78) nil_Ar1286194111le_alt))->((forall (Ys:list_A2115238852le_alt) (Y_1:arrow_475358991le_alt), (not (((eq list_A2115238852le_alt) Xs_78) ((append179082452le_alt Ys) ((cons_A228743023le_alt Y_1) nil_Ar1286194111le_alt)))))->False))) of role axiom named fact_401_rev__cases
% A new axiom: (forall (Xs_78:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_78) nil_Ar1286194111le_alt))->((forall (Ys:list_A2115238852le_alt) (Y_1:arrow_475358991le_alt), (not (((eq list_A2115238852le_alt) Xs_78) ((append179082452le_alt Ys) ((cons_A228743023le_alt Y_1) nil_Ar1286194111le_alt)))))->False)))
% FOF formula (forall (Xs_77:list_l1475218533le_alt) (X_38:list_A2115238852le_alt) (Ys_29:list_l1475218533le_alt) (Y_16:list_A2115238852le_alt) (R_27:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((append1166001599le_alt Xs_77) ((cons_l635097956le_alt X_38) nil_li1907286804le_alt))) ((append1166001599le_alt Ys_29) ((cons_l635097956le_alt Y_16) nil_li1907286804le_alt)))) (listre620555643le_alt R_27))) ((or ((and ((member1732936276le_alt ((produc1317709143le_alt Xs_77) Ys_29)) (listre620555643le_alt R_27))) (((eq list_A2115238852le_alt) X_38) Y_16))) ((and (((eq list_l1475218533le_alt) Xs_77) Ys_29)) ((member28618436le_alt ((produc776457805le_alt X_38) Y_16)) R_27))))) of role axiom named fact_402_snoc__listrel1__snoc__iff
% A new axiom: (forall (Xs_77:list_l1475218533le_alt) (X_38:list_A2115238852le_alt) (Ys_29:list_l1475218533le_alt) (Y_16:list_A2115238852le_alt) (R_27:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((append1166001599le_alt Xs_77) ((cons_l635097956le_alt X_38) nil_li1907286804le_alt))) ((append1166001599le_alt Ys_29) ((cons_l635097956le_alt Y_16) nil_li1907286804le_alt)))) (listre620555643le_alt R_27))) ((or ((and ((member1732936276le_alt ((produc1317709143le_alt Xs_77) Ys_29)) (listre620555643le_alt R_27))) (((eq list_A2115238852le_alt) X_38) Y_16))) ((and (((eq list_l1475218533le_alt) Xs_77) Ys_29)) ((member28618436le_alt ((produc776457805le_alt X_38) Y_16)) R_27)))))
% FOF formula (forall (Xs_77:list_A2115238852le_alt) (X_38:arrow_475358991le_alt) (Ys_29:list_A2115238852le_alt) (Y_16:arrow_475358991le_alt) (R_27:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt Xs_77) ((cons_A228743023le_alt X_38) nil_Ar1286194111le_alt))) ((append179082452le_alt Ys_29) ((cons_A228743023le_alt Y_16) nil_Ar1286194111le_alt)))) (listre2064003096le_alt R_27))) ((or ((and ((member28618436le_alt ((produc776457805le_alt Xs_77) Ys_29)) (listre2064003096le_alt R_27))) (((eq arrow_475358991le_alt) X_38) Y_16))) ((and (((eq list_A2115238852le_alt) Xs_77) Ys_29)) ((member214075476le_alt ((produc1347929815le_alt X_38) Y_16)) R_27))))) of role axiom named fact_403_snoc__listrel1__snoc__iff
% A new axiom: (forall (Xs_77:list_A2115238852le_alt) (X_38:arrow_475358991le_alt) (Ys_29:list_A2115238852le_alt) (Y_16:arrow_475358991le_alt) (R_27:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt Xs_77) ((cons_A228743023le_alt X_38) nil_Ar1286194111le_alt))) ((append179082452le_alt Ys_29) ((cons_A228743023le_alt Y_16) nil_Ar1286194111le_alt)))) (listre2064003096le_alt R_27))) ((or ((and ((member28618436le_alt ((produc776457805le_alt Xs_77) Ys_29)) (listre2064003096le_alt R_27))) (((eq arrow_475358991le_alt) X_38) Y_16))) ((and (((eq list_A2115238852le_alt) Xs_77) Ys_29)) ((member214075476le_alt ((produc1347929815le_alt X_38) Y_16)) R_27)))))
% FOF formula (forall (Xs_76:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rotate335349260le_alt Xs_76)) (((list_c1623890103le_alt nil_Ar1286194111le_alt) (fun (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt)=> ((append179082452le_alt Xs_21) ((cons_A228743023le_alt X_2) nil_Ar1286194111le_alt)))) Xs_76))) of role axiom named fact_404_rotate1__def
% A new axiom: (forall (Xs_76:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rotate335349260le_alt Xs_76)) (((list_c1623890103le_alt nil_Ar1286194111le_alt) (fun (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt)=> ((append179082452le_alt Xs_21) ((cons_A228743023le_alt X_2) nil_Ar1286194111le_alt)))) Xs_76)))
% FOF formula (forall (Xs_75:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) (rotate335349260le_alt Xs_75)) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Xs_75) nil_Ar1286194111le_alt))) of role axiom named fact_405_rotate1__is__Nil__conv
% A new axiom: (forall (Xs_75:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) (rotate335349260le_alt Xs_75)) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Xs_75) nil_Ar1286194111le_alt)))
% FOF formula (forall (Xs_74:list_A2115238852le_alt), ((iff (distin236324274le_alt (rotate335349260le_alt Xs_74))) (distin236324274le_alt Xs_74))) of role axiom named fact_406_distinct1__rotate
% A new axiom: (forall (Xs_74:list_A2115238852le_alt), ((iff (distin236324274le_alt (rotate335349260le_alt Xs_74))) (distin236324274le_alt Xs_74)))
% FOF formula (forall (X_37:arrow_475358991le_alt) (Xs_73:list_A2115238852le_alt) (Ys_28:list_A2115238852le_alt) (R_26:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_73) Ys_28)) (listre2064003096le_alt R_26))->((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_37) Xs_73)) ((cons_A228743023le_alt X_37) Ys_28))) (listre2064003096le_alt R_26)))) of role axiom named fact_407_listrel1I2
% A new axiom: (forall (X_37:arrow_475358991le_alt) (Xs_73:list_A2115238852le_alt) (Ys_28:list_A2115238852le_alt) (R_26:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_73) Ys_28)) (listre2064003096le_alt R_26))->((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_37) Xs_73)) ((cons_A228743023le_alt X_37) Ys_28))) (listre2064003096le_alt R_26))))
% FOF formula (forall (Xs_72:list_A2115238852le_alt) (R_25:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_72) nil_Ar1286194111le_alt)) (listre2064003096le_alt R_25))->False)) of role axiom named fact_408_not__listrel1__Nil
% A new axiom: (forall (Xs_72:list_A2115238852le_alt) (R_25:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_72) nil_Ar1286194111le_alt)) (listre2064003096le_alt R_25))->False))
% FOF formula (forall (Xs_71:list_A2115238852le_alt) (R_24:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Xs_71)) (listre2064003096le_alt R_24))->False)) of role axiom named fact_409_not__Nil__listrel1
% A new axiom: (forall (Xs_71:list_A2115238852le_alt) (R_24:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Xs_71)) (listre2064003096le_alt R_24))->False))
% FOF formula (forall (Us_2:list_A2115238852le_alt) (Vs_2:list_A2115238852le_alt) (Xs_70:list_A2115238852le_alt) (Ys_27:list_A2115238852le_alt) (R_23:(produc1501160679le_alt->Prop)), (((or ((and ((member28618436le_alt ((produc776457805le_alt Xs_70) Ys_27)) (listre2064003096le_alt R_23))) (((eq list_A2115238852le_alt) Us_2) Vs_2))) ((and (((eq list_A2115238852le_alt) Xs_70) Ys_27)) ((member28618436le_alt ((produc776457805le_alt Us_2) Vs_2)) (listre2064003096le_alt R_23))))->((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt Xs_70) Us_2)) ((append179082452le_alt Ys_27) Vs_2))) (listre2064003096le_alt R_23)))) of role axiom named fact_410_append__listrel1I
% A new axiom: (forall (Us_2:list_A2115238852le_alt) (Vs_2:list_A2115238852le_alt) (Xs_70:list_A2115238852le_alt) (Ys_27:list_A2115238852le_alt) (R_23:(produc1501160679le_alt->Prop)), (((or ((and ((member28618436le_alt ((produc776457805le_alt Xs_70) Ys_27)) (listre2064003096le_alt R_23))) (((eq list_A2115238852le_alt) Us_2) Vs_2))) ((and (((eq list_A2115238852le_alt) Xs_70) Ys_27)) ((member28618436le_alt ((produc776457805le_alt Us_2) Vs_2)) (listre2064003096le_alt R_23))))->((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt Xs_70) Us_2)) ((append179082452le_alt Ys_27) Vs_2))) (listre2064003096le_alt R_23))))
% FOF formula (forall (X_36:list_A2115238852le_alt) (Xs_69:list_l1475218533le_alt) (Y_15:list_A2115238852le_alt) (Ys_26:list_l1475218533le_alt) (R_22:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_36) Xs_69)) ((cons_l635097956le_alt Y_15) Ys_26))) (listre620555643le_alt R_22))) ((or ((and ((member28618436le_alt ((produc776457805le_alt X_36) Y_15)) R_22)) (((eq list_l1475218533le_alt) Xs_69) Ys_26))) ((and (((eq list_A2115238852le_alt) X_36) Y_15)) ((member1732936276le_alt ((produc1317709143le_alt Xs_69) Ys_26)) (listre620555643le_alt R_22)))))) of role axiom named fact_411_Cons__listrel1__Cons
% A new axiom: (forall (X_36:list_A2115238852le_alt) (Xs_69:list_l1475218533le_alt) (Y_15:list_A2115238852le_alt) (Ys_26:list_l1475218533le_alt) (R_22:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_36) Xs_69)) ((cons_l635097956le_alt Y_15) Ys_26))) (listre620555643le_alt R_22))) ((or ((and ((member28618436le_alt ((produc776457805le_alt X_36) Y_15)) R_22)) (((eq list_l1475218533le_alt) Xs_69) Ys_26))) ((and (((eq list_A2115238852le_alt) X_36) Y_15)) ((member1732936276le_alt ((produc1317709143le_alt Xs_69) Ys_26)) (listre620555643le_alt R_22))))))
% FOF formula (forall (X_36:arrow_475358991le_alt) (Xs_69:list_A2115238852le_alt) (Y_15:arrow_475358991le_alt) (Ys_26:list_A2115238852le_alt) (R_22:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_36) Xs_69)) ((cons_A228743023le_alt Y_15) Ys_26))) (listre2064003096le_alt R_22))) ((or ((and ((member214075476le_alt ((produc1347929815le_alt X_36) Y_15)) R_22)) (((eq list_A2115238852le_alt) Xs_69) Ys_26))) ((and (((eq arrow_475358991le_alt) X_36) Y_15)) ((member28618436le_alt ((produc776457805le_alt Xs_69) Ys_26)) (listre2064003096le_alt R_22)))))) of role axiom named fact_412_Cons__listrel1__Cons
% A new axiom: (forall (X_36:arrow_475358991le_alt) (Xs_69:list_A2115238852le_alt) (Y_15:arrow_475358991le_alt) (Ys_26:list_A2115238852le_alt) (R_22:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_36) Xs_69)) ((cons_A228743023le_alt Y_15) Ys_26))) (listre2064003096le_alt R_22))) ((or ((and ((member214075476le_alt ((produc1347929815le_alt X_36) Y_15)) R_22)) (((eq list_A2115238852le_alt) Xs_69) Ys_26))) ((and (((eq arrow_475358991le_alt) X_36) Y_15)) ((member28618436le_alt ((produc776457805le_alt Xs_69) Ys_26)) (listre2064003096le_alt R_22))))))
% FOF formula (forall (Xs_68:list_A2115238852le_alt) (X_35:arrow_475358991le_alt) (Y_14:arrow_475358991le_alt) (R_21:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt X_35) Y_14)) R_21)->((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_35) Xs_68)) ((cons_A228743023le_alt Y_14) Xs_68))) (listre2064003096le_alt R_21)))) of role axiom named fact_413_listrel1I1
% A new axiom: (forall (Xs_68:list_A2115238852le_alt) (X_35:arrow_475358991le_alt) (Y_14:arrow_475358991le_alt) (R_21:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt X_35) Y_14)) R_21)->((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_35) Xs_68)) ((cons_A228743023le_alt Y_14) Xs_68))) (listre2064003096le_alt R_21))))
% FOF formula (forall (Xs_68:list_l1475218533le_alt) (X_35:list_A2115238852le_alt) (Y_14:list_A2115238852le_alt) (R_21:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_35) Y_14)) R_21)->((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_35) Xs_68)) ((cons_l635097956le_alt Y_14) Xs_68))) (listre620555643le_alt R_21)))) of role axiom named fact_414_listrel1I1
% A new axiom: (forall (Xs_68:list_l1475218533le_alt) (X_35:list_A2115238852le_alt) (Y_14:list_A2115238852le_alt) (R_21:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_35) Y_14)) R_21)->((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_35) Xs_68)) ((cons_l635097956le_alt Y_14) Xs_68))) (listre620555643le_alt R_21))))
% FOF formula (forall (Ys_25:list_A2115238852le_alt) (Xs_67:list_A2115238852le_alt) (Us_1:list_A2115238852le_alt) (Vs_1:list_A2115238852le_alt) (X_34:arrow_475358991le_alt) (Y_13:arrow_475358991le_alt) (R_20:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt X_34) Y_13)) R_20)->((((eq list_A2115238852le_alt) Xs_67) ((append179082452le_alt Us_1) ((cons_A228743023le_alt X_34) Vs_1)))->((((eq list_A2115238852le_alt) Ys_25) ((append179082452le_alt Us_1) ((cons_A228743023le_alt Y_13) Vs_1)))->((member28618436le_alt ((produc776457805le_alt Xs_67) Ys_25)) (listre2064003096le_alt R_20)))))) of role axiom named fact_415_listrel1I
% A new axiom: (forall (Ys_25:list_A2115238852le_alt) (Xs_67:list_A2115238852le_alt) (Us_1:list_A2115238852le_alt) (Vs_1:list_A2115238852le_alt) (X_34:arrow_475358991le_alt) (Y_13:arrow_475358991le_alt) (R_20:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt X_34) Y_13)) R_20)->((((eq list_A2115238852le_alt) Xs_67) ((append179082452le_alt Us_1) ((cons_A228743023le_alt X_34) Vs_1)))->((((eq list_A2115238852le_alt) Ys_25) ((append179082452le_alt Us_1) ((cons_A228743023le_alt Y_13) Vs_1)))->((member28618436le_alt ((produc776457805le_alt Xs_67) Ys_25)) (listre2064003096le_alt R_20))))))
% FOF formula (forall (Ys_25:list_l1475218533le_alt) (Xs_67:list_l1475218533le_alt) (Us_1:list_l1475218533le_alt) (Vs_1:list_l1475218533le_alt) (X_34:list_A2115238852le_alt) (Y_13:list_A2115238852le_alt) (R_20:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_34) Y_13)) R_20)->((((eq list_l1475218533le_alt) Xs_67) ((append1166001599le_alt Us_1) ((cons_l635097956le_alt X_34) Vs_1)))->((((eq list_l1475218533le_alt) Ys_25) ((append1166001599le_alt Us_1) ((cons_l635097956le_alt Y_13) Vs_1)))->((member1732936276le_alt ((produc1317709143le_alt Xs_67) Ys_25)) (listre620555643le_alt R_20)))))) of role axiom named fact_416_listrel1I
% A new axiom: (forall (Ys_25:list_l1475218533le_alt) (Xs_67:list_l1475218533le_alt) (Us_1:list_l1475218533le_alt) (Vs_1:list_l1475218533le_alt) (X_34:list_A2115238852le_alt) (Y_13:list_A2115238852le_alt) (R_20:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_34) Y_13)) R_20)->((((eq list_l1475218533le_alt) Xs_67) ((append1166001599le_alt Us_1) ((cons_l635097956le_alt X_34) Vs_1)))->((((eq list_l1475218533le_alt) Ys_25) ((append1166001599le_alt Us_1) ((cons_l635097956le_alt Y_13) Vs_1)))->((member1732936276le_alt ((produc1317709143le_alt Xs_67) Ys_25)) (listre620555643le_alt R_20))))))
% FOF formula (forall (Xs_66:list_l1475218533le_alt) (Ys_24:list_l1475218533le_alt) (R_19:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt Xs_66) Ys_24)) (listre620555643le_alt R_19))->((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt), (((member28618436le_alt ((produc776457805le_alt X_2) Y_1)) R_19)->(forall (Us:list_l1475218533le_alt) (Vs:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_66) ((append1166001599le_alt Us) ((cons_l635097956le_alt X_2) Vs)))->(not (((eq list_l1475218533le_alt) Ys_24) ((append1166001599le_alt Us) ((cons_l635097956le_alt Y_1) Vs))))))))->False))) of role axiom named fact_417_listrel1E
% A new axiom: (forall (Xs_66:list_l1475218533le_alt) (Ys_24:list_l1475218533le_alt) (R_19:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt Xs_66) Ys_24)) (listre620555643le_alt R_19))->((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt), (((member28618436le_alt ((produc776457805le_alt X_2) Y_1)) R_19)->(forall (Us:list_l1475218533le_alt) (Vs:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_66) ((append1166001599le_alt Us) ((cons_l635097956le_alt X_2) Vs)))->(not (((eq list_l1475218533le_alt) Ys_24) ((append1166001599le_alt Us) ((cons_l635097956le_alt Y_1) Vs))))))))->False)))
% FOF formula (forall (Xs_66:list_A2115238852le_alt) (Ys_24:list_A2115238852le_alt) (R_19:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_66) Ys_24)) (listre2064003096le_alt R_19))->((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt), (((member214075476le_alt ((produc1347929815le_alt X_2) Y_1)) R_19)->(forall (Us:list_A2115238852le_alt) (Vs:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_66) ((append179082452le_alt Us) ((cons_A228743023le_alt X_2) Vs)))->(not (((eq list_A2115238852le_alt) Ys_24) ((append179082452le_alt Us) ((cons_A228743023le_alt Y_1) Vs))))))))->False))) of role axiom named fact_418_listrel1E
% A new axiom: (forall (Xs_66:list_A2115238852le_alt) (Ys_24:list_A2115238852le_alt) (R_19:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_66) Ys_24)) (listre2064003096le_alt R_19))->((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt), (((member214075476le_alt ((produc1347929815le_alt X_2) Y_1)) R_19)->(forall (Us:list_A2115238852le_alt) (Vs:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_66) ((append179082452le_alt Us) ((cons_A228743023le_alt X_2) Vs)))->(not (((eq list_A2115238852le_alt) Ys_24) ((append179082452le_alt Us) ((cons_A228743023le_alt Y_1) Vs))))))))->False)))
% FOF formula (forall (X_33:list_A2115238852le_alt) (Xs_65:list_l1475218533le_alt) (Ys_23:list_l1475218533le_alt) (R_18:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_33) Xs_65)) Ys_23)) (listre620555643le_alt R_18))->((forall (Y_1:list_A2115238852le_alt), ((((eq list_l1475218533le_alt) Ys_23) ((cons_l635097956le_alt Y_1) Xs_65))->(((member28618436le_alt ((produc776457805le_alt X_33) Y_1)) R_18)->False)))->((forall (Zs:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Ys_23) ((cons_l635097956le_alt X_33) Zs))->(((member1732936276le_alt ((produc1317709143le_alt Xs_65) Zs)) (listre620555643le_alt R_18))->False)))->False)))) of role axiom named fact_419_Cons__listrel1E1
% A new axiom: (forall (X_33:list_A2115238852le_alt) (Xs_65:list_l1475218533le_alt) (Ys_23:list_l1475218533le_alt) (R_18:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_33) Xs_65)) Ys_23)) (listre620555643le_alt R_18))->((forall (Y_1:list_A2115238852le_alt), ((((eq list_l1475218533le_alt) Ys_23) ((cons_l635097956le_alt Y_1) Xs_65))->(((member28618436le_alt ((produc776457805le_alt X_33) Y_1)) R_18)->False)))->((forall (Zs:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Ys_23) ((cons_l635097956le_alt X_33) Zs))->(((member1732936276le_alt ((produc1317709143le_alt Xs_65) Zs)) (listre620555643le_alt R_18))->False)))->False))))
% FOF formula (forall (X_33:arrow_475358991le_alt) (Xs_65:list_A2115238852le_alt) (Ys_23:list_A2115238852le_alt) (R_18:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_33) Xs_65)) Ys_23)) (listre2064003096le_alt R_18))->((forall (Y_1:arrow_475358991le_alt), ((((eq list_A2115238852le_alt) Ys_23) ((cons_A228743023le_alt Y_1) Xs_65))->(((member214075476le_alt ((produc1347929815le_alt X_33) Y_1)) R_18)->False)))->((forall (Zs:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Ys_23) ((cons_A228743023le_alt X_33) Zs))->(((member28618436le_alt ((produc776457805le_alt Xs_65) Zs)) (listre2064003096le_alt R_18))->False)))->False)))) of role axiom named fact_420_Cons__listrel1E1
% A new axiom: (forall (X_33:arrow_475358991le_alt) (Xs_65:list_A2115238852le_alt) (Ys_23:list_A2115238852le_alt) (R_18:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_33) Xs_65)) Ys_23)) (listre2064003096le_alt R_18))->((forall (Y_1:arrow_475358991le_alt), ((((eq list_A2115238852le_alt) Ys_23) ((cons_A228743023le_alt Y_1) Xs_65))->(((member214075476le_alt ((produc1347929815le_alt X_33) Y_1)) R_18)->False)))->((forall (Zs:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Ys_23) ((cons_A228743023le_alt X_33) Zs))->(((member28618436le_alt ((produc776457805le_alt Xs_65) Zs)) (listre2064003096le_alt R_18))->False)))->False))))
% FOF formula (forall (Xs_64:list_l1475218533le_alt) (Y_12:list_A2115238852le_alt) (Ys_22:list_l1475218533le_alt) (R_17:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt Xs_64) ((cons_l635097956le_alt Y_12) Ys_22))) (listre620555643le_alt R_17))->((forall (X_2:list_A2115238852le_alt), ((((eq list_l1475218533le_alt) Xs_64) ((cons_l635097956le_alt X_2) Ys_22))->(((member28618436le_alt ((produc776457805le_alt X_2) Y_12)) R_17)->False)))->((forall (Zs:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_64) ((cons_l635097956le_alt Y_12) Zs))->(((member1732936276le_alt ((produc1317709143le_alt Zs) Ys_22)) (listre620555643le_alt R_17))->False)))->False)))) of role axiom named fact_421_Cons__listrel1E2
% A new axiom: (forall (Xs_64:list_l1475218533le_alt) (Y_12:list_A2115238852le_alt) (Ys_22:list_l1475218533le_alt) (R_17:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt Xs_64) ((cons_l635097956le_alt Y_12) Ys_22))) (listre620555643le_alt R_17))->((forall (X_2:list_A2115238852le_alt), ((((eq list_l1475218533le_alt) Xs_64) ((cons_l635097956le_alt X_2) Ys_22))->(((member28618436le_alt ((produc776457805le_alt X_2) Y_12)) R_17)->False)))->((forall (Zs:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_64) ((cons_l635097956le_alt Y_12) Zs))->(((member1732936276le_alt ((produc1317709143le_alt Zs) Ys_22)) (listre620555643le_alt R_17))->False)))->False))))
% FOF formula (forall (Xs_64:list_A2115238852le_alt) (Y_12:arrow_475358991le_alt) (Ys_22:list_A2115238852le_alt) (R_17:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_64) ((cons_A228743023le_alt Y_12) Ys_22))) (listre2064003096le_alt R_17))->((forall (X_2:arrow_475358991le_alt), ((((eq list_A2115238852le_alt) Xs_64) ((cons_A228743023le_alt X_2) Ys_22))->(((member214075476le_alt ((produc1347929815le_alt X_2) Y_12)) R_17)->False)))->((forall (Zs:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_64) ((cons_A228743023le_alt Y_12) Zs))->(((member28618436le_alt ((produc776457805le_alt Zs) Ys_22)) (listre2064003096le_alt R_17))->False)))->False)))) of role axiom named fact_422_Cons__listrel1E2
% A new axiom: (forall (Xs_64:list_A2115238852le_alt) (Y_12:arrow_475358991le_alt) (Ys_22:list_A2115238852le_alt) (R_17:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_64) ((cons_A228743023le_alt Y_12) Ys_22))) (listre2064003096le_alt R_17))->((forall (X_2:arrow_475358991le_alt), ((((eq list_A2115238852le_alt) Xs_64) ((cons_A228743023le_alt X_2) Ys_22))->(((member214075476le_alt ((produc1347929815le_alt X_2) Y_12)) R_17)->False)))->((forall (Zs:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_64) ((cons_A228743023le_alt Y_12) Zs))->(((member28618436le_alt ((produc776457805le_alt Zs) Ys_22)) (listre2064003096le_alt R_17))->False)))->False))))
% FOF formula (forall (X_32:list_A2115238852le_alt) (Xs_63:list_l1475218533le_alt) (Y_11:list_A2115238852le_alt) (Ys_21:list_l1475218533le_alt) (R_16:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_32) Xs_63)) ((cons_l635097956le_alt Y_11) Ys_21))) (lex_li663137712le_alt R_16))) ((or ((and ((member28618436le_alt ((produc776457805le_alt X_32) Y_11)) R_16)) (((eq nat) (size_s1911906171le_alt Xs_63)) (size_s1911906171le_alt Ys_21)))) ((and (((eq list_A2115238852le_alt) X_32) Y_11)) ((member1732936276le_alt ((produc1317709143le_alt Xs_63) Ys_21)) (lex_li663137712le_alt R_16)))))) of role axiom named fact_423_Cons__in__lex
% A new axiom: (forall (X_32:list_A2115238852le_alt) (Xs_63:list_l1475218533le_alt) (Y_11:list_A2115238852le_alt) (Ys_21:list_l1475218533le_alt) (R_16:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_32) Xs_63)) ((cons_l635097956le_alt Y_11) Ys_21))) (lex_li663137712le_alt R_16))) ((or ((and ((member28618436le_alt ((produc776457805le_alt X_32) Y_11)) R_16)) (((eq nat) (size_s1911906171le_alt Xs_63)) (size_s1911906171le_alt Ys_21)))) ((and (((eq list_A2115238852le_alt) X_32) Y_11)) ((member1732936276le_alt ((produc1317709143le_alt Xs_63) Ys_21)) (lex_li663137712le_alt R_16))))))
% FOF formula (forall (X_32:arrow_475358991le_alt) (Xs_63:list_A2115238852le_alt) (Y_11:arrow_475358991le_alt) (Ys_21:list_A2115238852le_alt) (R_16:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_32) Xs_63)) ((cons_A228743023le_alt Y_11) Ys_21))) (lex_Ar1415517219le_alt R_16))) ((or ((and ((member214075476le_alt ((produc1347929815le_alt X_32) Y_11)) R_16)) (((eq nat) (size_s1858781230le_alt Xs_63)) (size_s1858781230le_alt Ys_21)))) ((and (((eq arrow_475358991le_alt) X_32) Y_11)) ((member28618436le_alt ((produc776457805le_alt Xs_63) Ys_21)) (lex_Ar1415517219le_alt R_16)))))) of role axiom named fact_424_Cons__in__lex
% A new axiom: (forall (X_32:arrow_475358991le_alt) (Xs_63:list_A2115238852le_alt) (Y_11:arrow_475358991le_alt) (Ys_21:list_A2115238852le_alt) (R_16:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_32) Xs_63)) ((cons_A228743023le_alt Y_11) Ys_21))) (lex_Ar1415517219le_alt R_16))) ((or ((and ((member214075476le_alt ((produc1347929815le_alt X_32) Y_11)) R_16)) (((eq nat) (size_s1858781230le_alt Xs_63)) (size_s1858781230le_alt Ys_21)))) ((and (((eq arrow_475358991le_alt) X_32) Y_11)) ((member28618436le_alt ((produc776457805le_alt Xs_63) Ys_21)) (lex_Ar1415517219le_alt R_16))))))
% FOF formula (forall (P_19:(arrow_475358991le_alt->Prop)) (Xs_62:list_A2115238852le_alt) (Y_10:arrow_475358991le_alt) (Ys_20:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_19) Xs_62)) ((cons_A228743023le_alt Y_10) Ys_20))) ((and (((eq list_A2115238852le_alt) Xs_62) ((append179082452le_alt ((takeWh1696291512le_alt P_19) Xs_62)) ((cons_A228743023le_alt Y_10) Ys_20)))) ((P_19 Y_10)->False)))) of role axiom named fact_425_dropWhile__eq__Cons__conv
% A new axiom: (forall (P_19:(arrow_475358991le_alt->Prop)) (Xs_62:list_A2115238852le_alt) (Y_10:arrow_475358991le_alt) (Ys_20:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_19) Xs_62)) ((cons_A228743023le_alt Y_10) Ys_20))) ((and (((eq list_A2115238852le_alt) Xs_62) ((append179082452le_alt ((takeWh1696291512le_alt P_19) Xs_62)) ((cons_A228743023le_alt Y_10) Ys_20)))) ((P_19 Y_10)->False))))
% FOF formula (forall (P_18:(arrow_475358991le_alt->Prop)) (X_31:arrow_475358991le_alt) (Xs_61:list_A2115238852le_alt), (((eq produc1362454231le_alt) ((partit1487577784le_alt P_18) ((cons_A228743023le_alt X_31) Xs_61))) ((produc677212559le_alt (fun (Yes_1:list_A2115238852le_alt) (No_1:list_A2115238852le_alt)=> (((if_Pro314693991le_alt (P_18 X_31)) ((produc776457805le_alt ((cons_A228743023le_alt X_31) Yes_1)) No_1)) ((produc776457805le_alt Yes_1) ((cons_A228743023le_alt X_31) No_1))))) ((partit1487577784le_alt P_18) Xs_61)))) of role axiom named fact_426_partition_Osimps_I2_J
% A new axiom: (forall (P_18:(arrow_475358991le_alt->Prop)) (X_31:arrow_475358991le_alt) (Xs_61:list_A2115238852le_alt), (((eq produc1362454231le_alt) ((partit1487577784le_alt P_18) ((cons_A228743023le_alt X_31) Xs_61))) ((produc677212559le_alt (fun (Yes_1:list_A2115238852le_alt) (No_1:list_A2115238852le_alt)=> (((if_Pro314693991le_alt (P_18 X_31)) ((produc776457805le_alt ((cons_A228743023le_alt X_31) Yes_1)) No_1)) ((produc776457805le_alt Yes_1) ((cons_A228743023le_alt X_31) No_1))))) ((partit1487577784le_alt P_18) Xs_61))))
% FOF formula (forall (Xs_60:list_A2115238852le_alt) (P_17:(arrow_475358991le_alt->Prop)) (X_30:arrow_475358991le_alt), ((and ((P_17 X_30)->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_17) ((cons_A228743023le_alt X_30) Xs_60))) ((dropWh1316781920le_alt P_17) Xs_60)))) (((P_17 X_30)->False)->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_17) ((cons_A228743023le_alt X_30) Xs_60))) ((cons_A228743023le_alt X_30) Xs_60))))) of role axiom named fact_427_dropWhile_Osimps_I2_J
% A new axiom: (forall (Xs_60:list_A2115238852le_alt) (P_17:(arrow_475358991le_alt->Prop)) (X_30:arrow_475358991le_alt), ((and ((P_17 X_30)->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_17) ((cons_A228743023le_alt X_30) Xs_60))) ((dropWh1316781920le_alt P_17) Xs_60)))) (((P_17 X_30)->False)->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_17) ((cons_A228743023le_alt X_30) Xs_60))) ((cons_A228743023le_alt X_30) Xs_60)))))
% FOF formula (forall (P_16:(arrow_475358991le_alt->Prop)), (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_16) nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt)) of role axiom named fact_428_dropWhile_Osimps_I1_J
% A new axiom: (forall (P_16:(arrow_475358991le_alt->Prop)), (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_16) nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt))
% FOF formula (forall (P_15:(arrow_475358991le_alt->Prop)) (Xs_59:list_A2115238852le_alt), ((distin236324274le_alt Xs_59)->(distin236324274le_alt ((dropWh1316781920le_alt P_15) Xs_59)))) of role axiom named fact_429_distinct__dropWhile
% A new axiom: (forall (P_15:(arrow_475358991le_alt->Prop)) (Xs_59:list_A2115238852le_alt), ((distin236324274le_alt Xs_59)->(distin236324274le_alt ((dropWh1316781920le_alt P_15) Xs_59))))
% FOF formula (forall (F_3:(produc1501160679le_alt->Prop)), (((eq (produc1501160679le_alt->Prop)) (produc362454893_alt_o (produc910278158_alt_o F_3))) F_3)) of role axiom named fact_430_split__curry
% A new axiom: (forall (F_3:(produc1501160679le_alt->Prop)), (((eq (produc1501160679le_alt->Prop)) (produc362454893_alt_o (produc910278158_alt_o F_3))) F_3))
% FOF formula (forall (F_2:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))), (((eq (arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (produc910278158_alt_o (produc362454893_alt_o F_2))) F_2)) of role axiom named fact_431_curry__split
% A new axiom: (forall (F_2:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))), (((eq (arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (produc910278158_alt_o (produc362454893_alt_o F_2))) F_2))
% FOF formula (forall (Xs_58:list_A2115238852le_alt) (Ys_19:list_A2115238852le_alt) (R_15:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_58) Ys_19)) (listre2064003096le_alt R_15))->(((eq nat) (size_s1858781230le_alt Xs_58)) (size_s1858781230le_alt Ys_19)))) of role axiom named fact_432_listrel1__eq__len
% A new axiom: (forall (Xs_58:list_A2115238852le_alt) (Ys_19:list_A2115238852le_alt) (R_15:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_58) Ys_19)) (listre2064003096le_alt R_15))->(((eq nat) (size_s1858781230le_alt Xs_58)) (size_s1858781230le_alt Ys_19))))
% FOF formula (forall (P_14:(arrow_475358991le_alt->Prop)) (Xs_57:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((takeWh1696291512le_alt P_14) Xs_57)) ((dropWh1316781920le_alt P_14) Xs_57))) Xs_57)) of role axiom named fact_433_takeWhile__dropWhile__id
% A new axiom: (forall (P_14:(arrow_475358991le_alt->Prop)) (Xs_57:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((takeWh1696291512le_alt P_14) Xs_57)) ((dropWh1316781920le_alt P_14) Xs_57))) Xs_57))
% FOF formula (forall (X_29:list_A2115238852le_alt) (Y_9:list_A2115238852le_alt) (R_14:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt X_29) Y_9)) (lex_Ar1415517219le_alt R_14))) ((and ((member28618436le_alt ((produc776457805le_alt X_29) Y_9)) (lexord958095404le_alt R_14))) (((eq nat) (size_s1858781230le_alt X_29)) (size_s1858781230le_alt Y_9))))) of role axiom named fact_434_lexord__lex
% A new axiom: (forall (X_29:list_A2115238852le_alt) (Y_9:list_A2115238852le_alt) (R_14:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt X_29) Y_9)) (lex_Ar1415517219le_alt R_14))) ((and ((member28618436le_alt ((produc776457805le_alt X_29) Y_9)) (lexord958095404le_alt R_14))) (((eq nat) (size_s1858781230le_alt X_29)) (size_s1858781230le_alt Y_9)))))
% FOF formula (forall (Xs_56:list_A2115238852le_alt) (Ys_18:list_A2115238852le_alt) (R_13:(produc1501160679le_alt->Prop)) (N_8:nat), (((member28618436le_alt ((produc776457805le_alt Xs_56) Ys_18)) ((lexn_A170361439le_alt R_13) N_8))->((and (((eq nat) (size_s1858781230le_alt Xs_56)) N_8)) (((eq nat) (size_s1858781230le_alt Ys_18)) N_8)))) of role axiom named fact_435_lexn__length
% A new axiom: (forall (Xs_56:list_A2115238852le_alt) (Ys_18:list_A2115238852le_alt) (R_13:(produc1501160679le_alt->Prop)) (N_8:nat), (((member28618436le_alt ((produc776457805le_alt Xs_56) Ys_18)) ((lexn_A170361439le_alt R_13) N_8))->((and (((eq nat) (size_s1858781230le_alt Xs_56)) N_8)) (((eq nat) (size_s1858781230le_alt Ys_18)) N_8))))
% FOF formula (forall (F_1:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (A_3:list_A2115238852le_alt) (B_3:list_A2115238852le_alt), (((F_1 A_3) B_3)->((produc1948161143_alt_o F_1) ((produc776457805le_alt A_3) B_3)))) of role axiom named fact_436_splitI
% A new axiom: (forall (F_1:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (A_3:list_A2115238852le_alt) (B_3:list_A2115238852le_alt), (((F_1 A_3) B_3)->((produc1948161143_alt_o F_1) ((produc776457805le_alt A_3) B_3))))
% FOF formula (forall (F_1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A_3:arrow_475358991le_alt) (B_3:arrow_475358991le_alt), (((F_1 A_3) B_3)->((produc362454893_alt_o F_1) ((produc1347929815le_alt A_3) B_3)))) of role axiom named fact_437_splitI
% A new axiom: (forall (F_1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A_3:arrow_475358991le_alt) (B_3:arrow_475358991le_alt), (((F_1 A_3) B_3)->((produc362454893_alt_o F_1) ((produc1347929815le_alt A_3) B_3))))
% FOF formula (forall (F1:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (A_2:list_A2115238852le_alt) (B_2:list_A2115238852le_alt), (((F1 A_2) B_2)->((produc1948161143_alt_o F1) ((produc776457805le_alt A_2) B_2)))) of role axiom named fact_438_prod__caseI
% A new axiom: (forall (F1:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (A_2:list_A2115238852le_alt) (B_2:list_A2115238852le_alt), (((F1 A_2) B_2)->((produc1948161143_alt_o F1) ((produc776457805le_alt A_2) B_2))))
% FOF formula (forall (F1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A_2:arrow_475358991le_alt) (B_2:arrow_475358991le_alt), (((F1 A_2) B_2)->((produc362454893_alt_o F1) ((produc1347929815le_alt A_2) B_2)))) of role axiom named fact_439_prod__caseI
% A new axiom: (forall (F1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A_2:arrow_475358991le_alt) (B_2:arrow_475358991le_alt), (((F1 A_2) B_2)->((produc362454893_alt_o F1) ((produc1347929815le_alt A_2) B_2))))
% FOF formula (forall (F:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (A_1:list_A2115238852le_alt) (B_1:list_A2115238852le_alt), (((produc1948161143_alt_o F) ((produc776457805le_alt A_1) B_1))->((F A_1) B_1))) of role axiom named fact_440_splitD
% A new axiom: (forall (F:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (A_1:list_A2115238852le_alt) (B_1:list_A2115238852le_alt), (((produc1948161143_alt_o F) ((produc776457805le_alt A_1) B_1))->((F A_1) B_1)))
% FOF formula (forall (F:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A_1:arrow_475358991le_alt) (B_1:arrow_475358991le_alt), (((produc362454893_alt_o F) ((produc1347929815le_alt A_1) B_1))->((F A_1) B_1))) of role axiom named fact_441_splitD
% A new axiom: (forall (F:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A_1:arrow_475358991le_alt) (B_1:arrow_475358991le_alt), (((produc362454893_alt_o F) ((produc1347929815le_alt A_1) B_1))->((F A_1) B_1)))
% FOF formula (forall (C_1:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (P_13:produc1362454231le_alt), ((forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), ((((eq produc1362454231le_alt) P_13) ((produc776457805le_alt A) B))->((C_1 A) B)))->((produc1948161143_alt_o C_1) P_13))) of role axiom named fact_442_splitI2
% A new axiom: (forall (C_1:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (P_13:produc1362454231le_alt), ((forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), ((((eq produc1362454231le_alt) P_13) ((produc776457805le_alt A) B))->((C_1 A) B)))->((produc1948161143_alt_o C_1) P_13)))
% FOF formula (forall (C_1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (P_13:produc1501160679le_alt), ((forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((((eq produc1501160679le_alt) P_13) ((produc1347929815le_alt A) B))->((C_1 A) B)))->((produc362454893_alt_o C_1) P_13))) of role axiom named fact_443_splitI2
% A new axiom: (forall (C_1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (P_13:produc1501160679le_alt), ((forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((((eq produc1501160679le_alt) P_13) ((produc1347929815le_alt A) B))->((C_1 A) B)))->((produc362454893_alt_o C_1) P_13)))
% FOF formula (forall (C:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (P_12:produc1362454231le_alt), (((produc1948161143_alt_o C) P_12)->((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt), ((((eq produc1362454231le_alt) P_12) ((produc776457805le_alt X_2) Y_1))->(((C X_2) Y_1)->False)))->False))) of role axiom named fact_444_splitE
% A new axiom: (forall (C:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (P_12:produc1362454231le_alt), (((produc1948161143_alt_o C) P_12)->((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt), ((((eq produc1362454231le_alt) P_12) ((produc776457805le_alt X_2) Y_1))->(((C X_2) Y_1)->False)))->False)))
% FOF formula (forall (C:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (P_12:produc1501160679le_alt), (((produc362454893_alt_o C) P_12)->((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt), ((((eq produc1501160679le_alt) P_12) ((produc1347929815le_alt X_2) Y_1))->(((C X_2) Y_1)->False)))->False))) of role axiom named fact_445_splitE
% A new axiom: (forall (C:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (P_12:produc1501160679le_alt), (((produc362454893_alt_o C) P_12)->((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt), ((((eq produc1501160679le_alt) P_12) ((produc1347929815le_alt X_2) Y_1))->(((C X_2) Y_1)->False)))->False)))
% FOF formula (forall (Ws:list_A2115238852le_alt), (((distin236324274le_alt Ws)->False)->((ex list_A2115238852le_alt) (fun (Xs_21:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Zs:list_A2115238852le_alt)=> ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> (((eq list_A2115238852le_alt) Ws) ((append179082452le_alt Xs_21) ((append179082452le_alt ((cons_A228743023le_alt Y_1) nil_Ar1286194111le_alt)) ((append179082452le_alt Ys) ((append179082452le_alt ((cons_A228743023le_alt Y_1) nil_Ar1286194111le_alt)) Zs))))))))))))))) of role axiom named fact_446_not__distinct__decomp
% A new axiom: (forall (Ws:list_A2115238852le_alt), (((distin236324274le_alt Ws)->False)->((ex list_A2115238852le_alt) (fun (Xs_21:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Zs:list_A2115238852le_alt)=> ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> (((eq list_A2115238852le_alt) Ws) ((append179082452le_alt Xs_21) ((append179082452le_alt ((cons_A228743023le_alt Y_1) nil_Ar1286194111le_alt)) ((append179082452le_alt Ys) ((append179082452le_alt ((cons_A228743023le_alt Y_1) nil_Ar1286194111le_alt)) Zs)))))))))))))))
% FOF formula (forall (Xs_55:list_A2115238852le_alt) (Ys_17:list_A2115238852le_alt) (X_28:arrow_475358991le_alt) (Y_8:arrow_475358991le_alt) (R_12:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt X_28) Y_8)) R_12)->(((member28618436le_alt ((produc776457805le_alt Xs_55) Ys_17)) (listre1920655591le_alt R_12))->((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_28) Xs_55)) ((cons_A228743023le_alt Y_8) Ys_17))) (listre1920655591le_alt R_12))))) of role axiom named fact_447_listrel_OCons
% A new axiom: (forall (Xs_55:list_A2115238852le_alt) (Ys_17:list_A2115238852le_alt) (X_28:arrow_475358991le_alt) (Y_8:arrow_475358991le_alt) (R_12:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt X_28) Y_8)) R_12)->(((member28618436le_alt ((produc776457805le_alt Xs_55) Ys_17)) (listre1920655591le_alt R_12))->((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_28) Xs_55)) ((cons_A228743023le_alt Y_8) Ys_17))) (listre1920655591le_alt R_12)))))
% FOF formula (forall (Xs_55:list_l1475218533le_alt) (Ys_17:list_l1475218533le_alt) (X_28:list_A2115238852le_alt) (Y_8:list_A2115238852le_alt) (R_12:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_28) Y_8)) R_12)->(((member1732936276le_alt ((produc1317709143le_alt Xs_55) Ys_17)) (listre623166444le_alt R_12))->((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_28) Xs_55)) ((cons_l635097956le_alt Y_8) Ys_17))) (listre623166444le_alt R_12))))) of role axiom named fact_448_listrel_OCons
% A new axiom: (forall (Xs_55:list_l1475218533le_alt) (Ys_17:list_l1475218533le_alt) (X_28:list_A2115238852le_alt) (Y_8:list_A2115238852le_alt) (R_12:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_28) Y_8)) R_12)->(((member1732936276le_alt ((produc1317709143le_alt Xs_55) Ys_17)) (listre623166444le_alt R_12))->((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_28) Xs_55)) ((cons_l635097956le_alt Y_8) Ys_17))) (listre623166444le_alt R_12)))))
% FOF formula (forall (Xs_54:list_A2115238852le_alt) (Ys_16:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (tl_Arr465451158le_alt ((append179082452le_alt Xs_54) Ys_16))) (((list_c1623890103le_alt (tl_Arr465451158le_alt Ys_16)) (fun (Z:arrow_475358991le_alt) (Zs:list_A2115238852le_alt)=> ((append179082452le_alt Zs) Ys_16))) Xs_54))) of role axiom named fact_449_tl__append
% A new axiom: (forall (Xs_54:list_A2115238852le_alt) (Ys_16:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (tl_Arr465451158le_alt ((append179082452le_alt Xs_54) Ys_16))) (((list_c1623890103le_alt (tl_Arr465451158le_alt Ys_16)) (fun (Z:arrow_475358991le_alt) (Zs:list_A2115238852le_alt)=> ((append179082452le_alt Zs) Ys_16))) Xs_54)))
% FOF formula (forall (Xs_53:list_A2115238852le_alt) (R_11:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_53) nil_Ar1286194111le_alt)) (listre1920655591le_alt R_11))->(((eq list_A2115238852le_alt) Xs_53) nil_Ar1286194111le_alt))) of role axiom named fact_450_listrel__Nil2
% A new axiom: (forall (Xs_53:list_A2115238852le_alt) (R_11:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_53) nil_Ar1286194111le_alt)) (listre1920655591le_alt R_11))->(((eq list_A2115238852le_alt) Xs_53) nil_Ar1286194111le_alt)))
% FOF formula (forall (Xs_52:list_A2115238852le_alt) (R_10:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Xs_52)) (listre1920655591le_alt R_10))->(((eq list_A2115238852le_alt) Xs_52) nil_Ar1286194111le_alt))) of role axiom named fact_451_listrel__Nil1
% A new axiom: (forall (Xs_52:list_A2115238852le_alt) (R_10:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Xs_52)) (listre1920655591le_alt R_10))->(((eq list_A2115238852le_alt) Xs_52) nil_Ar1286194111le_alt)))
% FOF formula (forall (X_27:arrow_475358991le_alt) (Xs_51:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (tl_Arr465451158le_alt ((cons_A228743023le_alt X_27) Xs_51))) Xs_51)) of role axiom named fact_452_tl_Osimps_I2_J
% A new axiom: (forall (X_27:arrow_475358991le_alt) (Xs_51:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (tl_Arr465451158le_alt ((cons_A228743023le_alt X_27) Xs_51))) Xs_51))
% FOF formula (((eq list_A2115238852le_alt) (tl_Arr465451158le_alt nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt) of role axiom named fact_453_tl_Osimps_I1_J
% A new axiom: (((eq list_A2115238852le_alt) (tl_Arr465451158le_alt nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt)
% FOF formula (forall (Xs_50:list_A2115238852le_alt), ((distin236324274le_alt Xs_50)->(distin236324274le_alt (tl_Arr465451158le_alt Xs_50)))) of role axiom named fact_454_distinct__tl
% A new axiom: (forall (Xs_50:list_A2115238852le_alt), ((distin236324274le_alt Xs_50)->(distin236324274le_alt (tl_Arr465451158le_alt Xs_50))))
% FOF formula (forall (R_9:(produc1501160679le_alt->Prop)), ((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) nil_Ar1286194111le_alt)) (listre1920655591le_alt R_9))) of role axiom named fact_455_listrel_ONil
% A new axiom: (forall (R_9:(produc1501160679le_alt->Prop)), ((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) nil_Ar1286194111le_alt)) (listre1920655591le_alt R_9)))
% FOF formula (forall (Xs_49:list_A2115238852le_alt) (Ys_15:list_A2115238852le_alt) (R_8:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_49) Ys_15)) (listre1920655591le_alt R_8))->(((eq nat) (size_s1858781230le_alt Xs_49)) (size_s1858781230le_alt Ys_15)))) of role axiom named fact_456_listrel__eq__len
% A new axiom: (forall (Xs_49:list_A2115238852le_alt) (Ys_15:list_A2115238852le_alt) (R_8:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_49) Ys_15)) (listre1920655591le_alt R_8))->(((eq nat) (size_s1858781230le_alt Xs_49)) (size_s1858781230le_alt Ys_15))))
% FOF formula (forall (Ys_14:list_A2115238852le_alt) (Xs_48:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_48) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (tl_Arr465451158le_alt ((append179082452le_alt Xs_48) Ys_14))) ((append179082452le_alt (tl_Arr465451158le_alt Xs_48)) Ys_14)))) of role axiom named fact_457_tl__append2
% A new axiom: (forall (Ys_14:list_A2115238852le_alt) (Xs_48:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_48) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (tl_Arr465451158le_alt ((append179082452le_alt Xs_48) Ys_14))) ((append179082452le_alt (tl_Arr465451158le_alt Xs_48)) Ys_14))))
% FOF formula (forall (Xs_47:list_l1475218533le_alt) (Y_7:list_A2115238852le_alt) (Ys_13:list_l1475218533le_alt) (R_7:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt Xs_47) ((cons_l635097956le_alt Y_7) Ys_13))) (listre623166444le_alt R_7))->((forall (X_2:list_A2115238852le_alt) (Xs_21:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_47) ((cons_l635097956le_alt X_2) Xs_21))->(((member28618436le_alt ((produc776457805le_alt X_2) Y_7)) R_7)->(((member1732936276le_alt ((produc1317709143le_alt Xs_21) Ys_13)) (listre623166444le_alt R_7))->False))))->False))) of role axiom named fact_458_listrel__Cons2
% A new axiom: (forall (Xs_47:list_l1475218533le_alt) (Y_7:list_A2115238852le_alt) (Ys_13:list_l1475218533le_alt) (R_7:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt Xs_47) ((cons_l635097956le_alt Y_7) Ys_13))) (listre623166444le_alt R_7))->((forall (X_2:list_A2115238852le_alt) (Xs_21:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_47) ((cons_l635097956le_alt X_2) Xs_21))->(((member28618436le_alt ((produc776457805le_alt X_2) Y_7)) R_7)->(((member1732936276le_alt ((produc1317709143le_alt Xs_21) Ys_13)) (listre623166444le_alt R_7))->False))))->False)))
% FOF formula (forall (Xs_47:list_A2115238852le_alt) (Y_7:arrow_475358991le_alt) (Ys_13:list_A2115238852le_alt) (R_7:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_47) ((cons_A228743023le_alt Y_7) Ys_13))) (listre1920655591le_alt R_7))->((forall (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_47) ((cons_A228743023le_alt X_2) Xs_21))->(((member214075476le_alt ((produc1347929815le_alt X_2) Y_7)) R_7)->(((member28618436le_alt ((produc776457805le_alt Xs_21) Ys_13)) (listre1920655591le_alt R_7))->False))))->False))) of role axiom named fact_459_listrel__Cons2
% A new axiom: (forall (Xs_47:list_A2115238852le_alt) (Y_7:arrow_475358991le_alt) (Ys_13:list_A2115238852le_alt) (R_7:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_47) ((cons_A228743023le_alt Y_7) Ys_13))) (listre1920655591le_alt R_7))->((forall (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_47) ((cons_A228743023le_alt X_2) Xs_21))->(((member214075476le_alt ((produc1347929815le_alt X_2) Y_7)) R_7)->(((member28618436le_alt ((produc776457805le_alt Xs_21) Ys_13)) (listre1920655591le_alt R_7))->False))))->False)))
% FOF formula (forall (Y_6:list_A2115238852le_alt) (Ys_12:list_l1475218533le_alt) (Xs_46:list_l1475218533le_alt) (R_6:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt Y_6) Ys_12)) Xs_46)) (listre623166444le_alt R_6))->((forall (Y_1:list_A2115238852le_alt) (Ys:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_46) ((cons_l635097956le_alt Y_1) Ys))->(((member28618436le_alt ((produc776457805le_alt Y_6) Y_1)) R_6)->(((member1732936276le_alt ((produc1317709143le_alt Ys_12) Ys)) (listre623166444le_alt R_6))->False))))->False))) of role axiom named fact_460_listrel__Cons1
% A new axiom: (forall (Y_6:list_A2115238852le_alt) (Ys_12:list_l1475218533le_alt) (Xs_46:list_l1475218533le_alt) (R_6:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt Y_6) Ys_12)) Xs_46)) (listre623166444le_alt R_6))->((forall (Y_1:list_A2115238852le_alt) (Ys:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_46) ((cons_l635097956le_alt Y_1) Ys))->(((member28618436le_alt ((produc776457805le_alt Y_6) Y_1)) R_6)->(((member1732936276le_alt ((produc1317709143le_alt Ys_12) Ys)) (listre623166444le_alt R_6))->False))))->False)))
% FOF formula (forall (Y_6:arrow_475358991le_alt) (Ys_12:list_A2115238852le_alt) (Xs_46:list_A2115238852le_alt) (R_6:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt Y_6) Ys_12)) Xs_46)) (listre1920655591le_alt R_6))->((forall (Y_1:arrow_475358991le_alt) (Ys:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_46) ((cons_A228743023le_alt Y_1) Ys))->(((member214075476le_alt ((produc1347929815le_alt Y_6) Y_1)) R_6)->(((member28618436le_alt ((produc776457805le_alt Ys_12) Ys)) (listre1920655591le_alt R_6))->False))))->False))) of role axiom named fact_461_listrel__Cons1
% A new axiom: (forall (Y_6:arrow_475358991le_alt) (Ys_12:list_A2115238852le_alt) (Xs_46:list_A2115238852le_alt) (R_6:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt Y_6) Ys_12)) Xs_46)) (listre1920655591le_alt R_6))->((forall (Y_1:arrow_475358991le_alt) (Ys:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_46) ((cons_A228743023le_alt Y_1) Ys))->(((member214075476le_alt ((produc1347929815le_alt Y_6) Y_1)) R_6)->(((member28618436le_alt ((produc776457805le_alt Ys_12) Ys)) (listre1920655591le_alt R_6))->False))))->False)))
% FOF formula (forall (R_5:(produc1501160679le_alt->Prop)) (X_2:list_A2115238852le_alt) (Xa:list_A2115238852le_alt), ((iff (((listre1213162009le_alt (fun (Y_1:arrow_475358991le_alt) (Z:arrow_475358991le_alt)=> ((member214075476le_alt ((produc1347929815le_alt Y_1) Z)) R_5))) X_2) Xa)) ((member28618436le_alt ((produc776457805le_alt X_2) Xa)) (listre1920655591le_alt R_5)))) of role axiom named fact_462_listrelp__listrel__eq
% A new axiom: (forall (R_5:(produc1501160679le_alt->Prop)) (X_2:list_A2115238852le_alt) (Xa:list_A2115238852le_alt), ((iff (((listre1213162009le_alt (fun (Y_1:arrow_475358991le_alt) (Z:arrow_475358991le_alt)=> ((member214075476le_alt ((produc1347929815le_alt Y_1) Z)) R_5))) X_2) Xa)) ((member28618436le_alt ((produc776457805le_alt X_2) Xa)) (listre1920655591le_alt R_5))))
% FOF formula (forall (R_5:(produc1362454231le_alt->Prop)) (X_2:list_l1475218533le_alt) (Xa:list_l1475218533le_alt), ((iff (((listre816681018le_alt (fun (Y_1:list_A2115238852le_alt) (Z:list_A2115238852le_alt)=> ((member28618436le_alt ((produc776457805le_alt Y_1) Z)) R_5))) X_2) Xa)) ((member1732936276le_alt ((produc1317709143le_alt X_2) Xa)) (listre623166444le_alt R_5)))) of role axiom named fact_463_listrelp__listrel__eq
% A new axiom: (forall (R_5:(produc1362454231le_alt->Prop)) (X_2:list_l1475218533le_alt) (Xa:list_l1475218533le_alt), ((iff (((listre816681018le_alt (fun (Y_1:list_A2115238852le_alt) (Z:list_A2115238852le_alt)=> ((member28618436le_alt ((produc776457805le_alt Y_1) Z)) R_5))) X_2) Xa)) ((member1732936276le_alt ((produc1317709143le_alt X_2) Xa)) (listre623166444le_alt R_5))))
% FOF formula (forall (Xs_45:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_45) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (rotate335349260le_alt Xs_45)) ((append179082452le_alt (tl_Arr465451158le_alt Xs_45)) ((cons_A228743023le_alt (hd_Arr1965683346le_alt Xs_45)) nil_Ar1286194111le_alt))))) of role axiom named fact_464_rotate1__hd__tl
% A new axiom: (forall (Xs_45:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_45) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (rotate335349260le_alt Xs_45)) ((append179082452le_alt (tl_Arr465451158le_alt Xs_45)) ((cons_A228743023le_alt (hd_Arr1965683346le_alt Xs_45)) nil_Ar1286194111le_alt)))))
% FOF formula (forall (A1_1:list_l1475218533le_alt) (A2_1:list_l1475218533le_alt) (R_4:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt A1_1) A2_1)) (listre623166444le_alt R_4))) ((or ((and (((eq list_l1475218533le_alt) A1_1) nil_li1907286804le_alt)) (((eq list_l1475218533le_alt) A2_1) nil_li1907286804le_alt))) ((ex list_A2115238852le_alt) (fun (X_2:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Y_1:list_A2115238852le_alt)=> ((ex list_l1475218533le_alt) (fun (Xs_21:list_l1475218533le_alt)=> ((ex list_l1475218533le_alt) (fun (Ys:list_l1475218533le_alt)=> ((and ((and ((and (((eq list_l1475218533le_alt) A1_1) ((cons_l635097956le_alt X_2) Xs_21))) (((eq list_l1475218533le_alt) A2_1) ((cons_l635097956le_alt Y_1) Ys)))) ((member28618436le_alt ((produc776457805le_alt X_2) Y_1)) R_4))) ((member1732936276le_alt ((produc1317709143le_alt Xs_21) Ys)) (listre623166444le_alt R_4)))))))))))))) of role axiom named fact_465_listrel_Osimps
% A new axiom: (forall (A1_1:list_l1475218533le_alt) (A2_1:list_l1475218533le_alt) (R_4:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt A1_1) A2_1)) (listre623166444le_alt R_4))) ((or ((and (((eq list_l1475218533le_alt) A1_1) nil_li1907286804le_alt)) (((eq list_l1475218533le_alt) A2_1) nil_li1907286804le_alt))) ((ex list_A2115238852le_alt) (fun (X_2:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Y_1:list_A2115238852le_alt)=> ((ex list_l1475218533le_alt) (fun (Xs_21:list_l1475218533le_alt)=> ((ex list_l1475218533le_alt) (fun (Ys:list_l1475218533le_alt)=> ((and ((and ((and (((eq list_l1475218533le_alt) A1_1) ((cons_l635097956le_alt X_2) Xs_21))) (((eq list_l1475218533le_alt) A2_1) ((cons_l635097956le_alt Y_1) Ys)))) ((member28618436le_alt ((produc776457805le_alt X_2) Y_1)) R_4))) ((member1732936276le_alt ((produc1317709143le_alt Xs_21) Ys)) (listre623166444le_alt R_4))))))))))))))
% FOF formula (forall (A1_1:list_A2115238852le_alt) (A2_1:list_A2115238852le_alt) (R_4:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt A1_1) A2_1)) (listre1920655591le_alt R_4))) ((or ((and (((eq list_A2115238852le_alt) A1_1) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) A2_1) nil_Ar1286194111le_alt))) ((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Xs_21:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> ((and ((and ((and (((eq list_A2115238852le_alt) A1_1) ((cons_A228743023le_alt X_2) Xs_21))) (((eq list_A2115238852le_alt) A2_1) ((cons_A228743023le_alt Y_1) Ys)))) ((member214075476le_alt ((produc1347929815le_alt X_2) Y_1)) R_4))) ((member28618436le_alt ((produc776457805le_alt Xs_21) Ys)) (listre1920655591le_alt R_4)))))))))))))) of role axiom named fact_466_listrel_Osimps
% A new axiom: (forall (A1_1:list_A2115238852le_alt) (A2_1:list_A2115238852le_alt) (R_4:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt A1_1) A2_1)) (listre1920655591le_alt R_4))) ((or ((and (((eq list_A2115238852le_alt) A1_1) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) A2_1) nil_Ar1286194111le_alt))) ((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Xs_21:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> ((and ((and ((and (((eq list_A2115238852le_alt) A1_1) ((cons_A228743023le_alt X_2) Xs_21))) (((eq list_A2115238852le_alt) A2_1) ((cons_A228743023le_alt Y_1) Ys)))) ((member214075476le_alt ((produc1347929815le_alt X_2) Y_1)) R_4))) ((member28618436le_alt ((produc776457805le_alt Xs_21) Ys)) (listre1920655591le_alt R_4))))))))))))))
% FOF formula (forall (X_26:arrow_475358991le_alt) (Xs_44:list_A2115238852le_alt), (((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((cons_A228743023le_alt X_26) Xs_44))) X_26)) of role axiom named fact_467_hd_Osimps
% A new axiom: (forall (X_26:arrow_475358991le_alt) (Xs_44:list_A2115238852le_alt), (((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((cons_A228743023le_alt X_26) Xs_44))) X_26))
% FOF formula (forall (Xs_43:list_A2115238852le_alt) (Ys_11:list_A2115238852le_alt) (R_3:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (X_25:arrow_475358991le_alt) (Y_5:arrow_475358991le_alt), (((R_3 X_25) Y_5)->((((listre1213162009le_alt R_3) Xs_43) Ys_11)->(((listre1213162009le_alt R_3) ((cons_A228743023le_alt X_25) Xs_43)) ((cons_A228743023le_alt Y_5) Ys_11))))) of role axiom named fact_468_listrelp_OCons
% A new axiom: (forall (Xs_43:list_A2115238852le_alt) (Ys_11:list_A2115238852le_alt) (R_3:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (X_25:arrow_475358991le_alt) (Y_5:arrow_475358991le_alt), (((R_3 X_25) Y_5)->((((listre1213162009le_alt R_3) Xs_43) Ys_11)->(((listre1213162009le_alt R_3) ((cons_A228743023le_alt X_25) Xs_43)) ((cons_A228743023le_alt Y_5) Ys_11)))))
% FOF formula (forall (R_2:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))), (((listre1213162009le_alt R_2) nil_Ar1286194111le_alt) nil_Ar1286194111le_alt)) of role axiom named fact_469_listrelp_ONil
% A new axiom: (forall (R_2:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))), (((listre1213162009le_alt R_2) nil_Ar1286194111le_alt) nil_Ar1286194111le_alt))
% FOF formula (forall (Ys_10:list_A2115238852le_alt) (Xs_42:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Xs_42) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((append179082452le_alt Xs_42) Ys_10))) (hd_Arr1965683346le_alt Ys_10)))) ((not (((eq list_A2115238852le_alt) Xs_42) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((append179082452le_alt Xs_42) Ys_10))) (hd_Arr1965683346le_alt Xs_42))))) of role axiom named fact_470_hd__append
% A new axiom: (forall (Ys_10:list_A2115238852le_alt) (Xs_42:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Xs_42) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((append179082452le_alt Xs_42) Ys_10))) (hd_Arr1965683346le_alt Ys_10)))) ((not (((eq list_A2115238852le_alt) Xs_42) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((append179082452le_alt Xs_42) Ys_10))) (hd_Arr1965683346le_alt Xs_42)))))
% FOF formula (forall (Ys_9:list_A2115238852le_alt) (Xs_41:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_41) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((append179082452le_alt Xs_41) Ys_9))) (hd_Arr1965683346le_alt Xs_41)))) of role axiom named fact_471_hd__append2
% A new axiom: (forall (Ys_9:list_A2115238852le_alt) (Xs_41:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_41) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((append179082452le_alt Xs_41) Ys_9))) (hd_Arr1965683346le_alt Xs_41))))
% FOF formula (forall (P_11:(arrow_475358991le_alt->Prop)) (Xs_40:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_11) Xs_40)) nil_Ar1286194111le_alt))->((P_11 (hd_Arr1965683346le_alt ((dropWh1316781920le_alt P_11) Xs_40)))->False))) of role axiom named fact_472_hd__dropWhile
% A new axiom: (forall (P_11:(arrow_475358991le_alt->Prop)) (Xs_40:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_11) Xs_40)) nil_Ar1286194111le_alt))->((P_11 (hd_Arr1965683346le_alt ((dropWh1316781920le_alt P_11) Xs_40)))->False)))
% FOF formula (forall (R_1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A1:list_A2115238852le_alt) (A2:list_A2115238852le_alt), ((iff (((listre1213162009le_alt R_1) A1) A2)) ((or ((and (((eq list_A2115238852le_alt) A1) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) A2) nil_Ar1286194111le_alt))) ((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Xs_21:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> ((and ((and ((and (((eq list_A2115238852le_alt) A1) ((cons_A228743023le_alt X_2) Xs_21))) (((eq list_A2115238852le_alt) A2) ((cons_A228743023le_alt Y_1) Ys)))) ((R_1 X_2) Y_1))) (((listre1213162009le_alt R_1) Xs_21) Ys))))))))))))) of role axiom named fact_473_listrelp_Osimps
% A new axiom: (forall (R_1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A1:list_A2115238852le_alt) (A2:list_A2115238852le_alt), ((iff (((listre1213162009le_alt R_1) A1) A2)) ((or ((and (((eq list_A2115238852le_alt) A1) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) A2) nil_Ar1286194111le_alt))) ((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Xs_21:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> ((and ((and ((and (((eq list_A2115238852le_alt) A1) ((cons_A228743023le_alt X_2) Xs_21))) (((eq list_A2115238852le_alt) A2) ((cons_A228743023le_alt Y_1) Ys)))) ((R_1 X_2) Y_1))) (((listre1213162009le_alt R_1) Xs_21) Ys)))))))))))))
% FOF formula (((eq (list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) equal_484611810le_alt) fequal781288069le_alt) of role axiom named fact_474_equal
% A new axiom: (((eq (list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) equal_484611810le_alt) fequal781288069le_alt)
% FOF formula (forall (X_24:list_A2115238852le_alt), ((equal_484611810le_alt X_24) X_24)) of role axiom named fact_475_equal__refl
% A new axiom: (forall (X_24:list_A2115238852le_alt), ((equal_484611810le_alt X_24) X_24))
% FOF formula (forall (X_23:list_A2115238852le_alt) (Y_4:list_A2115238852le_alt), ((iff ((equal_484611810le_alt X_23) Y_4)) (((eq list_A2115238852le_alt) X_23) Y_4))) of role axiom named fact_476_equal__eq
% A new axiom: (forall (X_23:list_A2115238852le_alt) (Y_4:list_A2115238852le_alt), ((iff ((equal_484611810le_alt X_23) Y_4)) (((eq list_A2115238852le_alt) X_23) Y_4)))
% FOF formula (((eq (list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) fequal781288069le_alt) equal_484611810le_alt) of role axiom named fact_477_eq__equal
% A new axiom: (((eq (list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) fequal781288069le_alt) equal_484611810le_alt)
% FOF formula (forall (Xs_39:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_39) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt (rev_Ar1106406943le_alt Xs_39))) (hd_Arr1965683346le_alt Xs_39)))) of role axiom named fact_478_last__rev
% A new axiom: (forall (Xs_39:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_39) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt (rev_Ar1106406943le_alt Xs_39))) (hd_Arr1965683346le_alt Xs_39))))
% FOF formula (forall (Xs_38:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_38) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt (rev_Ar1106406943le_alt Xs_38))) (last_A1217315288le_alt Xs_38)))) of role axiom named fact_479_hd__rev
% A new axiom: (forall (Xs_38:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_38) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt (rev_Ar1106406943le_alt Xs_38))) (last_A1217315288le_alt Xs_38))))
% FOF formula (forall (I_3:nat) (X_22:arrow_475358991le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((replic1511538809le_alt I_3) X_22)) ((cons_A228743023le_alt X_22) nil_Ar1286194111le_alt))) ((cons_A228743023le_alt X_22) ((replic1511538809le_alt I_3) X_22)))) of role axiom named fact_480_replicate__append__same
% A new axiom: (forall (I_3:nat) (X_22:arrow_475358991le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((replic1511538809le_alt I_3) X_22)) ((cons_A228743023le_alt X_22) nil_Ar1286194111le_alt))) ((cons_A228743023le_alt X_22) ((replic1511538809le_alt I_3) X_22))))
% FOF formula (forall (P_10:(arrow_475358991le_alt->Prop)) (Xs_37:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_10) Xs_37)) ((drop_A1346709759le_alt (size_s1858781230le_alt ((takeWh1696291512le_alt P_10) Xs_37))) Xs_37))) of role axiom named fact_481_dropWhile__eq__drop
% A new axiom: (forall (P_10:(arrow_475358991le_alt->Prop)) (Xs_37:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_10) Xs_37)) ((drop_A1346709759le_alt (size_s1858781230le_alt ((takeWh1696291512le_alt P_10) Xs_37))) Xs_37)))
% FOF formula (forall (N_7:nat) (Xs_36:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (butlas274947851le_alt ((drop_A1346709759le_alt N_7) Xs_36))) ((drop_A1346709759le_alt N_7) (butlas274947851le_alt Xs_36)))) of role axiom named fact_482_butlast__drop
% A new axiom: (forall (N_7:nat) (Xs_36:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (butlas274947851le_alt ((drop_A1346709759le_alt N_7) Xs_36))) ((drop_A1346709759le_alt N_7) (butlas274947851le_alt Xs_36))))
% FOF formula (forall (N_6:nat) (Xs_35:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((drop_A1346709759le_alt N_6) (butlas274947851le_alt Xs_35))) (butlas274947851le_alt ((drop_A1346709759le_alt N_6) Xs_35)))) of role axiom named fact_483_drop__butlast
% A new axiom: (forall (N_6:nat) (Xs_35:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((drop_A1346709759le_alt N_6) (butlas274947851le_alt Xs_35))) (butlas274947851le_alt ((drop_A1346709759le_alt N_6) Xs_35))))
% FOF formula (forall (N_5:nat), (((eq list_A2115238852le_alt) ((drop_A1346709759le_alt N_5) nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt)) of role axiom named fact_484_drop__Nil
% A new axiom: (forall (N_5:nat), (((eq list_A2115238852le_alt) ((drop_A1346709759le_alt N_5) nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt))
% FOF formula (forall (I_2:nat) (Xs_34:list_A2115238852le_alt), ((distin236324274le_alt Xs_34)->(distin236324274le_alt ((drop_A1346709759le_alt I_2) Xs_34)))) of role axiom named fact_485_distinct__drop
% A new axiom: (forall (I_2:nat) (Xs_34:list_A2115238852le_alt), ((distin236324274le_alt Xs_34)->(distin236324274le_alt ((drop_A1346709759le_alt I_2) Xs_34))))
% FOF formula (forall (Xs_33:list_A2115238852le_alt) (Ys_8:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt ((append179082452le_alt Xs_33) Ys_8))) ((append179082452le_alt (rev_Ar1106406943le_alt Ys_8)) (rev_Ar1106406943le_alt Xs_33)))) of role axiom named fact_486_rev__append
% A new axiom: (forall (Xs_33:list_A2115238852le_alt) (Ys_8:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt ((append179082452le_alt Xs_33) Ys_8))) ((append179082452le_alt (rev_Ar1106406943le_alt Ys_8)) (rev_Ar1106406943le_alt Xs_33))))
% FOF formula (forall (Xs_32:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_32)) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Xs_32) nil_Ar1286194111le_alt))) of role axiom named fact_487_rev__is__Nil__conv
% A new axiom: (forall (Xs_32:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_32)) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Xs_32) nil_Ar1286194111le_alt)))
% FOF formula (forall (Xs_31:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) nil_Ar1286194111le_alt) (rev_Ar1106406943le_alt Xs_31))) (((eq list_A2115238852le_alt) Xs_31) nil_Ar1286194111le_alt))) of role axiom named fact_488_Nil__is__rev__conv
% A new axiom: (forall (Xs_31:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) nil_Ar1286194111le_alt) (rev_Ar1106406943le_alt Xs_31))) (((eq list_A2115238852le_alt) Xs_31) nil_Ar1286194111le_alt)))
% FOF formula (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt) of role axiom named fact_489_rev_Osimps_I1_J
% A new axiom: (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt)
% FOF formula (forall (N_4:nat) (X_21:arrow_475358991le_alt) (K_1:nat), (((eq list_A2115238852le_alt) ((append179082452le_alt ((replic1511538809le_alt N_4) X_21)) ((replic1511538809le_alt K_1) X_21))) ((append179082452le_alt ((replic1511538809le_alt K_1) X_21)) ((replic1511538809le_alt N_4) X_21)))) of role axiom named fact_490_append__replicate__commute
% A new axiom: (forall (N_4:nat) (X_21:arrow_475358991le_alt) (K_1:nat), (((eq list_A2115238852le_alt) ((append179082452le_alt ((replic1511538809le_alt N_4) X_21)) ((replic1511538809le_alt K_1) X_21))) ((append179082452le_alt ((replic1511538809le_alt K_1) X_21)) ((replic1511538809le_alt N_4) X_21))))
% FOF formula (forall (Xs_30:list_A2115238852le_alt), ((iff (distin236324274le_alt (rev_Ar1106406943le_alt Xs_30))) (distin236324274le_alt Xs_30))) of role axiom named fact_491_distinct__rev
% A new axiom: (forall (Xs_30:list_A2115238852le_alt), ((iff (distin236324274le_alt (rev_Ar1106406943le_alt Xs_30))) (distin236324274le_alt Xs_30)))
% FOF formula (forall (Xs_29:list_A2115238852le_alt) (X_20:arrow_475358991le_alt), ((iff (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_29)) ((cons_A228743023le_alt X_20) nil_Ar1286194111le_alt))) (((eq list_A2115238852le_alt) Xs_29) ((cons_A228743023le_alt X_20) nil_Ar1286194111le_alt)))) of role axiom named fact_492_rev__singleton__conv
% A new axiom: (forall (Xs_29:list_A2115238852le_alt) (X_20:arrow_475358991le_alt), ((iff (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_29)) ((cons_A228743023le_alt X_20) nil_Ar1286194111le_alt))) (((eq list_A2115238852le_alt) Xs_29) ((cons_A228743023le_alt X_20) nil_Ar1286194111le_alt))))
% FOF formula (forall (X_19:arrow_475358991le_alt) (Xs_28:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_19) nil_Ar1286194111le_alt)) (rev_Ar1106406943le_alt Xs_28))) (((eq list_A2115238852le_alt) Xs_28) ((cons_A228743023le_alt X_19) nil_Ar1286194111le_alt)))) of role axiom named fact_493_singleton__rev__conv
% A new axiom: (forall (X_19:arrow_475358991le_alt) (Xs_28:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_19) nil_Ar1286194111le_alt)) (rev_Ar1106406943le_alt Xs_28))) (((eq list_A2115238852le_alt) Xs_28) ((cons_A228743023le_alt X_19) nil_Ar1286194111le_alt))))
% FOF formula (forall (N_3:nat) (X_18:arrow_475358991le_alt) (Xs_27:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((replic1511538809le_alt N_3) X_18)) ((cons_A228743023le_alt X_18) Xs_27))) ((cons_A228743023le_alt X_18) ((append179082452le_alt ((replic1511538809le_alt N_3) X_18)) Xs_27)))) of role axiom named fact_494_replicate__app__Cons__same
% A new axiom: (forall (N_3:nat) (X_18:arrow_475358991le_alt) (Xs_27:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((replic1511538809le_alt N_3) X_18)) ((cons_A228743023le_alt X_18) Xs_27))) ((cons_A228743023le_alt X_18) ((append179082452le_alt ((replic1511538809le_alt N_3) X_18)) Xs_27))))
% FOF formula (forall (X_17:arrow_475358991le_alt) (Xs_26:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt ((cons_A228743023le_alt X_17) Xs_26))) ((append179082452le_alt (rev_Ar1106406943le_alt Xs_26)) ((cons_A228743023le_alt X_17) nil_Ar1286194111le_alt)))) of role axiom named fact_495_rev_Osimps_I2_J
% A new axiom: (forall (X_17:arrow_475358991le_alt) (Xs_26:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt ((cons_A228743023le_alt X_17) Xs_26))) ((append179082452le_alt (rev_Ar1106406943le_alt Xs_26)) ((cons_A228743023le_alt X_17) nil_Ar1286194111le_alt))))
% FOF formula (forall (Xs_25:list_A2115238852le_alt) (Y_3:arrow_475358991le_alt) (Ys_7:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_25)) ((cons_A228743023le_alt Y_3) Ys_7))) (((eq list_A2115238852le_alt) Xs_25) ((append179082452le_alt (rev_Ar1106406943le_alt Ys_7)) ((cons_A228743023le_alt Y_3) nil_Ar1286194111le_alt))))) of role axiom named fact_496_rev__eq__Cons__iff
% A new axiom: (forall (Xs_25:list_A2115238852le_alt) (Y_3:arrow_475358991le_alt) (Ys_7:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_25)) ((cons_A228743023le_alt Y_3) Ys_7))) (((eq list_A2115238852le_alt) Xs_25) ((append179082452le_alt (rev_Ar1106406943le_alt Ys_7)) ((cons_A228743023le_alt Y_3) nil_Ar1286194111le_alt)))))
% FOF formula (forall (X_16:arrow_475358991le_alt) (Xs_24:list_A2115238852le_alt), ((distin236324274le_alt Xs_24)->(((member84363362le_alt X_16) (set_Ar577454304le_alt Xs_24))->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_16)))) (rev_Ar1106406943le_alt Xs_24))) (rev_Ar1106406943le_alt (tl_Arr465451158le_alt ((dropWh1316781920le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_16)))) Xs_24))))))) of role axiom named fact_497_takeWhile__neq__rev
% A new axiom: (forall (X_16:arrow_475358991le_alt) (Xs_24:list_A2115238852le_alt), ((distin236324274le_alt Xs_24)->(((member84363362le_alt X_16) (set_Ar577454304le_alt Xs_24))->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_16)))) (rev_Ar1106406943le_alt Xs_24))) (rev_Ar1106406943le_alt (tl_Arr465451158le_alt ((dropWh1316781920le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_16)))) Xs_24)))))))
% FOF formula (forall (X_16:produc1362454231le_alt) (Xs_24:list_P1295265784le_alt), ((distin561495412le_alt Xs_24)->(((member28618436le_alt X_16) (set_Pr412222150le_alt Xs_24))->(((eq list_P1295265784le_alt) ((takeWh1571807982le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_16)))) (rev_Pr1619606471le_alt Xs_24))) (rev_Pr1619606471le_alt (tl_Pro1448262032le_alt ((dropWh612508742le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_16)))) Xs_24))))))) of role axiom named fact_498_takeWhile__neq__rev
% A new axiom: (forall (X_16:produc1362454231le_alt) (Xs_24:list_P1295265784le_alt), ((distin561495412le_alt Xs_24)->(((member28618436le_alt X_16) (set_Pr412222150le_alt Xs_24))->(((eq list_P1295265784le_alt) ((takeWh1571807982le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_16)))) (rev_Pr1619606471le_alt Xs_24))) (rev_Pr1619606471le_alt (tl_Pro1448262032le_alt ((dropWh612508742le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_16)))) Xs_24)))))))
% FOF formula (forall (X_16:arrow_1429601828e_indi) (Xs_24:list_A1484739013e_indi), ((distin1916799041e_indi Xs_24)->(((member2052026769e_indi X_16) (set_Ar778541203e_indi Xs_24))->(((eq list_A1484739013e_indi) ((takeWh831911099e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_16)))) (rev_Ar501922580e_indi Xs_24))) (rev_Ar501922580e_indi (tl_Arr25726557e_indi ((dropWh1160116755e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_16)))) Xs_24))))))) of role axiom named fact_499_takeWhile__neq__rev
% A new axiom: (forall (X_16:arrow_1429601828e_indi) (Xs_24:list_A1484739013e_indi), ((distin1916799041e_indi Xs_24)->(((member2052026769e_indi X_16) (set_Ar778541203e_indi Xs_24))->(((eq list_A1484739013e_indi) ((takeWh831911099e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_16)))) (rev_Ar501922580e_indi Xs_24))) (rev_Ar501922580e_indi (tl_Arr25726557e_indi ((dropWh1160116755e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_16)))) Xs_24)))))))
% FOF formula (forall (X_16:Prop) (Xs_24:list_o), ((distinct_o Xs_24)->(((member_o X_16) (set_o Xs_24))->(((eq list_o) ((takeWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_16)))) (rev_o Xs_24))) (rev_o (tl_o ((dropWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_16)))) Xs_24))))))) of role axiom named fact_500_takeWhile__neq__rev
% A new axiom: (forall (X_16:Prop) (Xs_24:list_o), ((distinct_o Xs_24)->(((member_o X_16) (set_o Xs_24))->(((eq list_o) ((takeWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_16)))) (rev_o Xs_24))) (rev_o (tl_o ((dropWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_16)))) Xs_24)))))))
% FOF formula (forall (X_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_24:list_A518015091_alt_o), ((distin1908010863_alt_o Xs_24)->(((member616898751_alt_o X_16) (set_Ar1356274881_alt_o Xs_24))->(((eq list_A518015091_alt_o) ((takeWh877796585_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_16)))) (rev_Ar5548482_alt_o Xs_24))) (rev_Ar5548482_alt_o (tl_Arr2017860491_alt_o ((dropWh583351873_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_16)))) Xs_24))))))) of role axiom named fact_501_takeWhile__neq__rev
% A new axiom: (forall (X_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_24:list_A518015091_alt_o), ((distin1908010863_alt_o Xs_24)->(((member616898751_alt_o X_16) (set_Ar1356274881_alt_o Xs_24))->(((eq list_A518015091_alt_o) ((takeWh877796585_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_16)))) (rev_Ar5548482_alt_o Xs_24))) (rev_Ar5548482_alt_o (tl_Arr2017860491_alt_o ((dropWh583351873_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_16)))) Xs_24)))))))
% FOF formula (forall (X_16:(produc1501160679le_alt->Prop)) (Xs_24:list_P1178103901_alt_o), ((distin1582710603_alt_o Xs_24)->(((member377231867_alt_o X_16) (set_Pr592386425_alt_o Xs_24))->(((eq list_P1178103901_alt_o) ((takeWh1715715921_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_16)))) (rev_Pr1006783032_alt_o Xs_24))) (rev_Pr1006783032_alt_o (tl_Pro1735316527_alt_o ((dropWh1049991161_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_16)))) Xs_24))))))) of role axiom named fact_502_takeWhile__neq__rev
% A new axiom: (forall (X_16:(produc1501160679le_alt->Prop)) (Xs_24:list_P1178103901_alt_o), ((distin1582710603_alt_o Xs_24)->(((member377231867_alt_o X_16) (set_Pr592386425_alt_o Xs_24))->(((eq list_P1178103901_alt_o) ((takeWh1715715921_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_16)))) (rev_Pr1006783032_alt_o Xs_24))) (rev_Pr1006783032_alt_o (tl_Pro1735316527_alt_o ((dropWh1049991161_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_16)))) Xs_24)))))))
% FOF formula (forall (X_16:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_24:list_A524553945_alt_o), ((distin1869760583_alt_o Xs_24)->(((member526088951_alt_o X_16) (set_Ar571341173_alt_o Xs_24))->(((eq list_A524553945_alt_o) ((takeWh1825606477_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_16)))) (rev_Ar413755828_alt_o Xs_24))) (rev_Ar413755828_alt_o (tl_Arr1704054571_alt_o ((dropWh73644021_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_16)))) Xs_24))))))) of role axiom named fact_503_takeWhile__neq__rev
% A new axiom: (forall (X_16:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_24:list_A524553945_alt_o), ((distin1869760583_alt_o Xs_24)->(((member526088951_alt_o X_16) (set_Ar571341173_alt_o Xs_24))->(((eq list_A524553945_alt_o) ((takeWh1825606477_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_16)))) (rev_Ar413755828_alt_o Xs_24))) (rev_Ar413755828_alt_o (tl_Arr1704054571_alt_o ((dropWh73644021_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_16)))) Xs_24)))))))
% FOF formula (forall (X_16:produc1501160679le_alt) (Xs_24:list_P736798472le_alt), ((distin1776819972le_alt Xs_24)->(((member214075476le_alt X_16) (set_Pr1525059414le_alt Xs_24))->(((eq list_P736798472le_alt) ((takeWh302148478le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_16)))) (rev_Pr1216324055le_alt Xs_24))) (rev_Pr1216324055le_alt (tl_Pro932635936le_alt ((dropWh680325334le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_16)))) Xs_24))))))) of role axiom named fact_504_takeWhile__neq__rev
% A new axiom: (forall (X_16:produc1501160679le_alt) (Xs_24:list_P736798472le_alt), ((distin1776819972le_alt Xs_24)->(((member214075476le_alt X_16) (set_Pr1525059414le_alt Xs_24))->(((eq list_P736798472le_alt) ((takeWh302148478le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_16)))) (rev_Pr1216324055le_alt Xs_24))) (rev_Pr1216324055le_alt (tl_Pro932635936le_alt ((dropWh680325334le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_16)))) Xs_24)))))))
% FOF formula (forall (X_15:arrow_475358991le_alt) (Xs_23:list_A2115238852le_alt), ((distin236324274le_alt Xs_23)->(((member84363362le_alt X_15) (set_Ar577454304le_alt Xs_23))->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_15)))) (rev_Ar1106406943le_alt Xs_23))) ((cons_A228743023le_alt X_15) (rev_Ar1106406943le_alt ((takeWh1696291512le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_15)))) Xs_23))))))) of role axiom named fact_505_dropWhile__neq__rev
% A new axiom: (forall (X_15:arrow_475358991le_alt) (Xs_23:list_A2115238852le_alt), ((distin236324274le_alt Xs_23)->(((member84363362le_alt X_15) (set_Ar577454304le_alt Xs_23))->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_15)))) (rev_Ar1106406943le_alt Xs_23))) ((cons_A228743023le_alt X_15) (rev_Ar1106406943le_alt ((takeWh1696291512le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_15)))) Xs_23)))))))
% FOF formula (forall (X_15:produc1362454231le_alt) (Xs_23:list_P1295265784le_alt), ((distin561495412le_alt Xs_23)->(((member28618436le_alt X_15) (set_Pr412222150le_alt Xs_23))->(((eq list_P1295265784le_alt) ((dropWh612508742le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_15)))) (rev_Pr1619606471le_alt Xs_23))) ((cons_P2048401015le_alt X_15) (rev_Pr1619606471le_alt ((takeWh1571807982le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_15)))) Xs_23))))))) of role axiom named fact_506_dropWhile__neq__rev
% A new axiom: (forall (X_15:produc1362454231le_alt) (Xs_23:list_P1295265784le_alt), ((distin561495412le_alt Xs_23)->(((member28618436le_alt X_15) (set_Pr412222150le_alt Xs_23))->(((eq list_P1295265784le_alt) ((dropWh612508742le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_15)))) (rev_Pr1619606471le_alt Xs_23))) ((cons_P2048401015le_alt X_15) (rev_Pr1619606471le_alt ((takeWh1571807982le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_15)))) Xs_23)))))))
% FOF formula (forall (X_15:arrow_1429601828e_indi) (Xs_23:list_A1484739013e_indi), ((distin1916799041e_indi Xs_23)->(((member2052026769e_indi X_15) (set_Ar778541203e_indi Xs_23))->(((eq list_A1484739013e_indi) ((dropWh1160116755e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_15)))) (rev_Ar501922580e_indi Xs_23))) ((cons_A663037380e_indi X_15) (rev_Ar501922580e_indi ((takeWh831911099e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_15)))) Xs_23))))))) of role axiom named fact_507_dropWhile__neq__rev
% A new axiom: (forall (X_15:arrow_1429601828e_indi) (Xs_23:list_A1484739013e_indi), ((distin1916799041e_indi Xs_23)->(((member2052026769e_indi X_15) (set_Ar778541203e_indi Xs_23))->(((eq list_A1484739013e_indi) ((dropWh1160116755e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_15)))) (rev_Ar501922580e_indi Xs_23))) ((cons_A663037380e_indi X_15) (rev_Ar501922580e_indi ((takeWh831911099e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_15)))) Xs_23)))))))
% FOF formula (forall (X_15:Prop) (Xs_23:list_o), ((distinct_o Xs_23)->(((member_o X_15) (set_o Xs_23))->(((eq list_o) ((dropWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_15)))) (rev_o Xs_23))) ((cons_o X_15) (rev_o ((takeWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_15)))) Xs_23))))))) of role axiom named fact_508_dropWhile__neq__rev
% A new axiom: (forall (X_15:Prop) (Xs_23:list_o), ((distinct_o Xs_23)->(((member_o X_15) (set_o Xs_23))->(((eq list_o) ((dropWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_15)))) (rev_o Xs_23))) ((cons_o X_15) (rev_o ((takeWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_15)))) Xs_23)))))))
% FOF formula (forall (X_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_23:list_A518015091_alt_o), ((distin1908010863_alt_o Xs_23)->(((member616898751_alt_o X_15) (set_Ar1356274881_alt_o Xs_23))->(((eq list_A518015091_alt_o) ((dropWh583351873_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_15)))) (rev_Ar5548482_alt_o Xs_23))) ((cons_A279268466_alt_o X_15) (rev_Ar5548482_alt_o ((takeWh877796585_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_15)))) Xs_23))))))) of role axiom named fact_509_dropWhile__neq__rev
% A new axiom: (forall (X_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_23:list_A518015091_alt_o), ((distin1908010863_alt_o Xs_23)->(((member616898751_alt_o X_15) (set_Ar1356274881_alt_o Xs_23))->(((eq list_A518015091_alt_o) ((dropWh583351873_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_15)))) (rev_Ar5548482_alt_o Xs_23))) ((cons_A279268466_alt_o X_15) (rev_Ar5548482_alt_o ((takeWh877796585_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_15)))) Xs_23)))))))
% FOF formula (forall (X_15:(produc1501160679le_alt->Prop)) (Xs_23:list_P1178103901_alt_o), ((distin1582710603_alt_o Xs_23)->(((member377231867_alt_o X_15) (set_Pr592386425_alt_o Xs_23))->(((eq list_P1178103901_alt_o) ((dropWh1049991161_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_15)))) (rev_Pr1006783032_alt_o Xs_23))) ((cons_P1239653256_alt_o X_15) (rev_Pr1006783032_alt_o ((takeWh1715715921_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_15)))) Xs_23))))))) of role axiom named fact_510_dropWhile__neq__rev
% A new axiom: (forall (X_15:(produc1501160679le_alt->Prop)) (Xs_23:list_P1178103901_alt_o), ((distin1582710603_alt_o Xs_23)->(((member377231867_alt_o X_15) (set_Pr592386425_alt_o Xs_23))->(((eq list_P1178103901_alt_o) ((dropWh1049991161_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_15)))) (rev_Pr1006783032_alt_o Xs_23))) ((cons_P1239653256_alt_o X_15) (rev_Pr1006783032_alt_o ((takeWh1715715921_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_15)))) Xs_23)))))))
% FOF formula (forall (X_15:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_23:list_A524553945_alt_o), ((distin1869760583_alt_o Xs_23)->(((member526088951_alt_o X_15) (set_Ar571341173_alt_o Xs_23))->(((eq list_A524553945_alt_o) ((dropWh73644021_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_15)))) (rev_Ar413755828_alt_o Xs_23))) ((cons_A2010997508_alt_o X_15) (rev_Ar413755828_alt_o ((takeWh1825606477_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_15)))) Xs_23))))))) of role axiom named fact_511_dropWhile__neq__rev
% A new axiom: (forall (X_15:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_23:list_A524553945_alt_o), ((distin1869760583_alt_o Xs_23)->(((member526088951_alt_o X_15) (set_Ar571341173_alt_o Xs_23))->(((eq list_A524553945_alt_o) ((dropWh73644021_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_15)))) (rev_Ar413755828_alt_o Xs_23))) ((cons_A2010997508_alt_o X_15) (rev_Ar413755828_alt_o ((takeWh1825606477_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_15)))) Xs_23)))))))
% FOF formula (forall (X_15:produc1501160679le_alt) (Xs_23:list_P736798472le_alt), ((distin1776819972le_alt Xs_23)->(((member214075476le_alt X_15) (set_Pr1525059414le_alt Xs_23))->(((eq list_P736798472le_alt) ((dropWh680325334le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_15)))) (rev_Pr1216324055le_alt Xs_23))) ((cons_P1913588871le_alt X_15) (rev_Pr1216324055le_alt ((takeWh302148478le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_15)))) Xs_23))))))) of role axiom named fact_512_dropWhile__neq__rev
% A new axiom: (forall (X_15:produc1501160679le_alt) (Xs_23:list_P736798472le_alt), ((distin1776819972le_alt Xs_23)->(((member214075476le_alt X_15) (set_Pr1525059414le_alt Xs_23))->(((eq list_P736798472le_alt) ((dropWh680325334le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_15)))) (rev_Pr1216324055le_alt Xs_23))) ((cons_P1913588871le_alt X_15) (rev_Pr1216324055le_alt ((takeWh302148478le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_15)))) Xs_23)))))))
% FOF formula (forall (N_2:nat) (X_14:arrow_475358991le_alt) (Xs_22:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((drop_A1346709759le_alt N_2) ((cons_A228743023le_alt X_14) Xs_22))) (((nat_ca2147365008le_alt ((cons_A228743023le_alt X_14) Xs_22)) (fun (M_1:nat)=> ((drop_A1346709759le_alt M_1) Xs_22))) N_2))) of role axiom named fact_513_drop__Cons
% A new axiom: (forall (N_2:nat) (X_14:arrow_475358991le_alt) (Xs_22:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((drop_A1346709759le_alt N_2) ((cons_A228743023le_alt X_14) Xs_22))) (((nat_ca2147365008le_alt ((cons_A228743023le_alt X_14) Xs_22)) (fun (M_1:nat)=> ((drop_A1346709759le_alt M_1) Xs_22))) N_2)))
% FOF formula (forall (Xs_20:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_20)) (((foldl_296410428le_alt (fun (Xs_21:list_A2115238852le_alt) (X_2:arrow_475358991le_alt)=> ((cons_A228743023le_alt X_2) Xs_21))) nil_Ar1286194111le_alt) Xs_20))) of role axiom named fact_514_rev__foldl__cons
% A new axiom: (forall (Xs_20:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_20)) (((foldl_296410428le_alt (fun (Xs_21:list_A2115238852le_alt) (X_2:arrow_475358991le_alt)=> ((cons_A228743023le_alt X_2) Xs_21))) nil_Ar1286194111le_alt) Xs_20)))
% FOF formula (forall (X_13:arrow_475358991le_alt) (N_1:nat) (Xs_19:list_A2115238852le_alt), (((member84363362le_alt X_13) (set_Ar577454304le_alt ((drop_A1346709759le_alt N_1) Xs_19)))->((member84363362le_alt X_13) (set_Ar577454304le_alt Xs_19)))) of role axiom named fact_515_in__set__dropD
% A new axiom: (forall (X_13:arrow_475358991le_alt) (N_1:nat) (Xs_19:list_A2115238852le_alt), (((member84363362le_alt X_13) (set_Ar577454304le_alt ((drop_A1346709759le_alt N_1) Xs_19)))->((member84363362le_alt X_13) (set_Ar577454304le_alt Xs_19))))
% FOF formula (forall (X_13:produc1362454231le_alt) (N_1:nat) (Xs_19:list_P1295265784le_alt), (((member28618436le_alt X_13) (set_Pr412222150le_alt ((drop_P1438419175le_alt N_1) Xs_19)))->((member28618436le_alt X_13) (set_Pr412222150le_alt Xs_19)))) of role axiom named fact_516_in__set__dropD
% A new axiom: (forall (X_13:produc1362454231le_alt) (N_1:nat) (Xs_19:list_P1295265784le_alt), (((member28618436le_alt X_13) (set_Pr412222150le_alt ((drop_P1438419175le_alt N_1) Xs_19)))->((member28618436le_alt X_13) (set_Pr412222150le_alt Xs_19))))
% FOF formula (forall (X_13:arrow_1429601828e_indi) (N_1:nat) (Xs_19:list_A1484739013e_indi), (((member2052026769e_indi X_13) (set_Ar778541203e_indi ((drop_A1596373044e_indi N_1) Xs_19)))->((member2052026769e_indi X_13) (set_Ar778541203e_indi Xs_19)))) of role axiom named fact_517_in__set__dropD
% A new axiom: (forall (X_13:arrow_1429601828e_indi) (N_1:nat) (Xs_19:list_A1484739013e_indi), (((member2052026769e_indi X_13) (set_Ar778541203e_indi ((drop_A1596373044e_indi N_1) Xs_19)))->((member2052026769e_indi X_13) (set_Ar778541203e_indi Xs_19))))
% FOF formula (forall (X_13:Prop) (N_1:nat) (Xs_19:list_o), (((member_o X_13) (set_o ((drop_o N_1) Xs_19)))->((member_o X_13) (set_o Xs_19)))) of role axiom named fact_518_in__set__dropD
% A new axiom: (forall (X_13:Prop) (N_1:nat) (Xs_19:list_o), (((member_o X_13) (set_o ((drop_o N_1) Xs_19)))->((member_o X_13) (set_o Xs_19))))
% FOF formula (forall (X_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (N_1:nat) (Xs_19:list_A518015091_alt_o), (((member616898751_alt_o X_13) (set_Ar1356274881_alt_o ((drop_A1326872290_alt_o N_1) Xs_19)))->((member616898751_alt_o X_13) (set_Ar1356274881_alt_o Xs_19)))) of role axiom named fact_519_in__set__dropD
% A new axiom: (forall (X_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (N_1:nat) (Xs_19:list_A518015091_alt_o), (((member616898751_alt_o X_13) (set_Ar1356274881_alt_o ((drop_A1326872290_alt_o N_1) Xs_19)))->((member616898751_alt_o X_13) (set_Ar1356274881_alt_o Xs_19))))
% FOF formula (forall (X_13:(produc1501160679le_alt->Prop)) (N_1:nat) (Xs_19:list_P1178103901_alt_o), (((member377231867_alt_o X_13) (set_Pr592386425_alt_o ((drop_P619902232_alt_o N_1) Xs_19)))->((member377231867_alt_o X_13) (set_Pr592386425_alt_o Xs_19)))) of role axiom named fact_520_in__set__dropD
% A new axiom: (forall (X_13:(produc1501160679le_alt->Prop)) (N_1:nat) (Xs_19:list_P1178103901_alt_o), (((member377231867_alt_o X_13) (set_Pr592386425_alt_o ((drop_P619902232_alt_o N_1) Xs_19)))->((member377231867_alt_o X_13) (set_Pr592386425_alt_o Xs_19))))
% FOF formula (forall (X_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (N_1:nat) (Xs_19:list_A524553945_alt_o), (((member526088951_alt_o X_13) (set_Ar571341173_alt_o ((drop_A776701076_alt_o N_1) Xs_19)))->((member526088951_alt_o X_13) (set_Ar571341173_alt_o Xs_19)))) of role axiom named fact_521_in__set__dropD
% A new axiom: (forall (X_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (N_1:nat) (Xs_19:list_A524553945_alt_o), (((member526088951_alt_o X_13) (set_Ar571341173_alt_o ((drop_A776701076_alt_o N_1) Xs_19)))->((member526088951_alt_o X_13) (set_Ar571341173_alt_o Xs_19))))
% FOF formula (forall (X_13:produc1501160679le_alt) (N_1:nat) (Xs_19:list_P736798472le_alt), (((member214075476le_alt X_13) (set_Pr1525059414le_alt ((drop_P933863159le_alt N_1) Xs_19)))->((member214075476le_alt X_13) (set_Pr1525059414le_alt Xs_19)))) of role axiom named fact_522_in__set__dropD
% A new axiom: (forall (X_13:produc1501160679le_alt) (N_1:nat) (Xs_19:list_P736798472le_alt), (((member214075476le_alt X_13) (set_Pr1525059414le_alt ((drop_P933863159le_alt N_1) Xs_19)))->((member214075476le_alt X_13) (set_Pr1525059414le_alt Xs_19))))
% FOF formula (forall (X_12:arrow_475358991le_alt) (P_9:(arrow_475358991le_alt->Prop)) (Xs_18:list_A2115238852le_alt), (((member84363362le_alt X_12) (set_Ar577454304le_alt ((takeWh1696291512le_alt P_9) Xs_18)))->((and ((member84363362le_alt X_12) (set_Ar577454304le_alt Xs_18))) (P_9 X_12)))) of role axiom named fact_523_set__takeWhileD
% A new axiom: (forall (X_12:arrow_475358991le_alt) (P_9:(arrow_475358991le_alt->Prop)) (Xs_18:list_A2115238852le_alt), (((member84363362le_alt X_12) (set_Ar577454304le_alt ((takeWh1696291512le_alt P_9) Xs_18)))->((and ((member84363362le_alt X_12) (set_Ar577454304le_alt Xs_18))) (P_9 X_12))))
% FOF formula (forall (X_12:produc1362454231le_alt) (P_9:(produc1362454231le_alt->Prop)) (Xs_18:list_P1295265784le_alt), (((member28618436le_alt X_12) (set_Pr412222150le_alt ((takeWh1571807982le_alt P_9) Xs_18)))->((and ((member28618436le_alt X_12) (set_Pr412222150le_alt Xs_18))) (P_9 X_12)))) of role axiom named fact_524_set__takeWhileD
% A new axiom: (forall (X_12:produc1362454231le_alt) (P_9:(produc1362454231le_alt->Prop)) (Xs_18:list_P1295265784le_alt), (((member28618436le_alt X_12) (set_Pr412222150le_alt ((takeWh1571807982le_alt P_9) Xs_18)))->((and ((member28618436le_alt X_12) (set_Pr412222150le_alt Xs_18))) (P_9 X_12))))
% FOF formula (forall (X_12:arrow_1429601828e_indi) (P_9:(arrow_1429601828e_indi->Prop)) (Xs_18:list_A1484739013e_indi), (((member2052026769e_indi X_12) (set_Ar778541203e_indi ((takeWh831911099e_indi P_9) Xs_18)))->((and ((member2052026769e_indi X_12) (set_Ar778541203e_indi Xs_18))) (P_9 X_12)))) of role axiom named fact_525_set__takeWhileD
% A new axiom: (forall (X_12:arrow_1429601828e_indi) (P_9:(arrow_1429601828e_indi->Prop)) (Xs_18:list_A1484739013e_indi), (((member2052026769e_indi X_12) (set_Ar778541203e_indi ((takeWh831911099e_indi P_9) Xs_18)))->((and ((member2052026769e_indi X_12) (set_Ar778541203e_indi Xs_18))) (P_9 X_12))))
% FOF formula (forall (X_12:Prop) (P_9:(Prop->Prop)) (Xs_18:list_o), (((member_o X_12) (set_o ((takeWhile_o P_9) Xs_18)))->((and ((member_o X_12) (set_o Xs_18))) (P_9 X_12)))) of role axiom named fact_526_set__takeWhileD
% A new axiom: (forall (X_12:Prop) (P_9:(Prop->Prop)) (Xs_18:list_o), (((member_o X_12) (set_o ((takeWhile_o P_9) Xs_18)))->((and ((member_o X_12) (set_o Xs_18))) (P_9 X_12))))
% FOF formula (forall (X_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (P_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (Xs_18:list_A518015091_alt_o), (((member616898751_alt_o X_12) (set_Ar1356274881_alt_o ((takeWh877796585_alt_o P_9) Xs_18)))->((and ((member616898751_alt_o X_12) (set_Ar1356274881_alt_o Xs_18))) (P_9 X_12)))) of role axiom named fact_527_set__takeWhileD
% A new axiom: (forall (X_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (P_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (Xs_18:list_A518015091_alt_o), (((member616898751_alt_o X_12) (set_Ar1356274881_alt_o ((takeWh877796585_alt_o P_9) Xs_18)))->((and ((member616898751_alt_o X_12) (set_Ar1356274881_alt_o Xs_18))) (P_9 X_12))))
% FOF formula (forall (X_12:(produc1501160679le_alt->Prop)) (P_9:((produc1501160679le_alt->Prop)->Prop)) (Xs_18:list_P1178103901_alt_o), (((member377231867_alt_o X_12) (set_Pr592386425_alt_o ((takeWh1715715921_alt_o P_9) Xs_18)))->((and ((member377231867_alt_o X_12) (set_Pr592386425_alt_o Xs_18))) (P_9 X_12)))) of role axiom named fact_528_set__takeWhileD
% A new axiom: (forall (X_12:(produc1501160679le_alt->Prop)) (P_9:((produc1501160679le_alt->Prop)->Prop)) (Xs_18:list_P1178103901_alt_o), (((member377231867_alt_o X_12) (set_Pr592386425_alt_o ((takeWh1715715921_alt_o P_9) Xs_18)))->((and ((member377231867_alt_o X_12) (set_Pr592386425_alt_o Xs_18))) (P_9 X_12))))
% FOF formula (forall (X_12:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (Xs_18:list_A524553945_alt_o), (((member526088951_alt_o X_12) (set_Ar571341173_alt_o ((takeWh1825606477_alt_o P_9) Xs_18)))->((and ((member526088951_alt_o X_12) (set_Ar571341173_alt_o Xs_18))) (P_9 X_12)))) of role axiom named fact_529_set__takeWhileD
% A new axiom: (forall (X_12:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (Xs_18:list_A524553945_alt_o), (((member526088951_alt_o X_12) (set_Ar571341173_alt_o ((takeWh1825606477_alt_o P_9) Xs_18)))->((and ((member526088951_alt_o X_12) (set_Ar571341173_alt_o Xs_18))) (P_9 X_12))))
% FOF formula (forall (X_12:produc1501160679le_alt) (P_9:(produc1501160679le_alt->Prop)) (Xs_18:list_P736798472le_alt), (((member214075476le_alt X_12) (set_Pr1525059414le_alt ((takeWh302148478le_alt P_9) Xs_18)))->((and ((member214075476le_alt X_12) (set_Pr1525059414le_alt Xs_18))) (P_9 X_12)))) of role axiom named fact_530_set__takeWhileD
% A new axiom: (forall (X_12:produc1501160679le_alt) (P_9:(produc1501160679le_alt->Prop)) (Xs_18:list_P736798472le_alt), (((member214075476le_alt X_12) (set_Pr1525059414le_alt ((takeWh302148478le_alt P_9) Xs_18)))->((and ((member214075476le_alt X_12) (set_Pr1525059414le_alt Xs_18))) (P_9 X_12))))
% FOF formula (forall (P_8:(arrow_475358991le_alt->Prop)) (Xs_17:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_8) Xs_17)) Xs_17)) (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_17))->(P_8 X_2))))) of role axiom named fact_531_takeWhile__eq__all__conv
% A new axiom: (forall (P_8:(arrow_475358991le_alt->Prop)) (Xs_17:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_8) Xs_17)) Xs_17)) (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_17))->(P_8 X_2)))))
% FOF formula (forall (X_11:arrow_475358991le_alt) (Xs_16:list_A2115238852le_alt), (((member84363362le_alt X_11) (set_Ar577454304le_alt (butlas274947851le_alt Xs_16)))->((member84363362le_alt X_11) (set_Ar577454304le_alt Xs_16)))) of role axiom named fact_532_in__set__butlastD
% A new axiom: (forall (X_11:arrow_475358991le_alt) (Xs_16:list_A2115238852le_alt), (((member84363362le_alt X_11) (set_Ar577454304le_alt (butlas274947851le_alt Xs_16)))->((member84363362le_alt X_11) (set_Ar577454304le_alt Xs_16))))
% FOF formula (forall (X_11:produc1362454231le_alt) (Xs_16:list_P1295265784le_alt), (((member28618436le_alt X_11) (set_Pr412222150le_alt (butlas464406491le_alt Xs_16)))->((member28618436le_alt X_11) (set_Pr412222150le_alt Xs_16)))) of role axiom named fact_533_in__set__butlastD
% A new axiom: (forall (X_11:produc1362454231le_alt) (Xs_16:list_P1295265784le_alt), (((member28618436le_alt X_11) (set_Pr412222150le_alt (butlas464406491le_alt Xs_16)))->((member28618436le_alt X_11) (set_Pr412222150le_alt Xs_16))))
% FOF formula (forall (X_11:arrow_1429601828e_indi) (Xs_16:list_A1484739013e_indi), (((member2052026769e_indi X_11) (set_Ar778541203e_indi (butlas1554122024e_indi Xs_16)))->((member2052026769e_indi X_11) (set_Ar778541203e_indi Xs_16)))) of role axiom named fact_534_in__set__butlastD
% A new axiom: (forall (X_11:arrow_1429601828e_indi) (Xs_16:list_A1484739013e_indi), (((member2052026769e_indi X_11) (set_Ar778541203e_indi (butlas1554122024e_indi Xs_16)))->((member2052026769e_indi X_11) (set_Ar778541203e_indi Xs_16))))
% FOF formula (forall (X_11:Prop) (Xs_16:list_o), (((member_o X_11) (set_o (butlast_o Xs_16)))->((member_o X_11) (set_o Xs_16)))) of role axiom named fact_535_in__set__butlastD
% A new axiom: (forall (X_11:Prop) (Xs_16:list_o), (((member_o X_11) (set_o (butlast_o Xs_16)))->((member_o X_11) (set_o Xs_16))))
% FOF formula (forall (X_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_16:list_A518015091_alt_o), (((member616898751_alt_o X_11) (set_Ar1356274881_alt_o (butlas1138247126_alt_o Xs_16)))->((member616898751_alt_o X_11) (set_Ar1356274881_alt_o Xs_16)))) of role axiom named fact_536_in__set__butlastD
% A new axiom: (forall (X_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_16:list_A518015091_alt_o), (((member616898751_alt_o X_11) (set_Ar1356274881_alt_o (butlas1138247126_alt_o Xs_16)))->((member616898751_alt_o X_11) (set_Ar1356274881_alt_o Xs_16))))
% FOF formula (forall (X_11:(produc1501160679le_alt->Prop)) (Xs_16:list_P1178103901_alt_o), (((member377231867_alt_o X_11) (set_Pr592386425_alt_o (butlas368541988_alt_o Xs_16)))->((member377231867_alt_o X_11) (set_Pr592386425_alt_o Xs_16)))) of role axiom named fact_537_in__set__butlastD
% A new axiom: (forall (X_11:(produc1501160679le_alt->Prop)) (Xs_16:list_P1178103901_alt_o), (((member377231867_alt_o X_11) (set_Pr592386425_alt_o (butlas368541988_alt_o Xs_16)))->((member377231867_alt_o X_11) (set_Pr592386425_alt_o Xs_16))))
% FOF formula (forall (X_11:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_16:list_A524553945_alt_o), (((member526088951_alt_o X_11) (set_Ar571341173_alt_o (butlas813143712_alt_o Xs_16)))->((member526088951_alt_o X_11) (set_Ar571341173_alt_o Xs_16)))) of role axiom named fact_538_in__set__butlastD
% A new axiom: (forall (X_11:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_16:list_A524553945_alt_o), (((member526088951_alt_o X_11) (set_Ar571341173_alt_o (butlas813143712_alt_o Xs_16)))->((member526088951_alt_o X_11) (set_Ar571341173_alt_o Xs_16))))
% FOF formula (forall (X_11:produc1501160679le_alt) (Xs_16:list_P736798472le_alt), (((member214075476le_alt X_11) (set_Pr1525059414le_alt (butlas661498859le_alt Xs_16)))->((member214075476le_alt X_11) (set_Pr1525059414le_alt Xs_16)))) of role axiom named fact_539_in__set__butlastD
% A new axiom: (forall (X_11:produc1501160679le_alt) (Xs_16:list_P736798472le_alt), (((member214075476le_alt X_11) (set_Pr1525059414le_alt (butlas661498859le_alt Xs_16)))->((member214075476le_alt X_11) (set_Pr1525059414le_alt Xs_16))))
% FOF formula (forall (Y_2:arrow_475358991le_alt) (X_10:arrow_475358991le_alt) (Xs_15:list_A2115238852le_alt), (((member84363362le_alt Y_2) (set_Ar577454304le_alt ((cons_A228743023le_alt X_10) Xs_15)))->((or (((eq arrow_475358991le_alt) Y_2) X_10)) ((member84363362le_alt Y_2) (set_Ar577454304le_alt Xs_15))))) of role axiom named fact_540_set__ConsD
% A new axiom: (forall (Y_2:arrow_475358991le_alt) (X_10:arrow_475358991le_alt) (Xs_15:list_A2115238852le_alt), (((member84363362le_alt Y_2) (set_Ar577454304le_alt ((cons_A228743023le_alt X_10) Xs_15)))->((or (((eq arrow_475358991le_alt) Y_2) X_10)) ((member84363362le_alt Y_2) (set_Ar577454304le_alt Xs_15)))))
% FOF formula (forall (Y_2:produc1362454231le_alt) (X_10:produc1362454231le_alt) (Xs_15:list_P1295265784le_alt), (((member28618436le_alt Y_2) (set_Pr412222150le_alt ((cons_P2048401015le_alt X_10) Xs_15)))->((or (((eq produc1362454231le_alt) Y_2) X_10)) ((member28618436le_alt Y_2) (set_Pr412222150le_alt Xs_15))))) of role axiom named fact_541_set__ConsD
% A new axiom: (forall (Y_2:produc1362454231le_alt) (X_10:produc1362454231le_alt) (Xs_15:list_P1295265784le_alt), (((member28618436le_alt Y_2) (set_Pr412222150le_alt ((cons_P2048401015le_alt X_10) Xs_15)))->((or (((eq produc1362454231le_alt) Y_2) X_10)) ((member28618436le_alt Y_2) (set_Pr412222150le_alt Xs_15)))))
% FOF formula (forall (Y_2:arrow_1429601828e_indi) (X_10:arrow_1429601828e_indi) (Xs_15:list_A1484739013e_indi), (((member2052026769e_indi Y_2) (set_Ar778541203e_indi ((cons_A663037380e_indi X_10) Xs_15)))->((or (((eq arrow_1429601828e_indi) Y_2) X_10)) ((member2052026769e_indi Y_2) (set_Ar778541203e_indi Xs_15))))) of role axiom named fact_542_set__ConsD
% A new axiom: (forall (Y_2:arrow_1429601828e_indi) (X_10:arrow_1429601828e_indi) (Xs_15:list_A1484739013e_indi), (((member2052026769e_indi Y_2) (set_Ar778541203e_indi ((cons_A663037380e_indi X_10) Xs_15)))->((or (((eq arrow_1429601828e_indi) Y_2) X_10)) ((member2052026769e_indi Y_2) (set_Ar778541203e_indi Xs_15)))))
% FOF formula (forall (Y_2:Prop) (X_10:Prop) (Xs_15:list_o), (((member_o Y_2) (set_o ((cons_o X_10) Xs_15)))->((or ((iff Y_2) X_10)) ((member_o Y_2) (set_o Xs_15))))) of role axiom named fact_543_set__ConsD
% A new axiom: (forall (Y_2:Prop) (X_10:Prop) (Xs_15:list_o), (((member_o Y_2) (set_o ((cons_o X_10) Xs_15)))->((or ((iff Y_2) X_10)) ((member_o Y_2) (set_o Xs_15)))))
% FOF formula (forall (Y_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (X_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_15:list_A518015091_alt_o), (((member616898751_alt_o Y_2) (set_Ar1356274881_alt_o ((cons_A279268466_alt_o X_10) Xs_15)))->((or (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_2) X_10)) ((member616898751_alt_o Y_2) (set_Ar1356274881_alt_o Xs_15))))) of role axiom named fact_544_set__ConsD
% A new axiom: (forall (Y_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (X_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_15:list_A518015091_alt_o), (((member616898751_alt_o Y_2) (set_Ar1356274881_alt_o ((cons_A279268466_alt_o X_10) Xs_15)))->((or (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_2) X_10)) ((member616898751_alt_o Y_2) (set_Ar1356274881_alt_o Xs_15)))))
% FOF formula (forall (Y_2:(produc1501160679le_alt->Prop)) (X_10:(produc1501160679le_alt->Prop)) (Xs_15:list_P1178103901_alt_o), (((member377231867_alt_o Y_2) (set_Pr592386425_alt_o ((cons_P1239653256_alt_o X_10) Xs_15)))->((or (((eq (produc1501160679le_alt->Prop)) Y_2) X_10)) ((member377231867_alt_o Y_2) (set_Pr592386425_alt_o Xs_15))))) of role axiom named fact_545_set__ConsD
% A new axiom: (forall (Y_2:(produc1501160679le_alt->Prop)) (X_10:(produc1501160679le_alt->Prop)) (Xs_15:list_P1178103901_alt_o), (((member377231867_alt_o Y_2) (set_Pr592386425_alt_o ((cons_P1239653256_alt_o X_10) Xs_15)))->((or (((eq (produc1501160679le_alt->Prop)) Y_2) X_10)) ((member377231867_alt_o Y_2) (set_Pr592386425_alt_o Xs_15)))))
% FOF formula (forall (Y_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (X_10:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_15:list_A524553945_alt_o), (((member526088951_alt_o Y_2) (set_Ar571341173_alt_o ((cons_A2010997508_alt_o X_10) Xs_15)))->((or (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_2) X_10)) ((member526088951_alt_o Y_2) (set_Ar571341173_alt_o Xs_15))))) of role axiom named fact_546_set__ConsD
% A new axiom: (forall (Y_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (X_10:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_15:list_A524553945_alt_o), (((member526088951_alt_o Y_2) (set_Ar571341173_alt_o ((cons_A2010997508_alt_o X_10) Xs_15)))->((or (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_2) X_10)) ((member526088951_alt_o Y_2) (set_Ar571341173_alt_o Xs_15)))))
% FOF formula (forall (Y_2:produc1501160679le_alt) (X_10:produc1501160679le_alt) (Xs_15:list_P736798472le_alt), (((member214075476le_alt Y_2) (set_Pr1525059414le_alt ((cons_P1913588871le_alt X_10) Xs_15)))->((or (((eq produc1501160679le_alt) Y_2) X_10)) ((member214075476le_alt Y_2) (set_Pr1525059414le_alt Xs_15))))) of role axiom named fact_547_set__ConsD
% A new axiom: (forall (Y_2:produc1501160679le_alt) (X_10:produc1501160679le_alt) (Xs_15:list_P736798472le_alt), (((member214075476le_alt Y_2) (set_Pr1525059414le_alt ((cons_P1913588871le_alt X_10) Xs_15)))->((or (((eq produc1501160679le_alt) Y_2) X_10)) ((member214075476le_alt Y_2) (set_Pr1525059414le_alt Xs_15)))))
% FOF formula (forall (X_9:arrow_475358991le_alt) (Xs_14:list_A2115238852le_alt), (((member84363362le_alt X_9) (set_Ar577454304le_alt Xs_14))->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_9) Xs_14)) Xs_14))) of role axiom named fact_548_in__set__insert
% A new axiom: (forall (X_9:arrow_475358991le_alt) (Xs_14:list_A2115238852le_alt), (((member84363362le_alt X_9) (set_Ar577454304le_alt Xs_14))->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_9) Xs_14)) Xs_14)))
% FOF formula (forall (X_9:produc1362454231le_alt) (Xs_14:list_P1295265784le_alt), (((member28618436le_alt X_9) (set_Pr412222150le_alt Xs_14))->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_9) Xs_14)) Xs_14))) of role axiom named fact_549_in__set__insert
% A new axiom: (forall (X_9:produc1362454231le_alt) (Xs_14:list_P1295265784le_alt), (((member28618436le_alt X_9) (set_Pr412222150le_alt Xs_14))->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_9) Xs_14)) Xs_14)))
% FOF formula (forall (X_9:arrow_1429601828e_indi) (Xs_14:list_A1484739013e_indi), (((member2052026769e_indi X_9) (set_Ar778541203e_indi Xs_14))->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_9) Xs_14)) Xs_14))) of role axiom named fact_550_in__set__insert
% A new axiom: (forall (X_9:arrow_1429601828e_indi) (Xs_14:list_A1484739013e_indi), (((member2052026769e_indi X_9) (set_Ar778541203e_indi Xs_14))->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_9) Xs_14)) Xs_14)))
% FOF formula (forall (X_9:Prop) (Xs_14:list_o), (((member_o X_9) (set_o Xs_14))->(((eq list_o) ((insert_o X_9) Xs_14)) Xs_14))) of role axiom named fact_551_in__set__insert
% A new axiom: (forall (X_9:Prop) (Xs_14:list_o), (((member_o X_9) (set_o Xs_14))->(((eq list_o) ((insert_o X_9) Xs_14)) Xs_14)))
% FOF formula (forall (X_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_14:list_A518015091_alt_o), (((member616898751_alt_o X_9) (set_Ar1356274881_alt_o Xs_14))->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_9) Xs_14)) Xs_14))) of role axiom named fact_552_in__set__insert
% A new axiom: (forall (X_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_14:list_A518015091_alt_o), (((member616898751_alt_o X_9) (set_Ar1356274881_alt_o Xs_14))->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_9) Xs_14)) Xs_14)))
% FOF formula (forall (X_9:(produc1501160679le_alt->Prop)) (Xs_14:list_P1178103901_alt_o), (((member377231867_alt_o X_9) (set_Pr592386425_alt_o Xs_14))->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_9) Xs_14)) Xs_14))) of role axiom named fact_553_in__set__insert
% A new axiom: (forall (X_9:(produc1501160679le_alt->Prop)) (Xs_14:list_P1178103901_alt_o), (((member377231867_alt_o X_9) (set_Pr592386425_alt_o Xs_14))->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_9) Xs_14)) Xs_14)))
% FOF formula (forall (X_9:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_14:list_A524553945_alt_o), (((member526088951_alt_o X_9) (set_Ar571341173_alt_o Xs_14))->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_9) Xs_14)) Xs_14))) of role axiom named fact_554_in__set__insert
% A new axiom: (forall (X_9:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_14:list_A524553945_alt_o), (((member526088951_alt_o X_9) (set_Ar571341173_alt_o Xs_14))->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_9) Xs_14)) Xs_14)))
% FOF formula (forall (X_9:produc1501160679le_alt) (Xs_14:list_P736798472le_alt), (((member214075476le_alt X_9) (set_Pr1525059414le_alt Xs_14))->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_9) Xs_14)) Xs_14))) of role axiom named fact_555_in__set__insert
% A new axiom: (forall (X_9:produc1501160679le_alt) (Xs_14:list_P736798472le_alt), (((member214075476le_alt X_9) (set_Pr1525059414le_alt Xs_14))->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_9) Xs_14)) Xs_14)))
% FOF formula (forall (X_8:arrow_475358991le_alt) (Xs_13:list_A2115238852le_alt), ((iff (distin236324274le_alt ((cons_A228743023le_alt X_8) Xs_13))) ((and (((member84363362le_alt X_8) (set_Ar577454304le_alt Xs_13))->False)) (distin236324274le_alt Xs_13)))) of role axiom named fact_556_distinct_Osimps_I2_J
% A new axiom: (forall (X_8:arrow_475358991le_alt) (Xs_13:list_A2115238852le_alt), ((iff (distin236324274le_alt ((cons_A228743023le_alt X_8) Xs_13))) ((and (((member84363362le_alt X_8) (set_Ar577454304le_alt Xs_13))->False)) (distin236324274le_alt Xs_13))))
% FOF formula (forall (X_8:produc1362454231le_alt) (Xs_13:list_P1295265784le_alt), ((iff (distin561495412le_alt ((cons_P2048401015le_alt X_8) Xs_13))) ((and (((member28618436le_alt X_8) (set_Pr412222150le_alt Xs_13))->False)) (distin561495412le_alt Xs_13)))) of role axiom named fact_557_distinct_Osimps_I2_J
% A new axiom: (forall (X_8:produc1362454231le_alt) (Xs_13:list_P1295265784le_alt), ((iff (distin561495412le_alt ((cons_P2048401015le_alt X_8) Xs_13))) ((and (((member28618436le_alt X_8) (set_Pr412222150le_alt Xs_13))->False)) (distin561495412le_alt Xs_13))))
% FOF formula (forall (X_8:arrow_1429601828e_indi) (Xs_13:list_A1484739013e_indi), ((iff (distin1916799041e_indi ((cons_A663037380e_indi X_8) Xs_13))) ((and (((member2052026769e_indi X_8) (set_Ar778541203e_indi Xs_13))->False)) (distin1916799041e_indi Xs_13)))) of role axiom named fact_558_distinct_Osimps_I2_J
% A new axiom: (forall (X_8:arrow_1429601828e_indi) (Xs_13:list_A1484739013e_indi), ((iff (distin1916799041e_indi ((cons_A663037380e_indi X_8) Xs_13))) ((and (((member2052026769e_indi X_8) (set_Ar778541203e_indi Xs_13))->False)) (distin1916799041e_indi Xs_13))))
% FOF formula (forall (X_8:Prop) (Xs_13:list_o), ((iff (distinct_o ((cons_o X_8) Xs_13))) ((and (((member_o X_8) (set_o Xs_13))->False)) (distinct_o Xs_13)))) of role axiom named fact_559_distinct_Osimps_I2_J
% A new axiom: (forall (X_8:Prop) (Xs_13:list_o), ((iff (distinct_o ((cons_o X_8) Xs_13))) ((and (((member_o X_8) (set_o Xs_13))->False)) (distinct_o Xs_13))))
% FOF formula (forall (X_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_13:list_A518015091_alt_o), ((iff (distin1908010863_alt_o ((cons_A279268466_alt_o X_8) Xs_13))) ((and (((member616898751_alt_o X_8) (set_Ar1356274881_alt_o Xs_13))->False)) (distin1908010863_alt_o Xs_13)))) of role axiom named fact_560_distinct_Osimps_I2_J
% A new axiom: (forall (X_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_13:list_A518015091_alt_o), ((iff (distin1908010863_alt_o ((cons_A279268466_alt_o X_8) Xs_13))) ((and (((member616898751_alt_o X_8) (set_Ar1356274881_alt_o Xs_13))->False)) (distin1908010863_alt_o Xs_13))))
% FOF formula (forall (X_8:(produc1501160679le_alt->Prop)) (Xs_13:list_P1178103901_alt_o), ((iff (distin1582710603_alt_o ((cons_P1239653256_alt_o X_8) Xs_13))) ((and (((member377231867_alt_o X_8) (set_Pr592386425_alt_o Xs_13))->False)) (distin1582710603_alt_o Xs_13)))) of role axiom named fact_561_distinct_Osimps_I2_J
% A new axiom: (forall (X_8:(produc1501160679le_alt->Prop)) (Xs_13:list_P1178103901_alt_o), ((iff (distin1582710603_alt_o ((cons_P1239653256_alt_o X_8) Xs_13))) ((and (((member377231867_alt_o X_8) (set_Pr592386425_alt_o Xs_13))->False)) (distin1582710603_alt_o Xs_13))))
% FOF formula (forall (X_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_13:list_A524553945_alt_o), ((iff (distin1869760583_alt_o ((cons_A2010997508_alt_o X_8) Xs_13))) ((and (((member526088951_alt_o X_8) (set_Ar571341173_alt_o Xs_13))->False)) (distin1869760583_alt_o Xs_13)))) of role axiom named fact_562_distinct_Osimps_I2_J
% A new axiom: (forall (X_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_13:list_A524553945_alt_o), ((iff (distin1869760583_alt_o ((cons_A2010997508_alt_o X_8) Xs_13))) ((and (((member526088951_alt_o X_8) (set_Ar571341173_alt_o Xs_13))->False)) (distin1869760583_alt_o Xs_13))))
% FOF formula (forall (X_8:produc1501160679le_alt) (Xs_13:list_P736798472le_alt), ((iff (distin1776819972le_alt ((cons_P1913588871le_alt X_8) Xs_13))) ((and (((member214075476le_alt X_8) (set_Pr1525059414le_alt Xs_13))->False)) (distin1776819972le_alt Xs_13)))) of role axiom named fact_563_distinct_Osimps_I2_J
% A new axiom: (forall (X_8:produc1501160679le_alt) (Xs_13:list_P736798472le_alt), ((iff (distin1776819972le_alt ((cons_P1913588871le_alt X_8) Xs_13))) ((and (((member214075476le_alt X_8) (set_Pr1525059414le_alt Xs_13))->False)) (distin1776819972le_alt Xs_13))))
% FOF formula (forall (Ys_6:list_A2115238852le_alt) (P_7:(arrow_475358991le_alt->Prop)) (X_7:arrow_475358991le_alt) (Xs_12:list_A2115238852le_alt), (((member84363362le_alt X_7) (set_Ar577454304le_alt Xs_12))->(((P_7 X_7)->False)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_7) ((append179082452le_alt Xs_12) Ys_6))) ((takeWh1696291512le_alt P_7) Xs_12))))) of role axiom named fact_564_takeWhile__append1
% A new axiom: (forall (Ys_6:list_A2115238852le_alt) (P_7:(arrow_475358991le_alt->Prop)) (X_7:arrow_475358991le_alt) (Xs_12:list_A2115238852le_alt), (((member84363362le_alt X_7) (set_Ar577454304le_alt Xs_12))->(((P_7 X_7)->False)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_7) ((append179082452le_alt Xs_12) Ys_6))) ((takeWh1696291512le_alt P_7) Xs_12)))))
% FOF formula (forall (Ys_6:list_P1295265784le_alt) (P_7:(produc1362454231le_alt->Prop)) (X_7:produc1362454231le_alt) (Xs_12:list_P1295265784le_alt), (((member28618436le_alt X_7) (set_Pr412222150le_alt Xs_12))->(((P_7 X_7)->False)->(((eq list_P1295265784le_alt) ((takeWh1571807982le_alt P_7) ((append423770578le_alt Xs_12) Ys_6))) ((takeWh1571807982le_alt P_7) Xs_12))))) of role axiom named fact_565_takeWhile__append1
% A new axiom: (forall (Ys_6:list_P1295265784le_alt) (P_7:(produc1362454231le_alt->Prop)) (X_7:produc1362454231le_alt) (Xs_12:list_P1295265784le_alt), (((member28618436le_alt X_7) (set_Pr412222150le_alt Xs_12))->(((P_7 X_7)->False)->(((eq list_P1295265784le_alt) ((takeWh1571807982le_alt P_7) ((append423770578le_alt Xs_12) Ys_6))) ((takeWh1571807982le_alt P_7) Xs_12)))))
% FOF formula (forall (Ys_6:list_A1484739013e_indi) (P_7:(arrow_1429601828e_indi->Prop)) (X_7:arrow_1429601828e_indi) (Xs_12:list_A1484739013e_indi), (((member2052026769e_indi X_7) (set_Ar778541203e_indi Xs_12))->(((P_7 X_7)->False)->(((eq list_A1484739013e_indi) ((takeWh831911099e_indi P_7) ((append711934367e_indi Xs_12) Ys_6))) ((takeWh831911099e_indi P_7) Xs_12))))) of role axiom named fact_566_takeWhile__append1
% A new axiom: (forall (Ys_6:list_A1484739013e_indi) (P_7:(arrow_1429601828e_indi->Prop)) (X_7:arrow_1429601828e_indi) (Xs_12:list_A1484739013e_indi), (((member2052026769e_indi X_7) (set_Ar778541203e_indi Xs_12))->(((P_7 X_7)->False)->(((eq list_A1484739013e_indi) ((takeWh831911099e_indi P_7) ((append711934367e_indi Xs_12) Ys_6))) ((takeWh831911099e_indi P_7) Xs_12)))))
% FOF formula (forall (Ys_6:list_o) (P_7:(Prop->Prop)) (X_7:Prop) (Xs_12:list_o), (((member_o X_7) (set_o Xs_12))->(((P_7 X_7)->False)->(((eq list_o) ((takeWhile_o P_7) ((append_o Xs_12) Ys_6))) ((takeWhile_o P_7) Xs_12))))) of role axiom named fact_567_takeWhile__append1
% A new axiom: (forall (Ys_6:list_o) (P_7:(Prop->Prop)) (X_7:Prop) (Xs_12:list_o), (((member_o X_7) (set_o Xs_12))->(((P_7 X_7)->False)->(((eq list_o) ((takeWhile_o P_7) ((append_o Xs_12) Ys_6))) ((takeWhile_o P_7) Xs_12)))))
% FOF formula (forall (Ys_6:list_A518015091_alt_o) (P_7:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (X_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_12:list_A518015091_alt_o), (((member616898751_alt_o X_7) (set_Ar1356274881_alt_o Xs_12))->(((P_7 X_7)->False)->(((eq list_A518015091_alt_o) ((takeWh877796585_alt_o P_7) ((append326058957_alt_o Xs_12) Ys_6))) ((takeWh877796585_alt_o P_7) Xs_12))))) of role axiom named fact_568_takeWhile__append1
% A new axiom: (forall (Ys_6:list_A518015091_alt_o) (P_7:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (X_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_12:list_A518015091_alt_o), (((member616898751_alt_o X_7) (set_Ar1356274881_alt_o Xs_12))->(((P_7 X_7)->False)->(((eq list_A518015091_alt_o) ((takeWh877796585_alt_o P_7) ((append326058957_alt_o Xs_12) Ys_6))) ((takeWh877796585_alt_o P_7) Xs_12)))))
% FOF formula (forall (Ys_6:list_P1178103901_alt_o) (P_7:((produc1501160679le_alt->Prop)->Prop)) (X_7:(produc1501160679le_alt->Prop)) (Xs_12:list_P1178103901_alt_o), (((member377231867_alt_o X_7) (set_Pr592386425_alt_o Xs_12))->(((P_7 X_7)->False)->(((eq list_P1178103901_alt_o) ((takeWh1715715921_alt_o P_7) ((append612833133_alt_o Xs_12) Ys_6))) ((takeWh1715715921_alt_o P_7) Xs_12))))) of role axiom named fact_569_takeWhile__append1
% A new axiom: (forall (Ys_6:list_P1178103901_alt_o) (P_7:((produc1501160679le_alt->Prop)->Prop)) (X_7:(produc1501160679le_alt->Prop)) (Xs_12:list_P1178103901_alt_o), (((member377231867_alt_o X_7) (set_Pr592386425_alt_o Xs_12))->(((P_7 X_7)->False)->(((eq list_P1178103901_alt_o) ((takeWh1715715921_alt_o P_7) ((append612833133_alt_o Xs_12) Ys_6))) ((takeWh1715715921_alt_o P_7) Xs_12)))))
% FOF formula (forall (Ys_6:list_A524553945_alt_o) (P_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (X_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_12:list_A524553945_alt_o), (((member526088951_alt_o X_7) (set_Ar571341173_alt_o Xs_12))->(((P_7 X_7)->False)->(((eq list_A524553945_alt_o) ((takeWh1825606477_alt_o P_7) ((append295924073_alt_o Xs_12) Ys_6))) ((takeWh1825606477_alt_o P_7) Xs_12))))) of role axiom named fact_570_takeWhile__append1
% A new axiom: (forall (Ys_6:list_A524553945_alt_o) (P_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (X_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_12:list_A524553945_alt_o), (((member526088951_alt_o X_7) (set_Ar571341173_alt_o Xs_12))->(((P_7 X_7)->False)->(((eq list_A524553945_alt_o) ((takeWh1825606477_alt_o P_7) ((append295924073_alt_o Xs_12) Ys_6))) ((takeWh1825606477_alt_o P_7) Xs_12)))))
% FOF formula (forall (Ys_6:list_P736798472le_alt) (P_7:(produc1501160679le_alt->Prop)) (X_7:produc1501160679le_alt) (Xs_12:list_P736798472le_alt), (((member214075476le_alt X_7) (set_Pr1525059414le_alt Xs_12))->(((P_7 X_7)->False)->(((eq list_P736798472le_alt) ((takeWh302148478le_alt P_7) ((append1229289570le_alt Xs_12) Ys_6))) ((takeWh302148478le_alt P_7) Xs_12))))) of role axiom named fact_571_takeWhile__append1
% A new axiom: (forall (Ys_6:list_P736798472le_alt) (P_7:(produc1501160679le_alt->Prop)) (X_7:produc1501160679le_alt) (Xs_12:list_P736798472le_alt), (((member214075476le_alt X_7) (set_Pr1525059414le_alt Xs_12))->(((P_7 X_7)->False)->(((eq list_P736798472le_alt) ((takeWh302148478le_alt P_7) ((append1229289570le_alt Xs_12) Ys_6))) ((takeWh302148478le_alt P_7) Xs_12)))))
% FOF formula (forall (As:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) As) nil_Ar1286194111le_alt))->((member84363362le_alt (last_A1217315288le_alt As)) (set_Ar577454304le_alt As)))) of role axiom named fact_572_last__in__set
% A new axiom: (forall (As:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) As) nil_Ar1286194111le_alt))->((member84363362le_alt (last_A1217315288le_alt As)) (set_Ar577454304le_alt As))))
% FOF formula (forall (As:list_P1295265784le_alt), ((not (((eq list_P1295265784le_alt) As) nil_Pr365739559le_alt))->((member28618436le_alt (last_P1879176142le_alt As)) (set_Pr412222150le_alt As)))) of role axiom named fact_573_last__in__set
% A new axiom: (forall (As:list_P1295265784le_alt), ((not (((eq list_P1295265784le_alt) As) nil_Pr365739559le_alt))->((member28618436le_alt (last_P1879176142le_alt As)) (set_Pr412222150le_alt As))))
% FOF formula (forall (As:list_A1484739013e_indi), ((not (((eq list_A1484739013e_indi) As) nil_Ar380161396e_indi))->((member2052026769e_indi (last_A303846811e_indi As)) (set_Ar778541203e_indi As)))) of role axiom named fact_574_last__in__set
% A new axiom: (forall (As:list_A1484739013e_indi), ((not (((eq list_A1484739013e_indi) As) nil_Ar380161396e_indi))->((member2052026769e_indi (last_A303846811e_indi As)) (set_Ar778541203e_indi As))))
% FOF formula (forall (As:list_o), ((not (((eq list_o) As) nil_o))->((member_o (last_o As)) (set_o As)))) of role axiom named fact_575_last__in__set
% A new axiom: (forall (As:list_o), ((not (((eq list_o) As) nil_o))->((member_o (last_o As)) (set_o As))))
% FOF formula (forall (As:list_A518015091_alt_o), ((not (((eq list_A518015091_alt_o) As) nil_Ar253733922_alt_o))->((member616898751_alt_o (last_A1273867721_alt_o As)) (set_Ar1356274881_alt_o As)))) of role axiom named fact_576_last__in__set
% A new axiom: (forall (As:list_A518015091_alt_o), ((not (((eq list_A518015091_alt_o) As) nil_Ar253733922_alt_o))->((member616898751_alt_o (last_A1273867721_alt_o As)) (set_Ar1356274881_alt_o As))))
% FOF formula (forall (As:list_P1178103901_alt_o), ((not (((eq list_P1178103901_alt_o) As) nil_Pr28438488_alt_o))->((member377231867_alt_o (last_P685913713_alt_o As)) (set_Pr592386425_alt_o As)))) of role axiom named fact_577_last__in__set
% A new axiom: (forall (As:list_P1178103901_alt_o), ((not (((eq list_P1178103901_alt_o) As) nil_Pr28438488_alt_o))->((member377231867_alt_o (last_P685913713_alt_o As)) (set_Pr592386425_alt_o As))))
% FOF formula (forall (As:list_A524553945_alt_o), ((not (((eq list_A524553945_alt_o) As) nil_Ar1876942676_alt_o))->((member526088951_alt_o (last_A1049530989_alt_o As)) (set_Ar571341173_alt_o As)))) of role axiom named fact_578_last__in__set
% A new axiom: (forall (As:list_A524553945_alt_o), ((not (((eq list_A524553945_alt_o) As) nil_Ar1876942676_alt_o))->((member526088951_alt_o (last_A1049530989_alt_o As)) (set_Ar571341173_alt_o As))))
% FOF formula (forall (As:list_P736798472le_alt), ((not (((eq list_P736798472le_alt) As) nil_Pr861385783le_alt))->((member214075476le_alt (last_P1656409182le_alt As)) (set_Pr1525059414le_alt As)))) of role axiom named fact_579_last__in__set
% A new axiom: (forall (As:list_P736798472le_alt), ((not (((eq list_P736798472le_alt) As) nil_Pr861385783le_alt))->((member214075476le_alt (last_P1656409182le_alt As)) (set_Pr1525059414le_alt As))))
% FOF formula (forall (P_6:(arrow_475358991le_alt->Prop)) (Xs_11:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_6) Xs_11)) nil_Ar1286194111le_alt)) (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_11))->(P_6 X_2))))) of role axiom named fact_580_dropWhile__eq__Nil__conv
% A new axiom: (forall (P_6:(arrow_475358991le_alt->Prop)) (Xs_11:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_6) Xs_11)) nil_Ar1286194111le_alt)) (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_11))->(P_6 X_2)))))
% FOF formula (forall (Ys_5:list_A2115238852le_alt) (X_6:arrow_475358991le_alt) (Xs_10:list_A2115238852le_alt), (((or ((member84363362le_alt X_6) (set_Ar577454304le_alt (butlas274947851le_alt Xs_10)))) ((member84363362le_alt X_6) (set_Ar577454304le_alt (butlas274947851le_alt Ys_5))))->((member84363362le_alt X_6) (set_Ar577454304le_alt (butlas274947851le_alt ((append179082452le_alt Xs_10) Ys_5)))))) of role axiom named fact_581_in__set__butlast__appendI
% A new axiom: (forall (Ys_5:list_A2115238852le_alt) (X_6:arrow_475358991le_alt) (Xs_10:list_A2115238852le_alt), (((or ((member84363362le_alt X_6) (set_Ar577454304le_alt (butlas274947851le_alt Xs_10)))) ((member84363362le_alt X_6) (set_Ar577454304le_alt (butlas274947851le_alt Ys_5))))->((member84363362le_alt X_6) (set_Ar577454304le_alt (butlas274947851le_alt ((append179082452le_alt Xs_10) Ys_5))))))
% FOF formula (forall (Ys_5:list_P1295265784le_alt) (X_6:produc1362454231le_alt) (Xs_10:list_P1295265784le_alt), (((or ((member28618436le_alt X_6) (set_Pr412222150le_alt (butlas464406491le_alt Xs_10)))) ((member28618436le_alt X_6) (set_Pr412222150le_alt (butlas464406491le_alt Ys_5))))->((member28618436le_alt X_6) (set_Pr412222150le_alt (butlas464406491le_alt ((append423770578le_alt Xs_10) Ys_5)))))) of role axiom named fact_582_in__set__butlast__appendI
% A new axiom: (forall (Ys_5:list_P1295265784le_alt) (X_6:produc1362454231le_alt) (Xs_10:list_P1295265784le_alt), (((or ((member28618436le_alt X_6) (set_Pr412222150le_alt (butlas464406491le_alt Xs_10)))) ((member28618436le_alt X_6) (set_Pr412222150le_alt (butlas464406491le_alt Ys_5))))->((member28618436le_alt X_6) (set_Pr412222150le_alt (butlas464406491le_alt ((append423770578le_alt Xs_10) Ys_5))))))
% FOF formula (forall (Ys_5:list_A1484739013e_indi) (X_6:arrow_1429601828e_indi) (Xs_10:list_A1484739013e_indi), (((or ((member2052026769e_indi X_6) (set_Ar778541203e_indi (butlas1554122024e_indi Xs_10)))) ((member2052026769e_indi X_6) (set_Ar778541203e_indi (butlas1554122024e_indi Ys_5))))->((member2052026769e_indi X_6) (set_Ar778541203e_indi (butlas1554122024e_indi ((append711934367e_indi Xs_10) Ys_5)))))) of role axiom named fact_583_in__set__butlast__appendI
% A new axiom: (forall (Ys_5:list_A1484739013e_indi) (X_6:arrow_1429601828e_indi) (Xs_10:list_A1484739013e_indi), (((or ((member2052026769e_indi X_6) (set_Ar778541203e_indi (butlas1554122024e_indi Xs_10)))) ((member2052026769e_indi X_6) (set_Ar778541203e_indi (butlas1554122024e_indi Ys_5))))->((member2052026769e_indi X_6) (set_Ar778541203e_indi (butlas1554122024e_indi ((append711934367e_indi Xs_10) Ys_5))))))
% FOF formula (forall (Ys_5:list_o) (X_6:Prop) (Xs_10:list_o), (((or ((member_o X_6) (set_o (butlast_o Xs_10)))) ((member_o X_6) (set_o (butlast_o Ys_5))))->((member_o X_6) (set_o (butlast_o ((append_o Xs_10) Ys_5)))))) of role axiom named fact_584_in__set__butlast__appendI
% A new axiom: (forall (Ys_5:list_o) (X_6:Prop) (Xs_10:list_o), (((or ((member_o X_6) (set_o (butlast_o Xs_10)))) ((member_o X_6) (set_o (butlast_o Ys_5))))->((member_o X_6) (set_o (butlast_o ((append_o Xs_10) Ys_5))))))
% FOF formula (forall (Ys_5:list_A518015091_alt_o) (X_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_10:list_A518015091_alt_o), (((or ((member616898751_alt_o X_6) (set_Ar1356274881_alt_o (butlas1138247126_alt_o Xs_10)))) ((member616898751_alt_o X_6) (set_Ar1356274881_alt_o (butlas1138247126_alt_o Ys_5))))->((member616898751_alt_o X_6) (set_Ar1356274881_alt_o (butlas1138247126_alt_o ((append326058957_alt_o Xs_10) Ys_5)))))) of role axiom named fact_585_in__set__butlast__appendI
% A new axiom: (forall (Ys_5:list_A518015091_alt_o) (X_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_10:list_A518015091_alt_o), (((or ((member616898751_alt_o X_6) (set_Ar1356274881_alt_o (butlas1138247126_alt_o Xs_10)))) ((member616898751_alt_o X_6) (set_Ar1356274881_alt_o (butlas1138247126_alt_o Ys_5))))->((member616898751_alt_o X_6) (set_Ar1356274881_alt_o (butlas1138247126_alt_o ((append326058957_alt_o Xs_10) Ys_5))))))
% FOF formula (forall (Ys_5:list_P1178103901_alt_o) (X_6:(produc1501160679le_alt->Prop)) (Xs_10:list_P1178103901_alt_o), (((or ((member377231867_alt_o X_6) (set_Pr592386425_alt_o (butlas368541988_alt_o Xs_10)))) ((member377231867_alt_o X_6) (set_Pr592386425_alt_o (butlas368541988_alt_o Ys_5))))->((member377231867_alt_o X_6) (set_Pr592386425_alt_o (butlas368541988_alt_o ((append612833133_alt_o Xs_10) Ys_5)))))) of role axiom named fact_586_in__set__butlast__appendI
% A new axiom: (forall (Ys_5:list_P1178103901_alt_o) (X_6:(produc1501160679le_alt->Prop)) (Xs_10:list_P1178103901_alt_o), (((or ((member377231867_alt_o X_6) (set_Pr592386425_alt_o (butlas368541988_alt_o Xs_10)))) ((member377231867_alt_o X_6) (set_Pr592386425_alt_o (butlas368541988_alt_o Ys_5))))->((member377231867_alt_o X_6) (set_Pr592386425_alt_o (butlas368541988_alt_o ((append612833133_alt_o Xs_10) Ys_5))))))
% FOF formula (forall (Ys_5:list_A524553945_alt_o) (X_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_10:list_A524553945_alt_o), (((or ((member526088951_alt_o X_6) (set_Ar571341173_alt_o (butlas813143712_alt_o Xs_10)))) ((member526088951_alt_o X_6) (set_Ar571341173_alt_o (butlas813143712_alt_o Ys_5))))->((member526088951_alt_o X_6) (set_Ar571341173_alt_o (butlas813143712_alt_o ((append295924073_alt_o Xs_10) Ys_5)))))) of role axiom named fact_587_in__set__butlast__appendI
% A new axiom: (forall (Ys_5:list_A524553945_alt_o) (X_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_10:list_A524553945_alt_o), (((or ((member526088951_alt_o X_6) (set_Ar571341173_alt_o (butlas813143712_alt_o Xs_10)))) ((member526088951_alt_o X_6) (set_Ar571341173_alt_o (butlas813143712_alt_o Ys_5))))->((member526088951_alt_o X_6) (set_Ar571341173_alt_o (butlas813143712_alt_o ((append295924073_alt_o Xs_10) Ys_5))))))
% FOF formula (forall (Ys_5:list_P736798472le_alt) (X_6:produc1501160679le_alt) (Xs_10:list_P736798472le_alt), (((or ((member214075476le_alt X_6) (set_Pr1525059414le_alt (butlas661498859le_alt Xs_10)))) ((member214075476le_alt X_6) (set_Pr1525059414le_alt (butlas661498859le_alt Ys_5))))->((member214075476le_alt X_6) (set_Pr1525059414le_alt (butlas661498859le_alt ((append1229289570le_alt Xs_10) Ys_5)))))) of role axiom named fact_588_in__set__butlast__appendI
% A new axiom: (forall (Ys_5:list_P736798472le_alt) (X_6:produc1501160679le_alt) (Xs_10:list_P736798472le_alt), (((or ((member214075476le_alt X_6) (set_Pr1525059414le_alt (butlas661498859le_alt Xs_10)))) ((member214075476le_alt X_6) (set_Pr1525059414le_alt (butlas661498859le_alt Ys_5))))->((member214075476le_alt X_6) (set_Pr1525059414le_alt (butlas661498859le_alt ((append1229289570le_alt Xs_10) Ys_5))))))
% FOF formula (forall (Xs_9:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_9) nil_Ar1286194111le_alt))->((member84363362le_alt (hd_Arr1965683346le_alt Xs_9)) (set_Ar577454304le_alt Xs_9)))) of role axiom named fact_589_hd__in__set
% A new axiom: (forall (Xs_9:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_9) nil_Ar1286194111le_alt))->((member84363362le_alt (hd_Arr1965683346le_alt Xs_9)) (set_Ar577454304le_alt Xs_9))))
% FOF formula (forall (Xs_9:list_P1295265784le_alt), ((not (((eq list_P1295265784le_alt) Xs_9) nil_Pr365739559le_alt))->((member28618436le_alt (hd_Pro856774804le_alt Xs_9)) (set_Pr412222150le_alt Xs_9)))) of role axiom named fact_590_hd__in__set
% A new axiom: (forall (Xs_9:list_P1295265784le_alt), ((not (((eq list_P1295265784le_alt) Xs_9) nil_Pr365739559le_alt))->((member28618436le_alt (hd_Pro856774804le_alt Xs_9)) (set_Pr412222150le_alt Xs_9))))
% FOF formula (forall (Xs_9:list_A1484739013e_indi), ((not (((eq list_A1484739013e_indi) Xs_9) nil_Ar380161396e_indi))->((member2052026769e_indi (hd_Arr1023890273e_indi Xs_9)) (set_Ar778541203e_indi Xs_9)))) of role axiom named fact_591_hd__in__set
% A new axiom: (forall (Xs_9:list_A1484739013e_indi), ((not (((eq list_A1484739013e_indi) Xs_9) nil_Ar380161396e_indi))->((member2052026769e_indi (hd_Arr1023890273e_indi Xs_9)) (set_Ar778541203e_indi Xs_9))))
% FOF formula (forall (Xs_9:list_o), ((not (((eq list_o) Xs_9) nil_o))->((member_o (hd_o Xs_9)) (set_o Xs_9)))) of role axiom named fact_592_hd__in__set
% A new axiom: (forall (Xs_9:list_o), ((not (((eq list_o) Xs_9) nil_o))->((member_o (hd_o Xs_9)) (set_o Xs_9))))
% FOF formula (forall (Xs_9:list_A518015091_alt_o), ((not (((eq list_A518015091_alt_o) Xs_9) nil_Ar253733922_alt_o))->((member616898751_alt_o (hd_Arr1786382991_alt_o Xs_9)) (set_Ar1356274881_alt_o Xs_9)))) of role axiom named fact_593_hd__in__set
% A new axiom: (forall (Xs_9:list_A518015091_alt_o), ((not (((eq list_A518015091_alt_o) Xs_9) nil_Ar253733922_alt_o))->((member616898751_alt_o (hd_Arr1786382991_alt_o Xs_9)) (set_Ar1356274881_alt_o Xs_9))))
% FOF formula (forall (Xs_9:list_P1178103901_alt_o), ((not (((eq list_P1178103901_alt_o) Xs_9) nil_Pr28438488_alt_o))->((member377231867_alt_o (hd_Pro622402603_alt_o Xs_9)) (set_Pr592386425_alt_o Xs_9)))) of role axiom named fact_594_hd__in__set
% A new axiom: (forall (Xs_9:list_P1178103901_alt_o), ((not (((eq list_P1178103901_alt_o) Xs_9) nil_Pr28438488_alt_o))->((member377231867_alt_o (hd_Pro622402603_alt_o Xs_9)) (set_Pr592386425_alt_o Xs_9))))
% FOF formula (forall (Xs_9:list_A524553945_alt_o), ((not (((eq list_A524553945_alt_o) Xs_9) nil_Ar1876942676_alt_o))->((member526088951_alt_o (hd_Arr574592295_alt_o Xs_9)) (set_Ar571341173_alt_o Xs_9)))) of role axiom named fact_595_hd__in__set
% A new axiom: (forall (Xs_9:list_A524553945_alt_o), ((not (((eq list_A524553945_alt_o) Xs_9) nil_Ar1876942676_alt_o))->((member526088951_alt_o (hd_Arr574592295_alt_o Xs_9)) (set_Ar571341173_alt_o Xs_9))))
% FOF formula (forall (Xs_9:list_P736798472le_alt), ((not (((eq list_P736798472le_alt) Xs_9) nil_Pr861385783le_alt))->((member214075476le_alt (hd_Pro297626148le_alt Xs_9)) (set_Pr1525059414le_alt Xs_9)))) of role axiom named fact_596_hd__in__set
% A new axiom: (forall (Xs_9:list_P736798472le_alt), ((not (((eq list_P736798472le_alt) Xs_9) nil_Pr861385783le_alt))->((member214075476le_alt (hd_Pro297626148le_alt Xs_9)) (set_Pr1525059414le_alt Xs_9))))
% FOF formula (forall (Ys_4:list_A2115238852le_alt) (P_5:(arrow_475358991le_alt->Prop)) (X_5:arrow_475358991le_alt) (Xs_8:list_A2115238852le_alt), (((member84363362le_alt X_5) (set_Ar577454304le_alt Xs_8))->(((P_5 X_5)->False)->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_5) ((append179082452le_alt Xs_8) Ys_4))) ((append179082452le_alt ((dropWh1316781920le_alt P_5) Xs_8)) Ys_4))))) of role axiom named fact_597_dropWhile__append1
% A new axiom: (forall (Ys_4:list_A2115238852le_alt) (P_5:(arrow_475358991le_alt->Prop)) (X_5:arrow_475358991le_alt) (Xs_8:list_A2115238852le_alt), (((member84363362le_alt X_5) (set_Ar577454304le_alt Xs_8))->(((P_5 X_5)->False)->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_5) ((append179082452le_alt Xs_8) Ys_4))) ((append179082452le_alt ((dropWh1316781920le_alt P_5) Xs_8)) Ys_4)))))
% FOF formula (forall (Ys_4:list_P1295265784le_alt) (P_5:(produc1362454231le_alt->Prop)) (X_5:produc1362454231le_alt) (Xs_8:list_P1295265784le_alt), (((member28618436le_alt X_5) (set_Pr412222150le_alt Xs_8))->(((P_5 X_5)->False)->(((eq list_P1295265784le_alt) ((dropWh612508742le_alt P_5) ((append423770578le_alt Xs_8) Ys_4))) ((append423770578le_alt ((dropWh612508742le_alt P_5) Xs_8)) Ys_4))))) of role axiom named fact_598_dropWhile__append1
% A new axiom: (forall (Ys_4:list_P1295265784le_alt) (P_5:(produc1362454231le_alt->Prop)) (X_5:produc1362454231le_alt) (Xs_8:list_P1295265784le_alt), (((member28618436le_alt X_5) (set_Pr412222150le_alt Xs_8))->(((P_5 X_5)->False)->(((eq list_P1295265784le_alt) ((dropWh612508742le_alt P_5) ((append423770578le_alt Xs_8) Ys_4))) ((append423770578le_alt ((dropWh612508742le_alt P_5) Xs_8)) Ys_4)))))
% FOF formula (forall (Ys_4:list_A1484739013e_indi) (P_5:(arrow_1429601828e_indi->Prop)) (X_5:arrow_1429601828e_indi) (Xs_8:list_A1484739013e_indi), (((member2052026769e_indi X_5) (set_Ar778541203e_indi Xs_8))->(((P_5 X_5)->False)->(((eq list_A1484739013e_indi) ((dropWh1160116755e_indi P_5) ((append711934367e_indi Xs_8) Ys_4))) ((append711934367e_indi ((dropWh1160116755e_indi P_5) Xs_8)) Ys_4))))) of role axiom named fact_599_dropWhile__append1
% A new axiom: (forall (Ys_4:list_A1484739013e_indi) (P_5:(arrow_1429601828e_indi->Prop)) (X_5:arrow_1429601828e_indi) (Xs_8:list_A1484739013e_indi), (((member2052026769e_indi X_5) (set_Ar778541203e_indi Xs_8))->(((P_5 X_5)->False)->(((eq list_A1484739013e_indi) ((dropWh1160116755e_indi P_5) ((append711934367e_indi Xs_8) Ys_4))) ((append711934367e_indi ((dropWh1160116755e_indi P_5) Xs_8)) Ys_4)))))
% FOF formula (forall (Ys_4:list_o) (P_5:(Prop->Prop)) (X_5:Prop) (Xs_8:list_o), (((member_o X_5) (set_o Xs_8))->(((P_5 X_5)->False)->(((eq list_o) ((dropWhile_o P_5) ((append_o Xs_8) Ys_4))) ((append_o ((dropWhile_o P_5) Xs_8)) Ys_4))))) of role axiom named fact_600_dropWhile__append1
% A new axiom: (forall (Ys_4:list_o) (P_5:(Prop->Prop)) (X_5:Prop) (Xs_8:list_o), (((member_o X_5) (set_o Xs_8))->(((P_5 X_5)->False)->(((eq list_o) ((dropWhile_o P_5) ((append_o Xs_8) Ys_4))) ((append_o ((dropWhile_o P_5) Xs_8)) Ys_4)))))
% FOF formula (forall (Ys_4:list_A518015091_alt_o) (P_5:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (X_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_8:list_A518015091_alt_o), (((member616898751_alt_o X_5) (set_Ar1356274881_alt_o Xs_8))->(((P_5 X_5)->False)->(((eq list_A518015091_alt_o) ((dropWh583351873_alt_o P_5) ((append326058957_alt_o Xs_8) Ys_4))) ((append326058957_alt_o ((dropWh583351873_alt_o P_5) Xs_8)) Ys_4))))) of role axiom named fact_601_dropWhile__append1
% A new axiom: (forall (Ys_4:list_A518015091_alt_o) (P_5:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (X_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_8:list_A518015091_alt_o), (((member616898751_alt_o X_5) (set_Ar1356274881_alt_o Xs_8))->(((P_5 X_5)->False)->(((eq list_A518015091_alt_o) ((dropWh583351873_alt_o P_5) ((append326058957_alt_o Xs_8) Ys_4))) ((append326058957_alt_o ((dropWh583351873_alt_o P_5) Xs_8)) Ys_4)))))
% FOF formula (forall (Ys_4:list_P1178103901_alt_o) (P_5:((produc1501160679le_alt->Prop)->Prop)) (X_5:(produc1501160679le_alt->Prop)) (Xs_8:list_P1178103901_alt_o), (((member377231867_alt_o X_5) (set_Pr592386425_alt_o Xs_8))->(((P_5 X_5)->False)->(((eq list_P1178103901_alt_o) ((dropWh1049991161_alt_o P_5) ((append612833133_alt_o Xs_8) Ys_4))) ((append612833133_alt_o ((dropWh1049991161_alt_o P_5) Xs_8)) Ys_4))))) of role axiom named fact_602_dropWhile__append1
% A new axiom: (forall (Ys_4:list_P1178103901_alt_o) (P_5:((produc1501160679le_alt->Prop)->Prop)) (X_5:(produc1501160679le_alt->Prop)) (Xs_8:list_P1178103901_alt_o), (((member377231867_alt_o X_5) (set_Pr592386425_alt_o Xs_8))->(((P_5 X_5)->False)->(((eq list_P1178103901_alt_o) ((dropWh1049991161_alt_o P_5) ((append612833133_alt_o Xs_8) Ys_4))) ((append612833133_alt_o ((dropWh1049991161_alt_o P_5) Xs_8)) Ys_4)))))
% FOF formula (forall (Ys_4:list_A524553945_alt_o) (P_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (X_5:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_8:list_A524553945_alt_o), (((member526088951_alt_o X_5) (set_Ar571341173_alt_o Xs_8))->(((P_5 X_5)->False)->(((eq list_A524553945_alt_o) ((dropWh73644021_alt_o P_5) ((append295924073_alt_o Xs_8) Ys_4))) ((append295924073_alt_o ((dropWh73644021_alt_o P_5) Xs_8)) Ys_4))))) of role axiom named fact_603_dropWhile__append1
% A new axiom: (forall (Ys_4:list_A524553945_alt_o) (P_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (X_5:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_8:list_A524553945_alt_o), (((member526088951_alt_o X_5) (set_Ar571341173_alt_o Xs_8))->(((P_5 X_5)->False)->(((eq list_A524553945_alt_o) ((dropWh73644021_alt_o P_5) ((append295924073_alt_o Xs_8) Ys_4))) ((append295924073_alt_o ((dropWh73644021_alt_o P_5) Xs_8)) Ys_4)))))
% FOF formula (forall (Ys_4:list_P736798472le_alt) (P_5:(produc1501160679le_alt->Prop)) (X_5:produc1501160679le_alt) (Xs_8:list_P736798472le_alt), (((member214075476le_alt X_5) (set_Pr1525059414le_alt Xs_8))->(((P_5 X_5)->False)->(((eq list_P736798472le_alt) ((dropWh680325334le_alt P_5) ((append1229289570le_alt Xs_8) Ys_4))) ((append1229289570le_alt ((dropWh680325334le_alt P_5) Xs_8)) Ys_4))))) of role axiom named fact_604_dropWhile__append1
% A new axiom: (forall (Ys_4:list_P736798472le_alt) (P_5:(produc1501160679le_alt->Prop)) (X_5:produc1501160679le_alt) (Xs_8:list_P736798472le_alt), (((member214075476le_alt X_5) (set_Pr1525059414le_alt Xs_8))->(((P_5 X_5)->False)->(((eq list_P736798472le_alt) ((dropWh680325334le_alt P_5) ((append1229289570le_alt Xs_8) Ys_4))) ((append1229289570le_alt ((dropWh680325334le_alt P_5) Xs_8)) Ys_4)))))
% FOF formula (forall (X_4:arrow_475358991le_alt) (Xs_7:list_A2115238852le_alt), ((and (((member84363362le_alt X_4) (set_Ar577454304le_alt Xs_7))->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_4) Xs_7)) Xs_7))) ((((member84363362le_alt X_4) (set_Ar577454304le_alt Xs_7))->False)->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_4) Xs_7)) ((cons_A228743023le_alt X_4) Xs_7))))) of role axiom named fact_605_List_Oinsert__def
% A new axiom: (forall (X_4:arrow_475358991le_alt) (Xs_7:list_A2115238852le_alt), ((and (((member84363362le_alt X_4) (set_Ar577454304le_alt Xs_7))->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_4) Xs_7)) Xs_7))) ((((member84363362le_alt X_4) (set_Ar577454304le_alt Xs_7))->False)->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_4) Xs_7)) ((cons_A228743023le_alt X_4) Xs_7)))))
% FOF formula (forall (X_4:produc1362454231le_alt) (Xs_7:list_P1295265784le_alt), ((and (((member28618436le_alt X_4) (set_Pr412222150le_alt Xs_7))->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_4) Xs_7)) Xs_7))) ((((member28618436le_alt X_4) (set_Pr412222150le_alt Xs_7))->False)->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_4) Xs_7)) ((cons_P2048401015le_alt X_4) Xs_7))))) of role axiom named fact_606_List_Oinsert__def
% A new axiom: (forall (X_4:produc1362454231le_alt) (Xs_7:list_P1295265784le_alt), ((and (((member28618436le_alt X_4) (set_Pr412222150le_alt Xs_7))->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_4) Xs_7)) Xs_7))) ((((member28618436le_alt X_4) (set_Pr412222150le_alt Xs_7))->False)->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_4) Xs_7)) ((cons_P2048401015le_alt X_4) Xs_7)))))
% FOF formula (forall (X_4:arrow_1429601828e_indi) (Xs_7:list_A1484739013e_indi), ((and (((member2052026769e_indi X_4) (set_Ar778541203e_indi Xs_7))->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_4) Xs_7)) Xs_7))) ((((member2052026769e_indi X_4) (set_Ar778541203e_indi Xs_7))->False)->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_4) Xs_7)) ((cons_A663037380e_indi X_4) Xs_7))))) of role axiom named fact_607_List_Oinsert__def
% A new axiom: (forall (X_4:arrow_1429601828e_indi) (Xs_7:list_A1484739013e_indi), ((and (((member2052026769e_indi X_4) (set_Ar778541203e_indi Xs_7))->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_4) Xs_7)) Xs_7))) ((((member2052026769e_indi X_4) (set_Ar778541203e_indi Xs_7))->False)->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_4) Xs_7)) ((cons_A663037380e_indi X_4) Xs_7)))))
% FOF formula (forall (X_4:Prop) (Xs_7:list_o), ((and (((member_o X_4) (set_o Xs_7))->(((eq list_o) ((insert_o X_4) Xs_7)) Xs_7))) ((((member_o X_4) (set_o Xs_7))->False)->(((eq list_o) ((insert_o X_4) Xs_7)) ((cons_o X_4) Xs_7))))) of role axiom named fact_608_List_Oinsert__def
% A new axiom: (forall (X_4:Prop) (Xs_7:list_o), ((and (((member_o X_4) (set_o Xs_7))->(((eq list_o) ((insert_o X_4) Xs_7)) Xs_7))) ((((member_o X_4) (set_o Xs_7))->False)->(((eq list_o) ((insert_o X_4) Xs_7)) ((cons_o X_4) Xs_7)))))
% FOF formula (forall (X_4:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_7:list_A518015091_alt_o), ((and (((member616898751_alt_o X_4) (set_Ar1356274881_alt_o Xs_7))->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_4) Xs_7)) Xs_7))) ((((member616898751_alt_o X_4) (set_Ar1356274881_alt_o Xs_7))->False)->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_4) Xs_7)) ((cons_A279268466_alt_o X_4) Xs_7))))) of role axiom named fact_609_List_Oinsert__def
% A new axiom: (forall (X_4:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_7:list_A518015091_alt_o), ((and (((member616898751_alt_o X_4) (set_Ar1356274881_alt_o Xs_7))->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_4) Xs_7)) Xs_7))) ((((member616898751_alt_o X_4) (set_Ar1356274881_alt_o Xs_7))->False)->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_4) Xs_7)) ((cons_A279268466_alt_o X_4) Xs_7)))))
% FOF formula (forall (X_4:(produc1501160679le_alt->Prop)) (Xs_7:list_P1178103901_alt_o), ((and (((member377231867_alt_o X_4) (set_Pr592386425_alt_o Xs_7))->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_4) Xs_7)) Xs_7))) ((((member377231867_alt_o X_4) (set_Pr592386425_alt_o Xs_7))->False)->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_4) Xs_7)) ((cons_P1239653256_alt_o X_4) Xs_7))))) of role axiom named fact_610_List_Oinsert__def
% A new axiom: (forall (X_4:(produc1501160679le_alt->Prop)) (Xs_7:list_P1178103901_alt_o), ((and (((member377231867_alt_o X_4) (set_Pr592386425_alt_o Xs_7))->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_4) Xs_7)) Xs_7))) ((((member377231867_alt_o X_4) (set_Pr592386425_alt_o Xs_7))->False)->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_4) Xs_7)) ((cons_P1239653256_alt_o X_4) Xs_7)))))
% FOF formula (forall (X_4:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_7:list_A524553945_alt_o), ((and (((member526088951_alt_o X_4) (set_Ar571341173_alt_o Xs_7))->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_4) Xs_7)) Xs_7))) ((((member526088951_alt_o X_4) (set_Ar571341173_alt_o Xs_7))->False)->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_4) Xs_7)) ((cons_A2010997508_alt_o X_4) Xs_7))))) of role axiom named fact_611_List_Oinsert__def
% A new axiom: (forall (X_4:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_7:list_A524553945_alt_o), ((and (((member526088951_alt_o X_4) (set_Ar571341173_alt_o Xs_7))->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_4) Xs_7)) Xs_7))) ((((member526088951_alt_o X_4) (set_Ar571341173_alt_o Xs_7))->False)->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_4) Xs_7)) ((cons_A2010997508_alt_o X_4) Xs_7)))))
% FOF formula (forall (X_4:produc1501160679le_alt) (Xs_7:list_P736798472le_alt), ((and (((member214075476le_alt X_4) (set_Pr1525059414le_alt Xs_7))->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_4) Xs_7)) Xs_7))) ((((member214075476le_alt X_4) (set_Pr1525059414le_alt Xs_7))->False)->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_4) Xs_7)) ((cons_P1913588871le_alt X_4) Xs_7))))) of role axiom named fact_612_List_Oinsert__def
% A new axiom: (forall (X_4:produc1501160679le_alt) (Xs_7:list_P736798472le_alt), ((and (((member214075476le_alt X_4) (set_Pr1525059414le_alt Xs_7))->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_4) Xs_7)) Xs_7))) ((((member214075476le_alt X_4) (set_Pr1525059414le_alt Xs_7))->False)->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_4) Xs_7)) ((cons_P1913588871le_alt X_4) Xs_7)))))
% FOF formula (forall (X_3:arrow_475358991le_alt) (Xs_6:list_A2115238852le_alt), ((((member84363362le_alt X_3) (set_Ar577454304le_alt Xs_6))->False)->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_3) Xs_6)) ((cons_A228743023le_alt X_3) Xs_6)))) of role axiom named fact_613_not__in__set__insert
% A new axiom: (forall (X_3:arrow_475358991le_alt) (Xs_6:list_A2115238852le_alt), ((((member84363362le_alt X_3) (set_Ar577454304le_alt Xs_6))->False)->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_3) Xs_6)) ((cons_A228743023le_alt X_3) Xs_6))))
% FOF formula (forall (X_3:produc1362454231le_alt) (Xs_6:list_P1295265784le_alt), ((((member28618436le_alt X_3) (set_Pr412222150le_alt Xs_6))->False)->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_3) Xs_6)) ((cons_P2048401015le_alt X_3) Xs_6)))) of role axiom named fact_614_not__in__set__insert
% A new axiom: (forall (X_3:produc1362454231le_alt) (Xs_6:list_P1295265784le_alt), ((((member28618436le_alt X_3) (set_Pr412222150le_alt Xs_6))->False)->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_3) Xs_6)) ((cons_P2048401015le_alt X_3) Xs_6))))
% FOF formula (forall (X_3:arrow_1429601828e_indi) (Xs_6:list_A1484739013e_indi), ((((member2052026769e_indi X_3) (set_Ar778541203e_indi Xs_6))->False)->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_3) Xs_6)) ((cons_A663037380e_indi X_3) Xs_6)))) of role axiom named fact_615_not__in__set__insert
% A new axiom: (forall (X_3:arrow_1429601828e_indi) (Xs_6:list_A1484739013e_indi), ((((member2052026769e_indi X_3) (set_Ar778541203e_indi Xs_6))->False)->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_3) Xs_6)) ((cons_A663037380e_indi X_3) Xs_6))))
% FOF formula (forall (X_3:Prop) (Xs_6:list_o), ((((member_o X_3) (set_o Xs_6))->False)->(((eq list_o) ((insert_o X_3) Xs_6)) ((cons_o X_3) Xs_6)))) of role axiom named fact_616_not__in__set__insert
% A new axiom: (forall (X_3:Prop) (Xs_6:list_o), ((((member_o X_3) (set_o Xs_6))->False)->(((eq list_o) ((insert_o X_3) Xs_6)) ((cons_o X_3) Xs_6))))
% FOF formula (forall (X_3:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_6:list_A518015091_alt_o), ((((member616898751_alt_o X_3) (set_Ar1356274881_alt_o Xs_6))->False)->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_3) Xs_6)) ((cons_A279268466_alt_o X_3) Xs_6)))) of role axiom named fact_617_not__in__set__insert
% A new axiom: (forall (X_3:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_6:list_A518015091_alt_o), ((((member616898751_alt_o X_3) (set_Ar1356274881_alt_o Xs_6))->False)->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_3) Xs_6)) ((cons_A279268466_alt_o X_3) Xs_6))))
% FOF formula (forall (X_3:(produc1501160679le_alt->Prop)) (Xs_6:list_P1178103901_alt_o), ((((member377231867_alt_o X_3) (set_Pr592386425_alt_o Xs_6))->False)->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_3) Xs_6)) ((cons_P1239653256_alt_o X_3) Xs_6)))) of role axiom named fact_618_not__in__set__insert
% A new axiom: (forall (X_3:(produc1501160679le_alt->Prop)) (Xs_6:list_P1178103901_alt_o), ((((member377231867_alt_o X_3) (set_Pr592386425_alt_o Xs_6))->False)->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_3) Xs_6)) ((cons_P1239653256_alt_o X_3) Xs_6))))
% FOF formula (forall (X_3:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_6:list_A524553945_alt_o), ((((member526088951_alt_o X_3) (set_Ar571341173_alt_o Xs_6))->False)->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_3) Xs_6)) ((cons_A2010997508_alt_o X_3) Xs_6)))) of role axiom named fact_619_not__in__set__insert
% A new axiom: (forall (X_3:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_6:list_A524553945_alt_o), ((((member526088951_alt_o X_3) (set_Ar571341173_alt_o Xs_6))->False)->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_3) Xs_6)) ((cons_A2010997508_alt_o X_3) Xs_6))))
% FOF formula (forall (X_3:produc1501160679le_alt) (Xs_6:list_P736798472le_alt), ((((member214075476le_alt X_3) (set_Pr1525059414le_alt Xs_6))->False)->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_3) Xs_6)) ((cons_P1913588871le_alt X_3) Xs_6)))) of role axiom named fact_620_not__in__set__insert
% A new axiom: (forall (X_3:produc1501160679le_alt) (Xs_6:list_P736798472le_alt), ((((member214075476le_alt X_3) (set_Pr1525059414le_alt Xs_6))->False)->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_3) Xs_6)) ((cons_P1913588871le_alt X_3) Xs_6))))
% FOF formula (forall (P_4:(arrow_475358991le_alt->Prop)) (Xs_5:list_A2115238852le_alt) (Yes:list_A2115238852le_alt) (No:list_A2115238852le_alt), ((((eq produc1362454231le_alt) ((partit1487577784le_alt P_4) Xs_5)) ((produc776457805le_alt Yes) No))->((and (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Yes))->(P_4 X_2)))) (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt No))->((P_4 X_2)->False)))))) of role axiom named fact_621_partition__P
% A new axiom: (forall (P_4:(arrow_475358991le_alt->Prop)) (Xs_5:list_A2115238852le_alt) (Yes:list_A2115238852le_alt) (No:list_A2115238852le_alt), ((((eq produc1362454231le_alt) ((partit1487577784le_alt P_4) Xs_5)) ((produc776457805le_alt Yes) No))->((and (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Yes))->(P_4 X_2)))) (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt No))->((P_4 X_2)->False))))))
% FOF formula (forall (Zs_1:list_A2115238852le_alt) (Ys_3:list_A2115238852le_alt) (R:(produc1501160679le_alt->Prop)) (Xs_4:list_A2115238852le_alt), ((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt) (Z:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_4))->(((member214075476le_alt ((produc1347929815le_alt X_2) Y_1)) R)->(((member214075476le_alt ((produc1347929815le_alt Y_1) Z)) R)->((member214075476le_alt ((produc1347929815le_alt X_2) Z)) R)))))->(((member28618436le_alt ((produc776457805le_alt Xs_4) Ys_3)) (lexord958095404le_alt R))->(((member28618436le_alt ((produc776457805le_alt Ys_3) Zs_1)) (lexord958095404le_alt R))->((member28618436le_alt ((produc776457805le_alt Xs_4) Zs_1)) (lexord958095404le_alt R)))))) of role axiom named fact_622_lexord__partial__trans
% A new axiom: (forall (Zs_1:list_A2115238852le_alt) (Ys_3:list_A2115238852le_alt) (R:(produc1501160679le_alt->Prop)) (Xs_4:list_A2115238852le_alt), ((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt) (Z:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_4))->(((member214075476le_alt ((produc1347929815le_alt X_2) Y_1)) R)->(((member214075476le_alt ((produc1347929815le_alt Y_1) Z)) R)->((member214075476le_alt ((produc1347929815le_alt X_2) Z)) R)))))->(((member28618436le_alt ((produc776457805le_alt Xs_4) Ys_3)) (lexord958095404le_alt R))->(((member28618436le_alt ((produc776457805le_alt Ys_3) Zs_1)) (lexord958095404le_alt R))->((member28618436le_alt ((produc776457805le_alt Xs_4) Zs_1)) (lexord958095404le_alt R))))))
% FOF formula (forall (Zs_1:list_l1475218533le_alt) (Ys_3:list_l1475218533le_alt) (R:(produc1362454231le_alt->Prop)) (Xs_4:list_l1475218533le_alt), ((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt) (Z:list_A2115238852le_alt), (((member998134961le_alt X_2) (set_li1631982259le_alt Xs_4))->(((member28618436le_alt ((produc776457805le_alt X_2) Y_1)) R)->(((member28618436le_alt ((produc776457805le_alt Y_1) Z)) R)->((member28618436le_alt ((produc776457805le_alt X_2) Z)) R)))))->(((member1732936276le_alt ((produc1317709143le_alt Xs_4) Ys_3)) (lexord469916775le_alt R))->(((member1732936276le_alt ((produc1317709143le_alt Ys_3) Zs_1)) (lexord469916775le_alt R))->((member1732936276le_alt ((produc1317709143le_alt Xs_4) Zs_1)) (lexord469916775le_alt R)))))) of role axiom named fact_623_lexord__partial__trans
% A new axiom: (forall (Zs_1:list_l1475218533le_alt) (Ys_3:list_l1475218533le_alt) (R:(produc1362454231le_alt->Prop)) (Xs_4:list_l1475218533le_alt), ((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt) (Z:list_A2115238852le_alt), (((member998134961le_alt X_2) (set_li1631982259le_alt Xs_4))->(((member28618436le_alt ((produc776457805le_alt X_2) Y_1)) R)->(((member28618436le_alt ((produc776457805le_alt Y_1) Z)) R)->((member28618436le_alt ((produc776457805le_alt X_2) Z)) R)))))->(((member1732936276le_alt ((produc1317709143le_alt Xs_4) Ys_3)) (lexord469916775le_alt R))->(((member1732936276le_alt ((produc1317709143le_alt Ys_3) Zs_1)) (lexord469916775le_alt R))->((member1732936276le_alt ((produc1317709143le_alt Xs_4) Zs_1)) (lexord469916775le_alt R))))))
% FOF formula (forall (Zs_1:list_P1295265784le_alt) (Ys_3:list_P1295265784le_alt) (R:(produc1787997437le_alt->Prop)) (Xs_4:list_P1295265784le_alt), ((forall (X_2:produc1362454231le_alt) (Y_1:produc1362454231le_alt) (Z:produc1362454231le_alt), (((member28618436le_alt X_2) (set_Pr412222150le_alt Xs_4))->(((member902484714le_alt ((produc1443807987le_alt X_2) Y_1)) R)->(((member902484714le_alt ((produc1443807987le_alt Y_1) Z)) R)->((member902484714le_alt ((produc1443807987le_alt X_2) Z)) R)))))->(((member608607380le_alt ((produc1065979415le_alt Xs_4) Ys_3)) (lexord973342842le_alt R))->(((member608607380le_alt ((produc1065979415le_alt Ys_3) Zs_1)) (lexord973342842le_alt R))->((member608607380le_alt ((produc1065979415le_alt Xs_4) Zs_1)) (lexord973342842le_alt R)))))) of role axiom named fact_624_lexord__partial__trans
% A new axiom: (forall (Zs_1:list_P1295265784le_alt) (Ys_3:list_P1295265784le_alt) (R:(produc1787997437le_alt->Prop)) (Xs_4:list_P1295265784le_alt), ((forall (X_2:produc1362454231le_alt) (Y_1:produc1362454231le_alt) (Z:produc1362454231le_alt), (((member28618436le_alt X_2) (set_Pr412222150le_alt Xs_4))->(((member902484714le_alt ((produc1443807987le_alt X_2) Y_1)) R)->(((member902484714le_alt ((produc1443807987le_alt Y_1) Z)) R)->((member902484714le_alt ((produc1443807987le_alt X_2) Z)) R)))))->(((member608607380le_alt ((produc1065979415le_alt Xs_4) Ys_3)) (lexord973342842le_alt R))->(((member608607380le_alt ((produc1065979415le_alt Ys_3) Zs_1)) (lexord973342842le_alt R))->((member608607380le_alt ((produc1065979415le_alt Xs_4) Zs_1)) (lexord973342842le_alt R))))))
% FOF formula (forall (Zs_1:list_A1484739013e_indi) (Ys_3:list_A1484739013e_indi) (R:(produc1091721111e_indi->Prop)) (Xs_4:list_A1484739013e_indi), ((forall (X_2:arrow_1429601828e_indi) (Y_1:arrow_1429601828e_indi) (Z:arrow_1429601828e_indi), (((member2052026769e_indi X_2) (set_Ar778541203e_indi Xs_4))->(((member1239815300e_indi ((produc1851452045e_indi X_2) Y_1)) R)->(((member1239815300e_indi ((produc1851452045e_indi Y_1) Z)) R)->((member1239815300e_indi ((produc1851452045e_indi X_2) Z)) R)))))->(((member1618636500e_indi ((produc1195920727e_indi Xs_4) Ys_3)) (lexord1661684807e_indi R))->(((member1618636500e_indi ((produc1195920727e_indi Ys_3) Zs_1)) (lexord1661684807e_indi R))->((member1618636500e_indi ((produc1195920727e_indi Xs_4) Zs_1)) (lexord1661684807e_indi R)))))) of role axiom named fact_625_lexord__partial__trans
% A new axiom: (forall (Zs_1:list_A1484739013e_indi) (Ys_3:list_A1484739013e_indi) (R:(produc1091721111e_indi->Prop)) (Xs_4:list_A1484739013e_indi), ((forall (X_2:arrow_1429601828e_indi) (Y_1:arrow_1429601828e_indi) (Z:arrow_1429601828e_indi), (((member2052026769e_indi X_2) (set_Ar778541203e_indi Xs_4))->(((member1239815300e_indi ((produc1851452045e_indi X_2) Y_1)) R)->(((member1239815300e_indi ((produc1851452045e_indi Y_1) Z)) R)->((member1239815300e_indi ((produc1851452045e_indi X_2) Z)) R)))))->(((member1618636500e_indi ((produc1195920727e_indi Xs_4) Ys_3)) (lexord1661684807e_indi R))->(((member1618636500e_indi ((produc1195920727e_indi Ys_3) Zs_1)) (lexord1661684807e_indi R))->((member1618636500e_indi ((produc1195920727e_indi Xs_4) Zs_1)) (lexord1661684807e_indi R))))))
% FOF formula (forall (Zs_1:list_o) (Ys_3:list_o) (R:(product_prod_o_o->Prop)) (Xs_4:list_o), ((forall (X_2:Prop) (Y_1:Prop) (Z:Prop), (((member_o X_2) (set_o Xs_4))->(((member1392690260od_o_o ((product_Pair_o_o X_2) Y_1)) R)->(((member1392690260od_o_o ((product_Pair_o_o Y_1) Z)) R)->((member1392690260od_o_o ((product_Pair_o_o X_2) Z)) R)))))->(((member806300420list_o ((produc1835210381list_o Xs_4) Ys_3)) (lexord_o R))->(((member806300420list_o ((produc1835210381list_o Ys_3) Zs_1)) (lexord_o R))->((member806300420list_o ((produc1835210381list_o Xs_4) Zs_1)) (lexord_o R)))))) of role axiom named fact_626_lexord__partial__trans
% A new axiom: (forall (Zs_1:list_o) (Ys_3:list_o) (R:(product_prod_o_o->Prop)) (Xs_4:list_o), ((forall (X_2:Prop) (Y_1:Prop) (Z:Prop), (((member_o X_2) (set_o Xs_4))->(((member1392690260od_o_o ((product_Pair_o_o X_2) Y_1)) R)->(((member1392690260od_o_o ((product_Pair_o_o Y_1) Z)) R)->((member1392690260od_o_o ((product_Pair_o_o X_2) Z)) R)))))->(((member806300420list_o ((produc1835210381list_o Xs_4) Ys_3)) (lexord_o R))->(((member806300420list_o ((produc1835210381list_o Ys_3) Zs_1)) (lexord_o R))->((member806300420list_o ((produc1835210381list_o Xs_4) Zs_1)) (lexord_o R))))))
% FOF formula (forall (Zs_1:list_A518015091_alt_o) (Ys_3:list_A518015091_alt_o) (R:(produc344885491_alt_o->Prop)) (Xs_4:list_A518015091_alt_o), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Z:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) (set_Ar1356274881_alt_o Xs_4))->(((member1909339872_alt_o ((produc434968681_alt_o X_2) Y_1)) R)->(((member1909339872_alt_o ((produc434968681_alt_o Y_1) Z)) R)->((member1909339872_alt_o ((produc434968681_alt_o X_2) Z)) R)))))->(((member119836116_alt_o ((produc385333463_alt_o Xs_4) Ys_3)) (lexord1104163445_alt_o R))->(((member119836116_alt_o ((produc385333463_alt_o Ys_3) Zs_1)) (lexord1104163445_alt_o R))->((member119836116_alt_o ((produc385333463_alt_o Xs_4) Zs_1)) (lexord1104163445_alt_o R)))))) of role axiom named fact_627_lexord__partial__trans
% A new axiom: (forall (Zs_1:list_A518015091_alt_o) (Ys_3:list_A518015091_alt_o) (R:(produc344885491_alt_o->Prop)) (Xs_4:list_A518015091_alt_o), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Z:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) (set_Ar1356274881_alt_o Xs_4))->(((member1909339872_alt_o ((produc434968681_alt_o X_2) Y_1)) R)->(((member1909339872_alt_o ((produc434968681_alt_o Y_1) Z)) R)->((member1909339872_alt_o ((produc434968681_alt_o X_2) Z)) R)))))->(((member119836116_alt_o ((produc385333463_alt_o Xs_4) Ys_3)) (lexord1104163445_alt_o R))->(((member119836116_alt_o ((produc385333463_alt_o Ys_3) Zs_1)) (lexord1104163445_alt_o R))->((member119836116_alt_o ((produc385333463_alt_o Xs_4) Zs_1)) (lexord1104163445_alt_o R))))))
% FOF formula (forall (Zs_1:list_P1178103901_alt_o) (Ys_3:list_P1178103901_alt_o) (R:(produc603869735_alt_o->Prop)) (Xs_4:list_P1178103901_alt_o), ((forall (X_2:(produc1501160679le_alt->Prop)) (Y_1:(produc1501160679le_alt->Prop)) (Z:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) (set_Pr592386425_alt_o Xs_4))->(((member1998617236_alt_o ((produc548346135_alt_o X_2) Y_1)) R)->(((member1998617236_alt_o ((produc548346135_alt_o Y_1) Z)) R)->((member1998617236_alt_o ((produc548346135_alt_o X_2) Z)) R)))))->(((member79660662_alt_o ((produc127168767_alt_o Xs_4) Ys_3)) (lexord842870469_alt_o R))->(((member79660662_alt_o ((produc127168767_alt_o Ys_3) Zs_1)) (lexord842870469_alt_o R))->((member79660662_alt_o ((produc127168767_alt_o Xs_4) Zs_1)) (lexord842870469_alt_o R)))))) of role axiom named fact_628_lexord__partial__trans
% A new axiom: (forall (Zs_1:list_P1178103901_alt_o) (Ys_3:list_P1178103901_alt_o) (R:(produc603869735_alt_o->Prop)) (Xs_4:list_P1178103901_alt_o), ((forall (X_2:(produc1501160679le_alt->Prop)) (Y_1:(produc1501160679le_alt->Prop)) (Z:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) (set_Pr592386425_alt_o Xs_4))->(((member1998617236_alt_o ((produc548346135_alt_o X_2) Y_1)) R)->(((member1998617236_alt_o ((produc548346135_alt_o Y_1) Z)) R)->((member1998617236_alt_o ((produc548346135_alt_o X_2) Z)) R)))))->(((member79660662_alt_o ((produc127168767_alt_o Xs_4) Ys_3)) (lexord842870469_alt_o R))->(((member79660662_alt_o ((produc127168767_alt_o Ys_3) Zs_1)) (lexord842870469_alt_o R))->((member79660662_alt_o ((produc127168767_alt_o Xs_4) Zs_1)) (lexord842870469_alt_o R))))))
% FOF formula (forall (Zs_1:list_A524553945_alt_o) (Ys_3:list_A524553945_alt_o) (R:(produc634020647_alt_o->Prop)) (Xs_4:list_A524553945_alt_o), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Z:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) (set_Ar571341173_alt_o Xs_4))->(((member423327892_alt_o ((produc425112727_alt_o X_2) Y_1)) R)->(((member423327892_alt_o ((produc425112727_alt_o Y_1) Z)) R)->((member423327892_alt_o ((produc425112727_alt_o X_2) Z)) R)))))->(((member1890873582_alt_o ((produc1301429239_alt_o Xs_4) Ys_3)) (lexord1645229249_alt_o R))->(((member1890873582_alt_o ((produc1301429239_alt_o Ys_3) Zs_1)) (lexord1645229249_alt_o R))->((member1890873582_alt_o ((produc1301429239_alt_o Xs_4) Zs_1)) (lexord1645229249_alt_o R)))))) of role axiom named fact_629_lexord__partial__trans
% A new axiom: (forall (Zs_1:list_A524553945_alt_o) (Ys_3:list_A524553945_alt_o) (R:(produc634020647_alt_o->Prop)) (Xs_4:list_A524553945_alt_o), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Z:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) (set_Ar571341173_alt_o Xs_4))->(((member423327892_alt_o ((produc425112727_alt_o X_2) Y_1)) R)->(((member423327892_alt_o ((produc425112727_alt_o Y_1) Z)) R)->((member423327892_alt_o ((produc425112727_alt_o X_2) Z)) R)))))->(((member1890873582_alt_o ((produc1301429239_alt_o Xs_4) Ys_3)) (lexord1645229249_alt_o R))->(((member1890873582_alt_o ((produc1301429239_alt_o Ys_3) Zs_1)) (lexord1645229249_alt_o R))->((member1890873582_alt_o ((produc1301429239_alt_o Xs_4) Zs_1)) (lexord1645229249_alt_o R))))))
% FOF formula (forall (Zs_1:list_P736798472le_alt) (Ys_3:list_P736798472le_alt) (R:(produc1076844957le_alt->Prop)) (Xs_4:list_P736798472le_alt), ((forall (X_2:produc1501160679le_alt) (Y_1:produc1501160679le_alt) (Z:produc1501160679le_alt), (((member214075476le_alt X_2) (set_Pr1525059414le_alt Xs_4))->(((member1664185994le_alt ((produc1348021779le_alt X_2) Y_1)) R)->(((member1664185994le_alt ((produc1348021779le_alt Y_1) Z)) R)->((member1664185994le_alt ((produc1348021779le_alt X_2) Z)) R)))))->(((member475755924le_alt ((produc1573901719le_alt Xs_4) Ys_3)) (lexord501678858le_alt R))->(((member475755924le_alt ((produc1573901719le_alt Ys_3) Zs_1)) (lexord501678858le_alt R))->((member475755924le_alt ((produc1573901719le_alt Xs_4) Zs_1)) (lexord501678858le_alt R)))))) of role axiom named fact_630_lexord__partial__trans
% A new axiom: (forall (Zs_1:list_P736798472le_alt) (Ys_3:list_P736798472le_alt) (R:(produc1076844957le_alt->Prop)) (Xs_4:list_P736798472le_alt), ((forall (X_2:produc1501160679le_alt) (Y_1:produc1501160679le_alt) (Z:produc1501160679le_alt), (((member214075476le_alt X_2) (set_Pr1525059414le_alt Xs_4))->(((member1664185994le_alt ((produc1348021779le_alt X_2) Y_1)) R)->(((member1664185994le_alt ((produc1348021779le_alt Y_1) Z)) R)->((member1664185994le_alt ((produc1348021779le_alt X_2) Z)) R)))))->(((member475755924le_alt ((produc1573901719le_alt Xs_4) Ys_3)) (lexord501678858le_alt R))->(((member475755924le_alt ((produc1573901719le_alt Ys_3) Zs_1)) (lexord501678858le_alt R))->((member475755924le_alt ((produc1573901719le_alt Xs_4) Zs_1)) (lexord501678858le_alt R))))))
% FOF formula (forall (Ys_2:list_A2115238852le_alt) (P_3:(arrow_475358991le_alt->Prop)) (Xs_3:list_A2115238852le_alt), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_3))->(P_3 X_2)))->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_3) ((append179082452le_alt Xs_3) Ys_2))) ((dropWh1316781920le_alt P_3) Ys_2)))) of role axiom named fact_631_dropWhile__append2
% A new axiom: (forall (Ys_2:list_A2115238852le_alt) (P_3:(arrow_475358991le_alt->Prop)) (Xs_3:list_A2115238852le_alt), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_3))->(P_3 X_2)))->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_3) ((append179082452le_alt Xs_3) Ys_2))) ((dropWh1316781920le_alt P_3) Ys_2))))
% FOF formula (forall (Ys_2:list_P1295265784le_alt) (P_3:(produc1362454231le_alt->Prop)) (Xs_3:list_P1295265784le_alt), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) (set_Pr412222150le_alt Xs_3))->(P_3 X_2)))->(((eq list_P1295265784le_alt) ((dropWh612508742le_alt P_3) ((append423770578le_alt Xs_3) Ys_2))) ((dropWh612508742le_alt P_3) Ys_2)))) of role axiom named fact_632_dropWhile__append2
% A new axiom: (forall (Ys_2:list_P1295265784le_alt) (P_3:(produc1362454231le_alt->Prop)) (Xs_3:list_P1295265784le_alt), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) (set_Pr412222150le_alt Xs_3))->(P_3 X_2)))->(((eq list_P1295265784le_alt) ((dropWh612508742le_alt P_3) ((append423770578le_alt Xs_3) Ys_2))) ((dropWh612508742le_alt P_3) Ys_2))))
% FOF formula (forall (Ys_2:list_A1484739013e_indi) (P_3:(arrow_1429601828e_indi->Prop)) (Xs_3:list_A1484739013e_indi), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) (set_Ar778541203e_indi Xs_3))->(P_3 X_2)))->(((eq list_A1484739013e_indi) ((dropWh1160116755e_indi P_3) ((append711934367e_indi Xs_3) Ys_2))) ((dropWh1160116755e_indi P_3) Ys_2)))) of role axiom named fact_633_dropWhile__append2
% A new axiom: (forall (Ys_2:list_A1484739013e_indi) (P_3:(arrow_1429601828e_indi->Prop)) (Xs_3:list_A1484739013e_indi), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) (set_Ar778541203e_indi Xs_3))->(P_3 X_2)))->(((eq list_A1484739013e_indi) ((dropWh1160116755e_indi P_3) ((append711934367e_indi Xs_3) Ys_2))) ((dropWh1160116755e_indi P_3) Ys_2))))
% FOF formula (forall (Ys_2:list_o) (P_3:(Prop->Prop)) (Xs_3:list_o), ((forall (X_2:Prop), (((member_o X_2) (set_o Xs_3))->(P_3 X_2)))->(((eq list_o) ((dropWhile_o P_3) ((append_o Xs_3) Ys_2))) ((dropWhile_o P_3) Ys_2)))) of role axiom named fact_634_dropWhile__append2
% A new axiom: (forall (Ys_2:list_o) (P_3:(Prop->Prop)) (Xs_3:list_o), ((forall (X_2:Prop), (((member_o X_2) (set_o Xs_3))->(P_3 X_2)))->(((eq list_o) ((dropWhile_o P_3) ((append_o Xs_3) Ys_2))) ((dropWhile_o P_3) Ys_2))))
% FOF formula (forall (Ys_2:list_A518015091_alt_o) (P_3:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (Xs_3:list_A518015091_alt_o), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) (set_Ar1356274881_alt_o Xs_3))->(P_3 X_2)))->(((eq list_A518015091_alt_o) ((dropWh583351873_alt_o P_3) ((append326058957_alt_o Xs_3) Ys_2))) ((dropWh583351873_alt_o P_3) Ys_2)))) of role axiom named fact_635_dropWhile__append2
% A new axiom: (forall (Ys_2:list_A518015091_alt_o) (P_3:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (Xs_3:list_A518015091_alt_o), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) (set_Ar1356274881_alt_o Xs_3))->(P_3 X_2)))->(((eq list_A518015091_alt_o) ((dropWh583351873_alt_o P_3) ((append326058957_alt_o Xs_3) Ys_2))) ((dropWh583351873_alt_o P_3) Ys_2))))
% FOF formula (forall (Ys_2:list_P1178103901_alt_o) (P_3:((produc1501160679le_alt->Prop)->Prop)) (Xs_3:list_P1178103901_alt_o), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) (set_Pr592386425_alt_o Xs_3))->(P_3 X_2)))->(((eq list_P1178103901_alt_o) ((dropWh1049991161_alt_o P_3) ((append612833133_alt_o Xs_3) Ys_2))) ((dropWh1049991161_alt_o P_3) Ys_2)))) of role axiom named fact_636_dropWhile__append2
% A new axiom: (forall (Ys_2:list_P1178103901_alt_o) (P_3:((produc1501160679le_alt->Prop)->Prop)) (Xs_3:list_P1178103901_alt_o), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) (set_Pr592386425_alt_o Xs_3))->(P_3 X_2)))->(((eq list_P1178103901_alt_o) ((dropWh1049991161_alt_o P_3) ((append612833133_alt_o Xs_3) Ys_2))) ((dropWh1049991161_alt_o P_3) Ys_2))))
% FOF formula (forall (Ys_2:list_A524553945_alt_o) (P_3:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (Xs_3:list_A524553945_alt_o), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) (set_Ar571341173_alt_o Xs_3))->(P_3 X_2)))->(((eq list_A524553945_alt_o) ((dropWh73644021_alt_o P_3) ((append295924073_alt_o Xs_3) Ys_2))) ((dropWh73644021_alt_o P_3) Ys_2)))) of role axiom named fact_637_dropWhile__append2
% A new axiom: (forall (Ys_2:list_A524553945_alt_o) (P_3:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (Xs_3:list_A524553945_alt_o), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) (set_Ar571341173_alt_o Xs_3))->(P_3 X_2)))->(((eq list_A524553945_alt_o) ((dropWh73644021_alt_o P_3) ((append295924073_alt_o Xs_3) Ys_2))) ((dropWh73644021_alt_o P_3) Ys_2))))
% FOF formula (forall (Ys_2:list_P736798472le_alt) (P_3:(produc1501160679le_alt->Prop)) (Xs_3:list_P736798472le_alt), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) (set_Pr1525059414le_alt Xs_3))->(P_3 X_2)))->(((eq list_P736798472le_alt) ((dropWh680325334le_alt P_3) ((append1229289570le_alt Xs_3) Ys_2))) ((dropWh680325334le_alt P_3) Ys_2)))) of role axiom named fact_638_dropWhile__append2
% A new axiom: (forall (Ys_2:list_P736798472le_alt) (P_3:(produc1501160679le_alt->Prop)) (Xs_3:list_P736798472le_alt), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) (set_Pr1525059414le_alt Xs_3))->(P_3 X_2)))->(((eq list_P736798472le_alt) ((dropWh680325334le_alt P_3) ((append1229289570le_alt Xs_3) Ys_2))) ((dropWh680325334le_alt P_3) Ys_2))))
% FOF formula (forall (Ys_1:list_A2115238852le_alt) (P_2:(arrow_475358991le_alt->Prop)) (Xs_2:list_A2115238852le_alt), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_2))->(P_2 X_2)))->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_2) ((append179082452le_alt Xs_2) Ys_1))) ((append179082452le_alt Xs_2) ((takeWh1696291512le_alt P_2) Ys_1))))) of role axiom named fact_639_takeWhile__append2
% A new axiom: (forall (Ys_1:list_A2115238852le_alt) (P_2:(arrow_475358991le_alt->Prop)) (Xs_2:list_A2115238852le_alt), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_2))->(P_2 X_2)))->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_2) ((append179082452le_alt Xs_2) Ys_1))) ((append179082452le_alt Xs_2) ((takeWh1696291512le_alt P_2) Ys_1)))))
% FOF formula (forall (Ys_1:list_P1295265784le_alt) (P_2:(produc1362454231le_alt->Prop)) (Xs_2:list_P1295265784le_alt), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) (set_Pr412222150le_alt Xs_2))->(P_2 X_2)))->(((eq list_P1295265784le_alt) ((takeWh1571807982le_alt P_2) ((append423770578le_alt Xs_2) Ys_1))) ((append423770578le_alt Xs_2) ((takeWh1571807982le_alt P_2) Ys_1))))) of role axiom named fact_640_takeWhile__append2
% A new axiom: (forall (Ys_1:list_P1295265784le_alt) (P_2:(produc1362454231le_alt->Prop)) (Xs_2:list_P1295265784le_alt), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) (set_Pr412222150le_alt Xs_2))->(P_2 X_2)))->(((eq list_P1295265784le_alt) ((takeWh1571807982le_alt P_2) ((append423770578le_alt Xs_2) Ys_1))) ((append423770578le_alt Xs_2) ((takeWh1571807982le_alt P_2) Ys_1)))))
% FOF formula (forall (Ys_1:list_A1484739013e_indi) (P_2:(arrow_1429601828e_indi->Prop)) (Xs_2:list_A1484739013e_indi), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) (set_Ar778541203e_indi Xs_2))->(P_2 X_2)))->(((eq list_A1484739013e_indi) ((takeWh831911099e_indi P_2) ((append711934367e_indi Xs_2) Ys_1))) ((append711934367e_indi Xs_2) ((takeWh831911099e_indi P_2) Ys_1))))) of role axiom named fact_641_takeWhile__append2
% A new axiom: (forall (Ys_1:list_A1484739013e_indi) (P_2:(arrow_1429601828e_indi->Prop)) (Xs_2:list_A1484739013e_indi), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) (set_Ar778541203e_indi Xs_2))->(P_2 X_2)))->(((eq list_A1484739013e_indi) ((takeWh831911099e_indi P_2) ((append711934367e_indi Xs_2) Ys_1))) ((append711934367e_indi Xs_2) ((takeWh831911099e_indi P_2) Ys_1)))))
% FOF formula (forall (Ys_1:list_o) (P_2:(Prop->Prop)) (Xs_2:list_o), ((forall (X_2:Prop), (((member_o X_2) (set_o Xs_2))->(P_2 X_2)))->(((eq list_o) ((takeWhile_o P_2) ((append_o Xs_2) Ys_1))) ((append_o Xs_2) ((takeWhile_o P_2) Ys_1))))) of role axiom named fact_642_takeWhile__append2
% A new axiom: (forall (Ys_1:list_o) (P_2:(Prop->Prop)) (Xs_2:list_o), ((forall (X_2:Prop), (((member_o X_2) (set_o Xs_2))->(P_2 X_2)))->(((eq list_o) ((takeWhile_o P_2) ((append_o Xs_2) Ys_1))) ((append_o Xs_2) ((takeWhile_o P_2) Ys_1)))))
% FOF formula (forall (Ys_1:list_A518015091_alt_o) (P_2:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (Xs_2:list_A518015091_alt_o), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) (set_Ar1356274881_alt_o Xs_2))->(P_2 X_2)))->(((eq list_A518015091_alt_o) ((takeWh877796585_alt_o P_2) ((append326058957_alt_o Xs_2) Ys_1))) ((append326058957_alt_o Xs_2) ((takeWh877796585_alt_o P_2) Ys_1))))) of role axiom named fact_643_takeWhile__append2
% A new axiom: (forall (Ys_1:list_A518015091_alt_o) (P_2:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (Xs_2:list_A518015091_alt_o), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) (set_Ar1356274881_alt_o Xs_2))->(P_2 X_2)))->(((eq list_A518015091_alt_o) ((takeWh877796585_alt_o P_2) ((append326058957_alt_o Xs_2) Ys_1))) ((append326058957_alt_o Xs_2) ((takeWh877796585_alt_o P_2) Ys_1)))))
% FOF formula (forall (Ys_1:list_P1178103901_alt_o) (P_2:((produc1501160679le_alt->Prop)->Prop)) (Xs_2:list_P1178103901_alt_o), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) (set_Pr592386425_alt_o Xs_2))->(P_2 X_2)))->(((eq list_P1178103901_alt_o) ((takeWh1715715921_alt_o P_2) ((append612833133_alt_o Xs_2) Ys_1))) ((append612833133_alt_o Xs_2) ((takeWh1715715921_alt_o P_2) Ys_1))))) of role axiom named fact_644_takeWhile__append2
% A new axiom: (forall (Ys_1:list_P1178103901_alt_o) (P_2:((produc1501160679le_alt->Prop)->Prop)) (Xs_2:list_P1178103901_alt_o), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) (set_Pr592386425_alt_o Xs_2))->(P_2 X_2)))->(((eq list_P1178103901_alt_o) ((takeWh1715715921_alt_o P_2) ((append612833133_alt_o Xs_2) Ys_1))) ((append612833133_alt_o Xs_2) ((takeWh1715715921_alt_o P_2) Ys_1)))))
% FOF formula (forall (Ys_1:list_A524553945_alt_o) (P_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (Xs_2:list_A524553945_alt_o), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) (set_Ar571341173_alt_o Xs_2))->(P_2 X_2)))->(((eq list_A524553945_alt_o) ((takeWh1825606477_alt_o P_2) ((append295924073_alt_o Xs_2) Ys_1))) ((append295924073_alt_o Xs_2) ((takeWh1825606477_alt_o P_2) Ys_1))))) of role axiom named fact_645_takeWhile__append2
% A new axiom: (forall (Ys_1:list_A524553945_alt_o) (P_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (Xs_2:list_A524553945_alt_o), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) (set_Ar571341173_alt_o Xs_2))->(P_2 X_2)))->(((eq list_A524553945_alt_o) ((takeWh1825606477_alt_o P_2) ((append295924073_alt_o Xs_2) Ys_1))) ((append295924073_alt_o Xs_2) ((takeWh1825606477_alt_o P_2) Ys_1)))))
% FOF formula (forall (Ys_1:list_P736798472le_alt) (P_2:(produc1501160679le_alt->Prop)) (Xs_2:list_P736798472le_alt), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) (set_Pr1525059414le_alt Xs_2))->(P_2 X_2)))->(((eq list_P736798472le_alt) ((takeWh302148478le_alt P_2) ((append1229289570le_alt Xs_2) Ys_1))) ((append1229289570le_alt Xs_2) ((takeWh302148478le_alt P_2) Ys_1))))) of role axiom named fact_646_takeWhile__append2
% A new axiom: (forall (Ys_1:list_P736798472le_alt) (P_2:(produc1501160679le_alt->Prop)) (Xs_2:list_P736798472le_alt), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) (set_Pr1525059414le_alt Xs_2))->(P_2 X_2)))->(((eq list_P736798472le_alt) ((takeWh302148478le_alt P_2) ((append1229289570le_alt Xs_2) Ys_1))) ((append1229289570le_alt Xs_2) ((takeWh302148478le_alt P_2) Ys_1)))))
% FOF formula (forall (P_1:(arrow_475358991le_alt->Prop)) (Xs_1:list_A2115238852le_alt), (((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((and ((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_1))) (P_1 X_2))))->((forall (Ys:list_A2115238852le_alt) (X_2:arrow_475358991le_alt), (((ex list_A2115238852le_alt) (fun (Zs:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Xs_1) ((append179082452le_alt Ys) ((cons_A228743023le_alt X_2) Zs)))))->((P_1 X_2)->False)))->False))) of role axiom named fact_647_split__list__propE
% A new axiom: (forall (P_1:(arrow_475358991le_alt->Prop)) (Xs_1:list_A2115238852le_alt), (((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((and ((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_1))) (P_1 X_2))))->((forall (Ys:list_A2115238852le_alt) (X_2:arrow_475358991le_alt), (((ex list_A2115238852le_alt) (fun (Zs:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Xs_1) ((append179082452le_alt Ys) ((cons_A228743023le_alt X_2) Zs)))))->((P_1 X_2)->False)))->False)))
% FOF formula (forall (X_1:(produc1501160679le_alt->Prop)) (Xs:list_P1178103901_alt_o), ((iff ((member377231867_alt_o X_1) (set_Pr592386425_alt_o Xs))) ((ex list_P1178103901_alt_o) (fun (Ys:list_P1178103901_alt_o)=> ((ex list_P1178103901_alt_o) (fun (Zs:list_P1178103901_alt_o)=> (((eq list_P1178103901_alt_o) Xs) ((append612833133_alt_o Ys) ((cons_P1239653256_alt_o X_1) Zs))))))))) of role axiom named fact_648_in__set__conv__decomp
% A new axiom: (forall (X_1:(produc1501160679le_alt->Prop)) (Xs:list_P1178103901_alt_o), ((iff ((member377231867_alt_o X_1) (set_Pr592386425_alt_o Xs))) ((ex list_P1178103901_alt_o) (fun (Ys:list_P1178103901_alt_o)=> ((ex list_P1178103901_alt_o) (fun (Zs:list_P1178103901_alt_o)=> (((eq list_P1178103901_alt_o) Xs) ((append612833133_alt_o Ys) ((cons_P1239653256_alt_o X_1) Zs)))))))))
% FOF formula (forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs:list_A524553945_alt_o), ((iff ((member526088951_alt_o X_1) (set_Ar571341173_alt_o Xs))) ((ex list_A524553945_alt_o) (fun (Ys:list_A524553945_alt_o)=> ((ex list_A524553945_alt_o) (fun (Zs:list_A524553945_alt_o)=> (((eq list_A524553945_alt_o) Xs) ((append295924073_alt_o Ys) ((cons_A2010997508_alt_o X_1) Zs))))))))) of role axiom named fact_649_in__set__conv__decomp
% A new axiom: (forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs:list_A524553945_alt_o), ((iff ((member526088951_alt_o X_1) (set_Ar571341173_alt_o Xs))) ((ex list_A524553945_alt_o) (fun (Ys:list_A524553945_alt_o)=> ((ex list_A524553945_alt_o) (fun (Zs:list_A524553945_alt_o)=> (((eq list_A524553945_alt_o) Xs) ((append295924073_alt_o Ys) ((cons_A2010997508_alt_o X_1) Zs)))))))))
% FOF formula (forall (X_1:produc1501160679le_alt) (Xs:list_P736798472le_alt), ((iff ((member214075476le_alt X_1) (set_Pr1525059414le_alt Xs))) ((ex list_P736798472le_alt) (fun (Ys:list_P736798472le_alt)=> ((ex list_P736798472le_alt) (fun (Zs:list_P736798472le_alt)=> (((eq list_P736798472le_alt) Xs) ((append1229289570le_alt Ys) ((cons_P1913588871le_alt X_1) Zs))))))))) of role axiom named fact_650_in__set__conv__decomp
% A new axiom: (forall (X_1:produc1501160679le_alt) (Xs:list_P736798472le_alt), ((iff ((member214075476le_alt X_1) (set_Pr1525059414le_alt Xs))) ((ex list_P736798472le_alt) (fun (Ys:list_P736798472le_alt)=> ((ex list_P736798472le_alt) (fun (Zs:list_P736798472le_alt)=> (((eq list_P736798472le_alt) Xs) ((append1229289570le_alt Ys) ((cons_P1913588871le_alt X_1) Zs)))))))))
% FOF formula (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y))) of role axiom named fact_651_termination__basic__simps_I5_J
% A new axiom: (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y)))
% FOF formula (forall (N:nat), ((ord_less_nat N) (suc N))) of role axiom named fact_652_lessI
% A new axiom: (forall (N:nat), ((ord_less_nat N) (suc N)))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat (suc M)) (suc N)))) of role axiom named fact_653_Suc__mono
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat (suc M)) (suc N))))
% FOF formula (forall (N:nat), (not (((eq nat) N) (suc N)))) of role axiom named fact_654_n__not__Suc__n
% A new axiom: (forall (N:nat), (not (((eq nat) N) (suc N))))
% FOF formula (forall (N:nat), (not (((eq nat) (suc N)) N))) of role axiom named fact_655_Suc__n__not__n
% A new axiom: (forall (N:nat), (not (((eq nat) (suc N)) N)))
% FOF formula (forall (Nat_1:nat) (Nat:nat), ((iff (((eq nat) (suc Nat_1)) (suc Nat))) (((eq nat) Nat_1) Nat))) of role axiom named fact_656_nat_Oinject
% A new axiom: (forall (Nat_1:nat) (Nat:nat), ((iff (((eq nat) (suc Nat_1)) (suc Nat))) (((eq nat) Nat_1) Nat)))
% FOF formula (forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y))) of role axiom named fact_657_Suc__inject
% A new axiom: (forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y)))
% FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_658_less__not__refl
% A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% FOF formula (forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))) of role axiom named fact_659_nat__neq__iff
% A new axiom: (forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M))))
% FOF formula (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))) of role axiom named fact_660_linorder__neqE__nat
% A new axiom: (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X))))
% FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_661_less__irrefl__nat
% A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% FOF formula (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))) of role axiom named fact_662_less__not__refl2
% A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N))))
% FOF formula (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) of role axiom named fact_663_less__not__refl3
% A new axiom: (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T))))
% FOF formula (forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))) of role axiom named fact_664_nat__less__cases
% A new axiom: (forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M)))))
% FOF formula (forall (N:nat), ((ord_less_eq_nat N) N)) of role axiom named fact_665_le__refl
% A new axiom: (forall (N:nat), ((ord_less_eq_nat N) N))
% FOF formula (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))) of role axiom named fact_666_nat__le__linear
% A new axiom: (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M)))
% FOF formula (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_667_eq__imp__le
% A new axiom: (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N)))
% FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat I_1) K)))) of role axiom named fact_668_le__trans
% A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat I_1) K))))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))) of role axiom named fact_669_le__antisym
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N))))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_nat (suc M)) (suc N))->((ord_less_nat M) N))) of role axiom named fact_670_Suc__less__SucD
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat (suc M)) (suc N))->((ord_less_nat M) N)))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_nat (suc M)) N)->((ord_less_nat M) N))) of role axiom named fact_671_Suc__lessD
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat (suc M)) N)->((ord_less_nat M) N)))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) (suc N))->((((ord_less_nat M) N)->False)->(((eq nat) M) N)))) of role axiom named fact_672_less__SucE
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) (suc N))->((((ord_less_nat M) N)->False)->(((eq nat) M) N))))
% FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat J) K)->((ord_less_nat (suc I_1)) K)))) of role axiom named fact_673_less__trans__Suc
% A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat J) K)->((ord_less_nat (suc I_1)) K))))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((not (((eq nat) (suc M)) N))->((ord_less_nat (suc M)) N)))) of role axiom named fact_674_Suc__lessI
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((not (((eq nat) (suc M)) N))->((ord_less_nat (suc M)) N))))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat M) (suc N)))) of role axiom named fact_675_less__SucI
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat M) (suc N))))
% FOF formula (forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->(((ord_less_nat N) (suc M))->(((eq nat) M) N)))) of role axiom named fact_676_less__antisym
% A new axiom: (forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->(((ord_less_nat N) (suc M))->(((eq nat) M) N))))
% FOF formula (forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->((iff ((ord_less_nat N) (suc M))) (((eq nat) N) M)))) of role axiom named fact_677_not__less__less__Suc__eq
% A new axiom: (forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->((iff ((ord_less_nat N) (suc M))) (((eq nat) N) M))))
% FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat (suc M)) (suc N))) ((ord_less_nat M) N))) of role axiom named fact_678_Suc__less__eq
% A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat (suc M)) (suc N))) ((ord_less_nat M) N)))
% FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))) of role axiom named fact_679_less__Suc__eq
% A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((or ((ord_less_nat M) N)) (((eq nat) M) N))))
% FOF formula (forall (M:nat) (N:nat), ((iff (((ord_less_nat M) N)->False)) ((ord_less_nat N) (suc M)))) of role axiom named fact_680_not__less__eq
% A new axiom: (forall (M:nat) (N:nat), ((iff (((ord_less_nat M) N)->False)) ((ord_less_nat N) (suc M))))
% FOF formula (forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False)) of role axiom named fact_681_Suc__n__not__le__n
% A new axiom: (forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False))
% FOF formula (forall (M:nat) (N:nat), ((iff (((ord_less_eq_nat M) N)->False)) ((ord_less_eq_nat (suc N)) M))) of role axiom named fact_682_not__less__eq__eq
% A new axiom: (forall (M:nat) (N:nat), ((iff (((ord_less_eq_nat M) N)->False)) ((ord_less_eq_nat (suc N)) M)))
% FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) (suc N))) ((or ((ord_less_eq_nat M) N)) (((eq nat) M) (suc N))))) of role axiom named fact_683_le__Suc__eq
% A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) (suc N))) ((or ((ord_less_eq_nat M) N)) (((eq nat) M) (suc N)))))
% FOF formula (forall (N:nat) (M:nat), ((iff ((ord_less_eq_nat (suc N)) (suc M))) ((ord_less_eq_nat N) M))) of role axiom named fact_684_Suc__le__mono
% A new axiom: (forall (N:nat) (M:nat), ((iff ((ord_less_eq_nat (suc N)) (suc M))) ((ord_less_eq_nat N) M)))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat M) (suc N)))) of role axiom named fact_685_le__SucI
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat M) (suc N))))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) (suc N))->((((ord_less_eq_nat M) N)->False)->(((eq nat) M) (suc N))))) of role axiom named fact_686_le__SucE
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) (suc N))->((((ord_less_eq_nat M) N)->False)->(((eq nat) M) (suc N)))))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_eq_nat M) N))) of role axiom named fact_687_Suc__leD
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_eq_nat M) N)))
% FOF formula (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N))) of role axiom named fact_688_less__or__eq__imp__le
% A new axiom: (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N)))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N)))) of role axiom named fact_689_le__neq__implies__less
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N))))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_690_less__imp__le__nat
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N)))
% FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))) of role axiom named fact_691_le__eq__less__or__eq
% A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((or ((ord_less_nat M) N)) (((eq nat) M) N))))
% FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((and ((ord_less_eq_nat M) N)) (not (((eq nat) M) N))))) of role axiom named fact_692_nat__less__le
% A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((and ((ord_less_eq_nat M) N)) (not (((eq nat) M) N)))))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_nat M) N))) of role axiom named fact_693_Suc__le__lessD
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_nat M) N)))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((iff ((ord_less_nat N) (suc M))) (((eq nat) N) M)))) of role axiom named fact_694_le__less__Suc__eq
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((iff ((ord_less_nat N) (suc M))) (((eq nat) N) M))))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat (suc M)) N))) of role axiom named fact_695_Suc__leI
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat (suc M)) N)))
% FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_nat M) (suc N)))) of role axiom named fact_696_le__imp__less__Suc
% A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_nat M) (suc N))))
% FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat (suc M)) N)) ((ord_less_nat M) N))) of role axiom named fact_697_Suc__le__eq
% A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat (suc M)) N)) ((ord_less_nat M) N)))
% FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((ord_less_eq_nat M) N))) of role axiom named fact_698_less__Suc__eq__le
% A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((ord_less_eq_nat M) N)))
% FOF formula (forall (N:nat) (M:nat), ((iff ((ord_less_nat N) M)) ((ord_less_eq_nat (suc N)) M))) of role axiom named fact_699_less__eq__Suc__le
% A new axiom: (forall (N:nat) (M:nat), ((iff ((ord_less_nat N) M)) ((ord_less_eq_nat (suc N)) M)))
% FOF formula (forall (X:list_A2115238852le_alt) (Y:list_A2115238852le_alt), ((or (((fequal781288069le_alt X) Y)->False)) (((eq list_A2115238852le_alt) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lc
% A new axiom: (forall (X:list_A2115238852le_alt) (Y:list_A2115238852le_alt), ((or (((fequal781288069le_alt X) Y)->False)) (((eq list_A2115238852le_alt) X) Y)))
% FOF formula (forall (X:list_A2115238852le_alt) (Y:list_A2115238852le_alt), ((or (not (((eq list_A2115238852le_alt) X) Y))) ((fequal781288069le_alt X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lc
% A new axiom: (forall (X:list_A2115238852le_alt) (Y:list_A2115238852le_alt), ((or (not (((eq list_A2115238852le_alt) X) Y))) ((fequal781288069le_alt X) Y)))
% FOF formula (forall (X:produc1362454231le_alt) (Y:produc1362454231le_alt), (((eq produc1362454231le_alt) (((if_Pro314693991le_alt True) X) Y)) X)) of role axiom named help_If_1_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____
% A new axiom: (forall (X:produc1362454231le_alt) (Y:produc1362454231le_alt), (((eq produc1362454231le_alt) (((if_Pro314693991le_alt True) X) Y)) X))
% FOF formula (forall (X:produc1362454231le_alt) (Y:produc1362454231le_alt), (((eq produc1362454231le_alt) (((if_Pro314693991le_alt False) X) Y)) Y)) of role axiom named help_If_2_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____
% A new axiom: (forall (X:produc1362454231le_alt) (Y:produc1362454231le_alt), (((eq produc1362454231le_alt) (((if_Pro314693991le_alt False) X) Y)) Y))
% FOF formula (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))) of role axiom named help_If_3_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____
% A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False)))
% FOF formula (forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt a) b)) (p _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt a) c)) (((arrow_2098199487_below (p _TPTP_I)) c) b)))) of role conjecture named conj_0
% Conjecture to prove = (forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt a) b)) (p _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt a) c)) (((arrow_2098199487_below (p _TPTP_I)) c) b)))):Prop
% Parameter arrow_1429601828e_indi_DUMMY:arrow_1429601828e_indi.
% Parameter nat_DUMMY:nat.
% Parameter produc344885491_alt_o_DUMMY:produc344885491_alt_o.
% Parameter produc634020647_alt_o_DUMMY:produc634020647_alt_o.
% Parameter produc603869735_alt_o_DUMMY:produc603869735_alt_o.
% Parameter product_prod_o_o_DUMMY:product_prod_o_o.
% Parameter produc1501160679le_alt_DUMMY:produc1501160679le_alt.
% Parameter produc1091721111e_indi_DUMMY:produc1091721111e_indi.
% Parameter produc1362754407_alt_o_DUMMY:produc1362754407_alt_o.
% Parameter produc2070394625_alt_o_DUMMY:produc2070394625_alt_o.
% Parameter produc1361459593_alt_o_DUMMY:produc1361459593_alt_o.
% Parameter produc1191881495list_o_DUMMY:produc1191881495list_o.
% Parameter produc1362454231le_alt_DUMMY:produc1362454231le_alt.
% Parameter produc343559527e_indi_DUMMY:produc343559527e_indi.
% Parameter produc938956263le_alt_DUMMY:produc938956263le_alt.
% Parameter produc347927591le_alt_DUMMY:produc347927591le_alt.
% Parameter produc1884787239le_alt_DUMMY:produc1884787239le_alt.
% Parameter produc1076844957le_alt_DUMMY:produc1076844957le_alt.
% Parameter produc1787997437le_alt_DUMMY:produc1787997437le_alt.
% We need to prove ['(forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt a) b)) (p _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt a) c)) (((arrow_2098199487_below (p _TPTP_I)) c) b))))']
% Parameter arrow_475358991le_alt:Type.
% Parameter arrow_1429601828e_indi:Type.
% Parameter list_A518015091_alt_o:Type.
% Parameter list_A524553945_alt_o:Type.
% Parameter list_P1178103901_alt_o:Type.
% Parameter list_o:Type.
% Parameter list_A2115238852le_alt:Type.
% Parameter list_A1484739013e_indi:Type.
% Parameter list_l1475218533le_alt:Type.
% Parameter list_P736798472le_alt:Type.
% Parameter list_P1295265784le_alt:Type.
% Parameter nat:Type.
% Parameter produc344885491_alt_o:Type.
% Parameter produc634020647_alt_o:Type.
% Parameter produc603869735_alt_o:Type.
% Parameter product_prod_o_o:Type.
% Parameter produc1501160679le_alt:Type.
% Parameter produc1091721111e_indi:Type.
% Parameter produc1362754407_alt_o:Type.
% Parameter produc2070394625_alt_o:Type.
% Parameter produc1361459593_alt_o:Type.
% Parameter produc1191881495list_o:Type.
% Parameter produc1362454231le_alt:Type.
% Parameter produc343559527e_indi:Type.
% Parameter produc938956263le_alt:Type.
% Parameter produc347927591le_alt:Type.
% Parameter produc1884787239le_alt:Type.
% Parameter produc1076844957le_alt:Type.
% Parameter produc1787997437le_alt:Type.
% Parameter all2:((produc1501160679le_alt->Prop)->Prop).
% Parameter all1:((produc1362454231le_alt->Prop)->Prop).
% Parameter arrow_797024463le_IIA:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop).
% Parameter arrow_823908191le_Lin:((produc1501160679le_alt->Prop)->Prop).
% Parameter arrow_734252939e_Prof:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop).
% Parameter arrow_789600939_above:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->(produc1501160679le_alt->Prop)))).
% Parameter arrow_2098199487_below:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->(produc1501160679le_alt->Prop)))).
% Parameter arrow_1212662430ctator:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop)).
% Parameter arrow_2054445623_mkbot:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(produc1501160679le_alt->Prop))).
% Parameter arrow_55669061_mktop:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(produc1501160679le_alt->Prop))).
% Parameter arrow_1706409458nimity:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop).
% Parameter ex2:((produc1501160679le_alt->Prop)->Prop).
% Parameter ex1:((produc1362454231le_alt->Prop)->Prop).
% Parameter in_rel1252994498le_alt:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))).
% Parameter in_rel1156631736le_alt:((produc1362454231le_alt->Prop)->(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))).
% Parameter pi_Arr195212324lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop))).
% Parameter pi_Arr1005837828le_alt:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->Prop))).
% Parameter pi_Arr338314351e_indi:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop))).
% Parameter pi_Arr2076738722le_alt:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->Prop))).
% Parameter pi_Arr1304755663_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))).
% Parameter pi_Arr952516694lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop))).
% Parameter pi_Arr1483346486le_alt:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->Prop))).
% Parameter pi_Arr1232280765e_indi:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop))).
% Parameter pi_Arr1957214192le_alt:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->Prop))).
% Parameter pi_Pro422690258lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(Prop->Prop))->(((produc1501160679le_alt->Prop)->Prop)->Prop))).
% Parameter pi_Pro1868152754le_alt:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))->(((produc1501160679le_alt->Prop)->arrow_475358991le_alt)->Prop))).
% Parameter pi_Pro468373057e_indi:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))->(((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->Prop))).
% Parameter pi_Pro1678345076le_alt:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))->(((produc1501160679le_alt->Prop)->produc1362454231le_alt)->Prop))).
% Parameter pi_o_A1186128886_alt_o:((Prop->Prop)->((Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_o_A1182933120_alt_o:((Prop->Prop)->((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_o_P553196292_alt_o:((Prop->Prop)->((Prop->((produc1501160679le_alt->Prop)->Prop))->((Prop->(produc1501160679le_alt->Prop))->Prop))).
% Parameter pi_o_P657324555le_alt:((Prop->Prop)->((Prop->(produc1501160679le_alt->Prop))->((Prop->produc1501160679le_alt)->Prop))).
% Parameter pi_Arr515871190_alt_o:((arrow_475358991le_alt->Prop)->((arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_Arr578767520_alt_o:((arrow_475358991le_alt->Prop)->((arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_Arr1520776484_alt_o:((arrow_475358991le_alt->Prop)->((arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))->((arrow_475358991le_alt->(produc1501160679le_alt->Prop))->Prop))).
% Parameter pi_Arr1786181611le_alt:((arrow_475358991le_alt->Prop)->((arrow_475358991le_alt->(produc1501160679le_alt->Prop))->((arrow_475358991le_alt->produc1501160679le_alt)->Prop))).
% Parameter pi_Arr1564509167_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_Arr1060328391_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_Arr1929480907_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))).
% Parameter pi_Arr329216900le_alt:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((arrow_1429601828e_indi->produc1501160679le_alt)->Prop))).
% Parameter pi_Pro1701359055_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(Prop->Prop))->((produc1501160679le_alt->Prop)->Prop))).
% Parameter pi_Pro315446191le_alt:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(arrow_475358991le_alt->Prop))->((produc1501160679le_alt->arrow_475358991le_alt)->Prop))).
% Parameter pi_Pro1767455108e_indi:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(arrow_1429601828e_indi->Prop))->((produc1501160679le_alt->arrow_1429601828e_indi)->Prop))).
% Parameter pi_Pro666407479le_alt:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(produc1362454231le_alt->Prop))->((produc1501160679le_alt->produc1362454231le_alt)->Prop))).
% Parameter pi_Pro441468706_alt_o:((produc1362454231le_alt->Prop)->((produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_Pro121963604_alt_o:((produc1362454231le_alt->Prop)->((produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_Pro589599960_alt_o:((produc1362454231le_alt->Prop)->((produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))->((produc1362454231le_alt->(produc1501160679le_alt->Prop))->Prop))).
% Parameter pi_Pro1708969783le_alt:((produc1362454231le_alt->Prop)->((produc1362454231le_alt->(produc1501160679le_alt->Prop))->((produc1362454231le_alt->produc1501160679le_alt)->Prop))).
% Parameter equal_484611810le_alt:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop)).
% Parameter if_Pro314693991le_alt:(Prop->(produc1362454231le_alt->(produc1362454231le_alt->produc1362454231le_alt))).
% Parameter append326058957_alt_o:(list_A518015091_alt_o->(list_A518015091_alt_o->list_A518015091_alt_o)).
% Parameter append295924073_alt_o:(list_A524553945_alt_o->(list_A524553945_alt_o->list_A524553945_alt_o)).
% Parameter append612833133_alt_o:(list_P1178103901_alt_o->(list_P1178103901_alt_o->list_P1178103901_alt_o)).
% Parameter append_o:(list_o->(list_o->list_o)).
% Parameter append179082452le_alt:(list_A2115238852le_alt->(list_A2115238852le_alt->list_A2115238852le_alt)).
% Parameter append711934367e_indi:(list_A1484739013e_indi->(list_A1484739013e_indi->list_A1484739013e_indi)).
% Parameter append1166001599le_alt:(list_l1475218533le_alt->(list_l1475218533le_alt->list_l1475218533le_alt)).
% Parameter append1229289570le_alt:(list_P736798472le_alt->(list_P736798472le_alt->list_P736798472le_alt)).
% Parameter append423770578le_alt:(list_P1295265784le_alt->(list_P1295265784le_alt->list_P1295265784le_alt)).
% Parameter butlas1138247126_alt_o:(list_A518015091_alt_o->list_A518015091_alt_o).
% Parameter butlas813143712_alt_o:(list_A524553945_alt_o->list_A524553945_alt_o).
% Parameter butlas368541988_alt_o:(list_P1178103901_alt_o->list_P1178103901_alt_o).
% Parameter butlast_o:(list_o->list_o).
% Parameter butlas274947851le_alt:(list_A2115238852le_alt->list_A2115238852le_alt).
% Parameter butlas1554122024e_indi:(list_A1484739013e_indi->list_A1484739013e_indi).
% Parameter butlas661498859le_alt:(list_P736798472le_alt->list_P736798472le_alt).
% Parameter butlas464406491le_alt:(list_P1295265784le_alt->list_P1295265784le_alt).
% Parameter distin1908010863_alt_o:(list_A518015091_alt_o->Prop).
% Parameter distin1869760583_alt_o:(list_A524553945_alt_o->Prop).
% Parameter distin1582710603_alt_o:(list_P1178103901_alt_o->Prop).
% Parameter distinct_o:(list_o->Prop).
% Parameter distin236324274le_alt:(list_A2115238852le_alt->Prop).
% Parameter distin1916799041e_indi:(list_A1484739013e_indi->Prop).
% Parameter distin1776819972le_alt:(list_P736798472le_alt->Prop).
% Parameter distin561495412le_alt:(list_P1295265784le_alt->Prop).
% Parameter dropWh583351873_alt_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(list_A518015091_alt_o->list_A518015091_alt_o)).
% Parameter dropWh73644021_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(list_A524553945_alt_o->list_A524553945_alt_o)).
% Parameter dropWh1049991161_alt_o:(((produc1501160679le_alt->Prop)->Prop)->(list_P1178103901_alt_o->list_P1178103901_alt_o)).
% Parameter dropWhile_o:((Prop->Prop)->(list_o->list_o)).
% Parameter dropWh1316781920le_alt:((arrow_475358991le_alt->Prop)->(list_A2115238852le_alt->list_A2115238852le_alt)).
% Parameter dropWh1160116755e_indi:((arrow_1429601828e_indi->Prop)->(list_A1484739013e_indi->list_A1484739013e_indi)).
% Parameter dropWh680325334le_alt:((produc1501160679le_alt->Prop)->(list_P736798472le_alt->list_P736798472le_alt)).
% Parameter dropWh612508742le_alt:((produc1362454231le_alt->Prop)->(list_P1295265784le_alt->list_P1295265784le_alt)).
% Parameter drop_A1326872290_alt_o:(nat->(list_A518015091_alt_o->list_A518015091_alt_o)).
% Parameter drop_A776701076_alt_o:(nat->(list_A524553945_alt_o->list_A524553945_alt_o)).
% Parameter drop_P619902232_alt_o:(nat->(list_P1178103901_alt_o->list_P1178103901_alt_o)).
% Parameter drop_o:(nat->(list_o->list_o)).
% Parameter drop_A1346709759le_alt:(nat->(list_A2115238852le_alt->list_A2115238852le_alt)).
% Parameter drop_A1596373044e_indi:(nat->(list_A1484739013e_indi->list_A1484739013e_indi)).
% Parameter drop_P933863159le_alt:(nat->(list_P736798472le_alt->list_P736798472le_alt)).
% Parameter drop_P1438419175le_alt:(nat->(list_P1295265784le_alt->list_P1295265784le_alt)).
% Parameter foldl_296410428le_alt:((list_A2115238852le_alt->(arrow_475358991le_alt->list_A2115238852le_alt))->(list_A2115238852le_alt->(list_A2115238852le_alt->list_A2115238852le_alt))).
% Parameter hd_Arr1786382991_alt_o:(list_A518015091_alt_o->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))).
% Parameter hd_Arr574592295_alt_o:(list_A524553945_alt_o->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))).
% Parameter hd_Pro622402603_alt_o:(list_P1178103901_alt_o->(produc1501160679le_alt->Prop)).
% Parameter hd_o:(list_o->Prop).
% Parameter hd_Arr1965683346le_alt:(list_A2115238852le_alt->arrow_475358991le_alt).
% Parameter hd_Arr1023890273e_indi:(list_A1484739013e_indi->arrow_1429601828e_indi).
% Parameter hd_Pro297626148le_alt:(list_P736798472le_alt->produc1501160679le_alt).
% Parameter hd_Pro856774804le_alt:(list_P1295265784le_alt->produc1362454231le_alt).
% Parameter insert81217164_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(list_A518015091_alt_o->list_A518015091_alt_o)).
% Parameter insert128393578_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(list_A524553945_alt_o->list_A524553945_alt_o)).
% Parameter insert451602158_alt_o:((produc1501160679le_alt->Prop)->(list_P1178103901_alt_o->list_P1178103901_alt_o)).
% Parameter insert_o:(Prop->(list_o->list_o)).
% Parameter insert2120566741le_alt:(arrow_475358991le_alt->(list_A2115238852le_alt->list_A2115238852le_alt)).
% Parameter insert1474580190e_indi:(arrow_1429601828e_indi->(list_A1484739013e_indi->list_A1484739013e_indi)).
% Parameter insert1177064865le_alt:(produc1501160679le_alt->(list_P736798472le_alt->list_P736798472le_alt)).
% Parameter insert1334153361le_alt:(produc1362454231le_alt->(list_P1295265784le_alt->list_P1295265784le_alt)).
% Parameter last_A1273867721_alt_o:(list_A518015091_alt_o->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))).
% Parameter last_A1049530989_alt_o:(list_A524553945_alt_o->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))).
% Parameter last_P685913713_alt_o:(list_P1178103901_alt_o->(produc1501160679le_alt->Prop)).
% Parameter last_o:(list_o->Prop).
% Parameter last_A1217315288le_alt:(list_A2115238852le_alt->arrow_475358991le_alt).
% Parameter last_A303846811e_indi:(list_A1484739013e_indi->arrow_1429601828e_indi).
% Parameter last_P1656409182le_alt:(list_P736798472le_alt->produc1501160679le_alt).
% Parameter last_P1879176142le_alt:(list_P1295265784le_alt->produc1362454231le_alt).
% Parameter lex_Ar1415517219le_alt:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop)).
% Parameter lex_li663137712le_alt:((produc1362454231le_alt->Prop)->(produc938956263le_alt->Prop)).
% Parameter lexn_A170361439le_alt:((produc1501160679le_alt->Prop)->(nat->(produc1362454231le_alt->Prop))).
% Parameter lexord1104163445_alt_o:((produc344885491_alt_o->Prop)->(produc1362754407_alt_o->Prop)).
% Parameter lexord1645229249_alt_o:((produc634020647_alt_o->Prop)->(produc2070394625_alt_o->Prop)).
% Parameter lexord842870469_alt_o:((produc603869735_alt_o->Prop)->(produc1361459593_alt_o->Prop)).
% Parameter lexord_o:((product_prod_o_o->Prop)->(produc1191881495list_o->Prop)).
% Parameter lexord958095404le_alt:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop)).
% Parameter lexord1661684807e_indi:((produc1091721111e_indi->Prop)->(produc343559527e_indi->Prop)).
% Parameter lexord469916775le_alt:((produc1362454231le_alt->Prop)->(produc938956263le_alt->Prop)).
% Parameter lexord501678858le_alt:((produc1076844957le_alt->Prop)->(produc347927591le_alt->Prop)).
% Parameter lexord973342842le_alt:((produc1787997437le_alt->Prop)->(produc1884787239le_alt->Prop)).
% Parameter cons_A279268466_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(list_A518015091_alt_o->list_A518015091_alt_o)).
% Parameter cons_A2010997508_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(list_A524553945_alt_o->list_A524553945_alt_o)).
% Parameter cons_P1239653256_alt_o:((produc1501160679le_alt->Prop)->(list_P1178103901_alt_o->list_P1178103901_alt_o)).
% Parameter cons_o:(Prop->(list_o->list_o)).
% Parameter cons_A228743023le_alt:(arrow_475358991le_alt->(list_A2115238852le_alt->list_A2115238852le_alt)).
% Parameter cons_A663037380e_indi:(arrow_1429601828e_indi->(list_A1484739013e_indi->list_A1484739013e_indi)).
% Parameter cons_l635097956le_alt:(list_A2115238852le_alt->(list_l1475218533le_alt->list_l1475218533le_alt)).
% Parameter cons_P1913588871le_alt:(produc1501160679le_alt->(list_P736798472le_alt->list_P736798472le_alt)).
% Parameter cons_P2048401015le_alt:(produc1362454231le_alt->(list_P1295265784le_alt->list_P1295265784le_alt)).
% Parameter nil_Ar253733922_alt_o:list_A518015091_alt_o.
% Parameter nil_Ar1876942676_alt_o:list_A524553945_alt_o.
% Parameter nil_Pr28438488_alt_o:list_P1178103901_alt_o.
% Parameter nil_o:list_o.
% Parameter nil_Ar1286194111le_alt:list_A2115238852le_alt.
% Parameter nil_Ar380161396e_indi:list_A1484739013e_indi.
% Parameter nil_li1907286804le_alt:list_l1475218533le_alt.
% Parameter nil_Pr861385783le_alt:list_P736798472le_alt.
% Parameter nil_Pr365739559le_alt:list_P1295265784le_alt.
% Parameter list_c1623890103le_alt:(list_A2115238852le_alt->((arrow_475358991le_alt->(list_A2115238852le_alt->list_A2115238852le_alt))->(list_A2115238852le_alt->list_A2115238852le_alt))).
% Parameter listre2064003096le_alt:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop)).
% Parameter listre620555643le_alt:((produc1362454231le_alt->Prop)->(produc938956263le_alt->Prop)).
% Parameter listre1920655591le_alt:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop)).
% Parameter listre623166444le_alt:((produc1362454231le_alt->Prop)->(produc938956263le_alt->Prop)).
% Parameter listre1213162009le_alt:((arrow_475358991le_alt->(arrow_475358991le_alt->Prop))->(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))).
% Parameter listre816681018le_alt:((list_A2115238852le_alt->(list_A2115238852le_alt->Prop))->(list_l1475218533le_alt->(list_l1475218533le_alt->Prop))).
% Parameter null_A1520965063le_alt:(list_A2115238852le_alt->Prop).
% Parameter partit1487577784le_alt:((arrow_475358991le_alt->Prop)->(list_A2115238852le_alt->produc1362454231le_alt)).
% Parameter replic1511538809le_alt:(nat->(arrow_475358991le_alt->list_A2115238852le_alt)).
% Parameter rev_Ar5548482_alt_o:(list_A518015091_alt_o->list_A518015091_alt_o).
% Parameter rev_Ar413755828_alt_o:(list_A524553945_alt_o->list_A524553945_alt_o).
% Parameter rev_Pr1006783032_alt_o:(list_P1178103901_alt_o->list_P1178103901_alt_o).
% Parameter rev_o:(list_o->list_o).
% Parameter rev_Ar1106406943le_alt:(list_A2115238852le_alt->list_A2115238852le_alt).
% Parameter rev_Ar501922580e_indi:(list_A1484739013e_indi->list_A1484739013e_indi).
% Parameter rev_Pr1216324055le_alt:(list_P736798472le_alt->list_P736798472le_alt).
% Parameter rev_Pr1619606471le_alt:(list_P1295265784le_alt->list_P1295265784le_alt).
% Parameter rotate335349260le_alt:(list_A2115238852le_alt->list_A2115238852le_alt).
% Parameter set_Ar1356274881_alt_o:(list_A518015091_alt_o->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)).
% Parameter set_Ar571341173_alt_o:(list_A524553945_alt_o->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)).
% Parameter set_Pr592386425_alt_o:(list_P1178103901_alt_o->((produc1501160679le_alt->Prop)->Prop)).
% Parameter set_o:(list_o->(Prop->Prop)).
% Parameter set_Ar577454304le_alt:(list_A2115238852le_alt->(arrow_475358991le_alt->Prop)).
% Parameter set_Ar778541203e_indi:(list_A1484739013e_indi->(arrow_1429601828e_indi->Prop)).
% Parameter set_li1631982259le_alt:(list_l1475218533le_alt->(list_A2115238852le_alt->Prop)).
% Parameter set_Pr1525059414le_alt:(list_P736798472le_alt->(produc1501160679le_alt->Prop)).
% Parameter set_Pr412222150le_alt:(list_P1295265784le_alt->(produc1362454231le_alt->Prop)).
% Parameter splice1520898450le_alt:(list_A2115238852le_alt->(list_A2115238852le_alt->list_A2115238852le_alt)).
% Parameter takeWh877796585_alt_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(list_A518015091_alt_o->list_A518015091_alt_o)).
% Parameter takeWh1825606477_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(list_A524553945_alt_o->list_A524553945_alt_o)).
% Parameter takeWh1715715921_alt_o:(((produc1501160679le_alt->Prop)->Prop)->(list_P1178103901_alt_o->list_P1178103901_alt_o)).
% Parameter takeWhile_o:((Prop->Prop)->(list_o->list_o)).
% Parameter takeWh1696291512le_alt:((arrow_475358991le_alt->Prop)->(list_A2115238852le_alt->list_A2115238852le_alt)).
% Parameter takeWh831911099e_indi:((arrow_1429601828e_indi->Prop)->(list_A1484739013e_indi->list_A1484739013e_indi)).
% Parameter takeWh302148478le_alt:((produc1501160679le_alt->Prop)->(list_P736798472le_alt->list_P736798472le_alt)).
% Parameter takeWh1571807982le_alt:((produc1362454231le_alt->Prop)->(list_P1295265784le_alt->list_P1295265784le_alt)).
% Parameter tl_Arr2017860491_alt_o:(list_A518015091_alt_o->list_A518015091_alt_o).
% Parameter tl_Arr1704054571_alt_o:(list_A524553945_alt_o->list_A524553945_alt_o).
% Parameter tl_Pro1735316527_alt_o:(list_P1178103901_alt_o->list_P1178103901_alt_o).
% Parameter tl_o:(list_o->list_o).
% Parameter tl_Arr465451158le_alt:(list_A2115238852le_alt->list_A2115238852le_alt).
% Parameter tl_Arr25726557e_indi:(list_A1484739013e_indi->list_A1484739013e_indi).
% Parameter tl_Pro932635936le_alt:(list_P736798472le_alt->list_P736798472le_alt).
% Parameter tl_Pro1448262032le_alt:(list_P1295265784le_alt->list_P1295265784le_alt).
% Parameter suc:(nat->nat).
% Parameter nat_ca2147365008le_alt:(list_A2115238852le_alt->((nat->list_A2115238852le_alt)->(nat->list_A2115238852le_alt))).
% Parameter size_s1858781230le_alt:(list_A2115238852le_alt->nat).
% Parameter size_s1911906171le_alt:(list_l1475218533le_alt->nat).
% Parameter order_1995917111le_alt:((arrow_475358991le_alt->Prop)->((produc1501160679le_alt->Prop)->Prop)).
% Parameter ord_less_nat:(nat->(nat->Prop)).
% Parameter ord_less_eq_nat:(nat->(nat->Prop)).
% Parameter top_to1969627639lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop).
% Parameter top_to2122763103lt_o_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop).
% Parameter top_to1842727771lt_o_o:((produc1501160679le_alt->Prop)->Prop).
% Parameter top_top_o_o:(Prop->Prop).
% Parameter top_to728987956_alt_o:(arrow_475358991le_alt->Prop).
% Parameter top_to988227749indi_o:(arrow_1429601828e_indi->Prop).
% Parameter top_to1841428258_alt_o:(produc1501160679le_alt->Prop).
% Parameter top_to1039387826_alt_o:(produc1362454231le_alt->Prop).
% Parameter top_top_o:Prop.
% Parameter produc434968681_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc344885491_alt_o)).
% Parameter produc425112727_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc634020647_alt_o)).
% Parameter produc548346135_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->Prop)->produc603869735_alt_o)).
% Parameter product_Pair_o_o:(Prop->(Prop->product_prod_o_o)).
% Parameter produc1347929815le_alt:(arrow_475358991le_alt->(arrow_475358991le_alt->produc1501160679le_alt)).
% Parameter produc1851452045e_indi:(arrow_1429601828e_indi->(arrow_1429601828e_indi->produc1091721111e_indi)).
% Parameter produc385333463_alt_o:(list_A518015091_alt_o->(list_A518015091_alt_o->produc1362754407_alt_o)).
% Parameter produc1301429239_alt_o:(list_A524553945_alt_o->(list_A524553945_alt_o->produc2070394625_alt_o)).
% Parameter produc127168767_alt_o:(list_P1178103901_alt_o->(list_P1178103901_alt_o->produc1361459593_alt_o)).
% Parameter produc1835210381list_o:(list_o->(list_o->produc1191881495list_o)).
% Parameter produc776457805le_alt:(list_A2115238852le_alt->(list_A2115238852le_alt->produc1362454231le_alt)).
% Parameter produc1195920727e_indi:(list_A1484739013e_indi->(list_A1484739013e_indi->produc343559527e_indi)).
% Parameter produc1317709143le_alt:(list_l1475218533le_alt->(list_l1475218533le_alt->produc938956263le_alt)).
% Parameter produc1573901719le_alt:(list_P736798472le_alt->(list_P736798472le_alt->produc347927591le_alt)).
% Parameter produc1065979415le_alt:(list_P1295265784le_alt->(list_P1295265784le_alt->produc1884787239le_alt)).
% Parameter produc1348021779le_alt:(produc1501160679le_alt->(produc1501160679le_alt->produc1076844957le_alt)).
% Parameter produc1443807987le_alt:(produc1362454231le_alt->(produc1362454231le_alt->produc1787997437le_alt)).
% Parameter produc910278158_alt_o:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))).
% Parameter produc1739499928_alt_o:((produc1362454231le_alt->Prop)->(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))).
% Parameter produc362454893_alt_o:((arrow_475358991le_alt->(arrow_475358991le_alt->Prop))->(produc1501160679le_alt->Prop)).
% Parameter produc1948161143_alt_o:((list_A2115238852le_alt->(list_A2115238852le_alt->Prop))->(produc1362454231le_alt->Prop)).
% Parameter produc677212559le_alt:((list_A2115238852le_alt->(list_A2115238852le_alt->produc1362454231le_alt))->(produc1362454231le_alt->produc1362454231le_alt)).
% Parameter collec2009291517_alt_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)).
% Parameter collec682858041_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)).
% Parameter collec94295101_alt_o:(((produc1501160679le_alt->Prop)->Prop)->((produc1501160679le_alt->Prop)->Prop)).
% Parameter collec742074788le_alt:((arrow_475358991le_alt->Prop)->(arrow_475358991le_alt->Prop)).
% Parameter collec22405327e_indi:((arrow_1429601828e_indi->Prop)->(arrow_1429601828e_indi->Prop)).
% Parameter collec869865362le_alt:((produc1501160679le_alt->Prop)->(produc1501160679le_alt->Prop)).
% Parameter fequal781288069le_alt:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop)).
% Parameter member1823529808lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop)->Prop)).
% Parameter member474974512le_alt:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->Prop)->Prop)).
% Parameter member1452482393e_indi:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)->Prop)).
% Parameter member845447052le_alt:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->Prop)->Prop)).
% Parameter member616898751_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter member939334982lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)->Prop)).
% Parameter member1596146470le_alt:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)->Prop)->Prop)).
% Parameter member44294883e_indi:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)->Prop)).
% Parameter member1849320470le_alt:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)->Prop)->Prop)).
% Parameter member1961363906lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->((((produc1501160679le_alt->Prop)->Prop)->Prop)->Prop)).
% Parameter member1524522914le_alt:(((produc1501160679le_alt->Prop)->arrow_475358991le_alt)->((((produc1501160679le_alt->Prop)->arrow_475358991le_alt)->Prop)->Prop)).
% Parameter member304866663e_indi:(((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->((((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->Prop)->Prop)).
% Parameter member1099563162le_alt:(((produc1501160679le_alt->Prop)->produc1362454231le_alt)->((((produc1501160679le_alt->Prop)->produc1362454231le_alt)->Prop)->Prop)).
% Parameter member1957863580_alt_o:((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member1394214384_alt_o:((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member1862122484_alt_o:((Prop->(produc1501160679le_alt->Prop))->(((Prop->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter member492167345le_alt:((Prop->produc1501160679le_alt)->(((Prop->produc1501160679le_alt)->Prop)->Prop)).
% Parameter member89384572_alt_o:((arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member1876989968_alt_o:((arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member1908358676_alt_o:((arrow_475358991le_alt->(produc1501160679le_alt->Prop))->(((arrow_475358991le_alt->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter member712472209le_alt:((arrow_475358991le_alt->produc1501160679le_alt)->(((arrow_475358991le_alt->produc1501160679le_alt)->Prop)->Prop)).
% Parameter member811956313_alt_o:((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member1234151027_alt_o:((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member526088951_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter member351225838le_alt:((arrow_1429601828e_indi->produc1501160679le_alt)->(((arrow_1429601828e_indi->produc1501160679le_alt)->Prop)->Prop)).
% Parameter member377231867_alt_o:((produc1501160679le_alt->Prop)->(((produc1501160679le_alt->Prop)->Prop)->Prop)).
% Parameter member1416774619le_alt:((produc1501160679le_alt->arrow_475358991le_alt)->(((produc1501160679le_alt->arrow_475358991le_alt)->Prop)->Prop)).
% Parameter member1640632174e_indi:((produc1501160679le_alt->arrow_1429601828e_indi)->(((produc1501160679le_alt->arrow_1429601828e_indi)->Prop)->Prop)).
% Parameter member220989473le_alt:((produc1501160679le_alt->produc1362454231le_alt)->(((produc1501160679le_alt->produc1362454231le_alt)->Prop)->Prop)).
% Parameter member654997644_alt_o:((produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member392452608_alt_o:((produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member2082473988_alt_o:((produc1362454231le_alt->(produc1501160679le_alt->Prop))->(((produc1362454231le_alt->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter member428957857le_alt:((produc1362454231le_alt->produc1501160679le_alt)->(((produc1362454231le_alt->produc1501160679le_alt)->Prop)->Prop)).
% Parameter member_o:(Prop->((Prop->Prop)->Prop)).
% Parameter member84363362le_alt:(arrow_475358991le_alt->((arrow_475358991le_alt->Prop)->Prop)).
% Parameter member2052026769e_indi:(arrow_1429601828e_indi->((arrow_1429601828e_indi->Prop)->Prop)).
% Parameter member998134961le_alt:(list_A2115238852le_alt->((list_A2115238852le_alt->Prop)->Prop)).
% Parameter member1909339872_alt_o:(produc344885491_alt_o->((produc344885491_alt_o->Prop)->Prop)).
% Parameter member423327892_alt_o:(produc634020647_alt_o->((produc634020647_alt_o->Prop)->Prop)).
% Parameter member1998617236_alt_o:(produc603869735_alt_o->((produc603869735_alt_o->Prop)->Prop)).
% Parameter member1392690260od_o_o:(product_prod_o_o->((product_prod_o_o->Prop)->Prop)).
% Parameter member214075476le_alt:(produc1501160679le_alt->((produc1501160679le_alt->Prop)->Prop)).
% Parameter member1239815300e_indi:(produc1091721111e_indi->((produc1091721111e_indi->Prop)->Prop)).
% Parameter member119836116_alt_o:(produc1362754407_alt_o->((produc1362754407_alt_o->Prop)->Prop)).
% Parameter member1890873582_alt_o:(produc2070394625_alt_o->((produc2070394625_alt_o->Prop)->Prop)).
% Parameter member79660662_alt_o:(produc1361459593_alt_o->((produc1361459593_alt_o->Prop)->Prop)).
% Parameter member806300420list_o:(produc1191881495list_o->((produc1191881495list_o->Prop)->Prop)).
% Parameter member28618436le_alt:(produc1362454231le_alt->((produc1362454231le_alt->Prop)->Prop)).
% Parameter member1618636500e_indi:(produc343559527e_indi->((produc343559527e_indi->Prop)->Prop)).
% Parameter member1732936276le_alt:(produc938956263le_alt->((produc938956263le_alt->Prop)->Prop)).
% Parameter member475755924le_alt:(produc347927591le_alt->((produc347927591le_alt->Prop)->Prop)).
% Parameter member608607380le_alt:(produc1884787239le_alt->((produc1884787239le_alt->Prop)->Prop)).
% Parameter member1664185994le_alt:(produc1076844957le_alt->((produc1076844957le_alt->Prop)->Prop)).
% Parameter member902484714le_alt:(produc1787997437le_alt->((produc1787997437le_alt->Prop)->Prop)).
% Parameter f:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)).
% Parameter p_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)).
% Parameter p:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)).
% Parameter a:arrow_475358991le_alt.
% Parameter b:arrow_475358991le_alt.
% Parameter c:arrow_475358991le_alt.
% Axiom fact_0__096P_A_058_AProf_096:((member526088951_alt_o p) arrow_734252939e_Prof).
% Axiom fact_1_assms_I3_J:(arrow_797024463le_IIA f).
% Axiom fact_2_u:(arrow_1706409458nimity f).
% Axiom fact_3__096a_A_126_061_Ab_096:(not (((eq arrow_475358991le_alt) a) b)).
% Axiom fact_4_dist:(distin236324274le_alt ((cons_A228743023le_alt a) ((cons_A228743023le_alt b) ((cons_A228743023le_alt c) nil_Ar1286194111le_alt)))).
% Axiom fact_5_iff:(forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt a) b)) (p _TPTP_I))) ((member214075476le_alt ((produc1347929815le_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_2:arrow_475358991le_alt), ((distin236324274le_alt ((cons_A228743023le_alt a) ((cons_A228743023le_alt b) ((cons_A228743023le_alt C_2) nil_Ar1286194111le_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:((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> (((arrow_2098199487_below (((arrow_2098199487_below (p P_30)) c) b)) b) a))) arrow_734252939e_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_:((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> (((arrow_2098199487_below (((arrow_2098199487_below (((arrow_2098199487_below (p P_30)) c) b)) b) a)) a) c))) arrow_734252939e_Prof).
% Axiom fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096:((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> (((arrow_2098199487_below (p P_30)) c) b))) arrow_734252939e_Prof).
% Axiom fact_10_in__mkbot:(forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (Z_1:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_2054445623_mkbot L_1) Z_1))) ((and ((and (not (((eq arrow_475358991le_alt) Y) Z_1))) ((((eq arrow_475358991le_alt) X) Z_1)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) X) Z_1))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1))))).
% Axiom fact_11_in__mktop:(forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (Z_1:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_55669061_mktop L_1) Z_1))) ((and ((and (not (((eq arrow_475358991le_alt) X) Z_1))) ((((eq arrow_475358991le_alt) Y) Z_1)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) Y) Z_1))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1))))).
% Axiom fact_12_in__below:(forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_2098199487_below L_1) A_24) B_17))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) Y) A_24)->((member214075476le_alt ((produc1347929815le_alt X) B_17)) L_1)))) ((not (((eq arrow_475358991le_alt) Y) A_24))->((and ((((eq arrow_475358991le_alt) X) A_24)->((or (((eq arrow_475358991le_alt) Y) B_17)) ((member214075476le_alt ((produc1347929815le_alt B_17) Y)) L_1)))) ((not (((eq arrow_475358991le_alt) X) A_24))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1))))))))).
% Axiom fact_13_split__paired__All:(forall (P_33:(produc1362454231le_alt->Prop)), ((iff (all1 P_33)) (forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), (P_33 ((produc776457805le_alt A) B))))).
% Axiom fact_14_split__paired__All:(forall (P_33:(produc1501160679le_alt->Prop)), ((iff (all2 P_33)) (forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), (P_33 ((produc1347929815le_alt A) B))))).
% Axiom fact_15_Pair__eq:(forall (A_30:list_A2115238852le_alt) (B_23:list_A2115238852le_alt) (A_29:list_A2115238852le_alt) (B_22:list_A2115238852le_alt), ((iff (((eq produc1362454231le_alt) ((produc776457805le_alt A_30) B_23)) ((produc776457805le_alt A_29) B_22))) ((and (((eq list_A2115238852le_alt) A_30) A_29)) (((eq list_A2115238852le_alt) B_23) B_22)))).
% Axiom fact_16_Pair__eq:(forall (A_30:arrow_475358991le_alt) (B_23:arrow_475358991le_alt) (A_29:arrow_475358991le_alt) (B_22:arrow_475358991le_alt), ((iff (((eq produc1501160679le_alt) ((produc1347929815le_alt A_30) B_23)) ((produc1347929815le_alt A_29) B_22))) ((and (((eq arrow_475358991le_alt) A_30) A_29)) (((eq arrow_475358991le_alt) B_23) B_22)))).
% Axiom fact_17_Pair__inject:(forall (A_28:list_A2115238852le_alt) (B_21:list_A2115238852le_alt) (A_27:list_A2115238852le_alt) (B_20:list_A2115238852le_alt), ((((eq produc1362454231le_alt) ((produc776457805le_alt A_28) B_21)) ((produc776457805le_alt A_27) B_20))->(((((eq list_A2115238852le_alt) A_28) A_27)->(not (((eq list_A2115238852le_alt) B_21) B_20)))->False))).
% Axiom fact_18_Pair__inject:(forall (A_28:arrow_475358991le_alt) (B_21:arrow_475358991le_alt) (A_27:arrow_475358991le_alt) (B_20:arrow_475358991le_alt), ((((eq produc1501160679le_alt) ((produc1347929815le_alt A_28) B_21)) ((produc1347929815le_alt A_27) B_20))->(((((eq arrow_475358991le_alt) A_28) A_27)->(not (((eq arrow_475358991le_alt) B_21) B_20)))->False))).
% Axiom fact_19_in__rel__def:(forall (R_40:(produc1362454231le_alt->Prop)) (X_75:list_A2115238852le_alt) (Y_27:list_A2115238852le_alt), ((iff (((in_rel1156631736le_alt R_40) X_75) Y_27)) ((member28618436le_alt ((produc776457805le_alt X_75) Y_27)) R_40))).
% Axiom fact_20_in__rel__def:(forall (R_40:(produc1501160679le_alt->Prop)) (X_75:arrow_475358991le_alt) (Y_27:arrow_475358991le_alt), ((iff (((in_rel1252994498le_alt R_40) X_75) Y_27)) ((member214075476le_alt ((produc1347929815le_alt X_75) Y_27)) R_40))).
% Axiom fact_21_below__Lin:(forall (L_1:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_2098199487_below L_1) X) Y)) arrow_823908191le_Lin)))).
% Axiom fact_22__096P_H_A_058_AProf_096:((member526088951_alt_o p_1) arrow_734252939e_Prof).
% Axiom fact_23__C1_C:(forall (P_32:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_31:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_26:arrow_475358991le_alt) (B_19:arrow_475358991le_alt) (A_25:arrow_475358991le_alt) (B_18:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_25) B_18))->((not (((eq arrow_475358991le_alt) A_26) B_19))->((not (((eq arrow_475358991le_alt) A_25) B_19))->((not (((eq arrow_475358991le_alt) B_18) A_26))->(((member526088951_alt_o P_31) arrow_734252939e_Prof)->(((member526088951_alt_o P_32) arrow_734252939e_Prof)->((forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (P_31 _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (P_32 _TPTP_I))))->(((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (f P_31))->((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (f P_32))))))))))).
% Axiom fact_24__C2_C:(forall (P_32:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_31:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_26:arrow_475358991le_alt) (B_19:arrow_475358991le_alt) (A_25:arrow_475358991le_alt) (B_18:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_25) B_18))->((not (((eq arrow_475358991le_alt) A_26) B_19))->((not (((eq arrow_475358991le_alt) A_25) B_19))->((not (((eq arrow_475358991le_alt) B_18) A_26))->(((member526088951_alt_o P_31) arrow_734252939e_Prof)->(((member526088951_alt_o P_32) arrow_734252939e_Prof)->((forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (P_31 _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (P_32 _TPTP_I))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_25) B_18)) (f P_31))) ((member214075476le_alt ((produc1347929815le_alt A_26) B_19)) (f P_32))))))))))).
% Axiom fact_25_assms_I1_J:((member616898751_alt_o f) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin))).
% Axiom fact_26_const__Lin__Prof:(forall (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member526088951_alt_o (fun (P_30:arrow_1429601828e_indi)=> L_1)) arrow_734252939e_Prof))).
% Axiom fact_27_mkbot__Lin:(forall (X:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_2054445623_mkbot L_1) X)) arrow_823908191le_Lin))).
% Axiom fact_28_mktop__Lin:(forall (X:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_55669061_mktop L_1) X)) arrow_823908191le_Lin))).
% Axiom fact_29_Lin__irrefl:(forall (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->(((member214075476le_alt ((produc1347929815le_alt A_24) B_17)) L_1)->(((member214075476le_alt ((produc1347929815le_alt B_17) A_24)) L_1)->False)))).
% Axiom fact_30_notin__Lin__iff:(forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_1) arrow_823908191le_Lin)->((not (((eq arrow_475358991le_alt) X) Y))->((iff (((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1)->False)) ((member214075476le_alt ((produc1347929815le_alt Y) X)) L_1))))).
% Axiom fact_31_third__alt:(forall (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->((ex arrow_475358991le_alt) (fun (C_2:arrow_475358991le_alt)=> (distin236324274le_alt ((cons_A228743023le_alt A_24) ((cons_A228743023le_alt B_17) ((cons_A228743023le_alt C_2) nil_Ar1286194111le_alt)))))))).
% Axiom fact_32_IIA__def:(forall (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_797024463le_IIA F_14)) (forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(forall (Xa:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o Xa) arrow_734252939e_Prof)->(forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((forall (_TPTP_I:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A) B)) (X_2 _TPTP_I))) ((member214075476le_alt ((produc1347929815le_alt A) B)) (Xa _TPTP_I))))->((iff ((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 X_2))) ((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 Xa))))))))))).
% Axiom fact_33_unanimity__def:(forall (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_1706409458nimity F_14)) (forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((forall (_TPTP_I:arrow_1429601828e_indi), ((member214075476le_alt ((produc1347929815le_alt A) B)) (X_2 _TPTP_I)))->((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 X_2)))))))).
% Axiom fact_34_complete__Lin:(forall (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->((ex (produc1501160679le_alt->Prop)) (fun (X_2:(produc1501160679le_alt->Prop))=> ((and ((member377231867_alt_o X_2) arrow_823908191le_Lin)) ((member214075476le_alt ((produc1347929815le_alt A_24) B_17)) X_2)))))).
% Axiom fact_35_in__above:(forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_1:(produc1501160679le_alt->Prop)) (A_24:arrow_475358991le_alt) (B_17:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_24) B_17))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_789600939_above L_1) A_24) B_17))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) X) B_17)->((member214075476le_alt ((produc1347929815le_alt A_24) Y)) L_1)))) ((not (((eq arrow_475358991le_alt) X) B_17))->((and ((((eq arrow_475358991le_alt) Y) B_17)->((or (((eq arrow_475358991le_alt) X) A_24)) ((member214075476le_alt ((produc1347929815le_alt X) A_24)) L_1)))) ((not (((eq arrow_475358991le_alt) Y) B_17))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_1))))))))).
% Axiom fact_36_distinct_Osimps_I1_J:(distin236324274le_alt nil_Ar1286194111le_alt).
% Axiom fact_37_list_Osimps_I2_J:(forall (A_23:arrow_475358991le_alt) (List_4:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) nil_Ar1286194111le_alt) ((cons_A228743023le_alt A_23) List_4)))).
% Axiom fact_38_list_Osimps_I3_J:(forall (A_22:arrow_475358991le_alt) (List_3:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) ((cons_A228743023le_alt A_22) List_3)) nil_Ar1286194111le_alt))).
% Axiom fact_39_alt3:((ex arrow_475358991le_alt) (fun (A:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (B:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (C_2:arrow_475358991le_alt)=> (distin236324274le_alt ((cons_A228743023le_alt A) ((cons_A228743023le_alt B) ((cons_A228743023le_alt C_2) nil_Ar1286194111le_alt)))))))))).
% Axiom fact_40_linear__alt:((ex (produc1501160679le_alt->Prop)) (fun (L_2:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o L_2) arrow_823908191le_Lin))).
% Axiom fact_41_list_Oinject:(forall (A_21:arrow_475358991le_alt) (List_2:list_A2115238852le_alt) (A_20:arrow_475358991le_alt) (List_1:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((cons_A228743023le_alt A_21) List_2)) ((cons_A228743023le_alt A_20) List_1))) ((and (((eq arrow_475358991le_alt) A_21) A_20)) (((eq list_A2115238852le_alt) List_2) List_1)))).
% Axiom fact_42_not__Cons__self2:(forall (X_74:arrow_475358991le_alt) (Xs_127:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_74) Xs_127)) Xs_127))).
% Axiom fact_43_not__Cons__self:(forall (Xs_126:list_A2115238852le_alt) (X_73:arrow_475358991le_alt), (not (((eq list_A2115238852le_alt) Xs_126) ((cons_A228743023le_alt X_73) Xs_126)))).
% Axiom fact_44_above__Lin:(forall (L_1:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_1) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_789600939_above L_1) X) Y)) arrow_823908191le_Lin)))).
% Axiom fact_45_dictatorI:(forall (I_1:arrow_1429601828e_indi) (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o F_14) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin)))->((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A) B))->(((member214075476le_alt ((produc1347929815le_alt A) B)) (X_2 I_1))->((member214075476le_alt ((produc1347929815le_alt A) B)) (F_14 X_2)))))))->((arrow_1212662430ctator F_14) I_1)))).
% Axiom fact_46_PiE:(forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->Prop)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_15) ((pi_Pro1701359055_alt_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False)))).
% Axiom fact_47_PiE:(forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->produc1501160679le_alt)) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))), (((member712472209le_alt F_15) ((pi_Arr1786181611le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False)))).
% Axiom fact_48_PiE:(forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member351225838le_alt F_15) ((pi_Arr329216900le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False)))).
% Axiom fact_49_PiE:(forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->produc1501160679le_alt)) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->(produc1501160679le_alt->Prop))), (((member428957857le_alt F_15) ((pi_Pro1708969783le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False)))).
% Axiom fact_50_PiE:(forall (X_72:Prop) (F_15:(Prop->produc1501160679le_alt)) (A_19:(Prop->Prop)) (B_16:(Prop->(produc1501160679le_alt->Prop))), (((member492167345le_alt F_15) ((pi_o_P657324555le_alt A_19) B_16))->((((member214075476le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False)))).
% Axiom fact_51_PiE:(forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1876989968_alt_o F_15) ((pi_Arr578767520_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False)))).
% Axiom fact_52_PiE:(forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1234151027_alt_o F_15) ((pi_Arr1060328391_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False)))).
% Axiom fact_53_PiE:(forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member392452608_alt_o F_15) ((pi_Pro121963604_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False)))).
% Axiom fact_54_PiE:(forall (X_72:Prop) (F_15:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_19:(Prop->Prop)) (B_16:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1394214384_alt_o F_15) ((pi_o_A1182933120_alt_o A_19) B_16))->((((member526088951_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False)))).
% Axiom fact_55_PiE:(forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member1908358676_alt_o F_15) ((pi_Arr1520776484_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False)))).
% Axiom fact_56_PiE:(forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member2082473988_alt_o F_15) ((pi_Pro589599960_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False)))).
% Axiom fact_57_PiE:(forall (X_72:Prop) (F_15:(Prop->(produc1501160679le_alt->Prop))) (A_19:(Prop->Prop)) (B_16:(Prop->((produc1501160679le_alt->Prop)->Prop))), (((member1862122484_alt_o F_15) ((pi_o_P553196292_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False)))).
% Axiom fact_58_PiE:(forall (X_72:arrow_475358991le_alt) (F_15:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(arrow_475358991le_alt->Prop)) (B_16:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member89384572_alt_o F_15) ((pi_Arr515871190_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member84363362le_alt X_72) A_19)->False)))).
% Axiom fact_59_PiE:(forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member811956313_alt_o F_15) ((pi_Arr1564509167_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False)))).
% Axiom fact_60_PiE:(forall (X_72:produc1362454231le_alt) (F_15:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(produc1362454231le_alt->Prop)) (B_16:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member654997644_alt_o F_15) ((pi_Pro441468706_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member28618436le_alt X_72) A_19)->False)))).
% Axiom fact_61_PiE:(forall (X_72:Prop) (F_15:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_19:(Prop->Prop)) (B_16:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1957863580_alt_o F_15) ((pi_o_A1186128886_alt_o A_19) B_16))->((((member616898751_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member_o X_72) A_19)->False)))).
% Axiom fact_62_PiE:(forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->arrow_475358991le_alt)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))), (((member1416774619le_alt F_15) ((pi_Pro315446191le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False)))).
% Axiom fact_63_PiE:(forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))), (((member1640632174e_indi F_15) ((pi_Pro1767455108e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False)))).
% Axiom fact_64_PiE:(forall (X_72:produc1501160679le_alt) (F_15:(produc1501160679le_alt->produc1362454231le_alt)) (A_19:(produc1501160679le_alt->Prop)) (B_16:(produc1501160679le_alt->(produc1362454231le_alt->Prop))), (((member220989473le_alt F_15) ((pi_Pro666407479le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member214075476le_alt X_72) A_19)->False)))).
% Axiom fact_65_PiE:(forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member1596146470le_alt F_15) ((pi_Arr1483346486le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False)))).
% Axiom fact_66_PiE:(forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member44294883e_indi F_15) ((pi_Arr1232280765e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False)))).
% Axiom fact_67_PiE:(forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member1849320470le_alt F_15) ((pi_Arr1957214192le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False)))).
% Axiom fact_68_PiE:(forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member939334982lt_o_o F_15) ((pi_Arr952516694lt_o_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False)))).
% Axiom fact_69_PiE:(forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))), (((member1524522914le_alt F_15) ((pi_Pro1868152754le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False)))).
% Axiom fact_70_PiE:(forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))), (((member304866663e_indi F_15) ((pi_Pro468373057e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False)))).
% Axiom fact_71_PiE:(forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))), (((member1099563162le_alt F_15) ((pi_Pro1678345076le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False)))).
% Axiom fact_72_PiE:(forall (X_72:(produc1501160679le_alt->Prop)) (F_15:((produc1501160679le_alt->Prop)->Prop)) (A_19:((produc1501160679le_alt->Prop)->Prop)) (B_16:((produc1501160679le_alt->Prop)->(Prop->Prop))), (((member1961363906lt_o_o F_15) ((pi_Pro422690258lt_o_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member377231867_alt_o X_72) A_19)->False)))).
% Axiom fact_73_PiE:(forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member474974512le_alt F_15) ((pi_Arr1005837828le_alt A_19) B_16))->((((member84363362le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False)))).
% Axiom fact_74_PiE:(forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member1452482393e_indi F_15) ((pi_Arr338314351e_indi A_19) B_16))->((((member2052026769e_indi (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False)))).
% Axiom fact_75_PiE:(forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member845447052le_alt F_15) ((pi_Arr2076738722le_alt A_19) B_16))->((((member28618436le_alt (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False)))).
% Axiom fact_76_PiE:(forall (X_72:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member1823529808lt_o_o F_15) ((pi_Arr195212324lt_o_o A_19) B_16))->((((member_o (F_15 X_72)) (B_16 X_72))->False)->(((member616898751_alt_o X_72) A_19)->False)))).
% Axiom fact_77_PiE:(forall (X_72:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_15) ((pi_Arr1304755663_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member526088951_alt_o X_72) A_19)->False)))).
% Axiom fact_78_PiE:(forall (X_72:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_19:(arrow_1429601828e_indi->Prop)) (B_16:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_15) ((pi_Arr1929480907_alt_o A_19) B_16))->((((member377231867_alt_o (F_15 X_72)) (B_16 X_72))->False)->(((member2052026769e_indi X_72) A_19)->False)))).
% Axiom fact_79_list_Oexhaust:(forall (Y_26:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Y_26) nil_Ar1286194111le_alt))->((forall (A:arrow_475358991le_alt) (List:list_A2115238852le_alt), (not (((eq list_A2115238852le_alt) Y_26) ((cons_A228743023le_alt A) List))))->False))).
% Axiom fact_80_neq__Nil__conv:(forall (Xs_125:list_A2115238852le_alt), ((iff (not (((eq list_A2115238852le_alt) Xs_125) nil_Ar1286194111le_alt))) ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Xs_125) ((cons_A228743023le_alt Y_1) Ys)))))))).
% Axiom fact_81_dictator__def:(forall (F_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (I_1:arrow_1429601828e_indi), ((iff ((arrow_1212662430ctator F_14) I_1)) (forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) arrow_734252939e_Prof)->(((eq (produc1501160679le_alt->Prop)) (F_14 X_2)) (X_2 I_1)))))).
% Axiom fact_82_funcset__mem:(forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->Prop)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(Prop->Prop)), (((member377231867_alt_o F_13) ((pi_Pro1701359055_alt_o A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member_o (F_13 X_71)) B_15)))).
% Axiom fact_83_funcset__mem:(forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->arrow_475358991le_alt)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member1416774619le_alt F_13) ((pi_Pro315446191le_alt A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15)))).
% Axiom fact_84_funcset__mem:(forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member1640632174e_indi F_13) ((pi_Pro1767455108e_indi A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15)))).
% Axiom fact_85_funcset__mem:(forall (X_71:produc1501160679le_alt) (F_13:(produc1501160679le_alt->produc1362454231le_alt)) (A_18:(produc1501160679le_alt->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member220989473le_alt F_13) ((pi_Pro666407479le_alt A_18) (fun (Uu:produc1501160679le_alt)=> B_15)))->(((member214075476le_alt X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15)))).
% Axiom fact_86_funcset__mem:(forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member1596146470le_alt F_13) ((pi_Arr1483346486le_alt A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15)))).
% Axiom fact_87_funcset__mem:(forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member44294883e_indi F_13) ((pi_Arr1232280765e_indi A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15)))).
% Axiom fact_88_funcset__mem:(forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member1849320470le_alt F_13) ((pi_Arr1957214192le_alt A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15)))).
% Axiom fact_89_funcset__mem:(forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:(Prop->Prop)), (((member939334982lt_o_o F_13) ((pi_Arr952516694lt_o_o A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member_o (F_13 X_71)) B_15)))).
% Axiom fact_90_funcset__mem:(forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member1524522914le_alt F_13) ((pi_Pro1868152754le_alt A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15)))).
% Axiom fact_91_funcset__mem:(forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member304866663e_indi F_13) ((pi_Pro468373057e_indi A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15)))).
% Axiom fact_92_funcset__mem:(forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member1099563162le_alt F_13) ((pi_Pro1678345076le_alt A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15)))).
% Axiom fact_93_funcset__mem:(forall (X_71:(produc1501160679le_alt->Prop)) (F_13:((produc1501160679le_alt->Prop)->Prop)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_15:(Prop->Prop)), (((member1961363906lt_o_o F_13) ((pi_Pro422690258lt_o_o A_18) (fun (Uu:(produc1501160679le_alt->Prop))=> B_15)))->(((member377231867_alt_o X_71) A_18)->((member_o (F_13 X_71)) B_15)))).
% Axiom fact_94_funcset__mem:(forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_475358991le_alt->Prop)), (((member474974512le_alt F_13) ((pi_Arr1005837828le_alt A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member84363362le_alt (F_13 X_71)) B_15)))).
% Axiom fact_95_funcset__mem:(forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((member1452482393e_indi F_13) ((pi_Arr338314351e_indi A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member2052026769e_indi (F_13 X_71)) B_15)))).
% Axiom fact_96_funcset__mem:(forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(produc1362454231le_alt->Prop)), (((member845447052le_alt F_13) ((pi_Arr2076738722le_alt A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member28618436le_alt (F_13 X_71)) B_15)))).
% Axiom fact_97_funcset__mem:(forall (X_71:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(Prop->Prop)), (((member1823529808lt_o_o F_13) ((pi_Arr195212324lt_o_o A_18) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_15)))->(((member616898751_alt_o X_71) A_18)->((member_o (F_13 X_71)) B_15)))).
% Axiom fact_98_funcset__mem:(forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->produc1501160679le_alt)) (A_18:(arrow_475358991le_alt->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member712472209le_alt F_13) ((pi_Arr1786181611le_alt A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15)))).
% Axiom fact_99_funcset__mem:(forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member351225838le_alt F_13) ((pi_Arr329216900le_alt A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15)))).
% Axiom fact_100_funcset__mem:(forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->produc1501160679le_alt)) (A_18:(produc1362454231le_alt->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member428957857le_alt F_13) ((pi_Pro1708969783le_alt A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15)))).
% Axiom fact_101_funcset__mem:(forall (X_71:Prop) (F_13:(Prop->produc1501160679le_alt)) (A_18:(Prop->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((member492167345le_alt F_13) ((pi_o_P657324555le_alt A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member214075476le_alt (F_13 X_71)) B_15)))).
% Axiom fact_102_funcset__mem:(forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(arrow_475358991le_alt->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member1876989968_alt_o F_13) ((pi_Arr578767520_alt_o A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_103_funcset__mem:(forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member1234151027_alt_o F_13) ((pi_Arr1060328391_alt_o A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_104_funcset__mem:(forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(produc1362454231le_alt->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member392452608_alt_o F_13) ((pi_Pro121963604_alt_o A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_105_funcset__mem:(forall (X_71:Prop) (F_13:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_18:(Prop->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member1394214384_alt_o F_13) ((pi_o_A1182933120_alt_o A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member526088951_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_106_funcset__mem:(forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_18:(arrow_475358991le_alt->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member1908358676_alt_o F_13) ((pi_Arr1520776484_alt_o A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_107_funcset__mem:(forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_18:(produc1362454231le_alt->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member2082473988_alt_o F_13) ((pi_Pro589599960_alt_o A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_108_funcset__mem:(forall (X_71:Prop) (F_13:(Prop->(produc1501160679le_alt->Prop))) (A_18:(Prop->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member1862122484_alt_o F_13) ((pi_o_P553196292_alt_o A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_109_funcset__mem:(forall (X_71:arrow_475358991le_alt) (F_13:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(arrow_475358991le_alt->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member89384572_alt_o F_13) ((pi_Arr515871190_alt_o A_18) (fun (Uu:arrow_475358991le_alt)=> B_15)))->(((member84363362le_alt X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_110_funcset__mem:(forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member811956313_alt_o F_13) ((pi_Arr1564509167_alt_o A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_111_funcset__mem:(forall (X_71:produc1362454231le_alt) (F_13:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(produc1362454231le_alt->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member654997644_alt_o F_13) ((pi_Pro441468706_alt_o A_18) (fun (Uu:produc1362454231le_alt)=> B_15)))->(((member28618436le_alt X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_112_funcset__mem:(forall (X_71:Prop) (F_13:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_18:(Prop->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member1957863580_alt_o F_13) ((pi_o_A1186128886_alt_o A_18) (fun (Uu:Prop)=> B_15)))->(((member_o X_71) A_18)->((member616898751_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_113_funcset__mem:(forall (X_71:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_13) ((pi_Arr1304755663_alt_o A_18) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_15)))->(((member526088951_alt_o X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_114_funcset__mem:(forall (X_71:arrow_1429601828e_indi) (F_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_18:(arrow_1429601828e_indi->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_13) ((pi_Arr1929480907_alt_o A_18) (fun (Uu:arrow_1429601828e_indi)=> B_15)))->(((member2052026769e_indi X_71) A_18)->((member377231867_alt_o (F_13 X_71)) B_15)))).
% Axiom fact_115_splice_Osimps_I2_J:(forall (V_2:arrow_475358991le_alt) (Va:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt ((cons_A228743023le_alt V_2) Va)) nil_Ar1286194111le_alt)) ((cons_A228743023le_alt V_2) Va))).
% Axiom fact_116_splice_Osimps_I3_J:(forall (X_70:arrow_475358991le_alt) (Xs_124:list_A2115238852le_alt) (Y_25:arrow_475358991le_alt) (Ys_56:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt ((cons_A228743023le_alt X_70) Xs_124)) ((cons_A228743023le_alt Y_25) Ys_56))) ((cons_A228743023le_alt X_70) ((cons_A228743023le_alt Y_25) ((splice1520898450le_alt Xs_124) Ys_56))))).
% Axiom fact_117_splice_Osimps_I1_J:(forall (Ys_55:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt nil_Ar1286194111le_alt) Ys_55)) Ys_55)).
% Axiom fact_118_splice__Nil2:(forall (Xs_123:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((splice1520898450le_alt Xs_123) nil_Ar1286194111le_alt)) Xs_123)).
% Axiom fact_119_Pi__mem:(forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->Prop)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_12) ((pi_Pro1701359055_alt_o A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_120_Pi__mem:(forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->arrow_475358991le_alt)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))), (((member1416774619le_alt F_12) ((pi_Pro315446191le_alt A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_121_Pi__mem:(forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))), (((member1640632174e_indi F_12) ((pi_Pro1767455108e_indi A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_122_Pi__mem:(forall (X_69:produc1501160679le_alt) (F_12:(produc1501160679le_alt->produc1362454231le_alt)) (A_17:(produc1501160679le_alt->Prop)) (B_14:(produc1501160679le_alt->(produc1362454231le_alt->Prop))), (((member220989473le_alt F_12) ((pi_Pro666407479le_alt A_17) B_14))->(((member214075476le_alt X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_123_Pi__mem:(forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member1596146470le_alt F_12) ((pi_Arr1483346486le_alt A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_124_Pi__mem:(forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member44294883e_indi F_12) ((pi_Arr1232280765e_indi A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_125_Pi__mem:(forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member1849320470le_alt F_12) ((pi_Arr1957214192le_alt A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_126_Pi__mem:(forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member939334982lt_o_o F_12) ((pi_Arr952516694lt_o_o A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_127_Pi__mem:(forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))), (((member1524522914le_alt F_12) ((pi_Pro1868152754le_alt A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_128_Pi__mem:(forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))), (((member304866663e_indi F_12) ((pi_Pro468373057e_indi A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_129_Pi__mem:(forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))), (((member1099563162le_alt F_12) ((pi_Pro1678345076le_alt A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_130_Pi__mem:(forall (X_69:(produc1501160679le_alt->Prop)) (F_12:((produc1501160679le_alt->Prop)->Prop)) (A_17:((produc1501160679le_alt->Prop)->Prop)) (B_14:((produc1501160679le_alt->Prop)->(Prop->Prop))), (((member1961363906lt_o_o F_12) ((pi_Pro422690258lt_o_o A_17) B_14))->(((member377231867_alt_o X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_131_Pi__mem:(forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))), (((member474974512le_alt F_12) ((pi_Arr1005837828le_alt A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member84363362le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_132_Pi__mem:(forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member1452482393e_indi F_12) ((pi_Arr338314351e_indi A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member2052026769e_indi (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_133_Pi__mem:(forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))), (((member845447052le_alt F_12) ((pi_Arr2076738722le_alt A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member28618436le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_134_Pi__mem:(forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_17:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member1823529808lt_o_o F_12) ((pi_Arr195212324lt_o_o A_17) B_14))->(((member616898751_alt_o X_69) A_17)->((member_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_135_Pi__mem:(forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->produc1501160679le_alt)) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))), (((member712472209le_alt F_12) ((pi_Arr1786181611le_alt A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_136_Pi__mem:(forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member351225838le_alt F_12) ((pi_Arr329216900le_alt A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_137_Pi__mem:(forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->produc1501160679le_alt)) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->(produc1501160679le_alt->Prop))), (((member428957857le_alt F_12) ((pi_Pro1708969783le_alt A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_138_Pi__mem:(forall (X_69:Prop) (F_12:(Prop->produc1501160679le_alt)) (A_17:(Prop->Prop)) (B_14:(Prop->(produc1501160679le_alt->Prop))), (((member492167345le_alt F_12) ((pi_o_P657324555le_alt A_17) B_14))->(((member_o X_69) A_17)->((member214075476le_alt (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_139_Pi__mem:(forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1876989968_alt_o F_12) ((pi_Arr578767520_alt_o A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_140_Pi__mem:(forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1234151027_alt_o F_12) ((pi_Arr1060328391_alt_o A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_141_Pi__mem:(forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member392452608_alt_o F_12) ((pi_Pro121963604_alt_o A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_142_Pi__mem:(forall (X_69:Prop) (F_12:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_17:(Prop->Prop)) (B_14:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1394214384_alt_o F_12) ((pi_o_A1182933120_alt_o A_17) B_14))->(((member_o X_69) A_17)->((member526088951_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_143_Pi__mem:(forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member1908358676_alt_o F_12) ((pi_Arr1520776484_alt_o A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_144_Pi__mem:(forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))), (((member2082473988_alt_o F_12) ((pi_Pro589599960_alt_o A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_145_Pi__mem:(forall (X_69:Prop) (F_12:(Prop->(produc1501160679le_alt->Prop))) (A_17:(Prop->Prop)) (B_14:(Prop->((produc1501160679le_alt->Prop)->Prop))), (((member1862122484_alt_o F_12) ((pi_o_P553196292_alt_o A_17) B_14))->(((member_o X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_146_Pi__mem:(forall (X_69:arrow_475358991le_alt) (F_12:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(arrow_475358991le_alt->Prop)) (B_14:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member89384572_alt_o F_12) ((pi_Arr515871190_alt_o A_17) B_14))->(((member84363362le_alt X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_147_Pi__mem:(forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member811956313_alt_o F_12) ((pi_Arr1564509167_alt_o A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_148_Pi__mem:(forall (X_69:produc1362454231le_alt) (F_12:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(produc1362454231le_alt->Prop)) (B_14:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member654997644_alt_o F_12) ((pi_Pro441468706_alt_o A_17) B_14))->(((member28618436le_alt X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_149_Pi__mem:(forall (X_69:Prop) (F_12:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_17:(Prop->Prop)) (B_14:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1957863580_alt_o F_12) ((pi_o_A1186128886_alt_o A_17) B_14))->(((member_o X_69) A_17)->((member616898751_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_150_Pi__mem:(forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_17:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_12) ((pi_Arr1304755663_alt_o A_17) B_14))->(((member526088951_alt_o X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_151_Pi__mem:(forall (X_69:arrow_1429601828e_indi) (F_12:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_17:(arrow_1429601828e_indi->Prop)) (B_14:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_12) ((pi_Arr1929480907_alt_o A_17) B_14))->(((member2052026769e_indi X_69) A_17)->((member377231867_alt_o (F_12 X_69)) (B_14 X_69))))).
% Axiom fact_152_Pi__I:(forall (F_11:(produc1501160679le_alt->arrow_475358991le_alt)) (B_13:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member1416774619le_alt F_11) ((pi_Pro315446191le_alt A_16) B_13)))).
% Axiom fact_153_Pi__I:(forall (F_11:(produc1501160679le_alt->arrow_1429601828e_indi)) (B_13:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member1640632174e_indi F_11) ((pi_Pro1767455108e_indi A_16) B_13)))).
% Axiom fact_154_Pi__I:(forall (F_11:(produc1501160679le_alt->produc1362454231le_alt)) (B_13:(produc1501160679le_alt->(produc1362454231le_alt->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member220989473le_alt F_11) ((pi_Pro666407479le_alt A_16) B_13)))).
% Axiom fact_155_Pi__I:(forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member1596146470le_alt F_11) ((pi_Arr1483346486le_alt A_16) B_13)))).
% Axiom fact_156_Pi__I:(forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member44294883e_indi F_11) ((pi_Arr1232280765e_indi A_16) B_13)))).
% Axiom fact_157_Pi__I:(forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member1849320470le_alt F_11) ((pi_Arr1957214192le_alt A_16) B_13)))).
% Axiom fact_158_Pi__I:(forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member939334982lt_o_o F_11) ((pi_Arr952516694lt_o_o A_16) B_13)))).
% Axiom fact_159_Pi__I:(forall (F_11:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (B_13:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member1524522914le_alt F_11) ((pi_Pro1868152754le_alt A_16) B_13)))).
% Axiom fact_160_Pi__I:(forall (F_11:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (B_13:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member304866663e_indi F_11) ((pi_Pro468373057e_indi A_16) B_13)))).
% Axiom fact_161_Pi__I:(forall (F_11:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (B_13:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member1099563162le_alt F_11) ((pi_Pro1678345076le_alt A_16) B_13)))).
% Axiom fact_162_Pi__I:(forall (F_11:((produc1501160679le_alt->Prop)->Prop)) (B_13:((produc1501160679le_alt->Prop)->(Prop->Prop))) (A_16:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member1961363906lt_o_o F_11) ((pi_Pro422690258lt_o_o A_16) B_13)))).
% Axiom fact_163_Pi__I:(forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member84363362le_alt (F_11 X_2)) (B_13 X_2))))->((member474974512le_alt F_11) ((pi_Arr1005837828le_alt A_16) B_13)))).
% Axiom fact_164_Pi__I:(forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member2052026769e_indi (F_11 X_2)) (B_13 X_2))))->((member1452482393e_indi F_11) ((pi_Arr338314351e_indi A_16) B_13)))).
% Axiom fact_165_Pi__I:(forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member28618436le_alt (F_11 X_2)) (B_13 X_2))))->((member845447052le_alt F_11) ((pi_Arr2076738722le_alt A_16) B_13)))).
% Axiom fact_166_Pi__I:(forall (F_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_16:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member1823529808lt_o_o F_11) ((pi_Arr195212324lt_o_o A_16) B_13)))).
% Axiom fact_167_Pi__I:(forall (F_11:(arrow_475358991le_alt->produc1501160679le_alt)) (B_13:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member712472209le_alt F_11) ((pi_Arr1786181611le_alt A_16) B_13)))).
% Axiom fact_168_Pi__I:(forall (F_11:(arrow_1429601828e_indi->produc1501160679le_alt)) (B_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member351225838le_alt F_11) ((pi_Arr329216900le_alt A_16) B_13)))).
% Axiom fact_169_Pi__I:(forall (F_11:(produc1362454231le_alt->produc1501160679le_alt)) (B_13:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member428957857le_alt F_11) ((pi_Pro1708969783le_alt A_16) B_13)))).
% Axiom fact_170_Pi__I:(forall (F_11:(Prop->produc1501160679le_alt)) (B_13:(Prop->(produc1501160679le_alt->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member214075476le_alt (F_11 X_2)) (B_13 X_2))))->((member492167345le_alt F_11) ((pi_o_P657324555le_alt A_16) B_13)))).
% Axiom fact_171_Pi__I:(forall (F_11:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member1876989968_alt_o F_11) ((pi_Arr578767520_alt_o A_16) B_13)))).
% Axiom fact_172_Pi__I:(forall (F_11:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member1234151027_alt_o F_11) ((pi_Arr1060328391_alt_o A_16) B_13)))).
% Axiom fact_173_Pi__I:(forall (F_11:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member392452608_alt_o F_11) ((pi_Pro121963604_alt_o A_16) B_13)))).
% Axiom fact_174_Pi__I:(forall (F_11:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_13:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member526088951_alt_o (F_11 X_2)) (B_13 X_2))))->((member1394214384_alt_o F_11) ((pi_o_A1182933120_alt_o A_16) B_13)))).
% Axiom fact_175_Pi__I:(forall (F_11:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (B_13:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member1908358676_alt_o F_11) ((pi_Arr1520776484_alt_o A_16) B_13)))).
% Axiom fact_176_Pi__I:(forall (F_11:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (B_13:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member2082473988_alt_o F_11) ((pi_Pro589599960_alt_o A_16) B_13)))).
% Axiom fact_177_Pi__I:(forall (F_11:(Prop->(produc1501160679le_alt->Prop))) (B_13:(Prop->((produc1501160679le_alt->Prop)->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member1862122484_alt_o F_11) ((pi_o_P553196292_alt_o A_16) B_13)))).
% Axiom fact_178_Pi__I:(forall (F_11:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member89384572_alt_o F_11) ((pi_Arr515871190_alt_o A_16) B_13)))).
% Axiom fact_179_Pi__I:(forall (F_11:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member811956313_alt_o F_11) ((pi_Arr1564509167_alt_o A_16) B_13)))).
% Axiom fact_180_Pi__I:(forall (F_11:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member654997644_alt_o F_11) ((pi_Pro441468706_alt_o A_16) B_13)))).
% Axiom fact_181_Pi__I:(forall (F_11:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_13:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_16:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_16)->((member616898751_alt_o (F_11 X_2)) (B_13 X_2))))->((member1957863580_alt_o F_11) ((pi_o_A1186128886_alt_o A_16) B_13)))).
% Axiom fact_182_Pi__I:(forall (F_11:(produc1501160679le_alt->Prop)) (B_13:(produc1501160679le_alt->(Prop->Prop))) (A_16:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_16)->((member_o (F_11 X_2)) (B_13 X_2))))->((member377231867_alt_o F_11) ((pi_Pro1701359055_alt_o A_16) B_13)))).
% Axiom fact_183_Pi__I:(forall (F_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member616898751_alt_o F_11) ((pi_Arr1304755663_alt_o A_16) B_13)))).
% Axiom fact_184_Pi__I:(forall (F_11:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_13:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_16:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_16)->((member377231867_alt_o (F_11 X_2)) (B_13 X_2))))->((member526088951_alt_o F_11) ((pi_Arr1929480907_alt_o A_16) B_13)))).
% Axiom fact_185_funcsetI:(forall (F_10:(produc1501160679le_alt->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member1416774619le_alt F_10) ((pi_Pro315446191le_alt A_15) (fun (Uu:produc1501160679le_alt)=> B_12))))).
% Axiom fact_186_funcsetI:(forall (F_10:(produc1501160679le_alt->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member1640632174e_indi F_10) ((pi_Pro1767455108e_indi A_15) (fun (Uu:produc1501160679le_alt)=> B_12))))).
% Axiom fact_187_funcsetI:(forall (F_10:(produc1501160679le_alt->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member220989473le_alt F_10) ((pi_Pro666407479le_alt A_15) (fun (Uu:produc1501160679le_alt)=> B_12))))).
% Axiom fact_188_funcsetI:(forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member1596146470le_alt F_10) ((pi_Arr1483346486le_alt A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12))))).
% Axiom fact_189_funcsetI:(forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member44294883e_indi F_10) ((pi_Arr1232280765e_indi A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12))))).
% Axiom fact_190_funcsetI:(forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member1849320470le_alt F_10) ((pi_Arr1957214192le_alt A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12))))).
% Axiom fact_191_funcsetI:(forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_12:(Prop->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member939334982lt_o_o F_10) ((pi_Arr952516694lt_o_o A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12))))).
% Axiom fact_192_funcsetI:(forall (F_10:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member1524522914le_alt F_10) ((pi_Pro1868152754le_alt A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12))))).
% Axiom fact_193_funcsetI:(forall (F_10:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member304866663e_indi F_10) ((pi_Pro468373057e_indi A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12))))).
% Axiom fact_194_funcsetI:(forall (F_10:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member1099563162le_alt F_10) ((pi_Pro1678345076le_alt A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12))))).
% Axiom fact_195_funcsetI:(forall (F_10:((produc1501160679le_alt->Prop)->Prop)) (B_12:(Prop->Prop)) (A_15:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member1961363906lt_o_o F_10) ((pi_Pro422690258lt_o_o A_15) (fun (Uu:(produc1501160679le_alt->Prop))=> B_12))))).
% Axiom fact_196_funcsetI:(forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_12:(arrow_475358991le_alt->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member84363362le_alt (F_10 X_2)) B_12)))->((member474974512le_alt F_10) ((pi_Arr1005837828le_alt A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12))))).
% Axiom fact_197_funcsetI:(forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_12:(arrow_1429601828e_indi->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member2052026769e_indi (F_10 X_2)) B_12)))->((member1452482393e_indi F_10) ((pi_Arr338314351e_indi A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12))))).
% Axiom fact_198_funcsetI:(forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_12:(produc1362454231le_alt->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member28618436le_alt (F_10 X_2)) B_12)))->((member845447052le_alt F_10) ((pi_Arr2076738722le_alt A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12))))).
% Axiom fact_199_funcsetI:(forall (F_10:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_12:(Prop->Prop)) (A_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member1823529808lt_o_o F_10) ((pi_Arr195212324lt_o_o A_15) (fun (Uu:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> B_12))))).
% Axiom fact_200_funcsetI:(forall (F_10:(arrow_475358991le_alt->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member712472209le_alt F_10) ((pi_Arr1786181611le_alt A_15) (fun (Uu:arrow_475358991le_alt)=> B_12))))).
% Axiom fact_201_funcsetI:(forall (F_10:(arrow_1429601828e_indi->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member351225838le_alt F_10) ((pi_Arr329216900le_alt A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12))))).
% Axiom fact_202_funcsetI:(forall (F_10:(produc1362454231le_alt->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member428957857le_alt F_10) ((pi_Pro1708969783le_alt A_15) (fun (Uu:produc1362454231le_alt)=> B_12))))).
% Axiom fact_203_funcsetI:(forall (F_10:(Prop->produc1501160679le_alt)) (B_12:(produc1501160679le_alt->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member214075476le_alt (F_10 X_2)) B_12)))->((member492167345le_alt F_10) ((pi_o_P657324555le_alt A_15) (fun (Uu:Prop)=> B_12))))).
% Axiom fact_204_funcsetI:(forall (F_10:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member1876989968_alt_o F_10) ((pi_Arr578767520_alt_o A_15) (fun (Uu:arrow_475358991le_alt)=> B_12))))).
% Axiom fact_205_funcsetI:(forall (F_10:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member1234151027_alt_o F_10) ((pi_Arr1060328391_alt_o A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12))))).
% Axiom fact_206_funcsetI:(forall (F_10:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member392452608_alt_o F_10) ((pi_Pro121963604_alt_o A_15) (fun (Uu:produc1362454231le_alt)=> B_12))))).
% Axiom fact_207_funcsetI:(forall (F_10:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member526088951_alt_o (F_10 X_2)) B_12)))->((member1394214384_alt_o F_10) ((pi_o_A1182933120_alt_o A_15) (fun (Uu:Prop)=> B_12))))).
% Axiom fact_208_funcsetI:(forall (F_10:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member1908358676_alt_o F_10) ((pi_Arr1520776484_alt_o A_15) (fun (Uu:arrow_475358991le_alt)=> B_12))))).
% Axiom fact_209_funcsetI:(forall (F_10:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member2082473988_alt_o F_10) ((pi_Pro589599960_alt_o A_15) (fun (Uu:produc1362454231le_alt)=> B_12))))).
% Axiom fact_210_funcsetI:(forall (F_10:(Prop->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member1862122484_alt_o F_10) ((pi_o_P553196292_alt_o A_15) (fun (Uu:Prop)=> B_12))))).
% Axiom fact_211_funcsetI:(forall (F_10:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member89384572_alt_o F_10) ((pi_Arr515871190_alt_o A_15) (fun (Uu:arrow_475358991le_alt)=> B_12))))).
% Axiom fact_212_funcsetI:(forall (F_10:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member811956313_alt_o F_10) ((pi_Arr1564509167_alt_o A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12))))).
% Axiom fact_213_funcsetI:(forall (F_10:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member654997644_alt_o F_10) ((pi_Pro441468706_alt_o A_15) (fun (Uu:produc1362454231le_alt)=> B_12))))).
% Axiom fact_214_funcsetI:(forall (F_10:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_15:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_15)->((member616898751_alt_o (F_10 X_2)) B_12)))->((member1957863580_alt_o F_10) ((pi_o_A1186128886_alt_o A_15) (fun (Uu:Prop)=> B_12))))).
% Axiom fact_215_funcsetI:(forall (F_10:(produc1501160679le_alt->Prop)) (B_12:(Prop->Prop)) (A_15:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_15)->((member_o (F_10 X_2)) B_12)))->((member377231867_alt_o F_10) ((pi_Pro1701359055_alt_o A_15) (fun (Uu:produc1501160679le_alt)=> B_12))))).
% Axiom fact_216_funcsetI:(forall (F_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member616898751_alt_o F_10) ((pi_Arr1304755663_alt_o A_15) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_12))))).
% Axiom fact_217_funcsetI:(forall (F_10:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_12:((produc1501160679le_alt->Prop)->Prop)) (A_15:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_15)->((member377231867_alt_o (F_10 X_2)) B_12)))->((member526088951_alt_o F_10) ((pi_Arr1929480907_alt_o A_15) (fun (Uu:arrow_1429601828e_indi)=> B_12))))).
% Axiom fact_218_Pi__I_H:(forall (F_9:(produc1501160679le_alt->arrow_475358991le_alt)) (B_11:(produc1501160679le_alt->(arrow_475358991le_alt->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member1416774619le_alt F_9) ((pi_Pro315446191le_alt A_14) B_11)))).
% Axiom fact_219_Pi__I_H:(forall (F_9:(produc1501160679le_alt->arrow_1429601828e_indi)) (B_11:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member1640632174e_indi F_9) ((pi_Pro1767455108e_indi A_14) B_11)))).
% Axiom fact_220_Pi__I_H:(forall (F_9:(produc1501160679le_alt->produc1362454231le_alt)) (B_11:(produc1501160679le_alt->(produc1362454231le_alt->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member220989473le_alt F_9) ((pi_Pro666407479le_alt A_14) B_11)))).
% Axiom fact_221_Pi__I_H:(forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member1596146470le_alt F_9) ((pi_Arr1483346486le_alt A_14) B_11)))).
% Axiom fact_222_Pi__I_H:(forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member44294883e_indi F_9) ((pi_Arr1232280765e_indi A_14) B_11)))).
% Axiom fact_223_Pi__I_H:(forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member1849320470le_alt F_9) ((pi_Arr1957214192le_alt A_14) B_11)))).
% Axiom fact_224_Pi__I_H:(forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member939334982lt_o_o F_9) ((pi_Arr952516694lt_o_o A_14) B_11)))).
% Axiom fact_225_Pi__I_H:(forall (F_9:((produc1501160679le_alt->Prop)->arrow_475358991le_alt)) (B_11:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member1524522914le_alt F_9) ((pi_Pro1868152754le_alt A_14) B_11)))).
% Axiom fact_226_Pi__I_H:(forall (F_9:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (B_11:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member304866663e_indi F_9) ((pi_Pro468373057e_indi A_14) B_11)))).
% Axiom fact_227_Pi__I_H:(forall (F_9:((produc1501160679le_alt->Prop)->produc1362454231le_alt)) (B_11:((produc1501160679le_alt->Prop)->(produc1362454231le_alt->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member1099563162le_alt F_9) ((pi_Pro1678345076le_alt A_14) B_11)))).
% Axiom fact_228_Pi__I_H:(forall (F_9:((produc1501160679le_alt->Prop)->Prop)) (B_11:((produc1501160679le_alt->Prop)->(Prop->Prop))) (A_14:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member1961363906lt_o_o F_9) ((pi_Pro422690258lt_o_o A_14) B_11)))).
% Axiom fact_229_Pi__I_H:(forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_475358991le_alt)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_475358991le_alt->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member84363362le_alt (F_9 X_2)) (B_11 X_2))))->((member474974512le_alt F_9) ((pi_Arr1005837828le_alt A_14) B_11)))).
% Axiom fact_230_Pi__I_H:(forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member2052026769e_indi (F_9 X_2)) (B_11 X_2))))->((member1452482393e_indi F_9) ((pi_Arr338314351e_indi A_14) B_11)))).
% Axiom fact_231_Pi__I_H:(forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->produc1362454231le_alt)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(produc1362454231le_alt->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member28618436le_alt (F_9 X_2)) (B_11 X_2))))->((member845447052le_alt F_9) ((pi_Arr2076738722le_alt A_14) B_11)))).
% Axiom fact_232_Pi__I_H:(forall (F_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))) (A_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member1823529808lt_o_o F_9) ((pi_Arr195212324lt_o_o A_14) B_11)))).
% Axiom fact_233_Pi__I_H:(forall (F_9:(arrow_475358991le_alt->produc1501160679le_alt)) (B_11:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member712472209le_alt F_9) ((pi_Arr1786181611le_alt A_14) B_11)))).
% Axiom fact_234_Pi__I_H:(forall (F_9:(arrow_1429601828e_indi->produc1501160679le_alt)) (B_11:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member351225838le_alt F_9) ((pi_Arr329216900le_alt A_14) B_11)))).
% Axiom fact_235_Pi__I_H:(forall (F_9:(produc1362454231le_alt->produc1501160679le_alt)) (B_11:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member428957857le_alt F_9) ((pi_Pro1708969783le_alt A_14) B_11)))).
% Axiom fact_236_Pi__I_H:(forall (F_9:(Prop->produc1501160679le_alt)) (B_11:(Prop->(produc1501160679le_alt->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member214075476le_alt (F_9 X_2)) (B_11 X_2))))->((member492167345le_alt F_9) ((pi_o_P657324555le_alt A_14) B_11)))).
% Axiom fact_237_Pi__I_H:(forall (F_9:(arrow_475358991le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member1876989968_alt_o F_9) ((pi_Arr578767520_alt_o A_14) B_11)))).
% Axiom fact_238_Pi__I_H:(forall (F_9:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member1234151027_alt_o F_9) ((pi_Arr1060328391_alt_o A_14) B_11)))).
% Axiom fact_239_Pi__I_H:(forall (F_9:(produc1362454231le_alt->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member392452608_alt_o F_9) ((pi_Pro121963604_alt_o A_14) B_11)))).
% Axiom fact_240_Pi__I_H:(forall (F_9:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (B_11:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member526088951_alt_o (F_9 X_2)) (B_11 X_2))))->((member1394214384_alt_o F_9) ((pi_o_A1182933120_alt_o A_14) B_11)))).
% Axiom fact_241_Pi__I_H:(forall (F_9:(arrow_475358991le_alt->(produc1501160679le_alt->Prop))) (B_11:(arrow_475358991le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member1908358676_alt_o F_9) ((pi_Arr1520776484_alt_o A_14) B_11)))).
% Axiom fact_242_Pi__I_H:(forall (F_9:(produc1362454231le_alt->(produc1501160679le_alt->Prop))) (B_11:(produc1362454231le_alt->((produc1501160679le_alt->Prop)->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member2082473988_alt_o F_9) ((pi_Pro589599960_alt_o A_14) B_11)))).
% Axiom fact_243_Pi__I_H:(forall (F_9:(Prop->(produc1501160679le_alt->Prop))) (B_11:(Prop->((produc1501160679le_alt->Prop)->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member1862122484_alt_o F_9) ((pi_o_P553196292_alt_o A_14) B_11)))).
% Axiom fact_244_Pi__I_H:(forall (F_9:(arrow_475358991le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(arrow_475358991le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member89384572_alt_o F_9) ((pi_Arr515871190_alt_o A_14) B_11)))).
% Axiom fact_245_Pi__I_H:(forall (F_9:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member811956313_alt_o F_9) ((pi_Arr1564509167_alt_o A_14) B_11)))).
% Axiom fact_246_Pi__I_H:(forall (F_9:(produc1362454231le_alt->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(produc1362454231le_alt->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member654997644_alt_o F_9) ((pi_Pro441468706_alt_o A_14) B_11)))).
% Axiom fact_247_Pi__I_H:(forall (F_9:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (B_11:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))) (A_14:(Prop->Prop)), ((forall (X_2:Prop), (((member_o X_2) A_14)->((member616898751_alt_o (F_9 X_2)) (B_11 X_2))))->((member1957863580_alt_o F_9) ((pi_o_A1186128886_alt_o A_14) B_11)))).
% Axiom fact_248_Pi__I_H:(forall (F_9:(produc1501160679le_alt->Prop)) (B_11:(produc1501160679le_alt->(Prop->Prop))) (A_14:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) A_14)->((member_o (F_9 X_2)) (B_11 X_2))))->((member377231867_alt_o F_9) ((pi_Pro1701359055_alt_o A_14) B_11)))).
% Axiom fact_249_Pi__I_H:(forall (F_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member616898751_alt_o F_9) ((pi_Arr1304755663_alt_o A_14) B_11)))).
% Axiom fact_250_Pi__I_H:(forall (F_9:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_11:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_14:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) A_14)->((member377231867_alt_o (F_9 X_2)) (B_11 X_2))))->((member526088951_alt_o F_9) ((pi_Arr1929480907_alt_o A_14) B_11)))).
% Axiom fact_251_Pi__cong:(forall (B_10:(produc1501160679le_alt->(Prop->Prop))) (G:(produc1501160679le_alt->Prop)) (F_8:(produc1501160679le_alt->Prop)) (A_13:(produc1501160679le_alt->Prop)), ((forall (W:produc1501160679le_alt), (((member214075476le_alt W) A_13)->((iff (F_8 W)) (G W))))->((iff ((member377231867_alt_o F_8) ((pi_Pro1701359055_alt_o A_13) B_10))) ((member377231867_alt_o G) ((pi_Pro1701359055_alt_o A_13) B_10))))).
% Axiom fact_252_Pi__cong:(forall (B_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (F_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (G:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (W:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o W) A_13)->(((eq (produc1501160679le_alt->Prop)) (F_8 W)) (G W))))->((iff ((member616898751_alt_o F_8) ((pi_Arr1304755663_alt_o A_13) B_10))) ((member616898751_alt_o G) ((pi_Arr1304755663_alt_o A_13) B_10))))).
% Axiom fact_253_Pi__cong:(forall (B_10:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (F_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (G:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_13:(arrow_1429601828e_indi->Prop)), ((forall (W:arrow_1429601828e_indi), (((member2052026769e_indi W) A_13)->(((eq (produc1501160679le_alt->Prop)) (F_8 W)) (G W))))->((iff ((member526088951_alt_o F_8) ((pi_Arr1929480907_alt_o A_13) B_10))) ((member526088951_alt_o G) ((pi_Arr1929480907_alt_o A_13) B_10))))).
% Axiom fact_254_pred__equals__eq2:(forall (S_1:(produc1362454231le_alt->Prop)) (R_39:(produc1362454231le_alt->Prop)), ((iff (forall (X_2:list_A2115238852le_alt) (Xa:list_A2115238852le_alt), ((iff ((member28618436le_alt ((produc776457805le_alt X_2) Xa)) R_39)) ((member28618436le_alt ((produc776457805le_alt X_2) Xa)) S_1)))) (((eq (produc1362454231le_alt->Prop)) R_39) S_1))).
% Axiom fact_255_pred__equals__eq2:(forall (S_1:(produc1501160679le_alt->Prop)) (R_39:(produc1501160679le_alt->Prop)), ((iff (forall (X_2:arrow_475358991le_alt) (Xa:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X_2) Xa)) R_39)) ((member214075476le_alt ((produc1347929815le_alt X_2) Xa)) S_1)))) (((eq (produc1501160679le_alt->Prop)) R_39) S_1))).
% Axiom fact_256_prod_Oexhaust:(forall (Y_24:produc1362454231le_alt), ((forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), (not (((eq produc1362454231le_alt) Y_24) ((produc776457805le_alt A) B))))->False)).
% Axiom fact_257_prod_Oexhaust:(forall (Y_24:produc1501160679le_alt), ((forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), (not (((eq produc1501160679le_alt) Y_24) ((produc1347929815le_alt A) B))))->False)).
% Axiom fact_258_PairE:(forall (P_29:produc1362454231le_alt), ((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt), (not (((eq produc1362454231le_alt) P_29) ((produc776457805le_alt X_2) Y_1))))->False)).
% Axiom fact_259_PairE:(forall (P_29:produc1501160679le_alt), ((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt), (not (((eq produc1501160679le_alt) P_29) ((produc1347929815le_alt X_2) Y_1))))->False)).
% Axiom fact_260_split__paired__Ex:(forall (P_28:(produc1362454231le_alt->Prop)), ((iff (ex1 P_28)) ((ex list_A2115238852le_alt) (fun (A:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (B:list_A2115238852le_alt)=> (P_28 ((produc776457805le_alt A) B)))))))).
% Axiom fact_261_split__paired__Ex:(forall (P_28:(produc1501160679le_alt->Prop)), ((iff (ex2 P_28)) ((ex arrow_475358991le_alt) (fun (A:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (B:arrow_475358991le_alt)=> (P_28 ((produc1347929815le_alt A) B)))))))).
% Axiom fact_262_insert__Nil:(forall (X_68:arrow_475358991le_alt), (((eq list_A2115238852le_alt) ((insert2120566741le_alt X_68) nil_Ar1286194111le_alt)) ((cons_A228743023le_alt X_68) nil_Ar1286194111le_alt))).
% Axiom fact_263_distinct__insert:(forall (X_67:arrow_475358991le_alt) (Xs_122:list_A2115238852le_alt), ((distin236324274le_alt Xs_122)->(distin236324274le_alt ((insert2120566741le_alt X_67) Xs_122)))).
% Axiom fact_264_mem__def:(forall (X_66:arrow_475358991le_alt) (A_12:(arrow_475358991le_alt->Prop)), ((iff ((member84363362le_alt X_66) A_12)) (A_12 X_66))).
% Axiom fact_265_mem__def:(forall (X_66:arrow_1429601828e_indi) (A_12:(arrow_1429601828e_indi->Prop)), ((iff ((member2052026769e_indi X_66) A_12)) (A_12 X_66))).
% Axiom fact_266_mem__def:(forall (X_66:produc1362454231le_alt) (A_12:(produc1362454231le_alt->Prop)), ((iff ((member28618436le_alt X_66) A_12)) (A_12 X_66))).
% Axiom fact_267_mem__def:(forall (X_66:Prop) (A_12:(Prop->Prop)), ((iff ((member_o X_66) A_12)) (A_12 X_66))).
% Axiom fact_268_mem__def:(forall (X_66:produc1501160679le_alt) (A_12:(produc1501160679le_alt->Prop)), ((iff ((member214075476le_alt X_66) A_12)) (A_12 X_66))).
% Axiom fact_269_mem__def:(forall (X_66:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member526088951_alt_o X_66) A_12)) (A_12 X_66))).
% Axiom fact_270_mem__def:(forall (X_66:(produc1501160679le_alt->Prop)) (A_12:((produc1501160679le_alt->Prop)->Prop)), ((iff ((member377231867_alt_o X_66) A_12)) (A_12 X_66))).
% Axiom fact_271_mem__def:(forall (X_66:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member616898751_alt_o X_66) A_12)) (A_12 X_66))).
% Axiom fact_272_Collect__def:(forall (P_27:(arrow_475358991le_alt->Prop)), (((eq (arrow_475358991le_alt->Prop)) (collec742074788le_alt P_27)) P_27)).
% Axiom fact_273_Collect__def:(forall (P_27:(arrow_1429601828e_indi->Prop)), (((eq (arrow_1429601828e_indi->Prop)) (collec22405327e_indi P_27)) P_27)).
% Axiom fact_274_Collect__def:(forall (P_27:((produc1501160679le_alt->Prop)->Prop)), (((eq ((produc1501160679le_alt->Prop)->Prop)) (collec94295101_alt_o P_27)) P_27)).
% Axiom fact_275_list__nonempty__induct:(forall (P_26:(list_A2115238852le_alt->Prop)) (Xs_121:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_121) nil_Ar1286194111le_alt))->((forall (X_2:arrow_475358991le_alt), (P_26 ((cons_A228743023le_alt X_2) nil_Ar1286194111le_alt)))->((forall (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_21) nil_Ar1286194111le_alt))->((P_26 Xs_21)->(P_26 ((cons_A228743023le_alt X_2) Xs_21)))))->(P_26 Xs_121))))).
% Axiom fact_276_curry__def:(forall (X_2:(produc1501160679le_alt->Prop)) (Xa:arrow_475358991le_alt) (Xb:arrow_475358991le_alt), ((iff (((produc910278158_alt_o X_2) Xa) Xb)) (X_2 ((produc1347929815le_alt Xa) Xb)))).
% Axiom fact_277_curryI:(forall (F_7:(produc1362454231le_alt->Prop)) (A_11:list_A2115238852le_alt) (B_9:list_A2115238852le_alt), ((F_7 ((produc776457805le_alt A_11) B_9))->(((produc1739499928_alt_o F_7) A_11) B_9))).
% Axiom fact_278_curryI:(forall (F_7:(produc1501160679le_alt->Prop)) (A_11:arrow_475358991le_alt) (B_9:arrow_475358991le_alt), ((F_7 ((produc1347929815le_alt A_11) B_9))->(((produc910278158_alt_o F_7) A_11) B_9))).
% Axiom fact_279_null__rec_I2_J:(null_A1520965063le_alt nil_Ar1286194111le_alt).
% Axiom fact_280_List_Onull__def:(forall (Xs_120:list_A2115238852le_alt), ((iff (null_A1520965063le_alt Xs_120)) (((eq list_A2115238852le_alt) Xs_120) nil_Ar1286194111le_alt))).
% Axiom fact_281_eq__Nil__null:(forall (Xs_119:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) Xs_119) nil_Ar1286194111le_alt)) (null_A1520965063le_alt Xs_119))).
% Axiom fact_282_null__rec_I1_J:(forall (X_65:arrow_475358991le_alt) (Xs_118:list_A2115238852le_alt), ((null_A1520965063le_alt ((cons_A228743023le_alt X_65) Xs_118))->False)).
% Axiom fact_283_curryD:(forall (F_6:(produc1362454231le_alt->Prop)) (A_10:list_A2115238852le_alt) (B_8:list_A2115238852le_alt), ((((produc1739499928_alt_o F_6) A_10) B_8)->(F_6 ((produc776457805le_alt A_10) B_8)))).
% Axiom fact_284_curryD:(forall (F_6:(produc1501160679le_alt->Prop)) (A_10:arrow_475358991le_alt) (B_8:arrow_475358991le_alt), ((((produc910278158_alt_o F_6) A_10) B_8)->(F_6 ((produc1347929815le_alt A_10) B_8)))).
% Axiom fact_285_curryE:(forall (F_5:(produc1362454231le_alt->Prop)) (A_9:list_A2115238852le_alt) (B_7:list_A2115238852le_alt), ((((produc1739499928_alt_o F_5) A_9) B_7)->(F_5 ((produc776457805le_alt A_9) B_7)))).
% Axiom fact_286_curryE:(forall (F_5:(produc1501160679le_alt->Prop)) (A_9:arrow_475358991le_alt) (B_7:arrow_475358991le_alt), ((((produc910278158_alt_o F_5) A_9) B_7)->(F_5 ((produc1347929815le_alt A_9) B_7)))).
% Axiom fact_287_curry__conv:(forall (F_4:(produc1501160679le_alt->Prop)) (A_8:arrow_475358991le_alt) (B_6:arrow_475358991le_alt), ((iff (((produc910278158_alt_o F_4) A_8) B_6)) (F_4 ((produc1347929815le_alt A_8) B_6)))).
% Axiom fact_288_equal__Nil__null:(forall (Xs_117:list_A2115238852le_alt), ((iff ((equal_484611810le_alt Xs_117) nil_Ar1286194111le_alt)) (null_A1520965063le_alt Xs_117))).
% Axiom fact_289_Prof__def:(((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) arrow_734252939e_Prof) ((pi_Arr1929480907_alt_o top_to988227749indi_o) (fun (Uu:arrow_1429601828e_indi)=> arrow_823908191le_Lin))).
% Axiom fact_290_lexord__cons__cons:(forall (A_7:list_A2115238852le_alt) (X_64:list_l1475218533le_alt) (B_5:list_A2115238852le_alt) (Y_23:list_l1475218533le_alt) (R_38:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt A_7) X_64)) ((cons_l635097956le_alt B_5) Y_23))) (lexord469916775le_alt R_38))) ((or ((member28618436le_alt ((produc776457805le_alt A_7) B_5)) R_38)) ((and (((eq list_A2115238852le_alt) A_7) B_5)) ((member1732936276le_alt ((produc1317709143le_alt X_64) Y_23)) (lexord469916775le_alt R_38)))))).
% Axiom fact_291_lexord__cons__cons:(forall (A_7:arrow_475358991le_alt) (X_64:list_A2115238852le_alt) (B_5:arrow_475358991le_alt) (Y_23:list_A2115238852le_alt) (R_38:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt A_7) X_64)) ((cons_A228743023le_alt B_5) Y_23))) (lexord958095404le_alt R_38))) ((or ((member214075476le_alt ((produc1347929815le_alt A_7) B_5)) R_38)) ((and (((eq arrow_475358991le_alt) A_7) B_5)) ((member28618436le_alt ((produc776457805le_alt X_64) Y_23)) (lexord958095404le_alt R_38)))))).
% Axiom fact_292_distinct__butlast:(forall (Xs_116:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_116) nil_Ar1286194111le_alt))->((distin236324274le_alt Xs_116)->(distin236324274le_alt (butlas274947851le_alt Xs_116))))).
% Axiom fact_293_last__ConsL:(forall (X_63:arrow_475358991le_alt) (Xs_115:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_115) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_63) Xs_115))) X_63))).
% Axiom fact_294_last__ConsR:(forall (X_62:arrow_475358991le_alt) (Xs_114:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_114) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_62) Xs_114))) (last_A1217315288le_alt Xs_114)))).
% Axiom fact_295_top1I:(forall (X_61:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (top_to1969627639lt_o_o X_61)).
% Axiom fact_296_top1I:(forall (X_61:(produc1501160679le_alt->Prop)), (top_to1842727771lt_o_o X_61)).
% Axiom fact_297_top1I:(forall (X_61:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (top_to2122763103lt_o_o X_61)).
% Axiom fact_298_top1I:(forall (X_61:produc1501160679le_alt), (top_to1841428258_alt_o X_61)).
% Axiom fact_299_top1I:(forall (X_61:arrow_1429601828e_indi), (top_to988227749indi_o X_61)).
% Axiom fact_300_top1I:(forall (X_61:arrow_475358991le_alt), (top_to728987956_alt_o X_61)).
% Axiom fact_301_equal__list__def:(forall (X_60:list_A2115238852le_alt) (Y_22:list_A2115238852le_alt), ((iff ((equal_484611810le_alt X_60) Y_22)) (((eq list_A2115238852le_alt) X_60) Y_22))).
% Axiom fact_302_Pi__UNIV:(forall (A_6:(produc1501160679le_alt->Prop)), (((eq ((produc1501160679le_alt->Prop)->Prop)) ((pi_Pro1701359055_alt_o A_6) (fun (Uu:produc1501160679le_alt)=> top_top_o_o))) top_to1842727771lt_o_o)).
% Axiom fact_303_Pi__UNIV:(forall (A_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1304755663_alt_o A_6) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> top_to1842727771lt_o_o))) top_to1969627639lt_o_o)).
% Axiom fact_304_Pi__UNIV:(forall (A_6:(arrow_1429601828e_indi->Prop)), (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1929480907_alt_o A_6) (fun (Uu:arrow_1429601828e_indi)=> top_to1842727771lt_o_o))) top_to2122763103lt_o_o)).
% Axiom fact_305_butlast_Osimps_I1_J:(((eq list_A2115238852le_alt) (butlas274947851le_alt nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt).
% Axiom fact_306_lexord__Nil__right:(forall (X_59:list_A2115238852le_alt) (R_37:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_59) nil_Ar1286194111le_alt)) (lexord958095404le_alt R_37))->False)).
% Axiom fact_307_butlast_Osimps_I2_J:(forall (X_58:arrow_475358991le_alt) (Xs_113:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Xs_113) nil_Ar1286194111le_alt)->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((cons_A228743023le_alt X_58) Xs_113))) nil_Ar1286194111le_alt))) ((not (((eq list_A2115238852le_alt) Xs_113) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((cons_A228743023le_alt X_58) Xs_113))) ((cons_A228743023le_alt X_58) (butlas274947851le_alt Xs_113)))))).
% Axiom fact_308_last_Osimps:(forall (X_57:arrow_475358991le_alt) (Xs_112:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Xs_112) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_57) Xs_112))) X_57))) ((not (((eq list_A2115238852le_alt) Xs_112) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((cons_A228743023le_alt X_57) Xs_112))) (last_A1217315288le_alt Xs_112))))).
% Axiom fact_309_lexord__Nil__left:(forall (Y_21:list_A2115238852le_alt) (R_36:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Y_21)) (lexord958095404le_alt R_36))) ((ex arrow_475358991le_alt) (fun (A:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (X_2:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Y_21) ((cons_A228743023le_alt A) X_2)))))))).
% Axiom fact_310_lexord__irreflexive:(forall (Xs_111:list_l1475218533le_alt) (R_35:(produc1362454231le_alt->Prop)), ((forall (X_2:list_A2115238852le_alt), (((member28618436le_alt ((produc776457805le_alt X_2) X_2)) R_35)->False))->(((member1732936276le_alt ((produc1317709143le_alt Xs_111) Xs_111)) (lexord469916775le_alt R_35))->False))).
% Axiom fact_311_lexord__irreflexive:(forall (Xs_111:list_A2115238852le_alt) (R_35:(produc1501160679le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), (((member214075476le_alt ((produc1347929815le_alt X_2) X_2)) R_35)->False))->(((member28618436le_alt ((produc776457805le_alt Xs_111) Xs_111)) (lexord958095404le_alt R_35))->False))).
% Axiom fact_312_lexord__linear:(forall (X_56:list_l1475218533le_alt) (Y_20:list_l1475218533le_alt) (R_34:(produc1362454231le_alt->Prop)), ((forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), ((or ((or ((member28618436le_alt ((produc776457805le_alt A) B)) R_34)) (((eq list_A2115238852le_alt) A) B))) ((member28618436le_alt ((produc776457805le_alt B) A)) R_34)))->((or ((or ((member1732936276le_alt ((produc1317709143le_alt X_56) Y_20)) (lexord469916775le_alt R_34))) (((eq list_l1475218533le_alt) X_56) Y_20))) ((member1732936276le_alt ((produc1317709143le_alt Y_20) X_56)) (lexord469916775le_alt R_34))))).
% Axiom fact_313_lexord__linear:(forall (X_56:list_A2115238852le_alt) (Y_20:list_A2115238852le_alt) (R_34:(produc1501160679le_alt->Prop)), ((forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((or ((or ((member214075476le_alt ((produc1347929815le_alt A) B)) R_34)) (((eq arrow_475358991le_alt) A) B))) ((member214075476le_alt ((produc1347929815le_alt B) A)) R_34)))->((or ((or ((member28618436le_alt ((produc776457805le_alt X_56) Y_20)) (lexord958095404le_alt R_34))) (((eq list_A2115238852le_alt) X_56) Y_20))) ((member28618436le_alt ((produc776457805le_alt Y_20) X_56)) (lexord958095404le_alt R_34))))).
% Axiom fact_314_UNIV__I:(forall (X_55:produc1362454231le_alt), ((member28618436le_alt X_55) top_to1039387826_alt_o)).
% Axiom fact_315_UNIV__I:(forall (X_55:Prop), ((member_o X_55) top_top_o_o)).
% Axiom fact_316_UNIV__I:(forall (X_55:arrow_1429601828e_indi), ((member2052026769e_indi X_55) top_to988227749indi_o)).
% Axiom fact_317_UNIV__I:(forall (X_55:arrow_475358991le_alt), ((member84363362le_alt X_55) top_to728987956_alt_o)).
% Axiom fact_318_UNIV__I:(forall (X_55:produc1501160679le_alt), ((member214075476le_alt X_55) top_to1841428258_alt_o)).
% Axiom fact_319_UNIV__I:(forall (X_55:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_55) top_to2122763103lt_o_o)).
% Axiom fact_320_UNIV__I:(forall (X_55:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_55) top_to1842727771lt_o_o)).
% Axiom fact_321_UNIV__I:(forall (X_55:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_55) top_to1969627639lt_o_o)).
% Axiom fact_322_iso__tuple__UNIV__I:(forall (X_54:produc1362454231le_alt), ((member28618436le_alt X_54) top_to1039387826_alt_o)).
% Axiom fact_323_iso__tuple__UNIV__I:(forall (X_54:Prop), ((member_o X_54) top_top_o_o)).
% Axiom fact_324_iso__tuple__UNIV__I:(forall (X_54:arrow_1429601828e_indi), ((member2052026769e_indi X_54) top_to988227749indi_o)).
% Axiom fact_325_iso__tuple__UNIV__I:(forall (X_54:arrow_475358991le_alt), ((member84363362le_alt X_54) top_to728987956_alt_o)).
% Axiom fact_326_iso__tuple__UNIV__I:(forall (X_54:produc1501160679le_alt), ((member214075476le_alt X_54) top_to1841428258_alt_o)).
% Axiom fact_327_iso__tuple__UNIV__I:(forall (X_54:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_54) top_to2122763103lt_o_o)).
% Axiom fact_328_iso__tuple__UNIV__I:(forall (X_54:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_54) top_to1842727771lt_o_o)).
% Axiom fact_329_iso__tuple__UNIV__I:(forall (X_54:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_54) top_to1969627639lt_o_o)).
% Axiom fact_330_top__apply:(forall (X_53:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (top_to1969627639lt_o_o X_53)) top_top_o)).
% Axiom fact_331_top__apply:(forall (X_53:(produc1501160679le_alt->Prop)), ((iff (top_to1842727771lt_o_o X_53)) top_top_o)).
% Axiom fact_332_top__apply:(forall (X_53:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((iff (top_to2122763103lt_o_o X_53)) top_top_o)).
% Axiom fact_333_top__apply:(forall (X_53:produc1501160679le_alt), ((iff (top_to1841428258_alt_o X_53)) top_top_o)).
% Axiom fact_334_top__apply:(forall (X_53:arrow_1429601828e_indi), ((iff (top_to988227749indi_o X_53)) top_top_o)).
% Axiom fact_335_top__apply:(forall (X_53:arrow_475358991le_alt), ((iff (top_to728987956_alt_o X_53)) top_top_o)).
% Axiom fact_336_takeWhile__not__last:(forall (Xs_110:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_110) nil_Ar1286194111le_alt))->((distin236324274le_alt Xs_110)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) (last_A1217315288le_alt Xs_110))))) Xs_110)) (butlas274947851le_alt Xs_110))))).
% Axiom fact_337_partition_Osimps_I1_J:(forall (P_25:(arrow_475358991le_alt->Prop)), (((eq produc1362454231le_alt) ((partit1487577784le_alt P_25) nil_Ar1286194111le_alt)) ((produc776457805le_alt nil_Ar1286194111le_alt) nil_Ar1286194111le_alt))).
% Axiom fact_338_takeWhile_Osimps_I1_J:(forall (P_24:(arrow_475358991le_alt->Prop)), (((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_24) nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt)).
% Axiom fact_339_distinct__takeWhile:(forall (P_23:(arrow_475358991le_alt->Prop)) (Xs_109:list_A2115238852le_alt), ((distin236324274le_alt Xs_109)->(distin236324274le_alt ((takeWh1696291512le_alt P_23) Xs_109)))).
% Axiom fact_340_takeWhile_Osimps_I2_J:(forall (Xs_108:list_A2115238852le_alt) (P_22:(arrow_475358991le_alt->Prop)) (X_52:arrow_475358991le_alt), ((and ((P_22 X_52)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_22) ((cons_A228743023le_alt X_52) Xs_108))) ((cons_A228743023le_alt X_52) ((takeWh1696291512le_alt P_22) Xs_108))))) (((P_22 X_52)->False)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_22) ((cons_A228743023le_alt X_52) Xs_108))) nil_Ar1286194111le_alt)))).
% Axiom fact_341_UNIV__def:(((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) top_to1969627639lt_o_o) (collec2009291517_alt_o (fun (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> True))).
% Axiom fact_342_UNIV__def:(((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) top_to2122763103lt_o_o) (collec682858041_alt_o (fun (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> True))).
% Axiom fact_343_UNIV__def:(((eq (produc1501160679le_alt->Prop)) top_to1841428258_alt_o) (collec869865362le_alt (fun (X_2:produc1501160679le_alt)=> True))).
% Axiom fact_344_UNIV__def:(((eq (arrow_1429601828e_indi->Prop)) top_to988227749indi_o) (collec22405327e_indi (fun (X_2:arrow_1429601828e_indi)=> True))).
% Axiom fact_345_UNIV__def:(((eq (arrow_475358991le_alt->Prop)) top_to728987956_alt_o) (collec742074788le_alt (fun (X_2:arrow_475358991le_alt)=> True))).
% Axiom fact_346_UNIV__def:(((eq ((produc1501160679le_alt->Prop)->Prop)) top_to1842727771lt_o_o) (collec94295101_alt_o (fun (X_2:(produc1501160679le_alt->Prop))=> True))).
% Axiom fact_347_UNIV__eq__I:(forall (A_5:(produc1362454231le_alt->Prop)), ((forall (X_2:produc1362454231le_alt), ((member28618436le_alt X_2) A_5))->(((eq (produc1362454231le_alt->Prop)) top_to1039387826_alt_o) A_5))).
% Axiom fact_348_UNIV__eq__I:(forall (A_5:(Prop->Prop)), ((forall (X_2:Prop), ((member_o X_2) A_5))->(((eq (Prop->Prop)) top_top_o_o) A_5))).
% Axiom fact_349_UNIV__eq__I:(forall (A_5:(arrow_1429601828e_indi->Prop)), ((forall (X_2:arrow_1429601828e_indi), ((member2052026769e_indi X_2) A_5))->(((eq (arrow_1429601828e_indi->Prop)) top_to988227749indi_o) A_5))).
% Axiom fact_350_UNIV__eq__I:(forall (A_5:(arrow_475358991le_alt->Prop)), ((forall (X_2:arrow_475358991le_alt), ((member84363362le_alt X_2) A_5))->(((eq (arrow_475358991le_alt->Prop)) top_to728987956_alt_o) A_5))).
% Axiom fact_351_UNIV__eq__I:(forall (A_5:(produc1501160679le_alt->Prop)), ((forall (X_2:produc1501160679le_alt), ((member214075476le_alt X_2) A_5))->(((eq (produc1501160679le_alt->Prop)) top_to1841428258_alt_o) A_5))).
% Axiom fact_352_UNIV__eq__I:(forall (A_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_2) A_5))->(((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) top_to2122763103lt_o_o) A_5))).
% Axiom fact_353_UNIV__eq__I:(forall (A_5:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_2:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_2) A_5))->(((eq ((produc1501160679le_alt->Prop)->Prop)) top_to1842727771lt_o_o) A_5))).
% Axiom fact_354_UNIV__eq__I:(forall (A_5:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_2) A_5))->(((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) top_to1969627639lt_o_o) A_5))).
% Axiom fact_355_UNIV__witness:((ex produc1362454231le_alt) (fun (X_2:produc1362454231le_alt)=> ((member28618436le_alt X_2) top_to1039387826_alt_o))).
% Axiom fact_356_UNIV__witness:((ex Prop) (fun (X_2:Prop)=> ((member_o X_2) top_top_o_o))).
% Axiom fact_357_UNIV__witness:((ex arrow_1429601828e_indi) (fun (X_2:arrow_1429601828e_indi)=> ((member2052026769e_indi X_2) top_to988227749indi_o))).
% Axiom fact_358_UNIV__witness:((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((member84363362le_alt X_2) top_to728987956_alt_o))).
% Axiom fact_359_UNIV__witness:((ex produc1501160679le_alt) (fun (X_2:produc1501160679le_alt)=> ((member214075476le_alt X_2) top_to1841428258_alt_o))).
% Axiom fact_360_UNIV__witness:((ex (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (fun (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> ((member526088951_alt_o X_2) top_to2122763103lt_o_o))).
% Axiom fact_361_UNIV__witness:((ex (produc1501160679le_alt->Prop)) (fun (X_2:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o X_2) top_to1842727771lt_o_o))).
% Axiom fact_362_UNIV__witness:((ex ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (fun (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> ((member616898751_alt_o X_2) top_to1969627639lt_o_o))).
% Axiom fact_363_Lin__def:(((eq ((produc1501160679le_alt->Prop)->Prop)) arrow_823908191le_Lin) (collec94295101_alt_o (order_1995917111le_alt top_to728987956_alt_o))).
% Axiom fact_364_append__butlast__last__id:(forall (Xs_107:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_107) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) ((append179082452le_alt (butlas274947851le_alt Xs_107)) ((cons_A228743023le_alt (last_A1217315288le_alt Xs_107)) nil_Ar1286194111le_alt))) Xs_107))).
% Axiom fact_365_snoc__eq__iff__butlast:(forall (Xs_106:list_A2115238852le_alt) (X_51:arrow_475358991le_alt) (Ys_54:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_106) ((cons_A228743023le_alt X_51) nil_Ar1286194111le_alt))) Ys_54)) ((and ((and (not (((eq list_A2115238852le_alt) Ys_54) nil_Ar1286194111le_alt))) (((eq list_A2115238852le_alt) (butlas274947851le_alt Ys_54)) Xs_106))) (((eq arrow_475358991le_alt) (last_A1217315288le_alt Ys_54)) X_51)))).
% Axiom fact_366_Nil2__notin__lex:(forall (Xs_105:list_A2115238852le_alt) (R_33:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_105) nil_Ar1286194111le_alt)) (lex_Ar1415517219le_alt R_33))->False)).
% Axiom fact_367_Nil__notin__lex:(forall (Ys_53:list_A2115238852le_alt) (R_32:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Ys_53)) (lex_Ar1415517219le_alt R_32))->False)).
% Axiom fact_368_append__eq__appendI:(forall (Ys_52:list_A2115238852le_alt) (Us_3:list_A2115238852le_alt) (Xs_104:list_A2115238852le_alt) (Xs1_1:list_A2115238852le_alt) (Zs_9:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) ((append179082452le_alt Xs_104) Xs1_1)) Zs_9)->((((eq list_A2115238852le_alt) Ys_52) ((append179082452le_alt Xs1_1) Us_3))->(((eq list_A2115238852le_alt) ((append179082452le_alt Xs_104) Ys_52)) ((append179082452le_alt Zs_9) Us_3))))).
% Axiom fact_369_append__same__eq:(forall (Ys_51:list_A2115238852le_alt) (Xs_103:list_A2115238852le_alt) (Zs_8:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Ys_51) Xs_103)) ((append179082452le_alt Zs_8) Xs_103))) (((eq list_A2115238852le_alt) Ys_51) Zs_8))).
% Axiom fact_370_same__append__eq:(forall (Xs_102:list_A2115238852le_alt) (Ys_50:list_A2115238852le_alt) (Zs_7:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_102) Ys_50)) ((append179082452le_alt Xs_102) Zs_7))) (((eq list_A2115238852le_alt) Ys_50) Zs_7))).
% Axiom fact_371_append__eq__append__conv2:(forall (Xs_101:list_A2115238852le_alt) (Ys_49:list_A2115238852le_alt) (Zs_6:list_A2115238852le_alt) (Ts:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_101) Ys_49)) ((append179082452le_alt Zs_6) Ts))) ((ex list_A2115238852le_alt) (fun (Us:list_A2115238852le_alt)=> ((or ((and (((eq list_A2115238852le_alt) Xs_101) ((append179082452le_alt Zs_6) Us))) (((eq list_A2115238852le_alt) ((append179082452le_alt Us) Ys_49)) Ts))) ((and (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_101) Us)) Zs_6)) (((eq list_A2115238852le_alt) Ys_49) ((append179082452le_alt Us) Ts)))))))).
% Axiom fact_372_append__assoc:(forall (Xs_100:list_A2115238852le_alt) (Ys_48:list_A2115238852le_alt) (Zs_5:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((append179082452le_alt Xs_100) Ys_48)) Zs_5)) ((append179082452le_alt Xs_100) ((append179082452le_alt Ys_48) Zs_5)))).
% Axiom fact_373_append__Cons:(forall (X_50:arrow_475358991le_alt) (Xs_99:list_A2115238852le_alt) (Ys_47:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((cons_A228743023le_alt X_50) Xs_99)) Ys_47)) ((cons_A228743023le_alt X_50) ((append179082452le_alt Xs_99) Ys_47)))).
% Axiom fact_374_Cons__eq__appendI:(forall (Xs_98:list_A2115238852le_alt) (Zs_4:list_A2115238852le_alt) (X_49:arrow_475358991le_alt) (Xs1:list_A2115238852le_alt) (Ys_46:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_49) Xs1)) Ys_46)->((((eq list_A2115238852le_alt) Xs_98) ((append179082452le_alt Xs1) Zs_4))->(((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_49) Xs_98)) ((append179082452le_alt Ys_46) Zs_4))))).
% Axiom fact_375_append__Nil:(forall (Ys_45:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt nil_Ar1286194111le_alt) Ys_45)) Ys_45)).
% Axiom fact_376_Nil__is__append__conv:(forall (Xs_97:list_A2115238852le_alt) (Ys_44:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) nil_Ar1286194111le_alt) ((append179082452le_alt Xs_97) Ys_44))) ((and (((eq list_A2115238852le_alt) Xs_97) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Ys_44) nil_Ar1286194111le_alt)))).
% Axiom fact_377_append__Nil2:(forall (Xs_96:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_96) nil_Ar1286194111le_alt)) Xs_96)).
% Axiom fact_378_self__append__conv:(forall (Xs_95:list_A2115238852le_alt) (Ys_43:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) Xs_95) ((append179082452le_alt Xs_95) Ys_43))) (((eq list_A2115238852le_alt) Ys_43) nil_Ar1286194111le_alt))).
% Axiom fact_379_self__append__conv2:(forall (Ys_42:list_A2115238852le_alt) (Xs_94:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) Ys_42) ((append179082452le_alt Xs_94) Ys_42))) (((eq list_A2115238852le_alt) Xs_94) nil_Ar1286194111le_alt))).
% Axiom fact_380_append__is__Nil__conv:(forall (Xs_93:list_A2115238852le_alt) (Ys_41:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_93) Ys_41)) nil_Ar1286194111le_alt)) ((and (((eq list_A2115238852le_alt) Xs_93) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Ys_41) nil_Ar1286194111le_alt)))).
% Axiom fact_381_append__self__conv:(forall (Xs_92:list_A2115238852le_alt) (Ys_40:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_92) Ys_40)) Xs_92)) (((eq list_A2115238852le_alt) Ys_40) nil_Ar1286194111le_alt))).
% Axiom fact_382_append__self__conv2:(forall (Xs_91:list_A2115238852le_alt) (Ys_39:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_91) Ys_39)) Ys_39)) (((eq list_A2115238852le_alt) Xs_91) nil_Ar1286194111le_alt))).
% Axiom fact_383_eq__Nil__appendI:(forall (Xs_90:list_A2115238852le_alt) (Ys_38:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_90) Ys_38)->(((eq list_A2115238852le_alt) Xs_90) ((append179082452le_alt nil_Ar1286194111le_alt) Ys_38)))).
% Axiom fact_384_append__eq__Cons__conv:(forall (Ys_37:list_A2115238852le_alt) (Zs_3:list_A2115238852le_alt) (X_48:arrow_475358991le_alt) (Xs_89:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Ys_37) Zs_3)) ((cons_A228743023le_alt X_48) Xs_89))) ((or ((and (((eq list_A2115238852le_alt) Ys_37) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Zs_3) ((cons_A228743023le_alt X_48) Xs_89)))) ((ex list_A2115238852le_alt) (fun (Ys_36:list_A2115238852le_alt)=> ((and (((eq list_A2115238852le_alt) Ys_37) ((cons_A228743023le_alt X_48) Ys_36))) (((eq list_A2115238852le_alt) ((append179082452le_alt Ys_36) Zs_3)) Xs_89))))))).
% Axiom fact_385_Cons__eq__append__conv:(forall (X_47:arrow_475358991le_alt) (Xs_88:list_A2115238852le_alt) (Ys_35:list_A2115238852le_alt) (Zs_2:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_47) Xs_88)) ((append179082452le_alt Ys_35) Zs_2))) ((or ((and (((eq list_A2115238852le_alt) Ys_35) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_47) Xs_88)) Zs_2))) ((ex list_A2115238852le_alt) (fun (Ys_36:list_A2115238852le_alt)=> ((and (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_47) Ys_36)) Ys_35)) (((eq list_A2115238852le_alt) Xs_88) ((append179082452le_alt Ys_36) Zs_2)))))))).
% Axiom fact_386_append1__eq__conv:(forall (Xs_87:list_A2115238852le_alt) (X_46:arrow_475358991le_alt) (Ys_34:list_A2115238852le_alt) (Y_19:arrow_475358991le_alt), ((iff (((eq list_A2115238852le_alt) ((append179082452le_alt Xs_87) ((cons_A228743023le_alt X_46) nil_Ar1286194111le_alt))) ((append179082452le_alt Ys_34) ((cons_A228743023le_alt Y_19) nil_Ar1286194111le_alt)))) ((and (((eq list_A2115238852le_alt) Xs_87) Ys_34)) (((eq arrow_475358991le_alt) X_46) Y_19)))).
% Axiom fact_387_takeWhile__tail:(forall (Xs_86:list_A2115238852le_alt) (L:list_A2115238852le_alt) (P_21:(arrow_475358991le_alt->Prop)) (X_45:arrow_475358991le_alt), (((P_21 X_45)->False)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_21) ((append179082452le_alt Xs_86) ((cons_A228743023le_alt X_45) L)))) ((takeWh1696291512le_alt P_21) Xs_86)))).
% Axiom fact_388_butlast__append:(forall (Xs_85:list_A2115238852le_alt) (Ys_33:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Ys_33) nil_Ar1286194111le_alt)->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((append179082452le_alt Xs_85) Ys_33))) (butlas274947851le_alt Xs_85)))) ((not (((eq list_A2115238852le_alt) Ys_33) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (butlas274947851le_alt ((append179082452le_alt Xs_85) Ys_33))) ((append179082452le_alt Xs_85) (butlas274947851le_alt Ys_33)))))).
% Axiom fact_389_last__append:(forall (Xs_84:list_A2115238852le_alt) (Ys_32:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Ys_32) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_84) Ys_32))) (last_A1217315288le_alt Xs_84)))) ((not (((eq list_A2115238852le_alt) Ys_32) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_84) Ys_32))) (last_A1217315288le_alt Ys_32))))).
% Axiom fact_390_last__appendR:(forall (Xs_83:list_A2115238852le_alt) (Ys_31:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Ys_31) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_83) Ys_31))) (last_A1217315288le_alt Ys_31)))).
% Axiom fact_391_last__appendL:(forall (Xs_82:list_A2115238852le_alt) (Ys_30:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Ys_30) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_82) Ys_30))) (last_A1217315288le_alt Xs_82)))).
% Axiom fact_392_lexord__append__leftI:(forall (X_44:list_A2115238852le_alt) (U_2:list_A2115238852le_alt) (V_1:list_A2115238852le_alt) (R_31:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt U_2) V_1)) (lexord958095404le_alt R_31))->((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt X_44) U_2)) ((append179082452le_alt X_44) V_1))) (lexord958095404le_alt R_31)))).
% Axiom fact_393_butlast__snoc:(forall (Xs_81:list_A2115238852le_alt) (X_43:arrow_475358991le_alt), (((eq list_A2115238852le_alt) (butlas274947851le_alt ((append179082452le_alt Xs_81) ((cons_A228743023le_alt X_43) nil_Ar1286194111le_alt)))) Xs_81)).
% Axiom fact_394_last__snoc:(forall (Xs_80:list_A2115238852le_alt) (X_42:arrow_475358991le_alt), (((eq arrow_475358991le_alt) (last_A1217315288le_alt ((append179082452le_alt Xs_80) ((cons_A228743023le_alt X_42) nil_Ar1286194111le_alt)))) X_42)).
% Axiom fact_395_lexord__append__left__rightI:(forall (U_1:list_A2115238852le_alt) (X_41:list_A2115238852le_alt) (Y_18:list_A2115238852le_alt) (A_4:arrow_475358991le_alt) (B_4:arrow_475358991le_alt) (R_30:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt A_4) B_4)) R_30)->((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt U_1) ((cons_A228743023le_alt A_4) X_41))) ((append179082452le_alt U_1) ((cons_A228743023le_alt B_4) Y_18)))) (lexord958095404le_alt R_30)))).
% Axiom fact_396_lexord__append__left__rightI:(forall (U_1:list_l1475218533le_alt) (X_41:list_l1475218533le_alt) (Y_18:list_l1475218533le_alt) (A_4:list_A2115238852le_alt) (B_4:list_A2115238852le_alt) (R_30:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt A_4) B_4)) R_30)->((member1732936276le_alt ((produc1317709143le_alt ((append1166001599le_alt U_1) ((cons_l635097956le_alt A_4) X_41))) ((append1166001599le_alt U_1) ((cons_l635097956le_alt B_4) Y_18)))) (lexord469916775le_alt R_30)))).
% Axiom fact_397_lexord__append__rightI:(forall (X_40:list_A2115238852le_alt) (R_29:(produc1501160679le_alt->Prop)) (Y_17:list_A2115238852le_alt), (((ex arrow_475358991le_alt) (fun (B:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Z:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Y_17) ((cons_A228743023le_alt B) Z))))))->((member28618436le_alt ((produc776457805le_alt X_40) ((append179082452le_alt X_40) Y_17))) (lexord958095404le_alt R_29)))).
% Axiom fact_398_lexord__append__leftD:(forall (X_39:list_l1475218533le_alt) (U:list_l1475218533le_alt) (V:list_l1475218533le_alt) (R_28:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt ((append1166001599le_alt X_39) U)) ((append1166001599le_alt X_39) V))) (lexord469916775le_alt R_28))->((forall (A:list_A2115238852le_alt), (((member28618436le_alt ((produc776457805le_alt A) A)) R_28)->False))->((member1732936276le_alt ((produc1317709143le_alt U) V)) (lexord469916775le_alt R_28))))).
% Axiom fact_399_lexord__append__leftD:(forall (X_39:list_A2115238852le_alt) (U:list_A2115238852le_alt) (V:list_A2115238852le_alt) (R_28:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt X_39) U)) ((append179082452le_alt X_39) V))) (lexord958095404le_alt R_28))->((forall (A:arrow_475358991le_alt), (((member214075476le_alt ((produc1347929815le_alt A) A)) R_28)->False))->((member28618436le_alt ((produc776457805le_alt U) V)) (lexord958095404le_alt R_28))))).
% Axiom fact_400_rev__induct:(forall (Xs_79:list_A2115238852le_alt) (P_20:(list_A2115238852le_alt->Prop)), ((P_20 nil_Ar1286194111le_alt)->((forall (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt), ((P_20 Xs_21)->(P_20 ((append179082452le_alt Xs_21) ((cons_A228743023le_alt X_2) nil_Ar1286194111le_alt)))))->(P_20 Xs_79)))).
% Axiom fact_401_rev__cases:(forall (Xs_78:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_78) nil_Ar1286194111le_alt))->((forall (Ys:list_A2115238852le_alt) (Y_1:arrow_475358991le_alt), (not (((eq list_A2115238852le_alt) Xs_78) ((append179082452le_alt Ys) ((cons_A228743023le_alt Y_1) nil_Ar1286194111le_alt)))))->False))).
% Axiom fact_402_snoc__listrel1__snoc__iff:(forall (Xs_77:list_l1475218533le_alt) (X_38:list_A2115238852le_alt) (Ys_29:list_l1475218533le_alt) (Y_16:list_A2115238852le_alt) (R_27:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((append1166001599le_alt Xs_77) ((cons_l635097956le_alt X_38) nil_li1907286804le_alt))) ((append1166001599le_alt Ys_29) ((cons_l635097956le_alt Y_16) nil_li1907286804le_alt)))) (listre620555643le_alt R_27))) ((or ((and ((member1732936276le_alt ((produc1317709143le_alt Xs_77) Ys_29)) (listre620555643le_alt R_27))) (((eq list_A2115238852le_alt) X_38) Y_16))) ((and (((eq list_l1475218533le_alt) Xs_77) Ys_29)) ((member28618436le_alt ((produc776457805le_alt X_38) Y_16)) R_27))))).
% Axiom fact_403_snoc__listrel1__snoc__iff:(forall (Xs_77:list_A2115238852le_alt) (X_38:arrow_475358991le_alt) (Ys_29:list_A2115238852le_alt) (Y_16:arrow_475358991le_alt) (R_27:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt Xs_77) ((cons_A228743023le_alt X_38) nil_Ar1286194111le_alt))) ((append179082452le_alt Ys_29) ((cons_A228743023le_alt Y_16) nil_Ar1286194111le_alt)))) (listre2064003096le_alt R_27))) ((or ((and ((member28618436le_alt ((produc776457805le_alt Xs_77) Ys_29)) (listre2064003096le_alt R_27))) (((eq arrow_475358991le_alt) X_38) Y_16))) ((and (((eq list_A2115238852le_alt) Xs_77) Ys_29)) ((member214075476le_alt ((produc1347929815le_alt X_38) Y_16)) R_27))))).
% Axiom fact_404_rotate1__def:(forall (Xs_76:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rotate335349260le_alt Xs_76)) (((list_c1623890103le_alt nil_Ar1286194111le_alt) (fun (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt)=> ((append179082452le_alt Xs_21) ((cons_A228743023le_alt X_2) nil_Ar1286194111le_alt)))) Xs_76))).
% Axiom fact_405_rotate1__is__Nil__conv:(forall (Xs_75:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) (rotate335349260le_alt Xs_75)) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Xs_75) nil_Ar1286194111le_alt))).
% Axiom fact_406_distinct1__rotate:(forall (Xs_74:list_A2115238852le_alt), ((iff (distin236324274le_alt (rotate335349260le_alt Xs_74))) (distin236324274le_alt Xs_74))).
% Axiom fact_407_listrel1I2:(forall (X_37:arrow_475358991le_alt) (Xs_73:list_A2115238852le_alt) (Ys_28:list_A2115238852le_alt) (R_26:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_73) Ys_28)) (listre2064003096le_alt R_26))->((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_37) Xs_73)) ((cons_A228743023le_alt X_37) Ys_28))) (listre2064003096le_alt R_26)))).
% Axiom fact_408_not__listrel1__Nil:(forall (Xs_72:list_A2115238852le_alt) (R_25:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_72) nil_Ar1286194111le_alt)) (listre2064003096le_alt R_25))->False)).
% Axiom fact_409_not__Nil__listrel1:(forall (Xs_71:list_A2115238852le_alt) (R_24:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Xs_71)) (listre2064003096le_alt R_24))->False)).
% Axiom fact_410_append__listrel1I:(forall (Us_2:list_A2115238852le_alt) (Vs_2:list_A2115238852le_alt) (Xs_70:list_A2115238852le_alt) (Ys_27:list_A2115238852le_alt) (R_23:(produc1501160679le_alt->Prop)), (((or ((and ((member28618436le_alt ((produc776457805le_alt Xs_70) Ys_27)) (listre2064003096le_alt R_23))) (((eq list_A2115238852le_alt) Us_2) Vs_2))) ((and (((eq list_A2115238852le_alt) Xs_70) Ys_27)) ((member28618436le_alt ((produc776457805le_alt Us_2) Vs_2)) (listre2064003096le_alt R_23))))->((member28618436le_alt ((produc776457805le_alt ((append179082452le_alt Xs_70) Us_2)) ((append179082452le_alt Ys_27) Vs_2))) (listre2064003096le_alt R_23)))).
% Axiom fact_411_Cons__listrel1__Cons:(forall (X_36:list_A2115238852le_alt) (Xs_69:list_l1475218533le_alt) (Y_15:list_A2115238852le_alt) (Ys_26:list_l1475218533le_alt) (R_22:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_36) Xs_69)) ((cons_l635097956le_alt Y_15) Ys_26))) (listre620555643le_alt R_22))) ((or ((and ((member28618436le_alt ((produc776457805le_alt X_36) Y_15)) R_22)) (((eq list_l1475218533le_alt) Xs_69) Ys_26))) ((and (((eq list_A2115238852le_alt) X_36) Y_15)) ((member1732936276le_alt ((produc1317709143le_alt Xs_69) Ys_26)) (listre620555643le_alt R_22)))))).
% Axiom fact_412_Cons__listrel1__Cons:(forall (X_36:arrow_475358991le_alt) (Xs_69:list_A2115238852le_alt) (Y_15:arrow_475358991le_alt) (Ys_26:list_A2115238852le_alt) (R_22:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_36) Xs_69)) ((cons_A228743023le_alt Y_15) Ys_26))) (listre2064003096le_alt R_22))) ((or ((and ((member214075476le_alt ((produc1347929815le_alt X_36) Y_15)) R_22)) (((eq list_A2115238852le_alt) Xs_69) Ys_26))) ((and (((eq arrow_475358991le_alt) X_36) Y_15)) ((member28618436le_alt ((produc776457805le_alt Xs_69) Ys_26)) (listre2064003096le_alt R_22)))))).
% Axiom fact_413_listrel1I1:(forall (Xs_68:list_A2115238852le_alt) (X_35:arrow_475358991le_alt) (Y_14:arrow_475358991le_alt) (R_21:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt X_35) Y_14)) R_21)->((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_35) Xs_68)) ((cons_A228743023le_alt Y_14) Xs_68))) (listre2064003096le_alt R_21)))).
% Axiom fact_414_listrel1I1:(forall (Xs_68:list_l1475218533le_alt) (X_35:list_A2115238852le_alt) (Y_14:list_A2115238852le_alt) (R_21:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_35) Y_14)) R_21)->((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_35) Xs_68)) ((cons_l635097956le_alt Y_14) Xs_68))) (listre620555643le_alt R_21)))).
% Axiom fact_415_listrel1I:(forall (Ys_25:list_A2115238852le_alt) (Xs_67:list_A2115238852le_alt) (Us_1:list_A2115238852le_alt) (Vs_1:list_A2115238852le_alt) (X_34:arrow_475358991le_alt) (Y_13:arrow_475358991le_alt) (R_20:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt X_34) Y_13)) R_20)->((((eq list_A2115238852le_alt) Xs_67) ((append179082452le_alt Us_1) ((cons_A228743023le_alt X_34) Vs_1)))->((((eq list_A2115238852le_alt) Ys_25) ((append179082452le_alt Us_1) ((cons_A228743023le_alt Y_13) Vs_1)))->((member28618436le_alt ((produc776457805le_alt Xs_67) Ys_25)) (listre2064003096le_alt R_20)))))).
% Axiom fact_416_listrel1I:(forall (Ys_25:list_l1475218533le_alt) (Xs_67:list_l1475218533le_alt) (Us_1:list_l1475218533le_alt) (Vs_1:list_l1475218533le_alt) (X_34:list_A2115238852le_alt) (Y_13:list_A2115238852le_alt) (R_20:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_34) Y_13)) R_20)->((((eq list_l1475218533le_alt) Xs_67) ((append1166001599le_alt Us_1) ((cons_l635097956le_alt X_34) Vs_1)))->((((eq list_l1475218533le_alt) Ys_25) ((append1166001599le_alt Us_1) ((cons_l635097956le_alt Y_13) Vs_1)))->((member1732936276le_alt ((produc1317709143le_alt Xs_67) Ys_25)) (listre620555643le_alt R_20)))))).
% Axiom fact_417_listrel1E:(forall (Xs_66:list_l1475218533le_alt) (Ys_24:list_l1475218533le_alt) (R_19:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt Xs_66) Ys_24)) (listre620555643le_alt R_19))->((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt), (((member28618436le_alt ((produc776457805le_alt X_2) Y_1)) R_19)->(forall (Us:list_l1475218533le_alt) (Vs:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_66) ((append1166001599le_alt Us) ((cons_l635097956le_alt X_2) Vs)))->(not (((eq list_l1475218533le_alt) Ys_24) ((append1166001599le_alt Us) ((cons_l635097956le_alt Y_1) Vs))))))))->False))).
% Axiom fact_418_listrel1E:(forall (Xs_66:list_A2115238852le_alt) (Ys_24:list_A2115238852le_alt) (R_19:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_66) Ys_24)) (listre2064003096le_alt R_19))->((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt), (((member214075476le_alt ((produc1347929815le_alt X_2) Y_1)) R_19)->(forall (Us:list_A2115238852le_alt) (Vs:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_66) ((append179082452le_alt Us) ((cons_A228743023le_alt X_2) Vs)))->(not (((eq list_A2115238852le_alt) Ys_24) ((append179082452le_alt Us) ((cons_A228743023le_alt Y_1) Vs))))))))->False))).
% Axiom fact_419_Cons__listrel1E1:(forall (X_33:list_A2115238852le_alt) (Xs_65:list_l1475218533le_alt) (Ys_23:list_l1475218533le_alt) (R_18:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_33) Xs_65)) Ys_23)) (listre620555643le_alt R_18))->((forall (Y_1:list_A2115238852le_alt), ((((eq list_l1475218533le_alt) Ys_23) ((cons_l635097956le_alt Y_1) Xs_65))->(((member28618436le_alt ((produc776457805le_alt X_33) Y_1)) R_18)->False)))->((forall (Zs:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Ys_23) ((cons_l635097956le_alt X_33) Zs))->(((member1732936276le_alt ((produc1317709143le_alt Xs_65) Zs)) (listre620555643le_alt R_18))->False)))->False)))).
% Axiom fact_420_Cons__listrel1E1:(forall (X_33:arrow_475358991le_alt) (Xs_65:list_A2115238852le_alt) (Ys_23:list_A2115238852le_alt) (R_18:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_33) Xs_65)) Ys_23)) (listre2064003096le_alt R_18))->((forall (Y_1:arrow_475358991le_alt), ((((eq list_A2115238852le_alt) Ys_23) ((cons_A228743023le_alt Y_1) Xs_65))->(((member214075476le_alt ((produc1347929815le_alt X_33) Y_1)) R_18)->False)))->((forall (Zs:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Ys_23) ((cons_A228743023le_alt X_33) Zs))->(((member28618436le_alt ((produc776457805le_alt Xs_65) Zs)) (listre2064003096le_alt R_18))->False)))->False)))).
% Axiom fact_421_Cons__listrel1E2:(forall (Xs_64:list_l1475218533le_alt) (Y_12:list_A2115238852le_alt) (Ys_22:list_l1475218533le_alt) (R_17:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt Xs_64) ((cons_l635097956le_alt Y_12) Ys_22))) (listre620555643le_alt R_17))->((forall (X_2:list_A2115238852le_alt), ((((eq list_l1475218533le_alt) Xs_64) ((cons_l635097956le_alt X_2) Ys_22))->(((member28618436le_alt ((produc776457805le_alt X_2) Y_12)) R_17)->False)))->((forall (Zs:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_64) ((cons_l635097956le_alt Y_12) Zs))->(((member1732936276le_alt ((produc1317709143le_alt Zs) Ys_22)) (listre620555643le_alt R_17))->False)))->False)))).
% Axiom fact_422_Cons__listrel1E2:(forall (Xs_64:list_A2115238852le_alt) (Y_12:arrow_475358991le_alt) (Ys_22:list_A2115238852le_alt) (R_17:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_64) ((cons_A228743023le_alt Y_12) Ys_22))) (listre2064003096le_alt R_17))->((forall (X_2:arrow_475358991le_alt), ((((eq list_A2115238852le_alt) Xs_64) ((cons_A228743023le_alt X_2) Ys_22))->(((member214075476le_alt ((produc1347929815le_alt X_2) Y_12)) R_17)->False)))->((forall (Zs:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_64) ((cons_A228743023le_alt Y_12) Zs))->(((member28618436le_alt ((produc776457805le_alt Zs) Ys_22)) (listre2064003096le_alt R_17))->False)))->False)))).
% Axiom fact_423_Cons__in__lex:(forall (X_32:list_A2115238852le_alt) (Xs_63:list_l1475218533le_alt) (Y_11:list_A2115238852le_alt) (Ys_21:list_l1475218533le_alt) (R_16:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_32) Xs_63)) ((cons_l635097956le_alt Y_11) Ys_21))) (lex_li663137712le_alt R_16))) ((or ((and ((member28618436le_alt ((produc776457805le_alt X_32) Y_11)) R_16)) (((eq nat) (size_s1911906171le_alt Xs_63)) (size_s1911906171le_alt Ys_21)))) ((and (((eq list_A2115238852le_alt) X_32) Y_11)) ((member1732936276le_alt ((produc1317709143le_alt Xs_63) Ys_21)) (lex_li663137712le_alt R_16)))))).
% Axiom fact_424_Cons__in__lex:(forall (X_32:arrow_475358991le_alt) (Xs_63:list_A2115238852le_alt) (Y_11:arrow_475358991le_alt) (Ys_21:list_A2115238852le_alt) (R_16:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_32) Xs_63)) ((cons_A228743023le_alt Y_11) Ys_21))) (lex_Ar1415517219le_alt R_16))) ((or ((and ((member214075476le_alt ((produc1347929815le_alt X_32) Y_11)) R_16)) (((eq nat) (size_s1858781230le_alt Xs_63)) (size_s1858781230le_alt Ys_21)))) ((and (((eq arrow_475358991le_alt) X_32) Y_11)) ((member28618436le_alt ((produc776457805le_alt Xs_63) Ys_21)) (lex_Ar1415517219le_alt R_16)))))).
% Axiom fact_425_dropWhile__eq__Cons__conv:(forall (P_19:(arrow_475358991le_alt->Prop)) (Xs_62:list_A2115238852le_alt) (Y_10:arrow_475358991le_alt) (Ys_20:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_19) Xs_62)) ((cons_A228743023le_alt Y_10) Ys_20))) ((and (((eq list_A2115238852le_alt) Xs_62) ((append179082452le_alt ((takeWh1696291512le_alt P_19) Xs_62)) ((cons_A228743023le_alt Y_10) Ys_20)))) ((P_19 Y_10)->False)))).
% Axiom fact_426_partition_Osimps_I2_J:(forall (P_18:(arrow_475358991le_alt->Prop)) (X_31:arrow_475358991le_alt) (Xs_61:list_A2115238852le_alt), (((eq produc1362454231le_alt) ((partit1487577784le_alt P_18) ((cons_A228743023le_alt X_31) Xs_61))) ((produc677212559le_alt (fun (Yes_1:list_A2115238852le_alt) (No_1:list_A2115238852le_alt)=> (((if_Pro314693991le_alt (P_18 X_31)) ((produc776457805le_alt ((cons_A228743023le_alt X_31) Yes_1)) No_1)) ((produc776457805le_alt Yes_1) ((cons_A228743023le_alt X_31) No_1))))) ((partit1487577784le_alt P_18) Xs_61)))).
% Axiom fact_427_dropWhile_Osimps_I2_J:(forall (Xs_60:list_A2115238852le_alt) (P_17:(arrow_475358991le_alt->Prop)) (X_30:arrow_475358991le_alt), ((and ((P_17 X_30)->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_17) ((cons_A228743023le_alt X_30) Xs_60))) ((dropWh1316781920le_alt P_17) Xs_60)))) (((P_17 X_30)->False)->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_17) ((cons_A228743023le_alt X_30) Xs_60))) ((cons_A228743023le_alt X_30) Xs_60))))).
% Axiom fact_428_dropWhile_Osimps_I1_J:(forall (P_16:(arrow_475358991le_alt->Prop)), (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_16) nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt)).
% Axiom fact_429_distinct__dropWhile:(forall (P_15:(arrow_475358991le_alt->Prop)) (Xs_59:list_A2115238852le_alt), ((distin236324274le_alt Xs_59)->(distin236324274le_alt ((dropWh1316781920le_alt P_15) Xs_59)))).
% Axiom fact_430_split__curry:(forall (F_3:(produc1501160679le_alt->Prop)), (((eq (produc1501160679le_alt->Prop)) (produc362454893_alt_o (produc910278158_alt_o F_3))) F_3)).
% Axiom fact_431_curry__split:(forall (F_2:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))), (((eq (arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (produc910278158_alt_o (produc362454893_alt_o F_2))) F_2)).
% Axiom fact_432_listrel1__eq__len:(forall (Xs_58:list_A2115238852le_alt) (Ys_19:list_A2115238852le_alt) (R_15:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_58) Ys_19)) (listre2064003096le_alt R_15))->(((eq nat) (size_s1858781230le_alt Xs_58)) (size_s1858781230le_alt Ys_19)))).
% Axiom fact_433_takeWhile__dropWhile__id:(forall (P_14:(arrow_475358991le_alt->Prop)) (Xs_57:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((takeWh1696291512le_alt P_14) Xs_57)) ((dropWh1316781920le_alt P_14) Xs_57))) Xs_57)).
% Axiom fact_434_lexord__lex:(forall (X_29:list_A2115238852le_alt) (Y_9:list_A2115238852le_alt) (R_14:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt X_29) Y_9)) (lex_Ar1415517219le_alt R_14))) ((and ((member28618436le_alt ((produc776457805le_alt X_29) Y_9)) (lexord958095404le_alt R_14))) (((eq nat) (size_s1858781230le_alt X_29)) (size_s1858781230le_alt Y_9))))).
% Axiom fact_435_lexn__length:(forall (Xs_56:list_A2115238852le_alt) (Ys_18:list_A2115238852le_alt) (R_13:(produc1501160679le_alt->Prop)) (N_8:nat), (((member28618436le_alt ((produc776457805le_alt Xs_56) Ys_18)) ((lexn_A170361439le_alt R_13) N_8))->((and (((eq nat) (size_s1858781230le_alt Xs_56)) N_8)) (((eq nat) (size_s1858781230le_alt Ys_18)) N_8)))).
% Axiom fact_436_splitI:(forall (F_1:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (A_3:list_A2115238852le_alt) (B_3:list_A2115238852le_alt), (((F_1 A_3) B_3)->((produc1948161143_alt_o F_1) ((produc776457805le_alt A_3) B_3)))).
% Axiom fact_437_splitI:(forall (F_1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A_3:arrow_475358991le_alt) (B_3:arrow_475358991le_alt), (((F_1 A_3) B_3)->((produc362454893_alt_o F_1) ((produc1347929815le_alt A_3) B_3)))).
% Axiom fact_438_prod__caseI:(forall (F1:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (A_2:list_A2115238852le_alt) (B_2:list_A2115238852le_alt), (((F1 A_2) B_2)->((produc1948161143_alt_o F1) ((produc776457805le_alt A_2) B_2)))).
% Axiom fact_439_prod__caseI:(forall (F1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A_2:arrow_475358991le_alt) (B_2:arrow_475358991le_alt), (((F1 A_2) B_2)->((produc362454893_alt_o F1) ((produc1347929815le_alt A_2) B_2)))).
% Axiom fact_440_splitD:(forall (F:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (A_1:list_A2115238852le_alt) (B_1:list_A2115238852le_alt), (((produc1948161143_alt_o F) ((produc776457805le_alt A_1) B_1))->((F A_1) B_1))).
% Axiom fact_441_splitD:(forall (F:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A_1:arrow_475358991le_alt) (B_1:arrow_475358991le_alt), (((produc362454893_alt_o F) ((produc1347929815le_alt A_1) B_1))->((F A_1) B_1))).
% Axiom fact_442_splitI2:(forall (C_1:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (P_13:produc1362454231le_alt), ((forall (A:list_A2115238852le_alt) (B:list_A2115238852le_alt), ((((eq produc1362454231le_alt) P_13) ((produc776457805le_alt A) B))->((C_1 A) B)))->((produc1948161143_alt_o C_1) P_13))).
% Axiom fact_443_splitI2:(forall (C_1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (P_13:produc1501160679le_alt), ((forall (A:arrow_475358991le_alt) (B:arrow_475358991le_alt), ((((eq produc1501160679le_alt) P_13) ((produc1347929815le_alt A) B))->((C_1 A) B)))->((produc362454893_alt_o C_1) P_13))).
% Axiom fact_444_splitE:(forall (C:(list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) (P_12:produc1362454231le_alt), (((produc1948161143_alt_o C) P_12)->((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt), ((((eq produc1362454231le_alt) P_12) ((produc776457805le_alt X_2) Y_1))->(((C X_2) Y_1)->False)))->False))).
% Axiom fact_445_splitE:(forall (C:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (P_12:produc1501160679le_alt), (((produc362454893_alt_o C) P_12)->((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt), ((((eq produc1501160679le_alt) P_12) ((produc1347929815le_alt X_2) Y_1))->(((C X_2) Y_1)->False)))->False))).
% Axiom fact_446_not__distinct__decomp:(forall (Ws:list_A2115238852le_alt), (((distin236324274le_alt Ws)->False)->((ex list_A2115238852le_alt) (fun (Xs_21:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Zs:list_A2115238852le_alt)=> ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> (((eq list_A2115238852le_alt) Ws) ((append179082452le_alt Xs_21) ((append179082452le_alt ((cons_A228743023le_alt Y_1) nil_Ar1286194111le_alt)) ((append179082452le_alt Ys) ((append179082452le_alt ((cons_A228743023le_alt Y_1) nil_Ar1286194111le_alt)) Zs))))))))))))))).
% Axiom fact_447_listrel_OCons:(forall (Xs_55:list_A2115238852le_alt) (Ys_17:list_A2115238852le_alt) (X_28:arrow_475358991le_alt) (Y_8:arrow_475358991le_alt) (R_12:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt X_28) Y_8)) R_12)->(((member28618436le_alt ((produc776457805le_alt Xs_55) Ys_17)) (listre1920655591le_alt R_12))->((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt X_28) Xs_55)) ((cons_A228743023le_alt Y_8) Ys_17))) (listre1920655591le_alt R_12))))).
% Axiom fact_448_listrel_OCons:(forall (Xs_55:list_l1475218533le_alt) (Ys_17:list_l1475218533le_alt) (X_28:list_A2115238852le_alt) (Y_8:list_A2115238852le_alt) (R_12:(produc1362454231le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt X_28) Y_8)) R_12)->(((member1732936276le_alt ((produc1317709143le_alt Xs_55) Ys_17)) (listre623166444le_alt R_12))->((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt X_28) Xs_55)) ((cons_l635097956le_alt Y_8) Ys_17))) (listre623166444le_alt R_12))))).
% Axiom fact_449_tl__append:(forall (Xs_54:list_A2115238852le_alt) (Ys_16:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (tl_Arr465451158le_alt ((append179082452le_alt Xs_54) Ys_16))) (((list_c1623890103le_alt (tl_Arr465451158le_alt Ys_16)) (fun (Z:arrow_475358991le_alt) (Zs:list_A2115238852le_alt)=> ((append179082452le_alt Zs) Ys_16))) Xs_54))).
% Axiom fact_450_listrel__Nil2:(forall (Xs_53:list_A2115238852le_alt) (R_11:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_53) nil_Ar1286194111le_alt)) (listre1920655591le_alt R_11))->(((eq list_A2115238852le_alt) Xs_53) nil_Ar1286194111le_alt))).
% Axiom fact_451_listrel__Nil1:(forall (Xs_52:list_A2115238852le_alt) (R_10:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) Xs_52)) (listre1920655591le_alt R_10))->(((eq list_A2115238852le_alt) Xs_52) nil_Ar1286194111le_alt))).
% Axiom fact_452_tl_Osimps_I2_J:(forall (X_27:arrow_475358991le_alt) (Xs_51:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (tl_Arr465451158le_alt ((cons_A228743023le_alt X_27) Xs_51))) Xs_51)).
% Axiom fact_453_tl_Osimps_I1_J:(((eq list_A2115238852le_alt) (tl_Arr465451158le_alt nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt).
% Axiom fact_454_distinct__tl:(forall (Xs_50:list_A2115238852le_alt), ((distin236324274le_alt Xs_50)->(distin236324274le_alt (tl_Arr465451158le_alt Xs_50)))).
% Axiom fact_455_listrel_ONil:(forall (R_9:(produc1501160679le_alt->Prop)), ((member28618436le_alt ((produc776457805le_alt nil_Ar1286194111le_alt) nil_Ar1286194111le_alt)) (listre1920655591le_alt R_9))).
% Axiom fact_456_listrel__eq__len:(forall (Xs_49:list_A2115238852le_alt) (Ys_15:list_A2115238852le_alt) (R_8:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_49) Ys_15)) (listre1920655591le_alt R_8))->(((eq nat) (size_s1858781230le_alt Xs_49)) (size_s1858781230le_alt Ys_15)))).
% Axiom fact_457_tl__append2:(forall (Ys_14:list_A2115238852le_alt) (Xs_48:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_48) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (tl_Arr465451158le_alt ((append179082452le_alt Xs_48) Ys_14))) ((append179082452le_alt (tl_Arr465451158le_alt Xs_48)) Ys_14)))).
% Axiom fact_458_listrel__Cons2:(forall (Xs_47:list_l1475218533le_alt) (Y_7:list_A2115238852le_alt) (Ys_13:list_l1475218533le_alt) (R_7:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt Xs_47) ((cons_l635097956le_alt Y_7) Ys_13))) (listre623166444le_alt R_7))->((forall (X_2:list_A2115238852le_alt) (Xs_21:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_47) ((cons_l635097956le_alt X_2) Xs_21))->(((member28618436le_alt ((produc776457805le_alt X_2) Y_7)) R_7)->(((member1732936276le_alt ((produc1317709143le_alt Xs_21) Ys_13)) (listre623166444le_alt R_7))->False))))->False))).
% Axiom fact_459_listrel__Cons2:(forall (Xs_47:list_A2115238852le_alt) (Y_7:arrow_475358991le_alt) (Ys_13:list_A2115238852le_alt) (R_7:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt Xs_47) ((cons_A228743023le_alt Y_7) Ys_13))) (listre1920655591le_alt R_7))->((forall (X_2:arrow_475358991le_alt) (Xs_21:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_47) ((cons_A228743023le_alt X_2) Xs_21))->(((member214075476le_alt ((produc1347929815le_alt X_2) Y_7)) R_7)->(((member28618436le_alt ((produc776457805le_alt Xs_21) Ys_13)) (listre1920655591le_alt R_7))->False))))->False))).
% Axiom fact_460_listrel__Cons1:(forall (Y_6:list_A2115238852le_alt) (Ys_12:list_l1475218533le_alt) (Xs_46:list_l1475218533le_alt) (R_6:(produc1362454231le_alt->Prop)), (((member1732936276le_alt ((produc1317709143le_alt ((cons_l635097956le_alt Y_6) Ys_12)) Xs_46)) (listre623166444le_alt R_6))->((forall (Y_1:list_A2115238852le_alt) (Ys:list_l1475218533le_alt), ((((eq list_l1475218533le_alt) Xs_46) ((cons_l635097956le_alt Y_1) Ys))->(((member28618436le_alt ((produc776457805le_alt Y_6) Y_1)) R_6)->(((member1732936276le_alt ((produc1317709143le_alt Ys_12) Ys)) (listre623166444le_alt R_6))->False))))->False))).
% Axiom fact_461_listrel__Cons1:(forall (Y_6:arrow_475358991le_alt) (Ys_12:list_A2115238852le_alt) (Xs_46:list_A2115238852le_alt) (R_6:(produc1501160679le_alt->Prop)), (((member28618436le_alt ((produc776457805le_alt ((cons_A228743023le_alt Y_6) Ys_12)) Xs_46)) (listre1920655591le_alt R_6))->((forall (Y_1:arrow_475358991le_alt) (Ys:list_A2115238852le_alt), ((((eq list_A2115238852le_alt) Xs_46) ((cons_A228743023le_alt Y_1) Ys))->(((member214075476le_alt ((produc1347929815le_alt Y_6) Y_1)) R_6)->(((member28618436le_alt ((produc776457805le_alt Ys_12) Ys)) (listre1920655591le_alt R_6))->False))))->False))).
% Axiom fact_462_listrelp__listrel__eq:(forall (R_5:(produc1501160679le_alt->Prop)) (X_2:list_A2115238852le_alt) (Xa:list_A2115238852le_alt), ((iff (((listre1213162009le_alt (fun (Y_1:arrow_475358991le_alt) (Z:arrow_475358991le_alt)=> ((member214075476le_alt ((produc1347929815le_alt Y_1) Z)) R_5))) X_2) Xa)) ((member28618436le_alt ((produc776457805le_alt X_2) Xa)) (listre1920655591le_alt R_5)))).
% Axiom fact_463_listrelp__listrel__eq:(forall (R_5:(produc1362454231le_alt->Prop)) (X_2:list_l1475218533le_alt) (Xa:list_l1475218533le_alt), ((iff (((listre816681018le_alt (fun (Y_1:list_A2115238852le_alt) (Z:list_A2115238852le_alt)=> ((member28618436le_alt ((produc776457805le_alt Y_1) Z)) R_5))) X_2) Xa)) ((member1732936276le_alt ((produc1317709143le_alt X_2) Xa)) (listre623166444le_alt R_5)))).
% Axiom fact_464_rotate1__hd__tl:(forall (Xs_45:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_45) nil_Ar1286194111le_alt))->(((eq list_A2115238852le_alt) (rotate335349260le_alt Xs_45)) ((append179082452le_alt (tl_Arr465451158le_alt Xs_45)) ((cons_A228743023le_alt (hd_Arr1965683346le_alt Xs_45)) nil_Ar1286194111le_alt))))).
% Axiom fact_465_listrel_Osimps:(forall (A1_1:list_l1475218533le_alt) (A2_1:list_l1475218533le_alt) (R_4:(produc1362454231le_alt->Prop)), ((iff ((member1732936276le_alt ((produc1317709143le_alt A1_1) A2_1)) (listre623166444le_alt R_4))) ((or ((and (((eq list_l1475218533le_alt) A1_1) nil_li1907286804le_alt)) (((eq list_l1475218533le_alt) A2_1) nil_li1907286804le_alt))) ((ex list_A2115238852le_alt) (fun (X_2:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Y_1:list_A2115238852le_alt)=> ((ex list_l1475218533le_alt) (fun (Xs_21:list_l1475218533le_alt)=> ((ex list_l1475218533le_alt) (fun (Ys:list_l1475218533le_alt)=> ((and ((and ((and (((eq list_l1475218533le_alt) A1_1) ((cons_l635097956le_alt X_2) Xs_21))) (((eq list_l1475218533le_alt) A2_1) ((cons_l635097956le_alt Y_1) Ys)))) ((member28618436le_alt ((produc776457805le_alt X_2) Y_1)) R_4))) ((member1732936276le_alt ((produc1317709143le_alt Xs_21) Ys)) (listre623166444le_alt R_4)))))))))))))).
% Axiom fact_466_listrel_Osimps:(forall (A1_1:list_A2115238852le_alt) (A2_1:list_A2115238852le_alt) (R_4:(produc1501160679le_alt->Prop)), ((iff ((member28618436le_alt ((produc776457805le_alt A1_1) A2_1)) (listre1920655591le_alt R_4))) ((or ((and (((eq list_A2115238852le_alt) A1_1) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) A2_1) nil_Ar1286194111le_alt))) ((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Xs_21:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> ((and ((and ((and (((eq list_A2115238852le_alt) A1_1) ((cons_A228743023le_alt X_2) Xs_21))) (((eq list_A2115238852le_alt) A2_1) ((cons_A228743023le_alt Y_1) Ys)))) ((member214075476le_alt ((produc1347929815le_alt X_2) Y_1)) R_4))) ((member28618436le_alt ((produc776457805le_alt Xs_21) Ys)) (listre1920655591le_alt R_4)))))))))))))).
% Axiom fact_467_hd_Osimps:(forall (X_26:arrow_475358991le_alt) (Xs_44:list_A2115238852le_alt), (((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((cons_A228743023le_alt X_26) Xs_44))) X_26)).
% Axiom fact_468_listrelp_OCons:(forall (Xs_43:list_A2115238852le_alt) (Ys_11:list_A2115238852le_alt) (R_3:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (X_25:arrow_475358991le_alt) (Y_5:arrow_475358991le_alt), (((R_3 X_25) Y_5)->((((listre1213162009le_alt R_3) Xs_43) Ys_11)->(((listre1213162009le_alt R_3) ((cons_A228743023le_alt X_25) Xs_43)) ((cons_A228743023le_alt Y_5) Ys_11))))).
% Axiom fact_469_listrelp_ONil:(forall (R_2:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))), (((listre1213162009le_alt R_2) nil_Ar1286194111le_alt) nil_Ar1286194111le_alt)).
% Axiom fact_470_hd__append:(forall (Ys_10:list_A2115238852le_alt) (Xs_42:list_A2115238852le_alt), ((and ((((eq list_A2115238852le_alt) Xs_42) nil_Ar1286194111le_alt)->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((append179082452le_alt Xs_42) Ys_10))) (hd_Arr1965683346le_alt Ys_10)))) ((not (((eq list_A2115238852le_alt) Xs_42) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((append179082452le_alt Xs_42) Ys_10))) (hd_Arr1965683346le_alt Xs_42))))).
% Axiom fact_471_hd__append2:(forall (Ys_9:list_A2115238852le_alt) (Xs_41:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_41) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt ((append179082452le_alt Xs_41) Ys_9))) (hd_Arr1965683346le_alt Xs_41)))).
% Axiom fact_472_hd__dropWhile:(forall (P_11:(arrow_475358991le_alt->Prop)) (Xs_40:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_11) Xs_40)) nil_Ar1286194111le_alt))->((P_11 (hd_Arr1965683346le_alt ((dropWh1316781920le_alt P_11) Xs_40)))->False))).
% Axiom fact_473_listrelp_Osimps:(forall (R_1:(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))) (A1:list_A2115238852le_alt) (A2:list_A2115238852le_alt), ((iff (((listre1213162009le_alt R_1) A1) A2)) ((or ((and (((eq list_A2115238852le_alt) A1) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) A2) nil_Ar1286194111le_alt))) ((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((ex arrow_475358991le_alt) (fun (Y_1:arrow_475358991le_alt)=> ((ex list_A2115238852le_alt) (fun (Xs_21:list_A2115238852le_alt)=> ((ex list_A2115238852le_alt) (fun (Ys:list_A2115238852le_alt)=> ((and ((and ((and (((eq list_A2115238852le_alt) A1) ((cons_A228743023le_alt X_2) Xs_21))) (((eq list_A2115238852le_alt) A2) ((cons_A228743023le_alt Y_1) Ys)))) ((R_1 X_2) Y_1))) (((listre1213162009le_alt R_1) Xs_21) Ys))))))))))))).
% Axiom fact_474_equal:(((eq (list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) equal_484611810le_alt) fequal781288069le_alt).
% Axiom fact_475_equal__refl:(forall (X_24:list_A2115238852le_alt), ((equal_484611810le_alt X_24) X_24)).
% Axiom fact_476_equal__eq:(forall (X_23:list_A2115238852le_alt) (Y_4:list_A2115238852le_alt), ((iff ((equal_484611810le_alt X_23) Y_4)) (((eq list_A2115238852le_alt) X_23) Y_4))).
% Axiom fact_477_eq__equal:(((eq (list_A2115238852le_alt->(list_A2115238852le_alt->Prop))) fequal781288069le_alt) equal_484611810le_alt).
% Axiom fact_478_last__rev:(forall (Xs_39:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_39) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (last_A1217315288le_alt (rev_Ar1106406943le_alt Xs_39))) (hd_Arr1965683346le_alt Xs_39)))).
% Axiom fact_479_hd__rev:(forall (Xs_38:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_38) nil_Ar1286194111le_alt))->(((eq arrow_475358991le_alt) (hd_Arr1965683346le_alt (rev_Ar1106406943le_alt Xs_38))) (last_A1217315288le_alt Xs_38)))).
% Axiom fact_480_replicate__append__same:(forall (I_3:nat) (X_22:arrow_475358991le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((replic1511538809le_alt I_3) X_22)) ((cons_A228743023le_alt X_22) nil_Ar1286194111le_alt))) ((cons_A228743023le_alt X_22) ((replic1511538809le_alt I_3) X_22)))).
% Axiom fact_481_dropWhile__eq__drop:(forall (P_10:(arrow_475358991le_alt->Prop)) (Xs_37:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_10) Xs_37)) ((drop_A1346709759le_alt (size_s1858781230le_alt ((takeWh1696291512le_alt P_10) Xs_37))) Xs_37))).
% Axiom fact_482_butlast__drop:(forall (N_7:nat) (Xs_36:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (butlas274947851le_alt ((drop_A1346709759le_alt N_7) Xs_36))) ((drop_A1346709759le_alt N_7) (butlas274947851le_alt Xs_36)))).
% Axiom fact_483_drop__butlast:(forall (N_6:nat) (Xs_35:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((drop_A1346709759le_alt N_6) (butlas274947851le_alt Xs_35))) (butlas274947851le_alt ((drop_A1346709759le_alt N_6) Xs_35)))).
% Axiom fact_484_drop__Nil:(forall (N_5:nat), (((eq list_A2115238852le_alt) ((drop_A1346709759le_alt N_5) nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt)).
% Axiom fact_485_distinct__drop:(forall (I_2:nat) (Xs_34:list_A2115238852le_alt), ((distin236324274le_alt Xs_34)->(distin236324274le_alt ((drop_A1346709759le_alt I_2) Xs_34)))).
% Axiom fact_486_rev__append:(forall (Xs_33:list_A2115238852le_alt) (Ys_8:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt ((append179082452le_alt Xs_33) Ys_8))) ((append179082452le_alt (rev_Ar1106406943le_alt Ys_8)) (rev_Ar1106406943le_alt Xs_33)))).
% Axiom fact_487_rev__is__Nil__conv:(forall (Xs_32:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_32)) nil_Ar1286194111le_alt)) (((eq list_A2115238852le_alt) Xs_32) nil_Ar1286194111le_alt))).
% Axiom fact_488_Nil__is__rev__conv:(forall (Xs_31:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) nil_Ar1286194111le_alt) (rev_Ar1106406943le_alt Xs_31))) (((eq list_A2115238852le_alt) Xs_31) nil_Ar1286194111le_alt))).
% Axiom fact_489_rev_Osimps_I1_J:(((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt nil_Ar1286194111le_alt)) nil_Ar1286194111le_alt).
% Axiom fact_490_append__replicate__commute:(forall (N_4:nat) (X_21:arrow_475358991le_alt) (K_1:nat), (((eq list_A2115238852le_alt) ((append179082452le_alt ((replic1511538809le_alt N_4) X_21)) ((replic1511538809le_alt K_1) X_21))) ((append179082452le_alt ((replic1511538809le_alt K_1) X_21)) ((replic1511538809le_alt N_4) X_21)))).
% Axiom fact_491_distinct__rev:(forall (Xs_30:list_A2115238852le_alt), ((iff (distin236324274le_alt (rev_Ar1106406943le_alt Xs_30))) (distin236324274le_alt Xs_30))).
% Axiom fact_492_rev__singleton__conv:(forall (Xs_29:list_A2115238852le_alt) (X_20:arrow_475358991le_alt), ((iff (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_29)) ((cons_A228743023le_alt X_20) nil_Ar1286194111le_alt))) (((eq list_A2115238852le_alt) Xs_29) ((cons_A228743023le_alt X_20) nil_Ar1286194111le_alt)))).
% Axiom fact_493_singleton__rev__conv:(forall (X_19:arrow_475358991le_alt) (Xs_28:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((cons_A228743023le_alt X_19) nil_Ar1286194111le_alt)) (rev_Ar1106406943le_alt Xs_28))) (((eq list_A2115238852le_alt) Xs_28) ((cons_A228743023le_alt X_19) nil_Ar1286194111le_alt)))).
% Axiom fact_494_replicate__app__Cons__same:(forall (N_3:nat) (X_18:arrow_475358991le_alt) (Xs_27:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((append179082452le_alt ((replic1511538809le_alt N_3) X_18)) ((cons_A228743023le_alt X_18) Xs_27))) ((cons_A228743023le_alt X_18) ((append179082452le_alt ((replic1511538809le_alt N_3) X_18)) Xs_27)))).
% Axiom fact_495_rev_Osimps_I2_J:(forall (X_17:arrow_475358991le_alt) (Xs_26:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt ((cons_A228743023le_alt X_17) Xs_26))) ((append179082452le_alt (rev_Ar1106406943le_alt Xs_26)) ((cons_A228743023le_alt X_17) nil_Ar1286194111le_alt)))).
% Axiom fact_496_rev__eq__Cons__iff:(forall (Xs_25:list_A2115238852le_alt) (Y_3:arrow_475358991le_alt) (Ys_7:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_25)) ((cons_A228743023le_alt Y_3) Ys_7))) (((eq list_A2115238852le_alt) Xs_25) ((append179082452le_alt (rev_Ar1106406943le_alt Ys_7)) ((cons_A228743023le_alt Y_3) nil_Ar1286194111le_alt))))).
% Axiom fact_497_takeWhile__neq__rev:(forall (X_16:arrow_475358991le_alt) (Xs_24:list_A2115238852le_alt), ((distin236324274le_alt Xs_24)->(((member84363362le_alt X_16) (set_Ar577454304le_alt Xs_24))->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_16)))) (rev_Ar1106406943le_alt Xs_24))) (rev_Ar1106406943le_alt (tl_Arr465451158le_alt ((dropWh1316781920le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_16)))) Xs_24))))))).
% Axiom fact_498_takeWhile__neq__rev:(forall (X_16:produc1362454231le_alt) (Xs_24:list_P1295265784le_alt), ((distin561495412le_alt Xs_24)->(((member28618436le_alt X_16) (set_Pr412222150le_alt Xs_24))->(((eq list_P1295265784le_alt) ((takeWh1571807982le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_16)))) (rev_Pr1619606471le_alt Xs_24))) (rev_Pr1619606471le_alt (tl_Pro1448262032le_alt ((dropWh612508742le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_16)))) Xs_24))))))).
% Axiom fact_499_takeWhile__neq__rev:(forall (X_16:arrow_1429601828e_indi) (Xs_24:list_A1484739013e_indi), ((distin1916799041e_indi Xs_24)->(((member2052026769e_indi X_16) (set_Ar778541203e_indi Xs_24))->(((eq list_A1484739013e_indi) ((takeWh831911099e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_16)))) (rev_Ar501922580e_indi Xs_24))) (rev_Ar501922580e_indi (tl_Arr25726557e_indi ((dropWh1160116755e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_16)))) Xs_24))))))).
% Axiom fact_500_takeWhile__neq__rev:(forall (X_16:Prop) (Xs_24:list_o), ((distinct_o Xs_24)->(((member_o X_16) (set_o Xs_24))->(((eq list_o) ((takeWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_16)))) (rev_o Xs_24))) (rev_o (tl_o ((dropWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_16)))) Xs_24))))))).
% Axiom fact_501_takeWhile__neq__rev:(forall (X_16:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_24:list_A518015091_alt_o), ((distin1908010863_alt_o Xs_24)->(((member616898751_alt_o X_16) (set_Ar1356274881_alt_o Xs_24))->(((eq list_A518015091_alt_o) ((takeWh877796585_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_16)))) (rev_Ar5548482_alt_o Xs_24))) (rev_Ar5548482_alt_o (tl_Arr2017860491_alt_o ((dropWh583351873_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_16)))) Xs_24))))))).
% Axiom fact_502_takeWhile__neq__rev:(forall (X_16:(produc1501160679le_alt->Prop)) (Xs_24:list_P1178103901_alt_o), ((distin1582710603_alt_o Xs_24)->(((member377231867_alt_o X_16) (set_Pr592386425_alt_o Xs_24))->(((eq list_P1178103901_alt_o) ((takeWh1715715921_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_16)))) (rev_Pr1006783032_alt_o Xs_24))) (rev_Pr1006783032_alt_o (tl_Pro1735316527_alt_o ((dropWh1049991161_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_16)))) Xs_24))))))).
% Axiom fact_503_takeWhile__neq__rev:(forall (X_16:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_24:list_A524553945_alt_o), ((distin1869760583_alt_o Xs_24)->(((member526088951_alt_o X_16) (set_Ar571341173_alt_o Xs_24))->(((eq list_A524553945_alt_o) ((takeWh1825606477_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_16)))) (rev_Ar413755828_alt_o Xs_24))) (rev_Ar413755828_alt_o (tl_Arr1704054571_alt_o ((dropWh73644021_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_16)))) Xs_24))))))).
% Axiom fact_504_takeWhile__neq__rev:(forall (X_16:produc1501160679le_alt) (Xs_24:list_P736798472le_alt), ((distin1776819972le_alt Xs_24)->(((member214075476le_alt X_16) (set_Pr1525059414le_alt Xs_24))->(((eq list_P736798472le_alt) ((takeWh302148478le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_16)))) (rev_Pr1216324055le_alt Xs_24))) (rev_Pr1216324055le_alt (tl_Pro932635936le_alt ((dropWh680325334le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_16)))) Xs_24))))))).
% Axiom fact_505_dropWhile__neq__rev:(forall (X_15:arrow_475358991le_alt) (Xs_23:list_A2115238852le_alt), ((distin236324274le_alt Xs_23)->(((member84363362le_alt X_15) (set_Ar577454304le_alt Xs_23))->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_15)))) (rev_Ar1106406943le_alt Xs_23))) ((cons_A228743023le_alt X_15) (rev_Ar1106406943le_alt ((takeWh1696291512le_alt (fun (Y_1:arrow_475358991le_alt)=> (not (((eq arrow_475358991le_alt) Y_1) X_15)))) Xs_23))))))).
% Axiom fact_506_dropWhile__neq__rev:(forall (X_15:produc1362454231le_alt) (Xs_23:list_P1295265784le_alt), ((distin561495412le_alt Xs_23)->(((member28618436le_alt X_15) (set_Pr412222150le_alt Xs_23))->(((eq list_P1295265784le_alt) ((dropWh612508742le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_15)))) (rev_Pr1619606471le_alt Xs_23))) ((cons_P2048401015le_alt X_15) (rev_Pr1619606471le_alt ((takeWh1571807982le_alt (fun (Y_1:produc1362454231le_alt)=> (not (((eq produc1362454231le_alt) Y_1) X_15)))) Xs_23))))))).
% Axiom fact_507_dropWhile__neq__rev:(forall (X_15:arrow_1429601828e_indi) (Xs_23:list_A1484739013e_indi), ((distin1916799041e_indi Xs_23)->(((member2052026769e_indi X_15) (set_Ar778541203e_indi Xs_23))->(((eq list_A1484739013e_indi) ((dropWh1160116755e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_15)))) (rev_Ar501922580e_indi Xs_23))) ((cons_A663037380e_indi X_15) (rev_Ar501922580e_indi ((takeWh831911099e_indi (fun (Y_1:arrow_1429601828e_indi)=> (not (((eq arrow_1429601828e_indi) Y_1) X_15)))) Xs_23))))))).
% Axiom fact_508_dropWhile__neq__rev:(forall (X_15:Prop) (Xs_23:list_o), ((distinct_o Xs_23)->(((member_o X_15) (set_o Xs_23))->(((eq list_o) ((dropWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_15)))) (rev_o Xs_23))) ((cons_o X_15) (rev_o ((takeWhile_o (fun (Y_1:Prop)=> (not (((eq Prop) Y_1) X_15)))) Xs_23))))))).
% Axiom fact_509_dropWhile__neq__rev:(forall (X_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_23:list_A518015091_alt_o), ((distin1908010863_alt_o Xs_23)->(((member616898751_alt_o X_15) (set_Ar1356274881_alt_o Xs_23))->(((eq list_A518015091_alt_o) ((dropWh583351873_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_15)))) (rev_Ar5548482_alt_o Xs_23))) ((cons_A279268466_alt_o X_15) (rev_Ar5548482_alt_o ((takeWh877796585_alt_o (fun (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_1) X_15)))) Xs_23))))))).
% Axiom fact_510_dropWhile__neq__rev:(forall (X_15:(produc1501160679le_alt->Prop)) (Xs_23:list_P1178103901_alt_o), ((distin1582710603_alt_o Xs_23)->(((member377231867_alt_o X_15) (set_Pr592386425_alt_o Xs_23))->(((eq list_P1178103901_alt_o) ((dropWh1049991161_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_15)))) (rev_Pr1006783032_alt_o Xs_23))) ((cons_P1239653256_alt_o X_15) (rev_Pr1006783032_alt_o ((takeWh1715715921_alt_o (fun (Y_1:(produc1501160679le_alt->Prop))=> (not (((eq (produc1501160679le_alt->Prop)) Y_1) X_15)))) Xs_23))))))).
% Axiom fact_511_dropWhile__neq__rev:(forall (X_15:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_23:list_A524553945_alt_o), ((distin1869760583_alt_o Xs_23)->(((member526088951_alt_o X_15) (set_Ar571341173_alt_o Xs_23))->(((eq list_A524553945_alt_o) ((dropWh73644021_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_15)))) (rev_Ar413755828_alt_o Xs_23))) ((cons_A2010997508_alt_o X_15) (rev_Ar413755828_alt_o ((takeWh1825606477_alt_o (fun (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> (not (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_1) X_15)))) Xs_23))))))).
% Axiom fact_512_dropWhile__neq__rev:(forall (X_15:produc1501160679le_alt) (Xs_23:list_P736798472le_alt), ((distin1776819972le_alt Xs_23)->(((member214075476le_alt X_15) (set_Pr1525059414le_alt Xs_23))->(((eq list_P736798472le_alt) ((dropWh680325334le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_15)))) (rev_Pr1216324055le_alt Xs_23))) ((cons_P1913588871le_alt X_15) (rev_Pr1216324055le_alt ((takeWh302148478le_alt (fun (Y_1:produc1501160679le_alt)=> (not (((eq produc1501160679le_alt) Y_1) X_15)))) Xs_23))))))).
% Axiom fact_513_drop__Cons:(forall (N_2:nat) (X_14:arrow_475358991le_alt) (Xs_22:list_A2115238852le_alt), (((eq list_A2115238852le_alt) ((drop_A1346709759le_alt N_2) ((cons_A228743023le_alt X_14) Xs_22))) (((nat_ca2147365008le_alt ((cons_A228743023le_alt X_14) Xs_22)) (fun (M_1:nat)=> ((drop_A1346709759le_alt M_1) Xs_22))) N_2))).
% Axiom fact_514_rev__foldl__cons:(forall (Xs_20:list_A2115238852le_alt), (((eq list_A2115238852le_alt) (rev_Ar1106406943le_alt Xs_20)) (((foldl_296410428le_alt (fun (Xs_21:list_A2115238852le_alt) (X_2:arrow_475358991le_alt)=> ((cons_A228743023le_alt X_2) Xs_21))) nil_Ar1286194111le_alt) Xs_20))).
% Axiom fact_515_in__set__dropD:(forall (X_13:arrow_475358991le_alt) (N_1:nat) (Xs_19:list_A2115238852le_alt), (((member84363362le_alt X_13) (set_Ar577454304le_alt ((drop_A1346709759le_alt N_1) Xs_19)))->((member84363362le_alt X_13) (set_Ar577454304le_alt Xs_19)))).
% Axiom fact_516_in__set__dropD:(forall (X_13:produc1362454231le_alt) (N_1:nat) (Xs_19:list_P1295265784le_alt), (((member28618436le_alt X_13) (set_Pr412222150le_alt ((drop_P1438419175le_alt N_1) Xs_19)))->((member28618436le_alt X_13) (set_Pr412222150le_alt Xs_19)))).
% Axiom fact_517_in__set__dropD:(forall (X_13:arrow_1429601828e_indi) (N_1:nat) (Xs_19:list_A1484739013e_indi), (((member2052026769e_indi X_13) (set_Ar778541203e_indi ((drop_A1596373044e_indi N_1) Xs_19)))->((member2052026769e_indi X_13) (set_Ar778541203e_indi Xs_19)))).
% Axiom fact_518_in__set__dropD:(forall (X_13:Prop) (N_1:nat) (Xs_19:list_o), (((member_o X_13) (set_o ((drop_o N_1) Xs_19)))->((member_o X_13) (set_o Xs_19)))).
% Axiom fact_519_in__set__dropD:(forall (X_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (N_1:nat) (Xs_19:list_A518015091_alt_o), (((member616898751_alt_o X_13) (set_Ar1356274881_alt_o ((drop_A1326872290_alt_o N_1) Xs_19)))->((member616898751_alt_o X_13) (set_Ar1356274881_alt_o Xs_19)))).
% Axiom fact_520_in__set__dropD:(forall (X_13:(produc1501160679le_alt->Prop)) (N_1:nat) (Xs_19:list_P1178103901_alt_o), (((member377231867_alt_o X_13) (set_Pr592386425_alt_o ((drop_P619902232_alt_o N_1) Xs_19)))->((member377231867_alt_o X_13) (set_Pr592386425_alt_o Xs_19)))).
% Axiom fact_521_in__set__dropD:(forall (X_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (N_1:nat) (Xs_19:list_A524553945_alt_o), (((member526088951_alt_o X_13) (set_Ar571341173_alt_o ((drop_A776701076_alt_o N_1) Xs_19)))->((member526088951_alt_o X_13) (set_Ar571341173_alt_o Xs_19)))).
% Axiom fact_522_in__set__dropD:(forall (X_13:produc1501160679le_alt) (N_1:nat) (Xs_19:list_P736798472le_alt), (((member214075476le_alt X_13) (set_Pr1525059414le_alt ((drop_P933863159le_alt N_1) Xs_19)))->((member214075476le_alt X_13) (set_Pr1525059414le_alt Xs_19)))).
% Axiom fact_523_set__takeWhileD:(forall (X_12:arrow_475358991le_alt) (P_9:(arrow_475358991le_alt->Prop)) (Xs_18:list_A2115238852le_alt), (((member84363362le_alt X_12) (set_Ar577454304le_alt ((takeWh1696291512le_alt P_9) Xs_18)))->((and ((member84363362le_alt X_12) (set_Ar577454304le_alt Xs_18))) (P_9 X_12)))).
% Axiom fact_524_set__takeWhileD:(forall (X_12:produc1362454231le_alt) (P_9:(produc1362454231le_alt->Prop)) (Xs_18:list_P1295265784le_alt), (((member28618436le_alt X_12) (set_Pr412222150le_alt ((takeWh1571807982le_alt P_9) Xs_18)))->((and ((member28618436le_alt X_12) (set_Pr412222150le_alt Xs_18))) (P_9 X_12)))).
% Axiom fact_525_set__takeWhileD:(forall (X_12:arrow_1429601828e_indi) (P_9:(arrow_1429601828e_indi->Prop)) (Xs_18:list_A1484739013e_indi), (((member2052026769e_indi X_12) (set_Ar778541203e_indi ((takeWh831911099e_indi P_9) Xs_18)))->((and ((member2052026769e_indi X_12) (set_Ar778541203e_indi Xs_18))) (P_9 X_12)))).
% Axiom fact_526_set__takeWhileD:(forall (X_12:Prop) (P_9:(Prop->Prop)) (Xs_18:list_o), (((member_o X_12) (set_o ((takeWhile_o P_9) Xs_18)))->((and ((member_o X_12) (set_o Xs_18))) (P_9 X_12)))).
% Axiom fact_527_set__takeWhileD:(forall (X_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (P_9:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (Xs_18:list_A518015091_alt_o), (((member616898751_alt_o X_12) (set_Ar1356274881_alt_o ((takeWh877796585_alt_o P_9) Xs_18)))->((and ((member616898751_alt_o X_12) (set_Ar1356274881_alt_o Xs_18))) (P_9 X_12)))).
% Axiom fact_528_set__takeWhileD:(forall (X_12:(produc1501160679le_alt->Prop)) (P_9:((produc1501160679le_alt->Prop)->Prop)) (Xs_18:list_P1178103901_alt_o), (((member377231867_alt_o X_12) (set_Pr592386425_alt_o ((takeWh1715715921_alt_o P_9) Xs_18)))->((and ((member377231867_alt_o X_12) (set_Pr592386425_alt_o Xs_18))) (P_9 X_12)))).
% Axiom fact_529_set__takeWhileD:(forall (X_12:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (Xs_18:list_A524553945_alt_o), (((member526088951_alt_o X_12) (set_Ar571341173_alt_o ((takeWh1825606477_alt_o P_9) Xs_18)))->((and ((member526088951_alt_o X_12) (set_Ar571341173_alt_o Xs_18))) (P_9 X_12)))).
% Axiom fact_530_set__takeWhileD:(forall (X_12:produc1501160679le_alt) (P_9:(produc1501160679le_alt->Prop)) (Xs_18:list_P736798472le_alt), (((member214075476le_alt X_12) (set_Pr1525059414le_alt ((takeWh302148478le_alt P_9) Xs_18)))->((and ((member214075476le_alt X_12) (set_Pr1525059414le_alt Xs_18))) (P_9 X_12)))).
% Axiom fact_531_takeWhile__eq__all__conv:(forall (P_8:(arrow_475358991le_alt->Prop)) (Xs_17:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_8) Xs_17)) Xs_17)) (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_17))->(P_8 X_2))))).
% Axiom fact_532_in__set__butlastD:(forall (X_11:arrow_475358991le_alt) (Xs_16:list_A2115238852le_alt), (((member84363362le_alt X_11) (set_Ar577454304le_alt (butlas274947851le_alt Xs_16)))->((member84363362le_alt X_11) (set_Ar577454304le_alt Xs_16)))).
% Axiom fact_533_in__set__butlastD:(forall (X_11:produc1362454231le_alt) (Xs_16:list_P1295265784le_alt), (((member28618436le_alt X_11) (set_Pr412222150le_alt (butlas464406491le_alt Xs_16)))->((member28618436le_alt X_11) (set_Pr412222150le_alt Xs_16)))).
% Axiom fact_534_in__set__butlastD:(forall (X_11:arrow_1429601828e_indi) (Xs_16:list_A1484739013e_indi), (((member2052026769e_indi X_11) (set_Ar778541203e_indi (butlas1554122024e_indi Xs_16)))->((member2052026769e_indi X_11) (set_Ar778541203e_indi Xs_16)))).
% Axiom fact_535_in__set__butlastD:(forall (X_11:Prop) (Xs_16:list_o), (((member_o X_11) (set_o (butlast_o Xs_16)))->((member_o X_11) (set_o Xs_16)))).
% Axiom fact_536_in__set__butlastD:(forall (X_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_16:list_A518015091_alt_o), (((member616898751_alt_o X_11) (set_Ar1356274881_alt_o (butlas1138247126_alt_o Xs_16)))->((member616898751_alt_o X_11) (set_Ar1356274881_alt_o Xs_16)))).
% Axiom fact_537_in__set__butlastD:(forall (X_11:(produc1501160679le_alt->Prop)) (Xs_16:list_P1178103901_alt_o), (((member377231867_alt_o X_11) (set_Pr592386425_alt_o (butlas368541988_alt_o Xs_16)))->((member377231867_alt_o X_11) (set_Pr592386425_alt_o Xs_16)))).
% Axiom fact_538_in__set__butlastD:(forall (X_11:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_16:list_A524553945_alt_o), (((member526088951_alt_o X_11) (set_Ar571341173_alt_o (butlas813143712_alt_o Xs_16)))->((member526088951_alt_o X_11) (set_Ar571341173_alt_o Xs_16)))).
% Axiom fact_539_in__set__butlastD:(forall (X_11:produc1501160679le_alt) (Xs_16:list_P736798472le_alt), (((member214075476le_alt X_11) (set_Pr1525059414le_alt (butlas661498859le_alt Xs_16)))->((member214075476le_alt X_11) (set_Pr1525059414le_alt Xs_16)))).
% Axiom fact_540_set__ConsD:(forall (Y_2:arrow_475358991le_alt) (X_10:arrow_475358991le_alt) (Xs_15:list_A2115238852le_alt), (((member84363362le_alt Y_2) (set_Ar577454304le_alt ((cons_A228743023le_alt X_10) Xs_15)))->((or (((eq arrow_475358991le_alt) Y_2) X_10)) ((member84363362le_alt Y_2) (set_Ar577454304le_alt Xs_15))))).
% Axiom fact_541_set__ConsD:(forall (Y_2:produc1362454231le_alt) (X_10:produc1362454231le_alt) (Xs_15:list_P1295265784le_alt), (((member28618436le_alt Y_2) (set_Pr412222150le_alt ((cons_P2048401015le_alt X_10) Xs_15)))->((or (((eq produc1362454231le_alt) Y_2) X_10)) ((member28618436le_alt Y_2) (set_Pr412222150le_alt Xs_15))))).
% Axiom fact_542_set__ConsD:(forall (Y_2:arrow_1429601828e_indi) (X_10:arrow_1429601828e_indi) (Xs_15:list_A1484739013e_indi), (((member2052026769e_indi Y_2) (set_Ar778541203e_indi ((cons_A663037380e_indi X_10) Xs_15)))->((or (((eq arrow_1429601828e_indi) Y_2) X_10)) ((member2052026769e_indi Y_2) (set_Ar778541203e_indi Xs_15))))).
% Axiom fact_543_set__ConsD:(forall (Y_2:Prop) (X_10:Prop) (Xs_15:list_o), (((member_o Y_2) (set_o ((cons_o X_10) Xs_15)))->((or ((iff Y_2) X_10)) ((member_o Y_2) (set_o Xs_15))))).
% Axiom fact_544_set__ConsD:(forall (Y_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (X_10:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_15:list_A518015091_alt_o), (((member616898751_alt_o Y_2) (set_Ar1356274881_alt_o ((cons_A279268466_alt_o X_10) Xs_15)))->((or (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) Y_2) X_10)) ((member616898751_alt_o Y_2) (set_Ar1356274881_alt_o Xs_15))))).
% Axiom fact_545_set__ConsD:(forall (Y_2:(produc1501160679le_alt->Prop)) (X_10:(produc1501160679le_alt->Prop)) (Xs_15:list_P1178103901_alt_o), (((member377231867_alt_o Y_2) (set_Pr592386425_alt_o ((cons_P1239653256_alt_o X_10) Xs_15)))->((or (((eq (produc1501160679le_alt->Prop)) Y_2) X_10)) ((member377231867_alt_o Y_2) (set_Pr592386425_alt_o Xs_15))))).
% Axiom fact_546_set__ConsD:(forall (Y_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (X_10:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_15:list_A524553945_alt_o), (((member526088951_alt_o Y_2) (set_Ar571341173_alt_o ((cons_A2010997508_alt_o X_10) Xs_15)))->((or (((eq (arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) Y_2) X_10)) ((member526088951_alt_o Y_2) (set_Ar571341173_alt_o Xs_15))))).
% Axiom fact_547_set__ConsD:(forall (Y_2:produc1501160679le_alt) (X_10:produc1501160679le_alt) (Xs_15:list_P736798472le_alt), (((member214075476le_alt Y_2) (set_Pr1525059414le_alt ((cons_P1913588871le_alt X_10) Xs_15)))->((or (((eq produc1501160679le_alt) Y_2) X_10)) ((member214075476le_alt Y_2) (set_Pr1525059414le_alt Xs_15))))).
% Axiom fact_548_in__set__insert:(forall (X_9:arrow_475358991le_alt) (Xs_14:list_A2115238852le_alt), (((member84363362le_alt X_9) (set_Ar577454304le_alt Xs_14))->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_9) Xs_14)) Xs_14))).
% Axiom fact_549_in__set__insert:(forall (X_9:produc1362454231le_alt) (Xs_14:list_P1295265784le_alt), (((member28618436le_alt X_9) (set_Pr412222150le_alt Xs_14))->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_9) Xs_14)) Xs_14))).
% Axiom fact_550_in__set__insert:(forall (X_9:arrow_1429601828e_indi) (Xs_14:list_A1484739013e_indi), (((member2052026769e_indi X_9) (set_Ar778541203e_indi Xs_14))->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_9) Xs_14)) Xs_14))).
% Axiom fact_551_in__set__insert:(forall (X_9:Prop) (Xs_14:list_o), (((member_o X_9) (set_o Xs_14))->(((eq list_o) ((insert_o X_9) Xs_14)) Xs_14))).
% Axiom fact_552_in__set__insert:(forall (X_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_14:list_A518015091_alt_o), (((member616898751_alt_o X_9) (set_Ar1356274881_alt_o Xs_14))->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_9) Xs_14)) Xs_14))).
% Axiom fact_553_in__set__insert:(forall (X_9:(produc1501160679le_alt->Prop)) (Xs_14:list_P1178103901_alt_o), (((member377231867_alt_o X_9) (set_Pr592386425_alt_o Xs_14))->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_9) Xs_14)) Xs_14))).
% Axiom fact_554_in__set__insert:(forall (X_9:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_14:list_A524553945_alt_o), (((member526088951_alt_o X_9) (set_Ar571341173_alt_o Xs_14))->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_9) Xs_14)) Xs_14))).
% Axiom fact_555_in__set__insert:(forall (X_9:produc1501160679le_alt) (Xs_14:list_P736798472le_alt), (((member214075476le_alt X_9) (set_Pr1525059414le_alt Xs_14))->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_9) Xs_14)) Xs_14))).
% Axiom fact_556_distinct_Osimps_I2_J:(forall (X_8:arrow_475358991le_alt) (Xs_13:list_A2115238852le_alt), ((iff (distin236324274le_alt ((cons_A228743023le_alt X_8) Xs_13))) ((and (((member84363362le_alt X_8) (set_Ar577454304le_alt Xs_13))->False)) (distin236324274le_alt Xs_13)))).
% Axiom fact_557_distinct_Osimps_I2_J:(forall (X_8:produc1362454231le_alt) (Xs_13:list_P1295265784le_alt), ((iff (distin561495412le_alt ((cons_P2048401015le_alt X_8) Xs_13))) ((and (((member28618436le_alt X_8) (set_Pr412222150le_alt Xs_13))->False)) (distin561495412le_alt Xs_13)))).
% Axiom fact_558_distinct_Osimps_I2_J:(forall (X_8:arrow_1429601828e_indi) (Xs_13:list_A1484739013e_indi), ((iff (distin1916799041e_indi ((cons_A663037380e_indi X_8) Xs_13))) ((and (((member2052026769e_indi X_8) (set_Ar778541203e_indi Xs_13))->False)) (distin1916799041e_indi Xs_13)))).
% Axiom fact_559_distinct_Osimps_I2_J:(forall (X_8:Prop) (Xs_13:list_o), ((iff (distinct_o ((cons_o X_8) Xs_13))) ((and (((member_o X_8) (set_o Xs_13))->False)) (distinct_o Xs_13)))).
% Axiom fact_560_distinct_Osimps_I2_J:(forall (X_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_13:list_A518015091_alt_o), ((iff (distin1908010863_alt_o ((cons_A279268466_alt_o X_8) Xs_13))) ((and (((member616898751_alt_o X_8) (set_Ar1356274881_alt_o Xs_13))->False)) (distin1908010863_alt_o Xs_13)))).
% Axiom fact_561_distinct_Osimps_I2_J:(forall (X_8:(produc1501160679le_alt->Prop)) (Xs_13:list_P1178103901_alt_o), ((iff (distin1582710603_alt_o ((cons_P1239653256_alt_o X_8) Xs_13))) ((and (((member377231867_alt_o X_8) (set_Pr592386425_alt_o Xs_13))->False)) (distin1582710603_alt_o Xs_13)))).
% Axiom fact_562_distinct_Osimps_I2_J:(forall (X_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_13:list_A524553945_alt_o), ((iff (distin1869760583_alt_o ((cons_A2010997508_alt_o X_8) Xs_13))) ((and (((member526088951_alt_o X_8) (set_Ar571341173_alt_o Xs_13))->False)) (distin1869760583_alt_o Xs_13)))).
% Axiom fact_563_distinct_Osimps_I2_J:(forall (X_8:produc1501160679le_alt) (Xs_13:list_P736798472le_alt), ((iff (distin1776819972le_alt ((cons_P1913588871le_alt X_8) Xs_13))) ((and (((member214075476le_alt X_8) (set_Pr1525059414le_alt Xs_13))->False)) (distin1776819972le_alt Xs_13)))).
% Axiom fact_564_takeWhile__append1:(forall (Ys_6:list_A2115238852le_alt) (P_7:(arrow_475358991le_alt->Prop)) (X_7:arrow_475358991le_alt) (Xs_12:list_A2115238852le_alt), (((member84363362le_alt X_7) (set_Ar577454304le_alt Xs_12))->(((P_7 X_7)->False)->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_7) ((append179082452le_alt Xs_12) Ys_6))) ((takeWh1696291512le_alt P_7) Xs_12))))).
% Axiom fact_565_takeWhile__append1:(forall (Ys_6:list_P1295265784le_alt) (P_7:(produc1362454231le_alt->Prop)) (X_7:produc1362454231le_alt) (Xs_12:list_P1295265784le_alt), (((member28618436le_alt X_7) (set_Pr412222150le_alt Xs_12))->(((P_7 X_7)->False)->(((eq list_P1295265784le_alt) ((takeWh1571807982le_alt P_7) ((append423770578le_alt Xs_12) Ys_6))) ((takeWh1571807982le_alt P_7) Xs_12))))).
% Axiom fact_566_takeWhile__append1:(forall (Ys_6:list_A1484739013e_indi) (P_7:(arrow_1429601828e_indi->Prop)) (X_7:arrow_1429601828e_indi) (Xs_12:list_A1484739013e_indi), (((member2052026769e_indi X_7) (set_Ar778541203e_indi Xs_12))->(((P_7 X_7)->False)->(((eq list_A1484739013e_indi) ((takeWh831911099e_indi P_7) ((append711934367e_indi Xs_12) Ys_6))) ((takeWh831911099e_indi P_7) Xs_12))))).
% Axiom fact_567_takeWhile__append1:(forall (Ys_6:list_o) (P_7:(Prop->Prop)) (X_7:Prop) (Xs_12:list_o), (((member_o X_7) (set_o Xs_12))->(((P_7 X_7)->False)->(((eq list_o) ((takeWhile_o P_7) ((append_o Xs_12) Ys_6))) ((takeWhile_o P_7) Xs_12))))).
% Axiom fact_568_takeWhile__append1:(forall (Ys_6:list_A518015091_alt_o) (P_7:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (X_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_12:list_A518015091_alt_o), (((member616898751_alt_o X_7) (set_Ar1356274881_alt_o Xs_12))->(((P_7 X_7)->False)->(((eq list_A518015091_alt_o) ((takeWh877796585_alt_o P_7) ((append326058957_alt_o Xs_12) Ys_6))) ((takeWh877796585_alt_o P_7) Xs_12))))).
% Axiom fact_569_takeWhile__append1:(forall (Ys_6:list_P1178103901_alt_o) (P_7:((produc1501160679le_alt->Prop)->Prop)) (X_7:(produc1501160679le_alt->Prop)) (Xs_12:list_P1178103901_alt_o), (((member377231867_alt_o X_7) (set_Pr592386425_alt_o Xs_12))->(((P_7 X_7)->False)->(((eq list_P1178103901_alt_o) ((takeWh1715715921_alt_o P_7) ((append612833133_alt_o Xs_12) Ys_6))) ((takeWh1715715921_alt_o P_7) Xs_12))))).
% Axiom fact_570_takeWhile__append1:(forall (Ys_6:list_A524553945_alt_o) (P_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (X_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_12:list_A524553945_alt_o), (((member526088951_alt_o X_7) (set_Ar571341173_alt_o Xs_12))->(((P_7 X_7)->False)->(((eq list_A524553945_alt_o) ((takeWh1825606477_alt_o P_7) ((append295924073_alt_o Xs_12) Ys_6))) ((takeWh1825606477_alt_o P_7) Xs_12))))).
% Axiom fact_571_takeWhile__append1:(forall (Ys_6:list_P736798472le_alt) (P_7:(produc1501160679le_alt->Prop)) (X_7:produc1501160679le_alt) (Xs_12:list_P736798472le_alt), (((member214075476le_alt X_7) (set_Pr1525059414le_alt Xs_12))->(((P_7 X_7)->False)->(((eq list_P736798472le_alt) ((takeWh302148478le_alt P_7) ((append1229289570le_alt Xs_12) Ys_6))) ((takeWh302148478le_alt P_7) Xs_12))))).
% Axiom fact_572_last__in__set:(forall (As:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) As) nil_Ar1286194111le_alt))->((member84363362le_alt (last_A1217315288le_alt As)) (set_Ar577454304le_alt As)))).
% Axiom fact_573_last__in__set:(forall (As:list_P1295265784le_alt), ((not (((eq list_P1295265784le_alt) As) nil_Pr365739559le_alt))->((member28618436le_alt (last_P1879176142le_alt As)) (set_Pr412222150le_alt As)))).
% Axiom fact_574_last__in__set:(forall (As:list_A1484739013e_indi), ((not (((eq list_A1484739013e_indi) As) nil_Ar380161396e_indi))->((member2052026769e_indi (last_A303846811e_indi As)) (set_Ar778541203e_indi As)))).
% Axiom fact_575_last__in__set:(forall (As:list_o), ((not (((eq list_o) As) nil_o))->((member_o (last_o As)) (set_o As)))).
% Axiom fact_576_last__in__set:(forall (As:list_A518015091_alt_o), ((not (((eq list_A518015091_alt_o) As) nil_Ar253733922_alt_o))->((member616898751_alt_o (last_A1273867721_alt_o As)) (set_Ar1356274881_alt_o As)))).
% Axiom fact_577_last__in__set:(forall (As:list_P1178103901_alt_o), ((not (((eq list_P1178103901_alt_o) As) nil_Pr28438488_alt_o))->((member377231867_alt_o (last_P685913713_alt_o As)) (set_Pr592386425_alt_o As)))).
% Axiom fact_578_last__in__set:(forall (As:list_A524553945_alt_o), ((not (((eq list_A524553945_alt_o) As) nil_Ar1876942676_alt_o))->((member526088951_alt_o (last_A1049530989_alt_o As)) (set_Ar571341173_alt_o As)))).
% Axiom fact_579_last__in__set:(forall (As:list_P736798472le_alt), ((not (((eq list_P736798472le_alt) As) nil_Pr861385783le_alt))->((member214075476le_alt (last_P1656409182le_alt As)) (set_Pr1525059414le_alt As)))).
% Axiom fact_580_dropWhile__eq__Nil__conv:(forall (P_6:(arrow_475358991le_alt->Prop)) (Xs_11:list_A2115238852le_alt), ((iff (((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_6) Xs_11)) nil_Ar1286194111le_alt)) (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_11))->(P_6 X_2))))).
% Axiom fact_581_in__set__butlast__appendI:(forall (Ys_5:list_A2115238852le_alt) (X_6:arrow_475358991le_alt) (Xs_10:list_A2115238852le_alt), (((or ((member84363362le_alt X_6) (set_Ar577454304le_alt (butlas274947851le_alt Xs_10)))) ((member84363362le_alt X_6) (set_Ar577454304le_alt (butlas274947851le_alt Ys_5))))->((member84363362le_alt X_6) (set_Ar577454304le_alt (butlas274947851le_alt ((append179082452le_alt Xs_10) Ys_5)))))).
% Axiom fact_582_in__set__butlast__appendI:(forall (Ys_5:list_P1295265784le_alt) (X_6:produc1362454231le_alt) (Xs_10:list_P1295265784le_alt), (((or ((member28618436le_alt X_6) (set_Pr412222150le_alt (butlas464406491le_alt Xs_10)))) ((member28618436le_alt X_6) (set_Pr412222150le_alt (butlas464406491le_alt Ys_5))))->((member28618436le_alt X_6) (set_Pr412222150le_alt (butlas464406491le_alt ((append423770578le_alt Xs_10) Ys_5)))))).
% Axiom fact_583_in__set__butlast__appendI:(forall (Ys_5:list_A1484739013e_indi) (X_6:arrow_1429601828e_indi) (Xs_10:list_A1484739013e_indi), (((or ((member2052026769e_indi X_6) (set_Ar778541203e_indi (butlas1554122024e_indi Xs_10)))) ((member2052026769e_indi X_6) (set_Ar778541203e_indi (butlas1554122024e_indi Ys_5))))->((member2052026769e_indi X_6) (set_Ar778541203e_indi (butlas1554122024e_indi ((append711934367e_indi Xs_10) Ys_5)))))).
% Axiom fact_584_in__set__butlast__appendI:(forall (Ys_5:list_o) (X_6:Prop) (Xs_10:list_o), (((or ((member_o X_6) (set_o (butlast_o Xs_10)))) ((member_o X_6) (set_o (butlast_o Ys_5))))->((member_o X_6) (set_o (butlast_o ((append_o Xs_10) Ys_5)))))).
% Axiom fact_585_in__set__butlast__appendI:(forall (Ys_5:list_A518015091_alt_o) (X_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_10:list_A518015091_alt_o), (((or ((member616898751_alt_o X_6) (set_Ar1356274881_alt_o (butlas1138247126_alt_o Xs_10)))) ((member616898751_alt_o X_6) (set_Ar1356274881_alt_o (butlas1138247126_alt_o Ys_5))))->((member616898751_alt_o X_6) (set_Ar1356274881_alt_o (butlas1138247126_alt_o ((append326058957_alt_o Xs_10) Ys_5)))))).
% Axiom fact_586_in__set__butlast__appendI:(forall (Ys_5:list_P1178103901_alt_o) (X_6:(produc1501160679le_alt->Prop)) (Xs_10:list_P1178103901_alt_o), (((or ((member377231867_alt_o X_6) (set_Pr592386425_alt_o (butlas368541988_alt_o Xs_10)))) ((member377231867_alt_o X_6) (set_Pr592386425_alt_o (butlas368541988_alt_o Ys_5))))->((member377231867_alt_o X_6) (set_Pr592386425_alt_o (butlas368541988_alt_o ((append612833133_alt_o Xs_10) Ys_5)))))).
% Axiom fact_587_in__set__butlast__appendI:(forall (Ys_5:list_A524553945_alt_o) (X_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_10:list_A524553945_alt_o), (((or ((member526088951_alt_o X_6) (set_Ar571341173_alt_o (butlas813143712_alt_o Xs_10)))) ((member526088951_alt_o X_6) (set_Ar571341173_alt_o (butlas813143712_alt_o Ys_5))))->((member526088951_alt_o X_6) (set_Ar571341173_alt_o (butlas813143712_alt_o ((append295924073_alt_o Xs_10) Ys_5)))))).
% Axiom fact_588_in__set__butlast__appendI:(forall (Ys_5:list_P736798472le_alt) (X_6:produc1501160679le_alt) (Xs_10:list_P736798472le_alt), (((or ((member214075476le_alt X_6) (set_Pr1525059414le_alt (butlas661498859le_alt Xs_10)))) ((member214075476le_alt X_6) (set_Pr1525059414le_alt (butlas661498859le_alt Ys_5))))->((member214075476le_alt X_6) (set_Pr1525059414le_alt (butlas661498859le_alt ((append1229289570le_alt Xs_10) Ys_5)))))).
% Axiom fact_589_hd__in__set:(forall (Xs_9:list_A2115238852le_alt), ((not (((eq list_A2115238852le_alt) Xs_9) nil_Ar1286194111le_alt))->((member84363362le_alt (hd_Arr1965683346le_alt Xs_9)) (set_Ar577454304le_alt Xs_9)))).
% Axiom fact_590_hd__in__set:(forall (Xs_9:list_P1295265784le_alt), ((not (((eq list_P1295265784le_alt) Xs_9) nil_Pr365739559le_alt))->((member28618436le_alt (hd_Pro856774804le_alt Xs_9)) (set_Pr412222150le_alt Xs_9)))).
% Axiom fact_591_hd__in__set:(forall (Xs_9:list_A1484739013e_indi), ((not (((eq list_A1484739013e_indi) Xs_9) nil_Ar380161396e_indi))->((member2052026769e_indi (hd_Arr1023890273e_indi Xs_9)) (set_Ar778541203e_indi Xs_9)))).
% Axiom fact_592_hd__in__set:(forall (Xs_9:list_o), ((not (((eq list_o) Xs_9) nil_o))->((member_o (hd_o Xs_9)) (set_o Xs_9)))).
% Axiom fact_593_hd__in__set:(forall (Xs_9:list_A518015091_alt_o), ((not (((eq list_A518015091_alt_o) Xs_9) nil_Ar253733922_alt_o))->((member616898751_alt_o (hd_Arr1786382991_alt_o Xs_9)) (set_Ar1356274881_alt_o Xs_9)))).
% Axiom fact_594_hd__in__set:(forall (Xs_9:list_P1178103901_alt_o), ((not (((eq list_P1178103901_alt_o) Xs_9) nil_Pr28438488_alt_o))->((member377231867_alt_o (hd_Pro622402603_alt_o Xs_9)) (set_Pr592386425_alt_o Xs_9)))).
% Axiom fact_595_hd__in__set:(forall (Xs_9:list_A524553945_alt_o), ((not (((eq list_A524553945_alt_o) Xs_9) nil_Ar1876942676_alt_o))->((member526088951_alt_o (hd_Arr574592295_alt_o Xs_9)) (set_Ar571341173_alt_o Xs_9)))).
% Axiom fact_596_hd__in__set:(forall (Xs_9:list_P736798472le_alt), ((not (((eq list_P736798472le_alt) Xs_9) nil_Pr861385783le_alt))->((member214075476le_alt (hd_Pro297626148le_alt Xs_9)) (set_Pr1525059414le_alt Xs_9)))).
% Axiom fact_597_dropWhile__append1:(forall (Ys_4:list_A2115238852le_alt) (P_5:(arrow_475358991le_alt->Prop)) (X_5:arrow_475358991le_alt) (Xs_8:list_A2115238852le_alt), (((member84363362le_alt X_5) (set_Ar577454304le_alt Xs_8))->(((P_5 X_5)->False)->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_5) ((append179082452le_alt Xs_8) Ys_4))) ((append179082452le_alt ((dropWh1316781920le_alt P_5) Xs_8)) Ys_4))))).
% Axiom fact_598_dropWhile__append1:(forall (Ys_4:list_P1295265784le_alt) (P_5:(produc1362454231le_alt->Prop)) (X_5:produc1362454231le_alt) (Xs_8:list_P1295265784le_alt), (((member28618436le_alt X_5) (set_Pr412222150le_alt Xs_8))->(((P_5 X_5)->False)->(((eq list_P1295265784le_alt) ((dropWh612508742le_alt P_5) ((append423770578le_alt Xs_8) Ys_4))) ((append423770578le_alt ((dropWh612508742le_alt P_5) Xs_8)) Ys_4))))).
% Axiom fact_599_dropWhile__append1:(forall (Ys_4:list_A1484739013e_indi) (P_5:(arrow_1429601828e_indi->Prop)) (X_5:arrow_1429601828e_indi) (Xs_8:list_A1484739013e_indi), (((member2052026769e_indi X_5) (set_Ar778541203e_indi Xs_8))->(((P_5 X_5)->False)->(((eq list_A1484739013e_indi) ((dropWh1160116755e_indi P_5) ((append711934367e_indi Xs_8) Ys_4))) ((append711934367e_indi ((dropWh1160116755e_indi P_5) Xs_8)) Ys_4))))).
% Axiom fact_600_dropWhile__append1:(forall (Ys_4:list_o) (P_5:(Prop->Prop)) (X_5:Prop) (Xs_8:list_o), (((member_o X_5) (set_o Xs_8))->(((P_5 X_5)->False)->(((eq list_o) ((dropWhile_o P_5) ((append_o Xs_8) Ys_4))) ((append_o ((dropWhile_o P_5) Xs_8)) Ys_4))))).
% Axiom fact_601_dropWhile__append1:(forall (Ys_4:list_A518015091_alt_o) (P_5:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (X_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_8:list_A518015091_alt_o), (((member616898751_alt_o X_5) (set_Ar1356274881_alt_o Xs_8))->(((P_5 X_5)->False)->(((eq list_A518015091_alt_o) ((dropWh583351873_alt_o P_5) ((append326058957_alt_o Xs_8) Ys_4))) ((append326058957_alt_o ((dropWh583351873_alt_o P_5) Xs_8)) Ys_4))))).
% Axiom fact_602_dropWhile__append1:(forall (Ys_4:list_P1178103901_alt_o) (P_5:((produc1501160679le_alt->Prop)->Prop)) (X_5:(produc1501160679le_alt->Prop)) (Xs_8:list_P1178103901_alt_o), (((member377231867_alt_o X_5) (set_Pr592386425_alt_o Xs_8))->(((P_5 X_5)->False)->(((eq list_P1178103901_alt_o) ((dropWh1049991161_alt_o P_5) ((append612833133_alt_o Xs_8) Ys_4))) ((append612833133_alt_o ((dropWh1049991161_alt_o P_5) Xs_8)) Ys_4))))).
% Axiom fact_603_dropWhile__append1:(forall (Ys_4:list_A524553945_alt_o) (P_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (X_5:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_8:list_A524553945_alt_o), (((member526088951_alt_o X_5) (set_Ar571341173_alt_o Xs_8))->(((P_5 X_5)->False)->(((eq list_A524553945_alt_o) ((dropWh73644021_alt_o P_5) ((append295924073_alt_o Xs_8) Ys_4))) ((append295924073_alt_o ((dropWh73644021_alt_o P_5) Xs_8)) Ys_4))))).
% Axiom fact_604_dropWhile__append1:(forall (Ys_4:list_P736798472le_alt) (P_5:(produc1501160679le_alt->Prop)) (X_5:produc1501160679le_alt) (Xs_8:list_P736798472le_alt), (((member214075476le_alt X_5) (set_Pr1525059414le_alt Xs_8))->(((P_5 X_5)->False)->(((eq list_P736798472le_alt) ((dropWh680325334le_alt P_5) ((append1229289570le_alt Xs_8) Ys_4))) ((append1229289570le_alt ((dropWh680325334le_alt P_5) Xs_8)) Ys_4))))).
% Axiom fact_605_List_Oinsert__def:(forall (X_4:arrow_475358991le_alt) (Xs_7:list_A2115238852le_alt), ((and (((member84363362le_alt X_4) (set_Ar577454304le_alt Xs_7))->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_4) Xs_7)) Xs_7))) ((((member84363362le_alt X_4) (set_Ar577454304le_alt Xs_7))->False)->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_4) Xs_7)) ((cons_A228743023le_alt X_4) Xs_7))))).
% Axiom fact_606_List_Oinsert__def:(forall (X_4:produc1362454231le_alt) (Xs_7:list_P1295265784le_alt), ((and (((member28618436le_alt X_4) (set_Pr412222150le_alt Xs_7))->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_4) Xs_7)) Xs_7))) ((((member28618436le_alt X_4) (set_Pr412222150le_alt Xs_7))->False)->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_4) Xs_7)) ((cons_P2048401015le_alt X_4) Xs_7))))).
% Axiom fact_607_List_Oinsert__def:(forall (X_4:arrow_1429601828e_indi) (Xs_7:list_A1484739013e_indi), ((and (((member2052026769e_indi X_4) (set_Ar778541203e_indi Xs_7))->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_4) Xs_7)) Xs_7))) ((((member2052026769e_indi X_4) (set_Ar778541203e_indi Xs_7))->False)->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_4) Xs_7)) ((cons_A663037380e_indi X_4) Xs_7))))).
% Axiom fact_608_List_Oinsert__def:(forall (X_4:Prop) (Xs_7:list_o), ((and (((member_o X_4) (set_o Xs_7))->(((eq list_o) ((insert_o X_4) Xs_7)) Xs_7))) ((((member_o X_4) (set_o Xs_7))->False)->(((eq list_o) ((insert_o X_4) Xs_7)) ((cons_o X_4) Xs_7))))).
% Axiom fact_609_List_Oinsert__def:(forall (X_4:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_7:list_A518015091_alt_o), ((and (((member616898751_alt_o X_4) (set_Ar1356274881_alt_o Xs_7))->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_4) Xs_7)) Xs_7))) ((((member616898751_alt_o X_4) (set_Ar1356274881_alt_o Xs_7))->False)->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_4) Xs_7)) ((cons_A279268466_alt_o X_4) Xs_7))))).
% Axiom fact_610_List_Oinsert__def:(forall (X_4:(produc1501160679le_alt->Prop)) (Xs_7:list_P1178103901_alt_o), ((and (((member377231867_alt_o X_4) (set_Pr592386425_alt_o Xs_7))->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_4) Xs_7)) Xs_7))) ((((member377231867_alt_o X_4) (set_Pr592386425_alt_o Xs_7))->False)->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_4) Xs_7)) ((cons_P1239653256_alt_o X_4) Xs_7))))).
% Axiom fact_611_List_Oinsert__def:(forall (X_4:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_7:list_A524553945_alt_o), ((and (((member526088951_alt_o X_4) (set_Ar571341173_alt_o Xs_7))->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_4) Xs_7)) Xs_7))) ((((member526088951_alt_o X_4) (set_Ar571341173_alt_o Xs_7))->False)->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_4) Xs_7)) ((cons_A2010997508_alt_o X_4) Xs_7))))).
% Axiom fact_612_List_Oinsert__def:(forall (X_4:produc1501160679le_alt) (Xs_7:list_P736798472le_alt), ((and (((member214075476le_alt X_4) (set_Pr1525059414le_alt Xs_7))->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_4) Xs_7)) Xs_7))) ((((member214075476le_alt X_4) (set_Pr1525059414le_alt Xs_7))->False)->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_4) Xs_7)) ((cons_P1913588871le_alt X_4) Xs_7))))).
% Axiom fact_613_not__in__set__insert:(forall (X_3:arrow_475358991le_alt) (Xs_6:list_A2115238852le_alt), ((((member84363362le_alt X_3) (set_Ar577454304le_alt Xs_6))->False)->(((eq list_A2115238852le_alt) ((insert2120566741le_alt X_3) Xs_6)) ((cons_A228743023le_alt X_3) Xs_6)))).
% Axiom fact_614_not__in__set__insert:(forall (X_3:produc1362454231le_alt) (Xs_6:list_P1295265784le_alt), ((((member28618436le_alt X_3) (set_Pr412222150le_alt Xs_6))->False)->(((eq list_P1295265784le_alt) ((insert1334153361le_alt X_3) Xs_6)) ((cons_P2048401015le_alt X_3) Xs_6)))).
% Axiom fact_615_not__in__set__insert:(forall (X_3:arrow_1429601828e_indi) (Xs_6:list_A1484739013e_indi), ((((member2052026769e_indi X_3) (set_Ar778541203e_indi Xs_6))->False)->(((eq list_A1484739013e_indi) ((insert1474580190e_indi X_3) Xs_6)) ((cons_A663037380e_indi X_3) Xs_6)))).
% Axiom fact_616_not__in__set__insert:(forall (X_3:Prop) (Xs_6:list_o), ((((member_o X_3) (set_o Xs_6))->False)->(((eq list_o) ((insert_o X_3) Xs_6)) ((cons_o X_3) Xs_6)))).
% Axiom fact_617_not__in__set__insert:(forall (X_3:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Xs_6:list_A518015091_alt_o), ((((member616898751_alt_o X_3) (set_Ar1356274881_alt_o Xs_6))->False)->(((eq list_A518015091_alt_o) ((insert81217164_alt_o X_3) Xs_6)) ((cons_A279268466_alt_o X_3) Xs_6)))).
% Axiom fact_618_not__in__set__insert:(forall (X_3:(produc1501160679le_alt->Prop)) (Xs_6:list_P1178103901_alt_o), ((((member377231867_alt_o X_3) (set_Pr592386425_alt_o Xs_6))->False)->(((eq list_P1178103901_alt_o) ((insert451602158_alt_o X_3) Xs_6)) ((cons_P1239653256_alt_o X_3) Xs_6)))).
% Axiom fact_619_not__in__set__insert:(forall (X_3:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs_6:list_A524553945_alt_o), ((((member526088951_alt_o X_3) (set_Ar571341173_alt_o Xs_6))->False)->(((eq list_A524553945_alt_o) ((insert128393578_alt_o X_3) Xs_6)) ((cons_A2010997508_alt_o X_3) Xs_6)))).
% Axiom fact_620_not__in__set__insert:(forall (X_3:produc1501160679le_alt) (Xs_6:list_P736798472le_alt), ((((member214075476le_alt X_3) (set_Pr1525059414le_alt Xs_6))->False)->(((eq list_P736798472le_alt) ((insert1177064865le_alt X_3) Xs_6)) ((cons_P1913588871le_alt X_3) Xs_6)))).
% Axiom fact_621_partition__P:(forall (P_4:(arrow_475358991le_alt->Prop)) (Xs_5:list_A2115238852le_alt) (Yes:list_A2115238852le_alt) (No:list_A2115238852le_alt), ((((eq produc1362454231le_alt) ((partit1487577784le_alt P_4) Xs_5)) ((produc776457805le_alt Yes) No))->((and (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Yes))->(P_4 X_2)))) (forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt No))->((P_4 X_2)->False)))))).
% Axiom fact_622_lexord__partial__trans:(forall (Zs_1:list_A2115238852le_alt) (Ys_3:list_A2115238852le_alt) (R:(produc1501160679le_alt->Prop)) (Xs_4:list_A2115238852le_alt), ((forall (X_2:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt) (Z:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_4))->(((member214075476le_alt ((produc1347929815le_alt X_2) Y_1)) R)->(((member214075476le_alt ((produc1347929815le_alt Y_1) Z)) R)->((member214075476le_alt ((produc1347929815le_alt X_2) Z)) R)))))->(((member28618436le_alt ((produc776457805le_alt Xs_4) Ys_3)) (lexord958095404le_alt R))->(((member28618436le_alt ((produc776457805le_alt Ys_3) Zs_1)) (lexord958095404le_alt R))->((member28618436le_alt ((produc776457805le_alt Xs_4) Zs_1)) (lexord958095404le_alt R)))))).
% Axiom fact_623_lexord__partial__trans:(forall (Zs_1:list_l1475218533le_alt) (Ys_3:list_l1475218533le_alt) (R:(produc1362454231le_alt->Prop)) (Xs_4:list_l1475218533le_alt), ((forall (X_2:list_A2115238852le_alt) (Y_1:list_A2115238852le_alt) (Z:list_A2115238852le_alt), (((member998134961le_alt X_2) (set_li1631982259le_alt Xs_4))->(((member28618436le_alt ((produc776457805le_alt X_2) Y_1)) R)->(((member28618436le_alt ((produc776457805le_alt Y_1) Z)) R)->((member28618436le_alt ((produc776457805le_alt X_2) Z)) R)))))->(((member1732936276le_alt ((produc1317709143le_alt Xs_4) Ys_3)) (lexord469916775le_alt R))->(((member1732936276le_alt ((produc1317709143le_alt Ys_3) Zs_1)) (lexord469916775le_alt R))->((member1732936276le_alt ((produc1317709143le_alt Xs_4) Zs_1)) (lexord469916775le_alt R)))))).
% Axiom fact_624_lexord__partial__trans:(forall (Zs_1:list_P1295265784le_alt) (Ys_3:list_P1295265784le_alt) (R:(produc1787997437le_alt->Prop)) (Xs_4:list_P1295265784le_alt), ((forall (X_2:produc1362454231le_alt) (Y_1:produc1362454231le_alt) (Z:produc1362454231le_alt), (((member28618436le_alt X_2) (set_Pr412222150le_alt Xs_4))->(((member902484714le_alt ((produc1443807987le_alt X_2) Y_1)) R)->(((member902484714le_alt ((produc1443807987le_alt Y_1) Z)) R)->((member902484714le_alt ((produc1443807987le_alt X_2) Z)) R)))))->(((member608607380le_alt ((produc1065979415le_alt Xs_4) Ys_3)) (lexord973342842le_alt R))->(((member608607380le_alt ((produc1065979415le_alt Ys_3) Zs_1)) (lexord973342842le_alt R))->((member608607380le_alt ((produc1065979415le_alt Xs_4) Zs_1)) (lexord973342842le_alt R)))))).
% Axiom fact_625_lexord__partial__trans:(forall (Zs_1:list_A1484739013e_indi) (Ys_3:list_A1484739013e_indi) (R:(produc1091721111e_indi->Prop)) (Xs_4:list_A1484739013e_indi), ((forall (X_2:arrow_1429601828e_indi) (Y_1:arrow_1429601828e_indi) (Z:arrow_1429601828e_indi), (((member2052026769e_indi X_2) (set_Ar778541203e_indi Xs_4))->(((member1239815300e_indi ((produc1851452045e_indi X_2) Y_1)) R)->(((member1239815300e_indi ((produc1851452045e_indi Y_1) Z)) R)->((member1239815300e_indi ((produc1851452045e_indi X_2) Z)) R)))))->(((member1618636500e_indi ((produc1195920727e_indi Xs_4) Ys_3)) (lexord1661684807e_indi R))->(((member1618636500e_indi ((produc1195920727e_indi Ys_3) Zs_1)) (lexord1661684807e_indi R))->((member1618636500e_indi ((produc1195920727e_indi Xs_4) Zs_1)) (lexord1661684807e_indi R)))))).
% Axiom fact_626_lexord__partial__trans:(forall (Zs_1:list_o) (Ys_3:list_o) (R:(product_prod_o_o->Prop)) (Xs_4:list_o), ((forall (X_2:Prop) (Y_1:Prop) (Z:Prop), (((member_o X_2) (set_o Xs_4))->(((member1392690260od_o_o ((product_Pair_o_o X_2) Y_1)) R)->(((member1392690260od_o_o ((product_Pair_o_o Y_1) Z)) R)->((member1392690260od_o_o ((product_Pair_o_o X_2) Z)) R)))))->(((member806300420list_o ((produc1835210381list_o Xs_4) Ys_3)) (lexord_o R))->(((member806300420list_o ((produc1835210381list_o Ys_3) Zs_1)) (lexord_o R))->((member806300420list_o ((produc1835210381list_o Xs_4) Zs_1)) (lexord_o R)))))).
% Axiom fact_627_lexord__partial__trans:(forall (Zs_1:list_A518015091_alt_o) (Ys_3:list_A518015091_alt_o) (R:(produc344885491_alt_o->Prop)) (Xs_4:list_A518015091_alt_o), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Y_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (Z:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) (set_Ar1356274881_alt_o Xs_4))->(((member1909339872_alt_o ((produc434968681_alt_o X_2) Y_1)) R)->(((member1909339872_alt_o ((produc434968681_alt_o Y_1) Z)) R)->((member1909339872_alt_o ((produc434968681_alt_o X_2) Z)) R)))))->(((member119836116_alt_o ((produc385333463_alt_o Xs_4) Ys_3)) (lexord1104163445_alt_o R))->(((member119836116_alt_o ((produc385333463_alt_o Ys_3) Zs_1)) (lexord1104163445_alt_o R))->((member119836116_alt_o ((produc385333463_alt_o Xs_4) Zs_1)) (lexord1104163445_alt_o R)))))).
% Axiom fact_628_lexord__partial__trans:(forall (Zs_1:list_P1178103901_alt_o) (Ys_3:list_P1178103901_alt_o) (R:(produc603869735_alt_o->Prop)) (Xs_4:list_P1178103901_alt_o), ((forall (X_2:(produc1501160679le_alt->Prop)) (Y_1:(produc1501160679le_alt->Prop)) (Z:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) (set_Pr592386425_alt_o Xs_4))->(((member1998617236_alt_o ((produc548346135_alt_o X_2) Y_1)) R)->(((member1998617236_alt_o ((produc548346135_alt_o Y_1) Z)) R)->((member1998617236_alt_o ((produc548346135_alt_o X_2) Z)) R)))))->(((member79660662_alt_o ((produc127168767_alt_o Xs_4) Ys_3)) (lexord842870469_alt_o R))->(((member79660662_alt_o ((produc127168767_alt_o Ys_3) Zs_1)) (lexord842870469_alt_o R))->((member79660662_alt_o ((produc127168767_alt_o Xs_4) Zs_1)) (lexord842870469_alt_o R)))))).
% Axiom fact_629_lexord__partial__trans:(forall (Zs_1:list_A524553945_alt_o) (Ys_3:list_A524553945_alt_o) (R:(produc634020647_alt_o->Prop)) (Xs_4:list_A524553945_alt_o), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Y_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Z:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) (set_Ar571341173_alt_o Xs_4))->(((member423327892_alt_o ((produc425112727_alt_o X_2) Y_1)) R)->(((member423327892_alt_o ((produc425112727_alt_o Y_1) Z)) R)->((member423327892_alt_o ((produc425112727_alt_o X_2) Z)) R)))))->(((member1890873582_alt_o ((produc1301429239_alt_o Xs_4) Ys_3)) (lexord1645229249_alt_o R))->(((member1890873582_alt_o ((produc1301429239_alt_o Ys_3) Zs_1)) (lexord1645229249_alt_o R))->((member1890873582_alt_o ((produc1301429239_alt_o Xs_4) Zs_1)) (lexord1645229249_alt_o R)))))).
% Axiom fact_630_lexord__partial__trans:(forall (Zs_1:list_P736798472le_alt) (Ys_3:list_P736798472le_alt) (R:(produc1076844957le_alt->Prop)) (Xs_4:list_P736798472le_alt), ((forall (X_2:produc1501160679le_alt) (Y_1:produc1501160679le_alt) (Z:produc1501160679le_alt), (((member214075476le_alt X_2) (set_Pr1525059414le_alt Xs_4))->(((member1664185994le_alt ((produc1348021779le_alt X_2) Y_1)) R)->(((member1664185994le_alt ((produc1348021779le_alt Y_1) Z)) R)->((member1664185994le_alt ((produc1348021779le_alt X_2) Z)) R)))))->(((member475755924le_alt ((produc1573901719le_alt Xs_4) Ys_3)) (lexord501678858le_alt R))->(((member475755924le_alt ((produc1573901719le_alt Ys_3) Zs_1)) (lexord501678858le_alt R))->((member475755924le_alt ((produc1573901719le_alt Xs_4) Zs_1)) (lexord501678858le_alt R)))))).
% Axiom fact_631_dropWhile__append2:(forall (Ys_2:list_A2115238852le_alt) (P_3:(arrow_475358991le_alt->Prop)) (Xs_3:list_A2115238852le_alt), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_3))->(P_3 X_2)))->(((eq list_A2115238852le_alt) ((dropWh1316781920le_alt P_3) ((append179082452le_alt Xs_3) Ys_2))) ((dropWh1316781920le_alt P_3) Ys_2)))).
% Axiom fact_632_dropWhile__append2:(forall (Ys_2:list_P1295265784le_alt) (P_3:(produc1362454231le_alt->Prop)) (Xs_3:list_P1295265784le_alt), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) (set_Pr412222150le_alt Xs_3))->(P_3 X_2)))->(((eq list_P1295265784le_alt) ((dropWh612508742le_alt P_3) ((append423770578le_alt Xs_3) Ys_2))) ((dropWh612508742le_alt P_3) Ys_2)))).
% Axiom fact_633_dropWhile__append2:(forall (Ys_2:list_A1484739013e_indi) (P_3:(arrow_1429601828e_indi->Prop)) (Xs_3:list_A1484739013e_indi), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) (set_Ar778541203e_indi Xs_3))->(P_3 X_2)))->(((eq list_A1484739013e_indi) ((dropWh1160116755e_indi P_3) ((append711934367e_indi Xs_3) Ys_2))) ((dropWh1160116755e_indi P_3) Ys_2)))).
% Axiom fact_634_dropWhile__append2:(forall (Ys_2:list_o) (P_3:(Prop->Prop)) (Xs_3:list_o), ((forall (X_2:Prop), (((member_o X_2) (set_o Xs_3))->(P_3 X_2)))->(((eq list_o) ((dropWhile_o P_3) ((append_o Xs_3) Ys_2))) ((dropWhile_o P_3) Ys_2)))).
% Axiom fact_635_dropWhile__append2:(forall (Ys_2:list_A518015091_alt_o) (P_3:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (Xs_3:list_A518015091_alt_o), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) (set_Ar1356274881_alt_o Xs_3))->(P_3 X_2)))->(((eq list_A518015091_alt_o) ((dropWh583351873_alt_o P_3) ((append326058957_alt_o Xs_3) Ys_2))) ((dropWh583351873_alt_o P_3) Ys_2)))).
% Axiom fact_636_dropWhile__append2:(forall (Ys_2:list_P1178103901_alt_o) (P_3:((produc1501160679le_alt->Prop)->Prop)) (Xs_3:list_P1178103901_alt_o), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) (set_Pr592386425_alt_o Xs_3))->(P_3 X_2)))->(((eq list_P1178103901_alt_o) ((dropWh1049991161_alt_o P_3) ((append612833133_alt_o Xs_3) Ys_2))) ((dropWh1049991161_alt_o P_3) Ys_2)))).
% Axiom fact_637_dropWhile__append2:(forall (Ys_2:list_A524553945_alt_o) (P_3:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (Xs_3:list_A524553945_alt_o), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) (set_Ar571341173_alt_o Xs_3))->(P_3 X_2)))->(((eq list_A524553945_alt_o) ((dropWh73644021_alt_o P_3) ((append295924073_alt_o Xs_3) Ys_2))) ((dropWh73644021_alt_o P_3) Ys_2)))).
% Axiom fact_638_dropWhile__append2:(forall (Ys_2:list_P736798472le_alt) (P_3:(produc1501160679le_alt->Prop)) (Xs_3:list_P736798472le_alt), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) (set_Pr1525059414le_alt Xs_3))->(P_3 X_2)))->(((eq list_P736798472le_alt) ((dropWh680325334le_alt P_3) ((append1229289570le_alt Xs_3) Ys_2))) ((dropWh680325334le_alt P_3) Ys_2)))).
% Axiom fact_639_takeWhile__append2:(forall (Ys_1:list_A2115238852le_alt) (P_2:(arrow_475358991le_alt->Prop)) (Xs_2:list_A2115238852le_alt), ((forall (X_2:arrow_475358991le_alt), (((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_2))->(P_2 X_2)))->(((eq list_A2115238852le_alt) ((takeWh1696291512le_alt P_2) ((append179082452le_alt Xs_2) Ys_1))) ((append179082452le_alt Xs_2) ((takeWh1696291512le_alt P_2) Ys_1))))).
% Axiom fact_640_takeWhile__append2:(forall (Ys_1:list_P1295265784le_alt) (P_2:(produc1362454231le_alt->Prop)) (Xs_2:list_P1295265784le_alt), ((forall (X_2:produc1362454231le_alt), (((member28618436le_alt X_2) (set_Pr412222150le_alt Xs_2))->(P_2 X_2)))->(((eq list_P1295265784le_alt) ((takeWh1571807982le_alt P_2) ((append423770578le_alt Xs_2) Ys_1))) ((append423770578le_alt Xs_2) ((takeWh1571807982le_alt P_2) Ys_1))))).
% Axiom fact_641_takeWhile__append2:(forall (Ys_1:list_A1484739013e_indi) (P_2:(arrow_1429601828e_indi->Prop)) (Xs_2:list_A1484739013e_indi), ((forall (X_2:arrow_1429601828e_indi), (((member2052026769e_indi X_2) (set_Ar778541203e_indi Xs_2))->(P_2 X_2)))->(((eq list_A1484739013e_indi) ((takeWh831911099e_indi P_2) ((append711934367e_indi Xs_2) Ys_1))) ((append711934367e_indi Xs_2) ((takeWh831911099e_indi P_2) Ys_1))))).
% Axiom fact_642_takeWhile__append2:(forall (Ys_1:list_o) (P_2:(Prop->Prop)) (Xs_2:list_o), ((forall (X_2:Prop), (((member_o X_2) (set_o Xs_2))->(P_2 X_2)))->(((eq list_o) ((takeWhile_o P_2) ((append_o Xs_2) Ys_1))) ((append_o Xs_2) ((takeWhile_o P_2) Ys_1))))).
% Axiom fact_643_takeWhile__append2:(forall (Ys_1:list_A518015091_alt_o) (P_2:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (Xs_2:list_A518015091_alt_o), ((forall (X_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_2) (set_Ar1356274881_alt_o Xs_2))->(P_2 X_2)))->(((eq list_A518015091_alt_o) ((takeWh877796585_alt_o P_2) ((append326058957_alt_o Xs_2) Ys_1))) ((append326058957_alt_o Xs_2) ((takeWh877796585_alt_o P_2) Ys_1))))).
% Axiom fact_644_takeWhile__append2:(forall (Ys_1:list_P1178103901_alt_o) (P_2:((produc1501160679le_alt->Prop)->Prop)) (Xs_2:list_P1178103901_alt_o), ((forall (X_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_2) (set_Pr592386425_alt_o Xs_2))->(P_2 X_2)))->(((eq list_P1178103901_alt_o) ((takeWh1715715921_alt_o P_2) ((append612833133_alt_o Xs_2) Ys_1))) ((append612833133_alt_o Xs_2) ((takeWh1715715921_alt_o P_2) Ys_1))))).
% Axiom fact_645_takeWhile__append2:(forall (Ys_1:list_A524553945_alt_o) (P_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (Xs_2:list_A524553945_alt_o), ((forall (X_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_2) (set_Ar571341173_alt_o Xs_2))->(P_2 X_2)))->(((eq list_A524553945_alt_o) ((takeWh1825606477_alt_o P_2) ((append295924073_alt_o Xs_2) Ys_1))) ((append295924073_alt_o Xs_2) ((takeWh1825606477_alt_o P_2) Ys_1))))).
% Axiom fact_646_takeWhile__append2:(forall (Ys_1:list_P736798472le_alt) (P_2:(produc1501160679le_alt->Prop)) (Xs_2:list_P736798472le_alt), ((forall (X_2:produc1501160679le_alt), (((member214075476le_alt X_2) (set_Pr1525059414le_alt Xs_2))->(P_2 X_2)))->(((eq list_P736798472le_alt) ((takeWh302148478le_alt P_2) ((append1229289570le_alt Xs_2) Ys_1))) ((append1229289570le_alt Xs_2) ((takeWh302148478le_alt P_2) Ys_1))))).
% Axiom fact_647_split__list__propE:(forall (P_1:(arrow_475358991le_alt->Prop)) (Xs_1:list_A2115238852le_alt), (((ex arrow_475358991le_alt) (fun (X_2:arrow_475358991le_alt)=> ((and ((member84363362le_alt X_2) (set_Ar577454304le_alt Xs_1))) (P_1 X_2))))->((forall (Ys:list_A2115238852le_alt) (X_2:arrow_475358991le_alt), (((ex list_A2115238852le_alt) (fun (Zs:list_A2115238852le_alt)=> (((eq list_A2115238852le_alt) Xs_1) ((append179082452le_alt Ys) ((cons_A228743023le_alt X_2) Zs)))))->((P_1 X_2)->False)))->False))).
% Axiom fact_648_in__set__conv__decomp:(forall (X_1:(produc1501160679le_alt->Prop)) (Xs:list_P1178103901_alt_o), ((iff ((member377231867_alt_o X_1) (set_Pr592386425_alt_o Xs))) ((ex list_P1178103901_alt_o) (fun (Ys:list_P1178103901_alt_o)=> ((ex list_P1178103901_alt_o) (fun (Zs:list_P1178103901_alt_o)=> (((eq list_P1178103901_alt_o) Xs) ((append612833133_alt_o Ys) ((cons_P1239653256_alt_o X_1) Zs))))))))).
% Axiom fact_649_in__set__conv__decomp:(forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (Xs:list_A524553945_alt_o), ((iff ((member526088951_alt_o X_1) (set_Ar571341173_alt_o Xs))) ((ex list_A524553945_alt_o) (fun (Ys:list_A524553945_alt_o)=> ((ex list_A524553945_alt_o) (fun (Zs:list_A524553945_alt_o)=> (((eq list_A524553945_alt_o) Xs) ((append295924073_alt_o Ys) ((cons_A2010997508_alt_o X_1) Zs))))))))).
% Axiom fact_650_in__set__conv__decomp:(forall (X_1:produc1501160679le_alt) (Xs:list_P736798472le_alt), ((iff ((member214075476le_alt X_1) (set_Pr1525059414le_alt Xs))) ((ex list_P736798472le_alt) (fun (Ys:list_P736798472le_alt)=> ((ex list_P736798472le_alt) (fun (Zs:list_P736798472le_alt)=> (((eq list_P736798472le_alt) Xs) ((append1229289570le_alt Ys) ((cons_P1913588871le_alt X_1) Zs))))))))).
% Axiom fact_651_termination__basic__simps_I5_J:(forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y))).
% Axiom fact_652_lessI:(forall (N:nat), ((ord_less_nat N) (suc N))).
% Axiom fact_653_Suc__mono:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat (suc M)) (suc N)))).
% Axiom fact_654_n__not__Suc__n:(forall (N:nat), (not (((eq nat) N) (suc N)))).
% Axiom fact_655_Suc__n__not__n:(forall (N:nat), (not (((eq nat) (suc N)) N))).
% Axiom fact_656_nat_Oinject:(forall (Nat_1:nat) (Nat:nat), ((iff (((eq nat) (suc Nat_1)) (suc Nat))) (((eq nat) Nat_1) Nat))).
% Axiom fact_657_Suc__inject:(forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y))).
% Axiom fact_658_less__not__refl:(forall (N:nat), (((ord_less_nat N) N)->False)).
% Axiom fact_659_nat__neq__iff:(forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))).
% Axiom fact_660_linorder__neqE__nat:(forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))).
% Axiom fact_661_less__irrefl__nat:(forall (N:nat), (((ord_less_nat N) N)->False)).
% Axiom fact_662_less__not__refl2:(forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))).
% Axiom fact_663_less__not__refl3:(forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))).
% Axiom fact_664_nat__less__cases:(forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))).
% Axiom fact_665_le__refl:(forall (N:nat), ((ord_less_eq_nat N) N)).
% Axiom fact_666_nat__le__linear:(forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))).
% Axiom fact_667_eq__imp__le:(forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))).
% Axiom fact_668_le__trans:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat I_1) K)))).
% Axiom fact_669_le__antisym:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))).
% Axiom fact_670_Suc__less__SucD:(forall (M:nat) (N:nat), (((ord_less_nat (suc M)) (suc N))->((ord_less_nat M) N))).
% Axiom fact_671_Suc__lessD:(forall (M:nat) (N:nat), (((ord_less_nat (suc M)) N)->((ord_less_nat M) N))).
% Axiom fact_672_less__SucE:(forall (M:nat) (N:nat), (((ord_less_nat M) (suc N))->((((ord_less_nat M) N)->False)->(((eq nat) M) N)))).
% Axiom fact_673_less__trans__Suc:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat J) K)->((ord_less_nat (suc I_1)) K)))).
% Axiom fact_674_Suc__lessI:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((not (((eq nat) (suc M)) N))->((ord_less_nat (suc M)) N)))).
% Axiom fact_675_less__SucI:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat M) (suc N)))).
% Axiom fact_676_less__antisym:(forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->(((ord_less_nat N) (suc M))->(((eq nat) M) N)))).
% Axiom fact_677_not__less__less__Suc__eq:(forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->((if
% EOF
%------------------------------------------------------------------------------