cocATP---0.2.0.TMO-Non.f

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SWW473^1 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n109.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 13:37:23 EDT 2014

% Result   : Timeout 300.03s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SWW473^1 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n109.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 09:19:36 CDT 2014
% % CPUTime  : 300.03 
% 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 0x15197e8>, <kernel.Type object at 0x15199e0>) of role type named ty_ty_t__a
% Using role type
% Declaring x_a:Type
% FOF formula (<kernel.Constant object at 0x17073f8>, <kernel.Type object at 0x1519fc8>) of role type named ty_ty_tc__Com__Opname
% Using role type
% Declaring pname:Type
% FOF formula (<kernel.Constant object at 0x1519a28>, <kernel.Type object at 0x1519a70>) of role type named ty_ty_tc__Nat__Onat
% Using role type
% Declaring nat:Type
% FOF formula (<kernel.Constant object at 0x15198c0>, <kernel.DependentProduct object at 0x15195a8>) of role type named sy_c_Finite__Set_Ocard_000_062_I_062_It__a_M_Eo_J_M_Eo_J
% Using role type
% Declaring finite_card_a_o_o:((((x_a->Prop)->Prop)->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x1519998>, <kernel.DependentProduct object at 0x15195f0>) of role type named sy_c_Finite__Set_Ocard_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J
% Using role type
% Declaring finite221134632me_o_o:((((pname->Prop)->Prop)->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x1519d40>, <kernel.DependentProduct object at 0x1519518>) of role type named sy_c_Finite__Set_Ocard_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J
% Using role type
% Declaring finite_card_nat_o_o:((((nat->Prop)->Prop)->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x15195a8>, <kernel.DependentProduct object at 0x1519560>) of role type named sy_c_Finite__Set_Ocard_000_062_It__a_M_Eo_J
% Using role type
% Declaring finite_card_a_o:(((x_a->Prop)->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x15195f0>, <kernel.DependentProduct object at 0x1519488>) of role type named sy_c_Finite__Set_Ocard_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring finite_card_pname_o:(((pname->Prop)->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x1519fc8>, <kernel.DependentProduct object at 0x15194d0>) of role type named sy_c_Finite__Set_Ocard_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring finite_card_nat_o:(((nat->Prop)->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x1519c20>, <kernel.DependentProduct object at 0x1519440>) of role type named sy_c_Finite__Set_Ocard_000t__a
% Using role type
% Declaring finite_card_a:((x_a->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x1519488>, <kernel.DependentProduct object at 0x1519fc8>) of role type named sy_c_Finite__Set_Ocard_000tc__Com__Opname
% Using role type
% Declaring finite_card_pname:((pname->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x15194d0>, <kernel.DependentProduct object at 0x1519368>) of role type named sy_c_Finite__Set_Ocard_000tc__Nat__Onat
% Using role type
% Declaring finite_card_nat:((nat->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x1519d40>, <kernel.DependentProduct object at 0x15193f8>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_It__a_M_Eo_J_M_Eo_J_M_Eo_J
% Using role type
% Declaring finite1302365357_o_o_o:(((((x_a->Prop)->Prop)->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x15195a8>, <kernel.DependentProduct object at 0x1519368>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo
% Using role type
% Declaring finite1648353812_o_o_o:(((((pname->Prop)->Prop)->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1519488>, <kernel.DependentProduct object at 0x15193f8>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_M_Eo_J
% Using role type
% Declaring finite1237261006_o_o_o:(((((nat->Prop)->Prop)->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1519758>, <kernel.DependentProduct object at 0x15193f8>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_It__a_M_Eo_J_M_Eo_J
% Using role type
% Declaring finite_finite_a_o_o:((((x_a->Prop)->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1519d40>, <kernel.DependentProduct object at 0x13f83b0>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J
% Using role type
% Declaring finite1066544169me_o_o:((((pname->Prop)->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1519368>, <kernel.DependentProduct object at 0x13f8f80>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J
% Using role type
% Declaring finite1676163439at_o_o:((((nat->Prop)->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1519758>, <kernel.DependentProduct object at 0x17262d8>) of role type named sy_c_Finite__Set_Ofinite_000_062_It__a_M_Eo_J
% Using role type
% Declaring finite_finite_a_o:(((x_a->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1519d40>, <kernel.DependentProduct object at 0x1726248>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring finite297249702name_o:(((pname->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1519560>, <kernel.DependentProduct object at 0x1726248>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring finite_finite_nat_o:(((nat->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1519368>, <kernel.DependentProduct object at 0x17261b8>) of role type named sy_c_Finite__Set_Ofinite_000t__a
% Using role type
% Declaring finite_finite_a:((x_a->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1519d40>, <kernel.DependentProduct object at 0x1726290>) of role type named sy_c_Finite__Set_Ofinite_000tc__Com__Opname
% Using role type
% Declaring finite_finite_pname:((pname->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1519d40>, <kernel.DependentProduct object at 0x17262d8>) of role type named sy_c_Finite__Set_Ofinite_000tc__Nat__Onat
% Using role type
% Declaring finite_finite_nat:((nat->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x13f83b0>, <kernel.DependentProduct object at 0x1726290>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat
% Using role type
% Declaring minus_minus_nat:(nat->(nat->nat))
% FOF formula (<kernel.Constant object at 0x13f8830>, <kernel.DependentProduct object at 0x1726ef0>) of role type named sy_c_Nat_OSuc
% Using role type
% Declaring suc:(nat->nat)
% FOF formula (<kernel.Constant object at 0x13f8830>, <kernel.DependentProduct object at 0x1726200>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_It__a_M_Eo_J_M_Eo_J_M_E
% Using role type
% Declaring ord_less_eq_a_o_o_o:((((x_a->Prop)->Prop)->Prop)->((((x_a->Prop)->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726290>, <kernel.DependentProduct object at 0x17262d8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring ord_le1828183645_o_o_o:((((pname->Prop)->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726fc8>, <kernel.DependentProduct object at 0x1726ef0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M
% Using role type
% Declaring ord_le124054423_o_o_o:((((nat->Prop)->Prop)->Prop)->((((nat->Prop)->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726200>, <kernel.DependentProduct object at 0x1726320>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_It__a_M_Eo_J_M_Eo_J
% Using role type
% Declaring ord_less_eq_a_o_o:(((x_a->Prop)->Prop)->(((x_a->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726c68>, <kernel.DependentProduct object at 0x1726d88>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_
% Using role type
% Declaring ord_le1205211808me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x17262d8>, <kernel.DependentProduct object at 0x1726d40>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J
% Using role type
% Declaring ord_less_eq_nat_o_o:(((nat->Prop)->Prop)->(((nat->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726320>, <kernel.DependentProduct object at 0x1726cf8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_It__a_M_Eo_J
% Using role type
% Declaring ord_less_eq_a_o:((x_a->Prop)->((x_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726fc8>, <kernel.DependentProduct object at 0x1726488>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring ord_less_eq_pname_o:((pname->Prop)->((pname->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726248>, <kernel.DependentProduct object at 0x17263f8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring ord_less_eq_nat_o:((nat->Prop)->((nat->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726638>, <kernel.DependentProduct object at 0x1726488>) 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 0x1726f80>, <kernel.DependentProduct object at 0x1726320>) of role type named sy_c_Set_OCollect_000_062_I_062_I_062_It__a_M_Eo_J_M_Eo_J_M_Eo_J
% Using role type
% Declaring collect_a_o_o_o:(((((x_a->Prop)->Prop)->Prop)->Prop)->((((x_a->Prop)->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x13ff7a0>, <kernel.DependentProduct object at 0x1726248>) of role type named sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo_J
% Using role type
% Declaring collect_pname_o_o_o:(((((pname->Prop)->Prop)->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x17263f8>, <kernel.DependentProduct object at 0x1726d40>) of role type named sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_M_Eo_J
% Using role type
% Declaring collect_nat_o_o_o:(((((nat->Prop)->Prop)->Prop)->Prop)->((((nat->Prop)->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726fc8>, <kernel.DependentProduct object at 0x1726248>) of role type named sy_c_Set_OCollect_000_062_I_062_It__a_M_Eo_J_M_Eo_J
% Using role type
% Declaring collect_a_o_o:((((x_a->Prop)->Prop)->Prop)->(((x_a->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x17261b8>, <kernel.DependentProduct object at 0x1534e60>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J
% Using role type
% Declaring collect_pname_o_o:((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726f80>, <kernel.DependentProduct object at 0x1534c20>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J
% Using role type
% Declaring collect_nat_o_o:((((nat->Prop)->Prop)->Prop)->(((nat->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726fc8>, <kernel.DependentProduct object at 0x1534a70>) of role type named sy_c_Set_OCollect_000_062_It__a_M_Eo_J
% Using role type
% Declaring collect_a_o:(((x_a->Prop)->Prop)->((x_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x17261b8>, <kernel.DependentProduct object at 0x1534b00>) of role type named sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring collect_pname_o:(((pname->Prop)->Prop)->((pname->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1726fc8>, <kernel.DependentProduct object at 0x1534950>) of role type named sy_c_Set_OCollect_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring collect_nat_o:(((nat->Prop)->Prop)->((nat->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x17261b8>, <kernel.DependentProduct object at 0x1534e60>) of role type named sy_c_Set_OCollect_000t__a
% Using role type
% Declaring collect_a:((x_a->Prop)->(x_a->Prop))
% FOF formula (<kernel.Constant object at 0x1726f80>, <kernel.DependentProduct object at 0x1534a70>) of role type named sy_c_Set_OCollect_000tc__Com__Opname
% Using role type
% Declaring collect_pname:((pname->Prop)->(pname->Prop))
% FOF formula (<kernel.Constant object at 0x1534fc8>, <kernel.DependentProduct object at 0x1534e60>) of role type named sy_c_Set_OCollect_000tc__Nat__Onat
% Using role type
% Declaring collect_nat:((nat->Prop)->(nat->Prop))
% FOF formula (<kernel.Constant object at 0x1534c20>, <kernel.DependentProduct object at 0x1534e60>) of role type named sy_c_Set_Oimage_000_062_I_062_It__a_M_Eo_J_M_Eo_J_000t__a
% Using role type
% Declaring image_a_o_o_a:((((x_a->Prop)->Prop)->x_a)->((((x_a->Prop)->Prop)->Prop)->(x_a->Prop)))
% FOF formula (<kernel.Constant object at 0x1534a70>, <kernel.DependentProduct object at 0x1534ef0>) of role type named sy_c_Set_Oimage_000_062_I_062_It__a_M_Eo_J_M_Eo_J_000tc__Com__Opname
% Using role type
% Declaring image_a_o_o_pname:((((x_a->Prop)->Prop)->pname)->((((x_a->Prop)->Prop)->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x1534cb0>, <kernel.DependentProduct object at 0x1534c20>) of role type named sy_c_Set_Oimage_000_062_I_062_It__a_M_Eo_J_M_Eo_J_000tc__Nat__Onat
% Using role type
% Declaring image_a_o_o_nat:((((x_a->Prop)->Prop)->nat)->((((x_a->Prop)->Prop)->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x1534dd0>, <kernel.DependentProduct object at 0x1534a70>) of role type named sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000t__a
% Using role type
% Declaring image_pname_o_o_a:((((pname->Prop)->Prop)->x_a)->((((pname->Prop)->Prop)->Prop)->(x_a->Prop)))
% FOF formula (<kernel.Constant object at 0x1534b00>, <kernel.DependentProduct object at 0x1534cb0>) of role type named sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Com__Opname
% Using role type
% Declaring image_471733107_pname:((((pname->Prop)->Prop)->pname)->((((pname->Prop)->Prop)->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x1534830>, <kernel.DependentProduct object at 0x1534dd0>) of role type named sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Nat__Onat
% Using role type
% Declaring image_pname_o_o_nat:((((pname->Prop)->Prop)->nat)->((((pname->Prop)->Prop)->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x15344d0>, <kernel.DependentProduct object at 0x1534b00>) of role type named sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000t__a
% Using role type
% Declaring image_nat_o_o_a:((((nat->Prop)->Prop)->x_a)->((((nat->Prop)->Prop)->Prop)->(x_a->Prop)))
% FOF formula (<kernel.Constant object at 0x1534560>, <kernel.DependentProduct object at 0x1534830>) of role type named sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000tc__Com__Opname
% Using role type
% Declaring image_nat_o_o_pname:((((nat->Prop)->Prop)->pname)->((((nat->Prop)->Prop)->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x1534b48>, <kernel.DependentProduct object at 0x15344d0>) of role type named sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000tc__Nat__Onat
% Using role type
% Declaring image_nat_o_o_nat:((((nat->Prop)->Prop)->nat)->((((nat->Prop)->Prop)->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x1534c68>, <kernel.DependentProduct object at 0x1534878>) of role type named sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000t__a
% Using role type
% Declaring image_a_o_a:(((x_a->Prop)->x_a)->(((x_a->Prop)->Prop)->(x_a->Prop)))
% FOF formula (<kernel.Constant object at 0x1534f38>, <kernel.DependentProduct object at 0x1534560>) of role type named sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Com__Opname
% Using role type
% Declaring image_a_o_pname:(((x_a->Prop)->pname)->(((x_a->Prop)->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x1534cf8>, <kernel.DependentProduct object at 0x1534b48>) of role type named sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Nat__Onat
% Using role type
% Declaring image_a_o_nat:(((x_a->Prop)->nat)->(((x_a->Prop)->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x15349e0>, <kernel.DependentProduct object at 0x1534c68>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000t__a
% Using role type
% Declaring image_pname_o_a:(((pname->Prop)->x_a)->(((pname->Prop)->Prop)->(x_a->Prop)))
% FOF formula (<kernel.Constant object at 0x15343b0>, <kernel.DependentProduct object at 0x1534f38>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname
% Using role type
% Declaring image_pname_o_pname:(((pname->Prop)->pname)->(((pname->Prop)->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x1534878>, <kernel.DependentProduct object at 0x1534c68>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Nat__Onat
% Using role type
% Declaring image_pname_o_nat:(((pname->Prop)->nat)->(((pname->Prop)->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x1402e60>, <kernel.DependentProduct object at 0x1534950>) of role type named sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000t__a
% Using role type
% Declaring image_nat_o_a:(((nat->Prop)->x_a)->(((nat->Prop)->Prop)->(x_a->Prop)))
% FOF formula (<kernel.Constant object at 0x1534560>, <kernel.DependentProduct object at 0x1534b90>) of role type named sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Com__Opname
% Using role type
% Declaring image_nat_o_pname:(((nat->Prop)->pname)->(((nat->Prop)->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x1534cf8>, <kernel.DependentProduct object at 0x1534f38>) of role type named sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Nat__Onat
% Using role type
% Declaring image_nat_o_nat:(((nat->Prop)->nat)->(((nat->Prop)->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x15343b0>, <kernel.DependentProduct object at 0x152a908>) of role type named sy_c_Set_Oimage_000t__a_000t__a
% Using role type
% Declaring image_a_a:((x_a->x_a)->((x_a->Prop)->(x_a->Prop)))
% FOF formula (<kernel.Constant object at 0x1534560>, <kernel.DependentProduct object at 0x152a8c0>) of role type named sy_c_Set_Oimage_000t__a_000tc__Com__Opname
% Using role type
% Declaring image_a_pname:((x_a->pname)->((x_a->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x15343b0>, <kernel.DependentProduct object at 0x152a830>) of role type named sy_c_Set_Oimage_000t__a_000tc__Nat__Onat
% Using role type
% Declaring image_a_nat:((x_a->nat)->((x_a->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x1534cf8>, <kernel.DependentProduct object at 0x152a908>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_It__a_M_Eo_J_M_Eo_J
% Using role type
% Declaring image_pname_a_o_o:((pname->((x_a->Prop)->Prop))->((pname->Prop)->(((x_a->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1534b90>, <kernel.DependentProduct object at 0x152a758>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J
% Using role type
% Declaring image_504089495me_o_o:((pname->((pname->Prop)->Prop))->((pname->Prop)->(((pname->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1534cf8>, <kernel.DependentProduct object at 0x152a908>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J
% Using role type
% Declaring image_pname_nat_o_o:((pname->((nat->Prop)->Prop))->((pname->Prop)->(((nat->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1534b90>, <kernel.DependentProduct object at 0x152a758>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_It__a_M_Eo_J
% Using role type
% Declaring image_pname_a_o:((pname->(x_a->Prop))->((pname->Prop)->((x_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1534b90>, <kernel.DependentProduct object at 0x152a908>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring image_pname_pname_o:((pname->(pname->Prop))->((pname->Prop)->((pname->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a8c0>, <kernel.DependentProduct object at 0x152a758>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring image_pname_nat_o:((pname->(nat->Prop))->((pname->Prop)->((nat->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a830>, <kernel.DependentProduct object at 0x152a680>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000t__a
% Using role type
% Declaring image_pname_a:((pname->x_a)->((pname->Prop)->(x_a->Prop)))
% FOF formula (<kernel.Constant object at 0x152a878>, <kernel.DependentProduct object at 0x152a518>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname
% Using role type
% Declaring image_pname_pname:((pname->pname)->((pname->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x152a5f0>, <kernel.DependentProduct object at 0x152a560>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Nat__Onat
% Using role type
% Declaring image_pname_nat:((pname->nat)->((pname->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x152a6c8>, <kernel.DependentProduct object at 0x152a710>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000_062_I_062_It__a_M_Eo_J_M_Eo_J
% Using role type
% Declaring image_nat_a_o_o:((nat->((x_a->Prop)->Prop))->((nat->Prop)->(((x_a->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a638>, <kernel.DependentProduct object at 0x152a518>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J
% Using role type
% Declaring image_nat_pname_o_o:((nat->((pname->Prop)->Prop))->((nat->Prop)->(((pname->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a488>, <kernel.DependentProduct object at 0x152a560>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J
% Using role type
% Declaring image_nat_nat_o_o:((nat->((nat->Prop)->Prop))->((nat->Prop)->(((nat->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a8c0>, <kernel.DependentProduct object at 0x152a518>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000_062_It__a_M_Eo_J
% Using role type
% Declaring image_nat_a_o:((nat->(x_a->Prop))->((nat->Prop)->((x_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a5a8>, <kernel.DependentProduct object at 0x152a560>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring image_nat_pname_o:((nat->(pname->Prop))->((nat->Prop)->((pname->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a638>, <kernel.DependentProduct object at 0x152a518>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring image_nat_nat_o:((nat->(nat->Prop))->((nat->Prop)->((nat->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a830>, <kernel.DependentProduct object at 0x152a2d8>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000t__a
% Using role type
% Declaring image_nat_a:((nat->x_a)->((nat->Prop)->(x_a->Prop)))
% FOF formula (<kernel.Constant object at 0x152a8c0>, <kernel.DependentProduct object at 0x152a290>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname
% Using role type
% Declaring image_nat_pname:((nat->pname)->((nat->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x152a560>, <kernel.DependentProduct object at 0x152a3f8>) of role type named sy_c_Set_Oinsert_000_062_I_062_It__a_M_Eo_J_M_Eo_J
% Using role type
% Declaring insert_a_o_o:(((x_a->Prop)->Prop)->((((x_a->Prop)->Prop)->Prop)->(((x_a->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a4d0>, <kernel.DependentProduct object at 0x152a1b8>) of role type named sy_c_Set_Oinsert_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J
% Using role type
% Declaring insert_pname_o_o:(((pname->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a638>, <kernel.DependentProduct object at 0x152a830>) of role type named sy_c_Set_Oinsert_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J
% Using role type
% Declaring insert_nat_o_o:(((nat->Prop)->Prop)->((((nat->Prop)->Prop)->Prop)->(((nat->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a200>, <kernel.DependentProduct object at 0x152a5a8>) of role type named sy_c_Set_Oinsert_000_062_It__a_M_Eo_J
% Using role type
% Declaring insert_a_o:((x_a->Prop)->(((x_a->Prop)->Prop)->((x_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a2d8>, <kernel.DependentProduct object at 0x152a830>) of role type named sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring insert_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a128>, <kernel.DependentProduct object at 0x152a5a8>) of role type named sy_c_Set_Oinsert_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring insert_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->((nat->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x152a098>, <kernel.DependentProduct object at 0x152a638>) of role type named sy_c_Set_Oinsert_000t__a
% Using role type
% Declaring insert_a:(x_a->((x_a->Prop)->(x_a->Prop)))
% FOF formula (<kernel.Constant object at 0x152a7a0>, <kernel.DependentProduct object at 0x152a200>) of role type named sy_c_Set_Oinsert_000tc__Com__Opname
% Using role type
% Declaring insert_pname:(pname->((pname->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x152a0e0>, <kernel.DependentProduct object at 0x152aa70>) of role type named sy_c_Set_Oinsert_000tc__Nat__Onat
% Using role type
% Declaring insert_nat:(nat->((nat->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x152a8c0>, <kernel.DependentProduct object at 0x152a098>) of role type named sy_c_member_000_062_It__a_M_Eo_J
% Using role type
% Declaring member_a_o:((x_a->Prop)->(((x_a->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x152a200>, <kernel.DependentProduct object at 0x152a2d8>) of role type named sy_c_member_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring member_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x152a0e0>, <kernel.DependentProduct object at 0x152aab8>) of role type named sy_c_member_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring member_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x152a638>, <kernel.DependentProduct object at 0x152ab00>) of role type named sy_c_member_000t__a
% Using role type
% Declaring member_a:(x_a->((x_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x152a4d0>, <kernel.DependentProduct object at 0x152ab90>) of role type named sy_c_member_000tc__Com__Opname
% Using role type
% Declaring member_pname:(pname->((pname->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x152a830>, <kernel.DependentProduct object at 0x152abd8>) of role type named sy_c_member_000tc__Nat__Onat
% Using role type
% Declaring member_nat:(nat->((nat->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x152a0e0>, <kernel.DependentProduct object at 0x152ab00>) of role type named sy_v_G
% Using role type
% Declaring g:(x_a->Prop)
% FOF formula (<kernel.Constant object at 0x152a4d0>, <kernel.DependentProduct object at 0x152ac20>) of role type named sy_v_P
% Using role type
% Declaring p:((x_a->Prop)->((x_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x152a830>, <kernel.DependentProduct object at 0x152aa28>) of role type named sy_v_U
% Using role type
% Declaring u:(pname->Prop)
% FOF formula (<kernel.Constant object at 0x152a638>, <kernel.DependentProduct object at 0x152ac68>) of role type named sy_v_mgt__call
% Using role type
% Declaring mgt_call:(pname->x_a)
% FOF formula (<kernel.Constant object at 0x152ac20>, <kernel.Constant object at 0x152ac68>) of role type named sy_v_na
% Using role type
% Declaring na:nat
% FOF formula (<kernel.Constant object at 0x152a830>, <kernel.Constant object at 0x152ac68>) of role type named sy_v_pn
% Using role type
% Declaring pn:pname
% FOF formula (forall (Ts:(x_a->Prop)) (G:(x_a->Prop)), (((ord_less_eq_a_o Ts) G)->((p G) Ts))) of role axiom named fact_0_assms_I1_J
% A new axiom: (forall (Ts:(x_a->Prop)) (G:(x_a->Prop)), (((ord_less_eq_a_o Ts) G)->((p G) Ts)))
% FOF formula (forall (A_59:(nat->Prop)), ((finite_finite_nat A_59)->(finite_finite_nat_o (collect_nat_o (fun (B_38:(nat->Prop))=> ((ord_less_eq_nat_o B_38) A_59)))))) of role axiom named fact_1_finite__Collect__subsets
% A new axiom: (forall (A_59:(nat->Prop)), ((finite_finite_nat A_59)->(finite_finite_nat_o (collect_nat_o (fun (B_38:(nat->Prop))=> ((ord_less_eq_nat_o B_38) A_59))))))
% FOF formula (forall (A_59:(pname->Prop)), ((finite_finite_pname A_59)->(finite297249702name_o (collect_pname_o (fun (B_38:(pname->Prop))=> ((ord_less_eq_pname_o B_38) A_59)))))) of role axiom named fact_2_finite__Collect__subsets
% A new axiom: (forall (A_59:(pname->Prop)), ((finite_finite_pname A_59)->(finite297249702name_o (collect_pname_o (fun (B_38:(pname->Prop))=> ((ord_less_eq_pname_o B_38) A_59))))))
% FOF formula (forall (A_59:(x_a->Prop)), ((finite_finite_a A_59)->(finite_finite_a_o (collect_a_o (fun (B_38:(x_a->Prop))=> ((ord_less_eq_a_o B_38) A_59)))))) of role axiom named fact_3_finite__Collect__subsets
% A new axiom: (forall (A_59:(x_a->Prop)), ((finite_finite_a A_59)->(finite_finite_a_o (collect_a_o (fun (B_38:(x_a->Prop))=> ((ord_less_eq_a_o B_38) A_59))))))
% FOF formula (forall (A_59:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o A_59)->(finite1237261006_o_o_o (collect_nat_o_o_o (fun (B_38:(((nat->Prop)->Prop)->Prop))=> ((ord_le124054423_o_o_o B_38) A_59)))))) of role axiom named fact_4_finite__Collect__subsets
% A new axiom: (forall (A_59:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o A_59)->(finite1237261006_o_o_o (collect_nat_o_o_o (fun (B_38:(((nat->Prop)->Prop)->Prop))=> ((ord_le124054423_o_o_o B_38) A_59))))))
% FOF formula (forall (A_59:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_59)->(finite1648353812_o_o_o (collect_pname_o_o_o (fun (B_38:(((pname->Prop)->Prop)->Prop))=> ((ord_le1828183645_o_o_o B_38) A_59)))))) of role axiom named fact_5_finite__Collect__subsets
% A new axiom: (forall (A_59:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_59)->(finite1648353812_o_o_o (collect_pname_o_o_o (fun (B_38:(((pname->Prop)->Prop)->Prop))=> ((ord_le1828183645_o_o_o B_38) A_59))))))
% FOF formula (forall (A_59:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o A_59)->(finite1302365357_o_o_o (collect_a_o_o_o (fun (B_38:(((x_a->Prop)->Prop)->Prop))=> ((ord_less_eq_a_o_o_o B_38) A_59)))))) of role axiom named fact_6_finite__Collect__subsets
% A new axiom: (forall (A_59:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o A_59)->(finite1302365357_o_o_o (collect_a_o_o_o (fun (B_38:(((x_a->Prop)->Prop)->Prop))=> ((ord_less_eq_a_o_o_o B_38) A_59))))))
% FOF formula (forall (A_59:((x_a->Prop)->Prop)), ((finite_finite_a_o A_59)->(finite_finite_a_o_o (collect_a_o_o (fun (B_38:((x_a->Prop)->Prop))=> ((ord_less_eq_a_o_o B_38) A_59)))))) of role axiom named fact_7_finite__Collect__subsets
% A new axiom: (forall (A_59:((x_a->Prop)->Prop)), ((finite_finite_a_o A_59)->(finite_finite_a_o_o (collect_a_o_o (fun (B_38:((x_a->Prop)->Prop))=> ((ord_less_eq_a_o_o B_38) A_59))))))
% FOF formula (forall (A_59:((pname->Prop)->Prop)), ((finite297249702name_o A_59)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_38:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_38) A_59)))))) of role axiom named fact_8_finite__Collect__subsets
% A new axiom: (forall (A_59:((pname->Prop)->Prop)), ((finite297249702name_o A_59)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_38:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_38) A_59))))))
% FOF formula (forall (A_59:((nat->Prop)->Prop)), ((finite_finite_nat_o A_59)->(finite1676163439at_o_o (collect_nat_o_o (fun (B_38:((nat->Prop)->Prop))=> ((ord_less_eq_nat_o_o B_38) A_59)))))) of role axiom named fact_9_finite__Collect__subsets
% A new axiom: (forall (A_59:((nat->Prop)->Prop)), ((finite_finite_nat_o A_59)->(finite1676163439at_o_o (collect_nat_o_o (fun (B_38:((nat->Prop)->Prop))=> ((ord_less_eq_nat_o_o B_38) A_59))))))
% FOF formula (forall (H:(pname->x_a)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_a ((image_pname_a H) F_15)))) of role axiom named fact_10_finite__imageI
% A new axiom: (forall (H:(pname->x_a)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_a ((image_pname_a H) F_15))))
% FOF formula (forall (H:(((nat->Prop)->Prop)->nat)) (F_15:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o F_15)->(finite_finite_nat ((image_nat_o_o_nat H) F_15)))) of role axiom named fact_11_finite__imageI
% A new axiom: (forall (H:(((nat->Prop)->Prop)->nat)) (F_15:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o F_15)->(finite_finite_nat ((image_nat_o_o_nat H) F_15))))
% FOF formula (forall (H:(((pname->Prop)->Prop)->nat)) (F_15:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_15)->(finite_finite_nat ((image_pname_o_o_nat H) F_15)))) of role axiom named fact_12_finite__imageI
% A new axiom: (forall (H:(((pname->Prop)->Prop)->nat)) (F_15:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_15)->(finite_finite_nat ((image_pname_o_o_nat H) F_15))))
% FOF formula (forall (H:(((x_a->Prop)->Prop)->nat)) (F_15:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o F_15)->(finite_finite_nat ((image_a_o_o_nat H) F_15)))) of role axiom named fact_13_finite__imageI
% A new axiom: (forall (H:(((x_a->Prop)->Prop)->nat)) (F_15:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o F_15)->(finite_finite_nat ((image_a_o_o_nat H) F_15))))
% FOF formula (forall (H:((x_a->Prop)->nat)) (F_15:((x_a->Prop)->Prop)), ((finite_finite_a_o F_15)->(finite_finite_nat ((image_a_o_nat H) F_15)))) of role axiom named fact_14_finite__imageI
% A new axiom: (forall (H:((x_a->Prop)->nat)) (F_15:((x_a->Prop)->Prop)), ((finite_finite_a_o F_15)->(finite_finite_nat ((image_a_o_nat H) F_15))))
% FOF formula (forall (H:((pname->Prop)->nat)) (F_15:((pname->Prop)->Prop)), ((finite297249702name_o F_15)->(finite_finite_nat ((image_pname_o_nat H) F_15)))) of role axiom named fact_15_finite__imageI
% A new axiom: (forall (H:((pname->Prop)->nat)) (F_15:((pname->Prop)->Prop)), ((finite297249702name_o F_15)->(finite_finite_nat ((image_pname_o_nat H) F_15))))
% FOF formula (forall (H:((nat->Prop)->nat)) (F_15:((nat->Prop)->Prop)), ((finite_finite_nat_o F_15)->(finite_finite_nat ((image_nat_o_nat H) F_15)))) of role axiom named fact_16_finite__imageI
% A new axiom: (forall (H:((nat->Prop)->nat)) (F_15:((nat->Prop)->Prop)), ((finite_finite_nat_o F_15)->(finite_finite_nat ((image_nat_o_nat H) F_15))))
% FOF formula (forall (H:(x_a->nat)) (F_15:(x_a->Prop)), ((finite_finite_a F_15)->(finite_finite_nat ((image_a_nat H) F_15)))) of role axiom named fact_17_finite__imageI
% A new axiom: (forall (H:(x_a->nat)) (F_15:(x_a->Prop)), ((finite_finite_a F_15)->(finite_finite_nat ((image_a_nat H) F_15))))
% FOF formula (forall (H:(((nat->Prop)->Prop)->pname)) (F_15:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o F_15)->(finite_finite_pname ((image_nat_o_o_pname H) F_15)))) of role axiom named fact_18_finite__imageI
% A new axiom: (forall (H:(((nat->Prop)->Prop)->pname)) (F_15:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o F_15)->(finite_finite_pname ((image_nat_o_o_pname H) F_15))))
% FOF formula (forall (H:(((pname->Prop)->Prop)->pname)) (F_15:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_15)->(finite_finite_pname ((image_471733107_pname H) F_15)))) of role axiom named fact_19_finite__imageI
% A new axiom: (forall (H:(((pname->Prop)->Prop)->pname)) (F_15:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_15)->(finite_finite_pname ((image_471733107_pname H) F_15))))
% FOF formula (forall (H:(((x_a->Prop)->Prop)->pname)) (F_15:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o F_15)->(finite_finite_pname ((image_a_o_o_pname H) F_15)))) of role axiom named fact_20_finite__imageI
% A new axiom: (forall (H:(((x_a->Prop)->Prop)->pname)) (F_15:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o F_15)->(finite_finite_pname ((image_a_o_o_pname H) F_15))))
% FOF formula (forall (H:((x_a->Prop)->pname)) (F_15:((x_a->Prop)->Prop)), ((finite_finite_a_o F_15)->(finite_finite_pname ((image_a_o_pname H) F_15)))) of role axiom named fact_21_finite__imageI
% A new axiom: (forall (H:((x_a->Prop)->pname)) (F_15:((x_a->Prop)->Prop)), ((finite_finite_a_o F_15)->(finite_finite_pname ((image_a_o_pname H) F_15))))
% FOF formula (forall (H:((pname->Prop)->pname)) (F_15:((pname->Prop)->Prop)), ((finite297249702name_o F_15)->(finite_finite_pname ((image_pname_o_pname H) F_15)))) of role axiom named fact_22_finite__imageI
% A new axiom: (forall (H:((pname->Prop)->pname)) (F_15:((pname->Prop)->Prop)), ((finite297249702name_o F_15)->(finite_finite_pname ((image_pname_o_pname H) F_15))))
% FOF formula (forall (H:((nat->Prop)->pname)) (F_15:((nat->Prop)->Prop)), ((finite_finite_nat_o F_15)->(finite_finite_pname ((image_nat_o_pname H) F_15)))) of role axiom named fact_23_finite__imageI
% A new axiom: (forall (H:((nat->Prop)->pname)) (F_15:((nat->Prop)->Prop)), ((finite_finite_nat_o F_15)->(finite_finite_pname ((image_nat_o_pname H) F_15))))
% FOF formula (forall (H:(x_a->pname)) (F_15:(x_a->Prop)), ((finite_finite_a F_15)->(finite_finite_pname ((image_a_pname H) F_15)))) of role axiom named fact_24_finite__imageI
% A new axiom: (forall (H:(x_a->pname)) (F_15:(x_a->Prop)), ((finite_finite_a F_15)->(finite_finite_pname ((image_a_pname H) F_15))))
% FOF formula (forall (H:(nat->((nat->Prop)->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite1676163439at_o_o ((image_nat_nat_o_o H) F_15)))) of role axiom named fact_25_finite__imageI
% A new axiom: (forall (H:(nat->((nat->Prop)->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite1676163439at_o_o ((image_nat_nat_o_o H) F_15))))
% FOF formula (forall (H:(nat->((pname->Prop)->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite1066544169me_o_o ((image_nat_pname_o_o H) F_15)))) of role axiom named fact_26_finite__imageI
% A new axiom: (forall (H:(nat->((pname->Prop)->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite1066544169me_o_o ((image_nat_pname_o_o H) F_15))))
% FOF formula (forall (H:(nat->((x_a->Prop)->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_a_o_o ((image_nat_a_o_o H) F_15)))) of role axiom named fact_27_finite__imageI
% A new axiom: (forall (H:(nat->((x_a->Prop)->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_a_o_o ((image_nat_a_o_o H) F_15))))
% FOF formula (forall (H:(nat->(x_a->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_a_o ((image_nat_a_o H) F_15)))) of role axiom named fact_28_finite__imageI
% A new axiom: (forall (H:(nat->(x_a->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_a_o ((image_nat_a_o H) F_15))))
% FOF formula (forall (H:(nat->(pname->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite297249702name_o ((image_nat_pname_o H) F_15)))) of role axiom named fact_29_finite__imageI
% A new axiom: (forall (H:(nat->(pname->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite297249702name_o ((image_nat_pname_o H) F_15))))
% FOF formula (forall (H:(nat->(nat->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_nat_o ((image_nat_nat_o H) F_15)))) of role axiom named fact_30_finite__imageI
% A new axiom: (forall (H:(nat->(nat->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_nat_o ((image_nat_nat_o H) F_15))))
% FOF formula (forall (H:(nat->x_a)) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_a ((image_nat_a H) F_15)))) of role axiom named fact_31_finite__imageI
% A new axiom: (forall (H:(nat->x_a)) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_a ((image_nat_a H) F_15))))
% FOF formula (forall (H:(pname->((nat->Prop)->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite1676163439at_o_o ((image_pname_nat_o_o H) F_15)))) of role axiom named fact_32_finite__imageI
% A new axiom: (forall (H:(pname->((nat->Prop)->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite1676163439at_o_o ((image_pname_nat_o_o H) F_15))))
% FOF formula (forall (H:(pname->((pname->Prop)->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite1066544169me_o_o ((image_504089495me_o_o H) F_15)))) of role axiom named fact_33_finite__imageI
% A new axiom: (forall (H:(pname->((pname->Prop)->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite1066544169me_o_o ((image_504089495me_o_o H) F_15))))
% FOF formula (forall (H:(pname->((x_a->Prop)->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_a_o_o ((image_pname_a_o_o H) F_15)))) of role axiom named fact_34_finite__imageI
% A new axiom: (forall (H:(pname->((x_a->Prop)->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_a_o_o ((image_pname_a_o_o H) F_15))))
% FOF formula (forall (H:(pname->(x_a->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_a_o ((image_pname_a_o H) F_15)))) of role axiom named fact_35_finite__imageI
% A new axiom: (forall (H:(pname->(x_a->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_a_o ((image_pname_a_o H) F_15))))
% FOF formula (forall (H:(pname->(pname->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite297249702name_o ((image_pname_pname_o H) F_15)))) of role axiom named fact_36_finite__imageI
% A new axiom: (forall (H:(pname->(pname->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite297249702name_o ((image_pname_pname_o H) F_15))))
% FOF formula (forall (H:(pname->(nat->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_nat_o ((image_pname_nat_o H) F_15)))) of role axiom named fact_37_finite__imageI
% A new axiom: (forall (H:(pname->(nat->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_nat_o ((image_pname_nat_o H) F_15))))
% FOF formula (forall (H:(pname->pname)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_pname ((image_pname_pname H) F_15)))) of role axiom named fact_38_finite__imageI
% A new axiom: (forall (H:(pname->pname)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_pname ((image_pname_pname H) F_15))))
% FOF formula (forall (H:(x_a->x_a)) (F_15:(x_a->Prop)), ((finite_finite_a F_15)->(finite_finite_a ((image_a_a H) F_15)))) of role axiom named fact_39_finite__imageI
% A new axiom: (forall (H:(x_a->x_a)) (F_15:(x_a->Prop)), ((finite_finite_a F_15)->(finite_finite_a ((image_a_a H) F_15))))
% FOF formula (forall (H:((nat->Prop)->x_a)) (F_15:((nat->Prop)->Prop)), ((finite_finite_nat_o F_15)->(finite_finite_a ((image_nat_o_a H) F_15)))) of role axiom named fact_40_finite__imageI
% A new axiom: (forall (H:((nat->Prop)->x_a)) (F_15:((nat->Prop)->Prop)), ((finite_finite_nat_o F_15)->(finite_finite_a ((image_nat_o_a H) F_15))))
% FOF formula (forall (H:((pname->Prop)->x_a)) (F_15:((pname->Prop)->Prop)), ((finite297249702name_o F_15)->(finite_finite_a ((image_pname_o_a H) F_15)))) of role axiom named fact_41_finite__imageI
% A new axiom: (forall (H:((pname->Prop)->x_a)) (F_15:((pname->Prop)->Prop)), ((finite297249702name_o F_15)->(finite_finite_a ((image_pname_o_a H) F_15))))
% FOF formula (forall (H:((x_a->Prop)->x_a)) (F_15:((x_a->Prop)->Prop)), ((finite_finite_a_o F_15)->(finite_finite_a ((image_a_o_a H) F_15)))) of role axiom named fact_42_finite__imageI
% A new axiom: (forall (H:((x_a->Prop)->x_a)) (F_15:((x_a->Prop)->Prop)), ((finite_finite_a_o F_15)->(finite_finite_a ((image_a_o_a H) F_15))))
% FOF formula (forall (H:(pname->nat)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_nat ((image_pname_nat H) F_15)))) of role axiom named fact_43_finite__imageI
% A new axiom: (forall (H:(pname->nat)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_nat ((image_pname_nat H) F_15))))
% FOF formula (forall (H:(nat->pname)) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_pname ((image_nat_pname H) F_15)))) of role axiom named fact_44_finite__imageI
% A new axiom: (forall (H:(nat->pname)) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_pname ((image_nat_pname H) F_15))))
% FOF formula (forall (A_58:x_a) (A_57:(x_a->Prop)), ((finite_finite_a A_57)->(finite_finite_a ((insert_a A_58) A_57)))) of role axiom named fact_45_finite_OinsertI
% A new axiom: (forall (A_58:x_a) (A_57:(x_a->Prop)), ((finite_finite_a A_57)->(finite_finite_a ((insert_a A_58) A_57))))
% FOF formula (forall (A_58:nat) (A_57:(nat->Prop)), ((finite_finite_nat A_57)->(finite_finite_nat ((insert_nat A_58) A_57)))) of role axiom named fact_46_finite_OinsertI
% A new axiom: (forall (A_58:nat) (A_57:(nat->Prop)), ((finite_finite_nat A_57)->(finite_finite_nat ((insert_nat A_58) A_57))))
% FOF formula (forall (A_58:pname) (A_57:(pname->Prop)), ((finite_finite_pname A_57)->(finite_finite_pname ((insert_pname A_58) A_57)))) of role axiom named fact_47_finite_OinsertI
% A new axiom: (forall (A_58:pname) (A_57:(pname->Prop)), ((finite_finite_pname A_57)->(finite_finite_pname ((insert_pname A_58) A_57))))
% FOF formula (forall (A_58:((nat->Prop)->Prop)) (A_57:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o A_57)->(finite1676163439at_o_o ((insert_nat_o_o A_58) A_57)))) of role axiom named fact_48_finite_OinsertI
% A new axiom: (forall (A_58:((nat->Prop)->Prop)) (A_57:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o A_57)->(finite1676163439at_o_o ((insert_nat_o_o A_58) A_57))))
% FOF formula (forall (A_58:((pname->Prop)->Prop)) (A_57:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_57)->(finite1066544169me_o_o ((insert_pname_o_o A_58) A_57)))) of role axiom named fact_49_finite_OinsertI
% A new axiom: (forall (A_58:((pname->Prop)->Prop)) (A_57:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_57)->(finite1066544169me_o_o ((insert_pname_o_o A_58) A_57))))
% FOF formula (forall (A_58:((x_a->Prop)->Prop)) (A_57:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o A_57)->(finite_finite_a_o_o ((insert_a_o_o A_58) A_57)))) of role axiom named fact_50_finite_OinsertI
% A new axiom: (forall (A_58:((x_a->Prop)->Prop)) (A_57:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o A_57)->(finite_finite_a_o_o ((insert_a_o_o A_58) A_57))))
% FOF formula (forall (A_58:(x_a->Prop)) (A_57:((x_a->Prop)->Prop)), ((finite_finite_a_o A_57)->(finite_finite_a_o ((insert_a_o A_58) A_57)))) of role axiom named fact_51_finite_OinsertI
% A new axiom: (forall (A_58:(x_a->Prop)) (A_57:((x_a->Prop)->Prop)), ((finite_finite_a_o A_57)->(finite_finite_a_o ((insert_a_o A_58) A_57))))
% FOF formula (forall (A_58:(pname->Prop)) (A_57:((pname->Prop)->Prop)), ((finite297249702name_o A_57)->(finite297249702name_o ((insert_pname_o A_58) A_57)))) of role axiom named fact_52_finite_OinsertI
% A new axiom: (forall (A_58:(pname->Prop)) (A_57:((pname->Prop)->Prop)), ((finite297249702name_o A_57)->(finite297249702name_o ((insert_pname_o A_58) A_57))))
% FOF formula (forall (A_58:(nat->Prop)) (A_57:((nat->Prop)->Prop)), ((finite_finite_nat_o A_57)->(finite_finite_nat_o ((insert_nat_o A_58) A_57)))) of role axiom named fact_53_finite_OinsertI
% A new axiom: (forall (A_58:(nat->Prop)) (A_57:((nat->Prop)->Prop)), ((finite_finite_nat_o A_57)->(finite_finite_nat_o ((insert_nat_o A_58) A_57))))
% FOF formula (forall (F_14:(pname->nat)) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_nat ((image_pname_nat F_14) A_56))) (finite_card_pname A_56)))) of role axiom named fact_54_card__image__le
% A new axiom: (forall (F_14:(pname->nat)) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_nat ((image_pname_nat F_14) A_56))) (finite_card_pname A_56))))
% FOF formula (forall (F_14:(x_a->nat)) (A_56:(x_a->Prop)), ((finite_finite_a A_56)->((ord_less_eq_nat (finite_card_nat ((image_a_nat F_14) A_56))) (finite_card_a A_56)))) of role axiom named fact_55_card__image__le
% A new axiom: (forall (F_14:(x_a->nat)) (A_56:(x_a->Prop)), ((finite_finite_a A_56)->((ord_less_eq_nat (finite_card_nat ((image_a_nat F_14) A_56))) (finite_card_a A_56))))
% FOF formula (forall (F_14:((nat->Prop)->nat)) (A_56:((nat->Prop)->Prop)), ((finite_finite_nat_o A_56)->((ord_less_eq_nat (finite_card_nat ((image_nat_o_nat F_14) A_56))) (finite_card_nat_o A_56)))) of role axiom named fact_56_card__image__le
% A new axiom: (forall (F_14:((nat->Prop)->nat)) (A_56:((nat->Prop)->Prop)), ((finite_finite_nat_o A_56)->((ord_less_eq_nat (finite_card_nat ((image_nat_o_nat F_14) A_56))) (finite_card_nat_o A_56))))
% FOF formula (forall (F_14:((pname->Prop)->nat)) (A_56:((pname->Prop)->Prop)), ((finite297249702name_o A_56)->((ord_less_eq_nat (finite_card_nat ((image_pname_o_nat F_14) A_56))) (finite_card_pname_o A_56)))) of role axiom named fact_57_card__image__le
% A new axiom: (forall (F_14:((pname->Prop)->nat)) (A_56:((pname->Prop)->Prop)), ((finite297249702name_o A_56)->((ord_less_eq_nat (finite_card_nat ((image_pname_o_nat F_14) A_56))) (finite_card_pname_o A_56))))
% FOF formula (forall (F_14:((x_a->Prop)->nat)) (A_56:((x_a->Prop)->Prop)), ((finite_finite_a_o A_56)->((ord_less_eq_nat (finite_card_nat ((image_a_o_nat F_14) A_56))) (finite_card_a_o A_56)))) of role axiom named fact_58_card__image__le
% A new axiom: (forall (F_14:((x_a->Prop)->nat)) (A_56:((x_a->Prop)->Prop)), ((finite_finite_a_o A_56)->((ord_less_eq_nat (finite_card_nat ((image_a_o_nat F_14) A_56))) (finite_card_a_o A_56))))
% FOF formula (forall (F_14:(x_a->pname)) (A_56:(x_a->Prop)), ((finite_finite_a A_56)->((ord_less_eq_nat (finite_card_pname ((image_a_pname F_14) A_56))) (finite_card_a A_56)))) of role axiom named fact_59_card__image__le
% A new axiom: (forall (F_14:(x_a->pname)) (A_56:(x_a->Prop)), ((finite_finite_a A_56)->((ord_less_eq_nat (finite_card_pname ((image_a_pname F_14) A_56))) (finite_card_a A_56))))
% FOF formula (forall (F_14:(nat->pname)) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_pname ((image_nat_pname F_14) A_56))) (finite_card_nat A_56)))) of role axiom named fact_60_card__image__le
% A new axiom: (forall (F_14:(nat->pname)) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_pname ((image_nat_pname F_14) A_56))) (finite_card_nat A_56))))
% FOF formula (forall (F_14:(pname->x_a)) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_a ((image_pname_a F_14) A_56))) (finite_card_pname A_56)))) of role axiom named fact_61_card__image__le
% A new axiom: (forall (F_14:(pname->x_a)) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_a ((image_pname_a F_14) A_56))) (finite_card_pname A_56))))
% FOF formula (forall (F_14:(((nat->Prop)->Prop)->x_a)) (A_56:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o A_56)->((ord_less_eq_nat (finite_card_a ((image_nat_o_o_a F_14) A_56))) (finite_card_nat_o_o A_56)))) of role axiom named fact_62_card__image__le
% A new axiom: (forall (F_14:(((nat->Prop)->Prop)->x_a)) (A_56:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o A_56)->((ord_less_eq_nat (finite_card_a ((image_nat_o_o_a F_14) A_56))) (finite_card_nat_o_o A_56))))
% FOF formula (forall (F_14:(((pname->Prop)->Prop)->x_a)) (A_56:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_56)->((ord_less_eq_nat (finite_card_a ((image_pname_o_o_a F_14) A_56))) (finite221134632me_o_o A_56)))) of role axiom named fact_63_card__image__le
% A new axiom: (forall (F_14:(((pname->Prop)->Prop)->x_a)) (A_56:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_56)->((ord_less_eq_nat (finite_card_a ((image_pname_o_o_a F_14) A_56))) (finite221134632me_o_o A_56))))
% FOF formula (forall (F_14:(((x_a->Prop)->Prop)->x_a)) (A_56:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o A_56)->((ord_less_eq_nat (finite_card_a ((image_a_o_o_a F_14) A_56))) (finite_card_a_o_o A_56)))) of role axiom named fact_64_card__image__le
% A new axiom: (forall (F_14:(((x_a->Prop)->Prop)->x_a)) (A_56:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o A_56)->((ord_less_eq_nat (finite_card_a ((image_a_o_o_a F_14) A_56))) (finite_card_a_o_o A_56))))
% FOF formula (forall (F_14:((x_a->Prop)->x_a)) (A_56:((x_a->Prop)->Prop)), ((finite_finite_a_o A_56)->((ord_less_eq_nat (finite_card_a ((image_a_o_a F_14) A_56))) (finite_card_a_o A_56)))) of role axiom named fact_65_card__image__le
% A new axiom: (forall (F_14:((x_a->Prop)->x_a)) (A_56:((x_a->Prop)->Prop)), ((finite_finite_a_o A_56)->((ord_less_eq_nat (finite_card_a ((image_a_o_a F_14) A_56))) (finite_card_a_o A_56))))
% FOF formula (forall (F_14:((pname->Prop)->x_a)) (A_56:((pname->Prop)->Prop)), ((finite297249702name_o A_56)->((ord_less_eq_nat (finite_card_a ((image_pname_o_a F_14) A_56))) (finite_card_pname_o A_56)))) of role axiom named fact_66_card__image__le
% A new axiom: (forall (F_14:((pname->Prop)->x_a)) (A_56:((pname->Prop)->Prop)), ((finite297249702name_o A_56)->((ord_less_eq_nat (finite_card_a ((image_pname_o_a F_14) A_56))) (finite_card_pname_o A_56))))
% FOF formula (forall (F_14:((nat->Prop)->x_a)) (A_56:((nat->Prop)->Prop)), ((finite_finite_nat_o A_56)->((ord_less_eq_nat (finite_card_a ((image_nat_o_a F_14) A_56))) (finite_card_nat_o A_56)))) of role axiom named fact_67_card__image__le
% A new axiom: (forall (F_14:((nat->Prop)->x_a)) (A_56:((nat->Prop)->Prop)), ((finite_finite_nat_o A_56)->((ord_less_eq_nat (finite_card_a ((image_nat_o_a F_14) A_56))) (finite_card_nat_o A_56))))
% FOF formula (forall (F_14:(x_a->x_a)) (A_56:(x_a->Prop)), ((finite_finite_a A_56)->((ord_less_eq_nat (finite_card_a ((image_a_a F_14) A_56))) (finite_card_a A_56)))) of role axiom named fact_68_card__image__le
% A new axiom: (forall (F_14:(x_a->x_a)) (A_56:(x_a->Prop)), ((finite_finite_a A_56)->((ord_less_eq_nat (finite_card_a ((image_a_a F_14) A_56))) (finite_card_a A_56))))
% FOF formula (forall (F_14:(pname->pname)) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_pname ((image_pname_pname F_14) A_56))) (finite_card_pname A_56)))) of role axiom named fact_69_card__image__le
% A new axiom: (forall (F_14:(pname->pname)) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_pname ((image_pname_pname F_14) A_56))) (finite_card_pname A_56))))
% FOF formula (forall (F_14:(pname->(nat->Prop))) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_nat_o ((image_pname_nat_o F_14) A_56))) (finite_card_pname A_56)))) of role axiom named fact_70_card__image__le
% A new axiom: (forall (F_14:(pname->(nat->Prop))) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_nat_o ((image_pname_nat_o F_14) A_56))) (finite_card_pname A_56))))
% FOF formula (forall (F_14:(pname->(pname->Prop))) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_pname_o ((image_pname_pname_o F_14) A_56))) (finite_card_pname A_56)))) of role axiom named fact_71_card__image__le
% A new axiom: (forall (F_14:(pname->(pname->Prop))) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_pname_o ((image_pname_pname_o F_14) A_56))) (finite_card_pname A_56))))
% FOF formula (forall (F_14:(pname->(x_a->Prop))) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_a_o ((image_pname_a_o F_14) A_56))) (finite_card_pname A_56)))) of role axiom named fact_72_card__image__le
% A new axiom: (forall (F_14:(pname->(x_a->Prop))) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_a_o ((image_pname_a_o F_14) A_56))) (finite_card_pname A_56))))
% FOF formula (forall (F_14:(nat->x_a)) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_a ((image_nat_a F_14) A_56))) (finite_card_nat A_56)))) of role axiom named fact_73_card__image__le
% A new axiom: (forall (F_14:(nat->x_a)) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_a ((image_nat_a F_14) A_56))) (finite_card_nat A_56))))
% FOF formula (forall (F_14:(nat->(nat->Prop))) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_nat_o ((image_nat_nat_o F_14) A_56))) (finite_card_nat A_56)))) of role axiom named fact_74_card__image__le
% A new axiom: (forall (F_14:(nat->(nat->Prop))) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_nat_o ((image_nat_nat_o F_14) A_56))) (finite_card_nat A_56))))
% FOF formula (forall (F_14:(nat->(pname->Prop))) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_pname_o ((image_nat_pname_o F_14) A_56))) (finite_card_nat A_56)))) of role axiom named fact_75_card__image__le
% A new axiom: (forall (F_14:(nat->(pname->Prop))) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_pname_o ((image_nat_pname_o F_14) A_56))) (finite_card_nat A_56))))
% FOF formula (forall (F_14:(nat->(x_a->Prop))) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_a_o ((image_nat_a_o F_14) A_56))) (finite_card_nat A_56)))) of role axiom named fact_76_card__image__le
% A new axiom: (forall (F_14:(nat->(x_a->Prop))) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_a_o ((image_nat_a_o F_14) A_56))) (finite_card_nat A_56))))
% FOF formula (forall (F_14:((nat->Prop)->pname)) (A_56:((nat->Prop)->Prop)), ((finite_finite_nat_o A_56)->((ord_less_eq_nat (finite_card_pname ((image_nat_o_pname F_14) A_56))) (finite_card_nat_o A_56)))) of role axiom named fact_77_card__image__le
% A new axiom: (forall (F_14:((nat->Prop)->pname)) (A_56:((nat->Prop)->Prop)), ((finite_finite_nat_o A_56)->((ord_less_eq_nat (finite_card_pname ((image_nat_o_pname F_14) A_56))) (finite_card_nat_o A_56))))
% FOF formula (forall (F_14:((pname->Prop)->pname)) (A_56:((pname->Prop)->Prop)), ((finite297249702name_o A_56)->((ord_less_eq_nat (finite_card_pname ((image_pname_o_pname F_14) A_56))) (finite_card_pname_o A_56)))) of role axiom named fact_78_card__image__le
% A new axiom: (forall (F_14:((pname->Prop)->pname)) (A_56:((pname->Prop)->Prop)), ((finite297249702name_o A_56)->((ord_less_eq_nat (finite_card_pname ((image_pname_o_pname F_14) A_56))) (finite_card_pname_o A_56))))
% FOF formula (forall (F_14:((x_a->Prop)->pname)) (A_56:((x_a->Prop)->Prop)), ((finite_finite_a_o A_56)->((ord_less_eq_nat (finite_card_pname ((image_a_o_pname F_14) A_56))) (finite_card_a_o A_56)))) of role axiom named fact_79_card__image__le
% A new axiom: (forall (F_14:((x_a->Prop)->pname)) (A_56:((x_a->Prop)->Prop)), ((finite_finite_a_o A_56)->((ord_less_eq_nat (finite_card_pname ((image_a_o_pname F_14) A_56))) (finite_card_a_o A_56))))
% FOF formula (forall (A_55:((nat->Prop)->Prop)) (B_37:((nat->Prop)->Prop)), ((finite_finite_nat_o B_37)->(((ord_less_eq_nat_o_o A_55) B_37)->((ord_less_eq_nat (finite_card_nat_o A_55)) (finite_card_nat_o B_37))))) of role axiom named fact_80_card__mono
% A new axiom: (forall (A_55:((nat->Prop)->Prop)) (B_37:((nat->Prop)->Prop)), ((finite_finite_nat_o B_37)->(((ord_less_eq_nat_o_o A_55) B_37)->((ord_less_eq_nat (finite_card_nat_o A_55)) (finite_card_nat_o B_37)))))
% FOF formula (forall (A_55:((pname->Prop)->Prop)) (B_37:((pname->Prop)->Prop)), ((finite297249702name_o B_37)->(((ord_le1205211808me_o_o A_55) B_37)->((ord_less_eq_nat (finite_card_pname_o A_55)) (finite_card_pname_o B_37))))) of role axiom named fact_81_card__mono
% A new axiom: (forall (A_55:((pname->Prop)->Prop)) (B_37:((pname->Prop)->Prop)), ((finite297249702name_o B_37)->(((ord_le1205211808me_o_o A_55) B_37)->((ord_less_eq_nat (finite_card_pname_o A_55)) (finite_card_pname_o B_37)))))
% FOF formula (forall (A_55:((x_a->Prop)->Prop)) (B_37:((x_a->Prop)->Prop)), ((finite_finite_a_o B_37)->(((ord_less_eq_a_o_o A_55) B_37)->((ord_less_eq_nat (finite_card_a_o A_55)) (finite_card_a_o B_37))))) of role axiom named fact_82_card__mono
% A new axiom: (forall (A_55:((x_a->Prop)->Prop)) (B_37:((x_a->Prop)->Prop)), ((finite_finite_a_o B_37)->(((ord_less_eq_a_o_o A_55) B_37)->((ord_less_eq_nat (finite_card_a_o A_55)) (finite_card_a_o B_37)))))
% FOF formula (forall (A_55:(pname->Prop)) (B_37:(pname->Prop)), ((finite_finite_pname B_37)->(((ord_less_eq_pname_o A_55) B_37)->((ord_less_eq_nat (finite_card_pname A_55)) (finite_card_pname B_37))))) of role axiom named fact_83_card__mono
% A new axiom: (forall (A_55:(pname->Prop)) (B_37:(pname->Prop)), ((finite_finite_pname B_37)->(((ord_less_eq_pname_o A_55) B_37)->((ord_less_eq_nat (finite_card_pname A_55)) (finite_card_pname B_37)))))
% FOF formula (forall (A_55:(x_a->Prop)) (B_37:(x_a->Prop)), ((finite_finite_a B_37)->(((ord_less_eq_a_o A_55) B_37)->((ord_less_eq_nat (finite_card_a A_55)) (finite_card_a B_37))))) of role axiom named fact_84_card__mono
% A new axiom: (forall (A_55:(x_a->Prop)) (B_37:(x_a->Prop)), ((finite_finite_a B_37)->(((ord_less_eq_a_o A_55) B_37)->((ord_less_eq_nat (finite_card_a A_55)) (finite_card_a B_37)))))
% FOF formula (forall (A_55:(nat->Prop)) (B_37:(nat->Prop)), ((finite_finite_nat B_37)->(((ord_less_eq_nat_o A_55) B_37)->((ord_less_eq_nat (finite_card_nat A_55)) (finite_card_nat B_37))))) of role axiom named fact_85_card__mono
% A new axiom: (forall (A_55:(nat->Prop)) (B_37:(nat->Prop)), ((finite_finite_nat B_37)->(((ord_less_eq_nat_o A_55) B_37)->((ord_less_eq_nat (finite_card_nat A_55)) (finite_card_nat B_37)))))
% FOF formula (forall (A_54:((nat->Prop)->Prop)) (B_36:((nat->Prop)->Prop)), ((finite_finite_nat_o B_36)->(((ord_less_eq_nat_o_o A_54) B_36)->(((ord_less_eq_nat (finite_card_nat_o B_36)) (finite_card_nat_o A_54))->(((eq ((nat->Prop)->Prop)) A_54) B_36))))) of role axiom named fact_86_card__seteq
% A new axiom: (forall (A_54:((nat->Prop)->Prop)) (B_36:((nat->Prop)->Prop)), ((finite_finite_nat_o B_36)->(((ord_less_eq_nat_o_o A_54) B_36)->(((ord_less_eq_nat (finite_card_nat_o B_36)) (finite_card_nat_o A_54))->(((eq ((nat->Prop)->Prop)) A_54) B_36)))))
% FOF formula (forall (A_54:((pname->Prop)->Prop)) (B_36:((pname->Prop)->Prop)), ((finite297249702name_o B_36)->(((ord_le1205211808me_o_o A_54) B_36)->(((ord_less_eq_nat (finite_card_pname_o B_36)) (finite_card_pname_o A_54))->(((eq ((pname->Prop)->Prop)) A_54) B_36))))) of role axiom named fact_87_card__seteq
% A new axiom: (forall (A_54:((pname->Prop)->Prop)) (B_36:((pname->Prop)->Prop)), ((finite297249702name_o B_36)->(((ord_le1205211808me_o_o A_54) B_36)->(((ord_less_eq_nat (finite_card_pname_o B_36)) (finite_card_pname_o A_54))->(((eq ((pname->Prop)->Prop)) A_54) B_36)))))
% FOF formula (forall (A_54:((x_a->Prop)->Prop)) (B_36:((x_a->Prop)->Prop)), ((finite_finite_a_o B_36)->(((ord_less_eq_a_o_o A_54) B_36)->(((ord_less_eq_nat (finite_card_a_o B_36)) (finite_card_a_o A_54))->(((eq ((x_a->Prop)->Prop)) A_54) B_36))))) of role axiom named fact_88_card__seteq
% A new axiom: (forall (A_54:((x_a->Prop)->Prop)) (B_36:((x_a->Prop)->Prop)), ((finite_finite_a_o B_36)->(((ord_less_eq_a_o_o A_54) B_36)->(((ord_less_eq_nat (finite_card_a_o B_36)) (finite_card_a_o A_54))->(((eq ((x_a->Prop)->Prop)) A_54) B_36)))))
% FOF formula (forall (A_54:(pname->Prop)) (B_36:(pname->Prop)), ((finite_finite_pname B_36)->(((ord_less_eq_pname_o A_54) B_36)->(((ord_less_eq_nat (finite_card_pname B_36)) (finite_card_pname A_54))->(((eq (pname->Prop)) A_54) B_36))))) of role axiom named fact_89_card__seteq
% A new axiom: (forall (A_54:(pname->Prop)) (B_36:(pname->Prop)), ((finite_finite_pname B_36)->(((ord_less_eq_pname_o A_54) B_36)->(((ord_less_eq_nat (finite_card_pname B_36)) (finite_card_pname A_54))->(((eq (pname->Prop)) A_54) B_36)))))
% FOF formula (forall (A_54:(x_a->Prop)) (B_36:(x_a->Prop)), ((finite_finite_a B_36)->(((ord_less_eq_a_o A_54) B_36)->(((ord_less_eq_nat (finite_card_a B_36)) (finite_card_a A_54))->(((eq (x_a->Prop)) A_54) B_36))))) of role axiom named fact_90_card__seteq
% A new axiom: (forall (A_54:(x_a->Prop)) (B_36:(x_a->Prop)), ((finite_finite_a B_36)->(((ord_less_eq_a_o A_54) B_36)->(((ord_less_eq_nat (finite_card_a B_36)) (finite_card_a A_54))->(((eq (x_a->Prop)) A_54) B_36)))))
% FOF formula (forall (A_54:(nat->Prop)) (B_36:(nat->Prop)), ((finite_finite_nat B_36)->(((ord_less_eq_nat_o A_54) B_36)->(((ord_less_eq_nat (finite_card_nat B_36)) (finite_card_nat A_54))->(((eq (nat->Prop)) A_54) B_36))))) of role axiom named fact_91_card__seteq
% A new axiom: (forall (A_54:(nat->Prop)) (B_36:(nat->Prop)), ((finite_finite_nat B_36)->(((ord_less_eq_nat_o A_54) B_36)->(((ord_less_eq_nat (finite_card_nat B_36)) (finite_card_nat A_54))->(((eq (nat->Prop)) A_54) B_36)))))
% FOF formula (forall (X_19:(nat->Prop)) (A_53:((nat->Prop)->Prop)), ((finite_finite_nat_o A_53)->((ord_less_eq_nat (finite_card_nat_o A_53)) (finite_card_nat_o ((insert_nat_o X_19) A_53))))) of role axiom named fact_92_card__insert__le
% A new axiom: (forall (X_19:(nat->Prop)) (A_53:((nat->Prop)->Prop)), ((finite_finite_nat_o A_53)->((ord_less_eq_nat (finite_card_nat_o A_53)) (finite_card_nat_o ((insert_nat_o X_19) A_53)))))
% FOF formula (forall (X_19:(pname->Prop)) (A_53:((pname->Prop)->Prop)), ((finite297249702name_o A_53)->((ord_less_eq_nat (finite_card_pname_o A_53)) (finite_card_pname_o ((insert_pname_o X_19) A_53))))) of role axiom named fact_93_card__insert__le
% A new axiom: (forall (X_19:(pname->Prop)) (A_53:((pname->Prop)->Prop)), ((finite297249702name_o A_53)->((ord_less_eq_nat (finite_card_pname_o A_53)) (finite_card_pname_o ((insert_pname_o X_19) A_53)))))
% FOF formula (forall (X_19:(x_a->Prop)) (A_53:((x_a->Prop)->Prop)), ((finite_finite_a_o A_53)->((ord_less_eq_nat (finite_card_a_o A_53)) (finite_card_a_o ((insert_a_o X_19) A_53))))) of role axiom named fact_94_card__insert__le
% A new axiom: (forall (X_19:(x_a->Prop)) (A_53:((x_a->Prop)->Prop)), ((finite_finite_a_o A_53)->((ord_less_eq_nat (finite_card_a_o A_53)) (finite_card_a_o ((insert_a_o X_19) A_53)))))
% FOF formula (forall (X_19:pname) (A_53:(pname->Prop)), ((finite_finite_pname A_53)->((ord_less_eq_nat (finite_card_pname A_53)) (finite_card_pname ((insert_pname X_19) A_53))))) of role axiom named fact_95_card__insert__le
% A new axiom: (forall (X_19:pname) (A_53:(pname->Prop)), ((finite_finite_pname A_53)->((ord_less_eq_nat (finite_card_pname A_53)) (finite_card_pname ((insert_pname X_19) A_53)))))
% FOF formula (forall (X_19:nat) (A_53:(nat->Prop)), ((finite_finite_nat A_53)->((ord_less_eq_nat (finite_card_nat A_53)) (finite_card_nat ((insert_nat X_19) A_53))))) of role axiom named fact_96_card__insert__le
% A new axiom: (forall (X_19:nat) (A_53:(nat->Prop)), ((finite_finite_nat A_53)->((ord_less_eq_nat (finite_card_nat A_53)) (finite_card_nat ((insert_nat X_19) A_53)))))
% FOF formula (forall (X_19:x_a) (A_53:(x_a->Prop)), ((finite_finite_a A_53)->((ord_less_eq_nat (finite_card_a A_53)) (finite_card_a ((insert_a X_19) A_53))))) of role axiom named fact_97_card__insert__le
% A new axiom: (forall (X_19:x_a) (A_53:(x_a->Prop)), ((finite_finite_a A_53)->((ord_less_eq_nat (finite_card_a A_53)) (finite_card_a ((insert_a X_19) A_53)))))
% FOF formula (forall (X_18:(nat->Prop)) (A_52:((nat->Prop)->Prop)), ((finite_finite_nat_o A_52)->((and (((member_nat_o X_18) A_52)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_18) A_52))) (finite_card_nat_o A_52)))) ((((member_nat_o X_18) A_52)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_18) A_52))) (suc (finite_card_nat_o A_52))))))) of role axiom named fact_98_card__insert__if
% A new axiom: (forall (X_18:(nat->Prop)) (A_52:((nat->Prop)->Prop)), ((finite_finite_nat_o A_52)->((and (((member_nat_o X_18) A_52)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_18) A_52))) (finite_card_nat_o A_52)))) ((((member_nat_o X_18) A_52)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_18) A_52))) (suc (finite_card_nat_o A_52)))))))
% FOF formula (forall (X_18:(pname->Prop)) (A_52:((pname->Prop)->Prop)), ((finite297249702name_o A_52)->((and (((member_pname_o X_18) A_52)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_18) A_52))) (finite_card_pname_o A_52)))) ((((member_pname_o X_18) A_52)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_18) A_52))) (suc (finite_card_pname_o A_52))))))) of role axiom named fact_99_card__insert__if
% A new axiom: (forall (X_18:(pname->Prop)) (A_52:((pname->Prop)->Prop)), ((finite297249702name_o A_52)->((and (((member_pname_o X_18) A_52)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_18) A_52))) (finite_card_pname_o A_52)))) ((((member_pname_o X_18) A_52)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_18) A_52))) (suc (finite_card_pname_o A_52)))))))
% FOF formula (forall (X_18:(x_a->Prop)) (A_52:((x_a->Prop)->Prop)), ((finite_finite_a_o A_52)->((and (((member_a_o X_18) A_52)->(((eq nat) (finite_card_a_o ((insert_a_o X_18) A_52))) (finite_card_a_o A_52)))) ((((member_a_o X_18) A_52)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_18) A_52))) (suc (finite_card_a_o A_52))))))) of role axiom named fact_100_card__insert__if
% A new axiom: (forall (X_18:(x_a->Prop)) (A_52:((x_a->Prop)->Prop)), ((finite_finite_a_o A_52)->((and (((member_a_o X_18) A_52)->(((eq nat) (finite_card_a_o ((insert_a_o X_18) A_52))) (finite_card_a_o A_52)))) ((((member_a_o X_18) A_52)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_18) A_52))) (suc (finite_card_a_o A_52)))))))
% FOF formula (forall (X_18:nat) (A_52:(nat->Prop)), ((finite_finite_nat A_52)->((and (((member_nat X_18) A_52)->(((eq nat) (finite_card_nat ((insert_nat X_18) A_52))) (finite_card_nat A_52)))) ((((member_nat X_18) A_52)->False)->(((eq nat) (finite_card_nat ((insert_nat X_18) A_52))) (suc (finite_card_nat A_52))))))) of role axiom named fact_101_card__insert__if
% A new axiom: (forall (X_18:nat) (A_52:(nat->Prop)), ((finite_finite_nat A_52)->((and (((member_nat X_18) A_52)->(((eq nat) (finite_card_nat ((insert_nat X_18) A_52))) (finite_card_nat A_52)))) ((((member_nat X_18) A_52)->False)->(((eq nat) (finite_card_nat ((insert_nat X_18) A_52))) (suc (finite_card_nat A_52)))))))
% FOF formula (forall (X_18:pname) (A_52:(pname->Prop)), ((finite_finite_pname A_52)->((and (((member_pname X_18) A_52)->(((eq nat) (finite_card_pname ((insert_pname X_18) A_52))) (finite_card_pname A_52)))) ((((member_pname X_18) A_52)->False)->(((eq nat) (finite_card_pname ((insert_pname X_18) A_52))) (suc (finite_card_pname A_52))))))) of role axiom named fact_102_card__insert__if
% A new axiom: (forall (X_18:pname) (A_52:(pname->Prop)), ((finite_finite_pname A_52)->((and (((member_pname X_18) A_52)->(((eq nat) (finite_card_pname ((insert_pname X_18) A_52))) (finite_card_pname A_52)))) ((((member_pname X_18) A_52)->False)->(((eq nat) (finite_card_pname ((insert_pname X_18) A_52))) (suc (finite_card_pname A_52)))))))
% FOF formula (forall (X_18:x_a) (A_52:(x_a->Prop)), ((finite_finite_a A_52)->((and (((member_a X_18) A_52)->(((eq nat) (finite_card_a ((insert_a X_18) A_52))) (finite_card_a A_52)))) ((((member_a X_18) A_52)->False)->(((eq nat) (finite_card_a ((insert_a X_18) A_52))) (suc (finite_card_a A_52))))))) of role axiom named fact_103_card__insert__if
% A new axiom: (forall (X_18:x_a) (A_52:(x_a->Prop)), ((finite_finite_a A_52)->((and (((member_a X_18) A_52)->(((eq nat) (finite_card_a ((insert_a X_18) A_52))) (finite_card_a A_52)))) ((((member_a X_18) A_52)->False)->(((eq nat) (finite_card_a ((insert_a X_18) A_52))) (suc (finite_card_a A_52)))))))
% FOF formula (forall (X_17:(nat->Prop)) (A_51:((nat->Prop)->Prop)), ((finite_finite_nat_o A_51)->((((member_nat_o X_17) A_51)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_17) A_51))) (suc (finite_card_nat_o A_51)))))) of role axiom named fact_104_card__insert__disjoint
% A new axiom: (forall (X_17:(nat->Prop)) (A_51:((nat->Prop)->Prop)), ((finite_finite_nat_o A_51)->((((member_nat_o X_17) A_51)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_17) A_51))) (suc (finite_card_nat_o A_51))))))
% FOF formula (forall (X_17:(pname->Prop)) (A_51:((pname->Prop)->Prop)), ((finite297249702name_o A_51)->((((member_pname_o X_17) A_51)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_17) A_51))) (suc (finite_card_pname_o A_51)))))) of role axiom named fact_105_card__insert__disjoint
% A new axiom: (forall (X_17:(pname->Prop)) (A_51:((pname->Prop)->Prop)), ((finite297249702name_o A_51)->((((member_pname_o X_17) A_51)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_17) A_51))) (suc (finite_card_pname_o A_51))))))
% FOF formula (forall (X_17:(x_a->Prop)) (A_51:((x_a->Prop)->Prop)), ((finite_finite_a_o A_51)->((((member_a_o X_17) A_51)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_17) A_51))) (suc (finite_card_a_o A_51)))))) of role axiom named fact_106_card__insert__disjoint
% A new axiom: (forall (X_17:(x_a->Prop)) (A_51:((x_a->Prop)->Prop)), ((finite_finite_a_o A_51)->((((member_a_o X_17) A_51)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_17) A_51))) (suc (finite_card_a_o A_51))))))
% FOF formula (forall (X_17:nat) (A_51:(nat->Prop)), ((finite_finite_nat A_51)->((((member_nat X_17) A_51)->False)->(((eq nat) (finite_card_nat ((insert_nat X_17) A_51))) (suc (finite_card_nat A_51)))))) of role axiom named fact_107_card__insert__disjoint
% A new axiom: (forall (X_17:nat) (A_51:(nat->Prop)), ((finite_finite_nat A_51)->((((member_nat X_17) A_51)->False)->(((eq nat) (finite_card_nat ((insert_nat X_17) A_51))) (suc (finite_card_nat A_51))))))
% FOF formula (forall (X_17:pname) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->((((member_pname X_17) A_51)->False)->(((eq nat) (finite_card_pname ((insert_pname X_17) A_51))) (suc (finite_card_pname A_51)))))) of role axiom named fact_108_card__insert__disjoint
% A new axiom: (forall (X_17:pname) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->((((member_pname X_17) A_51)->False)->(((eq nat) (finite_card_pname ((insert_pname X_17) A_51))) (suc (finite_card_pname A_51))))))
% FOF formula (forall (X_17:x_a) (A_51:(x_a->Prop)), ((finite_finite_a A_51)->((((member_a X_17) A_51)->False)->(((eq nat) (finite_card_a ((insert_a X_17) A_51))) (suc (finite_card_a A_51)))))) of role axiom named fact_109_card__insert__disjoint
% A new axiom: (forall (X_17:x_a) (A_51:(x_a->Prop)), ((finite_finite_a A_51)->((((member_a X_17) A_51)->False)->(((eq nat) (finite_card_a ((insert_a X_17) A_51))) (suc (finite_card_a A_51))))))
% FOF formula (forall (Q_1:((nat->Prop)->Prop)) (P_4:((nat->Prop)->Prop)), (((or (finite_finite_nat_o (collect_nat_o P_4))) (finite_finite_nat_o (collect_nat_o Q_1)))->(finite_finite_nat_o (collect_nat_o (fun (X:(nat->Prop))=> ((and (P_4 X)) (Q_1 X))))))) of role axiom named fact_110_finite__Collect__conjI
% A new axiom: (forall (Q_1:((nat->Prop)->Prop)) (P_4:((nat->Prop)->Prop)), (((or (finite_finite_nat_o (collect_nat_o P_4))) (finite_finite_nat_o (collect_nat_o Q_1)))->(finite_finite_nat_o (collect_nat_o (fun (X:(nat->Prop))=> ((and (P_4 X)) (Q_1 X)))))))
% FOF formula (forall (Q_1:((pname->Prop)->Prop)) (P_4:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_4))) (finite297249702name_o (collect_pname_o Q_1)))->(finite297249702name_o (collect_pname_o (fun (X:(pname->Prop))=> ((and (P_4 X)) (Q_1 X))))))) of role axiom named fact_111_finite__Collect__conjI
% A new axiom: (forall (Q_1:((pname->Prop)->Prop)) (P_4:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_4))) (finite297249702name_o (collect_pname_o Q_1)))->(finite297249702name_o (collect_pname_o (fun (X:(pname->Prop))=> ((and (P_4 X)) (Q_1 X)))))))
% FOF formula (forall (Q_1:((x_a->Prop)->Prop)) (P_4:((x_a->Prop)->Prop)), (((or (finite_finite_a_o (collect_a_o P_4))) (finite_finite_a_o (collect_a_o Q_1)))->(finite_finite_a_o (collect_a_o (fun (X:(x_a->Prop))=> ((and (P_4 X)) (Q_1 X))))))) of role axiom named fact_112_finite__Collect__conjI
% A new axiom: (forall (Q_1:((x_a->Prop)->Prop)) (P_4:((x_a->Prop)->Prop)), (((or (finite_finite_a_o (collect_a_o P_4))) (finite_finite_a_o (collect_a_o Q_1)))->(finite_finite_a_o (collect_a_o (fun (X:(x_a->Prop))=> ((and (P_4 X)) (Q_1 X)))))))
% FOF formula (forall (Q_1:(x_a->Prop)) (P_4:(x_a->Prop)), (((or (finite_finite_a (collect_a P_4))) (finite_finite_a (collect_a Q_1)))->(finite_finite_a (collect_a (fun (X:x_a)=> ((and (P_4 X)) (Q_1 X))))))) of role axiom named fact_113_finite__Collect__conjI
% A new axiom: (forall (Q_1:(x_a->Prop)) (P_4:(x_a->Prop)), (((or (finite_finite_a (collect_a P_4))) (finite_finite_a (collect_a Q_1)))->(finite_finite_a (collect_a (fun (X:x_a)=> ((and (P_4 X)) (Q_1 X)))))))
% FOF formula (forall (Q_1:(pname->Prop)) (P_4:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_4))) (finite_finite_pname (collect_pname Q_1)))->(finite_finite_pname (collect_pname (fun (X:pname)=> ((and (P_4 X)) (Q_1 X))))))) of role axiom named fact_114_finite__Collect__conjI
% A new axiom: (forall (Q_1:(pname->Prop)) (P_4:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_4))) (finite_finite_pname (collect_pname Q_1)))->(finite_finite_pname (collect_pname (fun (X:pname)=> ((and (P_4 X)) (Q_1 X)))))))
% FOF formula (forall (Q_1:(nat->Prop)) (P_4:(nat->Prop)), (((or (finite_finite_nat (collect_nat P_4))) (finite_finite_nat (collect_nat Q_1)))->(finite_finite_nat (collect_nat (fun (X:nat)=> ((and (P_4 X)) (Q_1 X))))))) of role axiom named fact_115_finite__Collect__conjI
% A new axiom: (forall (Q_1:(nat->Prop)) (P_4:(nat->Prop)), (((or (finite_finite_nat (collect_nat P_4))) (finite_finite_nat (collect_nat Q_1)))->(finite_finite_nat (collect_nat (fun (X:nat)=> ((and (P_4 X)) (Q_1 X)))))))
% FOF formula (forall (N_1:nat) (M_2:nat), (((ord_less_eq_nat N_1) M_2)->(((eq nat) ((minus_minus_nat (suc M_2)) N_1)) (suc ((minus_minus_nat M_2) N_1))))) of role axiom named fact_116_Suc__diff__le
% A new axiom: (forall (N_1:nat) (M_2:nat), (((ord_less_eq_nat N_1) M_2)->(((eq nat) ((minus_minus_nat (suc M_2)) N_1)) (suc ((minus_minus_nat M_2) N_1)))))
% FOF formula (forall (K:nat), (finite_finite_nat (collect_nat (fun (N_2:nat)=> ((ord_less_eq_nat N_2) K))))) of role axiom named fact_117_finite__Collect__le__nat
% A new axiom: (forall (K:nat), (finite_finite_nat (collect_nat (fun (N_2:nat)=> ((ord_less_eq_nat N_2) K)))))
% FOF formula (forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_eq_nat I_1) N_1))))) (suc N_1))) of role axiom named fact_118_card__Collect__le__nat
% A new axiom: (forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_eq_nat I_1) N_1))))) (suc N_1)))
% FOF formula (forall (X_16:nat) (Y_3:nat), ((((eq nat) (suc X_16)) (suc Y_3))->(((eq nat) X_16) Y_3))) of role axiom named fact_119_Suc__inject
% A new axiom: (forall (X_16:nat) (Y_3:nat), ((((eq nat) (suc X_16)) (suc Y_3))->(((eq nat) X_16) Y_3)))
% 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_120_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 (N_1:nat), (not (((eq nat) (suc N_1)) N_1))) of role axiom named fact_121_Suc__n__not__n
% A new axiom: (forall (N_1:nat), (not (((eq nat) (suc N_1)) N_1)))
% FOF formula (forall (N_1:nat), (not (((eq nat) N_1) (suc N_1)))) of role axiom named fact_122_n__not__Suc__n
% A new axiom: (forall (N_1:nat), (not (((eq nat) N_1) (suc N_1))))
% FOF formula (forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->(((ord_less_eq_nat N_1) M_2)->(((eq nat) M_2) N_1)))) of role axiom named fact_123_le__antisym
% A new axiom: (forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->(((ord_less_eq_nat N_1) M_2)->(((eq nat) M_2) N_1))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat _TPTP_I) K)))) of role axiom named fact_124_le__trans
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat _TPTP_I) K))))
% FOF formula (forall (M_2:nat) (N_1:nat), ((((eq nat) M_2) N_1)->((ord_less_eq_nat M_2) N_1))) of role axiom named fact_125_eq__imp__le
% A new axiom: (forall (M_2:nat) (N_1:nat), ((((eq nat) M_2) N_1)->((ord_less_eq_nat M_2) N_1)))
% FOF formula (forall (M_2:nat) (N_1:nat), ((or ((ord_less_eq_nat M_2) N_1)) ((ord_less_eq_nat N_1) M_2))) of role axiom named fact_126_nat__le__linear
% A new axiom: (forall (M_2:nat) (N_1:nat), ((or ((ord_less_eq_nat M_2) N_1)) ((ord_less_eq_nat N_1) M_2)))
% FOF formula (forall (N_1:nat), ((ord_less_eq_nat N_1) N_1)) of role axiom named fact_127_le__refl
% A new axiom: (forall (N_1:nat), ((ord_less_eq_nat N_1) N_1))
% FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat _TPTP_I) J)) K)) ((minus_minus_nat ((minus_minus_nat _TPTP_I) K)) J))) of role axiom named fact_128_diff__commute
% A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat _TPTP_I) J)) K)) ((minus_minus_nat ((minus_minus_nat _TPTP_I) K)) J)))
% FOF formula (forall (P_3:(pname->Prop)) (Q:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X:pname)=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_pname (collect_pname P_3))) (finite_finite_pname (collect_pname Q))))) of role axiom named fact_129_finite__Collect__disjI
% A new axiom: (forall (P_3:(pname->Prop)) (Q:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X:pname)=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_pname (collect_pname P_3))) (finite_finite_pname (collect_pname Q)))))
% FOF formula (forall (P_3:((nat->Prop)->Prop)) (Q:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o (collect_nat_o (fun (X:(nat->Prop))=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_nat_o (collect_nat_o P_3))) (finite_finite_nat_o (collect_nat_o Q))))) of role axiom named fact_130_finite__Collect__disjI
% A new axiom: (forall (P_3:((nat->Prop)->Prop)) (Q:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o (collect_nat_o (fun (X:(nat->Prop))=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_nat_o (collect_nat_o P_3))) (finite_finite_nat_o (collect_nat_o Q)))))
% FOF formula (forall (P_3:((pname->Prop)->Prop)) (Q:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X:(pname->Prop))=> ((or (P_3 X)) (Q X)))))) ((and (finite297249702name_o (collect_pname_o P_3))) (finite297249702name_o (collect_pname_o Q))))) of role axiom named fact_131_finite__Collect__disjI
% A new axiom: (forall (P_3:((pname->Prop)->Prop)) (Q:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X:(pname->Prop))=> ((or (P_3 X)) (Q X)))))) ((and (finite297249702name_o (collect_pname_o P_3))) (finite297249702name_o (collect_pname_o Q)))))
% FOF formula (forall (P_3:((x_a->Prop)->Prop)) (Q:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o (collect_a_o (fun (X:(x_a->Prop))=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_a_o (collect_a_o P_3))) (finite_finite_a_o (collect_a_o Q))))) of role axiom named fact_132_finite__Collect__disjI
% A new axiom: (forall (P_3:((x_a->Prop)->Prop)) (Q:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o (collect_a_o (fun (X:(x_a->Prop))=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_a_o (collect_a_o P_3))) (finite_finite_a_o (collect_a_o Q)))))
% FOF formula (forall (P_3:(nat->Prop)) (Q:(nat->Prop)), ((iff (finite_finite_nat (collect_nat (fun (X:nat)=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_nat (collect_nat P_3))) (finite_finite_nat (collect_nat Q))))) of role axiom named fact_133_finite__Collect__disjI
% A new axiom: (forall (P_3:(nat->Prop)) (Q:(nat->Prop)), ((iff (finite_finite_nat (collect_nat (fun (X:nat)=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_nat (collect_nat P_3))) (finite_finite_nat (collect_nat Q)))))
% FOF formula (forall (P_3:(x_a->Prop)) (Q:(x_a->Prop)), ((iff (finite_finite_a (collect_a (fun (X:x_a)=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_a (collect_a P_3))) (finite_finite_a (collect_a Q))))) of role axiom named fact_134_finite__Collect__disjI
% A new axiom: (forall (P_3:(x_a->Prop)) (Q:(x_a->Prop)), ((iff (finite_finite_a (collect_a (fun (X:x_a)=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_a (collect_a P_3))) (finite_finite_a (collect_a Q)))))
% FOF formula (forall (A_50:nat) (A_49:(nat->Prop)), ((iff (finite_finite_nat ((insert_nat A_50) A_49))) (finite_finite_nat A_49))) of role axiom named fact_135_finite__insert
% A new axiom: (forall (A_50:nat) (A_49:(nat->Prop)), ((iff (finite_finite_nat ((insert_nat A_50) A_49))) (finite_finite_nat A_49)))
% FOF formula (forall (A_50:pname) (A_49:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_50) A_49))) (finite_finite_pname A_49))) of role axiom named fact_136_finite__insert
% A new axiom: (forall (A_50:pname) (A_49:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_50) A_49))) (finite_finite_pname A_49)))
% FOF formula (forall (A_50:x_a) (A_49:(x_a->Prop)), ((iff (finite_finite_a ((insert_a A_50) A_49))) (finite_finite_a A_49))) of role axiom named fact_137_finite__insert
% A new axiom: (forall (A_50:x_a) (A_49:(x_a->Prop)), ((iff (finite_finite_a ((insert_a A_50) A_49))) (finite_finite_a A_49)))
% FOF formula (forall (A_50:(nat->Prop)) (A_49:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o ((insert_nat_o A_50) A_49))) (finite_finite_nat_o A_49))) of role axiom named fact_138_finite__insert
% A new axiom: (forall (A_50:(nat->Prop)) (A_49:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o ((insert_nat_o A_50) A_49))) (finite_finite_nat_o A_49)))
% FOF formula (forall (A_50:(pname->Prop)) (A_49:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_50) A_49))) (finite297249702name_o A_49))) of role axiom named fact_139_finite__insert
% A new axiom: (forall (A_50:(pname->Prop)) (A_49:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_50) A_49))) (finite297249702name_o A_49)))
% FOF formula (forall (A_50:(x_a->Prop)) (A_49:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o ((insert_a_o A_50) A_49))) (finite_finite_a_o A_49))) of role axiom named fact_140_finite__insert
% A new axiom: (forall (A_50:(x_a->Prop)) (A_49:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o ((insert_a_o A_50) A_49))) (finite_finite_a_o A_49)))
% FOF formula (forall (A_48:((nat->Prop)->Prop)) (B_35:((nat->Prop)->Prop)), (((ord_less_eq_nat_o_o A_48) B_35)->((finite_finite_nat_o B_35)->(finite_finite_nat_o A_48)))) of role axiom named fact_141_finite__subset
% A new axiom: (forall (A_48:((nat->Prop)->Prop)) (B_35:((nat->Prop)->Prop)), (((ord_less_eq_nat_o_o A_48) B_35)->((finite_finite_nat_o B_35)->(finite_finite_nat_o A_48))))
% FOF formula (forall (A_48:((pname->Prop)->Prop)) (B_35:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_48) B_35)->((finite297249702name_o B_35)->(finite297249702name_o A_48)))) of role axiom named fact_142_finite__subset
% A new axiom: (forall (A_48:((pname->Prop)->Prop)) (B_35:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_48) B_35)->((finite297249702name_o B_35)->(finite297249702name_o A_48))))
% FOF formula (forall (A_48:(x_a->Prop)) (B_35:(x_a->Prop)), (((ord_less_eq_a_o A_48) B_35)->((finite_finite_a B_35)->(finite_finite_a A_48)))) of role axiom named fact_143_finite__subset
% A new axiom: (forall (A_48:(x_a->Prop)) (B_35:(x_a->Prop)), (((ord_less_eq_a_o A_48) B_35)->((finite_finite_a B_35)->(finite_finite_a A_48))))
% FOF formula (forall (A_48:((x_a->Prop)->Prop)) (B_35:((x_a->Prop)->Prop)), (((ord_less_eq_a_o_o A_48) B_35)->((finite_finite_a_o B_35)->(finite_finite_a_o A_48)))) of role axiom named fact_144_finite__subset
% A new axiom: (forall (A_48:((x_a->Prop)->Prop)) (B_35:((x_a->Prop)->Prop)), (((ord_less_eq_a_o_o A_48) B_35)->((finite_finite_a_o B_35)->(finite_finite_a_o A_48))))
% FOF formula (forall (A_48:(nat->Prop)) (B_35:(nat->Prop)), (((ord_less_eq_nat_o A_48) B_35)->((finite_finite_nat B_35)->(finite_finite_nat A_48)))) of role axiom named fact_145_finite__subset
% A new axiom: (forall (A_48:(nat->Prop)) (B_35:(nat->Prop)), (((ord_less_eq_nat_o A_48) B_35)->((finite_finite_nat B_35)->(finite_finite_nat A_48))))
% FOF formula (forall (A_48:(pname->Prop)) (B_35:(pname->Prop)), (((ord_less_eq_pname_o A_48) B_35)->((finite_finite_pname B_35)->(finite_finite_pname A_48)))) of role axiom named fact_146_finite__subset
% A new axiom: (forall (A_48:(pname->Prop)) (B_35:(pname->Prop)), (((ord_less_eq_pname_o A_48) B_35)->((finite_finite_pname B_35)->(finite_finite_pname A_48))))
% FOF formula (forall (A_47:((nat->Prop)->Prop)) (B_34:((nat->Prop)->Prop)), ((finite_finite_nat_o B_34)->(((ord_less_eq_nat_o_o A_47) B_34)->(finite_finite_nat_o A_47)))) of role axiom named fact_147_rev__finite__subset
% A new axiom: (forall (A_47:((nat->Prop)->Prop)) (B_34:((nat->Prop)->Prop)), ((finite_finite_nat_o B_34)->(((ord_less_eq_nat_o_o A_47) B_34)->(finite_finite_nat_o A_47))))
% FOF formula (forall (A_47:((pname->Prop)->Prop)) (B_34:((pname->Prop)->Prop)), ((finite297249702name_o B_34)->(((ord_le1205211808me_o_o A_47) B_34)->(finite297249702name_o A_47)))) of role axiom named fact_148_rev__finite__subset
% A new axiom: (forall (A_47:((pname->Prop)->Prop)) (B_34:((pname->Prop)->Prop)), ((finite297249702name_o B_34)->(((ord_le1205211808me_o_o A_47) B_34)->(finite297249702name_o A_47))))
% FOF formula (forall (A_47:(x_a->Prop)) (B_34:(x_a->Prop)), ((finite_finite_a B_34)->(((ord_less_eq_a_o A_47) B_34)->(finite_finite_a A_47)))) of role axiom named fact_149_rev__finite__subset
% A new axiom: (forall (A_47:(x_a->Prop)) (B_34:(x_a->Prop)), ((finite_finite_a B_34)->(((ord_less_eq_a_o A_47) B_34)->(finite_finite_a A_47))))
% FOF formula (forall (A_47:((x_a->Prop)->Prop)) (B_34:((x_a->Prop)->Prop)), ((finite_finite_a_o B_34)->(((ord_less_eq_a_o_o A_47) B_34)->(finite_finite_a_o A_47)))) of role axiom named fact_150_rev__finite__subset
% A new axiom: (forall (A_47:((x_a->Prop)->Prop)) (B_34:((x_a->Prop)->Prop)), ((finite_finite_a_o B_34)->(((ord_less_eq_a_o_o A_47) B_34)->(finite_finite_a_o A_47))))
% FOF formula (forall (A_47:(nat->Prop)) (B_34:(nat->Prop)), ((finite_finite_nat B_34)->(((ord_less_eq_nat_o A_47) B_34)->(finite_finite_nat A_47)))) of role axiom named fact_151_rev__finite__subset
% A new axiom: (forall (A_47:(nat->Prop)) (B_34:(nat->Prop)), ((finite_finite_nat B_34)->(((ord_less_eq_nat_o A_47) B_34)->(finite_finite_nat A_47))))
% FOF formula (forall (A_47:(pname->Prop)) (B_34:(pname->Prop)), ((finite_finite_pname B_34)->(((ord_less_eq_pname_o A_47) B_34)->(finite_finite_pname A_47)))) of role axiom named fact_152_rev__finite__subset
% A new axiom: (forall (A_47:(pname->Prop)) (B_34:(pname->Prop)), ((finite_finite_pname B_34)->(((ord_less_eq_pname_o A_47) B_34)->(finite_finite_pname A_47))))
% FOF formula (forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat (suc M_2)) N_1)->((ord_less_eq_nat M_2) N_1))) of role axiom named fact_153_Suc__leD
% A new axiom: (forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat (suc M_2)) N_1)->((ord_less_eq_nat M_2) N_1)))
% FOF formula (forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) (suc N_1))->((((ord_less_eq_nat M_2) N_1)->False)->(((eq nat) M_2) (suc N_1))))) of role axiom named fact_154_le__SucE
% A new axiom: (forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) (suc N_1))->((((ord_less_eq_nat M_2) N_1)->False)->(((eq nat) M_2) (suc N_1)))))
% FOF formula (forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->((ord_less_eq_nat M_2) (suc N_1)))) of role axiom named fact_155_le__SucI
% A new axiom: (forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->((ord_less_eq_nat M_2) (suc N_1))))
% FOF formula (forall (N_1:nat) (M_2:nat), ((iff ((ord_less_eq_nat (suc N_1)) (suc M_2))) ((ord_less_eq_nat N_1) M_2))) of role axiom named fact_156_Suc__le__mono
% A new axiom: (forall (N_1:nat) (M_2:nat), ((iff ((ord_less_eq_nat (suc N_1)) (suc M_2))) ((ord_less_eq_nat N_1) M_2)))
% FOF formula (forall (M_2:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_2) (suc N_1))) ((or ((ord_less_eq_nat M_2) N_1)) (((eq nat) M_2) (suc N_1))))) of role axiom named fact_157_le__Suc__eq
% A new axiom: (forall (M_2:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_2) (suc N_1))) ((or ((ord_less_eq_nat M_2) N_1)) (((eq nat) M_2) (suc N_1)))))
% FOF formula (forall (M_2:nat) (N_1:nat), ((iff (((ord_less_eq_nat M_2) N_1)->False)) ((ord_less_eq_nat (suc N_1)) M_2))) of role axiom named fact_158_not__less__eq__eq
% A new axiom: (forall (M_2:nat) (N_1:nat), ((iff (((ord_less_eq_nat M_2) N_1)->False)) ((ord_less_eq_nat (suc N_1)) M_2)))
% FOF formula (forall (N_1:nat), (((ord_less_eq_nat (suc N_1)) N_1)->False)) of role axiom named fact_159_Suc__n__not__le__n
% A new axiom: (forall (N_1:nat), (((ord_less_eq_nat (suc N_1)) N_1)->False))
% FOF formula (forall (M_2:nat) (N_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M_2)) N_1)) (suc K))) ((minus_minus_nat ((minus_minus_nat M_2) N_1)) K))) of role axiom named fact_160_Suc__diff__diff
% A new axiom: (forall (M_2:nat) (N_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M_2)) N_1)) (suc K))) ((minus_minus_nat ((minus_minus_nat M_2) N_1)) K)))
% FOF formula (forall (M_2:nat) (N_1:nat), (((eq nat) ((minus_minus_nat (suc M_2)) (suc N_1))) ((minus_minus_nat M_2) N_1))) of role axiom named fact_161_diff__Suc__Suc
% A new axiom: (forall (M_2:nat) (N_1:nat), (((eq nat) ((minus_minus_nat (suc M_2)) (suc N_1))) ((minus_minus_nat M_2) N_1)))
% FOF formula (forall (N_1:nat) (K:nat) (M_2:nat), (((ord_less_eq_nat K) M_2)->(((ord_less_eq_nat K) N_1)->((iff ((ord_less_eq_nat ((minus_minus_nat M_2) K)) ((minus_minus_nat N_1) K))) ((ord_less_eq_nat M_2) N_1))))) of role axiom named fact_162_le__diff__iff
% A new axiom: (forall (N_1:nat) (K:nat) (M_2:nat), (((ord_less_eq_nat K) M_2)->(((ord_less_eq_nat K) N_1)->((iff ((ord_less_eq_nat ((minus_minus_nat M_2) K)) ((minus_minus_nat N_1) K))) ((ord_less_eq_nat M_2) N_1)))))
% FOF formula (forall (N_1:nat) (K:nat) (M_2:nat), (((ord_less_eq_nat K) M_2)->(((ord_less_eq_nat K) N_1)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M_2) K)) ((minus_minus_nat N_1) K))) ((minus_minus_nat M_2) N_1))))) of role axiom named fact_163_Nat_Odiff__diff__eq
% A new axiom: (forall (N_1:nat) (K:nat) (M_2:nat), (((ord_less_eq_nat K) M_2)->(((ord_less_eq_nat K) N_1)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M_2) K)) ((minus_minus_nat N_1) K))) ((minus_minus_nat M_2) N_1)))))
% FOF formula (forall (N_1:nat) (K:nat) (M_2:nat), (((ord_less_eq_nat K) M_2)->(((ord_less_eq_nat K) N_1)->((iff (((eq nat) ((minus_minus_nat M_2) K)) ((minus_minus_nat N_1) K))) (((eq nat) M_2) N_1))))) of role axiom named fact_164_eq__diff__iff
% A new axiom: (forall (N_1:nat) (K:nat) (M_2:nat), (((ord_less_eq_nat K) M_2)->(((ord_less_eq_nat K) N_1)->((iff (((eq nat) ((minus_minus_nat M_2) K)) ((minus_minus_nat N_1) K))) (((eq nat) M_2) N_1)))))
% FOF formula (forall (_TPTP_I:nat) (N_1:nat), (((ord_less_eq_nat _TPTP_I) N_1)->(((eq nat) ((minus_minus_nat N_1) ((minus_minus_nat N_1) _TPTP_I))) _TPTP_I))) of role axiom named fact_165_diff__diff__cancel
% A new axiom: (forall (_TPTP_I:nat) (N_1:nat), (((ord_less_eq_nat _TPTP_I) N_1)->(((eq nat) ((minus_minus_nat N_1) ((minus_minus_nat N_1) _TPTP_I))) _TPTP_I)))
% FOF formula (forall (L:nat) (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->((ord_less_eq_nat ((minus_minus_nat M_2) L)) ((minus_minus_nat N_1) L)))) of role axiom named fact_166_diff__le__mono
% A new axiom: (forall (L:nat) (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->((ord_less_eq_nat ((minus_minus_nat M_2) L)) ((minus_minus_nat N_1) L))))
% FOF formula (forall (L:nat) (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->((ord_less_eq_nat ((minus_minus_nat L) N_1)) ((minus_minus_nat L) M_2)))) of role axiom named fact_167_diff__le__mono2
% A new axiom: (forall (L:nat) (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->((ord_less_eq_nat ((minus_minus_nat L) N_1)) ((minus_minus_nat L) M_2))))
% FOF formula (forall (M_2:nat) (N_1:nat), ((ord_less_eq_nat ((minus_minus_nat M_2) N_1)) M_2)) of role axiom named fact_168_diff__le__self
% A new axiom: (forall (M_2:nat) (N_1:nat), ((ord_less_eq_nat ((minus_minus_nat M_2) N_1)) M_2))
% FOF formula (forall (B_33:(x_a->Prop)) (F_13:(pname->x_a)) (A_46:(pname->Prop)), ((finite_finite_pname A_46)->(((ord_less_eq_a_o B_33) ((image_pname_a F_13) A_46))->(finite_finite_a B_33)))) of role axiom named fact_169_finite__surj
% A new axiom: (forall (B_33:(x_a->Prop)) (F_13:(pname->x_a)) (A_46:(pname->Prop)), ((finite_finite_pname A_46)->(((ord_less_eq_a_o B_33) ((image_pname_a F_13) A_46))->(finite_finite_a B_33))))
% FOF formula (forall (F_12:(pname->x_a)) (A_45:(pname->Prop)) (B_32:(x_a->Prop)), ((finite_finite_a B_32)->(((ord_less_eq_a_o B_32) ((image_pname_a F_12) A_45))->((ex (pname->Prop)) (fun (C_3:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_3) A_45)) (finite_finite_pname C_3))) (((eq (x_a->Prop)) B_32) ((image_pname_a F_12) C_3)))))))) of role axiom named fact_170_finite__subset__image
% A new axiom: (forall (F_12:(pname->x_a)) (A_45:(pname->Prop)) (B_32:(x_a->Prop)), ((finite_finite_a B_32)->(((ord_less_eq_a_o B_32) ((image_pname_a F_12) A_45))->((ex (pname->Prop)) (fun (C_3:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_3) A_45)) (finite_finite_pname C_3))) (((eq (x_a->Prop)) B_32) ((image_pname_a F_12) C_3))))))))
% FOF formula (forall (N_4:nat) (N_3:nat) (F_11:(nat->(nat->Prop))), ((forall (N_2:nat), ((ord_less_eq_nat_o (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat_o (F_11 N_4)) (F_11 N_3))))) of role axiom named fact_171_lift__Suc__mono__le
% A new axiom: (forall (N_4:nat) (N_3:nat) (F_11:(nat->(nat->Prop))), ((forall (N_2:nat), ((ord_less_eq_nat_o (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat_o (F_11 N_4)) (F_11 N_3)))))
% FOF formula (forall (N_4:nat) (N_3:nat) (F_11:(nat->(pname->Prop))), ((forall (N_2:nat), ((ord_less_eq_pname_o (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_pname_o (F_11 N_4)) (F_11 N_3))))) of role axiom named fact_172_lift__Suc__mono__le
% A new axiom: (forall (N_4:nat) (N_3:nat) (F_11:(nat->(pname->Prop))), ((forall (N_2:nat), ((ord_less_eq_pname_o (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_pname_o (F_11 N_4)) (F_11 N_3)))))
% FOF formula (forall (N_4:nat) (N_3:nat) (F_11:(nat->nat)), ((forall (N_2:nat), ((ord_less_eq_nat (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat (F_11 N_4)) (F_11 N_3))))) of role axiom named fact_173_lift__Suc__mono__le
% A new axiom: (forall (N_4:nat) (N_3:nat) (F_11:(nat->nat)), ((forall (N_2:nat), ((ord_less_eq_nat (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat (F_11 N_4)) (F_11 N_3)))))
% FOF formula (forall (N_4:nat) (N_3:nat) (F_11:(nat->(x_a->Prop))), ((forall (N_2:nat), ((ord_less_eq_a_o (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_a_o (F_11 N_4)) (F_11 N_3))))) of role axiom named fact_174_lift__Suc__mono__le
% A new axiom: (forall (N_4:nat) (N_3:nat) (F_11:(nat->(x_a->Prop))), ((forall (N_2:nat), ((ord_less_eq_a_o (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_a_o (F_11 N_4)) (F_11 N_3)))))
% FOF formula (forall (F_10:(pname->x_a)) (A_43:(pname->Prop)), (((finite_finite_pname A_43)->False)->((finite_finite_a ((image_pname_a F_10) A_43))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_43)) ((finite_finite_pname (collect_pname (fun (A_44:pname)=> ((and ((member_pname A_44) A_43)) (((eq x_a) (F_10 A_44)) (F_10 X))))))->False))))))) of role axiom named fact_175_pigeonhole__infinite
% A new axiom: (forall (F_10:(pname->x_a)) (A_43:(pname->Prop)), (((finite_finite_pname A_43)->False)->((finite_finite_a ((image_pname_a F_10) A_43))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_43)) ((finite_finite_pname (collect_pname (fun (A_44:pname)=> ((and ((member_pname A_44) A_43)) (((eq x_a) (F_10 A_44)) (F_10 X))))))->False)))))))
% FOF formula (forall (A_42:(pname->Prop)) (B_31:x_a) (F_9:(pname->x_a)) (X_15:pname), ((((eq x_a) B_31) (F_9 X_15))->(((member_pname X_15) A_42)->((member_a B_31) ((image_pname_a F_9) A_42))))) of role axiom named fact_176_image__eqI
% A new axiom: (forall (A_42:(pname->Prop)) (B_31:x_a) (F_9:(pname->x_a)) (X_15:pname), ((((eq x_a) B_31) (F_9 X_15))->(((member_pname X_15) A_42)->((member_a B_31) ((image_pname_a F_9) A_42)))))
% FOF formula (forall (A_41:(nat->Prop)) (B_30:(nat->Prop)), (((ord_less_eq_nat_o A_41) B_30)->(((ord_less_eq_nat_o B_30) A_41)->(((eq (nat->Prop)) A_41) B_30)))) of role axiom named fact_177_equalityI
% A new axiom: (forall (A_41:(nat->Prop)) (B_30:(nat->Prop)), (((ord_less_eq_nat_o A_41) B_30)->(((ord_less_eq_nat_o B_30) A_41)->(((eq (nat->Prop)) A_41) B_30))))
% FOF formula (forall (A_41:(pname->Prop)) (B_30:(pname->Prop)), (((ord_less_eq_pname_o A_41) B_30)->(((ord_less_eq_pname_o B_30) A_41)->(((eq (pname->Prop)) A_41) B_30)))) of role axiom named fact_178_equalityI
% A new axiom: (forall (A_41:(pname->Prop)) (B_30:(pname->Prop)), (((ord_less_eq_pname_o A_41) B_30)->(((ord_less_eq_pname_o B_30) A_41)->(((eq (pname->Prop)) A_41) B_30))))
% FOF formula (forall (A_41:(x_a->Prop)) (B_30:(x_a->Prop)), (((ord_less_eq_a_o A_41) B_30)->(((ord_less_eq_a_o B_30) A_41)->(((eq (x_a->Prop)) A_41) B_30)))) of role axiom named fact_179_equalityI
% A new axiom: (forall (A_41:(x_a->Prop)) (B_30:(x_a->Prop)), (((ord_less_eq_a_o A_41) B_30)->(((ord_less_eq_a_o B_30) A_41)->(((eq (x_a->Prop)) A_41) B_30))))
% FOF formula (forall (C_2:nat) (A_40:(nat->Prop)) (B_29:(nat->Prop)), (((ord_less_eq_nat_o A_40) B_29)->(((member_nat C_2) A_40)->((member_nat C_2) B_29)))) of role axiom named fact_180_subsetD
% A new axiom: (forall (C_2:nat) (A_40:(nat->Prop)) (B_29:(nat->Prop)), (((ord_less_eq_nat_o A_40) B_29)->(((member_nat C_2) A_40)->((member_nat C_2) B_29))))
% FOF formula (forall (C_2:x_a) (A_40:(x_a->Prop)) (B_29:(x_a->Prop)), (((ord_less_eq_a_o A_40) B_29)->(((member_a C_2) A_40)->((member_a C_2) B_29)))) of role axiom named fact_181_subsetD
% A new axiom: (forall (C_2:x_a) (A_40:(x_a->Prop)) (B_29:(x_a->Prop)), (((ord_less_eq_a_o A_40) B_29)->(((member_a C_2) A_40)->((member_a C_2) B_29))))
% FOF formula (forall (C_2:pname) (A_40:(pname->Prop)) (B_29:(pname->Prop)), (((ord_less_eq_pname_o A_40) B_29)->(((member_pname C_2) A_40)->((member_pname C_2) B_29)))) of role axiom named fact_182_subsetD
% A new axiom: (forall (C_2:pname) (A_40:(pname->Prop)) (B_29:(pname->Prop)), (((ord_less_eq_pname_o A_40) B_29)->(((member_pname C_2) A_40)->((member_pname C_2) B_29))))
% FOF formula (forall (B_28:nat) (A_39:nat) (B_27:(nat->Prop)), (((((member_nat A_39) B_27)->False)->(((eq nat) A_39) B_28))->((member_nat A_39) ((insert_nat B_28) B_27)))) of role axiom named fact_183_insertCI
% A new axiom: (forall (B_28:nat) (A_39:nat) (B_27:(nat->Prop)), (((((member_nat A_39) B_27)->False)->(((eq nat) A_39) B_28))->((member_nat A_39) ((insert_nat B_28) B_27))))
% FOF formula (forall (B_28:pname) (A_39:pname) (B_27:(pname->Prop)), (((((member_pname A_39) B_27)->False)->(((eq pname) A_39) B_28))->((member_pname A_39) ((insert_pname B_28) B_27)))) of role axiom named fact_184_insertCI
% A new axiom: (forall (B_28:pname) (A_39:pname) (B_27:(pname->Prop)), (((((member_pname A_39) B_27)->False)->(((eq pname) A_39) B_28))->((member_pname A_39) ((insert_pname B_28) B_27))))
% FOF formula (forall (B_28:x_a) (A_39:x_a) (B_27:(x_a->Prop)), (((((member_a A_39) B_27)->False)->(((eq x_a) A_39) B_28))->((member_a A_39) ((insert_a B_28) B_27)))) of role axiom named fact_185_insertCI
% A new axiom: (forall (B_28:x_a) (A_39:x_a) (B_27:(x_a->Prop)), (((((member_a A_39) B_27)->False)->(((eq x_a) A_39) B_28))->((member_a A_39) ((insert_a B_28) B_27))))
% FOF formula (forall (A_38:nat) (B_26:nat) (A_37:(nat->Prop)), (((member_nat A_38) ((insert_nat B_26) A_37))->((not (((eq nat) A_38) B_26))->((member_nat A_38) A_37)))) of role axiom named fact_186_insertE
% A new axiom: (forall (A_38:nat) (B_26:nat) (A_37:(nat->Prop)), (((member_nat A_38) ((insert_nat B_26) A_37))->((not (((eq nat) A_38) B_26))->((member_nat A_38) A_37))))
% FOF formula (forall (A_38:pname) (B_26:pname) (A_37:(pname->Prop)), (((member_pname A_38) ((insert_pname B_26) A_37))->((not (((eq pname) A_38) B_26))->((member_pname A_38) A_37)))) of role axiom named fact_187_insertE
% A new axiom: (forall (A_38:pname) (B_26:pname) (A_37:(pname->Prop)), (((member_pname A_38) ((insert_pname B_26) A_37))->((not (((eq pname) A_38) B_26))->((member_pname A_38) A_37))))
% FOF formula (forall (A_38:x_a) (B_26:x_a) (A_37:(x_a->Prop)), (((member_a A_38) ((insert_a B_26) A_37))->((not (((eq x_a) A_38) B_26))->((member_a A_38) A_37)))) of role axiom named fact_188_insertE
% A new axiom: (forall (A_38:x_a) (B_26:x_a) (A_37:(x_a->Prop)), (((member_a A_38) ((insert_a B_26) A_37))->((not (((eq x_a) A_38) B_26))->((member_a A_38) A_37))))
% FOF formula (forall (A_36:nat) (B_25:(nat->Prop)), ((member_nat A_36) ((insert_nat A_36) B_25))) of role axiom named fact_189_insertI1
% A new axiom: (forall (A_36:nat) (B_25:(nat->Prop)), ((member_nat A_36) ((insert_nat A_36) B_25)))
% FOF formula (forall (A_36:pname) (B_25:(pname->Prop)), ((member_pname A_36) ((insert_pname A_36) B_25))) of role axiom named fact_190_insertI1
% A new axiom: (forall (A_36:pname) (B_25:(pname->Prop)), ((member_pname A_36) ((insert_pname A_36) B_25)))
% FOF formula (forall (A_36:x_a) (B_25:(x_a->Prop)), ((member_a A_36) ((insert_a A_36) B_25))) of role axiom named fact_191_insertI1
% A new axiom: (forall (A_36:x_a) (B_25:(x_a->Prop)), ((member_a A_36) ((insert_a A_36) B_25)))
% FOF formula (forall (A_35:nat) (B_24:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_35) B_24)) (collect_nat (fun (X:nat)=> ((or (((eq nat) X) A_35)) ((member_nat X) B_24)))))) of role axiom named fact_192_insert__compr
% A new axiom: (forall (A_35:nat) (B_24:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_35) B_24)) (collect_nat (fun (X:nat)=> ((or (((eq nat) X) A_35)) ((member_nat X) B_24))))))
% FOF formula (forall (A_35:pname) (B_24:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_35) B_24)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_35)) ((member_pname X) B_24)))))) of role axiom named fact_193_insert__compr
% A new axiom: (forall (A_35:pname) (B_24:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_35) B_24)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_35)) ((member_pname X) B_24))))))
% FOF formula (forall (A_35:x_a) (B_24:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_35) B_24)) (collect_a (fun (X:x_a)=> ((or (((eq x_a) X) A_35)) ((member_a X) B_24)))))) of role axiom named fact_194_insert__compr
% A new axiom: (forall (A_35:x_a) (B_24:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_35) B_24)) (collect_a (fun (X:x_a)=> ((or (((eq x_a) X) A_35)) ((member_a X) B_24))))))
% FOF formula (forall (A_35:(nat->Prop)) (B_24:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) ((insert_nat_o A_35) B_24)) (collect_nat_o (fun (X:(nat->Prop))=> ((or (((eq (nat->Prop)) X) A_35)) ((member_nat_o X) B_24)))))) of role axiom named fact_195_insert__compr
% A new axiom: (forall (A_35:(nat->Prop)) (B_24:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) ((insert_nat_o A_35) B_24)) (collect_nat_o (fun (X:(nat->Prop))=> ((or (((eq (nat->Prop)) X) A_35)) ((member_nat_o X) B_24))))))
% FOF formula (forall (A_35:(pname->Prop)) (B_24:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_35) B_24)) (collect_pname_o (fun (X:(pname->Prop))=> ((or (((eq (pname->Prop)) X) A_35)) ((member_pname_o X) B_24)))))) of role axiom named fact_196_insert__compr
% A new axiom: (forall (A_35:(pname->Prop)) (B_24:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_35) B_24)) (collect_pname_o (fun (X:(pname->Prop))=> ((or (((eq (pname->Prop)) X) A_35)) ((member_pname_o X) B_24))))))
% FOF formula (forall (A_35:(x_a->Prop)) (B_24:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) ((insert_a_o A_35) B_24)) (collect_a_o (fun (X:(x_a->Prop))=> ((or (((eq (x_a->Prop)) X) A_35)) ((member_a_o X) B_24)))))) of role axiom named fact_197_insert__compr
% A new axiom: (forall (A_35:(x_a->Prop)) (B_24:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) ((insert_a_o A_35) B_24)) (collect_a_o (fun (X:(x_a->Prop))=> ((or (((eq (x_a->Prop)) X) A_35)) ((member_a_o X) B_24))))))
% FOF formula (forall (A_34:nat) (P_2:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_34) (collect_nat P_2))) (collect_nat (fun (U:nat)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq nat) U) A_34))) (P_2 U)))))) of role axiom named fact_198_insert__Collect
% A new axiom: (forall (A_34:nat) (P_2:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_34) (collect_nat P_2))) (collect_nat (fun (U:nat)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq nat) U) A_34))) (P_2 U))))))
% FOF formula (forall (A_34:pname) (P_2:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_34) (collect_pname P_2))) (collect_pname (fun (U:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U) A_34))) (P_2 U)))))) of role axiom named fact_199_insert__Collect
% A new axiom: (forall (A_34:pname) (P_2:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_34) (collect_pname P_2))) (collect_pname (fun (U:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U) A_34))) (P_2 U))))))
% FOF formula (forall (A_34:x_a) (P_2:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_34) (collect_a P_2))) (collect_a (fun (U:x_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq x_a) U) A_34))) (P_2 U)))))) of role axiom named fact_200_insert__Collect
% A new axiom: (forall (A_34:x_a) (P_2:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_34) (collect_a P_2))) (collect_a (fun (U:x_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq x_a) U) A_34))) (P_2 U))))))
% FOF formula (forall (A_34:(nat->Prop)) (P_2:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) ((insert_nat_o A_34) (collect_nat_o P_2))) (collect_nat_o (fun (U:(nat->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (nat->Prop)) U) A_34))) (P_2 U)))))) of role axiom named fact_201_insert__Collect
% A new axiom: (forall (A_34:(nat->Prop)) (P_2:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) ((insert_nat_o A_34) (collect_nat_o P_2))) (collect_nat_o (fun (U:(nat->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (nat->Prop)) U) A_34))) (P_2 U))))))
% FOF formula (forall (A_34:(pname->Prop)) (P_2:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_34) (collect_pname_o P_2))) (collect_pname_o (fun (U:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U) A_34))) (P_2 U)))))) of role axiom named fact_202_insert__Collect
% A new axiom: (forall (A_34:(pname->Prop)) (P_2:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_34) (collect_pname_o P_2))) (collect_pname_o (fun (U:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U) A_34))) (P_2 U))))))
% FOF formula (forall (A_34:(x_a->Prop)) (P_2:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) ((insert_a_o A_34) (collect_a_o P_2))) (collect_a_o (fun (U:(x_a->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (x_a->Prop)) U) A_34))) (P_2 U)))))) of role axiom named fact_203_insert__Collect
% A new axiom: (forall (A_34:(x_a->Prop)) (P_2:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) ((insert_a_o A_34) (collect_a_o P_2))) (collect_a_o (fun (U:(x_a->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (x_a->Prop)) U) A_34))) (P_2 U))))))
% FOF formula (forall (X_14:nat) (A_33:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_14) ((insert_nat X_14) A_33))) ((insert_nat X_14) A_33))) of role axiom named fact_204_insert__absorb2
% A new axiom: (forall (X_14:nat) (A_33:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_14) ((insert_nat X_14) A_33))) ((insert_nat X_14) A_33)))
% FOF formula (forall (X_14:pname) (A_33:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_14) ((insert_pname X_14) A_33))) ((insert_pname X_14) A_33))) of role axiom named fact_205_insert__absorb2
% A new axiom: (forall (X_14:pname) (A_33:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_14) ((insert_pname X_14) A_33))) ((insert_pname X_14) A_33)))
% FOF formula (forall (X_14:x_a) (A_33:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_14) ((insert_a X_14) A_33))) ((insert_a X_14) A_33))) of role axiom named fact_206_insert__absorb2
% A new axiom: (forall (X_14:x_a) (A_33:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_14) ((insert_a X_14) A_33))) ((insert_a X_14) A_33)))
% FOF formula (forall (X_13:nat) (Y_2:nat) (A_32:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_13) ((insert_nat Y_2) A_32))) ((insert_nat Y_2) ((insert_nat X_13) A_32)))) of role axiom named fact_207_insert__commute
% A new axiom: (forall (X_13:nat) (Y_2:nat) (A_32:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_13) ((insert_nat Y_2) A_32))) ((insert_nat Y_2) ((insert_nat X_13) A_32))))
% FOF formula (forall (X_13:pname) (Y_2:pname) (A_32:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_13) ((insert_pname Y_2) A_32))) ((insert_pname Y_2) ((insert_pname X_13) A_32)))) of role axiom named fact_208_insert__commute
% A new axiom: (forall (X_13:pname) (Y_2:pname) (A_32:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_13) ((insert_pname Y_2) A_32))) ((insert_pname Y_2) ((insert_pname X_13) A_32))))
% FOF formula (forall (X_13:x_a) (Y_2:x_a) (A_32:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_13) ((insert_a Y_2) A_32))) ((insert_a Y_2) ((insert_a X_13) A_32)))) of role axiom named fact_209_insert__commute
% A new axiom: (forall (X_13:x_a) (Y_2:x_a) (A_32:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_13) ((insert_a Y_2) A_32))) ((insert_a Y_2) ((insert_a X_13) A_32))))
% FOF formula (forall (A_31:nat) (B_23:nat) (A_30:(nat->Prop)), ((iff ((member_nat A_31) ((insert_nat B_23) A_30))) ((or (((eq nat) A_31) B_23)) ((member_nat A_31) A_30)))) of role axiom named fact_210_insert__iff
% A new axiom: (forall (A_31:nat) (B_23:nat) (A_30:(nat->Prop)), ((iff ((member_nat A_31) ((insert_nat B_23) A_30))) ((or (((eq nat) A_31) B_23)) ((member_nat A_31) A_30))))
% FOF formula (forall (A_31:pname) (B_23:pname) (A_30:(pname->Prop)), ((iff ((member_pname A_31) ((insert_pname B_23) A_30))) ((or (((eq pname) A_31) B_23)) ((member_pname A_31) A_30)))) of role axiom named fact_211_insert__iff
% A new axiom: (forall (A_31:pname) (B_23:pname) (A_30:(pname->Prop)), ((iff ((member_pname A_31) ((insert_pname B_23) A_30))) ((or (((eq pname) A_31) B_23)) ((member_pname A_31) A_30))))
% FOF formula (forall (A_31:x_a) (B_23:x_a) (A_30:(x_a->Prop)), ((iff ((member_a A_31) ((insert_a B_23) A_30))) ((or (((eq x_a) A_31) B_23)) ((member_a A_31) A_30)))) of role axiom named fact_212_insert__iff
% A new axiom: (forall (A_31:x_a) (B_23:x_a) (A_30:(x_a->Prop)), ((iff ((member_a A_31) ((insert_a B_23) A_30))) ((or (((eq x_a) A_31) B_23)) ((member_a A_31) A_30))))
% FOF formula (forall (Y_1:nat) (A_29:(nat->Prop)) (X_12:nat), ((iff (((insert_nat Y_1) A_29) X_12)) ((or (((eq nat) Y_1) X_12)) (A_29 X_12)))) of role axiom named fact_213_insert__code
% A new axiom: (forall (Y_1:nat) (A_29:(nat->Prop)) (X_12:nat), ((iff (((insert_nat Y_1) A_29) X_12)) ((or (((eq nat) Y_1) X_12)) (A_29 X_12))))
% FOF formula (forall (Y_1:pname) (A_29:(pname->Prop)) (X_12:pname), ((iff (((insert_pname Y_1) A_29) X_12)) ((or (((eq pname) Y_1) X_12)) (A_29 X_12)))) of role axiom named fact_214_insert__code
% A new axiom: (forall (Y_1:pname) (A_29:(pname->Prop)) (X_12:pname), ((iff (((insert_pname Y_1) A_29) X_12)) ((or (((eq pname) Y_1) X_12)) (A_29 X_12))))
% FOF formula (forall (Y_1:x_a) (A_29:(x_a->Prop)) (X_12:x_a), ((iff (((insert_a Y_1) A_29) X_12)) ((or (((eq x_a) Y_1) X_12)) (A_29 X_12)))) of role axiom named fact_215_insert__code
% A new axiom: (forall (Y_1:x_a) (A_29:(x_a->Prop)) (X_12:x_a), ((iff (((insert_a Y_1) A_29) X_12)) ((or (((eq x_a) Y_1) X_12)) (A_29 X_12))))
% FOF formula (forall (B_22:(nat->Prop)) (X_11:nat) (A_28:(nat->Prop)), ((((member_nat X_11) A_28)->False)->((((member_nat X_11) B_22)->False)->((iff (((eq (nat->Prop)) ((insert_nat X_11) A_28)) ((insert_nat X_11) B_22))) (((eq (nat->Prop)) A_28) B_22))))) of role axiom named fact_216_insert__ident
% A new axiom: (forall (B_22:(nat->Prop)) (X_11:nat) (A_28:(nat->Prop)), ((((member_nat X_11) A_28)->False)->((((member_nat X_11) B_22)->False)->((iff (((eq (nat->Prop)) ((insert_nat X_11) A_28)) ((insert_nat X_11) B_22))) (((eq (nat->Prop)) A_28) B_22)))))
% FOF formula (forall (B_22:(pname->Prop)) (X_11:pname) (A_28:(pname->Prop)), ((((member_pname X_11) A_28)->False)->((((member_pname X_11) B_22)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_11) A_28)) ((insert_pname X_11) B_22))) (((eq (pname->Prop)) A_28) B_22))))) of role axiom named fact_217_insert__ident
% A new axiom: (forall (B_22:(pname->Prop)) (X_11:pname) (A_28:(pname->Prop)), ((((member_pname X_11) A_28)->False)->((((member_pname X_11) B_22)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_11) A_28)) ((insert_pname X_11) B_22))) (((eq (pname->Prop)) A_28) B_22)))))
% FOF formula (forall (B_22:(x_a->Prop)) (X_11:x_a) (A_28:(x_a->Prop)), ((((member_a X_11) A_28)->False)->((((member_a X_11) B_22)->False)->((iff (((eq (x_a->Prop)) ((insert_a X_11) A_28)) ((insert_a X_11) B_22))) (((eq (x_a->Prop)) A_28) B_22))))) of role axiom named fact_218_insert__ident
% A new axiom: (forall (B_22:(x_a->Prop)) (X_11:x_a) (A_28:(x_a->Prop)), ((((member_a X_11) A_28)->False)->((((member_a X_11) B_22)->False)->((iff (((eq (x_a->Prop)) ((insert_a X_11) A_28)) ((insert_a X_11) B_22))) (((eq (x_a->Prop)) A_28) B_22)))))
% FOF formula (forall (B_21:nat) (A_27:nat) (B_20:(nat->Prop)), (((member_nat A_27) B_20)->((member_nat A_27) ((insert_nat B_21) B_20)))) of role axiom named fact_219_insertI2
% A new axiom: (forall (B_21:nat) (A_27:nat) (B_20:(nat->Prop)), (((member_nat A_27) B_20)->((member_nat A_27) ((insert_nat B_21) B_20))))
% FOF formula (forall (B_21:pname) (A_27:pname) (B_20:(pname->Prop)), (((member_pname A_27) B_20)->((member_pname A_27) ((insert_pname B_21) B_20)))) of role axiom named fact_220_insertI2
% A new axiom: (forall (B_21:pname) (A_27:pname) (B_20:(pname->Prop)), (((member_pname A_27) B_20)->((member_pname A_27) ((insert_pname B_21) B_20))))
% FOF formula (forall (B_21:x_a) (A_27:x_a) (B_20:(x_a->Prop)), (((member_a A_27) B_20)->((member_a A_27) ((insert_a B_21) B_20)))) of role axiom named fact_221_insertI2
% A new axiom: (forall (B_21:x_a) (A_27:x_a) (B_20:(x_a->Prop)), (((member_a A_27) B_20)->((member_a A_27) ((insert_a B_21) B_20))))
% FOF formula (forall (A_26:nat) (A_25:(nat->Prop)), (((member_nat A_26) A_25)->(((eq (nat->Prop)) ((insert_nat A_26) A_25)) A_25))) of role axiom named fact_222_insert__absorb
% A new axiom: (forall (A_26:nat) (A_25:(nat->Prop)), (((member_nat A_26) A_25)->(((eq (nat->Prop)) ((insert_nat A_26) A_25)) A_25)))
% FOF formula (forall (A_26:pname) (A_25:(pname->Prop)), (((member_pname A_26) A_25)->(((eq (pname->Prop)) ((insert_pname A_26) A_25)) A_25))) of role axiom named fact_223_insert__absorb
% A new axiom: (forall (A_26:pname) (A_25:(pname->Prop)), (((member_pname A_26) A_25)->(((eq (pname->Prop)) ((insert_pname A_26) A_25)) A_25)))
% FOF formula (forall (A_26:x_a) (A_25:(x_a->Prop)), (((member_a A_26) A_25)->(((eq (x_a->Prop)) ((insert_a A_26) A_25)) A_25))) of role axiom named fact_224_insert__absorb
% A new axiom: (forall (A_26:x_a) (A_25:(x_a->Prop)), (((member_a A_26) A_25)->(((eq (x_a->Prop)) ((insert_a A_26) A_25)) A_25)))
% FOF formula (forall (A_24:(nat->Prop)), ((ord_less_eq_nat_o A_24) A_24)) of role axiom named fact_225_subset__refl
% A new axiom: (forall (A_24:(nat->Prop)), ((ord_less_eq_nat_o A_24) A_24))
% FOF formula (forall (A_24:(pname->Prop)), ((ord_less_eq_pname_o A_24) A_24)) of role axiom named fact_226_subset__refl
% A new axiom: (forall (A_24:(pname->Prop)), ((ord_less_eq_pname_o A_24) A_24))
% FOF formula (forall (A_24:(x_a->Prop)), ((ord_less_eq_a_o A_24) A_24)) of role axiom named fact_227_subset__refl
% A new axiom: (forall (A_24:(x_a->Prop)), ((ord_less_eq_a_o A_24) A_24))
% FOF formula (forall (A_23:(nat->Prop)) (B_19:(nat->Prop)), ((iff (((eq (nat->Prop)) A_23) B_19)) ((and ((ord_less_eq_nat_o A_23) B_19)) ((ord_less_eq_nat_o B_19) A_23)))) of role axiom named fact_228_set__eq__subset
% A new axiom: (forall (A_23:(nat->Prop)) (B_19:(nat->Prop)), ((iff (((eq (nat->Prop)) A_23) B_19)) ((and ((ord_less_eq_nat_o A_23) B_19)) ((ord_less_eq_nat_o B_19) A_23))))
% FOF formula (forall (A_23:(pname->Prop)) (B_19:(pname->Prop)), ((iff (((eq (pname->Prop)) A_23) B_19)) ((and ((ord_less_eq_pname_o A_23) B_19)) ((ord_less_eq_pname_o B_19) A_23)))) of role axiom named fact_229_set__eq__subset
% A new axiom: (forall (A_23:(pname->Prop)) (B_19:(pname->Prop)), ((iff (((eq (pname->Prop)) A_23) B_19)) ((and ((ord_less_eq_pname_o A_23) B_19)) ((ord_less_eq_pname_o B_19) A_23))))
% FOF formula (forall (A_23:(x_a->Prop)) (B_19:(x_a->Prop)), ((iff (((eq (x_a->Prop)) A_23) B_19)) ((and ((ord_less_eq_a_o A_23) B_19)) ((ord_less_eq_a_o B_19) A_23)))) of role axiom named fact_230_set__eq__subset
% A new axiom: (forall (A_23:(x_a->Prop)) (B_19:(x_a->Prop)), ((iff (((eq (x_a->Prop)) A_23) B_19)) ((and ((ord_less_eq_a_o A_23) B_19)) ((ord_less_eq_a_o B_19) A_23))))
% FOF formula (forall (A_22:(nat->Prop)) (B_18:(nat->Prop)), ((((eq (nat->Prop)) A_22) B_18)->((ord_less_eq_nat_o A_22) B_18))) of role axiom named fact_231_equalityD1
% A new axiom: (forall (A_22:(nat->Prop)) (B_18:(nat->Prop)), ((((eq (nat->Prop)) A_22) B_18)->((ord_less_eq_nat_o A_22) B_18)))
% FOF formula (forall (A_22:(pname->Prop)) (B_18:(pname->Prop)), ((((eq (pname->Prop)) A_22) B_18)->((ord_less_eq_pname_o A_22) B_18))) of role axiom named fact_232_equalityD1
% A new axiom: (forall (A_22:(pname->Prop)) (B_18:(pname->Prop)), ((((eq (pname->Prop)) A_22) B_18)->((ord_less_eq_pname_o A_22) B_18)))
% FOF formula (forall (A_22:(x_a->Prop)) (B_18:(x_a->Prop)), ((((eq (x_a->Prop)) A_22) B_18)->((ord_less_eq_a_o A_22) B_18))) of role axiom named fact_233_equalityD1
% A new axiom: (forall (A_22:(x_a->Prop)) (B_18:(x_a->Prop)), ((((eq (x_a->Prop)) A_22) B_18)->((ord_less_eq_a_o A_22) B_18)))
% FOF formula (forall (A_21:(nat->Prop)) (B_17:(nat->Prop)), ((((eq (nat->Prop)) A_21) B_17)->((ord_less_eq_nat_o B_17) A_21))) of role axiom named fact_234_equalityD2
% A new axiom: (forall (A_21:(nat->Prop)) (B_17:(nat->Prop)), ((((eq (nat->Prop)) A_21) B_17)->((ord_less_eq_nat_o B_17) A_21)))
% FOF formula (forall (A_21:(pname->Prop)) (B_17:(pname->Prop)), ((((eq (pname->Prop)) A_21) B_17)->((ord_less_eq_pname_o B_17) A_21))) of role axiom named fact_235_equalityD2
% A new axiom: (forall (A_21:(pname->Prop)) (B_17:(pname->Prop)), ((((eq (pname->Prop)) A_21) B_17)->((ord_less_eq_pname_o B_17) A_21)))
% FOF formula (forall (A_21:(x_a->Prop)) (B_17:(x_a->Prop)), ((((eq (x_a->Prop)) A_21) B_17)->((ord_less_eq_a_o B_17) A_21))) of role axiom named fact_236_equalityD2
% A new axiom: (forall (A_21:(x_a->Prop)) (B_17:(x_a->Prop)), ((((eq (x_a->Prop)) A_21) B_17)->((ord_less_eq_a_o B_17) A_21)))
% FOF formula (forall (X_10:nat) (A_20:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_20) B_16)->(((member_nat X_10) A_20)->((member_nat X_10) B_16)))) of role axiom named fact_237_in__mono
% A new axiom: (forall (X_10:nat) (A_20:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_20) B_16)->(((member_nat X_10) A_20)->((member_nat X_10) B_16))))
% FOF formula (forall (X_10:x_a) (A_20:(x_a->Prop)) (B_16:(x_a->Prop)), (((ord_less_eq_a_o A_20) B_16)->(((member_a X_10) A_20)->((member_a X_10) B_16)))) of role axiom named fact_238_in__mono
% A new axiom: (forall (X_10:x_a) (A_20:(x_a->Prop)) (B_16:(x_a->Prop)), (((ord_less_eq_a_o A_20) B_16)->(((member_a X_10) A_20)->((member_a X_10) B_16))))
% FOF formula (forall (X_10:pname) (A_20:(pname->Prop)) (B_16:(pname->Prop)), (((ord_less_eq_pname_o A_20) B_16)->(((member_pname X_10) A_20)->((member_pname X_10) B_16)))) of role axiom named fact_239_in__mono
% A new axiom: (forall (X_10:pname) (A_20:(pname->Prop)) (B_16:(pname->Prop)), (((ord_less_eq_pname_o A_20) B_16)->(((member_pname X_10) A_20)->((member_pname X_10) B_16))))
% FOF formula (forall (B_15:(nat->Prop)) (X_9:nat) (A_19:(nat->Prop)), (((member_nat X_9) A_19)->(((ord_less_eq_nat_o A_19) B_15)->((member_nat X_9) B_15)))) of role axiom named fact_240_set__rev__mp
% A new axiom: (forall (B_15:(nat->Prop)) (X_9:nat) (A_19:(nat->Prop)), (((member_nat X_9) A_19)->(((ord_less_eq_nat_o A_19) B_15)->((member_nat X_9) B_15))))
% FOF formula (forall (B_15:(x_a->Prop)) (X_9:x_a) (A_19:(x_a->Prop)), (((member_a X_9) A_19)->(((ord_less_eq_a_o A_19) B_15)->((member_a X_9) B_15)))) of role axiom named fact_241_set__rev__mp
% A new axiom: (forall (B_15:(x_a->Prop)) (X_9:x_a) (A_19:(x_a->Prop)), (((member_a X_9) A_19)->(((ord_less_eq_a_o A_19) B_15)->((member_a X_9) B_15))))
% FOF formula (forall (B_15:(pname->Prop)) (X_9:pname) (A_19:(pname->Prop)), (((member_pname X_9) A_19)->(((ord_less_eq_pname_o A_19) B_15)->((member_pname X_9) B_15)))) of role axiom named fact_242_set__rev__mp
% A new axiom: (forall (B_15:(pname->Prop)) (X_9:pname) (A_19:(pname->Prop)), (((member_pname X_9) A_19)->(((ord_less_eq_pname_o A_19) B_15)->((member_pname X_9) B_15))))
% FOF formula (forall (X_8:nat) (A_18:(nat->Prop)) (B_14:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_14)->(((member_nat X_8) A_18)->((member_nat X_8) B_14)))) of role axiom named fact_243_set__mp
% A new axiom: (forall (X_8:nat) (A_18:(nat->Prop)) (B_14:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_14)->(((member_nat X_8) A_18)->((member_nat X_8) B_14))))
% FOF formula (forall (X_8:x_a) (A_18:(x_a->Prop)) (B_14:(x_a->Prop)), (((ord_less_eq_a_o A_18) B_14)->(((member_a X_8) A_18)->((member_a X_8) B_14)))) of role axiom named fact_244_set__mp
% A new axiom: (forall (X_8:x_a) (A_18:(x_a->Prop)) (B_14:(x_a->Prop)), (((ord_less_eq_a_o A_18) B_14)->(((member_a X_8) A_18)->((member_a X_8) B_14))))
% FOF formula (forall (X_8:pname) (A_18:(pname->Prop)) (B_14:(pname->Prop)), (((ord_less_eq_pname_o A_18) B_14)->(((member_pname X_8) A_18)->((member_pname X_8) B_14)))) of role axiom named fact_245_set__mp
% A new axiom: (forall (X_8:pname) (A_18:(pname->Prop)) (B_14:(pname->Prop)), (((ord_less_eq_pname_o A_18) B_14)->(((member_pname X_8) A_18)->((member_pname X_8) B_14))))
% FOF formula (forall (C_1:(nat->Prop)) (A_17:(nat->Prop)) (B_13:(nat->Prop)), (((ord_less_eq_nat_o A_17) B_13)->(((ord_less_eq_nat_o B_13) C_1)->((ord_less_eq_nat_o A_17) C_1)))) of role axiom named fact_246_subset__trans
% A new axiom: (forall (C_1:(nat->Prop)) (A_17:(nat->Prop)) (B_13:(nat->Prop)), (((ord_less_eq_nat_o A_17) B_13)->(((ord_less_eq_nat_o B_13) C_1)->((ord_less_eq_nat_o A_17) C_1))))
% FOF formula (forall (C_1:(pname->Prop)) (A_17:(pname->Prop)) (B_13:(pname->Prop)), (((ord_less_eq_pname_o A_17) B_13)->(((ord_less_eq_pname_o B_13) C_1)->((ord_less_eq_pname_o A_17) C_1)))) of role axiom named fact_247_subset__trans
% A new axiom: (forall (C_1:(pname->Prop)) (A_17:(pname->Prop)) (B_13:(pname->Prop)), (((ord_less_eq_pname_o A_17) B_13)->(((ord_less_eq_pname_o B_13) C_1)->((ord_less_eq_pname_o A_17) C_1))))
% FOF formula (forall (C_1:(x_a->Prop)) (A_17:(x_a->Prop)) (B_13:(x_a->Prop)), (((ord_less_eq_a_o A_17) B_13)->(((ord_less_eq_a_o B_13) C_1)->((ord_less_eq_a_o A_17) C_1)))) of role axiom named fact_248_subset__trans
% A new axiom: (forall (C_1:(x_a->Prop)) (A_17:(x_a->Prop)) (B_13:(x_a->Prop)), (((ord_less_eq_a_o A_17) B_13)->(((ord_less_eq_a_o B_13) C_1)->((ord_less_eq_a_o A_17) C_1))))
% FOF formula (forall (A_16:(nat->Prop)) (B_12:(nat->Prop)), ((((eq (nat->Prop)) A_16) B_12)->((((ord_less_eq_nat_o A_16) B_12)->(((ord_less_eq_nat_o B_12) A_16)->False))->False))) of role axiom named fact_249_equalityE
% A new axiom: (forall (A_16:(nat->Prop)) (B_12:(nat->Prop)), ((((eq (nat->Prop)) A_16) B_12)->((((ord_less_eq_nat_o A_16) B_12)->(((ord_less_eq_nat_o B_12) A_16)->False))->False)))
% FOF formula (forall (A_16:(pname->Prop)) (B_12:(pname->Prop)), ((((eq (pname->Prop)) A_16) B_12)->((((ord_less_eq_pname_o A_16) B_12)->(((ord_less_eq_pname_o B_12) A_16)->False))->False))) of role axiom named fact_250_equalityE
% A new axiom: (forall (A_16:(pname->Prop)) (B_12:(pname->Prop)), ((((eq (pname->Prop)) A_16) B_12)->((((ord_less_eq_pname_o A_16) B_12)->(((ord_less_eq_pname_o B_12) A_16)->False))->False)))
% FOF formula (forall (A_16:(x_a->Prop)) (B_12:(x_a->Prop)), ((((eq (x_a->Prop)) A_16) B_12)->((((ord_less_eq_a_o A_16) B_12)->(((ord_less_eq_a_o B_12) A_16)->False))->False))) of role axiom named fact_251_equalityE
% A new axiom: (forall (A_16:(x_a->Prop)) (B_12:(x_a->Prop)), ((((eq (x_a->Prop)) A_16) B_12)->((((ord_less_eq_a_o A_16) B_12)->(((ord_less_eq_a_o B_12) A_16)->False))->False)))
% FOF formula (forall (X_7:nat) (A_15:(nat->Prop)), ((iff ((member_nat X_7) A_15)) (A_15 X_7))) of role axiom named fact_252_mem__def
% A new axiom: (forall (X_7:nat) (A_15:(nat->Prop)), ((iff ((member_nat X_7) A_15)) (A_15 X_7)))
% FOF formula (forall (X_7:x_a) (A_15:(x_a->Prop)), ((iff ((member_a X_7) A_15)) (A_15 X_7))) of role axiom named fact_253_mem__def
% A new axiom: (forall (X_7:x_a) (A_15:(x_a->Prop)), ((iff ((member_a X_7) A_15)) (A_15 X_7)))
% FOF formula (forall (X_7:pname) (A_15:(pname->Prop)), ((iff ((member_pname X_7) A_15)) (A_15 X_7))) of role axiom named fact_254_mem__def
% A new axiom: (forall (X_7:pname) (A_15:(pname->Prop)), ((iff ((member_pname X_7) A_15)) (A_15 X_7)))
% FOF formula (forall (P_1:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_1)) P_1)) of role axiom named fact_255_Collect__def
% A new axiom: (forall (P_1:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_1)) P_1))
% FOF formula (forall (P_1:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) (collect_nat_o P_1)) P_1)) of role axiom named fact_256_Collect__def
% A new axiom: (forall (P_1:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) (collect_nat_o P_1)) P_1))
% FOF formula (forall (P_1:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_1)) P_1)) of role axiom named fact_257_Collect__def
% A new axiom: (forall (P_1:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_1)) P_1))
% FOF formula (forall (P_1:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) (collect_a_o P_1)) P_1)) of role axiom named fact_258_Collect__def
% A new axiom: (forall (P_1:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) (collect_a_o P_1)) P_1))
% FOF formula (forall (P_1:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_1)) P_1)) of role axiom named fact_259_Collect__def
% A new axiom: (forall (P_1:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_1)) P_1))
% FOF formula (forall (Z:x_a) (F_8:(pname->x_a)) (A_14:(pname->Prop)), ((iff ((member_a Z) ((image_pname_a F_8) A_14))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_14)) (((eq x_a) Z) (F_8 X))))))) of role axiom named fact_260_image__iff
% A new axiom: (forall (Z:x_a) (F_8:(pname->x_a)) (A_14:(pname->Prop)), ((iff ((member_a Z) ((image_pname_a F_8) A_14))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_14)) (((eq x_a) Z) (F_8 X)))))))
% FOF formula (forall (F_7:(pname->x_a)) (X_6:pname) (A_13:(pname->Prop)), (((member_pname X_6) A_13)->((member_a (F_7 X_6)) ((image_pname_a F_7) A_13)))) of role axiom named fact_261_imageI
% A new axiom: (forall (F_7:(pname->x_a)) (X_6:pname) (A_13:(pname->Prop)), (((member_pname X_6) A_13)->((member_a (F_7 X_6)) ((image_pname_a F_7) A_13))))
% FOF formula (forall (B_11:x_a) (F_6:(pname->x_a)) (X_5:pname) (A_12:(pname->Prop)), (((member_pname X_5) A_12)->((((eq x_a) B_11) (F_6 X_5))->((member_a B_11) ((image_pname_a F_6) A_12))))) of role axiom named fact_262_rev__image__eqI
% A new axiom: (forall (B_11:x_a) (F_6:(pname->x_a)) (X_5:pname) (A_12:(pname->Prop)), (((member_pname X_5) A_12)->((((eq x_a) B_11) (F_6 X_5))->((member_a B_11) ((image_pname_a F_6) A_12)))))
% FOF formula (forall (X:nat) (Xa:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X) Xa)) (collect_nat (fun (Y:nat)=> ((or (((eq nat) Y) X)) ((member_nat Y) Xa)))))) of role axiom named fact_263_insert__compr__raw
% A new axiom: (forall (X:nat) (Xa:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X) Xa)) (collect_nat (fun (Y:nat)=> ((or (((eq nat) Y) X)) ((member_nat Y) Xa))))))
% FOF formula (forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y:pname)=> ((or (((eq pname) Y) X)) ((member_pname Y) Xa)))))) of role axiom named fact_264_insert__compr__raw
% A new axiom: (forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y:pname)=> ((or (((eq pname) Y) X)) ((member_pname Y) Xa))))))
% FOF formula (forall (X:x_a) (Xa:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X) Xa)) (collect_a (fun (Y:x_a)=> ((or (((eq x_a) Y) X)) ((member_a Y) Xa)))))) of role axiom named fact_265_insert__compr__raw
% A new axiom: (forall (X:x_a) (Xa:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X) Xa)) (collect_a (fun (Y:x_a)=> ((or (((eq x_a) Y) X)) ((member_a Y) Xa))))))
% FOF formula (forall (X:(nat->Prop)) (Xa:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) ((insert_nat_o X) Xa)) (collect_nat_o (fun (Y:(nat->Prop))=> ((or (((eq (nat->Prop)) Y) X)) ((member_nat_o Y) Xa)))))) of role axiom named fact_266_insert__compr__raw
% A new axiom: (forall (X:(nat->Prop)) (Xa:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) ((insert_nat_o X) Xa)) (collect_nat_o (fun (Y:(nat->Prop))=> ((or (((eq (nat->Prop)) Y) X)) ((member_nat_o Y) Xa))))))
% FOF formula (forall (X:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X) Xa)) (collect_pname_o (fun (Y:(pname->Prop))=> ((or (((eq (pname->Prop)) Y) X)) ((member_pname_o Y) Xa)))))) of role axiom named fact_267_insert__compr__raw
% A new axiom: (forall (X:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X) Xa)) (collect_pname_o (fun (Y:(pname->Prop))=> ((or (((eq (pname->Prop)) Y) X)) ((member_pname_o Y) Xa))))))
% FOF formula (forall (X:(x_a->Prop)) (Xa:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) ((insert_a_o X) Xa)) (collect_a_o (fun (Y:(x_a->Prop))=> ((or (((eq (x_a->Prop)) Y) X)) ((member_a_o Y) Xa)))))) of role axiom named fact_268_insert__compr__raw
% A new axiom: (forall (X:(x_a->Prop)) (Xa:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) ((insert_a_o X) Xa)) (collect_a_o (fun (Y:(x_a->Prop))=> ((or (((eq (x_a->Prop)) Y) X)) ((member_a_o Y) Xa))))))
% FOF formula (forall (B_10:(nat->Prop)) (A_11:nat), ((ord_less_eq_nat_o B_10) ((insert_nat A_11) B_10))) of role axiom named fact_269_subset__insertI
% A new axiom: (forall (B_10:(nat->Prop)) (A_11:nat), ((ord_less_eq_nat_o B_10) ((insert_nat A_11) B_10)))
% FOF formula (forall (B_10:(pname->Prop)) (A_11:pname), ((ord_less_eq_pname_o B_10) ((insert_pname A_11) B_10))) of role axiom named fact_270_subset__insertI
% A new axiom: (forall (B_10:(pname->Prop)) (A_11:pname), ((ord_less_eq_pname_o B_10) ((insert_pname A_11) B_10)))
% FOF formula (forall (B_10:(x_a->Prop)) (A_11:x_a), ((ord_less_eq_a_o B_10) ((insert_a A_11) B_10))) of role axiom named fact_271_subset__insertI
% A new axiom: (forall (B_10:(x_a->Prop)) (A_11:x_a), ((ord_less_eq_a_o B_10) ((insert_a A_11) B_10)))
% FOF formula (forall (X_4:nat) (A_10:(nat->Prop)) (B_9:(nat->Prop)), ((iff ((ord_less_eq_nat_o ((insert_nat X_4) A_10)) B_9)) ((and ((member_nat X_4) B_9)) ((ord_less_eq_nat_o A_10) B_9)))) of role axiom named fact_272_insert__subset
% A new axiom: (forall (X_4:nat) (A_10:(nat->Prop)) (B_9:(nat->Prop)), ((iff ((ord_less_eq_nat_o ((insert_nat X_4) A_10)) B_9)) ((and ((member_nat X_4) B_9)) ((ord_less_eq_nat_o A_10) B_9))))
% FOF formula (forall (X_4:pname) (A_10:(pname->Prop)) (B_9:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_4) A_10)) B_9)) ((and ((member_pname X_4) B_9)) ((ord_less_eq_pname_o A_10) B_9)))) of role axiom named fact_273_insert__subset
% A new axiom: (forall (X_4:pname) (A_10:(pname->Prop)) (B_9:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_4) A_10)) B_9)) ((and ((member_pname X_4) B_9)) ((ord_less_eq_pname_o A_10) B_9))))
% FOF formula (forall (X_4:x_a) (A_10:(x_a->Prop)) (B_9:(x_a->Prop)), ((iff ((ord_less_eq_a_o ((insert_a X_4) A_10)) B_9)) ((and ((member_a X_4) B_9)) ((ord_less_eq_a_o A_10) B_9)))) of role axiom named fact_274_insert__subset
% A new axiom: (forall (X_4:x_a) (A_10:(x_a->Prop)) (B_9:(x_a->Prop)), ((iff ((ord_less_eq_a_o ((insert_a X_4) A_10)) B_9)) ((and ((member_a X_4) B_9)) ((ord_less_eq_a_o A_10) B_9))))
% FOF formula (forall (B_8:(nat->Prop)) (X_3:nat) (A_9:(nat->Prop)), ((((member_nat X_3) A_9)->False)->((iff ((ord_less_eq_nat_o A_9) ((insert_nat X_3) B_8))) ((ord_less_eq_nat_o A_9) B_8)))) of role axiom named fact_275_subset__insert
% A new axiom: (forall (B_8:(nat->Prop)) (X_3:nat) (A_9:(nat->Prop)), ((((member_nat X_3) A_9)->False)->((iff ((ord_less_eq_nat_o A_9) ((insert_nat X_3) B_8))) ((ord_less_eq_nat_o A_9) B_8))))
% FOF formula (forall (B_8:(pname->Prop)) (X_3:pname) (A_9:(pname->Prop)), ((((member_pname X_3) A_9)->False)->((iff ((ord_less_eq_pname_o A_9) ((insert_pname X_3) B_8))) ((ord_less_eq_pname_o A_9) B_8)))) of role axiom named fact_276_subset__insert
% A new axiom: (forall (B_8:(pname->Prop)) (X_3:pname) (A_9:(pname->Prop)), ((((member_pname X_3) A_9)->False)->((iff ((ord_less_eq_pname_o A_9) ((insert_pname X_3) B_8))) ((ord_less_eq_pname_o A_9) B_8))))
% FOF formula (forall (B_8:(x_a->Prop)) (X_3:x_a) (A_9:(x_a->Prop)), ((((member_a X_3) A_9)->False)->((iff ((ord_less_eq_a_o A_9) ((insert_a X_3) B_8))) ((ord_less_eq_a_o A_9) B_8)))) of role axiom named fact_277_subset__insert
% A new axiom: (forall (B_8:(x_a->Prop)) (X_3:x_a) (A_9:(x_a->Prop)), ((((member_a X_3) A_9)->False)->((iff ((ord_less_eq_a_o A_9) ((insert_a X_3) B_8))) ((ord_less_eq_a_o A_9) B_8))))
% FOF formula (forall (B_7:nat) (A_8:(nat->Prop)) (B_6:(nat->Prop)), (((ord_less_eq_nat_o A_8) B_6)->((ord_less_eq_nat_o A_8) ((insert_nat B_7) B_6)))) of role axiom named fact_278_subset__insertI2
% A new axiom: (forall (B_7:nat) (A_8:(nat->Prop)) (B_6:(nat->Prop)), (((ord_less_eq_nat_o A_8) B_6)->((ord_less_eq_nat_o A_8) ((insert_nat B_7) B_6))))
% FOF formula (forall (B_7:pname) (A_8:(pname->Prop)) (B_6:(pname->Prop)), (((ord_less_eq_pname_o A_8) B_6)->((ord_less_eq_pname_o A_8) ((insert_pname B_7) B_6)))) of role axiom named fact_279_subset__insertI2
% A new axiom: (forall (B_7:pname) (A_8:(pname->Prop)) (B_6:(pname->Prop)), (((ord_less_eq_pname_o A_8) B_6)->((ord_less_eq_pname_o A_8) ((insert_pname B_7) B_6))))
% FOF formula (forall (B_7:x_a) (A_8:(x_a->Prop)) (B_6:(x_a->Prop)), (((ord_less_eq_a_o A_8) B_6)->((ord_less_eq_a_o A_8) ((insert_a B_7) B_6)))) of role axiom named fact_280_subset__insertI2
% A new axiom: (forall (B_7:x_a) (A_8:(x_a->Prop)) (B_6:(x_a->Prop)), (((ord_less_eq_a_o A_8) B_6)->((ord_less_eq_a_o A_8) ((insert_a B_7) B_6))))
% FOF formula (forall (A_7:nat) (C:(nat->Prop)) (D:(nat->Prop)), (((ord_less_eq_nat_o C) D)->((ord_less_eq_nat_o ((insert_nat A_7) C)) ((insert_nat A_7) D)))) of role axiom named fact_281_insert__mono
% A new axiom: (forall (A_7:nat) (C:(nat->Prop)) (D:(nat->Prop)), (((ord_less_eq_nat_o C) D)->((ord_less_eq_nat_o ((insert_nat A_7) C)) ((insert_nat A_7) D))))
% FOF formula (forall (A_7:pname) (C:(pname->Prop)) (D:(pname->Prop)), (((ord_less_eq_pname_o C) D)->((ord_less_eq_pname_o ((insert_pname A_7) C)) ((insert_pname A_7) D)))) of role axiom named fact_282_insert__mono
% A new axiom: (forall (A_7:pname) (C:(pname->Prop)) (D:(pname->Prop)), (((ord_less_eq_pname_o C) D)->((ord_less_eq_pname_o ((insert_pname A_7) C)) ((insert_pname A_7) D))))
% FOF formula (forall (A_7:x_a) (C:(x_a->Prop)) (D:(x_a->Prop)), (((ord_less_eq_a_o C) D)->((ord_less_eq_a_o ((insert_a A_7) C)) ((insert_a A_7) D)))) of role axiom named fact_283_insert__mono
% A new axiom: (forall (A_7:x_a) (C:(x_a->Prop)) (D:(x_a->Prop)), (((ord_less_eq_a_o C) D)->((ord_less_eq_a_o ((insert_a A_7) C)) ((insert_a A_7) D))))
% FOF formula (forall (F_5:(pname->x_a)) (A_6:pname) (B_5:(pname->Prop)), (((eq (x_a->Prop)) ((image_pname_a F_5) ((insert_pname A_6) B_5))) ((insert_a (F_5 A_6)) ((image_pname_a F_5) B_5)))) of role axiom named fact_284_image__insert
% A new axiom: (forall (F_5:(pname->x_a)) (A_6:pname) (B_5:(pname->Prop)), (((eq (x_a->Prop)) ((image_pname_a F_5) ((insert_pname A_6) B_5))) ((insert_a (F_5 A_6)) ((image_pname_a F_5) B_5))))
% FOF formula (forall (F_4:(pname->x_a)) (X_2:pname) (A_5:(pname->Prop)), (((member_pname X_2) A_5)->(((eq (x_a->Prop)) ((insert_a (F_4 X_2)) ((image_pname_a F_4) A_5))) ((image_pname_a F_4) A_5)))) of role axiom named fact_285_insert__image
% A new axiom: (forall (F_4:(pname->x_a)) (X_2:pname) (A_5:(pname->Prop)), (((member_pname X_2) A_5)->(((eq (x_a->Prop)) ((insert_a (F_4 X_2)) ((image_pname_a F_4) A_5))) ((image_pname_a F_4) A_5))))
% FOF formula (forall (B_4:(x_a->Prop)) (F_3:(pname->x_a)) (A_4:(pname->Prop)), ((iff ((ord_less_eq_a_o B_4) ((image_pname_a F_3) A_4))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_4)) (((eq (x_a->Prop)) B_4) ((image_pname_a F_3) AA))))))) of role axiom named fact_286_subset__image__iff
% A new axiom: (forall (B_4:(x_a->Prop)) (F_3:(pname->x_a)) (A_4:(pname->Prop)), ((iff ((ord_less_eq_a_o B_4) ((image_pname_a F_3) A_4))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_4)) (((eq (x_a->Prop)) B_4) ((image_pname_a F_3) AA)))))))
% FOF formula (forall (F_2:(pname->x_a)) (A_3:(pname->Prop)) (B_3:(pname->Prop)), (((ord_less_eq_pname_o A_3) B_3)->((ord_less_eq_a_o ((image_pname_a F_2) A_3)) ((image_pname_a F_2) B_3)))) of role axiom named fact_287_image__mono
% A new axiom: (forall (F_2:(pname->x_a)) (A_3:(pname->Prop)) (B_3:(pname->Prop)), (((ord_less_eq_pname_o A_3) B_3)->((ord_less_eq_a_o ((image_pname_a F_2) A_3)) ((image_pname_a F_2) B_3))))
% FOF formula (forall (B_2:x_a) (F_1:(pname->x_a)) (A_2:(pname->Prop)), (((member_a B_2) ((image_pname_a F_1) A_2))->((forall (X:pname), ((((eq x_a) B_2) (F_1 X))->(((member_pname X) A_2)->False)))->False))) of role axiom named fact_288_imageE
% A new axiom: (forall (B_2:x_a) (F_1:(pname->x_a)) (A_2:(pname->Prop)), (((member_a B_2) ((image_pname_a F_1) A_2))->((forall (X:pname), ((((eq x_a) B_2) (F_1 X))->(((member_pname X) A_2)->False)))->False)))
% FOF formula (forall (B_1:(nat->Prop)) (A_1:(nat->Prop)), ((forall (X:nat), (((member_nat X) A_1)->((member_nat X) B_1)))->((ord_less_eq_nat_o A_1) B_1))) of role axiom named fact_289_subsetI
% A new axiom: (forall (B_1:(nat->Prop)) (A_1:(nat->Prop)), ((forall (X:nat), (((member_nat X) A_1)->((member_nat X) B_1)))->((ord_less_eq_nat_o A_1) B_1)))
% FOF formula (forall (B_1:(x_a->Prop)) (A_1:(x_a->Prop)), ((forall (X:x_a), (((member_a X) A_1)->((member_a X) B_1)))->((ord_less_eq_a_o A_1) B_1))) of role axiom named fact_290_subsetI
% A new axiom: (forall (B_1:(x_a->Prop)) (A_1:(x_a->Prop)), ((forall (X:x_a), (((member_a X) A_1)->((member_a X) B_1)))->((ord_less_eq_a_o A_1) B_1)))
% FOF formula (forall (B_1:(pname->Prop)) (A_1:(pname->Prop)), ((forall (X:pname), (((member_pname X) A_1)->((member_pname X) B_1)))->((ord_less_eq_pname_o A_1) B_1))) of role axiom named fact_291_subsetI
% A new axiom: (forall (B_1:(pname->Prop)) (A_1:(pname->Prop)), ((forall (X:pname), (((member_pname X) A_1)->((member_pname X) B_1)))->((ord_less_eq_pname_o A_1) B_1)))
% FOF formula (forall (_TPTP_I:nat) (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_2:nat), ((P (suc N_2))->(P N_2)))->(P ((minus_minus_nat K) _TPTP_I))))) of role axiom named fact_292_zero__induct__lemma
% A new axiom: (forall (_TPTP_I:nat) (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_2:nat), ((P (suc N_2))->(P N_2)))->(P ((minus_minus_nat K) _TPTP_I)))))
% FOF formula (forall (N_1:nat) (M_1:nat), (((ord_less_eq_nat (suc N_1)) M_1)->((ex nat) (fun (M:nat)=> (((eq nat) M_1) (suc M)))))) of role axiom named fact_293_Suc__le__D
% A new axiom: (forall (N_1:nat) (M_1:nat), (((ord_less_eq_nat (suc N_1)) M_1)->((ex nat) (fun (M:nat)=> (((eq nat) M_1) (suc M))))))
% FOF formula (forall (F:(pname->x_a)) (B:(x_a->Prop)) (A:(pname->Prop)), ((forall (X:pname), (((member_pname X) A)->((member_a (F X)) B)))->((ord_less_eq_a_o ((image_pname_a F) A)) B))) of role axiom named fact_294_image__subsetI
% A new axiom: (forall (F:(pname->x_a)) (B:(x_a->Prop)) (A:(pname->Prop)), ((forall (X:pname), (((member_pname X) A)->((member_a (F X)) B)))->((ord_less_eq_a_o ((image_pname_a F) A)) B)))
% FOF formula (forall (X_1:(nat->Prop)), ((ord_less_eq_nat_o X_1) X_1)) of role axiom named fact_295_order__refl
% A new axiom: (forall (X_1:(nat->Prop)), ((ord_less_eq_nat_o X_1) X_1))
% FOF formula (forall (X_1:(pname->Prop)), ((ord_less_eq_pname_o X_1) X_1)) of role axiom named fact_296_order__refl
% A new axiom: (forall (X_1:(pname->Prop)), ((ord_less_eq_pname_o X_1) X_1))
% FOF formula (forall (X_1:nat), ((ord_less_eq_nat X_1) X_1)) of role axiom named fact_297_order__refl
% A new axiom: (forall (X_1:nat), ((ord_less_eq_nat X_1) X_1))
% FOF formula (forall (X_1:(x_a->Prop)), ((ord_less_eq_a_o X_1) X_1)) of role axiom named fact_298_order__refl
% A new axiom: (forall (X_1:(x_a->Prop)), ((ord_less_eq_a_o X_1) X_1))
% FOF formula (forall (N:(nat->Prop)), ((iff (finite_finite_nat N)) ((ex nat) (fun (M:nat)=> (forall (X:nat), (((member_nat X) N)->((ord_less_eq_nat X) M))))))) of role axiom named fact_299_finite__nat__set__iff__bounded__le
% A new axiom: (forall (N:(nat->Prop)), ((iff (finite_finite_nat N)) ((ex nat) (fun (M:nat)=> (forall (X:nat), (((member_nat X) N)->((ord_less_eq_nat X) M)))))))
% FOF formula (finite_finite_pname u) of role hypothesis named conj_0
% A new axiom: (finite_finite_pname u)
% FOF formula ((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) of role hypothesis named conj_1
% A new axiom: ((ord_less_eq_a_o g) ((image_pname_a mgt_call) u))
% FOF formula ((ord_less_eq_nat (suc na)) (finite_card_a ((image_pname_a mgt_call) u))) of role hypothesis named conj_2
% A new axiom: ((ord_less_eq_nat (suc na)) (finite_card_a ((image_pname_a mgt_call) u)))
% FOF formula (((eq nat) (finite_card_a g)) ((minus_minus_nat (finite_card_a ((image_pname_a mgt_call) u))) (suc na))) of role hypothesis named conj_3
% A new axiom: (((eq nat) (finite_card_a g)) ((minus_minus_nat (finite_card_a ((image_pname_a mgt_call) u))) (suc na)))
% FOF formula ((member_pname pn) u) of role hypothesis named conj_4
% A new axiom: ((member_pname pn) u)
% FOF formula (((member_a (mgt_call pn)) g)->False) of role hypothesis named conj_5
% A new axiom: (((member_a (mgt_call pn)) g)->False)
% FOF formula ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((image_pname_a mgt_call) u)) of role conjecture named conj_6
% Conjecture to prove = ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((image_pname_a mgt_call) u)):Prop
% Parameter x_a_DUMMY:x_a.
% We need to prove ['((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((image_pname_a mgt_call) u))']
% Parameter x_a:Type.
% Parameter pname:Type.
% Parameter nat:Type.
% Parameter finite_card_a_o_o:((((x_a->Prop)->Prop)->Prop)->nat).
% Parameter finite221134632me_o_o:((((pname->Prop)->Prop)->Prop)->nat).
% Parameter finite_card_nat_o_o:((((nat->Prop)->Prop)->Prop)->nat).
% Parameter finite_card_a_o:(((x_a->Prop)->Prop)->nat).
% Parameter finite_card_pname_o:(((pname->Prop)->Prop)->nat).
% Parameter finite_card_nat_o:(((nat->Prop)->Prop)->nat).
% Parameter finite_card_a:((x_a->Prop)->nat).
% Parameter finite_card_pname:((pname->Prop)->nat).
% Parameter finite_card_nat:((nat->Prop)->nat).
% Parameter finite1302365357_o_o_o:(((((x_a->Prop)->Prop)->Prop)->Prop)->Prop).
% Parameter finite1648353812_o_o_o:(((((pname->Prop)->Prop)->Prop)->Prop)->Prop).
% Parameter finite1237261006_o_o_o:(((((nat->Prop)->Prop)->Prop)->Prop)->Prop).
% Parameter finite_finite_a_o_o:((((x_a->Prop)->Prop)->Prop)->Prop).
% Parameter finite1066544169me_o_o:((((pname->Prop)->Prop)->Prop)->Prop).
% Parameter finite1676163439at_o_o:((((nat->Prop)->Prop)->Prop)->Prop).
% Parameter finite_finite_a_o:(((x_a->Prop)->Prop)->Prop).
% Parameter finite297249702name_o:(((pname->Prop)->Prop)->Prop).
% Parameter finite_finite_nat_o:(((nat->Prop)->Prop)->Prop).
% Parameter finite_finite_a:((x_a->Prop)->Prop).
% Parameter finite_finite_pname:((pname->Prop)->Prop).
% Parameter finite_finite_nat:((nat->Prop)->Prop).
% Parameter minus_minus_nat:(nat->(nat->nat)).
% Parameter suc:(nat->nat).
% Parameter ord_less_eq_a_o_o_o:((((x_a->Prop)->Prop)->Prop)->((((x_a->Prop)->Prop)->Prop)->Prop)).
% Parameter ord_le1828183645_o_o_o:((((pname->Prop)->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->Prop)).
% Parameter ord_le124054423_o_o_o:((((nat->Prop)->Prop)->Prop)->((((nat->Prop)->Prop)->Prop)->Prop)).
% Parameter ord_less_eq_a_o_o:(((x_a->Prop)->Prop)->(((x_a->Prop)->Prop)->Prop)).
% Parameter ord_le1205211808me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)).
% Parameter ord_less_eq_nat_o_o:(((nat->Prop)->Prop)->(((nat->Prop)->Prop)->Prop)).
% Parameter ord_less_eq_a_o:((x_a->Prop)->((x_a->Prop)->Prop)).
% Parameter ord_less_eq_pname_o:((pname->Prop)->((pname->Prop)->Prop)).
% Parameter ord_less_eq_nat_o:((nat->Prop)->((nat->Prop)->Prop)).
% Parameter ord_less_eq_nat:(nat->(nat->Prop)).
% Parameter collect_a_o_o_o:(((((x_a->Prop)->Prop)->Prop)->Prop)->((((x_a->Prop)->Prop)->Prop)->Prop)).
% Parameter collect_pname_o_o_o:(((((pname->Prop)->Prop)->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->Prop)).
% Parameter collect_nat_o_o_o:(((((nat->Prop)->Prop)->Prop)->Prop)->((((nat->Prop)->Prop)->Prop)->Prop)).
% Parameter collect_a_o_o:((((x_a->Prop)->Prop)->Prop)->(((x_a->Prop)->Prop)->Prop)).
% Parameter collect_pname_o_o:((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)).
% Parameter collect_nat_o_o:((((nat->Prop)->Prop)->Prop)->(((nat->Prop)->Prop)->Prop)).
% Parameter collect_a_o:(((x_a->Prop)->Prop)->((x_a->Prop)->Prop)).
% Parameter collect_pname_o:(((pname->Prop)->Prop)->((pname->Prop)->Prop)).
% Parameter collect_nat_o:(((nat->Prop)->Prop)->((nat->Prop)->Prop)).
% Parameter collect_a:((x_a->Prop)->(x_a->Prop)).
% Parameter collect_pname:((pname->Prop)->(pname->Prop)).
% Parameter collect_nat:((nat->Prop)->(nat->Prop)).
% Parameter image_a_o_o_a:((((x_a->Prop)->Prop)->x_a)->((((x_a->Prop)->Prop)->Prop)->(x_a->Prop))).
% Parameter image_a_o_o_pname:((((x_a->Prop)->Prop)->pname)->((((x_a->Prop)->Prop)->Prop)->(pname->Prop))).
% Parameter image_a_o_o_nat:((((x_a->Prop)->Prop)->nat)->((((x_a->Prop)->Prop)->Prop)->(nat->Prop))).
% Parameter image_pname_o_o_a:((((pname->Prop)->Prop)->x_a)->((((pname->Prop)->Prop)->Prop)->(x_a->Prop))).
% Parameter image_471733107_pname:((((pname->Prop)->Prop)->pname)->((((pname->Prop)->Prop)->Prop)->(pname->Prop))).
% Parameter image_pname_o_o_nat:((((pname->Prop)->Prop)->nat)->((((pname->Prop)->Prop)->Prop)->(nat->Prop))).
% Parameter image_nat_o_o_a:((((nat->Prop)->Prop)->x_a)->((((nat->Prop)->Prop)->Prop)->(x_a->Prop))).
% Parameter image_nat_o_o_pname:((((nat->Prop)->Prop)->pname)->((((nat->Prop)->Prop)->Prop)->(pname->Prop))).
% Parameter image_nat_o_o_nat:((((nat->Prop)->Prop)->nat)->((((nat->Prop)->Prop)->Prop)->(nat->Prop))).
% Parameter image_a_o_a:(((x_a->Prop)->x_a)->(((x_a->Prop)->Prop)->(x_a->Prop))).
% Parameter image_a_o_pname:(((x_a->Prop)->pname)->(((x_a->Prop)->Prop)->(pname->Prop))).
% Parameter image_a_o_nat:(((x_a->Prop)->nat)->(((x_a->Prop)->Prop)->(nat->Prop))).
% Parameter image_pname_o_a:(((pname->Prop)->x_a)->(((pname->Prop)->Prop)->(x_a->Prop))).
% Parameter image_pname_o_pname:(((pname->Prop)->pname)->(((pname->Prop)->Prop)->(pname->Prop))).
% Parameter image_pname_o_nat:(((pname->Prop)->nat)->(((pname->Prop)->Prop)->(nat->Prop))).
% Parameter image_nat_o_a:(((nat->Prop)->x_a)->(((nat->Prop)->Prop)->(x_a->Prop))).
% Parameter image_nat_o_pname:(((nat->Prop)->pname)->(((nat->Prop)->Prop)->(pname->Prop))).
% Parameter image_nat_o_nat:(((nat->Prop)->nat)->(((nat->Prop)->Prop)->(nat->Prop))).
% Parameter image_a_a:((x_a->x_a)->((x_a->Prop)->(x_a->Prop))).
% Parameter image_a_pname:((x_a->pname)->((x_a->Prop)->(pname->Prop))).
% Parameter image_a_nat:((x_a->nat)->((x_a->Prop)->(nat->Prop))).
% Parameter image_pname_a_o_o:((pname->((x_a->Prop)->Prop))->((pname->Prop)->(((x_a->Prop)->Prop)->Prop))).
% Parameter image_504089495me_o_o:((pname->((pname->Prop)->Prop))->((pname->Prop)->(((pname->Prop)->Prop)->Prop))).
% Parameter image_pname_nat_o_o:((pname->((nat->Prop)->Prop))->((pname->Prop)->(((nat->Prop)->Prop)->Prop))).
% Parameter image_pname_a_o:((pname->(x_a->Prop))->((pname->Prop)->((x_a->Prop)->Prop))).
% Parameter image_pname_pname_o:((pname->(pname->Prop))->((pname->Prop)->((pname->Prop)->Prop))).
% Parameter image_pname_nat_o:((pname->(nat->Prop))->((pname->Prop)->((nat->Prop)->Prop))).
% Parameter image_pname_a:((pname->x_a)->((pname->Prop)->(x_a->Prop))).
% Parameter image_pname_pname:((pname->pname)->((pname->Prop)->(pname->Prop))).
% Parameter image_pname_nat:((pname->nat)->((pname->Prop)->(nat->Prop))).
% Parameter image_nat_a_o_o:((nat->((x_a->Prop)->Prop))->((nat->Prop)->(((x_a->Prop)->Prop)->Prop))).
% Parameter image_nat_pname_o_o:((nat->((pname->Prop)->Prop))->((nat->Prop)->(((pname->Prop)->Prop)->Prop))).
% Parameter image_nat_nat_o_o:((nat->((nat->Prop)->Prop))->((nat->Prop)->(((nat->Prop)->Prop)->Prop))).
% Parameter image_nat_a_o:((nat->(x_a->Prop))->((nat->Prop)->((x_a->Prop)->Prop))).
% Parameter image_nat_pname_o:((nat->(pname->Prop))->((nat->Prop)->((pname->Prop)->Prop))).
% Parameter image_nat_nat_o:((nat->(nat->Prop))->((nat->Prop)->((nat->Prop)->Prop))).
% Parameter image_nat_a:((nat->x_a)->((nat->Prop)->(x_a->Prop))).
% Parameter image_nat_pname:((nat->pname)->((nat->Prop)->(pname->Prop))).
% Parameter insert_a_o_o:(((x_a->Prop)->Prop)->((((x_a->Prop)->Prop)->Prop)->(((x_a->Prop)->Prop)->Prop))).
% Parameter insert_pname_o_o:(((pname->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop))).
% Parameter insert_nat_o_o:(((nat->Prop)->Prop)->((((nat->Prop)->Prop)->Prop)->(((nat->Prop)->Prop)->Prop))).
% Parameter insert_a_o:((x_a->Prop)->(((x_a->Prop)->Prop)->((x_a->Prop)->Prop))).
% Parameter insert_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter insert_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->((nat->Prop)->Prop))).
% Parameter insert_a:(x_a->((x_a->Prop)->(x_a->Prop))).
% Parameter insert_pname:(pname->((pname->Prop)->(pname->Prop))).
% Parameter insert_nat:(nat->((nat->Prop)->(nat->Prop))).
% Parameter member_a_o:((x_a->Prop)->(((x_a->Prop)->Prop)->Prop)).
% Parameter member_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->Prop)).
% Parameter member_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->Prop)).
% Parameter member_a:(x_a->((x_a->Prop)->Prop)).
% Parameter member_pname:(pname->((pname->Prop)->Prop)).
% Parameter member_nat:(nat->((nat->Prop)->Prop)).
% Parameter g:(x_a->Prop).
% Parameter p:((x_a->Prop)->((x_a->Prop)->Prop)).
% Parameter u:(pname->Prop).
% Parameter mgt_call:(pname->x_a).
% Parameter na:nat.
% Parameter pn:pname.
% Axiom fact_0_assms_I1_J:(forall (Ts:(x_a->Prop)) (G:(x_a->Prop)), (((ord_less_eq_a_o Ts) G)->((p G) Ts))).
% Axiom fact_1_finite__Collect__subsets:(forall (A_59:(nat->Prop)), ((finite_finite_nat A_59)->(finite_finite_nat_o (collect_nat_o (fun (B_38:(nat->Prop))=> ((ord_less_eq_nat_o B_38) A_59)))))).
% Axiom fact_2_finite__Collect__subsets:(forall (A_59:(pname->Prop)), ((finite_finite_pname A_59)->(finite297249702name_o (collect_pname_o (fun (B_38:(pname->Prop))=> ((ord_less_eq_pname_o B_38) A_59)))))).
% Axiom fact_3_finite__Collect__subsets:(forall (A_59:(x_a->Prop)), ((finite_finite_a A_59)->(finite_finite_a_o (collect_a_o (fun (B_38:(x_a->Prop))=> ((ord_less_eq_a_o B_38) A_59)))))).
% Axiom fact_4_finite__Collect__subsets:(forall (A_59:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o A_59)->(finite1237261006_o_o_o (collect_nat_o_o_o (fun (B_38:(((nat->Prop)->Prop)->Prop))=> ((ord_le124054423_o_o_o B_38) A_59)))))).
% Axiom fact_5_finite__Collect__subsets:(forall (A_59:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_59)->(finite1648353812_o_o_o (collect_pname_o_o_o (fun (B_38:(((pname->Prop)->Prop)->Prop))=> ((ord_le1828183645_o_o_o B_38) A_59)))))).
% Axiom fact_6_finite__Collect__subsets:(forall (A_59:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o A_59)->(finite1302365357_o_o_o (collect_a_o_o_o (fun (B_38:(((x_a->Prop)->Prop)->Prop))=> ((ord_less_eq_a_o_o_o B_38) A_59)))))).
% Axiom fact_7_finite__Collect__subsets:(forall (A_59:((x_a->Prop)->Prop)), ((finite_finite_a_o A_59)->(finite_finite_a_o_o (collect_a_o_o (fun (B_38:((x_a->Prop)->Prop))=> ((ord_less_eq_a_o_o B_38) A_59)))))).
% Axiom fact_8_finite__Collect__subsets:(forall (A_59:((pname->Prop)->Prop)), ((finite297249702name_o A_59)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_38:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_38) A_59)))))).
% Axiom fact_9_finite__Collect__subsets:(forall (A_59:((nat->Prop)->Prop)), ((finite_finite_nat_o A_59)->(finite1676163439at_o_o (collect_nat_o_o (fun (B_38:((nat->Prop)->Prop))=> ((ord_less_eq_nat_o_o B_38) A_59)))))).
% Axiom fact_10_finite__imageI:(forall (H:(pname->x_a)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_a ((image_pname_a H) F_15)))).
% Axiom fact_11_finite__imageI:(forall (H:(((nat->Prop)->Prop)->nat)) (F_15:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o F_15)->(finite_finite_nat ((image_nat_o_o_nat H) F_15)))).
% Axiom fact_12_finite__imageI:(forall (H:(((pname->Prop)->Prop)->nat)) (F_15:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_15)->(finite_finite_nat ((image_pname_o_o_nat H) F_15)))).
% Axiom fact_13_finite__imageI:(forall (H:(((x_a->Prop)->Prop)->nat)) (F_15:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o F_15)->(finite_finite_nat ((image_a_o_o_nat H) F_15)))).
% Axiom fact_14_finite__imageI:(forall (H:((x_a->Prop)->nat)) (F_15:((x_a->Prop)->Prop)), ((finite_finite_a_o F_15)->(finite_finite_nat ((image_a_o_nat H) F_15)))).
% Axiom fact_15_finite__imageI:(forall (H:((pname->Prop)->nat)) (F_15:((pname->Prop)->Prop)), ((finite297249702name_o F_15)->(finite_finite_nat ((image_pname_o_nat H) F_15)))).
% Axiom fact_16_finite__imageI:(forall (H:((nat->Prop)->nat)) (F_15:((nat->Prop)->Prop)), ((finite_finite_nat_o F_15)->(finite_finite_nat ((image_nat_o_nat H) F_15)))).
% Axiom fact_17_finite__imageI:(forall (H:(x_a->nat)) (F_15:(x_a->Prop)), ((finite_finite_a F_15)->(finite_finite_nat ((image_a_nat H) F_15)))).
% Axiom fact_18_finite__imageI:(forall (H:(((nat->Prop)->Prop)->pname)) (F_15:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o F_15)->(finite_finite_pname ((image_nat_o_o_pname H) F_15)))).
% Axiom fact_19_finite__imageI:(forall (H:(((pname->Prop)->Prop)->pname)) (F_15:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_15)->(finite_finite_pname ((image_471733107_pname H) F_15)))).
% Axiom fact_20_finite__imageI:(forall (H:(((x_a->Prop)->Prop)->pname)) (F_15:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o F_15)->(finite_finite_pname ((image_a_o_o_pname H) F_15)))).
% Axiom fact_21_finite__imageI:(forall (H:((x_a->Prop)->pname)) (F_15:((x_a->Prop)->Prop)), ((finite_finite_a_o F_15)->(finite_finite_pname ((image_a_o_pname H) F_15)))).
% Axiom fact_22_finite__imageI:(forall (H:((pname->Prop)->pname)) (F_15:((pname->Prop)->Prop)), ((finite297249702name_o F_15)->(finite_finite_pname ((image_pname_o_pname H) F_15)))).
% Axiom fact_23_finite__imageI:(forall (H:((nat->Prop)->pname)) (F_15:((nat->Prop)->Prop)), ((finite_finite_nat_o F_15)->(finite_finite_pname ((image_nat_o_pname H) F_15)))).
% Axiom fact_24_finite__imageI:(forall (H:(x_a->pname)) (F_15:(x_a->Prop)), ((finite_finite_a F_15)->(finite_finite_pname ((image_a_pname H) F_15)))).
% Axiom fact_25_finite__imageI:(forall (H:(nat->((nat->Prop)->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite1676163439at_o_o ((image_nat_nat_o_o H) F_15)))).
% Axiom fact_26_finite__imageI:(forall (H:(nat->((pname->Prop)->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite1066544169me_o_o ((image_nat_pname_o_o H) F_15)))).
% Axiom fact_27_finite__imageI:(forall (H:(nat->((x_a->Prop)->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_a_o_o ((image_nat_a_o_o H) F_15)))).
% Axiom fact_28_finite__imageI:(forall (H:(nat->(x_a->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_a_o ((image_nat_a_o H) F_15)))).
% Axiom fact_29_finite__imageI:(forall (H:(nat->(pname->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite297249702name_o ((image_nat_pname_o H) F_15)))).
% Axiom fact_30_finite__imageI:(forall (H:(nat->(nat->Prop))) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_nat_o ((image_nat_nat_o H) F_15)))).
% Axiom fact_31_finite__imageI:(forall (H:(nat->x_a)) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_a ((image_nat_a H) F_15)))).
% Axiom fact_32_finite__imageI:(forall (H:(pname->((nat->Prop)->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite1676163439at_o_o ((image_pname_nat_o_o H) F_15)))).
% Axiom fact_33_finite__imageI:(forall (H:(pname->((pname->Prop)->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite1066544169me_o_o ((image_504089495me_o_o H) F_15)))).
% Axiom fact_34_finite__imageI:(forall (H:(pname->((x_a->Prop)->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_a_o_o ((image_pname_a_o_o H) F_15)))).
% Axiom fact_35_finite__imageI:(forall (H:(pname->(x_a->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_a_o ((image_pname_a_o H) F_15)))).
% Axiom fact_36_finite__imageI:(forall (H:(pname->(pname->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite297249702name_o ((image_pname_pname_o H) F_15)))).
% Axiom fact_37_finite__imageI:(forall (H:(pname->(nat->Prop))) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_nat_o ((image_pname_nat_o H) F_15)))).
% Axiom fact_38_finite__imageI:(forall (H:(pname->pname)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_pname ((image_pname_pname H) F_15)))).
% Axiom fact_39_finite__imageI:(forall (H:(x_a->x_a)) (F_15:(x_a->Prop)), ((finite_finite_a F_15)->(finite_finite_a ((image_a_a H) F_15)))).
% Axiom fact_40_finite__imageI:(forall (H:((nat->Prop)->x_a)) (F_15:((nat->Prop)->Prop)), ((finite_finite_nat_o F_15)->(finite_finite_a ((image_nat_o_a H) F_15)))).
% Axiom fact_41_finite__imageI:(forall (H:((pname->Prop)->x_a)) (F_15:((pname->Prop)->Prop)), ((finite297249702name_o F_15)->(finite_finite_a ((image_pname_o_a H) F_15)))).
% Axiom fact_42_finite__imageI:(forall (H:((x_a->Prop)->x_a)) (F_15:((x_a->Prop)->Prop)), ((finite_finite_a_o F_15)->(finite_finite_a ((image_a_o_a H) F_15)))).
% Axiom fact_43_finite__imageI:(forall (H:(pname->nat)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->(finite_finite_nat ((image_pname_nat H) F_15)))).
% Axiom fact_44_finite__imageI:(forall (H:(nat->pname)) (F_15:(nat->Prop)), ((finite_finite_nat F_15)->(finite_finite_pname ((image_nat_pname H) F_15)))).
% Axiom fact_45_finite_OinsertI:(forall (A_58:x_a) (A_57:(x_a->Prop)), ((finite_finite_a A_57)->(finite_finite_a ((insert_a A_58) A_57)))).
% Axiom fact_46_finite_OinsertI:(forall (A_58:nat) (A_57:(nat->Prop)), ((finite_finite_nat A_57)->(finite_finite_nat ((insert_nat A_58) A_57)))).
% Axiom fact_47_finite_OinsertI:(forall (A_58:pname) (A_57:(pname->Prop)), ((finite_finite_pname A_57)->(finite_finite_pname ((insert_pname A_58) A_57)))).
% Axiom fact_48_finite_OinsertI:(forall (A_58:((nat->Prop)->Prop)) (A_57:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o A_57)->(finite1676163439at_o_o ((insert_nat_o_o A_58) A_57)))).
% Axiom fact_49_finite_OinsertI:(forall (A_58:((pname->Prop)->Prop)) (A_57:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_57)->(finite1066544169me_o_o ((insert_pname_o_o A_58) A_57)))).
% Axiom fact_50_finite_OinsertI:(forall (A_58:((x_a->Prop)->Prop)) (A_57:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o A_57)->(finite_finite_a_o_o ((insert_a_o_o A_58) A_57)))).
% Axiom fact_51_finite_OinsertI:(forall (A_58:(x_a->Prop)) (A_57:((x_a->Prop)->Prop)), ((finite_finite_a_o A_57)->(finite_finite_a_o ((insert_a_o A_58) A_57)))).
% Axiom fact_52_finite_OinsertI:(forall (A_58:(pname->Prop)) (A_57:((pname->Prop)->Prop)), ((finite297249702name_o A_57)->(finite297249702name_o ((insert_pname_o A_58) A_57)))).
% Axiom fact_53_finite_OinsertI:(forall (A_58:(nat->Prop)) (A_57:((nat->Prop)->Prop)), ((finite_finite_nat_o A_57)->(finite_finite_nat_o ((insert_nat_o A_58) A_57)))).
% Axiom fact_54_card__image__le:(forall (F_14:(pname->nat)) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_nat ((image_pname_nat F_14) A_56))) (finite_card_pname A_56)))).
% Axiom fact_55_card__image__le:(forall (F_14:(x_a->nat)) (A_56:(x_a->Prop)), ((finite_finite_a A_56)->((ord_less_eq_nat (finite_card_nat ((image_a_nat F_14) A_56))) (finite_card_a A_56)))).
% Axiom fact_56_card__image__le:(forall (F_14:((nat->Prop)->nat)) (A_56:((nat->Prop)->Prop)), ((finite_finite_nat_o A_56)->((ord_less_eq_nat (finite_card_nat ((image_nat_o_nat F_14) A_56))) (finite_card_nat_o A_56)))).
% Axiom fact_57_card__image__le:(forall (F_14:((pname->Prop)->nat)) (A_56:((pname->Prop)->Prop)), ((finite297249702name_o A_56)->((ord_less_eq_nat (finite_card_nat ((image_pname_o_nat F_14) A_56))) (finite_card_pname_o A_56)))).
% Axiom fact_58_card__image__le:(forall (F_14:((x_a->Prop)->nat)) (A_56:((x_a->Prop)->Prop)), ((finite_finite_a_o A_56)->((ord_less_eq_nat (finite_card_nat ((image_a_o_nat F_14) A_56))) (finite_card_a_o A_56)))).
% Axiom fact_59_card__image__le:(forall (F_14:(x_a->pname)) (A_56:(x_a->Prop)), ((finite_finite_a A_56)->((ord_less_eq_nat (finite_card_pname ((image_a_pname F_14) A_56))) (finite_card_a A_56)))).
% Axiom fact_60_card__image__le:(forall (F_14:(nat->pname)) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_pname ((image_nat_pname F_14) A_56))) (finite_card_nat A_56)))).
% Axiom fact_61_card__image__le:(forall (F_14:(pname->x_a)) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_a ((image_pname_a F_14) A_56))) (finite_card_pname A_56)))).
% Axiom fact_62_card__image__le:(forall (F_14:(((nat->Prop)->Prop)->x_a)) (A_56:(((nat->Prop)->Prop)->Prop)), ((finite1676163439at_o_o A_56)->((ord_less_eq_nat (finite_card_a ((image_nat_o_o_a F_14) A_56))) (finite_card_nat_o_o A_56)))).
% Axiom fact_63_card__image__le:(forall (F_14:(((pname->Prop)->Prop)->x_a)) (A_56:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_56)->((ord_less_eq_nat (finite_card_a ((image_pname_o_o_a F_14) A_56))) (finite221134632me_o_o A_56)))).
% Axiom fact_64_card__image__le:(forall (F_14:(((x_a->Prop)->Prop)->x_a)) (A_56:(((x_a->Prop)->Prop)->Prop)), ((finite_finite_a_o_o A_56)->((ord_less_eq_nat (finite_card_a ((image_a_o_o_a F_14) A_56))) (finite_card_a_o_o A_56)))).
% Axiom fact_65_card__image__le:(forall (F_14:((x_a->Prop)->x_a)) (A_56:((x_a->Prop)->Prop)), ((finite_finite_a_o A_56)->((ord_less_eq_nat (finite_card_a ((image_a_o_a F_14) A_56))) (finite_card_a_o A_56)))).
% Axiom fact_66_card__image__le:(forall (F_14:((pname->Prop)->x_a)) (A_56:((pname->Prop)->Prop)), ((finite297249702name_o A_56)->((ord_less_eq_nat (finite_card_a ((image_pname_o_a F_14) A_56))) (finite_card_pname_o A_56)))).
% Axiom fact_67_card__image__le:(forall (F_14:((nat->Prop)->x_a)) (A_56:((nat->Prop)->Prop)), ((finite_finite_nat_o A_56)->((ord_less_eq_nat (finite_card_a ((image_nat_o_a F_14) A_56))) (finite_card_nat_o A_56)))).
% Axiom fact_68_card__image__le:(forall (F_14:(x_a->x_a)) (A_56:(x_a->Prop)), ((finite_finite_a A_56)->((ord_less_eq_nat (finite_card_a ((image_a_a F_14) A_56))) (finite_card_a A_56)))).
% Axiom fact_69_card__image__le:(forall (F_14:(pname->pname)) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_pname ((image_pname_pname F_14) A_56))) (finite_card_pname A_56)))).
% Axiom fact_70_card__image__le:(forall (F_14:(pname->(nat->Prop))) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_nat_o ((image_pname_nat_o F_14) A_56))) (finite_card_pname A_56)))).
% Axiom fact_71_card__image__le:(forall (F_14:(pname->(pname->Prop))) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_pname_o ((image_pname_pname_o F_14) A_56))) (finite_card_pname A_56)))).
% Axiom fact_72_card__image__le:(forall (F_14:(pname->(x_a->Prop))) (A_56:(pname->Prop)), ((finite_finite_pname A_56)->((ord_less_eq_nat (finite_card_a_o ((image_pname_a_o F_14) A_56))) (finite_card_pname A_56)))).
% Axiom fact_73_card__image__le:(forall (F_14:(nat->x_a)) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_a ((image_nat_a F_14) A_56))) (finite_card_nat A_56)))).
% Axiom fact_74_card__image__le:(forall (F_14:(nat->(nat->Prop))) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_nat_o ((image_nat_nat_o F_14) A_56))) (finite_card_nat A_56)))).
% Axiom fact_75_card__image__le:(forall (F_14:(nat->(pname->Prop))) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_pname_o ((image_nat_pname_o F_14) A_56))) (finite_card_nat A_56)))).
% Axiom fact_76_card__image__le:(forall (F_14:(nat->(x_a->Prop))) (A_56:(nat->Prop)), ((finite_finite_nat A_56)->((ord_less_eq_nat (finite_card_a_o ((image_nat_a_o F_14) A_56))) (finite_card_nat A_56)))).
% Axiom fact_77_card__image__le:(forall (F_14:((nat->Prop)->pname)) (A_56:((nat->Prop)->Prop)), ((finite_finite_nat_o A_56)->((ord_less_eq_nat (finite_card_pname ((image_nat_o_pname F_14) A_56))) (finite_card_nat_o A_56)))).
% Axiom fact_78_card__image__le:(forall (F_14:((pname->Prop)->pname)) (A_56:((pname->Prop)->Prop)), ((finite297249702name_o A_56)->((ord_less_eq_nat (finite_card_pname ((image_pname_o_pname F_14) A_56))) (finite_card_pname_o A_56)))).
% Axiom fact_79_card__image__le:(forall (F_14:((x_a->Prop)->pname)) (A_56:((x_a->Prop)->Prop)), ((finite_finite_a_o A_56)->((ord_less_eq_nat (finite_card_pname ((image_a_o_pname F_14) A_56))) (finite_card_a_o A_56)))).
% Axiom fact_80_card__mono:(forall (A_55:((nat->Prop)->Prop)) (B_37:((nat->Prop)->Prop)), ((finite_finite_nat_o B_37)->(((ord_less_eq_nat_o_o A_55) B_37)->((ord_less_eq_nat (finite_card_nat_o A_55)) (finite_card_nat_o B_37))))).
% Axiom fact_81_card__mono:(forall (A_55:((pname->Prop)->Prop)) (B_37:((pname->Prop)->Prop)), ((finite297249702name_o B_37)->(((ord_le1205211808me_o_o A_55) B_37)->((ord_less_eq_nat (finite_card_pname_o A_55)) (finite_card_pname_o B_37))))).
% Axiom fact_82_card__mono:(forall (A_55:((x_a->Prop)->Prop)) (B_37:((x_a->Prop)->Prop)), ((finite_finite_a_o B_37)->(((ord_less_eq_a_o_o A_55) B_37)->((ord_less_eq_nat (finite_card_a_o A_55)) (finite_card_a_o B_37))))).
% Axiom fact_83_card__mono:(forall (A_55:(pname->Prop)) (B_37:(pname->Prop)), ((finite_finite_pname B_37)->(((ord_less_eq_pname_o A_55) B_37)->((ord_less_eq_nat (finite_card_pname A_55)) (finite_card_pname B_37))))).
% Axiom fact_84_card__mono:(forall (A_55:(x_a->Prop)) (B_37:(x_a->Prop)), ((finite_finite_a B_37)->(((ord_less_eq_a_o A_55) B_37)->((ord_less_eq_nat (finite_card_a A_55)) (finite_card_a B_37))))).
% Axiom fact_85_card__mono:(forall (A_55:(nat->Prop)) (B_37:(nat->Prop)), ((finite_finite_nat B_37)->(((ord_less_eq_nat_o A_55) B_37)->((ord_less_eq_nat (finite_card_nat A_55)) (finite_card_nat B_37))))).
% Axiom fact_86_card__seteq:(forall (A_54:((nat->Prop)->Prop)) (B_36:((nat->Prop)->Prop)), ((finite_finite_nat_o B_36)->(((ord_less_eq_nat_o_o A_54) B_36)->(((ord_less_eq_nat (finite_card_nat_o B_36)) (finite_card_nat_o A_54))->(((eq ((nat->Prop)->Prop)) A_54) B_36))))).
% Axiom fact_87_card__seteq:(forall (A_54:((pname->Prop)->Prop)) (B_36:((pname->Prop)->Prop)), ((finite297249702name_o B_36)->(((ord_le1205211808me_o_o A_54) B_36)->(((ord_less_eq_nat (finite_card_pname_o B_36)) (finite_card_pname_o A_54))->(((eq ((pname->Prop)->Prop)) A_54) B_36))))).
% Axiom fact_88_card__seteq:(forall (A_54:((x_a->Prop)->Prop)) (B_36:((x_a->Prop)->Prop)), ((finite_finite_a_o B_36)->(((ord_less_eq_a_o_o A_54) B_36)->(((ord_less_eq_nat (finite_card_a_o B_36)) (finite_card_a_o A_54))->(((eq ((x_a->Prop)->Prop)) A_54) B_36))))).
% Axiom fact_89_card__seteq:(forall (A_54:(pname->Prop)) (B_36:(pname->Prop)), ((finite_finite_pname B_36)->(((ord_less_eq_pname_o A_54) B_36)->(((ord_less_eq_nat (finite_card_pname B_36)) (finite_card_pname A_54))->(((eq (pname->Prop)) A_54) B_36))))).
% Axiom fact_90_card__seteq:(forall (A_54:(x_a->Prop)) (B_36:(x_a->Prop)), ((finite_finite_a B_36)->(((ord_less_eq_a_o A_54) B_36)->(((ord_less_eq_nat (finite_card_a B_36)) (finite_card_a A_54))->(((eq (x_a->Prop)) A_54) B_36))))).
% Axiom fact_91_card__seteq:(forall (A_54:(nat->Prop)) (B_36:(nat->Prop)), ((finite_finite_nat B_36)->(((ord_less_eq_nat_o A_54) B_36)->(((ord_less_eq_nat (finite_card_nat B_36)) (finite_card_nat A_54))->(((eq (nat->Prop)) A_54) B_36))))).
% Axiom fact_92_card__insert__le:(forall (X_19:(nat->Prop)) (A_53:((nat->Prop)->Prop)), ((finite_finite_nat_o A_53)->((ord_less_eq_nat (finite_card_nat_o A_53)) (finite_card_nat_o ((insert_nat_o X_19) A_53))))).
% Axiom fact_93_card__insert__le:(forall (X_19:(pname->Prop)) (A_53:((pname->Prop)->Prop)), ((finite297249702name_o A_53)->((ord_less_eq_nat (finite_card_pname_o A_53)) (finite_card_pname_o ((insert_pname_o X_19) A_53))))).
% Axiom fact_94_card__insert__le:(forall (X_19:(x_a->Prop)) (A_53:((x_a->Prop)->Prop)), ((finite_finite_a_o A_53)->((ord_less_eq_nat (finite_card_a_o A_53)) (finite_card_a_o ((insert_a_o X_19) A_53))))).
% Axiom fact_95_card__insert__le:(forall (X_19:pname) (A_53:(pname->Prop)), ((finite_finite_pname A_53)->((ord_less_eq_nat (finite_card_pname A_53)) (finite_card_pname ((insert_pname X_19) A_53))))).
% Axiom fact_96_card__insert__le:(forall (X_19:nat) (A_53:(nat->Prop)), ((finite_finite_nat A_53)->((ord_less_eq_nat (finite_card_nat A_53)) (finite_card_nat ((insert_nat X_19) A_53))))).
% Axiom fact_97_card__insert__le:(forall (X_19:x_a) (A_53:(x_a->Prop)), ((finite_finite_a A_53)->((ord_less_eq_nat (finite_card_a A_53)) (finite_card_a ((insert_a X_19) A_53))))).
% Axiom fact_98_card__insert__if:(forall (X_18:(nat->Prop)) (A_52:((nat->Prop)->Prop)), ((finite_finite_nat_o A_52)->((and (((member_nat_o X_18) A_52)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_18) A_52))) (finite_card_nat_o A_52)))) ((((member_nat_o X_18) A_52)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_18) A_52))) (suc (finite_card_nat_o A_52))))))).
% Axiom fact_99_card__insert__if:(forall (X_18:(pname->Prop)) (A_52:((pname->Prop)->Prop)), ((finite297249702name_o A_52)->((and (((member_pname_o X_18) A_52)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_18) A_52))) (finite_card_pname_o A_52)))) ((((member_pname_o X_18) A_52)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_18) A_52))) (suc (finite_card_pname_o A_52))))))).
% Axiom fact_100_card__insert__if:(forall (X_18:(x_a->Prop)) (A_52:((x_a->Prop)->Prop)), ((finite_finite_a_o A_52)->((and (((member_a_o X_18) A_52)->(((eq nat) (finite_card_a_o ((insert_a_o X_18) A_52))) (finite_card_a_o A_52)))) ((((member_a_o X_18) A_52)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_18) A_52))) (suc (finite_card_a_o A_52))))))).
% Axiom fact_101_card__insert__if:(forall (X_18:nat) (A_52:(nat->Prop)), ((finite_finite_nat A_52)->((and (((member_nat X_18) A_52)->(((eq nat) (finite_card_nat ((insert_nat X_18) A_52))) (finite_card_nat A_52)))) ((((member_nat X_18) A_52)->False)->(((eq nat) (finite_card_nat ((insert_nat X_18) A_52))) (suc (finite_card_nat A_52))))))).
% Axiom fact_102_card__insert__if:(forall (X_18:pname) (A_52:(pname->Prop)), ((finite_finite_pname A_52)->((and (((member_pname X_18) A_52)->(((eq nat) (finite_card_pname ((insert_pname X_18) A_52))) (finite_card_pname A_52)))) ((((member_pname X_18) A_52)->False)->(((eq nat) (finite_card_pname ((insert_pname X_18) A_52))) (suc (finite_card_pname A_52))))))).
% Axiom fact_103_card__insert__if:(forall (X_18:x_a) (A_52:(x_a->Prop)), ((finite_finite_a A_52)->((and (((member_a X_18) A_52)->(((eq nat) (finite_card_a ((insert_a X_18) A_52))) (finite_card_a A_52)))) ((((member_a X_18) A_52)->False)->(((eq nat) (finite_card_a ((insert_a X_18) A_52))) (suc (finite_card_a A_52))))))).
% Axiom fact_104_card__insert__disjoint:(forall (X_17:(nat->Prop)) (A_51:((nat->Prop)->Prop)), ((finite_finite_nat_o A_51)->((((member_nat_o X_17) A_51)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_17) A_51))) (suc (finite_card_nat_o A_51)))))).
% Axiom fact_105_card__insert__disjoint:(forall (X_17:(pname->Prop)) (A_51:((pname->Prop)->Prop)), ((finite297249702name_o A_51)->((((member_pname_o X_17) A_51)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_17) A_51))) (suc (finite_card_pname_o A_51)))))).
% Axiom fact_106_card__insert__disjoint:(forall (X_17:(x_a->Prop)) (A_51:((x_a->Prop)->Prop)), ((finite_finite_a_o A_51)->((((member_a_o X_17) A_51)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_17) A_51))) (suc (finite_card_a_o A_51)))))).
% Axiom fact_107_card__insert__disjoint:(forall (X_17:nat) (A_51:(nat->Prop)), ((finite_finite_nat A_51)->((((member_nat X_17) A_51)->False)->(((eq nat) (finite_card_nat ((insert_nat X_17) A_51))) (suc (finite_card_nat A_51)))))).
% Axiom fact_108_card__insert__disjoint:(forall (X_17:pname) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->((((member_pname X_17) A_51)->False)->(((eq nat) (finite_card_pname ((insert_pname X_17) A_51))) (suc (finite_card_pname A_51)))))).
% Axiom fact_109_card__insert__disjoint:(forall (X_17:x_a) (A_51:(x_a->Prop)), ((finite_finite_a A_51)->((((member_a X_17) A_51)->False)->(((eq nat) (finite_card_a ((insert_a X_17) A_51))) (suc (finite_card_a A_51)))))).
% Axiom fact_110_finite__Collect__conjI:(forall (Q_1:((nat->Prop)->Prop)) (P_4:((nat->Prop)->Prop)), (((or (finite_finite_nat_o (collect_nat_o P_4))) (finite_finite_nat_o (collect_nat_o Q_1)))->(finite_finite_nat_o (collect_nat_o (fun (X:(nat->Prop))=> ((and (P_4 X)) (Q_1 X))))))).
% Axiom fact_111_finite__Collect__conjI:(forall (Q_1:((pname->Prop)->Prop)) (P_4:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_4))) (finite297249702name_o (collect_pname_o Q_1)))->(finite297249702name_o (collect_pname_o (fun (X:(pname->Prop))=> ((and (P_4 X)) (Q_1 X))))))).
% Axiom fact_112_finite__Collect__conjI:(forall (Q_1:((x_a->Prop)->Prop)) (P_4:((x_a->Prop)->Prop)), (((or (finite_finite_a_o (collect_a_o P_4))) (finite_finite_a_o (collect_a_o Q_1)))->(finite_finite_a_o (collect_a_o (fun (X:(x_a->Prop))=> ((and (P_4 X)) (Q_1 X))))))).
% Axiom fact_113_finite__Collect__conjI:(forall (Q_1:(x_a->Prop)) (P_4:(x_a->Prop)), (((or (finite_finite_a (collect_a P_4))) (finite_finite_a (collect_a Q_1)))->(finite_finite_a (collect_a (fun (X:x_a)=> ((and (P_4 X)) (Q_1 X))))))).
% Axiom fact_114_finite__Collect__conjI:(forall (Q_1:(pname->Prop)) (P_4:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_4))) (finite_finite_pname (collect_pname Q_1)))->(finite_finite_pname (collect_pname (fun (X:pname)=> ((and (P_4 X)) (Q_1 X))))))).
% Axiom fact_115_finite__Collect__conjI:(forall (Q_1:(nat->Prop)) (P_4:(nat->Prop)), (((or (finite_finite_nat (collect_nat P_4))) (finite_finite_nat (collect_nat Q_1)))->(finite_finite_nat (collect_nat (fun (X:nat)=> ((and (P_4 X)) (Q_1 X))))))).
% Axiom fact_116_Suc__diff__le:(forall (N_1:nat) (M_2:nat), (((ord_less_eq_nat N_1) M_2)->(((eq nat) ((minus_minus_nat (suc M_2)) N_1)) (suc ((minus_minus_nat M_2) N_1))))).
% Axiom fact_117_finite__Collect__le__nat:(forall (K:nat), (finite_finite_nat (collect_nat (fun (N_2:nat)=> ((ord_less_eq_nat N_2) K))))).
% Axiom fact_118_card__Collect__le__nat:(forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_eq_nat I_1) N_1))))) (suc N_1))).
% Axiom fact_119_Suc__inject:(forall (X_16:nat) (Y_3:nat), ((((eq nat) (suc X_16)) (suc Y_3))->(((eq nat) X_16) Y_3))).
% Axiom fact_120_nat_Oinject:(forall (Nat_1:nat) (Nat:nat), ((iff (((eq nat) (suc Nat_1)) (suc Nat))) (((eq nat) Nat_1) Nat))).
% Axiom fact_121_Suc__n__not__n:(forall (N_1:nat), (not (((eq nat) (suc N_1)) N_1))).
% Axiom fact_122_n__not__Suc__n:(forall (N_1:nat), (not (((eq nat) N_1) (suc N_1)))).
% Axiom fact_123_le__antisym:(forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->(((ord_less_eq_nat N_1) M_2)->(((eq nat) M_2) N_1)))).
% Axiom fact_124_le__trans:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat _TPTP_I) K)))).
% Axiom fact_125_eq__imp__le:(forall (M_2:nat) (N_1:nat), ((((eq nat) M_2) N_1)->((ord_less_eq_nat M_2) N_1))).
% Axiom fact_126_nat__le__linear:(forall (M_2:nat) (N_1:nat), ((or ((ord_less_eq_nat M_2) N_1)) ((ord_less_eq_nat N_1) M_2))).
% Axiom fact_127_le__refl:(forall (N_1:nat), ((ord_less_eq_nat N_1) N_1)).
% Axiom fact_128_diff__commute:(forall (_TPTP_I:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat _TPTP_I) J)) K)) ((minus_minus_nat ((minus_minus_nat _TPTP_I) K)) J))).
% Axiom fact_129_finite__Collect__disjI:(forall (P_3:(pname->Prop)) (Q:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X:pname)=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_pname (collect_pname P_3))) (finite_finite_pname (collect_pname Q))))).
% Axiom fact_130_finite__Collect__disjI:(forall (P_3:((nat->Prop)->Prop)) (Q:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o (collect_nat_o (fun (X:(nat->Prop))=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_nat_o (collect_nat_o P_3))) (finite_finite_nat_o (collect_nat_o Q))))).
% Axiom fact_131_finite__Collect__disjI:(forall (P_3:((pname->Prop)->Prop)) (Q:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X:(pname->Prop))=> ((or (P_3 X)) (Q X)))))) ((and (finite297249702name_o (collect_pname_o P_3))) (finite297249702name_o (collect_pname_o Q))))).
% Axiom fact_132_finite__Collect__disjI:(forall (P_3:((x_a->Prop)->Prop)) (Q:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o (collect_a_o (fun (X:(x_a->Prop))=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_a_o (collect_a_o P_3))) (finite_finite_a_o (collect_a_o Q))))).
% Axiom fact_133_finite__Collect__disjI:(forall (P_3:(nat->Prop)) (Q:(nat->Prop)), ((iff (finite_finite_nat (collect_nat (fun (X:nat)=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_nat (collect_nat P_3))) (finite_finite_nat (collect_nat Q))))).
% Axiom fact_134_finite__Collect__disjI:(forall (P_3:(x_a->Prop)) (Q:(x_a->Prop)), ((iff (finite_finite_a (collect_a (fun (X:x_a)=> ((or (P_3 X)) (Q X)))))) ((and (finite_finite_a (collect_a P_3))) (finite_finite_a (collect_a Q))))).
% Axiom fact_135_finite__insert:(forall (A_50:nat) (A_49:(nat->Prop)), ((iff (finite_finite_nat ((insert_nat A_50) A_49))) (finite_finite_nat A_49))).
% Axiom fact_136_finite__insert:(forall (A_50:pname) (A_49:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_50) A_49))) (finite_finite_pname A_49))).
% Axiom fact_137_finite__insert:(forall (A_50:x_a) (A_49:(x_a->Prop)), ((iff (finite_finite_a ((insert_a A_50) A_49))) (finite_finite_a A_49))).
% Axiom fact_138_finite__insert:(forall (A_50:(nat->Prop)) (A_49:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o ((insert_nat_o A_50) A_49))) (finite_finite_nat_o A_49))).
% Axiom fact_139_finite__insert:(forall (A_50:(pname->Prop)) (A_49:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_50) A_49))) (finite297249702name_o A_49))).
% Axiom fact_140_finite__insert:(forall (A_50:(x_a->Prop)) (A_49:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o ((insert_a_o A_50) A_49))) (finite_finite_a_o A_49))).
% Axiom fact_141_finite__subset:(forall (A_48:((nat->Prop)->Prop)) (B_35:((nat->Prop)->Prop)), (((ord_less_eq_nat_o_o A_48) B_35)->((finite_finite_nat_o B_35)->(finite_finite_nat_o A_48)))).
% Axiom fact_142_finite__subset:(forall (A_48:((pname->Prop)->Prop)) (B_35:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_48) B_35)->((finite297249702name_o B_35)->(finite297249702name_o A_48)))).
% Axiom fact_143_finite__subset:(forall (A_48:(x_a->Prop)) (B_35:(x_a->Prop)), (((ord_less_eq_a_o A_48) B_35)->((finite_finite_a B_35)->(finite_finite_a A_48)))).
% Axiom fact_144_finite__subset:(forall (A_48:((x_a->Prop)->Prop)) (B_35:((x_a->Prop)->Prop)), (((ord_less_eq_a_o_o A_48) B_35)->((finite_finite_a_o B_35)->(finite_finite_a_o A_48)))).
% Axiom fact_145_finite__subset:(forall (A_48:(nat->Prop)) (B_35:(nat->Prop)), (((ord_less_eq_nat_o A_48) B_35)->((finite_finite_nat B_35)->(finite_finite_nat A_48)))).
% Axiom fact_146_finite__subset:(forall (A_48:(pname->Prop)) (B_35:(pname->Prop)), (((ord_less_eq_pname_o A_48) B_35)->((finite_finite_pname B_35)->(finite_finite_pname A_48)))).
% Axiom fact_147_rev__finite__subset:(forall (A_47:((nat->Prop)->Prop)) (B_34:((nat->Prop)->Prop)), ((finite_finite_nat_o B_34)->(((ord_less_eq_nat_o_o A_47) B_34)->(finite_finite_nat_o A_47)))).
% Axiom fact_148_rev__finite__subset:(forall (A_47:((pname->Prop)->Prop)) (B_34:((pname->Prop)->Prop)), ((finite297249702name_o B_34)->(((ord_le1205211808me_o_o A_47) B_34)->(finite297249702name_o A_47)))).
% Axiom fact_149_rev__finite__subset:(forall (A_47:(x_a->Prop)) (B_34:(x_a->Prop)), ((finite_finite_a B_34)->(((ord_less_eq_a_o A_47) B_34)->(finite_finite_a A_47)))).
% Axiom fact_150_rev__finite__subset:(forall (A_47:((x_a->Prop)->Prop)) (B_34:((x_a->Prop)->Prop)), ((finite_finite_a_o B_34)->(((ord_less_eq_a_o_o A_47) B_34)->(finite_finite_a_o A_47)))).
% Axiom fact_151_rev__finite__subset:(forall (A_47:(nat->Prop)) (B_34:(nat->Prop)), ((finite_finite_nat B_34)->(((ord_less_eq_nat_o A_47) B_34)->(finite_finite_nat A_47)))).
% Axiom fact_152_rev__finite__subset:(forall (A_47:(pname->Prop)) (B_34:(pname->Prop)), ((finite_finite_pname B_34)->(((ord_less_eq_pname_o A_47) B_34)->(finite_finite_pname A_47)))).
% Axiom fact_153_Suc__leD:(forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat (suc M_2)) N_1)->((ord_less_eq_nat M_2) N_1))).
% Axiom fact_154_le__SucE:(forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) (suc N_1))->((((ord_less_eq_nat M_2) N_1)->False)->(((eq nat) M_2) (suc N_1))))).
% Axiom fact_155_le__SucI:(forall (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->((ord_less_eq_nat M_2) (suc N_1)))).
% Axiom fact_156_Suc__le__mono:(forall (N_1:nat) (M_2:nat), ((iff ((ord_less_eq_nat (suc N_1)) (suc M_2))) ((ord_less_eq_nat N_1) M_2))).
% Axiom fact_157_le__Suc__eq:(forall (M_2:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_2) (suc N_1))) ((or ((ord_less_eq_nat M_2) N_1)) (((eq nat) M_2) (suc N_1))))).
% Axiom fact_158_not__less__eq__eq:(forall (M_2:nat) (N_1:nat), ((iff (((ord_less_eq_nat M_2) N_1)->False)) ((ord_less_eq_nat (suc N_1)) M_2))).
% Axiom fact_159_Suc__n__not__le__n:(forall (N_1:nat), (((ord_less_eq_nat (suc N_1)) N_1)->False)).
% Axiom fact_160_Suc__diff__diff:(forall (M_2:nat) (N_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M_2)) N_1)) (suc K))) ((minus_minus_nat ((minus_minus_nat M_2) N_1)) K))).
% Axiom fact_161_diff__Suc__Suc:(forall (M_2:nat) (N_1:nat), (((eq nat) ((minus_minus_nat (suc M_2)) (suc N_1))) ((minus_minus_nat M_2) N_1))).
% Axiom fact_162_le__diff__iff:(forall (N_1:nat) (K:nat) (M_2:nat), (((ord_less_eq_nat K) M_2)->(((ord_less_eq_nat K) N_1)->((iff ((ord_less_eq_nat ((minus_minus_nat M_2) K)) ((minus_minus_nat N_1) K))) ((ord_less_eq_nat M_2) N_1))))).
% Axiom fact_163_Nat_Odiff__diff__eq:(forall (N_1:nat) (K:nat) (M_2:nat), (((ord_less_eq_nat K) M_2)->(((ord_less_eq_nat K) N_1)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M_2) K)) ((minus_minus_nat N_1) K))) ((minus_minus_nat M_2) N_1))))).
% Axiom fact_164_eq__diff__iff:(forall (N_1:nat) (K:nat) (M_2:nat), (((ord_less_eq_nat K) M_2)->(((ord_less_eq_nat K) N_1)->((iff (((eq nat) ((minus_minus_nat M_2) K)) ((minus_minus_nat N_1) K))) (((eq nat) M_2) N_1))))).
% Axiom fact_165_diff__diff__cancel:(forall (_TPTP_I:nat) (N_1:nat), (((ord_less_eq_nat _TPTP_I) N_1)->(((eq nat) ((minus_minus_nat N_1) ((minus_minus_nat N_1) _TPTP_I))) _TPTP_I))).
% Axiom fact_166_diff__le__mono:(forall (L:nat) (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->((ord_less_eq_nat ((minus_minus_nat M_2) L)) ((minus_minus_nat N_1) L)))).
% Axiom fact_167_diff__le__mono2:(forall (L:nat) (M_2:nat) (N_1:nat), (((ord_less_eq_nat M_2) N_1)->((ord_less_eq_nat ((minus_minus_nat L) N_1)) ((minus_minus_nat L) M_2)))).
% Axiom fact_168_diff__le__self:(forall (M_2:nat) (N_1:nat), ((ord_less_eq_nat ((minus_minus_nat M_2) N_1)) M_2)).
% Axiom fact_169_finite__surj:(forall (B_33:(x_a->Prop)) (F_13:(pname->x_a)) (A_46:(pname->Prop)), ((finite_finite_pname A_46)->(((ord_less_eq_a_o B_33) ((image_pname_a F_13) A_46))->(finite_finite_a B_33)))).
% Axiom fact_170_finite__subset__image:(forall (F_12:(pname->x_a)) (A_45:(pname->Prop)) (B_32:(x_a->Prop)), ((finite_finite_a B_32)->(((ord_less_eq_a_o B_32) ((image_pname_a F_12) A_45))->((ex (pname->Prop)) (fun (C_3:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_3) A_45)) (finite_finite_pname C_3))) (((eq (x_a->Prop)) B_32) ((image_pname_a F_12) C_3)))))))).
% Axiom fact_171_lift__Suc__mono__le:(forall (N_4:nat) (N_3:nat) (F_11:(nat->(nat->Prop))), ((forall (N_2:nat), ((ord_less_eq_nat_o (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat_o (F_11 N_4)) (F_11 N_3))))).
% Axiom fact_172_lift__Suc__mono__le:(forall (N_4:nat) (N_3:nat) (F_11:(nat->(pname->Prop))), ((forall (N_2:nat), ((ord_less_eq_pname_o (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_pname_o (F_11 N_4)) (F_11 N_3))))).
% Axiom fact_173_lift__Suc__mono__le:(forall (N_4:nat) (N_3:nat) (F_11:(nat->nat)), ((forall (N_2:nat), ((ord_less_eq_nat (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat (F_11 N_4)) (F_11 N_3))))).
% Axiom fact_174_lift__Suc__mono__le:(forall (N_4:nat) (N_3:nat) (F_11:(nat->(x_a->Prop))), ((forall (N_2:nat), ((ord_less_eq_a_o (F_11 N_2)) (F_11 (suc N_2))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_a_o (F_11 N_4)) (F_11 N_3))))).
% Axiom fact_175_pigeonhole__infinite:(forall (F_10:(pname->x_a)) (A_43:(pname->Prop)), (((finite_finite_pname A_43)->False)->((finite_finite_a ((image_pname_a F_10) A_43))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_43)) ((finite_finite_pname (collect_pname (fun (A_44:pname)=> ((and ((member_pname A_44) A_43)) (((eq x_a) (F_10 A_44)) (F_10 X))))))->False))))))).
% Axiom fact_176_image__eqI:(forall (A_42:(pname->Prop)) (B_31:x_a) (F_9:(pname->x_a)) (X_15:pname), ((((eq x_a) B_31) (F_9 X_15))->(((member_pname X_15) A_42)->((member_a B_31) ((image_pname_a F_9) A_42))))).
% Axiom fact_177_equalityI:(forall (A_41:(nat->Prop)) (B_30:(nat->Prop)), (((ord_less_eq_nat_o A_41) B_30)->(((ord_less_eq_nat_o B_30) A_41)->(((eq (nat->Prop)) A_41) B_30)))).
% Axiom fact_178_equalityI:(forall (A_41:(pname->Prop)) (B_30:(pname->Prop)), (((ord_less_eq_pname_o A_41) B_30)->(((ord_less_eq_pname_o B_30) A_41)->(((eq (pname->Prop)) A_41) B_30)))).
% Axiom fact_179_equalityI:(forall (A_41:(x_a->Prop)) (B_30:(x_a->Prop)), (((ord_less_eq_a_o A_41) B_30)->(((ord_less_eq_a_o B_30) A_41)->(((eq (x_a->Prop)) A_41) B_30)))).
% Axiom fact_180_subsetD:(forall (C_2:nat) (A_40:(nat->Prop)) (B_29:(nat->Prop)), (((ord_less_eq_nat_o A_40) B_29)->(((member_nat C_2) A_40)->((member_nat C_2) B_29)))).
% Axiom fact_181_subsetD:(forall (C_2:x_a) (A_40:(x_a->Prop)) (B_29:(x_a->Prop)), (((ord_less_eq_a_o A_40) B_29)->(((member_a C_2) A_40)->((member_a C_2) B_29)))).
% Axiom fact_182_subsetD:(forall (C_2:pname) (A_40:(pname->Prop)) (B_29:(pname->Prop)), (((ord_less_eq_pname_o A_40) B_29)->(((member_pname C_2) A_40)->((member_pname C_2) B_29)))).
% Axiom fact_183_insertCI:(forall (B_28:nat) (A_39:nat) (B_27:(nat->Prop)), (((((member_nat A_39) B_27)->False)->(((eq nat) A_39) B_28))->((member_nat A_39) ((insert_nat B_28) B_27)))).
% Axiom fact_184_insertCI:(forall (B_28:pname) (A_39:pname) (B_27:(pname->Prop)), (((((member_pname A_39) B_27)->False)->(((eq pname) A_39) B_28))->((member_pname A_39) ((insert_pname B_28) B_27)))).
% Axiom fact_185_insertCI:(forall (B_28:x_a) (A_39:x_a) (B_27:(x_a->Prop)), (((((member_a A_39) B_27)->False)->(((eq x_a) A_39) B_28))->((member_a A_39) ((insert_a B_28) B_27)))).
% Axiom fact_186_insertE:(forall (A_38:nat) (B_26:nat) (A_37:(nat->Prop)), (((member_nat A_38) ((insert_nat B_26) A_37))->((not (((eq nat) A_38) B_26))->((member_nat A_38) A_37)))).
% Axiom fact_187_insertE:(forall (A_38:pname) (B_26:pname) (A_37:(pname->Prop)), (((member_pname A_38) ((insert_pname B_26) A_37))->((not (((eq pname) A_38) B_26))->((member_pname A_38) A_37)))).
% Axiom fact_188_insertE:(forall (A_38:x_a) (B_26:x_a) (A_37:(x_a->Prop)), (((member_a A_38) ((insert_a B_26) A_37))->((not (((eq x_a) A_38) B_26))->((member_a A_38) A_37)))).
% Axiom fact_189_insertI1:(forall (A_36:nat) (B_25:(nat->Prop)), ((member_nat A_36) ((insert_nat A_36) B_25))).
% Axiom fact_190_insertI1:(forall (A_36:pname) (B_25:(pname->Prop)), ((member_pname A_36) ((insert_pname A_36) B_25))).
% Axiom fact_191_insertI1:(forall (A_36:x_a) (B_25:(x_a->Prop)), ((member_a A_36) ((insert_a A_36) B_25))).
% Axiom fact_192_insert__compr:(forall (A_35:nat) (B_24:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_35) B_24)) (collect_nat (fun (X:nat)=> ((or (((eq nat) X) A_35)) ((member_nat X) B_24)))))).
% Axiom fact_193_insert__compr:(forall (A_35:pname) (B_24:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_35) B_24)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_35)) ((member_pname X) B_24)))))).
% Axiom fact_194_insert__compr:(forall (A_35:x_a) (B_24:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_35) B_24)) (collect_a (fun (X:x_a)=> ((or (((eq x_a) X) A_35)) ((member_a X) B_24)))))).
% Axiom fact_195_insert__compr:(forall (A_35:(nat->Prop)) (B_24:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) ((insert_nat_o A_35) B_24)) (collect_nat_o (fun (X:(nat->Prop))=> ((or (((eq (nat->Prop)) X) A_35)) ((member_nat_o X) B_24)))))).
% Axiom fact_196_insert__compr:(forall (A_35:(pname->Prop)) (B_24:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_35) B_24)) (collect_pname_o (fun (X:(pname->Prop))=> ((or (((eq (pname->Prop)) X) A_35)) ((member_pname_o X) B_24)))))).
% Axiom fact_197_insert__compr:(forall (A_35:(x_a->Prop)) (B_24:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) ((insert_a_o A_35) B_24)) (collect_a_o (fun (X:(x_a->Prop))=> ((or (((eq (x_a->Prop)) X) A_35)) ((member_a_o X) B_24)))))).
% Axiom fact_198_insert__Collect:(forall (A_34:nat) (P_2:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_34) (collect_nat P_2))) (collect_nat (fun (U:nat)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq nat) U) A_34))) (P_2 U)))))).
% Axiom fact_199_insert__Collect:(forall (A_34:pname) (P_2:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_34) (collect_pname P_2))) (collect_pname (fun (U:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U) A_34))) (P_2 U)))))).
% Axiom fact_200_insert__Collect:(forall (A_34:x_a) (P_2:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_34) (collect_a P_2))) (collect_a (fun (U:x_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq x_a) U) A_34))) (P_2 U)))))).
% Axiom fact_201_insert__Collect:(forall (A_34:(nat->Prop)) (P_2:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) ((insert_nat_o A_34) (collect_nat_o P_2))) (collect_nat_o (fun (U:(nat->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (nat->Prop)) U) A_34))) (P_2 U)))))).
% Axiom fact_202_insert__Collect:(forall (A_34:(pname->Prop)) (P_2:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_34) (collect_pname_o P_2))) (collect_pname_o (fun (U:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U) A_34))) (P_2 U)))))).
% Axiom fact_203_insert__Collect:(forall (A_34:(x_a->Prop)) (P_2:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) ((insert_a_o A_34) (collect_a_o P_2))) (collect_a_o (fun (U:(x_a->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (x_a->Prop)) U) A_34))) (P_2 U)))))).
% Axiom fact_204_insert__absorb2:(forall (X_14:nat) (A_33:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_14) ((insert_nat X_14) A_33))) ((insert_nat X_14) A_33))).
% Axiom fact_205_insert__absorb2:(forall (X_14:pname) (A_33:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_14) ((insert_pname X_14) A_33))) ((insert_pname X_14) A_33))).
% Axiom fact_206_insert__absorb2:(forall (X_14:x_a) (A_33:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_14) ((insert_a X_14) A_33))) ((insert_a X_14) A_33))).
% Axiom fact_207_insert__commute:(forall (X_13:nat) (Y_2:nat) (A_32:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_13) ((insert_nat Y_2) A_32))) ((insert_nat Y_2) ((insert_nat X_13) A_32)))).
% Axiom fact_208_insert__commute:(forall (X_13:pname) (Y_2:pname) (A_32:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_13) ((insert_pname Y_2) A_32))) ((insert_pname Y_2) ((insert_pname X_13) A_32)))).
% Axiom fact_209_insert__commute:(forall (X_13:x_a) (Y_2:x_a) (A_32:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_13) ((insert_a Y_2) A_32))) ((insert_a Y_2) ((insert_a X_13) A_32)))).
% Axiom fact_210_insert__iff:(forall (A_31:nat) (B_23:nat) (A_30:(nat->Prop)), ((iff ((member_nat A_31) ((insert_nat B_23) A_30))) ((or (((eq nat) A_31) B_23)) ((member_nat A_31) A_30)))).
% Axiom fact_211_insert__iff:(forall (A_31:pname) (B_23:pname) (A_30:(pname->Prop)), ((iff ((member_pname A_31) ((insert_pname B_23) A_30))) ((or (((eq pname) A_31) B_23)) ((member_pname A_31) A_30)))).
% Axiom fact_212_insert__iff:(forall (A_31:x_a) (B_23:x_a) (A_30:(x_a->Prop)), ((iff ((member_a A_31) ((insert_a B_23) A_30))) ((or (((eq x_a) A_31) B_23)) ((member_a A_31) A_30)))).
% Axiom fact_213_insert__code:(forall (Y_1:nat) (A_29:(nat->Prop)) (X_12:nat), ((iff (((insert_nat Y_1) A_29) X_12)) ((or (((eq nat) Y_1) X_12)) (A_29 X_12)))).
% Axiom fact_214_insert__code:(forall (Y_1:pname) (A_29:(pname->Prop)) (X_12:pname), ((iff (((insert_pname Y_1) A_29) X_12)) ((or (((eq pname) Y_1) X_12)) (A_29 X_12)))).
% Axiom fact_215_insert__code:(forall (Y_1:x_a) (A_29:(x_a->Prop)) (X_12:x_a), ((iff (((insert_a Y_1) A_29) X_12)) ((or (((eq x_a) Y_1) X_12)) (A_29 X_12)))).
% Axiom fact_216_insert__ident:(forall (B_22:(nat->Prop)) (X_11:nat) (A_28:(nat->Prop)), ((((member_nat X_11) A_28)->False)->((((member_nat X_11) B_22)->False)->((iff (((eq (nat->Prop)) ((insert_nat X_11) A_28)) ((insert_nat X_11) B_22))) (((eq (nat->Prop)) A_28) B_22))))).
% Axiom fact_217_insert__ident:(forall (B_22:(pname->Prop)) (X_11:pname) (A_28:(pname->Prop)), ((((member_pname X_11) A_28)->False)->((((member_pname X_11) B_22)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_11) A_28)) ((insert_pname X_11) B_22))) (((eq (pname->Prop)) A_28) B_22))))).
% Axiom fact_218_insert__ident:(forall (B_22:(x_a->Prop)) (X_11:x_a) (A_28:(x_a->Prop)), ((((member_a X_11) A_28)->False)->((((member_a X_11) B_22)->False)->((iff (((eq (x_a->Prop)) ((insert_a X_11) A_28)) ((insert_a X_11) B_22))) (((eq (x_a->Prop)) A_28) B_22))))).
% Axiom fact_219_insertI2:(forall (B_21:nat) (A_27:nat) (B_20:(nat->Prop)), (((member_nat A_27) B_20)->((member_nat A_27) ((insert_nat B_21) B_20)))).
% Axiom fact_220_insertI2:(forall (B_21:pname) (A_27:pname) (B_20:(pname->Prop)), (((member_pname A_27) B_20)->((member_pname A_27) ((insert_pname B_21) B_20)))).
% Axiom fact_221_insertI2:(forall (B_21:x_a) (A_27:x_a) (B_20:(x_a->Prop)), (((member_a A_27) B_20)->((member_a A_27) ((insert_a B_21) B_20)))).
% Axiom fact_222_insert__absorb:(forall (A_26:nat) (A_25:(nat->Prop)), (((member_nat A_26) A_25)->(((eq (nat->Prop)) ((insert_nat A_26) A_25)) A_25))).
% Axiom fact_223_insert__absorb:(forall (A_26:pname) (A_25:(pname->Prop)), (((member_pname A_26) A_25)->(((eq (pname->Prop)) ((insert_pname A_26) A_25)) A_25))).
% Axiom fact_224_insert__absorb:(forall (A_26:x_a) (A_25:(x_a->Prop)), (((member_a A_26) A_25)->(((eq (x_a->Prop)) ((insert_a A_26) A_25)) A_25))).
% Axiom fact_225_subset__refl:(forall (A_24:(nat->Prop)), ((ord_less_eq_nat_o A_24) A_24)).
% Axiom fact_226_subset__refl:(forall (A_24:(pname->Prop)), ((ord_less_eq_pname_o A_24) A_24)).
% Axiom fact_227_subset__refl:(forall (A_24:(x_a->Prop)), ((ord_less_eq_a_o A_24) A_24)).
% Axiom fact_228_set__eq__subset:(forall (A_23:(nat->Prop)) (B_19:(nat->Prop)), ((iff (((eq (nat->Prop)) A_23) B_19)) ((and ((ord_less_eq_nat_o A_23) B_19)) ((ord_less_eq_nat_o B_19) A_23)))).
% Axiom fact_229_set__eq__subset:(forall (A_23:(pname->Prop)) (B_19:(pname->Prop)), ((iff (((eq (pname->Prop)) A_23) B_19)) ((and ((ord_less_eq_pname_o A_23) B_19)) ((ord_less_eq_pname_o B_19) A_23)))).
% Axiom fact_230_set__eq__subset:(forall (A_23:(x_a->Prop)) (B_19:(x_a->Prop)), ((iff (((eq (x_a->Prop)) A_23) B_19)) ((and ((ord_less_eq_a_o A_23) B_19)) ((ord_less_eq_a_o B_19) A_23)))).
% Axiom fact_231_equalityD1:(forall (A_22:(nat->Prop)) (B_18:(nat->Prop)), ((((eq (nat->Prop)) A_22) B_18)->((ord_less_eq_nat_o A_22) B_18))).
% Axiom fact_232_equalityD1:(forall (A_22:(pname->Prop)) (B_18:(pname->Prop)), ((((eq (pname->Prop)) A_22) B_18)->((ord_less_eq_pname_o A_22) B_18))).
% Axiom fact_233_equalityD1:(forall (A_22:(x_a->Prop)) (B_18:(x_a->Prop)), ((((eq (x_a->Prop)) A_22) B_18)->((ord_less_eq_a_o A_22) B_18))).
% Axiom fact_234_equalityD2:(forall (A_21:(nat->Prop)) (B_17:(nat->Prop)), ((((eq (nat->Prop)) A_21) B_17)->((ord_less_eq_nat_o B_17) A_21))).
% Axiom fact_235_equalityD2:(forall (A_21:(pname->Prop)) (B_17:(pname->Prop)), ((((eq (pname->Prop)) A_21) B_17)->((ord_less_eq_pname_o B_17) A_21))).
% Axiom fact_236_equalityD2:(forall (A_21:(x_a->Prop)) (B_17:(x_a->Prop)), ((((eq (x_a->Prop)) A_21) B_17)->((ord_less_eq_a_o B_17) A_21))).
% Axiom fact_237_in__mono:(forall (X_10:nat) (A_20:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_20) B_16)->(((member_nat X_10) A_20)->((member_nat X_10) B_16)))).
% Axiom fact_238_in__mono:(forall (X_10:x_a) (A_20:(x_a->Prop)) (B_16:(x_a->Prop)), (((ord_less_eq_a_o A_20) B_16)->(((member_a X_10) A_20)->((member_a X_10) B_16)))).
% Axiom fact_239_in__mono:(forall (X_10:pname) (A_20:(pname->Prop)) (B_16:(pname->Prop)), (((ord_less_eq_pname_o A_20) B_16)->(((member_pname X_10) A_20)->((member_pname X_10) B_16)))).
% Axiom fact_240_set__rev__mp:(forall (B_15:(nat->Prop)) (X_9:nat) (A_19:(nat->Prop)), (((member_nat X_9) A_19)->(((ord_less_eq_nat_o A_19) B_15)->((member_nat X_9) B_15)))).
% Axiom fact_241_set__rev__mp:(forall (B_15:(x_a->Prop)) (X_9:x_a) (A_19:(x_a->Prop)), (((member_a X_9) A_19)->(((ord_less_eq_a_o A_19) B_15)->((member_a X_9) B_15)))).
% Axiom fact_242_set__rev__mp:(forall (B_15:(pname->Prop)) (X_9:pname) (A_19:(pname->Prop)), (((member_pname X_9) A_19)->(((ord_less_eq_pname_o A_19) B_15)->((member_pname X_9) B_15)))).
% Axiom fact_243_set__mp:(forall (X_8:nat) (A_18:(nat->Prop)) (B_14:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_14)->(((member_nat X_8) A_18)->((member_nat X_8) B_14)))).
% Axiom fact_244_set__mp:(forall (X_8:x_a) (A_18:(x_a->Prop)) (B_14:(x_a->Prop)), (((ord_less_eq_a_o A_18) B_14)->(((member_a X_8) A_18)->((member_a X_8) B_14)))).
% Axiom fact_245_set__mp:(forall (X_8:pname) (A_18:(pname->Prop)) (B_14:(pname->Prop)), (((ord_less_eq_pname_o A_18) B_14)->(((member_pname X_8) A_18)->((member_pname X_8) B_14)))).
% Axiom fact_246_subset__trans:(forall (C_1:(nat->Prop)) (A_17:(nat->Prop)) (B_13:(nat->Prop)), (((ord_less_eq_nat_o A_17) B_13)->(((ord_less_eq_nat_o B_13) C_1)->((ord_less_eq_nat_o A_17) C_1)))).
% Axiom fact_247_subset__trans:(forall (C_1:(pname->Prop)) (A_17:(pname->Prop)) (B_13:(pname->Prop)), (((ord_less_eq_pname_o A_17) B_13)->(((ord_less_eq_pname_o B_13) C_1)->((ord_less_eq_pname_o A_17) C_1)))).
% Axiom fact_248_subset__trans:(forall (C_1:(x_a->Prop)) (A_17:(x_a->Prop)) (B_13:(x_a->Prop)), (((ord_less_eq_a_o A_17) B_13)->(((ord_less_eq_a_o B_13) C_1)->((ord_less_eq_a_o A_17) C_1)))).
% Axiom fact_249_equalityE:(forall (A_16:(nat->Prop)) (B_12:(nat->Prop)), ((((eq (nat->Prop)) A_16) B_12)->((((ord_less_eq_nat_o A_16) B_12)->(((ord_less_eq_nat_o B_12) A_16)->False))->False))).
% Axiom fact_250_equalityE:(forall (A_16:(pname->Prop)) (B_12:(pname->Prop)), ((((eq (pname->Prop)) A_16) B_12)->((((ord_less_eq_pname_o A_16) B_12)->(((ord_less_eq_pname_o B_12) A_16)->False))->False))).
% Axiom fact_251_equalityE:(forall (A_16:(x_a->Prop)) (B_12:(x_a->Prop)), ((((eq (x_a->Prop)) A_16) B_12)->((((ord_less_eq_a_o A_16) B_12)->(((ord_less_eq_a_o B_12) A_16)->False))->False))).
% Axiom fact_252_mem__def:(forall (X_7:nat) (A_15:(nat->Prop)), ((iff ((member_nat X_7) A_15)) (A_15 X_7))).
% Axiom fact_253_mem__def:(forall (X_7:x_a) (A_15:(x_a->Prop)), ((iff ((member_a X_7) A_15)) (A_15 X_7))).
% Axiom fact_254_mem__def:(forall (X_7:pname) (A_15:(pname->Prop)), ((iff ((member_pname X_7) A_15)) (A_15 X_7))).
% Axiom fact_255_Collect__def:(forall (P_1:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_1)) P_1)).
% Axiom fact_256_Collect__def:(forall (P_1:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) (collect_nat_o P_1)) P_1)).
% Axiom fact_257_Collect__def:(forall (P_1:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_1)) P_1)).
% Axiom fact_258_Collect__def:(forall (P_1:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) (collect_a_o P_1)) P_1)).
% Axiom fact_259_Collect__def:(forall (P_1:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_1)) P_1)).
% Axiom fact_260_image__iff:(forall (Z:x_a) (F_8:(pname->x_a)) (A_14:(pname->Prop)), ((iff ((member_a Z) ((image_pname_a F_8) A_14))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_14)) (((eq x_a) Z) (F_8 X))))))).
% Axiom fact_261_imageI:(forall (F_7:(pname->x_a)) (X_6:pname) (A_13:(pname->Prop)), (((member_pname X_6) A_13)->((member_a (F_7 X_6)) ((image_pname_a F_7) A_13)))).
% Axiom fact_262_rev__image__eqI:(forall (B_11:x_a) (F_6:(pname->x_a)) (X_5:pname) (A_12:(pname->Prop)), (((member_pname X_5) A_12)->((((eq x_a) B_11) (F_6 X_5))->((member_a B_11) ((image_pname_a F_6) A_12))))).
% Axiom fact_263_insert__compr__raw:(forall (X:nat) (Xa:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X) Xa)) (collect_nat (fun (Y:nat)=> ((or (((eq nat) Y) X)) ((member_nat Y) Xa)))))).
% Axiom fact_264_insert__compr__raw:(forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y:pname)=> ((or (((eq pname) Y) X)) ((member_pname Y) Xa)))))).
% Axiom fact_265_insert__compr__raw:(forall (X:x_a) (Xa:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X) Xa)) (collect_a (fun (Y:x_a)=> ((or (((eq x_a) Y) X)) ((member_a Y) Xa)))))).
% Axiom fact_266_insert__compr__raw:(forall (X:(nat->Prop)) (Xa:((nat->Prop)->Prop)), (((eq ((nat->Prop)->Prop)) ((insert_nat_o X) Xa)) (collect_nat_o (fun (Y:(nat->Prop))=> ((or (((eq (nat->Prop)) Y) X)) ((member_nat_o Y) Xa)))))).
% Axiom fact_267_insert__compr__raw:(forall (X:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X) Xa)) (collect_pname_o (fun (Y:(pname->Prop))=> ((or (((eq (pname->Prop)) Y) X)) ((member_pname_o Y) Xa)))))).
% Axiom fact_268_insert__compr__raw:(forall (X:(x_a->Prop)) (Xa:((x_a->Prop)->Prop)), (((eq ((x_a->Prop)->Prop)) ((insert_a_o X) Xa)) (collect_a_o (fun (Y:(x_a->Prop))=> ((or (((eq (x_a->Prop)) Y) X)) ((member_a_o Y) Xa)))))).
% Axiom fact_269_subset__insertI:(forall (B_10:(nat->Prop)) (A_11:nat), ((ord_less_eq_nat_o B_10) ((insert_nat A_11) B_10))).
% Axiom fact_270_subset__insertI:(forall (B_10:(pname->Prop)) (A_11:pname), ((ord_less_eq_pname_o B_10) ((insert_pname A_11) B_10))).
% Axiom fact_271_subset__insertI:(forall (B_10:(x_a->Prop)) (A_11:x_a), ((ord_less_eq_a_o B_10) ((insert_a A_11) B_10))).
% Axiom fact_272_insert__subset:(forall (X_4:nat) (A_10:(nat->Prop)) (B_9:(nat->Prop)), ((iff ((ord_less_eq_nat_o ((insert_nat X_4) A_10)) B_9)) ((and ((member_nat X_4) B_9)) ((ord_less_eq_nat_o A_10) B_9)))).
% Axiom fact_273_insert__subset:(forall (X_4:pname) (A_10:(pname->Prop)) (B_9:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_4) A_10)) B_9)) ((and ((member_pname X_4) B_9)) ((ord_less_eq_pname_o A_10) B_9)))).
% Axiom fact_274_insert__subset:(forall (X_4:x_a) (A_10:(x_a->Prop)) (B_9:(x_a->Prop)), ((iff ((ord_less_eq_a_o ((insert_a X_4) A_10)) B_9)) ((and ((member_a X_4) B_9)) ((ord_less_eq_a_o A_10) B_9)))).
% Axiom fact_275_subset__insert:(forall (B_8:(nat->Prop)) (X_3:nat) (A_9:(nat->Prop)), ((((member_nat X_3) A_9)->False)->((iff ((ord_less_eq_nat_o A_9) ((insert_nat X_3) B_8))) ((ord_less_eq_nat_o A_9) B_8)))).
% Axiom fact_276_subset__insert:(forall (B_8:(pname->Prop)) (X_3:pname) (A_9:(pname->Prop)), ((((member_pname X_3) A_9)->False)->((iff ((ord_less_eq_pname_o A_9) ((insert_pname X_3) B_8))) ((ord_less_eq_pname_o A_9) B_8)))).
% Axiom fact_277_subset__insert:(forall (B_8:(x_a->Prop)) (X_3:x_a) (A_9:(x_a->Prop)), ((((member_a X_3) A_9)->False)->((iff ((ord_less_eq_a_o A_9) ((insert_a X_3) B_8))) ((ord_less_eq_a_o A_9) B_8)))).
% Axiom fact_278_subset__insertI2:(forall (B_7:nat) (A_8:(nat->Prop)) (B_6:(nat->Prop)), (((ord_less_eq_nat_o A_8) B_6)->((ord_less_eq_nat_o A_8) ((insert_nat B_7) B_6)))).
% Axiom fact_279_subset__insertI2:(forall (B_7:pname) (A_8:(pname->Prop)) (B_6:(pname->Prop)), (((ord_less_eq_pname_o A_8) B_6)->((ord_less_eq_pname_o A_8) ((insert_pname B_7) B_6)))).
% Axiom fact_280_subset__insertI2:(forall (B_7:x_a) (A_8:(x_a->Prop)) (B_6:(x_a->Prop)), (((ord_less_eq_a_o A_8) B_6)->((ord_less_eq_a_o A_8) ((insert_a B_7) B_6)))).
% Axiom fact_281_insert__mono:(forall (A_7:nat) (C:(nat->Prop)) (D:(nat->Prop)), (((ord_less_eq_nat_o C) D)->((ord_less_eq_nat_o ((insert_nat A_7) C)) ((insert_nat A_7) D)))).
% Axiom fact_282_insert__mono:(forall (A_7:pname) (C:(pname->Prop)) (D:(pname->Prop)), (((ord_less_eq_pname_o C) D)->((ord_less_eq_pname_o ((insert_pname A_7) C)) ((insert_pname A_7) D)))).
% Axiom fact_283_insert__mono:(forall (A_7:x_a) (C:(x_a->Prop)) (D:(x_a->Prop)), (((ord_less_eq_a_o C) D)->((ord_less_eq_a_o ((insert_a A_7) C)) ((insert_a A_7) D)))).
% Axiom fact_284_image__insert:(forall (F_5:(pname->x_a)) (A_6:pname) (B_5:(pname->Prop)), (((eq (x_a->Prop)) ((image_pname_a F_5) ((insert_pname A_6) B_5))) ((insert_a (F_5 A_6)) ((image_pname_a F_5) B_5)))).
% Axiom fact_285_insert__image:(forall (F_4:(pname->x_a)) (X_2:pname) (A_5:(pname->Prop)), (((member_pname X_2) A_5)->(((eq (x_a->Prop)) ((insert_a (F_4 X_2)) ((image_pname_a F_4) A_5))) ((image_pname_a F_4) A_5)))).
% Axiom fact_286_subset__image__iff:(forall (B_4:(x_a->Prop)) (F_3:(pname->x_a)) (A_4:(pname->Prop)), ((iff ((ord_less_eq_a_o B_4) ((image_pname_a F_3) A_4))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_4)) (((eq (x_a->Prop)) B_4) ((image_pname_a F_3) AA))))))).
% Axiom fact_287_image__mono:(forall (F_2:(pname->x_a)) (A_3:(pname->Prop)) (B_3:(pname->Prop)), (((ord_less_eq_pname_o A_3) B_3)->((ord_less_eq_a_o ((image_pname_a F_2) A_3)) ((image_pname_a F_2) B_3)))).
% Axiom fact_288_imageE:(forall (B_2:x_a) (F_1:(pname->x_a)) (A_2:(pname->Prop)), (((member_a B_2) ((image_pname_a F_1) A_2))->((forall (X:pname), ((((eq x_a) B_2) (F_1 X))->(((member_pname X) A_2)->False)))->False))).
% Axiom fact_289_subsetI:(forall (B_1:(nat->Prop)) (A_1:(nat->Prop)), ((forall (X:nat), (((member_nat X) A_1)->((member_nat X) B_1)))->((ord_less_eq_nat_o A_1) B_1))).
% Axiom fact_290_subsetI:(forall (B_1:(x_a->Prop)) (A_1:(x_a->Prop)), ((forall (X:x_a), (((member_a X) A_1)->((member_a X) B_1)))->((ord_less_eq_a_o A_1) B_1))).
% Axiom fact_291_subsetI:(forall (B_1:(pname->Prop)) (A_1:(pname->Prop)), ((forall (X:pname), (((member_pname X) A_1)->((member_pname X) B_1)))->((ord_less_eq_pname_o A_1) B_1))).
% Axiom fact_292_zero__induct__lemma:(forall (_TPTP_I:nat) (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_2:nat), ((P (suc N_2))->(P N_2)))->(P ((minus_minus_nat K) _TPTP_I))))).
% Axiom fact_293_Suc__le__D:(forall (N_1:nat) (M_1:nat), (((ord_less_eq_nat (suc N_1)) M_1)->((ex nat) (fun (M:nat)=> (((eq nat) M_1) (suc M)))))).
% Axiom fact_294_image__subsetI:(forall (F:(pname->x_a)) (B:(x_a->Prop)) (A:(pname->Prop)), ((forall (X:pname), (((member_pname X) A)->((member_a (F X)) B)))->((ord_less_eq_a_o ((image_pname_a F) A)) B))).
% Axiom fact_295_order__refl:(forall (X_1:(nat->Prop)), ((ord_less_eq_nat_o X_1) X_1)).
% Axiom fact_296_order__refl:(forall (X_1:(pname->Prop)), ((ord_less_eq_pname_o X_1) X_1)).
% Axiom fact_297_order__refl:(forall (X_1:nat), ((ord_less_eq_nat X_1) X_1)).
% Axiom fact_298_order__refl:(forall (X_1:(x_a->Prop)), ((ord_less_eq_a_o X_1) X_1)).
% Axiom fact_299_finite__nat__set__iff__bounded__le:(forall (N:(nat->Prop)), ((iff (finite_finite_nat N)) ((ex nat) (fun (M:nat)=> (forall (X:nat), (((member_nat X) N)->((ord_less_eq_nat X) M))))))).
% Axiom conj_0:(finite_finite_pname u).
% Axiom conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)).
% Axiom conj_2:((ord_less_eq_nat (suc na)) (finite_card_a ((image_pname_a mgt_call) u))).
% Axiom conj_3:(((eq nat) (finite_card_a g)) ((minus_minus_nat (finite_card_a ((image_pname_a mgt_call) u))) (suc na))).
% Axiom conj_4:((member_pname pn) u).
% Axiom conj_5:(((member_a (mgt_call pn)) g)->False).
% Trying to prove ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((image_pname_a mgt_call) u))
% Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u))
% Found conj_1 as proof of ((ord_less_eq_a_o g) ((image_pname_a mgt_call) u))
% Found conj_30:=(conj_3 (fun (x:nat)=> (P ((insert_a (mgt_call pn)) g)))):((P ((insert_a (mgt_call pn)) g))->(P ((insert_a (mgt_call pn)) g)))
% Found (conj_3 (fun (x:nat)=> (P ((insert_a (mgt_call pn)) g)))) as proof of (P0 ((insert_a (mgt_call pn)) g))
% Found (conj_3 (fun (x:nat)=> (P ((insert_a (mgt_call pn)) g)))) as proof of (P0 ((insert_a (mgt_call pn)) g))
% Found conj_30:=(conj_3 (fun (x:nat)=> (P ((image_pname_a mgt_call) u)))):((P ((image_pname_a mgt_call) u))->(P ((image_pname_a mgt_call) u)))
% Found (conj_3 (fun (x:nat)=> (P ((image_pname_a mgt_call) u)))) as proof of (P0 ((image_pname_a mgt_call) u))
% Found (conj_3 (fun (x:nat)=> (P ((image_pname_a mgt_call) u)))) as proof of (P0 ((image_pname_a mgt_call) u))
% Found fact_298_order__refl0:=(fact_298_order__refl B_13):((ord_less_eq_a_o B_13) B_13)
% Found (fact_298_order__refl B_13) as proof of ((ord_less_eq_a_o B_13) g)
% Found (fact_298_order__refl B_13) as proof of ((ord_less_eq_a_o B_13) g)
% Found (fact_298_order__refl B_13) as proof of ((ord_less_eq_a_o B_13) g)
% Found fact_227_subset__refl0:=(fact_227_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g))
% Found (fact_227_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_13)
% Found (fact_227_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_13)
% Found (fact_227_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_13)
% Found conj_30:=(conj_3 (fun (x:nat)=> (P ((insert_a (mgt_call pn)) g)))):((P ((insert_a (mgt_call pn)) g))->(P ((insert_a (mgt_call pn)) g)))
% Found (conj_3 (fun (x:nat)=> (P ((insert_a (mgt_call pn)) g)))) as proof of (P0 ((insert_a (mgt_call pn)) g))
% Found (conj_3 (fun (x:nat)=> (P ((insert_a (mgt_call pn)) g)))) as proof of (P0 ((insert_a (mgt_call pn)) g))
% Found conj_30:=(conj_3 (fun (x:nat)=> (P ((insert_a (mgt_call pn)) g)))):((P ((insert_a (mgt_call pn)) g))->(P ((insert_a (mgt_call pn)) g)))
% Found (conj_3 (fun (x:nat)=> (P ((insert_a (mgt_call pn)) g)))) as proof of (P0 ((insert_a (mgt_call pn)) g))
% Found (conj_3 (fun (x:nat)=> (P ((insert_a (mgt_call pn)) g)))) as proof of (P0 ((insert_a (mgt_call pn)) g))
% Found conj_30:=(conj_3 (fun (x:nat)=> (P ((image_pname_a mgt_call) u)))):((P ((image_pname_a mgt_call) u))->(P ((image_pname_a mgt_call) u)))
% Found (conj_3 (fun (x:nat)=> (P ((image_pname_a mgt_call) u)))) as proof of (P0 ((image_pname_a mgt_call) u))
% Found (conj_3 (fun (x:nat)=> (P ((image_pname_a mgt_call) u)))) as proof of (P0 ((image_pname_a mgt_call) u))
% Found conj_30:=(conj_3 (fun (x:nat)=> (P ((image_pname_a mgt_call) u)))):((P ((image_pname_a mgt_call) u))->(P ((image_pname_a mgt_call) u)))
% Found (conj_3 (fun (x:nat)=> (P ((image_pname_a mgt_call) u)))) as proof of (P0 ((image_pname_a mgt_call) u))
% Found (conj_3 (fun (x:nat)=> (P ((image_pname_a mgt_call) u)))) as proof of (P0 ((image_pname_a mgt_call) u))
% Found fact_227_subset__refl0:=(fact_227_subset__refl B_13):((ord_less_eq_a_o B_13) B_13)
% Found (fact_227_subset__refl B_13) as proof of ((ord_less_eq_a_o B_13) g)
% Found (fact_227_subset__refl B_13) as proof of ((ord_less_eq_a_o B_13) g)
% Found (fact_227_subset__refl B_13) as proof of ((ord_less_eq_a_o B_13) g)
% Found fact_298_order__refl0:=(fact_298_order__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g))
% Found (fact_298_order__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_13)
% Found (fact_298_order__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_13)
% Found (fact_298_order__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_13)
% Found x:((member_a X) ((insert_a (mgt_call pn)) g))
% Instantiate: A_40:=((insert_a (mgt_call pn)) g):(x_a->Prop)
% Found x as proof of ((member_a X) A_40)
% Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u))
% Instantiate: A_40:=g:(x_a->Prop)
% Found conj_1 as proof of ((ord_less_eq_a_o A_40) ((image_pname_a mgt_call) u))
% Found x:((member_a X) ((insert_a (mgt_call pn)) g))
% Instantiate: A_20:=((insert_a (mgt_call pn)) g):(x_a->Prop)
% Found x as proof of ((member_a X) A_20)
% Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u))
% Instantiate: A_20:=g:(x_a->Prop)
% Found conj_1 as proof of ((ord_less_eq_a_o A_20) ((image_pname_a mgt_call) u))
% Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u))
% Instantiate: A_18:=g:(x_a->Prop)
% Found conj_1 as proof of ((ord_less_eq_a_o A_18) ((image_pname_a mgt_call) u))
% Found x:((member_a X) ((insert_a (mgt_call pn)) g))
% Instantiate: A_18:=((insert_a (mgt_call pn)) g):(x_a->Prop)
% Found x as proof of ((member_a X) A_18)
% Found eq_ref00:=(eq_ref0 b):(((eq (x_a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (x_a->Prop)) b) ((image_pname_a mgt_call) u))
% Found ((eq_ref (x_a->Prop)) b) as proof of (((eq (x_a->Prop)) b) ((image_pname_a mgt_call) u))
% Found ((eq_ref (x_a->Prop)) b) as proof of (((eq (x_a->Prop)) b) ((image_pname_a mgt_call) u))
% Found ((eq_ref (x_a->Prop)) b) as proof of (((eq (x_a->Prop)) b) ((image_pname_a mgt_call) u))
% Found eta_expansion_dep000:=(eta_expansion_dep00 ((insert_a (mgt_call pn)) g)):(((eq (x_a->Prop)) ((insert_a (mgt_call pn)) g)) (fun (x:x_a)=> (((insert_a (mgt_call pn)) g) x)))
% Found (eta_expansion_dep00 ((insert_a (mgt_call pn)) g)) as proof of (((eq (x_a->Prop)) ((insert_a (mgt_call pn)) g)) b)
% Found ((eta_expansion_dep0 (fun (x1:x_a)=> Prop)) ((insert_a (mgt_call pn)) g)) as proof of (((eq (x_a->Prop)) ((insert_a (mgt_call pn)) g)) b)
% Found (((eta_expansion_dep x_a) (fun (x1:x_a)=> Prop)) ((insert_a (mgt_call pn)) g)) as proof of (((eq (x_a->Prop)) ((insert_a (mgt_call pn)) g)) b)
% Found (((eta_expansion_dep x_a) (fun (x1:x_a)=> Prop)) ((insert_a (mgt_call pn)) g)) as proof of (((eq (x_a->Prop)) ((insert_a (mgt_call pn)) g)) b)
% Found (((eta_expansion_dep x_a) (fun (x1:x_a)=> Prop)) ((insert_a (mgt_call pn)) g)) as proof of (((eq (x_a->Prop)) ((insert_a (mgt_call pn)) g)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (x_a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (x_a->Prop)) b) ((insert_a (mgt_call pn)) g))
% Found ((eq_ref (x_a->Prop)) b) as proof of (((eq (x_a->Prop)) b) ((insert_a (mgt_call pn)) g))
% Found ((eq_ref (x_a->Prop)) b) as proof of (((eq (x_a->Prop)) b) ((insert_a (mgt_call pn)) g))
% Found ((eq_ref (x_a->Prop)) b) as proof of (((eq (x_a->Prop)) b) ((insert_a (mgt_call pn)) g))
% Found eta_expansion000:=(eta_expansion00 ((image_pname_a mgt_call) u)):(((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) (fun (x:x_a)=> (((image_pname_a mgt_call) u) x)))
% Found (eta_expansion00 ((image_pname_a mgt_call) u)) as proof of (((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) b)
% Found ((eta_expansion0 Prop) ((image_pname_a mgt_call) u)) as proof of (((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) b)
% Found (((eta_expansion x_a) Prop) ((image_pname_a mgt_call) u)) as proof of (((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) b)
% Found (((eta_expansion x_a) Prop) ((image_pname_a mgt_call) u)) as proof of (((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) b)
% Found (((eta_expansion x_a) Prop) ((image_pname_a mgt_call) u)) as proof of (((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) b)
% Found fact_191_insertI100:=(fact_191_insertI10 ((image_pname_a mgt_call) u)):((member_a X) ((insert_a X) ((image_pname_a mgt_call) u)))
% Found (fact_191_insertI10 ((image_pname_a mgt_call) u)) as proof of ((member_a X) ((insert_a B_26) ((image_pname_a mgt_call) u)))
% Found ((fact_191_insertI1 X) ((image_pname_a mgt_call) u)) as proof of ((member_a X) ((insert_a B_26) ((image_pname_a mgt_call) u)))
% Found ((fact_191_insertI1 X) ((image_pname_a mgt_call) u)) as proof of ((member_a X) ((insert_a B_26) ((image_pname_a mgt_call) u)))
% Found ((fact_191_insertI1 X) ((image_pname_a mgt_call) u)) as proof of ((member_a X) ((insert_a B_26) ((image_pname_a mgt_call) u)))
% Found fact_206_insert__absorb200:=(fact_206_insert__absorb20 g):(((eq (x_a->Prop)) ((insert_a (mgt_call pn)) ((insert_a (mgt_call pn)) g))) ((insert_a (mgt_call pn)) g))
% Instantiate: b:=((insert_a (mgt_call pn)) g):(x_a->Prop)
% Found fact_206_insert__absorb200 as proof of (((eq (x_a->Prop)) ((insert_a (mgt_call pn)) ((insert_a (mgt_call pn)) g))) b)
% Found conj_4:((member_pname pn) u)
% Instantiate: X_5:=pn:pname
% Found conj_4 as proof of ((member_pname X_5) u)
% Found eq_ref00:=(eq_ref0 b):(((eq (x_a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (x_a->Prop)) b) ((image_pname_a mgt_call) u))
% Found ((eq_ref (x_a->Prop)) b) as proof of (((eq (x_a->Prop)) b) ((image_pname_a mgt_call) u))
% Found ((eq_ref (x_a->Prop)) b) as proof of (((eq (x_a->Prop)) b) ((image_pname_a mgt_call) u))
% Found ((eq_ref (x_a->Prop)) b) as proof of (((eq (x_a->Prop)) b) ((image_pname_a mgt_call) u))
% Found conj_4:((member_pname pn) u)
% Instantiate: X_15:=pn:pname
% Found conj_4 as proof of ((member_pname X_15) u)
% Found fact_209_insert__commute0000:=(fact_209_insert__commute000 P):((P ((insert_a (mgt_call pn)) ((insert_a (mgt_call pn)) g)))->(P ((insert_a (mgt_call pn)) ((insert_a (mgt_call pn)) g))))
% Found (fact_209_insert__commute000 P) as proof of (P0 ((insert_a (mgt_call pn)) ((insert_a (mgt_call pn)) g)))
% Found ((fact_209_insert__commute00 g) P) as proof of (P0 ((insert_a (mgt_call pn)) ((insert_a (mgt_call pn)) g)))
% Found (((fact_209_insert__commute0 (mgt_call pn)) g) P) as proof of (P0 ((insert_a (mgt_call pn)) ((insert_a (mgt_call pn)) g)))
% Found ((((fact_209_insert__commute (mgt_call pn)) (mgt_call pn)) g) P) as proof of (P0 ((insert_a (mgt_call pn)) ((insert_a (mgt_call pn)) g)))
% Found ((((fact_209_insert__commute (mgt_call pn)) (mgt_call pn)) g) P) as proof of (P0 ((insert_a (mgt_call pn)) ((insert_a (mgt_call pn)) g)))
% Found conj_30:=(conj_3 (
% EOF
%------------------------------------------------------------------------------