%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SWW474^3 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n099.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 13:37:24 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SWW474^3 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n099.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 09:22:26 CDT 2014
% % CPUTime  : 300.10 
% 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 0x14425f0>, <kernel.Type object at 0x1442ef0>) of role type named ty_ty_tc__Com__Ocom
% Using role type
% Declaring com:Type
% FOF formula (<kernel.Constant object at 0x1733440>, <kernel.Type object at 0x14423b0>) of role type named ty_ty_tc__Com__Opname
% Using role type
% Declaring pname:Type
% FOF formula (<kernel.Constant object at 0x14423f8>, <kernel.Type object at 0x1442290>) of role type named ty_ty_tc__Com__Ostate
% Using role type
% Declaring state:Type
% FOF formula (<kernel.Constant object at 0x1442ef0>, <kernel.Type object at 0x1442758>) of role type named ty_ty_tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J
% Using role type
% Declaring hoare_1708887482_state:Type
% FOF formula (<kernel.Constant object at 0x14423b0>, <kernel.Type object at 0x1442290>) of role type named ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J
% Using role type
% Declaring option_com:Type
% FOF formula (<kernel.Constant object at 0x1442d88>, <kernel.Type object at 0x157ae60>) of role type named ty_ty_tc__Option__Ooption_Itc__Com__Opname_J
% Using role type
% Declaring option_pname:Type
% FOF formula (<kernel.Constant object at 0x1442758>, <kernel.Type object at 0x157ae60>) of role type named ty_ty_tc__Option__Ooption_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Co
% Using role type
% Declaring option1624383643_state:Type
% FOF formula (<kernel.Constant object at 0x1442b00>, <kernel.DependentProduct object at 0x157a5f0>) of role type named sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring big_la1126801287name_o:(((pname->Prop)->Prop)->(pname->Prop))
% FOF formula (<kernel.Constant object at 0x1442758>, <kernel.DependentProduct object at 0x157a7a0>) of role type named sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Hoare____Mirabelle___
% Using role type
% Declaring big_la781588935tate_o:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))
% FOF formula (<kernel.Constant object at 0x1442b00>, <kernel.DependentProduct object at 0x157a9e0>) of role type named sy_c_Com_OWT
% Using role type
% Declaring wt:(com->Prop)
% FOF formula (<kernel.Constant object at 0x1442d88>, <kernel.Sort object at 0x1440518>) of role type named sy_c_Com_OWT__bodies
% Using role type
% Declaring wT_bodies:Prop
% FOF formula (<kernel.Constant object at 0x1442d88>, <kernel.DependentProduct object at 0x157a710>) of role type named sy_c_Com_Obody
% Using role type
% Declaring body:(pname->option_com)
% FOF formula (<kernel.Constant object at 0x157a5f0>, <kernel.DependentProduct object at 0x157a320>) of role type named sy_c_Com_Ocom_OBODY
% Using role type
% Declaring body_1:(pname->com)
% FOF formula (<kernel.Constant object at 0x157a560>, <kernel.Constant object at 0x157a320>) of role type named sy_c_Com_Ocom_OSKIP
% Using role type
% Declaring skip:com
% FOF formula (<kernel.Constant object at 0x157ac20>, <kernel.DependentProduct object at 0x157a710>) of role type named sy_c_Com_Ocom_OSemi
% Using role type
% Declaring semi:(com->(com->com))
% FOF formula (<kernel.Constant object at 0x157a7a0>, <kernel.DependentProduct object at 0x157a950>) of role type named sy_c_Com_Ocom_OWhile
% Using role type
% Declaring while:((state->Prop)->(com->com))
% FOF formula (<kernel.Constant object at 0x1751cf8>, <kernel.DependentProduct object at 0x157a878>) of role type named sy_c_Finite__Set_Ocomp__fun__idem_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__C
% Using role type
% Declaring finite138924780name_o:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->Prop)
% FOF formula (<kernel.Constant object at 0x157a320>, <kernel.DependentProduct object at 0x157a9e0>) of role type named sy_c_Finite__Set_Ocomp__fun__idem_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv_
% Using role type
% Declaring finite2034616076tate_o:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->Prop)
% FOF formula (<kernel.Constant object at 0x157a710>, <kernel.DependentProduct object at 0x157a7a0>) of role type named sy_c_Finite__Set_Ocomp__fun__idem_000_Eo_000_Eo
% Using role type
% Declaring finite2048025996em_o_o:((Prop->(Prop->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x157a9e0>, <kernel.DependentProduct object at 0x157a3b0>) of role type named sy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Ocom_000_062_Itc__Com__Ocom_M_Eo_J
% Using role type
% Declaring finite567462577_com_o:((com->((com->Prop)->(com->Prop)))->Prop)
% FOF formula (<kernel.Constant object at 0x157ac20>, <kernel.DependentProduct object at 0x143f368>) of role type named sy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Opname_000_062_Itc__Com__Opname_M_
% Using role type
% Declaring finite1123817265name_o:((pname->((pname->Prop)->(pname->Prop)))->Prop)
% FOF formula (<kernel.Constant object at 0x157a320>, <kernel.DependentProduct object at 0x143f7a0>) of role type named sy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otrip
% Using role type
% Declaring finite662762081tate_o:((hoare_1708887482_state->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->Prop)
% FOF formula (<kernel.Constant object at 0x157a7a0>, <kernel.DependentProduct object at 0x143f290>) 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 0x157ac20>, <kernel.DependentProduct object at 0x143f440>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot
% Using role type
% Declaring finite1019950101te_o_o:((((hoare_1708887482_state->Prop)->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x157a320>, <kernel.DependentProduct object at 0x143f290>) 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 0x157a3b0>, <kernel.DependentProduct object at 0x143f7a0>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_
% Using role type
% Declaring finite1329924456tate_o:(((hoare_1708887482_state->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x157a7a0>, <kernel.DependentProduct object at 0x143f050>) of role type named sy_c_Finite__Set_Ofinite_000_Eo
% Using role type
% Declaring finite_finite_o:((Prop->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x157a320>, <kernel.DependentProduct object at 0x143fb00>) of role type named sy_c_Finite__Set_Ofinite_000tc__Com__Ocom
% Using role type
% Declaring finite_finite_com:((com->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x157a320>, <kernel.DependentProduct object at 0x143f440>) 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 0x143f560>, <kernel.DependentProduct object at 0x143fb00>) of role type named sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__C
% Using role type
% Declaring finite1625599783_state:((hoare_1708887482_state->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x143fbd8>, <kernel.DependentProduct object at 0x143f320>) of role type named sy_c_Finite__Set_Ofold_000_062_Itc__Com__Opname_M_Eo_J_000_062_I_062_Itc__Com__O
% Using role type
% Declaring finite1849951719me_o_o:(((pname->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop)))->(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))))
% FOF formula (<kernel.Constant object at 0x143fe18>, <kernel.DependentProduct object at 0x143f320>) of role type named sy_c_Finite__Set_Ofold_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_
% Using role type
% Declaring finite472615016name_o:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->((pname->Prop)->(((pname->Prop)->Prop)->(pname->Prop))))
% FOF formula (<kernel.Constant object at 0x143f488>, <kernel.DependentProduct object at 0x143f7e8>) of role type named sy_c_Finite__Set_Ofold_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It
% Using role type
% Declaring finite463603445te_o_o:(((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop)))->(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop))))
% FOF formula (<kernel.Constant object at 0x143f440>, <kernel.DependentProduct object at 0x143f7e8>) of role type named sy_c_Finite__Set_Ofold_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It_001
% Using role type
% Declaring finite822533768tate_o:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))))
% FOF formula (<kernel.Constant object at 0x143fb00>, <kernel.DependentProduct object at 0x143f050>) of role type named sy_c_Finite__Set_Ofold_000_Eo_000_Eo
% Using role type
% Declaring finite_fold_o_o:((Prop->(Prop->Prop))->(Prop->((Prop->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x143f488>, <kernel.DependentProduct object at 0x143f2d8>) of role type named sy_c_Finite__Set_Ofold_000tc__Com__Ocom_000_062_Itc__Com__Ocom_M_Eo_J
% Using role type
% Declaring finite504235573_com_o:((com->((com->Prop)->(com->Prop)))->((com->Prop)->((com->Prop)->(com->Prop))))
% FOF formula (<kernel.Constant object at 0x143f7e8>, <kernel.DependentProduct object at 0x143f098>) of role type named sy_c_Finite__Set_Ofold_000tc__Com__Ocom_000tc__Com__Ocom
% Using role type
% Declaring finite_fold_com_com:((com->(com->com))->(com->((com->Prop)->com)))
% FOF formula (<kernel.Constant object at 0x1444950>, <kernel.DependentProduct object at 0x143fbd8>) of role type named sy_c_Finite__Set_Ofold_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring finite603803317name_o:((pname->((pname->Prop)->(pname->Prop)))->((pname->Prop)->((pname->Prop)->(pname->Prop))))
% FOF formula (<kernel.Constant object at 0x143f440>, <kernel.DependentProduct object at 0x143f050>) of role type named sy_c_Finite__Set_Ofold_000tc__Com__Opname_000tc__Com__Opname
% Using role type
% Declaring finite1657623752_pname:((pname->(pname->pname))->(pname->((pname->Prop)->pname)))
% FOF formula (<kernel.Constant object at 0x143fb90>, <kernel.DependentProduct object at 0x143fb00>) of role type named sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com
% Using role type
% Declaring finite96880613tate_o:((hoare_1708887482_state->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))))
% FOF formula (<kernel.Constant object at 0x143f2d8>, <kernel.DependentProduct object at 0x143f320>) of role type named sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com_002
% Using role type
% Declaring finite309095018_state:((hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))->(hoare_1708887482_state->((hoare_1708887482_state->Prop)->hoare_1708887482_state)))
% FOF formula (<kernel.Constant object at 0x143fbd8>, <kernel.DependentProduct object at 0x143f440>) of role type named sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr
% Using role type
% Declaring finite2139561282_pname:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((pname->(hoare_1708887482_state->Prop))->((hoare_1708887482_state->Prop)->((pname->Prop)->(hoare_1708887482_state->Prop)))))
% FOF formula (<kernel.Constant object at 0x143f098>, <kernel.DependentProduct object at 0x1752950>) of role type named sy_c_Finite__Set_Ofolding__one_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring finite349908348name_o:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->((((pname->Prop)->Prop)->(pname->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x143f320>, <kernel.DependentProduct object at 0x1752950>) of role type named sy_c_Finite__Set_Ofolding__one_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot
% Using role type
% Declaring finite928843026tate_o:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x143f440>, <kernel.DependentProduct object at 0x1752c20>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Com__Ocom
% Using role type
% Declaring finite860057415ne_com:((com->(com->com))->(((com->Prop)->com)->Prop))
% FOF formula (<kernel.Constant object at 0x143f098>, <kernel.DependentProduct object at 0x1752c20>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Com__Opname
% Using role type
% Declaring finite1282449217_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop))
% FOF formula (<kernel.Constant object at 0x143f320>, <kernel.DependentProduct object at 0x1752c20>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_
% Using role type
% Declaring finite1615457021_state:((hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))->(((hoare_1708887482_state->Prop)->hoare_1708887482_state)->Prop))
% FOF formula (<kernel.Constant object at 0x143f098>, <kernel.DependentProduct object at 0x1752170>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring finite697516351name_o:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->((((pname->Prop)->Prop)->(pname->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x143f320>, <kernel.DependentProduct object at 0x1752440>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Hoare____Mirabelle____nqhfsdfv
% Using role type
% Declaring finite621643279tate_o:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x143f098>, <kernel.DependentProduct object at 0x1752cb0>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Ocom
% Using role type
% Declaring finite666746948em_com:((com->(com->com))->(((com->Prop)->com)->Prop))
% FOF formula (<kernel.Constant object at 0x143f098>, <kernel.DependentProduct object at 0x1752c20>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname
% Using role type
% Declaring finite89670078_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop))
% FOF formula (<kernel.Constant object at 0x1752950>, <kernel.DependentProduct object at 0x1752e60>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot
% Using role type
% Declaring finite1347568576_state:((hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))->(((hoare_1708887482_state->Prop)->hoare_1708887482_state)->Prop))
% FOF formula (<kernel.Constant object at 0x1752440>, <kernel.DependentProduct object at 0x1752b00>) of role type named sy_c_Fun_Ofun__upd_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__O
% Using role type
% Declaring fun_up1986763201_state:((pname->hoare_1708887482_state)->(pname->(hoare_1708887482_state->(pname->hoare_1708887482_state))))
% FOF formula (<kernel.Constant object at 0x1752320>, <kernel.DependentProduct object at 0x1752950>) of role type named sy_c_Fun_Ofun__upd_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J
% Using role type
% Declaring fun_up879233478on_com:((pname->option_com)->(pname->(option_com->(pname->option_com))))
% FOF formula (<kernel.Constant object at 0x17528c0>, <kernel.DependentProduct object at 0x1752b00>) of role type named sy_c_Fun_Oinj__on_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_M_Eo_
% Using role type
% Declaring inj_on691924881name_o:(((pname->Prop)->(pname->Prop))->(((pname->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x17526c8>, <kernel.DependentProduct object at 0x1752b90>) of role type named sy_c_Fun_Oinj__on_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Co
% Using role type
% Declaring inj_on176908593tate_o:(((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))->(((hoare_1708887482_state->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1752440>, <kernel.DependentProduct object at 0x1752758>) of role type named sy_c_Fun_Oinj__on_000tc__Com__Ocom_000tc__Option__Ooption_Itc__Com__Ocom_J
% Using role type
% Declaring inj_on11367768on_com:((com->option_com)->((com->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1752b00>, <kernel.DependentProduct object at 0x1752170>) of role type named sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Com__Opname
% Using role type
% Declaring inj_on_pname_pname:((pname->pname)->((pname->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1752830>, <kernel.DependentProduct object at 0x1752ef0>) of role type named sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot
% Using role type
% Declaring inj_on1553129421_state:((pname->hoare_1708887482_state)->((pname->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x17528c0>, <kernel.DependentProduct object at 0x1752d40>) of role type named sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Opname_J
% Using role type
% Declaring inj_on737724108_pname:((pname->option_pname)->((pname->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x17526c8>, <kernel.DependentProduct object at 0x17525f0>) of role type named sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost
% Using role type
% Declaring inj_on1945914667_pname:((hoare_1708887482_state->pname)->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1752440>, <kernel.DependentProduct object at 0x17528c0>) of role type named sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost_003
% Using role type
% Declaring inj_on632008595_state:((hoare_1708887482_state->hoare_1708887482_state)->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1752b00>, <kernel.DependentProduct object at 0x17526c8>) of role type named sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost_004
% Using role type
% Declaring inj_on945311362_state:((hoare_1708887482_state->option1624383643_state)->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1752830>, <kernel.DependentProduct object at 0x17525f0>) of role type named sy_c_Fun_Ooverride__on_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_
% Using role type
% Declaring overri1496249029on_com:((pname->option_com)->((pname->option_com)->((pname->Prop)->(pname->option_com))))
% FOF formula (<kernel.Constant object at 0x1752a70>, <kernel.DependentProduct object at 0x17525f0>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J
% Using role type
% Declaring minus_1480864103me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1752440>, <kernel.DependentProduct object at 0x1753638>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsd
% Using role type
% Declaring minus_548038231te_o_o:(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x17525f0>, <kernel.DependentProduct object at 0x1753488>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Ocom_M_Eo_J
% Using role type
% Declaring minus_minus_com_o:((com->Prop)->((com->Prop)->(com->Prop)))
% FOF formula (<kernel.Constant object at 0x1752a70>, <kernel.DependentProduct object at 0x1753098>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring minus_minus_pname_o:((pname->Prop)->((pname->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x17525f0>, <kernel.DependentProduct object at 0x1753680>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__
% Using role type
% Declaring minus_2056855718tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x17525f0>, <kernel.DependentProduct object at 0x1753878>) of role type named sy_c_HOL_OThe_000tc__Com__Ocom
% Using role type
% Declaring the_com_1:((com->Prop)->com)
% FOF formula (<kernel.Constant object at 0x17525f0>, <kernel.DependentProduct object at 0x17537a0>) of role type named sy_c_HOL_OThe_000tc__Com__Opname
% Using role type
% Declaring the_pname:((pname->Prop)->pname)
% FOF formula (<kernel.Constant object at 0x17525f0>, <kernel.DependentProduct object at 0x1753638>) of role type named sy_c_HOL_OThe_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_
% Using role type
% Declaring the_Ho851197897_state:((hoare_1708887482_state->Prop)->hoare_1708887482_state)
% FOF formula (<kernel.Constant object at 0x1753488>, <kernel.DependentProduct object at 0x1753128>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_OMGT
% Using role type
% Declaring hoare_Mirabelle_MGT:(com->hoare_1708887482_state)
% FOF formula (<kernel.Constant object at 0x1753b48>, <kernel.DependentProduct object at 0x1753c68>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__derivs_000tc__Com__Ostate
% Using role type
% Declaring hoare_90032982_state:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1753638>, <kernel.DependentProduct object at 0x1753128>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__valids_000tc__Com__Ostate
% Using role type
% Declaring hoare_496444244_state:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1753098>, <kernel.Sort object at 0x1440518>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ostate__not__singleton
% Using role type
% Declaring hoare_1160767572gleton:Prop
% FOF formula (<kernel.Constant object at 0x1753c68>, <kernel.DependentProduct object at 0x17530e0>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple_000tc__Com__Ostate
% Using role type
% Declaring hoare_858012674_state:((state->(state->Prop))->(com->((state->(state->Prop))->hoare_1708887482_state)))
% FOF formula (<kernel.Constant object at 0x1753488>, <kernel.DependentProduct object at 0x155f908>) of role type named sy_c_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J
% Using role type
% Declaring if_Hoa1374726218_state:(Prop->(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state)))
% FOF formula (<kernel.Constant object at 0x1753098>, <kernel.DependentProduct object at 0x155f758>) of role type named sy_c_If_000tc__Option__Ooption_Itc__Com__Ocom_J
% Using role type
% Declaring if_option_com:(Prop->(option_com->(option_com->option_com)))
% FOF formula (<kernel.Constant object at 0x1753638>, <kernel.DependentProduct object at 0x155f830>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Com__Opname_M_Eo_
% Using role type
% Declaring semila2013987940me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1753488>, <kernel.DependentProduct object at 0x155f950>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell
% Using role type
% Declaring semila598060698te_o_o:(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1753638>, <kernel.DependentProduct object at 0x155f758>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Ocom_M_Eo_J
% Using role type
% Declaring semila513601829_com_o:((com->Prop)->((com->Prop)->(com->Prop)))
% FOF formula (<kernel.Constant object at 0x1753488>, <kernel.DependentProduct object at 0x155f710>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring semila1673364395name_o:((pname->Prop)->((pname->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x1753098>, <kernel.DependentProduct object at 0x155f638>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____n
% Using role type
% Declaring semila129691299tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x1753098>, <kernel.DependentProduct object at 0x155f710>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_Eo
% Using role type
% Declaring semila854092349_inf_o:(Prop->(Prop->Prop))
% FOF formula (<kernel.Constant object at 0x155f7e8>, <kernel.DependentProduct object at 0x155f680>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Com__Opname_M_Eo_
% Using role type
% Declaring semila181081674me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x155f638>, <kernel.DependentProduct object at 0x155f878>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell
% Using role type
% Declaring semila1853742644te_o_o:(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x155f6c8>, <kernel.DependentProduct object at 0x155f7a0>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Ocom_M_Eo_J
% Using role type
% Declaring semila1562558655_com_o:((com->Prop)->((com->Prop)->(com->Prop)))
% FOF formula (<kernel.Constant object at 0x155f830>, <kernel.DependentProduct object at 0x155f560>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring semila1780557381name_o:((pname->Prop)->((pname->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x155f518>, <kernel.DependentProduct object at 0x155f488>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____n
% Using role type
% Declaring semila1122118281tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x155f908>, <kernel.DependentProduct object at 0x155f560>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_Eo
% Using role type
% Declaring semila10642723_sup_o:(Prop->(Prop->Prop))
% FOF formula (<kernel.Constant object at 0x155f830>, <kernel.DependentProduct object at 0x155f518>) of role type named sy_c_Map_Odom_000tc__Com__Ocom_000tc__Com__Ocom
% Using role type
% Declaring dom_com_com:((com->option_com)->(com->Prop))
% FOF formula (<kernel.Constant object at 0x155f488>, <kernel.DependentProduct object at 0x155f908>) of role type named sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom
% Using role type
% Declaring dom_pname_com:((pname->option_com)->(pname->Prop))
% FOF formula (<kernel.Constant object at 0x155f4d0>, <kernel.DependentProduct object at 0x155f830>) of role type named sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Opname
% Using role type
% Declaring dom_pname_pname:((pname->option_pname)->(pname->Prop))
% FOF formula (<kernel.Constant object at 0x155f7a0>, <kernel.DependentProduct object at 0x155f488>) of role type named sy_c_Map_Odom_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otripl
% Using role type
% Declaring dom_pn1412407212_state:((pname->option1624383643_state)->(pname->Prop))
% FOF formula (<kernel.Constant object at 0x155f560>, <kernel.DependentProduct object at 0x155f4d0>) of role type named sy_c_Map_Odom_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_
% Using role type
% Declaring dom_Ho1805192458_pname:((hoare_1708887482_state->option_pname)->(hoare_1708887482_state->Prop))
% FOF formula (<kernel.Constant object at 0x155f518>, <kernel.DependentProduct object at 0x155f7a0>) of role type named sy_c_Map_Odom_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate__005
% Using role type
% Declaring dom_Ho1703271284_state:((hoare_1708887482_state->option1624383643_state)->(hoare_1708887482_state->Prop))
% FOF formula (<kernel.Constant object at 0x155f9e0>, <kernel.DependentProduct object at 0x155fab8>) of role type named sy_c_Map_Orestrict__map_000tc__Com__Opname_000tc__Com__Ocom
% Using role type
% Declaring restri1382200118me_com:((pname->option_com)->((pname->Prop)->(pname->option_com)))
% FOF formula (<kernel.Constant object at 0x155fa28>, <kernel.DependentProduct object at 0x155f4d0>) of role type named sy_c_Natural_Oevalc
% Using role type
% Declaring evalc:(com->(state->(state->Prop)))
% FOF formula (<kernel.Constant object at 0x155f488>, <kernel.DependentProduct object at 0x155f518>) of role type named sy_c_Option_Ois__none_000tc__Com__Ocom
% Using role type
% Declaring is_none_com:(option_com->Prop)
% FOF formula (<kernel.Constant object at 0x155fab8>, <kernel.DependentProduct object at 0x155fb00>) of role type named sy_c_Option_Ois__none_000tc__Com__Opname
% Using role type
% Declaring is_none_pname:(option_pname->Prop)
% FOF formula (<kernel.Constant object at 0x155f4d0>, <kernel.DependentProduct object at 0x155f7a0>) of role type named sy_c_Option_Ois__none_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com_
% Using role type
% Declaring is_non163157940_state:(option1624383643_state->Prop)
% FOF formula (<kernel.Constant object at 0x155f518>, <kernel.Constant object at 0x155f7a0>) of role type named sy_c_Option_Ooption_ONone_000tc__Com__Ocom
% Using role type
% Declaring none_com:option_com
% FOF formula (<kernel.Constant object at 0x155fab8>, <kernel.Constant object at 0x155f7a0>) of role type named sy_c_Option_Ooption_ONone_000tc__Com__Opname
% Using role type
% Declaring none_pname:option_pname
% FOF formula (<kernel.Constant object at 0x155f4d0>, <kernel.Constant object at 0x155f7a0>) of role type named sy_c_Option_Ooption_ONone_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__
% Using role type
% Declaring none_H1106584047_state:option1624383643_state
% FOF formula (<kernel.Constant object at 0x155f518>, <kernel.DependentProduct object at 0x155fcb0>) of role type named sy_c_Option_Ooption_OSome_000tc__Com__Ocom
% Using role type
% Declaring some_com:(com->option_com)
% FOF formula (<kernel.Constant object at 0x155fbd8>, <kernel.DependentProduct object at 0x155fcf8>) of role type named sy_c_Option_Ooption_OSome_000tc__Com__Opname
% Using role type
% Declaring some_pname:(pname->option_pname)
% FOF formula (<kernel.Constant object at 0x155f7a0>, <kernel.DependentProduct object at 0x155fd40>) of role type named sy_c_Option_Ooption_OSome_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__
% Using role type
% Declaring some_H1974565227_state:(hoare_1708887482_state->option1624383643_state)
% FOF formula (<kernel.Constant object at 0x155f8c0>, <kernel.DependentProduct object at 0x155f7a0>) of role type named sy_c_Option_Oset_000tc__Com__Ocom
% Using role type
% Declaring set_com:(option_com->(com->Prop))
% FOF formula (<kernel.Constant object at 0x155fcb0>, <kernel.DependentProduct object at 0x155f4d0>) of role type named sy_c_Option_Oset_000tc__Com__Opname
% Using role type
% Declaring set_pname:(option_pname->(pname->Prop))
% FOF formula (<kernel.Constant object at 0x155fbd8>, <kernel.DependentProduct object at 0x155f518>) of role type named sy_c_Option_Oset_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Osta
% Using role type
% Declaring set_Ho525251890_state:(option1624383643_state->(hoare_1708887482_state->Prop))
% FOF formula (<kernel.Constant object at 0x155fab8>, <kernel.DependentProduct object at 0x155fea8>) of role type named sy_c_Option_Othe_000tc__Com__Ocom
% Using role type
% Declaring the_com:(option_com->com)
% FOF formula (<kernel.Constant object at 0x155f8c0>, <kernel.DependentProduct object at 0x155fef0>) of role type named sy_c_Option_Othe_000tc__Com__Opname
% Using role type
% Declaring the_pname_1:(option_pname->pname)
% FOF formula (<kernel.Constant object at 0x155fcf8>, <kernel.DependentProduct object at 0x155fd40>) of role type named sy_c_Option_Othe_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Osta
% Using role type
% Declaring the_Ho963921505_state:(option1624383643_state->hoare_1708887482_state)
% FOF formula (<kernel.Constant object at 0x155fab8>, <kernel.DependentProduct object at 0x155fbd8>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J
% Using role type
% Declaring bot_bot_pname_o_o:((pname->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x155f8c0>, <kernel.DependentProduct object at 0x155fd40>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdf
% Using role type
% Declaring bot_bo1678742418te_o_o:((hoare_1708887482_state->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x155f7a0>, <kernel.DependentProduct object at 0x155ff80>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Ocom_M_Eo_J
% Using role type
% Declaring bot_bot_com_o:(com->Prop)
% FOF formula (<kernel.Constant object at 0x155ff38>, <kernel.DependentProduct object at 0x155ffc8>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring bot_bot_pname_o:(pname->Prop)
% FOF formula (<kernel.Constant object at 0x155fd40>, <kernel.DependentProduct object at 0x174b050>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__O
% Using role type
% Declaring bot_bo19817387tate_o:(hoare_1708887482_state->Prop)
% FOF formula (<kernel.Constant object at 0x155ff80>, <kernel.Sort object at 0x1440518>) of role type named sy_c_Orderings_Obot__class_Obot_000_Eo
% Using role type
% Declaring bot_bot_o:Prop
% FOF formula (<kernel.Constant object at 0x155fef0>, <kernel.DependentProduct object at 0x174b128>) 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 0x155fd40>, <kernel.DependentProduct object at 0x174b170>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Hoare____Mirabelle____nq
% Using role type
% Declaring ord_le1728773982te_o_o:(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x155ff80>, <kernel.DependentProduct object at 0x174b200>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Ocom_M_Eo_J
% Using role type
% Declaring ord_less_eq_com_o:((com->Prop)->((com->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x155fd40>, <kernel.DependentProduct object at 0x174b248>) 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 0x155ff80>, <kernel.DependentProduct object at 0x174b290>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____nqhfsdfv
% Using role type
% Declaring ord_le777019615tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x155fef0>, <kernel.DependentProduct object at 0x174b248>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_Eo
% Using role type
% Declaring ord_less_eq_o:(Prop->(Prop->Prop))
% FOF formula (<kernel.Constant object at 0x155fef0>, <kernel.DependentProduct object at 0x174b098>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__Com__Ocom_M_Eo_J
% Using role type
% Declaring top_top_com_o:(com->Prop)
% FOF formula (<kernel.Constant object at 0x174b290>, <kernel.DependentProduct object at 0x174b2d8>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring top_top_pname_o:(pname->Prop)
% FOF formula (<kernel.Constant object at 0x174b248>, <kernel.DependentProduct object at 0x174b320>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__O
% Using role type
% Declaring top_to832624271tate_o:(hoare_1708887482_state->Prop)
% FOF formula (<kernel.Constant object at 0x174b098>, <kernel.DependentProduct object at 0x174b3f8>) of role type named sy_c_Partial__Function_Oflat__lub_000tc__Com__Ocom
% Using role type
% Declaring partial_flat_lub_com:(com->((com->Prop)->com))
% FOF formula (<kernel.Constant object at 0x174b2d8>, <kernel.DependentProduct object at 0x174b290>) of role type named sy_c_Partial__Function_Oflat__lub_000tc__Com__Opname
% Using role type
% Declaring partia752020666_pname:(pname->((pname->Prop)->pname))
% FOF formula (<kernel.Constant object at 0x174b320>, <kernel.DependentProduct object at 0x174b248>) of role type named sy_c_Partial__Function_Oflat__lub_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otrip
% Using role type
% Declaring partia1256728516_state:(hoare_1708887482_state->((hoare_1708887482_state->Prop)->hoare_1708887482_state))
% FOF formula (<kernel.Constant object at 0x174b3f8>, <kernel.DependentProduct object at 0x174b3b0>) 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 0x174b290>, <kernel.DependentProduct object at 0x174b098>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_I
% Using role type
% Declaring collec58007891te_o_o:((((hoare_1708887482_state->Prop)->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x174b4d0>, <kernel.DependentProduct object at 0x174b560>) 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 0x174b3b0>, <kernel.DependentProduct object at 0x174b5a8>) of role type named sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Co
% Using role type
% Declaring collec219771562tate_o:(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x174b128>, <kernel.DependentProduct object at 0x174b3b0>) of role type named sy_c_Set_OCollect_000tc__Com__Ocom
% Using role type
% Declaring collect_com:((com->Prop)->(com->Prop))
% FOF formula (<kernel.Constant object at 0x174b290>, <kernel.DependentProduct object at 0x174b518>) 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 0x174b5a8>, <kernel.DependentProduct object at 0x174b128>) of role type named sy_c_Set_OCollect_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost
% Using role type
% Declaring collec1568722789_state:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))
% FOF formula (<kernel.Constant object at 0x174b3f8>, <kernel.DependentProduct object at 0x174b6c8>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring image_1085733413name_o:(((pname->Prop)->(pname->Prop))->(((pname->Prop)->Prop)->((pname->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x174b3b0>, <kernel.DependentProduct object at 0x174b128>) 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 0x174b518>, <kernel.DependentProduct object at 0x174b5a8>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Hoare____Mirabelle____nqh
% Using role type
% Declaring image_1922967206_state:(((pname->Prop)->hoare_1708887482_state)->(((pname->Prop)->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x174b680>, <kernel.DependentProduct object at 0x174b7e8>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com_
% Using role type
% Declaring image_909543877tate_o:(((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x174b7a0>, <kernel.DependentProduct object at 0x174b5a8>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__006
% Using role type
% Declaring image_2051418740_pname:(((hoare_1708887482_state->Prop)->pname)->(((hoare_1708887482_state->Prop)->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x174b830>, <kernel.DependentProduct object at 0x174b518>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__007
% Using role type
% Declaring image_27005066_state:(((hoare_1708887482_state->Prop)->hoare_1708887482_state)->(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x174b128>, <kernel.DependentProduct object at 0x174b8c0>) of role type named sy_c_Set_Oimage_000tc__Com__Ocom_000tc__Com__Ocom
% Using role type
% Declaring image_com_com:((com->com)->((com->Prop)->(com->Prop)))
% FOF formula (<kernel.Constant object at 0x174b878>, <kernel.DependentProduct object at 0x174b908>) of role type named sy_c_Set_Oimage_000tc__Com__Ocom_000tc__Com__Opname
% Using role type
% Declaring image_com_pname:((com->pname)->((com->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x174b7e8>, <kernel.DependentProduct object at 0x174b950>) of role type named sy_c_Set_Oimage_000tc__Com__Ocom_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otripl
% Using role type
% Declaring image_934102463_state:((com->hoare_1708887482_state)->((com->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x174b6c8>, <kernel.DependentProduct object at 0x174b908>) 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 0x174b8c0>, <kernel.DependentProduct object at 0x174b950>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv
% Using role type
% Declaring image_425134806tate_o:((pname->(hoare_1708887482_state->Prop))->((pname->Prop)->((hoare_1708887482_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x174b680>, <kernel.DependentProduct object at 0x174b128>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Ocom
% Using role type
% Declaring image_pname_com:((pname->com)->((pname->Prop)->(com->Prop)))
% FOF formula (<kernel.Constant object at 0x174b830>, <kernel.DependentProduct object at 0x174ba70>) 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 0x174ba28>, <kernel.DependentProduct object at 0x174bab8>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otri
% Using role type
% Declaring image_1116629049_state:((pname->hoare_1708887482_state)->((pname->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x174b998>, <kernel.DependentProduct object at 0x174ba70>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat
% Using role type
% Declaring image_1552895654name_o:((hoare_1708887482_state->(pname->Prop))->((hoare_1708887482_state->Prop)->((pname->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x174b128>, <kernel.DependentProduct object at 0x174bab8>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_008
% Using role type
% Declaring image_1551509096tate_o:((hoare_1708887482_state->(hoare_1708887482_state->Prop))->((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x174b758>, <kernel.DependentProduct object at 0x174b680>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_009
% Using role type
% Declaring image_1604448413te_com:((hoare_1708887482_state->com)->((hoare_1708887482_state->Prop)->(com->Prop)))
% FOF formula (<kernel.Constant object at 0x174b8c0>, <kernel.DependentProduct object at 0x174bbd8>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_010
% Using role type
% Declaring image_1509414295_pname:((hoare_1708887482_state->pname)->((hoare_1708887482_state->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x174ba70>, <kernel.DependentProduct object at 0x174bc20>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_011
% Using role type
% Declaring image_757158439_state:((hoare_1708887482_state->hoare_1708887482_state)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x174bab8>, <kernel.DependentProduct object at 0x174bbd8>) 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 0x174b128>, <kernel.DependentProduct object at 0x174bc20>) of role type named sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com
% Using role type
% Declaring insert949073679tate_o:((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x174b758>, <kernel.DependentProduct object at 0x174bcf8>) of role type named sy_c_Set_Oinsert_000_Eo
% Using role type
% Declaring insert_o:(Prop->((Prop->Prop)->(Prop->Prop)))
% FOF formula (<kernel.Constant object at 0x174b320>, <kernel.DependentProduct object at 0x174bd40>) of role type named sy_c_Set_Oinsert_000tc__Com__Ocom
% Using role type
% Declaring insert_com:(com->((com->Prop)->(com->Prop)))
% FOF formula (<kernel.Constant object at 0x174bab8>, <kernel.DependentProduct object at 0x174bdd0>) 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 0x174b128>, <kernel.DependentProduct object at 0x174b758>) of role type named sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Osta
% Using role type
% Declaring insert528405184_state:(hoare_1708887482_state->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x174b320>, <kernel.DependentProduct object at 0x174b9e0>) of role type named sy_c_Set_Othe__elem_000tc__Com__Ocom
% Using role type
% Declaring the_elem_com:((com->Prop)->com)
% FOF formula (<kernel.Constant object at 0x174bdd0>, <kernel.DependentProduct object at 0x174bd88>) of role type named sy_c_Set_Othe__elem_000tc__Com__Opname
% Using role type
% Declaring the_elem_pname:((pname->Prop)->pname)
% FOF formula (<kernel.Constant object at 0x174bb48>, <kernel.DependentProduct object at 0x174be18>) of role type named sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__O
% Using role type
% Declaring the_el864710747_state:((hoare_1708887482_state->Prop)->hoare_1708887482_state)
% FOF formula (<kernel.Constant object at 0x174bcf8>, <kernel.DependentProduct object at 0x174bea8>) of role type named sy_c_Set_Ovimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otr
% Using role type
% Declaring vimage1943311875_state:((pname->hoare_1708887482_state)->((hoare_1708887482_state->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x174bc20>, <kernel.DependentProduct object at 0x174bf38>) of role type named sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring fequal_pname_o:((pname->Prop)->((pname->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x174be60>, <kernel.DependentProduct object at 0x174bef0>) of role type named sy_c_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost
% Using role type
% Declaring fequal1436017556tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x174bbd8>, <kernel.DependentProduct object at 0x174be60>) of role type named sy_c_fequal_000tc__Com__Ocom
% Using role type
% Declaring fequal_com:(com->(com->Prop))
% FOF formula (<kernel.Constant object at 0x174bab8>, <kernel.DependentProduct object at 0x174b320>) of role type named sy_c_fequal_000tc__Com__Opname
% Using role type
% Declaring fequal_pname:(pname->(pname->Prop))
% FOF formula (<kernel.Constant object at 0x174bcf8>, <kernel.DependentProduct object at 0x174be18>) of role type named sy_c_fequal_000tc__Com__Ostate
% Using role type
% Declaring fequal_state:(state->(state->Prop))
% FOF formula (<kernel.Constant object at 0x174be60>, <kernel.DependentProduct object at 0x174bf38>) of role type named sy_c_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J
% Using role type
% Declaring fequal224822779_state:(hoare_1708887482_state->(hoare_1708887482_state->Prop))
% FOF formula (<kernel.Constant object at 0x174bab8>, <kernel.DependentProduct object at 0x174b320>) 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 0x174bbd8>, <kernel.DependentProduct object at 0x1582098>) of role type named sy_c_member_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost
% Using role type
% Declaring member814030440tate_o:((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x174be18>, <kernel.DependentProduct object at 0x1582050>) of role type named sy_c_member_000_Eo
% Using role type
% Declaring member_o:(Prop->((Prop->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x174bc20>, <kernel.DependentProduct object at 0x1582200>) of role type named sy_c_member_000tc__Com__Ocom
% Using role type
% Declaring member_com:(com->((com->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x174be60>, <kernel.DependentProduct object at 0x1582248>) 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 0x174be18>, <kernel.DependentProduct object at 0x15821b8>) of role type named sy_c_member_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J
% Using role type
% Declaring member451959335_state:(hoare_1708887482_state->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x174be60>, <kernel.DependentProduct object at 0x1582170>) of role type named sy_v_Fa
% Using role type
% Declaring fa:(hoare_1708887482_state->Prop)
% FOF formula (<kernel.Constant object at 0x174bbd8>, <kernel.Constant object at 0x1582170>) of role type named sy_v_pn
% Using role type
% Declaring pn:pname
% FOF formula (<kernel.Constant object at 0x174bbd8>, <kernel.Constant object at 0x1582170>) of role type named sy_v_y
% Using role type
% Declaring y:com
% FOF formula (forall (G_7:(hoare_1708887482_state->Prop)), ((hoare_90032982_state G_7) bot_bo19817387tate_o)) of role axiom named fact_0_empty
% A new axiom: (forall (G_7:(hoare_1708887482_state->Prop)), ((hoare_90032982_state G_7) bot_bo19817387tate_o))
% FOF formula (forall (Ts_7:(hoare_1708887482_state->Prop)) (G_39:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Ts_7) G_39)->((hoare_90032982_state G_39) Ts_7))) of role axiom named fact_1_asm
% A new axiom: (forall (Ts_7:(hoare_1708887482_state->Prop)) (G_39:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Ts_7) G_39)->((hoare_90032982_state G_39) Ts_7)))
% FOF formula (forall (Ts_6:(hoare_1708887482_state->Prop)) (G_38:(hoare_1708887482_state->Prop)) (Ts_5:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_38) Ts_5)->(((ord_le777019615tate_o Ts_6) Ts_5)->((hoare_90032982_state G_38) Ts_6)))) of role axiom named fact_2_weaken
% A new axiom: (forall (Ts_6:(hoare_1708887482_state->Prop)) (G_38:(hoare_1708887482_state->Prop)) (Ts_5:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_38) Ts_5)->(((ord_le777019615tate_o Ts_6) Ts_5)->((hoare_90032982_state G_38) Ts_6))))
% FOF formula (forall (G_37:(hoare_1708887482_state->Prop)) (G_36:(hoare_1708887482_state->Prop)) (Ts_4:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_36) Ts_4)->(((ord_le777019615tate_o G_36) G_37)->((hoare_90032982_state G_37) Ts_4)))) of role axiom named fact_3_thin
% A new axiom: (forall (G_37:(hoare_1708887482_state->Prop)) (G_36:(hoare_1708887482_state->Prop)) (Ts_4:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_36) Ts_4)->(((ord_le777019615tate_o G_36) G_37)->((hoare_90032982_state G_37) Ts_4))))
% FOF formula (forall (G_35:(hoare_1708887482_state->Prop)) (G_34:(hoare_1708887482_state->Prop)) (Ts_3:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_34) Ts_3)->(((hoare_90032982_state G_35) G_34)->((hoare_90032982_state G_35) Ts_3)))) of role axiom named fact_4_cut
% A new axiom: (forall (G_35:(hoare_1708887482_state->Prop)) (G_34:(hoare_1708887482_state->Prop)) (Ts_3:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_34) Ts_3)->(((hoare_90032982_state G_35) G_34)->((hoare_90032982_state G_35) Ts_3))))
% FOF formula (forall (Ts_2:(hoare_1708887482_state->Prop)) (G_33:(hoare_1708887482_state->Prop)) (T_3:hoare_1708887482_state), (((hoare_90032982_state G_33) ((insert528405184_state T_3) bot_bo19817387tate_o))->(((hoare_90032982_state G_33) Ts_2)->((hoare_90032982_state G_33) ((insert528405184_state T_3) Ts_2))))) of role axiom named fact_5_hoare__derivs_Oinsert
% A new axiom: (forall (Ts_2:(hoare_1708887482_state->Prop)) (G_33:(hoare_1708887482_state->Prop)) (T_3:hoare_1708887482_state), (((hoare_90032982_state G_33) ((insert528405184_state T_3) bot_bo19817387tate_o))->(((hoare_90032982_state G_33) Ts_2)->((hoare_90032982_state G_33) ((insert528405184_state T_3) Ts_2)))))
% FOF formula (forall (G_32:(hoare_1708887482_state->Prop)) (T_2:hoare_1708887482_state) (Ts_1:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_32) ((insert528405184_state T_2) Ts_1))->((and ((hoare_90032982_state G_32) ((insert528405184_state T_2) bot_bo19817387tate_o))) ((hoare_90032982_state G_32) Ts_1)))) of role axiom named fact_6_derivs__insertD
% A new axiom: (forall (G_32:(hoare_1708887482_state->Prop)) (T_2:hoare_1708887482_state) (Ts_1:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_32) ((insert528405184_state T_2) Ts_1))->((and ((hoare_90032982_state G_32) ((insert528405184_state T_2) bot_bo19817387tate_o))) ((hoare_90032982_state G_32) Ts_1))))
% FOF formula (forall (Pn_1:pname) (G_7:(hoare_1708887482_state->Prop)), (((hoare_90032982_state ((insert528405184_state (hoare_Mirabelle_MGT (body_1 Pn_1))) G_7)) ((insert528405184_state (hoare_Mirabelle_MGT (the_com (body Pn_1)))) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT (body_1 Pn_1))) bot_bo19817387tate_o)))) of role axiom named fact_7_MGT__BodyN
% A new axiom: (forall (Pn_1:pname) (G_7:(hoare_1708887482_state->Prop)), (((hoare_90032982_state ((insert528405184_state (hoare_Mirabelle_MGT (body_1 Pn_1))) G_7)) ((insert528405184_state (hoare_Mirabelle_MGT (the_com (body Pn_1)))) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT (body_1 Pn_1))) bot_bo19817387tate_o))))
% FOF formula (forall (A_274:((pname->Prop)->Prop)), ((finite297249702name_o A_274)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_84:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_84) A_274)))))) of role axiom named fact_8_finite__Collect__subsets
% A new axiom: (forall (A_274:((pname->Prop)->Prop)), ((finite297249702name_o A_274)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_84:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_84) A_274))))))
% FOF formula (forall (A_274:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_274)->(finite1019950101te_o_o (collec58007891te_o_o (fun (B_84:((hoare_1708887482_state->Prop)->Prop))=> ((ord_le1728773982te_o_o B_84) A_274)))))) of role axiom named fact_9_finite__Collect__subsets
% A new axiom: (forall (A_274:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_274)->(finite1019950101te_o_o (collec58007891te_o_o (fun (B_84:((hoare_1708887482_state->Prop)->Prop))=> ((ord_le1728773982te_o_o B_84) A_274))))))
% FOF formula (forall (A_274:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_274)->(finite1329924456tate_o (collec219771562tate_o (fun (B_84:(hoare_1708887482_state->Prop))=> ((ord_le777019615tate_o B_84) A_274)))))) of role axiom named fact_10_finite__Collect__subsets
% A new axiom: (forall (A_274:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_274)->(finite1329924456tate_o (collec219771562tate_o (fun (B_84:(hoare_1708887482_state->Prop))=> ((ord_le777019615tate_o B_84) A_274))))))
% FOF formula (forall (A_274:(pname->Prop)), ((finite_finite_pname A_274)->(finite297249702name_o (collect_pname_o (fun (B_84:(pname->Prop))=> ((ord_less_eq_pname_o B_84) A_274)))))) of role axiom named fact_11_finite__Collect__subsets
% A new axiom: (forall (A_274:(pname->Prop)), ((finite_finite_pname A_274)->(finite297249702name_o (collect_pname_o (fun (B_84:(pname->Prop))=> ((ord_less_eq_pname_o B_84) A_274))))))
% FOF formula (forall (H_2:(hoare_1708887482_state->(pname->Prop))) (F_88:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_88)->(finite297249702name_o ((image_1552895654name_o H_2) F_88)))) of role axiom named fact_12_finite__imageI
% A new axiom: (forall (H_2:(hoare_1708887482_state->(pname->Prop))) (F_88:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_88)->(finite297249702name_o ((image_1552895654name_o H_2) F_88))))
% FOF formula (forall (H_2:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (F_88:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_88)->(finite1329924456tate_o ((image_1551509096tate_o H_2) F_88)))) of role axiom named fact_13_finite__imageI
% A new axiom: (forall (H_2:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (F_88:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_88)->(finite1329924456tate_o ((image_1551509096tate_o H_2) F_88))))
% FOF formula (forall (H_2:(pname->(pname->Prop))) (F_88:(pname->Prop)), ((finite_finite_pname F_88)->(finite297249702name_o ((image_pname_pname_o H_2) F_88)))) of role axiom named fact_14_finite__imageI
% A new axiom: (forall (H_2:(pname->(pname->Prop))) (F_88:(pname->Prop)), ((finite_finite_pname F_88)->(finite297249702name_o ((image_pname_pname_o H_2) F_88))))
% FOF formula (forall (H_2:(pname->(hoare_1708887482_state->Prop))) (F_88:(pname->Prop)), ((finite_finite_pname F_88)->(finite1329924456tate_o ((image_425134806tate_o H_2) F_88)))) of role axiom named fact_15_finite__imageI
% A new axiom: (forall (H_2:(pname->(hoare_1708887482_state->Prop))) (F_88:(pname->Prop)), ((finite_finite_pname F_88)->(finite1329924456tate_o ((image_425134806tate_o H_2) F_88))))
% FOF formula (forall (H_2:((pname->Prop)->hoare_1708887482_state)) (F_88:((pname->Prop)->Prop)), ((finite297249702name_o F_88)->(finite1625599783_state ((image_1922967206_state H_2) F_88)))) of role axiom named fact_16_finite__imageI
% A new axiom: (forall (H_2:((pname->Prop)->hoare_1708887482_state)) (F_88:((pname->Prop)->Prop)), ((finite297249702name_o F_88)->(finite1625599783_state ((image_1922967206_state H_2) F_88))))
% FOF formula (forall (H_2:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (F_88:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_88)->(finite1625599783_state ((image_27005066_state H_2) F_88)))) of role axiom named fact_17_finite__imageI
% A new axiom: (forall (H_2:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (F_88:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_88)->(finite1625599783_state ((image_27005066_state H_2) F_88))))
% FOF formula (forall (H_2:((pname->Prop)->pname)) (F_88:((pname->Prop)->Prop)), ((finite297249702name_o F_88)->(finite_finite_pname ((image_pname_o_pname H_2) F_88)))) of role axiom named fact_18_finite__imageI
% A new axiom: (forall (H_2:((pname->Prop)->pname)) (F_88:((pname->Prop)->Prop)), ((finite297249702name_o F_88)->(finite_finite_pname ((image_pname_o_pname H_2) F_88))))
% FOF formula (forall (H_2:((hoare_1708887482_state->Prop)->pname)) (F_88:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_88)->(finite_finite_pname ((image_2051418740_pname H_2) F_88)))) of role axiom named fact_19_finite__imageI
% A new axiom: (forall (H_2:((hoare_1708887482_state->Prop)->pname)) (F_88:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_88)->(finite_finite_pname ((image_2051418740_pname H_2) F_88))))
% FOF formula (forall (H_2:(pname->hoare_1708887482_state)) (F_88:(pname->Prop)), ((finite_finite_pname F_88)->(finite1625599783_state ((image_1116629049_state H_2) F_88)))) of role axiom named fact_20_finite__imageI
% A new axiom: (forall (H_2:(pname->hoare_1708887482_state)) (F_88:(pname->Prop)), ((finite_finite_pname F_88)->(finite1625599783_state ((image_1116629049_state H_2) F_88))))
% FOF formula (forall (A_273:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_273)) of role axiom named fact_21_empty__subsetI
% A new axiom: (forall (A_273:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_273))
% FOF formula (forall (A_273:(com->Prop)), ((ord_less_eq_com_o bot_bot_com_o) A_273)) of role axiom named fact_22_empty__subsetI
% A new axiom: (forall (A_273:(com->Prop)), ((ord_less_eq_com_o bot_bot_com_o) A_273))
% FOF formula (forall (A_273:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o bot_bo19817387tate_o) A_273)) of role axiom named fact_23_empty__subsetI
% A new axiom: (forall (A_273:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o bot_bo19817387tate_o) A_273))
% FOF formula (forall (A_272:com) (A_271:(com->Prop)), ((finite_finite_com A_271)->(finite_finite_com ((insert_com A_272) A_271)))) of role axiom named fact_24_finite_OinsertI
% A new axiom: (forall (A_272:com) (A_271:(com->Prop)), ((finite_finite_com A_271)->(finite_finite_com ((insert_com A_272) A_271))))
% FOF formula (forall (A_272:(pname->Prop)) (A_271:((pname->Prop)->Prop)), ((finite297249702name_o A_271)->(finite297249702name_o ((insert_pname_o A_272) A_271)))) of role axiom named fact_25_finite_OinsertI
% A new axiom: (forall (A_272:(pname->Prop)) (A_271:((pname->Prop)->Prop)), ((finite297249702name_o A_271)->(finite297249702name_o ((insert_pname_o A_272) A_271))))
% FOF formula (forall (A_272:(hoare_1708887482_state->Prop)) (A_271:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_271)->(finite1329924456tate_o ((insert949073679tate_o A_272) A_271)))) of role axiom named fact_26_finite_OinsertI
% A new axiom: (forall (A_272:(hoare_1708887482_state->Prop)) (A_271:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_271)->(finite1329924456tate_o ((insert949073679tate_o A_272) A_271))))
% FOF formula (forall (A_272:pname) (A_271:(pname->Prop)), ((finite_finite_pname A_271)->(finite_finite_pname ((insert_pname A_272) A_271)))) of role axiom named fact_27_finite_OinsertI
% A new axiom: (forall (A_272:pname) (A_271:(pname->Prop)), ((finite_finite_pname A_271)->(finite_finite_pname ((insert_pname A_272) A_271))))
% FOF formula (forall (A_272:hoare_1708887482_state) (A_271:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_271)->(finite1625599783_state ((insert528405184_state A_272) A_271)))) of role axiom named fact_28_finite_OinsertI
% A new axiom: (forall (A_272:hoare_1708887482_state) (A_271:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_271)->(finite1625599783_state ((insert528405184_state A_272) A_271))))
% FOF formula (finite297249702name_o bot_bot_pname_o_o) of role axiom named fact_29_finite_OemptyI
% A new axiom: (finite297249702name_o bot_bot_pname_o_o)
% FOF formula (finite1329924456tate_o bot_bo1678742418te_o_o) of role axiom named fact_30_finite_OemptyI
% A new axiom: (finite1329924456tate_o bot_bo1678742418te_o_o)
% FOF formula (finite_finite_com bot_bot_com_o) of role axiom named fact_31_finite_OemptyI
% A new axiom: (finite_finite_com bot_bot_com_o)
% FOF formula (finite1625599783_state bot_bo19817387tate_o) of role axiom named fact_32_finite_OemptyI
% A new axiom: (finite1625599783_state bot_bo19817387tate_o)
% FOF formula (finite_finite_pname bot_bot_pname_o) of role axiom named fact_33_finite_OemptyI
% A new axiom: (finite_finite_pname bot_bot_pname_o)
% FOF formula (forall (Q_26:((pname->Prop)->Prop)) (P_45:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_45))) (finite297249702name_o (collect_pname_o Q_26)))->(finite297249702name_o (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (P_45 X_3)) (Q_26 X_3))))))) of role axiom named fact_34_finite__Collect__conjI
% A new axiom: (forall (Q_26:((pname->Prop)->Prop)) (P_45:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_45))) (finite297249702name_o (collect_pname_o Q_26)))->(finite297249702name_o (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (P_45 X_3)) (Q_26 X_3)))))))
% FOF formula (forall (Q_26:((hoare_1708887482_state->Prop)->Prop)) (P_45:((hoare_1708887482_state->Prop)->Prop)), (((or (finite1329924456tate_o (collec219771562tate_o P_45))) (finite1329924456tate_o (collec219771562tate_o Q_26)))->(finite1329924456tate_o (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (P_45 X_3)) (Q_26 X_3))))))) of role axiom named fact_35_finite__Collect__conjI
% A new axiom: (forall (Q_26:((hoare_1708887482_state->Prop)->Prop)) (P_45:((hoare_1708887482_state->Prop)->Prop)), (((or (finite1329924456tate_o (collec219771562tate_o P_45))) (finite1329924456tate_o (collec219771562tate_o Q_26)))->(finite1329924456tate_o (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (P_45 X_3)) (Q_26 X_3)))))))
% FOF formula (forall (Q_26:(hoare_1708887482_state->Prop)) (P_45:(hoare_1708887482_state->Prop)), (((or (finite1625599783_state (collec1568722789_state P_45))) (finite1625599783_state (collec1568722789_state Q_26)))->(finite1625599783_state (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (P_45 X_3)) (Q_26 X_3))))))) of role axiom named fact_36_finite__Collect__conjI
% A new axiom: (forall (Q_26:(hoare_1708887482_state->Prop)) (P_45:(hoare_1708887482_state->Prop)), (((or (finite1625599783_state (collec1568722789_state P_45))) (finite1625599783_state (collec1568722789_state Q_26)))->(finite1625599783_state (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (P_45 X_3)) (Q_26 X_3)))))))
% FOF formula (forall (Q_26:(pname->Prop)) (P_45:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_45))) (finite_finite_pname (collect_pname Q_26)))->(finite_finite_pname (collect_pname (fun (X_3:pname)=> ((and (P_45 X_3)) (Q_26 X_3))))))) of role axiom named fact_37_finite__Collect__conjI
% A new axiom: (forall (Q_26:(pname->Prop)) (P_45:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_45))) (finite_finite_pname (collect_pname Q_26)))->(finite_finite_pname (collect_pname (fun (X_3:pname)=> ((and (P_45 X_3)) (Q_26 X_3)))))))
% FOF formula (forall (C_68:pname) (A_270:(hoare_1708887482_state->Prop)), ((and ((((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o)->(((eq (pname->Prop)) ((image_1509414295_pname (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) bot_bot_pname_o))) ((not (((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o))->(((eq (pname->Prop)) ((image_1509414295_pname (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) ((insert_pname C_68) bot_bot_pname_o))))) of role axiom named fact_38_image__constant__conv
% A new axiom: (forall (C_68:pname) (A_270:(hoare_1708887482_state->Prop)), ((and ((((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o)->(((eq (pname->Prop)) ((image_1509414295_pname (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) bot_bot_pname_o))) ((not (((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o))->(((eq (pname->Prop)) ((image_1509414295_pname (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) ((insert_pname C_68) bot_bot_pname_o)))))
% FOF formula (forall (C_68:com) (A_270:(hoare_1708887482_state->Prop)), ((and ((((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o)->(((eq (com->Prop)) ((image_1604448413te_com (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) bot_bot_com_o))) ((not (((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o))->(((eq (com->Prop)) ((image_1604448413te_com (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) ((insert_com C_68) bot_bot_com_o))))) of role axiom named fact_39_image__constant__conv
% A new axiom: (forall (C_68:com) (A_270:(hoare_1708887482_state->Prop)), ((and ((((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o)->(((eq (com->Prop)) ((image_1604448413te_com (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) bot_bot_com_o))) ((not (((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o))->(((eq (com->Prop)) ((image_1604448413te_com (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) ((insert_com C_68) bot_bot_com_o)))))
% FOF formula (forall (C_68:hoare_1708887482_state) (A_270:(com->Prop)), ((and ((((eq (com->Prop)) A_270) bot_bot_com_o)->(((eq (hoare_1708887482_state->Prop)) ((image_934102463_state (fun (X_3:com)=> C_68)) A_270)) bot_bo19817387tate_o))) ((not (((eq (com->Prop)) A_270) bot_bot_com_o))->(((eq (hoare_1708887482_state->Prop)) ((image_934102463_state (fun (X_3:com)=> C_68)) A_270)) ((insert528405184_state C_68) bot_bo19817387tate_o))))) of role axiom named fact_40_image__constant__conv
% A new axiom: (forall (C_68:hoare_1708887482_state) (A_270:(com->Prop)), ((and ((((eq (com->Prop)) A_270) bot_bot_com_o)->(((eq (hoare_1708887482_state->Prop)) ((image_934102463_state (fun (X_3:com)=> C_68)) A_270)) bot_bo19817387tate_o))) ((not (((eq (com->Prop)) A_270) bot_bot_com_o))->(((eq (hoare_1708887482_state->Prop)) ((image_934102463_state (fun (X_3:com)=> C_68)) A_270)) ((insert528405184_state C_68) bot_bo19817387tate_o)))))
% FOF formula (forall (C_68:hoare_1708887482_state) (A_270:(pname->Prop)), ((and ((((eq (pname->Prop)) A_270) bot_bot_pname_o)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> C_68)) A_270)) bot_bo19817387tate_o))) ((not (((eq (pname->Prop)) A_270) bot_bot_pname_o))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> C_68)) A_270)) ((insert528405184_state C_68) bot_bo19817387tate_o))))) of role axiom named fact_41_image__constant__conv
% A new axiom: (forall (C_68:hoare_1708887482_state) (A_270:(pname->Prop)), ((and ((((eq (pname->Prop)) A_270) bot_bot_pname_o)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> C_68)) A_270)) bot_bo19817387tate_o))) ((not (((eq (pname->Prop)) A_270) bot_bot_pname_o))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> C_68)) A_270)) ((insert528405184_state C_68) bot_bo19817387tate_o)))))
% FOF formula (forall (C_67:pname) (X_119:hoare_1708887482_state) (A_269:(hoare_1708887482_state->Prop)), (((member451959335_state X_119) A_269)->(((eq (pname->Prop)) ((image_1509414295_pname (fun (X_3:hoare_1708887482_state)=> C_67)) A_269)) ((insert_pname C_67) bot_bot_pname_o)))) of role axiom named fact_42_image__constant
% A new axiom: (forall (C_67:pname) (X_119:hoare_1708887482_state) (A_269:(hoare_1708887482_state->Prop)), (((member451959335_state X_119) A_269)->(((eq (pname->Prop)) ((image_1509414295_pname (fun (X_3:hoare_1708887482_state)=> C_67)) A_269)) ((insert_pname C_67) bot_bot_pname_o))))
% FOF formula (forall (C_67:com) (X_119:hoare_1708887482_state) (A_269:(hoare_1708887482_state->Prop)), (((member451959335_state X_119) A_269)->(((eq (com->Prop)) ((image_1604448413te_com (fun (X_3:hoare_1708887482_state)=> C_67)) A_269)) ((insert_com C_67) bot_bot_com_o)))) of role axiom named fact_43_image__constant
% A new axiom: (forall (C_67:com) (X_119:hoare_1708887482_state) (A_269:(hoare_1708887482_state->Prop)), (((member451959335_state X_119) A_269)->(((eq (com->Prop)) ((image_1604448413te_com (fun (X_3:hoare_1708887482_state)=> C_67)) A_269)) ((insert_com C_67) bot_bot_com_o))))
% FOF formula (forall (C_67:pname) (X_119:pname) (A_269:(pname->Prop)), (((member_pname X_119) A_269)->(((eq (pname->Prop)) ((image_pname_pname (fun (X_3:pname)=> C_67)) A_269)) ((insert_pname C_67) bot_bot_pname_o)))) of role axiom named fact_44_image__constant
% A new axiom: (forall (C_67:pname) (X_119:pname) (A_269:(pname->Prop)), (((member_pname X_119) A_269)->(((eq (pname->Prop)) ((image_pname_pname (fun (X_3:pname)=> C_67)) A_269)) ((insert_pname C_67) bot_bot_pname_o))))
% FOF formula (forall (C_67:com) (X_119:pname) (A_269:(pname->Prop)), (((member_pname X_119) A_269)->(((eq (com->Prop)) ((image_pname_com (fun (X_3:pname)=> C_67)) A_269)) ((insert_com C_67) bot_bot_com_o)))) of role axiom named fact_45_image__constant
% A new axiom: (forall (C_67:com) (X_119:pname) (A_269:(pname->Prop)), (((member_pname X_119) A_269)->(((eq (com->Prop)) ((image_pname_com (fun (X_3:pname)=> C_67)) A_269)) ((insert_com C_67) bot_bot_com_o))))
% FOF formula (forall (C_67:hoare_1708887482_state) (X_119:com) (A_269:(com->Prop)), (((member_com X_119) A_269)->(((eq (hoare_1708887482_state->Prop)) ((image_934102463_state (fun (X_3:com)=> C_67)) A_269)) ((insert528405184_state C_67) bot_bo19817387tate_o)))) of role axiom named fact_46_image__constant
% A new axiom: (forall (C_67:hoare_1708887482_state) (X_119:com) (A_269:(com->Prop)), (((member_com X_119) A_269)->(((eq (hoare_1708887482_state->Prop)) ((image_934102463_state (fun (X_3:com)=> C_67)) A_269)) ((insert528405184_state C_67) bot_bo19817387tate_o))))
% FOF formula (forall (C_67:hoare_1708887482_state) (X_119:pname) (A_269:(pname->Prop)), (((member_pname X_119) A_269)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> C_67)) A_269)) ((insert528405184_state C_67) bot_bo19817387tate_o)))) of role axiom named fact_47_image__constant
% A new axiom: (forall (C_67:hoare_1708887482_state) (X_119:pname) (A_269:(pname->Prop)), (((member_pname X_119) A_269)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> C_67)) A_269)) ((insert528405184_state C_67) bot_bo19817387tate_o))))
% FOF formula (forall (F_87:(com->option_com)) (X_118:com) (Y_53:com), ((((eq option_com) (F_87 X_118)) (some_com Y_53))->(((eq (com->Prop)) ((insert_com X_118) (dom_com_com F_87))) (dom_com_com F_87)))) of role axiom named fact_48_insert__dom
% A new axiom: (forall (F_87:(com->option_com)) (X_118:com) (Y_53:com), ((((eq option_com) (F_87 X_118)) (some_com Y_53))->(((eq (com->Prop)) ((insert_com X_118) (dom_com_com F_87))) (dom_com_com F_87))))
% FOF formula (forall (F_87:(hoare_1708887482_state->option_pname)) (X_118:hoare_1708887482_state) (Y_53:pname), ((((eq option_pname) (F_87 X_118)) (some_pname Y_53))->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_118) (dom_Ho1805192458_pname F_87))) (dom_Ho1805192458_pname F_87)))) of role axiom named fact_49_insert__dom
% A new axiom: (forall (F_87:(hoare_1708887482_state->option_pname)) (X_118:hoare_1708887482_state) (Y_53:pname), ((((eq option_pname) (F_87 X_118)) (some_pname Y_53))->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_118) (dom_Ho1805192458_pname F_87))) (dom_Ho1805192458_pname F_87))))
% FOF formula (forall (F_87:(hoare_1708887482_state->option1624383643_state)) (X_118:hoare_1708887482_state) (Y_53:hoare_1708887482_state), ((((eq option1624383643_state) (F_87 X_118)) (some_H1974565227_state Y_53))->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_118) (dom_Ho1703271284_state F_87))) (dom_Ho1703271284_state F_87)))) of role axiom named fact_50_insert__dom
% A new axiom: (forall (F_87:(hoare_1708887482_state->option1624383643_state)) (X_118:hoare_1708887482_state) (Y_53:hoare_1708887482_state), ((((eq option1624383643_state) (F_87 X_118)) (some_H1974565227_state Y_53))->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_118) (dom_Ho1703271284_state F_87))) (dom_Ho1703271284_state F_87))))
% FOF formula (forall (F_87:(pname->option_com)) (X_118:pname) (Y_53:com), ((((eq option_com) (F_87 X_118)) (some_com Y_53))->(((eq (pname->Prop)) ((insert_pname X_118) (dom_pname_com F_87))) (dom_pname_com F_87)))) of role axiom named fact_51_insert__dom
% A new axiom: (forall (F_87:(pname->option_com)) (X_118:pname) (Y_53:com), ((((eq option_com) (F_87 X_118)) (some_com Y_53))->(((eq (pname->Prop)) ((insert_pname X_118) (dom_pname_com F_87))) (dom_pname_com F_87))))
% FOF formula (forall (B_171:((pname->Prop)->Prop)) (F_86:(hoare_1708887482_state->(pname->Prop))) (A_268:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_268)->(((ord_le1205211808me_o_o B_171) ((image_1552895654name_o F_86) A_268))->(finite297249702name_o B_171)))) of role axiom named fact_52_finite__surj
% A new axiom: (forall (B_171:((pname->Prop)->Prop)) (F_86:(hoare_1708887482_state->(pname->Prop))) (A_268:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_268)->(((ord_le1205211808me_o_o B_171) ((image_1552895654name_o F_86) A_268))->(finite297249702name_o B_171))))
% FOF formula (forall (B_171:((hoare_1708887482_state->Prop)->Prop)) (F_86:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (A_268:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_268)->(((ord_le1728773982te_o_o B_171) ((image_1551509096tate_o F_86) A_268))->(finite1329924456tate_o B_171)))) of role axiom named fact_53_finite__surj
% A new axiom: (forall (B_171:((hoare_1708887482_state->Prop)->Prop)) (F_86:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (A_268:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_268)->(((ord_le1728773982te_o_o B_171) ((image_1551509096tate_o F_86) A_268))->(finite1329924456tate_o B_171))))
% FOF formula (forall (B_171:(pname->Prop)) (F_86:(hoare_1708887482_state->pname)) (A_268:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_268)->(((ord_less_eq_pname_o B_171) ((image_1509414295_pname F_86) A_268))->(finite_finite_pname B_171)))) of role axiom named fact_54_finite__surj
% A new axiom: (forall (B_171:(pname->Prop)) (F_86:(hoare_1708887482_state->pname)) (A_268:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_268)->(((ord_less_eq_pname_o B_171) ((image_1509414295_pname F_86) A_268))->(finite_finite_pname B_171))))
% FOF formula (forall (B_171:((pname->Prop)->Prop)) (F_86:(pname->(pname->Prop))) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_le1205211808me_o_o B_171) ((image_pname_pname_o F_86) A_268))->(finite297249702name_o B_171)))) of role axiom named fact_55_finite__surj
% A new axiom: (forall (B_171:((pname->Prop)->Prop)) (F_86:(pname->(pname->Prop))) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_le1205211808me_o_o B_171) ((image_pname_pname_o F_86) A_268))->(finite297249702name_o B_171))))
% FOF formula (forall (B_171:((hoare_1708887482_state->Prop)->Prop)) (F_86:(pname->(hoare_1708887482_state->Prop))) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_le1728773982te_o_o B_171) ((image_425134806tate_o F_86) A_268))->(finite1329924456tate_o B_171)))) of role axiom named fact_56_finite__surj
% A new axiom: (forall (B_171:((hoare_1708887482_state->Prop)->Prop)) (F_86:(pname->(hoare_1708887482_state->Prop))) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_le1728773982te_o_o B_171) ((image_425134806tate_o F_86) A_268))->(finite1329924456tate_o B_171))))
% FOF formula (forall (B_171:(pname->Prop)) (F_86:(pname->pname)) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_less_eq_pname_o B_171) ((image_pname_pname F_86) A_268))->(finite_finite_pname B_171)))) of role axiom named fact_57_finite__surj
% A new axiom: (forall (B_171:(pname->Prop)) (F_86:(pname->pname)) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_less_eq_pname_o B_171) ((image_pname_pname F_86) A_268))->(finite_finite_pname B_171))))
% FOF formula (forall (B_171:(hoare_1708887482_state->Prop)) (F_86:((pname->Prop)->hoare_1708887482_state)) (A_268:((pname->Prop)->Prop)), ((finite297249702name_o A_268)->(((ord_le777019615tate_o B_171) ((image_1922967206_state F_86) A_268))->(finite1625599783_state B_171)))) of role axiom named fact_58_finite__surj
% A new axiom: (forall (B_171:(hoare_1708887482_state->Prop)) (F_86:((pname->Prop)->hoare_1708887482_state)) (A_268:((pname->Prop)->Prop)), ((finite297249702name_o A_268)->(((ord_le777019615tate_o B_171) ((image_1922967206_state F_86) A_268))->(finite1625599783_state B_171))))
% FOF formula (forall (B_171:(hoare_1708887482_state->Prop)) (F_86:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (A_268:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_268)->(((ord_le777019615tate_o B_171) ((image_27005066_state F_86) A_268))->(finite1625599783_state B_171)))) of role axiom named fact_59_finite__surj
% A new axiom: (forall (B_171:(hoare_1708887482_state->Prop)) (F_86:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (A_268:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_268)->(((ord_le777019615tate_o B_171) ((image_27005066_state F_86) A_268))->(finite1625599783_state B_171))))
% FOF formula (forall (B_171:(pname->Prop)) (F_86:((pname->Prop)->pname)) (A_268:((pname->Prop)->Prop)), ((finite297249702name_o A_268)->(((ord_less_eq_pname_o B_171) ((image_pname_o_pname F_86) A_268))->(finite_finite_pname B_171)))) of role axiom named fact_60_finite__surj
% A new axiom: (forall (B_171:(pname->Prop)) (F_86:((pname->Prop)->pname)) (A_268:((pname->Prop)->Prop)), ((finite297249702name_o A_268)->(((ord_less_eq_pname_o B_171) ((image_pname_o_pname F_86) A_268))->(finite_finite_pname B_171))))
% FOF formula (forall (B_171:(pname->Prop)) (F_86:((hoare_1708887482_state->Prop)->pname)) (A_268:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_268)->(((ord_less_eq_pname_o B_171) ((image_2051418740_pname F_86) A_268))->(finite_finite_pname B_171)))) of role axiom named fact_61_finite__surj
% A new axiom: (forall (B_171:(pname->Prop)) (F_86:((hoare_1708887482_state->Prop)->pname)) (A_268:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_268)->(((ord_less_eq_pname_o B_171) ((image_2051418740_pname F_86) A_268))->(finite_finite_pname B_171))))
% FOF formula (forall (B_171:(hoare_1708887482_state->Prop)) (F_86:(pname->hoare_1708887482_state)) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_le777019615tate_o B_171) ((image_1116629049_state F_86) A_268))->(finite1625599783_state B_171)))) of role axiom named fact_62_finite__surj
% A new axiom: (forall (B_171:(hoare_1708887482_state->Prop)) (F_86:(pname->hoare_1708887482_state)) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_le777019615tate_o B_171) ((image_1116629049_state F_86) A_268))->(finite1625599783_state B_171))))
% FOF formula (forall (A_267:(pname->Prop)) (X_117:pname), (((ord_less_eq_pname_o A_267) ((insert_pname X_117) bot_bot_pname_o))->((or (((eq (pname->Prop)) A_267) bot_bot_pname_o)) (((eq (pname->Prop)) A_267) ((insert_pname X_117) bot_bot_pname_o))))) of role axiom named fact_63_subset__singletonD
% A new axiom: (forall (A_267:(pname->Prop)) (X_117:pname), (((ord_less_eq_pname_o A_267) ((insert_pname X_117) bot_bot_pname_o))->((or (((eq (pname->Prop)) A_267) bot_bot_pname_o)) (((eq (pname->Prop)) A_267) ((insert_pname X_117) bot_bot_pname_o)))))
% FOF formula (forall (A_267:(com->Prop)) (X_117:com), (((ord_less_eq_com_o A_267) ((insert_com X_117) bot_bot_com_o))->((or (((eq (com->Prop)) A_267) bot_bot_com_o)) (((eq (com->Prop)) A_267) ((insert_com X_117) bot_bot_com_o))))) of role axiom named fact_64_subset__singletonD
% A new axiom: (forall (A_267:(com->Prop)) (X_117:com), (((ord_less_eq_com_o A_267) ((insert_com X_117) bot_bot_com_o))->((or (((eq (com->Prop)) A_267) bot_bot_com_o)) (((eq (com->Prop)) A_267) ((insert_com X_117) bot_bot_com_o)))))
% FOF formula (forall (A_267:(hoare_1708887482_state->Prop)) (X_117:hoare_1708887482_state), (((ord_le777019615tate_o A_267) ((insert528405184_state X_117) bot_bo19817387tate_o))->((or (((eq (hoare_1708887482_state->Prop)) A_267) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) A_267) ((insert528405184_state X_117) bot_bo19817387tate_o))))) of role axiom named fact_65_subset__singletonD
% A new axiom: (forall (A_267:(hoare_1708887482_state->Prop)) (X_117:hoare_1708887482_state), (((ord_le777019615tate_o A_267) ((insert528405184_state X_117) bot_bo19817387tate_o))->((or (((eq (hoare_1708887482_state->Prop)) A_267) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) A_267) ((insert528405184_state X_117) bot_bo19817387tate_o)))))
% FOF formula (forall (C_34:com), (hoare_1160767572gleton->(wT_bodies->((wt C_34)->((hoare_90032982_state bot_bo19817387tate_o) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o)))))) of role axiom named fact_66_MGF
% A new axiom: (forall (C_34:com), (hoare_1160767572gleton->(wT_bodies->((wt C_34)->((hoare_90032982_state bot_bo19817387tate_o) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o))))))
% FOF formula (forall (A_266:com), (((member_com A_266) bot_bot_com_o)->False)) of role axiom named fact_67_emptyE
% A new axiom: (forall (A_266:com), (((member_com A_266) bot_bot_com_o)->False))
% FOF formula (forall (A_266:hoare_1708887482_state), (((member451959335_state A_266) bot_bo19817387tate_o)->False)) of role axiom named fact_68_emptyE
% A new axiom: (forall (A_266:hoare_1708887482_state), (((member451959335_state A_266) bot_bo19817387tate_o)->False))
% FOF formula (forall (A_266:pname), (((member_pname A_266) bot_bot_pname_o)->False)) of role axiom named fact_69_emptyE
% A new axiom: (forall (A_266:pname), (((member_pname A_266) bot_bot_pname_o)->False))
% FOF formula (forall (B_170:com) (A_265:com) (B_169:(com->Prop)), (((((member_com A_265) B_169)->False)->(((eq com) A_265) B_170))->((member_com A_265) ((insert_com B_170) B_169)))) of role axiom named fact_70_insertCI
% A new axiom: (forall (B_170:com) (A_265:com) (B_169:(com->Prop)), (((((member_com A_265) B_169)->False)->(((eq com) A_265) B_170))->((member_com A_265) ((insert_com B_170) B_169))))
% FOF formula (forall (B_170:pname) (A_265:pname) (B_169:(pname->Prop)), (((((member_pname A_265) B_169)->False)->(((eq pname) A_265) B_170))->((member_pname A_265) ((insert_pname B_170) B_169)))) of role axiom named fact_71_insertCI
% A new axiom: (forall (B_170:pname) (A_265:pname) (B_169:(pname->Prop)), (((((member_pname A_265) B_169)->False)->(((eq pname) A_265) B_170))->((member_pname A_265) ((insert_pname B_170) B_169))))
% FOF formula (forall (B_170:hoare_1708887482_state) (A_265:hoare_1708887482_state) (B_169:(hoare_1708887482_state->Prop)), (((((member451959335_state A_265) B_169)->False)->(((eq hoare_1708887482_state) A_265) B_170))->((member451959335_state A_265) ((insert528405184_state B_170) B_169)))) of role axiom named fact_72_insertCI
% A new axiom: (forall (B_170:hoare_1708887482_state) (A_265:hoare_1708887482_state) (B_169:(hoare_1708887482_state->Prop)), (((((member451959335_state A_265) B_169)->False)->(((eq hoare_1708887482_state) A_265) B_170))->((member451959335_state A_265) ((insert528405184_state B_170) B_169))))
% FOF formula (forall (A_264:com) (B_168:com) (A_263:(com->Prop)), (((member_com A_264) ((insert_com B_168) A_263))->((not (((eq com) A_264) B_168))->((member_com A_264) A_263)))) of role axiom named fact_73_insertE
% A new axiom: (forall (A_264:com) (B_168:com) (A_263:(com->Prop)), (((member_com A_264) ((insert_com B_168) A_263))->((not (((eq com) A_264) B_168))->((member_com A_264) A_263))))
% FOF formula (forall (A_264:pname) (B_168:pname) (A_263:(pname->Prop)), (((member_pname A_264) ((insert_pname B_168) A_263))->((not (((eq pname) A_264) B_168))->((member_pname A_264) A_263)))) of role axiom named fact_74_insertE
% A new axiom: (forall (A_264:pname) (B_168:pname) (A_263:(pname->Prop)), (((member_pname A_264) ((insert_pname B_168) A_263))->((not (((eq pname) A_264) B_168))->((member_pname A_264) A_263))))
% FOF formula (forall (A_264:hoare_1708887482_state) (B_168:hoare_1708887482_state) (A_263:(hoare_1708887482_state->Prop)), (((member451959335_state A_264) ((insert528405184_state B_168) A_263))->((not (((eq hoare_1708887482_state) A_264) B_168))->((member451959335_state A_264) A_263)))) of role axiom named fact_75_insertE
% A new axiom: (forall (A_264:hoare_1708887482_state) (B_168:hoare_1708887482_state) (A_263:(hoare_1708887482_state->Prop)), (((member451959335_state A_264) ((insert528405184_state B_168) A_263))->((not (((eq hoare_1708887482_state) A_264) B_168))->((member451959335_state A_264) A_263))))
% FOF formula (forall (A_262:(pname->Prop)) (B_167:(pname->Prop)), (((ord_less_eq_pname_o A_262) B_167)->(((ord_less_eq_pname_o B_167) A_262)->(((eq (pname->Prop)) A_262) B_167)))) of role axiom named fact_76_equalityI
% A new axiom: (forall (A_262:(pname->Prop)) (B_167:(pname->Prop)), (((ord_less_eq_pname_o A_262) B_167)->(((ord_less_eq_pname_o B_167) A_262)->(((eq (pname->Prop)) A_262) B_167))))
% FOF formula (forall (A_262:(hoare_1708887482_state->Prop)) (B_167:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_262) B_167)->(((ord_le777019615tate_o B_167) A_262)->(((eq (hoare_1708887482_state->Prop)) A_262) B_167)))) of role axiom named fact_77_equalityI
% A new axiom: (forall (A_262:(hoare_1708887482_state->Prop)) (B_167:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_262) B_167)->(((ord_le777019615tate_o B_167) A_262)->(((eq (hoare_1708887482_state->Prop)) A_262) B_167))))
% FOF formula (forall (C_66:com) (A_261:(com->Prop)) (B_166:(com->Prop)), (((ord_less_eq_com_o A_261) B_166)->(((member_com C_66) A_261)->((member_com C_66) B_166)))) of role axiom named fact_78_subsetD
% A new axiom: (forall (C_66:com) (A_261:(com->Prop)) (B_166:(com->Prop)), (((ord_less_eq_com_o A_261) B_166)->(((member_com C_66) A_261)->((member_com C_66) B_166))))
% FOF formula (forall (C_66:hoare_1708887482_state) (A_261:(hoare_1708887482_state->Prop)) (B_166:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_261) B_166)->(((member451959335_state C_66) A_261)->((member451959335_state C_66) B_166)))) of role axiom named fact_79_subsetD
% A new axiom: (forall (C_66:hoare_1708887482_state) (A_261:(hoare_1708887482_state->Prop)) (B_166:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_261) B_166)->(((member451959335_state C_66) A_261)->((member451959335_state C_66) B_166))))
% FOF formula (forall (C_66:pname) (A_261:(pname->Prop)) (B_166:(pname->Prop)), (((ord_less_eq_pname_o A_261) B_166)->(((member_pname C_66) A_261)->((member_pname C_66) B_166)))) of role axiom named fact_80_subsetD
% A new axiom: (forall (C_66:pname) (A_261:(pname->Prop)) (B_166:(pname->Prop)), (((ord_less_eq_pname_o A_261) B_166)->(((member_pname C_66) A_261)->((member_pname C_66) B_166))))
% FOF formula (forall (A_260:(hoare_1708887482_state->Prop)) (B_165:com) (F_85:(hoare_1708887482_state->com)) (X_116:hoare_1708887482_state), ((((eq com) B_165) (F_85 X_116))->(((member451959335_state X_116) A_260)->((member_com B_165) ((image_1604448413te_com F_85) A_260))))) of role axiom named fact_81_image__eqI
% A new axiom: (forall (A_260:(hoare_1708887482_state->Prop)) (B_165:com) (F_85:(hoare_1708887482_state->com)) (X_116:hoare_1708887482_state), ((((eq com) B_165) (F_85 X_116))->(((member451959335_state X_116) A_260)->((member_com B_165) ((image_1604448413te_com F_85) A_260)))))
% FOF formula (forall (A_260:(pname->Prop)) (B_165:com) (F_85:(pname->com)) (X_116:pname), ((((eq com) B_165) (F_85 X_116))->(((member_pname X_116) A_260)->((member_com B_165) ((image_pname_com F_85) A_260))))) of role axiom named fact_82_image__eqI
% A new axiom: (forall (A_260:(pname->Prop)) (B_165:com) (F_85:(pname->com)) (X_116:pname), ((((eq com) B_165) (F_85 X_116))->(((member_pname X_116) A_260)->((member_com B_165) ((image_pname_com F_85) A_260)))))
% FOF formula (forall (A_260:(com->Prop)) (B_165:hoare_1708887482_state) (F_85:(com->hoare_1708887482_state)) (X_116:com), ((((eq hoare_1708887482_state) B_165) (F_85 X_116))->(((member_com X_116) A_260)->((member451959335_state B_165) ((image_934102463_state F_85) A_260))))) of role axiom named fact_83_image__eqI
% A new axiom: (forall (A_260:(com->Prop)) (B_165:hoare_1708887482_state) (F_85:(com->hoare_1708887482_state)) (X_116:com), ((((eq hoare_1708887482_state) B_165) (F_85 X_116))->(((member_com X_116) A_260)->((member451959335_state B_165) ((image_934102463_state F_85) A_260)))))
% FOF formula (forall (A_260:(com->Prop)) (B_165:pname) (F_85:(com->pname)) (X_116:com), ((((eq pname) B_165) (F_85 X_116))->(((member_com X_116) A_260)->((member_pname B_165) ((image_com_pname F_85) A_260))))) of role axiom named fact_84_image__eqI
% A new axiom: (forall (A_260:(com->Prop)) (B_165:pname) (F_85:(com->pname)) (X_116:com), ((((eq pname) B_165) (F_85 X_116))->(((member_com X_116) A_260)->((member_pname B_165) ((image_com_pname F_85) A_260)))))
% FOF formula (forall (A_260:(pname->Prop)) (B_165:hoare_1708887482_state) (F_85:(pname->hoare_1708887482_state)) (X_116:pname), ((((eq hoare_1708887482_state) B_165) (F_85 X_116))->(((member_pname X_116) A_260)->((member451959335_state B_165) ((image_1116629049_state F_85) A_260))))) of role axiom named fact_85_image__eqI
% A new axiom: (forall (A_260:(pname->Prop)) (B_165:hoare_1708887482_state) (F_85:(pname->hoare_1708887482_state)) (X_116:pname), ((((eq hoare_1708887482_state) B_165) (F_85 X_116))->(((member_pname X_116) A_260)->((member451959335_state B_165) ((image_1116629049_state F_85) A_260)))))
% FOF formula (forall (A_259:com) (A_258:(com->Prop)), ((((eq (com->Prop)) A_258) bot_bot_com_o)->(((member_com A_259) A_258)->False))) of role axiom named fact_86_equals0D
% A new axiom: (forall (A_259:com) (A_258:(com->Prop)), ((((eq (com->Prop)) A_258) bot_bot_com_o)->(((member_com A_259) A_258)->False)))
% FOF formula (forall (A_259:hoare_1708887482_state) (A_258:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_258) bot_bo19817387tate_o)->(((member451959335_state A_259) A_258)->False))) of role axiom named fact_87_equals0D
% A new axiom: (forall (A_259:hoare_1708887482_state) (A_258:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_258) bot_bo19817387tate_o)->(((member451959335_state A_259) A_258)->False)))
% FOF formula (forall (A_259:pname) (A_258:(pname->Prop)), ((((eq (pname->Prop)) A_258) bot_bot_pname_o)->(((member_pname A_259) A_258)->False))) of role axiom named fact_88_equals0D
% A new axiom: (forall (A_259:pname) (A_258:(pname->Prop)), ((((eq (pname->Prop)) A_258) bot_bot_pname_o)->(((member_pname A_259) A_258)->False)))
% FOF formula (forall (P_44:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_44)) bot_bot_pname_o)) (forall (X_3:pname), ((P_44 X_3)->False)))) of role axiom named fact_89_Collect__empty__eq
% A new axiom: (forall (P_44:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_44)) bot_bot_pname_o)) (forall (X_3:pname), ((P_44 X_3)->False))))
% FOF formula (forall (P_44:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) (collect_pname_o P_44)) bot_bot_pname_o_o)) (forall (X_3:(pname->Prop)), ((P_44 X_3)->False)))) of role axiom named fact_90_Collect__empty__eq
% A new axiom: (forall (P_44:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) (collect_pname_o P_44)) bot_bot_pname_o_o)) (forall (X_3:(pname->Prop)), ((P_44 X_3)->False))))
% FOF formula (forall (P_44:((hoare_1708887482_state->Prop)->Prop)), ((iff (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o P_44)) bot_bo1678742418te_o_o)) (forall (X_3:(hoare_1708887482_state->Prop)), ((P_44 X_3)->False)))) of role axiom named fact_91_Collect__empty__eq
% A new axiom: (forall (P_44:((hoare_1708887482_state->Prop)->Prop)), ((iff (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o P_44)) bot_bo1678742418te_o_o)) (forall (X_3:(hoare_1708887482_state->Prop)), ((P_44 X_3)->False))))
% FOF formula (forall (P_44:(com->Prop)), ((iff (((eq (com->Prop)) (collect_com P_44)) bot_bot_com_o)) (forall (X_3:com), ((P_44 X_3)->False)))) of role axiom named fact_92_Collect__empty__eq
% A new axiom: (forall (P_44:(com->Prop)), ((iff (((eq (com->Prop)) (collect_com P_44)) bot_bot_com_o)) (forall (X_3:com), ((P_44 X_3)->False))))
% FOF formula (forall (P_44:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state P_44)) bot_bo19817387tate_o)) (forall (X_3:hoare_1708887482_state), ((P_44 X_3)->False)))) of role axiom named fact_93_Collect__empty__eq
% A new axiom: (forall (P_44:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state P_44)) bot_bo19817387tate_o)) (forall (X_3:hoare_1708887482_state), ((P_44 X_3)->False))))
% FOF formula (forall (C_65:com), (((member_com C_65) bot_bot_com_o)->False)) of role axiom named fact_94_empty__iff
% A new axiom: (forall (C_65:com), (((member_com C_65) bot_bot_com_o)->False))
% FOF formula (forall (C_65:hoare_1708887482_state), (((member451959335_state C_65) bot_bo19817387tate_o)->False)) of role axiom named fact_95_empty__iff
% A new axiom: (forall (C_65:hoare_1708887482_state), (((member451959335_state C_65) bot_bo19817387tate_o)->False))
% FOF formula (forall (C_65:pname), (((member_pname C_65) bot_bot_pname_o)->False)) of role axiom named fact_96_empty__iff
% A new axiom: (forall (C_65:pname), (((member_pname C_65) bot_bot_pname_o)->False))
% FOF formula (forall (P_43:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_43))) (forall (X_3:pname), ((P_43 X_3)->False)))) of role axiom named fact_97_empty__Collect__eq
% A new axiom: (forall (P_43:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_43))) (forall (X_3:pname), ((P_43 X_3)->False))))
% FOF formula (forall (P_43:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o P_43))) (forall (X_3:(pname->Prop)), ((P_43 X_3)->False)))) of role axiom named fact_98_empty__Collect__eq
% A new axiom: (forall (P_43:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o P_43))) (forall (X_3:(pname->Prop)), ((P_43 X_3)->False))))
% FOF formula (forall (P_43:((hoare_1708887482_state->Prop)->Prop)), ((iff (((eq ((hoare_1708887482_state->Prop)->Prop)) bot_bo1678742418te_o_o) (collec219771562tate_o P_43))) (forall (X_3:(hoare_1708887482_state->Prop)), ((P_43 X_3)->False)))) of role axiom named fact_99_empty__Collect__eq
% A new axiom: (forall (P_43:((hoare_1708887482_state->Prop)->Prop)), ((iff (((eq ((hoare_1708887482_state->Prop)->Prop)) bot_bo1678742418te_o_o) (collec219771562tate_o P_43))) (forall (X_3:(hoare_1708887482_state->Prop)), ((P_43 X_3)->False))))
% FOF formula (forall (P_43:(com->Prop)), ((iff (((eq (com->Prop)) bot_bot_com_o) (collect_com P_43))) (forall (X_3:com), ((P_43 X_3)->False)))) of role axiom named fact_100_empty__Collect__eq
% A new axiom: (forall (P_43:(com->Prop)), ((iff (((eq (com->Prop)) bot_bot_com_o) (collect_com P_43))) (forall (X_3:com), ((P_43 X_3)->False))))
% FOF formula (forall (P_43:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state P_43))) (forall (X_3:hoare_1708887482_state), ((P_43 X_3)->False)))) of role axiom named fact_101_empty__Collect__eq
% A new axiom: (forall (P_43:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state P_43))) (forall (X_3:hoare_1708887482_state), ((P_43 X_3)->False))))
% FOF formula (forall (A_257:(com->Prop)), ((iff ((ex com) (fun (X_3:com)=> ((member_com X_3) A_257)))) (not (((eq (com->Prop)) A_257) bot_bot_com_o)))) of role axiom named fact_102_ex__in__conv
% A new axiom: (forall (A_257:(com->Prop)), ((iff ((ex com) (fun (X_3:com)=> ((member_com X_3) A_257)))) (not (((eq (com->Prop)) A_257) bot_bot_com_o))))
% FOF formula (forall (A_257:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) A_257)))) (not (((eq (hoare_1708887482_state->Prop)) A_257) bot_bo19817387tate_o)))) of role axiom named fact_103_ex__in__conv
% A new axiom: (forall (A_257:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) A_257)))) (not (((eq (hoare_1708887482_state->Prop)) A_257) bot_bo19817387tate_o))))
% FOF formula (forall (A_257:(pname->Prop)), ((iff ((ex pname) (fun (X_3:pname)=> ((member_pname X_3) A_257)))) (not (((eq (pname->Prop)) A_257) bot_bot_pname_o)))) of role axiom named fact_104_ex__in__conv
% A new axiom: (forall (A_257:(pname->Prop)), ((iff ((ex pname) (fun (X_3:pname)=> ((member_pname X_3) A_257)))) (not (((eq (pname->Prop)) A_257) bot_bot_pname_o))))
% FOF formula (forall (A_256:(com->Prop)), ((iff (forall (X_3:com), (((member_com X_3) A_256)->False))) (((eq (com->Prop)) A_256) bot_bot_com_o))) of role axiom named fact_105_all__not__in__conv
% A new axiom: (forall (A_256:(com->Prop)), ((iff (forall (X_3:com), (((member_com X_3) A_256)->False))) (((eq (com->Prop)) A_256) bot_bot_com_o)))
% FOF formula (forall (A_256:(hoare_1708887482_state->Prop)), ((iff (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_256)->False))) (((eq (hoare_1708887482_state->Prop)) A_256) bot_bo19817387tate_o))) of role axiom named fact_106_all__not__in__conv
% A new axiom: (forall (A_256:(hoare_1708887482_state->Prop)), ((iff (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_256)->False))) (((eq (hoare_1708887482_state->Prop)) A_256) bot_bo19817387tate_o)))
% FOF formula (forall (A_256:(pname->Prop)), ((iff (forall (X_3:pname), (((member_pname X_3) A_256)->False))) (((eq (pname->Prop)) A_256) bot_bot_pname_o))) of role axiom named fact_107_all__not__in__conv
% A new axiom: (forall (A_256:(pname->Prop)), ((iff (forall (X_3:pname), (((member_pname X_3) A_256)->False))) (((eq (pname->Prop)) A_256) bot_bot_pname_o)))
% FOF formula (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X_3:pname)=> False))) of role axiom named fact_108_empty__def
% A new axiom: (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X_3:pname)=> False)))
% FOF formula (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o (fun (X_3:(pname->Prop))=> False))) of role axiom named fact_109_empty__def
% A new axiom: (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o (fun (X_3:(pname->Prop))=> False)))
% FOF formula (((eq ((hoare_1708887482_state->Prop)->Prop)) bot_bo1678742418te_o_o) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> False))) of role axiom named fact_110_empty__def
% A new axiom: (((eq ((hoare_1708887482_state->Prop)->Prop)) bot_bo1678742418te_o_o) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> False)))
% FOF formula (((eq (com->Prop)) bot_bot_com_o) (collect_com (fun (X_3:com)=> False))) of role axiom named fact_111_empty__def
% A new axiom: (((eq (com->Prop)) bot_bot_com_o) (collect_com (fun (X_3:com)=> False)))
% FOF formula (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> False))) of role axiom named fact_112_empty__def
% A new axiom: (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> False)))
% FOF formula (forall (A_255:com) (A_254:(com->Prop)), (((member_com A_255) A_254)->(((eq (com->Prop)) ((insert_com A_255) A_254)) A_254))) of role axiom named fact_113_insert__absorb
% A new axiom: (forall (A_255:com) (A_254:(com->Prop)), (((member_com A_255) A_254)->(((eq (com->Prop)) ((insert_com A_255) A_254)) A_254)))
% FOF formula (forall (A_255:pname) (A_254:(pname->Prop)), (((member_pname A_255) A_254)->(((eq (pname->Prop)) ((insert_pname A_255) A_254)) A_254))) of role axiom named fact_114_insert__absorb
% A new axiom: (forall (A_255:pname) (A_254:(pname->Prop)), (((member_pname A_255) A_254)->(((eq (pname->Prop)) ((insert_pname A_255) A_254)) A_254)))
% FOF formula (forall (A_255:hoare_1708887482_state) (A_254:(hoare_1708887482_state->Prop)), (((member451959335_state A_255) A_254)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_255) A_254)) A_254))) of role axiom named fact_115_insert__absorb
% A new axiom: (forall (A_255:hoare_1708887482_state) (A_254:(hoare_1708887482_state->Prop)), (((member451959335_state A_255) A_254)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_255) A_254)) A_254)))
% FOF formula (forall (B_164:com) (A_253:com) (B_163:(com->Prop)), (((member_com A_253) B_163)->((member_com A_253) ((insert_com B_164) B_163)))) of role axiom named fact_116_insertI2
% A new axiom: (forall (B_164:com) (A_253:com) (B_163:(com->Prop)), (((member_com A_253) B_163)->((member_com A_253) ((insert_com B_164) B_163))))
% FOF formula (forall (B_164:pname) (A_253:pname) (B_163:(pname->Prop)), (((member_pname A_253) B_163)->((member_pname A_253) ((insert_pname B_164) B_163)))) of role axiom named fact_117_insertI2
% A new axiom: (forall (B_164:pname) (A_253:pname) (B_163:(pname->Prop)), (((member_pname A_253) B_163)->((member_pname A_253) ((insert_pname B_164) B_163))))
% FOF formula (forall (B_164:hoare_1708887482_state) (A_253:hoare_1708887482_state) (B_163:(hoare_1708887482_state->Prop)), (((member451959335_state A_253) B_163)->((member451959335_state A_253) ((insert528405184_state B_164) B_163)))) of role axiom named fact_118_insertI2
% A new axiom: (forall (B_164:hoare_1708887482_state) (A_253:hoare_1708887482_state) (B_163:(hoare_1708887482_state->Prop)), (((member451959335_state A_253) B_163)->((member451959335_state A_253) ((insert528405184_state B_164) B_163))))
% FOF formula (forall (B_162:(com->Prop)) (X_115:com) (A_252:(com->Prop)), ((((member_com X_115) A_252)->False)->((((member_com X_115) B_162)->False)->((iff (((eq (com->Prop)) ((insert_com X_115) A_252)) ((insert_com X_115) B_162))) (((eq (com->Prop)) A_252) B_162))))) of role axiom named fact_119_insert__ident
% A new axiom: (forall (B_162:(com->Prop)) (X_115:com) (A_252:(com->Prop)), ((((member_com X_115) A_252)->False)->((((member_com X_115) B_162)->False)->((iff (((eq (com->Prop)) ((insert_com X_115) A_252)) ((insert_com X_115) B_162))) (((eq (com->Prop)) A_252) B_162)))))
% FOF formula (forall (B_162:(pname->Prop)) (X_115:pname) (A_252:(pname->Prop)), ((((member_pname X_115) A_252)->False)->((((member_pname X_115) B_162)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_115) A_252)) ((insert_pname X_115) B_162))) (((eq (pname->Prop)) A_252) B_162))))) of role axiom named fact_120_insert__ident
% A new axiom: (forall (B_162:(pname->Prop)) (X_115:pname) (A_252:(pname->Prop)), ((((member_pname X_115) A_252)->False)->((((member_pname X_115) B_162)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_115) A_252)) ((insert_pname X_115) B_162))) (((eq (pname->Prop)) A_252) B_162)))))
% FOF formula (forall (B_162:(hoare_1708887482_state->Prop)) (X_115:hoare_1708887482_state) (A_252:(hoare_1708887482_state->Prop)), ((((member451959335_state X_115) A_252)->False)->((((member451959335_state X_115) B_162)->False)->((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_115) A_252)) ((insert528405184_state X_115) B_162))) (((eq (hoare_1708887482_state->Prop)) A_252) B_162))))) of role axiom named fact_121_insert__ident
% A new axiom: (forall (B_162:(hoare_1708887482_state->Prop)) (X_115:hoare_1708887482_state) (A_252:(hoare_1708887482_state->Prop)), ((((member451959335_state X_115) A_252)->False)->((((member451959335_state X_115) B_162)->False)->((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_115) A_252)) ((insert528405184_state X_115) B_162))) (((eq (hoare_1708887482_state->Prop)) A_252) B_162)))))
% FOF formula (forall (Y_52:pname) (A_251:(pname->Prop)) (X_114:pname), ((iff (((insert_pname Y_52) A_251) X_114)) ((or (((eq pname) Y_52) X_114)) (A_251 X_114)))) of role axiom named fact_122_insert__code
% A new axiom: (forall (Y_52:pname) (A_251:(pname->Prop)) (X_114:pname), ((iff (((insert_pname Y_52) A_251) X_114)) ((or (((eq pname) Y_52) X_114)) (A_251 X_114))))
% FOF formula (forall (Y_52:com) (A_251:(com->Prop)) (X_114:com), ((iff (((insert_com Y_52) A_251) X_114)) ((or (((eq com) Y_52) X_114)) (A_251 X_114)))) of role axiom named fact_123_insert__code
% A new axiom: (forall (Y_52:com) (A_251:(com->Prop)) (X_114:com), ((iff (((insert_com Y_52) A_251) X_114)) ((or (((eq com) Y_52) X_114)) (A_251 X_114))))
% FOF formula (forall (Y_52:hoare_1708887482_state) (A_251:(hoare_1708887482_state->Prop)) (X_114:hoare_1708887482_state), ((iff (((insert528405184_state Y_52) A_251) X_114)) ((or (((eq hoare_1708887482_state) Y_52) X_114)) (A_251 X_114)))) of role axiom named fact_124_insert__code
% A new axiom: (forall (Y_52:hoare_1708887482_state) (A_251:(hoare_1708887482_state->Prop)) (X_114:hoare_1708887482_state), ((iff (((insert528405184_state Y_52) A_251) X_114)) ((or (((eq hoare_1708887482_state) Y_52) X_114)) (A_251 X_114))))
% FOF formula (forall (A_250:com) (B_161:com) (A_249:(com->Prop)), ((iff ((member_com A_250) ((insert_com B_161) A_249))) ((or (((eq com) A_250) B_161)) ((member_com A_250) A_249)))) of role axiom named fact_125_insert__iff
% A new axiom: (forall (A_250:com) (B_161:com) (A_249:(com->Prop)), ((iff ((member_com A_250) ((insert_com B_161) A_249))) ((or (((eq com) A_250) B_161)) ((member_com A_250) A_249))))
% FOF formula (forall (A_250:pname) (B_161:pname) (A_249:(pname->Prop)), ((iff ((member_pname A_250) ((insert_pname B_161) A_249))) ((or (((eq pname) A_250) B_161)) ((member_pname A_250) A_249)))) of role axiom named fact_126_insert__iff
% A new axiom: (forall (A_250:pname) (B_161:pname) (A_249:(pname->Prop)), ((iff ((member_pname A_250) ((insert_pname B_161) A_249))) ((or (((eq pname) A_250) B_161)) ((member_pname A_250) A_249))))
% FOF formula (forall (A_250:hoare_1708887482_state) (B_161:hoare_1708887482_state) (A_249:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state A_250) ((insert528405184_state B_161) A_249))) ((or (((eq hoare_1708887482_state) A_250) B_161)) ((member451959335_state A_250) A_249)))) of role axiom named fact_127_insert__iff
% A new axiom: (forall (A_250:hoare_1708887482_state) (B_161:hoare_1708887482_state) (A_249:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state A_250) ((insert528405184_state B_161) A_249))) ((or (((eq hoare_1708887482_state) A_250) B_161)) ((member451959335_state A_250) A_249))))
% FOF formula (forall (X_113:pname) (Y_51:pname) (A_248:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_113) ((insert_pname Y_51) A_248))) ((insert_pname Y_51) ((insert_pname X_113) A_248)))) of role axiom named fact_128_insert__commute
% A new axiom: (forall (X_113:pname) (Y_51:pname) (A_248:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_113) ((insert_pname Y_51) A_248))) ((insert_pname Y_51) ((insert_pname X_113) A_248))))
% FOF formula (forall (X_113:com) (Y_51:com) (A_248:(com->Prop)), (((eq (com->Prop)) ((insert_com X_113) ((insert_com Y_51) A_248))) ((insert_com Y_51) ((insert_com X_113) A_248)))) of role axiom named fact_129_insert__commute
% A new axiom: (forall (X_113:com) (Y_51:com) (A_248:(com->Prop)), (((eq (com->Prop)) ((insert_com X_113) ((insert_com Y_51) A_248))) ((insert_com Y_51) ((insert_com X_113) A_248))))
% FOF formula (forall (X_113:hoare_1708887482_state) (Y_51:hoare_1708887482_state) (A_248:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_113) ((insert528405184_state Y_51) A_248))) ((insert528405184_state Y_51) ((insert528405184_state X_113) A_248)))) of role axiom named fact_130_insert__commute
% A new axiom: (forall (X_113:hoare_1708887482_state) (Y_51:hoare_1708887482_state) (A_248:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_113) ((insert528405184_state Y_51) A_248))) ((insert528405184_state Y_51) ((insert528405184_state X_113) A_248))))
% FOF formula (forall (X_112:pname) (A_247:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_112) ((insert_pname X_112) A_247))) ((insert_pname X_112) A_247))) of role axiom named fact_131_insert__absorb2
% A new axiom: (forall (X_112:pname) (A_247:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_112) ((insert_pname X_112) A_247))) ((insert_pname X_112) A_247)))
% FOF formula (forall (X_112:com) (A_247:(com->Prop)), (((eq (com->Prop)) ((insert_com X_112) ((insert_com X_112) A_247))) ((insert_com X_112) A_247))) of role axiom named fact_132_insert__absorb2
% A new axiom: (forall (X_112:com) (A_247:(com->Prop)), (((eq (com->Prop)) ((insert_com X_112) ((insert_com X_112) A_247))) ((insert_com X_112) A_247)))
% FOF formula (forall (X_112:hoare_1708887482_state) (A_247:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_112) ((insert528405184_state X_112) A_247))) ((insert528405184_state X_112) A_247))) of role axiom named fact_133_insert__absorb2
% A new axiom: (forall (X_112:hoare_1708887482_state) (A_247:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_112) ((insert528405184_state X_112) A_247))) ((insert528405184_state X_112) A_247)))
% FOF formula (forall (A_246:pname) (P_42:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_246) (collect_pname P_42))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_246))) (P_42 U_2)))))) of role axiom named fact_134_insert__Collect
% A new axiom: (forall (A_246:pname) (P_42:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_246) (collect_pname P_42))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_246))) (P_42 U_2))))))
% FOF formula (forall (A_246:com) (P_42:(com->Prop)), (((eq (com->Prop)) ((insert_com A_246) (collect_com P_42))) (collect_com (fun (U_2:com)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq com) U_2) A_246))) (P_42 U_2)))))) of role axiom named fact_135_insert__Collect
% A new axiom: (forall (A_246:com) (P_42:(com->Prop)), (((eq (com->Prop)) ((insert_com A_246) (collect_com P_42))) (collect_com (fun (U_2:com)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq com) U_2) A_246))) (P_42 U_2))))))
% FOF formula (forall (A_246:(pname->Prop)) (P_42:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_246) (collect_pname_o P_42))) (collect_pname_o (fun (U_2:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U_2) A_246))) (P_42 U_2)))))) of role axiom named fact_136_insert__Collect
% A new axiom: (forall (A_246:(pname->Prop)) (P_42:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_246) (collect_pname_o P_42))) (collect_pname_o (fun (U_2:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U_2) A_246))) (P_42 U_2))))))
% FOF formula (forall (A_246:(hoare_1708887482_state->Prop)) (P_42:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o A_246) (collec219771562tate_o P_42))) (collec219771562tate_o (fun (U_2:(hoare_1708887482_state->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_1708887482_state->Prop)) U_2) A_246))) (P_42 U_2)))))) of role axiom named fact_137_insert__Collect
% A new axiom: (forall (A_246:(hoare_1708887482_state->Prop)) (P_42:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o A_246) (collec219771562tate_o P_42))) (collec219771562tate_o (fun (U_2:(hoare_1708887482_state->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_1708887482_state->Prop)) U_2) A_246))) (P_42 U_2))))))
% FOF formula (forall (A_246:hoare_1708887482_state) (P_42:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_246) (collec1568722789_state P_42))) (collec1568722789_state (fun (U_2:hoare_1708887482_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1708887482_state) U_2) A_246))) (P_42 U_2)))))) of role axiom named fact_138_insert__Collect
% A new axiom: (forall (A_246:hoare_1708887482_state) (P_42:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_246) (collec1568722789_state P_42))) (collec1568722789_state (fun (U_2:hoare_1708887482_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1708887482_state) U_2) A_246))) (P_42 U_2))))))
% FOF formula (forall (A_245:com) (B_160:(com->Prop)), (((eq (com->Prop)) ((insert_com A_245) B_160)) (collect_com (fun (X_3:com)=> ((or (((eq com) X_3) A_245)) ((member_com X_3) B_160)))))) of role axiom named fact_139_insert__compr
% A new axiom: (forall (A_245:com) (B_160:(com->Prop)), (((eq (com->Prop)) ((insert_com A_245) B_160)) (collect_com (fun (X_3:com)=> ((or (((eq com) X_3) A_245)) ((member_com X_3) B_160))))))
% FOF formula (forall (A_245:(pname->Prop)) (B_160:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_245) B_160)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((or (((eq (pname->Prop)) X_3) A_245)) ((member_pname_o X_3) B_160)))))) of role axiom named fact_140_insert__compr
% A new axiom: (forall (A_245:(pname->Prop)) (B_160:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_245) B_160)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((or (((eq (pname->Prop)) X_3) A_245)) ((member_pname_o X_3) B_160))))))
% FOF formula (forall (A_245:(hoare_1708887482_state->Prop)) (B_160:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o A_245) B_160)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or (((eq (hoare_1708887482_state->Prop)) X_3) A_245)) ((member814030440tate_o X_3) B_160)))))) of role axiom named fact_141_insert__compr
% A new axiom: (forall (A_245:(hoare_1708887482_state->Prop)) (B_160:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o A_245) B_160)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or (((eq (hoare_1708887482_state->Prop)) X_3) A_245)) ((member814030440tate_o X_3) B_160))))))
% FOF formula (forall (A_245:pname) (B_160:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_245) B_160)) (collect_pname (fun (X_3:pname)=> ((or (((eq pname) X_3) A_245)) ((member_pname X_3) B_160)))))) of role axiom named fact_142_insert__compr
% A new axiom: (forall (A_245:pname) (B_160:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_245) B_160)) (collect_pname (fun (X_3:pname)=> ((or (((eq pname) X_3) A_245)) ((member_pname X_3) B_160))))))
% FOF formula (forall (A_245:hoare_1708887482_state) (B_160:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_245) B_160)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) X_3) A_245)) ((member451959335_state X_3) B_160)))))) of role axiom named fact_143_insert__compr
% A new axiom: (forall (A_245:hoare_1708887482_state) (B_160:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_245) B_160)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) X_3) A_245)) ((member451959335_state X_3) B_160))))))
% FOF formula (forall (A_244:com) (B_159:(com->Prop)), ((member_com A_244) ((insert_com A_244) B_159))) of role axiom named fact_144_insertI1
% A new axiom: (forall (A_244:com) (B_159:(com->Prop)), ((member_com A_244) ((insert_com A_244) B_159)))
% FOF formula (forall (A_244:pname) (B_159:(pname->Prop)), ((member_pname A_244) ((insert_pname A_244) B_159))) of role axiom named fact_145_insertI1
% A new axiom: (forall (A_244:pname) (B_159:(pname->Prop)), ((member_pname A_244) ((insert_pname A_244) B_159)))
% FOF formula (forall (A_244:hoare_1708887482_state) (B_159:(hoare_1708887482_state->Prop)), ((member451959335_state A_244) ((insert528405184_state A_244) B_159))) of role axiom named fact_146_insertI1
% A new axiom: (forall (A_244:hoare_1708887482_state) (B_159:(hoare_1708887482_state->Prop)), ((member451959335_state A_244) ((insert528405184_state A_244) B_159)))
% FOF formula (forall (A_243:(pname->Prop)) (B_158:(pname->Prop)), ((((eq (pname->Prop)) A_243) B_158)->((((ord_less_eq_pname_o A_243) B_158)->(((ord_less_eq_pname_o B_158) A_243)->False))->False))) of role axiom named fact_147_equalityE
% A new axiom: (forall (A_243:(pname->Prop)) (B_158:(pname->Prop)), ((((eq (pname->Prop)) A_243) B_158)->((((ord_less_eq_pname_o A_243) B_158)->(((ord_less_eq_pname_o B_158) A_243)->False))->False)))
% FOF formula (forall (A_243:(hoare_1708887482_state->Prop)) (B_158:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_243) B_158)->((((ord_le777019615tate_o A_243) B_158)->(((ord_le777019615tate_o B_158) A_243)->False))->False))) of role axiom named fact_148_equalityE
% A new axiom: (forall (A_243:(hoare_1708887482_state->Prop)) (B_158:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_243) B_158)->((((ord_le777019615tate_o A_243) B_158)->(((ord_le777019615tate_o B_158) A_243)->False))->False)))
% FOF formula (forall (C_64:(pname->Prop)) (A_242:(pname->Prop)) (B_157:(pname->Prop)), (((ord_less_eq_pname_o A_242) B_157)->(((ord_less_eq_pname_o B_157) C_64)->((ord_less_eq_pname_o A_242) C_64)))) of role axiom named fact_149_subset__trans
% A new axiom: (forall (C_64:(pname->Prop)) (A_242:(pname->Prop)) (B_157:(pname->Prop)), (((ord_less_eq_pname_o A_242) B_157)->(((ord_less_eq_pname_o B_157) C_64)->((ord_less_eq_pname_o A_242) C_64))))
% FOF formula (forall (C_64:(hoare_1708887482_state->Prop)) (A_242:(hoare_1708887482_state->Prop)) (B_157:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_242) B_157)->(((ord_le777019615tate_o B_157) C_64)->((ord_le777019615tate_o A_242) C_64)))) of role axiom named fact_150_subset__trans
% A new axiom: (forall (C_64:(hoare_1708887482_state->Prop)) (A_242:(hoare_1708887482_state->Prop)) (B_157:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_242) B_157)->(((ord_le777019615tate_o B_157) C_64)->((ord_le777019615tate_o A_242) C_64))))
% FOF formula (forall (X_111:com) (A_241:(com->Prop)) (B_156:(com->Prop)), (((ord_less_eq_com_o A_241) B_156)->(((member_com X_111) A_241)->((member_com X_111) B_156)))) of role axiom named fact_151_set__mp
% A new axiom: (forall (X_111:com) (A_241:(com->Prop)) (B_156:(com->Prop)), (((ord_less_eq_com_o A_241) B_156)->(((member_com X_111) A_241)->((member_com X_111) B_156))))
% FOF formula (forall (X_111:hoare_1708887482_state) (A_241:(hoare_1708887482_state->Prop)) (B_156:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_241) B_156)->(((member451959335_state X_111) A_241)->((member451959335_state X_111) B_156)))) of role axiom named fact_152_set__mp
% A new axiom: (forall (X_111:hoare_1708887482_state) (A_241:(hoare_1708887482_state->Prop)) (B_156:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_241) B_156)->(((member451959335_state X_111) A_241)->((member451959335_state X_111) B_156))))
% FOF formula (forall (X_111:pname) (A_241:(pname->Prop)) (B_156:(pname->Prop)), (((ord_less_eq_pname_o A_241) B_156)->(((member_pname X_111) A_241)->((member_pname X_111) B_156)))) of role axiom named fact_153_set__mp
% A new axiom: (forall (X_111:pname) (A_241:(pname->Prop)) (B_156:(pname->Prop)), (((ord_less_eq_pname_o A_241) B_156)->(((member_pname X_111) A_241)->((member_pname X_111) B_156))))
% FOF formula (forall (B_155:(com->Prop)) (X_110:com) (A_240:(com->Prop)), (((member_com X_110) A_240)->(((ord_less_eq_com_o A_240) B_155)->((member_com X_110) B_155)))) of role axiom named fact_154_set__rev__mp
% A new axiom: (forall (B_155:(com->Prop)) (X_110:com) (A_240:(com->Prop)), (((member_com X_110) A_240)->(((ord_less_eq_com_o A_240) B_155)->((member_com X_110) B_155))))
% FOF formula (forall (B_155:(hoare_1708887482_state->Prop)) (X_110:hoare_1708887482_state) (A_240:(hoare_1708887482_state->Prop)), (((member451959335_state X_110) A_240)->(((ord_le777019615tate_o A_240) B_155)->((member451959335_state X_110) B_155)))) of role axiom named fact_155_set__rev__mp
% A new axiom: (forall (B_155:(hoare_1708887482_state->Prop)) (X_110:hoare_1708887482_state) (A_240:(hoare_1708887482_state->Prop)), (((member451959335_state X_110) A_240)->(((ord_le777019615tate_o A_240) B_155)->((member451959335_state X_110) B_155))))
% FOF formula (forall (B_155:(pname->Prop)) (X_110:pname) (A_240:(pname->Prop)), (((member_pname X_110) A_240)->(((ord_less_eq_pname_o A_240) B_155)->((member_pname X_110) B_155)))) of role axiom named fact_156_set__rev__mp
% A new axiom: (forall (B_155:(pname->Prop)) (X_110:pname) (A_240:(pname->Prop)), (((member_pname X_110) A_240)->(((ord_less_eq_pname_o A_240) B_155)->((member_pname X_110) B_155))))
% FOF formula (forall (X_109:com) (A_239:(com->Prop)) (B_154:(com->Prop)), (((ord_less_eq_com_o A_239) B_154)->(((member_com X_109) A_239)->((member_com X_109) B_154)))) of role axiom named fact_157_in__mono
% A new axiom: (forall (X_109:com) (A_239:(com->Prop)) (B_154:(com->Prop)), (((ord_less_eq_com_o A_239) B_154)->(((member_com X_109) A_239)->((member_com X_109) B_154))))
% FOF formula (forall (X_109:hoare_1708887482_state) (A_239:(hoare_1708887482_state->Prop)) (B_154:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_239) B_154)->(((member451959335_state X_109) A_239)->((member451959335_state X_109) B_154)))) of role axiom named fact_158_in__mono
% A new axiom: (forall (X_109:hoare_1708887482_state) (A_239:(hoare_1708887482_state->Prop)) (B_154:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_239) B_154)->(((member451959335_state X_109) A_239)->((member451959335_state X_109) B_154))))
% FOF formula (forall (X_109:pname) (A_239:(pname->Prop)) (B_154:(pname->Prop)), (((ord_less_eq_pname_o A_239) B_154)->(((member_pname X_109) A_239)->((member_pname X_109) B_154)))) of role axiom named fact_159_in__mono
% A new axiom: (forall (X_109:pname) (A_239:(pname->Prop)) (B_154:(pname->Prop)), (((ord_less_eq_pname_o A_239) B_154)->(((member_pname X_109) A_239)->((member_pname X_109) B_154))))
% FOF formula (forall (A_238:(pname->Prop)) (B_153:(pname->Prop)), ((((eq (pname->Prop)) A_238) B_153)->((ord_less_eq_pname_o B_153) A_238))) of role axiom named fact_160_equalityD2
% A new axiom: (forall (A_238:(pname->Prop)) (B_153:(pname->Prop)), ((((eq (pname->Prop)) A_238) B_153)->((ord_less_eq_pname_o B_153) A_238)))
% FOF formula (forall (A_238:(hoare_1708887482_state->Prop)) (B_153:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_238) B_153)->((ord_le777019615tate_o B_153) A_238))) of role axiom named fact_161_equalityD2
% A new axiom: (forall (A_238:(hoare_1708887482_state->Prop)) (B_153:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_238) B_153)->((ord_le777019615tate_o B_153) A_238)))
% FOF formula (forall (A_237:(pname->Prop)) (B_152:(pname->Prop)), ((((eq (pname->Prop)) A_237) B_152)->((ord_less_eq_pname_o A_237) B_152))) of role axiom named fact_162_equalityD1
% A new axiom: (forall (A_237:(pname->Prop)) (B_152:(pname->Prop)), ((((eq (pname->Prop)) A_237) B_152)->((ord_less_eq_pname_o A_237) B_152)))
% FOF formula (forall (A_237:(hoare_1708887482_state->Prop)) (B_152:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_237) B_152)->((ord_le777019615tate_o A_237) B_152))) of role axiom named fact_163_equalityD1
% A new axiom: (forall (A_237:(hoare_1708887482_state->Prop)) (B_152:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_237) B_152)->((ord_le777019615tate_o A_237) B_152)))
% FOF formula (forall (A_236:(pname->Prop)) (B_151:(pname->Prop)), ((iff (((eq (pname->Prop)) A_236) B_151)) ((and ((ord_less_eq_pname_o A_236) B_151)) ((ord_less_eq_pname_o B_151) A_236)))) of role axiom named fact_164_set__eq__subset
% A new axiom: (forall (A_236:(pname->Prop)) (B_151:(pname->Prop)), ((iff (((eq (pname->Prop)) A_236) B_151)) ((and ((ord_less_eq_pname_o A_236) B_151)) ((ord_less_eq_pname_o B_151) A_236))))
% FOF formula (forall (A_236:(hoare_1708887482_state->Prop)) (B_151:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) A_236) B_151)) ((and ((ord_le777019615tate_o A_236) B_151)) ((ord_le777019615tate_o B_151) A_236)))) of role axiom named fact_165_set__eq__subset
% A new axiom: (forall (A_236:(hoare_1708887482_state->Prop)) (B_151:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) A_236) B_151)) ((and ((ord_le777019615tate_o A_236) B_151)) ((ord_le777019615tate_o B_151) A_236))))
% FOF formula (forall (A_235:(pname->Prop)), ((ord_less_eq_pname_o A_235) A_235)) of role axiom named fact_166_subset__refl
% A new axiom: (forall (A_235:(pname->Prop)), ((ord_less_eq_pname_o A_235) A_235))
% FOF formula (forall (A_235:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o A_235) A_235)) of role axiom named fact_167_subset__refl
% A new axiom: (forall (A_235:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o A_235) A_235))
% FOF formula (forall (B_150:com) (F_84:(hoare_1708887482_state->com)) (X_108:hoare_1708887482_state) (A_234:(hoare_1708887482_state->Prop)), (((member451959335_state X_108) A_234)->((((eq com) B_150) (F_84 X_108))->((member_com B_150) ((image_1604448413te_com F_84) A_234))))) of role axiom named fact_168_rev__image__eqI
% A new axiom: (forall (B_150:com) (F_84:(hoare_1708887482_state->com)) (X_108:hoare_1708887482_state) (A_234:(hoare_1708887482_state->Prop)), (((member451959335_state X_108) A_234)->((((eq com) B_150) (F_84 X_108))->((member_com B_150) ((image_1604448413te_com F_84) A_234)))))
% FOF formula (forall (B_150:com) (F_84:(pname->com)) (X_108:pname) (A_234:(pname->Prop)), (((member_pname X_108) A_234)->((((eq com) B_150) (F_84 X_108))->((member_com B_150) ((image_pname_com F_84) A_234))))) of role axiom named fact_169_rev__image__eqI
% A new axiom: (forall (B_150:com) (F_84:(pname->com)) (X_108:pname) (A_234:(pname->Prop)), (((member_pname X_108) A_234)->((((eq com) B_150) (F_84 X_108))->((member_com B_150) ((image_pname_com F_84) A_234)))))
% FOF formula (forall (B_150:hoare_1708887482_state) (F_84:(com->hoare_1708887482_state)) (X_108:com) (A_234:(com->Prop)), (((member_com X_108) A_234)->((((eq hoare_1708887482_state) B_150) (F_84 X_108))->((member451959335_state B_150) ((image_934102463_state F_84) A_234))))) of role axiom named fact_170_rev__image__eqI
% A new axiom: (forall (B_150:hoare_1708887482_state) (F_84:(com->hoare_1708887482_state)) (X_108:com) (A_234:(com->Prop)), (((member_com X_108) A_234)->((((eq hoare_1708887482_state) B_150) (F_84 X_108))->((member451959335_state B_150) ((image_934102463_state F_84) A_234)))))
% FOF formula (forall (B_150:pname) (F_84:(com->pname)) (X_108:com) (A_234:(com->Prop)), (((member_com X_108) A_234)->((((eq pname) B_150) (F_84 X_108))->((member_pname B_150) ((image_com_pname F_84) A_234))))) of role axiom named fact_171_rev__image__eqI
% A new axiom: (forall (B_150:pname) (F_84:(com->pname)) (X_108:com) (A_234:(com->Prop)), (((member_com X_108) A_234)->((((eq pname) B_150) (F_84 X_108))->((member_pname B_150) ((image_com_pname F_84) A_234)))))
% FOF formula (forall (B_150:hoare_1708887482_state) (F_84:(pname->hoare_1708887482_state)) (X_108:pname) (A_234:(pname->Prop)), (((member_pname X_108) A_234)->((((eq hoare_1708887482_state) B_150) (F_84 X_108))->((member451959335_state B_150) ((image_1116629049_state F_84) A_234))))) of role axiom named fact_172_rev__image__eqI
% A new axiom: (forall (B_150:hoare_1708887482_state) (F_84:(pname->hoare_1708887482_state)) (X_108:pname) (A_234:(pname->Prop)), (((member_pname X_108) A_234)->((((eq hoare_1708887482_state) B_150) (F_84 X_108))->((member451959335_state B_150) ((image_1116629049_state F_84) A_234)))))
% FOF formula (forall (F_83:(hoare_1708887482_state->com)) (X_107:hoare_1708887482_state) (A_233:(hoare_1708887482_state->Prop)), (((member451959335_state X_107) A_233)->((member_com (F_83 X_107)) ((image_1604448413te_com F_83) A_233)))) of role axiom named fact_173_imageI
% A new axiom: (forall (F_83:(hoare_1708887482_state->com)) (X_107:hoare_1708887482_state) (A_233:(hoare_1708887482_state->Prop)), (((member451959335_state X_107) A_233)->((member_com (F_83 X_107)) ((image_1604448413te_com F_83) A_233))))
% FOF formula (forall (F_83:(pname->com)) (X_107:pname) (A_233:(pname->Prop)), (((member_pname X_107) A_233)->((member_com (F_83 X_107)) ((image_pname_com F_83) A_233)))) of role axiom named fact_174_imageI
% A new axiom: (forall (F_83:(pname->com)) (X_107:pname) (A_233:(pname->Prop)), (((member_pname X_107) A_233)->((member_com (F_83 X_107)) ((image_pname_com F_83) A_233))))
% FOF formula (forall (F_83:(com->hoare_1708887482_state)) (X_107:com) (A_233:(com->Prop)), (((member_com X_107) A_233)->((member451959335_state (F_83 X_107)) ((image_934102463_state F_83) A_233)))) of role axiom named fact_175_imageI
% A new axiom: (forall (F_83:(com->hoare_1708887482_state)) (X_107:com) (A_233:(com->Prop)), (((member_com X_107) A_233)->((member451959335_state (F_83 X_107)) ((image_934102463_state F_83) A_233))))
% FOF formula (forall (F_83:(com->pname)) (X_107:com) (A_233:(com->Prop)), (((member_com X_107) A_233)->((member_pname (F_83 X_107)) ((image_com_pname F_83) A_233)))) of role axiom named fact_176_imageI
% A new axiom: (forall (F_83:(com->pname)) (X_107:com) (A_233:(com->Prop)), (((member_com X_107) A_233)->((member_pname (F_83 X_107)) ((image_com_pname F_83) A_233))))
% FOF formula (forall (F_83:(pname->hoare_1708887482_state)) (X_107:pname) (A_233:(pname->Prop)), (((member_pname X_107) A_233)->((member451959335_state (F_83 X_107)) ((image_1116629049_state F_83) A_233)))) of role axiom named fact_177_imageI
% A new axiom: (forall (F_83:(pname->hoare_1708887482_state)) (X_107:pname) (A_233:(pname->Prop)), (((member_pname X_107) A_233)->((member451959335_state (F_83 X_107)) ((image_1116629049_state F_83) A_233))))
% FOF formula (forall (Z_21:hoare_1708887482_state) (F_82:(pname->hoare_1708887482_state)) (A_232:(pname->Prop)), ((iff ((member451959335_state Z_21) ((image_1116629049_state F_82) A_232))) ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_232)) (((eq hoare_1708887482_state) Z_21) (F_82 X_3))))))) of role axiom named fact_178_image__iff
% A new axiom: (forall (Z_21:hoare_1708887482_state) (F_82:(pname->hoare_1708887482_state)) (A_232:(pname->Prop)), ((iff ((member451959335_state Z_21) ((image_1116629049_state F_82) A_232))) ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_232)) (((eq hoare_1708887482_state) Z_21) (F_82 X_3)))))))
% FOF formula (forall (P_41:((pname->Prop)->Prop)) (Q_25:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_3:(pname->Prop))=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite297249702name_o (collect_pname_o P_41))) (finite297249702name_o (collect_pname_o Q_25))))) of role axiom named fact_179_finite__Collect__disjI
% A new axiom: (forall (P_41:((pname->Prop)->Prop)) (Q_25:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_3:(pname->Prop))=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite297249702name_o (collect_pname_o P_41))) (finite297249702name_o (collect_pname_o Q_25)))))
% FOF formula (forall (P_41:((hoare_1708887482_state->Prop)->Prop)) (Q_25:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite1329924456tate_o (collec219771562tate_o P_41))) (finite1329924456tate_o (collec219771562tate_o Q_25))))) of role axiom named fact_180_finite__Collect__disjI
% A new axiom: (forall (P_41:((hoare_1708887482_state->Prop)->Prop)) (Q_25:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite1329924456tate_o (collec219771562tate_o P_41))) (finite1329924456tate_o (collec219771562tate_o Q_25)))))
% FOF formula (forall (P_41:(hoare_1708887482_state->Prop)) (Q_25:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite1625599783_state (collec1568722789_state P_41))) (finite1625599783_state (collec1568722789_state Q_25))))) of role axiom named fact_181_finite__Collect__disjI
% A new axiom: (forall (P_41:(hoare_1708887482_state->Prop)) (Q_25:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite1625599783_state (collec1568722789_state P_41))) (finite1625599783_state (collec1568722789_state Q_25)))))
% FOF formula (forall (P_41:(pname->Prop)) (Q_25:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_3:pname)=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite_finite_pname (collect_pname P_41))) (finite_finite_pname (collect_pname Q_25))))) of role axiom named fact_182_finite__Collect__disjI
% A new axiom: (forall (P_41:(pname->Prop)) (Q_25:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_3:pname)=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite_finite_pname (collect_pname P_41))) (finite_finite_pname (collect_pname Q_25)))))
% FOF formula (forall (X_3:com) (Xa:(com->Prop)), (((eq (com->Prop)) ((insert_com X_3) Xa)) (collect_com (fun (Y_4:com)=> ((or (((eq com) Y_4) X_3)) ((member_com Y_4) Xa)))))) of role axiom named fact_183_insert__compr__raw
% A new axiom: (forall (X_3:com) (Xa:(com->Prop)), (((eq (com->Prop)) ((insert_com X_3) Xa)) (collect_com (fun (Y_4:com)=> ((or (((eq com) Y_4) X_3)) ((member_com Y_4) Xa))))))
% FOF formula (forall (X_3:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X_3) Xa)) (collect_pname_o (fun (Y_4:(pname->Prop))=> ((or (((eq (pname->Prop)) Y_4) X_3)) ((member_pname_o Y_4) Xa)))))) of role axiom named fact_184_insert__compr__raw
% A new axiom: (forall (X_3:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X_3) Xa)) (collect_pname_o (fun (Y_4:(pname->Prop))=> ((or (((eq (pname->Prop)) Y_4) X_3)) ((member_pname_o Y_4) Xa))))))
% FOF formula (forall (X_3:(hoare_1708887482_state->Prop)) (Xa:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o X_3) Xa)) (collec219771562tate_o (fun (Y_4:(hoare_1708887482_state->Prop))=> ((or (((eq (hoare_1708887482_state->Prop)) Y_4) X_3)) ((member814030440tate_o Y_4) Xa)))))) of role axiom named fact_185_insert__compr__raw
% A new axiom: (forall (X_3:(hoare_1708887482_state->Prop)) (Xa:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o X_3) Xa)) (collec219771562tate_o (fun (Y_4:(hoare_1708887482_state->Prop))=> ((or (((eq (hoare_1708887482_state->Prop)) Y_4) X_3)) ((member814030440tate_o Y_4) Xa))))))
% FOF formula (forall (X_3:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_3) Xa)) (collect_pname (fun (Y_4:pname)=> ((or (((eq pname) Y_4) X_3)) ((member_pname Y_4) Xa)))))) of role axiom named fact_186_insert__compr__raw
% A new axiom: (forall (X_3:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_3) Xa)) (collect_pname (fun (Y_4:pname)=> ((or (((eq pname) Y_4) X_3)) ((member_pname Y_4) Xa))))))
% FOF formula (forall (X_3:hoare_1708887482_state) (Xa:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_3) Xa)) (collec1568722789_state (fun (Y_4:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) Y_4) X_3)) ((member451959335_state Y_4) Xa)))))) of role axiom named fact_187_insert__compr__raw
% A new axiom: (forall (X_3:hoare_1708887482_state) (Xa:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_3) Xa)) (collec1568722789_state (fun (Y_4:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) Y_4) X_3)) ((member451959335_state Y_4) Xa))))))
% FOF formula (forall (A_231:pname) (B_149:pname), ((((eq (pname->Prop)) ((insert_pname A_231) bot_bot_pname_o)) ((insert_pname B_149) bot_bot_pname_o))->(((eq pname) A_231) B_149))) of role axiom named fact_188_singleton__inject
% A new axiom: (forall (A_231:pname) (B_149:pname), ((((eq (pname->Prop)) ((insert_pname A_231) bot_bot_pname_o)) ((insert_pname B_149) bot_bot_pname_o))->(((eq pname) A_231) B_149)))
% FOF formula (forall (A_231:com) (B_149:com), ((((eq (com->Prop)) ((insert_com A_231) bot_bot_com_o)) ((insert_com B_149) bot_bot_com_o))->(((eq com) A_231) B_149))) of role axiom named fact_189_singleton__inject
% A new axiom: (forall (A_231:com) (B_149:com), ((((eq (com->Prop)) ((insert_com A_231) bot_bot_com_o)) ((insert_com B_149) bot_bot_com_o))->(((eq com) A_231) B_149)))
% FOF formula (forall (A_231:hoare_1708887482_state) (B_149:hoare_1708887482_state), ((((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_231) bot_bo19817387tate_o)) ((insert528405184_state B_149) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) A_231) B_149))) of role axiom named fact_190_singleton__inject
% A new axiom: (forall (A_231:hoare_1708887482_state) (B_149:hoare_1708887482_state), ((((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_231) bot_bo19817387tate_o)) ((insert528405184_state B_149) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) A_231) B_149)))
% FOF formula (forall (B_148:com) (A_230:com), (((member_com B_148) ((insert_com A_230) bot_bot_com_o))->(((eq com) B_148) A_230))) of role axiom named fact_191_singletonE
% A new axiom: (forall (B_148:com) (A_230:com), (((member_com B_148) ((insert_com A_230) bot_bot_com_o))->(((eq com) B_148) A_230)))
% FOF formula (forall (B_148:pname) (A_230:pname), (((member_pname B_148) ((insert_pname A_230) bot_bot_pname_o))->(((eq pname) B_148) A_230))) of role axiom named fact_192_singletonE
% A new axiom: (forall (B_148:pname) (A_230:pname), (((member_pname B_148) ((insert_pname A_230) bot_bot_pname_o))->(((eq pname) B_148) A_230)))
% FOF formula (forall (B_148:hoare_1708887482_state) (A_230:hoare_1708887482_state), (((member451959335_state B_148) ((insert528405184_state A_230) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) B_148) A_230))) of role axiom named fact_193_singletonE
% A new axiom: (forall (B_148:hoare_1708887482_state) (A_230:hoare_1708887482_state), (((member451959335_state B_148) ((insert528405184_state A_230) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) B_148) A_230)))
% FOF formula (forall (A_229:pname) (B_147:pname) (C_63:pname) (D_7:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_229) ((insert_pname B_147) bot_bot_pname_o))) ((insert_pname C_63) ((insert_pname D_7) bot_bot_pname_o)))) ((or ((and (((eq pname) A_229) C_63)) (((eq pname) B_147) D_7))) ((and (((eq pname) A_229) D_7)) (((eq pname) B_147) C_63))))) of role axiom named fact_194_doubleton__eq__iff
% A new axiom: (forall (A_229:pname) (B_147:pname) (C_63:pname) (D_7:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_229) ((insert_pname B_147) bot_bot_pname_o))) ((insert_pname C_63) ((insert_pname D_7) bot_bot_pname_o)))) ((or ((and (((eq pname) A_229) C_63)) (((eq pname) B_147) D_7))) ((and (((eq pname) A_229) D_7)) (((eq pname) B_147) C_63)))))
% FOF formula (forall (A_229:com) (B_147:com) (C_63:com) (D_7:com), ((iff (((eq (com->Prop)) ((insert_com A_229) ((insert_com B_147) bot_bot_com_o))) ((insert_com C_63) ((insert_com D_7) bot_bot_com_o)))) ((or ((and (((eq com) A_229) C_63)) (((eq com) B_147) D_7))) ((and (((eq com) A_229) D_7)) (((eq com) B_147) C_63))))) of role axiom named fact_195_doubleton__eq__iff
% A new axiom: (forall (A_229:com) (B_147:com) (C_63:com) (D_7:com), ((iff (((eq (com->Prop)) ((insert_com A_229) ((insert_com B_147) bot_bot_com_o))) ((insert_com C_63) ((insert_com D_7) bot_bot_com_o)))) ((or ((and (((eq com) A_229) C_63)) (((eq com) B_147) D_7))) ((and (((eq com) A_229) D_7)) (((eq com) B_147) C_63)))))
% FOF formula (forall (A_229:hoare_1708887482_state) (B_147:hoare_1708887482_state) (C_63:hoare_1708887482_state) (D_7:hoare_1708887482_state), ((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_229) ((insert528405184_state B_147) bot_bo19817387tate_o))) ((insert528405184_state C_63) ((insert528405184_state D_7) bot_bo19817387tate_o)))) ((or ((and (((eq hoare_1708887482_state) A_229) C_63)) (((eq hoare_1708887482_state) B_147) D_7))) ((and (((eq hoare_1708887482_state) A_229) D_7)) (((eq hoare_1708887482_state) B_147) C_63))))) of role axiom named fact_196_doubleton__eq__iff
% A new axiom: (forall (A_229:hoare_1708887482_state) (B_147:hoare_1708887482_state) (C_63:hoare_1708887482_state) (D_7:hoare_1708887482_state), ((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_229) ((insert528405184_state B_147) bot_bo19817387tate_o))) ((insert528405184_state C_63) ((insert528405184_state D_7) bot_bo19817387tate_o)))) ((or ((and (((eq hoare_1708887482_state) A_229) C_63)) (((eq hoare_1708887482_state) B_147) D_7))) ((and (((eq hoare_1708887482_state) A_229) D_7)) (((eq hoare_1708887482_state) B_147) C_63)))))
% FOF formula (forall (B_146:com) (A_228:com), ((iff ((member_com B_146) ((insert_com A_228) bot_bot_com_o))) (((eq com) B_146) A_228))) of role axiom named fact_197_singleton__iff
% A new axiom: (forall (B_146:com) (A_228:com), ((iff ((member_com B_146) ((insert_com A_228) bot_bot_com_o))) (((eq com) B_146) A_228)))
% FOF formula (forall (B_146:pname) (A_228:pname), ((iff ((member_pname B_146) ((insert_pname A_228) bot_bot_pname_o))) (((eq pname) B_146) A_228))) of role axiom named fact_198_singleton__iff
% A new axiom: (forall (B_146:pname) (A_228:pname), ((iff ((member_pname B_146) ((insert_pname A_228) bot_bot_pname_o))) (((eq pname) B_146) A_228)))
% FOF formula (forall (B_146:hoare_1708887482_state) (A_228:hoare_1708887482_state), ((iff ((member451959335_state B_146) ((insert528405184_state A_228) bot_bo19817387tate_o))) (((eq hoare_1708887482_state) B_146) A_228))) of role axiom named fact_199_singleton__iff
% A new axiom: (forall (B_146:hoare_1708887482_state) (A_228:hoare_1708887482_state), ((iff ((member451959335_state B_146) ((insert528405184_state A_228) bot_bo19817387tate_o))) (((eq hoare_1708887482_state) B_146) A_228)))
% FOF formula (forall (A_227:pname) (A_226:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_227) A_226)) bot_bot_pname_o))) of role axiom named fact_200_insert__not__empty
% A new axiom: (forall (A_227:pname) (A_226:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_227) A_226)) bot_bot_pname_o)))
% FOF formula (forall (A_227:com) (A_226:(com->Prop)), (not (((eq (com->Prop)) ((insert_com A_227) A_226)) bot_bot_com_o))) of role axiom named fact_201_insert__not__empty
% A new axiom: (forall (A_227:com) (A_226:(com->Prop)), (not (((eq (com->Prop)) ((insert_com A_227) A_226)) bot_bot_com_o)))
% FOF formula (forall (A_227:hoare_1708887482_state) (A_226:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_227) A_226)) bot_bo19817387tate_o))) of role axiom named fact_202_insert__not__empty
% A new axiom: (forall (A_227:hoare_1708887482_state) (A_226:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_227) A_226)) bot_bo19817387tate_o)))
% FOF formula (forall (A_225:pname) (A_224:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_225) A_224)))) of role axiom named fact_203_empty__not__insert
% A new axiom: (forall (A_225:pname) (A_224:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_225) A_224))))
% FOF formula (forall (A_225:com) (A_224:(com->Prop)), (not (((eq (com->Prop)) bot_bot_com_o) ((insert_com A_225) A_224)))) of role axiom named fact_204_empty__not__insert
% A new axiom: (forall (A_225:com) (A_224:(com->Prop)), (not (((eq (com->Prop)) bot_bot_com_o) ((insert_com A_225) A_224))))
% FOF formula (forall (A_225:hoare_1708887482_state) (A_224:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((insert528405184_state A_225) A_224)))) of role axiom named fact_205_empty__not__insert
% A new axiom: (forall (A_225:hoare_1708887482_state) (A_224:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((insert528405184_state A_225) A_224))))
% FOF formula (forall (A_223:com) (A_222:(com->Prop)), ((iff (finite_finite_com ((insert_com A_223) A_222))) (finite_finite_com A_222))) of role axiom named fact_206_finite__insert
% A new axiom: (forall (A_223:com) (A_222:(com->Prop)), ((iff (finite_finite_com ((insert_com A_223) A_222))) (finite_finite_com A_222)))
% FOF formula (forall (A_223:(pname->Prop)) (A_222:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_223) A_222))) (finite297249702name_o A_222))) of role axiom named fact_207_finite__insert
% A new axiom: (forall (A_223:(pname->Prop)) (A_222:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_223) A_222))) (finite297249702name_o A_222)))
% FOF formula (forall (A_223:(hoare_1708887482_state->Prop)) (A_222:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o ((insert949073679tate_o A_223) A_222))) (finite1329924456tate_o A_222))) of role axiom named fact_208_finite__insert
% A new axiom: (forall (A_223:(hoare_1708887482_state->Prop)) (A_222:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o ((insert949073679tate_o A_223) A_222))) (finite1329924456tate_o A_222)))
% FOF formula (forall (A_223:pname) (A_222:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_223) A_222))) (finite_finite_pname A_222))) of role axiom named fact_209_finite__insert
% A new axiom: (forall (A_223:pname) (A_222:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_223) A_222))) (finite_finite_pname A_222)))
% FOF formula (forall (A_223:hoare_1708887482_state) (A_222:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((insert528405184_state A_223) A_222))) (finite1625599783_state A_222))) of role axiom named fact_210_finite__insert
% A new axiom: (forall (A_223:hoare_1708887482_state) (A_222:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((insert528405184_state A_223) A_222))) (finite1625599783_state A_222)))
% FOF formula (forall (A_221:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_221) bot_bot_pname_o)) (((eq (pname->Prop)) A_221) bot_bot_pname_o))) of role axiom named fact_211_subset__empty
% A new axiom: (forall (A_221:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_221) bot_bot_pname_o)) (((eq (pname->Prop)) A_221) bot_bot_pname_o)))
% FOF formula (forall (A_221:(com->Prop)), ((iff ((ord_less_eq_com_o A_221) bot_bot_com_o)) (((eq (com->Prop)) A_221) bot_bot_com_o))) of role axiom named fact_212_subset__empty
% A new axiom: (forall (A_221:(com->Prop)), ((iff ((ord_less_eq_com_o A_221) bot_bot_com_o)) (((eq (com->Prop)) A_221) bot_bot_com_o)))
% FOF formula (forall (A_221:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_221) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) A_221) bot_bo19817387tate_o))) of role axiom named fact_213_subset__empty
% A new axiom: (forall (A_221:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_221) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) A_221) bot_bo19817387tate_o)))
% FOF formula (forall (F_81:(com->hoare_1708887482_state)) (A_220:(com->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((image_934102463_state F_81) A_220)) bot_bo19817387tate_o)) (((eq (com->Prop)) A_220) bot_bot_com_o))) of role axiom named fact_214_image__is__empty
% A new axiom: (forall (F_81:(com->hoare_1708887482_state)) (A_220:(com->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((image_934102463_state F_81) A_220)) bot_bo19817387tate_o)) (((eq (com->Prop)) A_220) bot_bot_com_o)))
% FOF formula (forall (F_81:(hoare_1708887482_state->pname)) (A_220:(hoare_1708887482_state->Prop)), ((iff (((eq (pname->Prop)) ((image_1509414295_pname F_81) A_220)) bot_bot_pname_o)) (((eq (hoare_1708887482_state->Prop)) A_220) bot_bo19817387tate_o))) of role axiom named fact_215_image__is__empty
% A new axiom: (forall (F_81:(hoare_1708887482_state->pname)) (A_220:(hoare_1708887482_state->Prop)), ((iff (((eq (pname->Prop)) ((image_1509414295_pname F_81) A_220)) bot_bot_pname_o)) (((eq (hoare_1708887482_state->Prop)) A_220) bot_bo19817387tate_o)))
% FOF formula (forall (F_81:(hoare_1708887482_state->com)) (A_220:(hoare_1708887482_state->Prop)), ((iff (((eq (com->Prop)) ((image_1604448413te_com F_81) A_220)) bot_bot_com_o)) (((eq (hoare_1708887482_state->Prop)) A_220) bot_bo19817387tate_o))) of role axiom named fact_216_image__is__empty
% A new axiom: (forall (F_81:(hoare_1708887482_state->com)) (A_220:(hoare_1708887482_state->Prop)), ((iff (((eq (com->Prop)) ((image_1604448413te_com F_81) A_220)) bot_bot_com_o)) (((eq (hoare_1708887482_state->Prop)) A_220) bot_bo19817387tate_o)))
% FOF formula (forall (F_81:(pname->hoare_1708887482_state)) (A_220:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_81) A_220)) bot_bo19817387tate_o)) (((eq (pname->Prop)) A_220) bot_bot_pname_o))) of role axiom named fact_217_image__is__empty
% A new axiom: (forall (F_81:(pname->hoare_1708887482_state)) (A_220:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_81) A_220)) bot_bo19817387tate_o)) (((eq (pname->Prop)) A_220) bot_bot_pname_o)))
% FOF formula (forall (F_80:(hoare_1708887482_state->pname)), (((eq (pname->Prop)) ((image_1509414295_pname F_80) bot_bo19817387tate_o)) bot_bot_pname_o)) of role axiom named fact_218_image__empty
% A new axiom: (forall (F_80:(hoare_1708887482_state->pname)), (((eq (pname->Prop)) ((image_1509414295_pname F_80) bot_bo19817387tate_o)) bot_bot_pname_o))
% FOF formula (forall (F_80:(hoare_1708887482_state->com)), (((eq (com->Prop)) ((image_1604448413te_com F_80) bot_bo19817387tate_o)) bot_bot_com_o)) of role axiom named fact_219_image__empty
% A new axiom: (forall (F_80:(hoare_1708887482_state->com)), (((eq (com->Prop)) ((image_1604448413te_com F_80) bot_bo19817387tate_o)) bot_bot_com_o))
% FOF formula (forall (F_80:(com->hoare_1708887482_state)), (((eq (hoare_1708887482_state->Prop)) ((image_934102463_state F_80) bot_bot_com_o)) bot_bo19817387tate_o)) of role axiom named fact_220_image__empty
% A new axiom: (forall (F_80:(com->hoare_1708887482_state)), (((eq (hoare_1708887482_state->Prop)) ((image_934102463_state F_80) bot_bot_com_o)) bot_bo19817387tate_o))
% FOF formula (forall (F_80:(pname->hoare_1708887482_state)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_80) bot_bot_pname_o)) bot_bo19817387tate_o)) of role axiom named fact_221_image__empty
% A new axiom: (forall (F_80:(pname->hoare_1708887482_state)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_80) bot_bot_pname_o)) bot_bo19817387tate_o))
% FOF formula (forall (F_79:(com->hoare_1708887482_state)) (A_219:(com->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((image_934102463_state F_79) A_219))) (((eq (com->Prop)) A_219) bot_bot_com_o))) of role axiom named fact_222_empty__is__image
% A new axiom: (forall (F_79:(com->hoare_1708887482_state)) (A_219:(com->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((image_934102463_state F_79) A_219))) (((eq (com->Prop)) A_219) bot_bot_com_o)))
% FOF formula (forall (F_79:(hoare_1708887482_state->pname)) (A_219:(hoare_1708887482_state->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) ((image_1509414295_pname F_79) A_219))) (((eq (hoare_1708887482_state->Prop)) A_219) bot_bo19817387tate_o))) of role axiom named fact_223_empty__is__image
% A new axiom: (forall (F_79:(hoare_1708887482_state->pname)) (A_219:(hoare_1708887482_state->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) ((image_1509414295_pname F_79) A_219))) (((eq (hoare_1708887482_state->Prop)) A_219) bot_bo19817387tate_o)))
% FOF formula (forall (F_79:(hoare_1708887482_state->com)) (A_219:(hoare_1708887482_state->Prop)), ((iff (((eq (com->Prop)) bot_bot_com_o) ((image_1604448413te_com F_79) A_219))) (((eq (hoare_1708887482_state->Prop)) A_219) bot_bo19817387tate_o))) of role axiom named fact_224_empty__is__image
% A new axiom: (forall (F_79:(hoare_1708887482_state->com)) (A_219:(hoare_1708887482_state->Prop)), ((iff (((eq (com->Prop)) bot_bot_com_o) ((image_1604448413te_com F_79) A_219))) (((eq (hoare_1708887482_state->Prop)) A_219) bot_bo19817387tate_o)))
% FOF formula (forall (F_79:(pname->hoare_1708887482_state)) (A_219:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((image_1116629049_state F_79) A_219))) (((eq (pname->Prop)) A_219) bot_bot_pname_o))) of role axiom named fact_225_empty__is__image
% A new axiom: (forall (F_79:(pname->hoare_1708887482_state)) (A_219:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((image_1116629049_state F_79) A_219))) (((eq (pname->Prop)) A_219) bot_bot_pname_o)))
% FOF formula (forall (A_218:((pname->Prop)->Prop)) (B_145:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_218) B_145)->((finite297249702name_o B_145)->(finite297249702name_o A_218)))) of role axiom named fact_226_finite__subset
% A new axiom: (forall (A_218:((pname->Prop)->Prop)) (B_145:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_218) B_145)->((finite297249702name_o B_145)->(finite297249702name_o A_218))))
% FOF formula (forall (A_218:((hoare_1708887482_state->Prop)->Prop)) (B_145:((hoare_1708887482_state->Prop)->Prop)), (((ord_le1728773982te_o_o A_218) B_145)->((finite1329924456tate_o B_145)->(finite1329924456tate_o A_218)))) of role axiom named fact_227_finite__subset
% A new axiom: (forall (A_218:((hoare_1708887482_state->Prop)->Prop)) (B_145:((hoare_1708887482_state->Prop)->Prop)), (((ord_le1728773982te_o_o A_218) B_145)->((finite1329924456tate_o B_145)->(finite1329924456tate_o A_218))))
% FOF formula (forall (A_218:(hoare_1708887482_state->Prop)) (B_145:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_218) B_145)->((finite1625599783_state B_145)->(finite1625599783_state A_218)))) of role axiom named fact_228_finite__subset
% A new axiom: (forall (A_218:(hoare_1708887482_state->Prop)) (B_145:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_218) B_145)->((finite1625599783_state B_145)->(finite1625599783_state A_218))))
% FOF formula (forall (A_218:(pname->Prop)) (B_145:(pname->Prop)), (((ord_less_eq_pname_o A_218) B_145)->((finite_finite_pname B_145)->(finite_finite_pname A_218)))) of role axiom named fact_229_finite__subset
% A new axiom: (forall (A_218:(pname->Prop)) (B_145:(pname->Prop)), (((ord_less_eq_pname_o A_218) B_145)->((finite_finite_pname B_145)->(finite_finite_pname A_218))))
% FOF formula (forall (A_217:((pname->Prop)->Prop)) (B_144:((pname->Prop)->Prop)), ((finite297249702name_o B_144)->(((ord_le1205211808me_o_o A_217) B_144)->(finite297249702name_o A_217)))) of role axiom named fact_230_rev__finite__subset
% A new axiom: (forall (A_217:((pname->Prop)->Prop)) (B_144:((pname->Prop)->Prop)), ((finite297249702name_o B_144)->(((ord_le1205211808me_o_o A_217) B_144)->(finite297249702name_o A_217))))
% FOF formula (forall (A_217:((hoare_1708887482_state->Prop)->Prop)) (B_144:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_144)->(((ord_le1728773982te_o_o A_217) B_144)->(finite1329924456tate_o A_217)))) of role axiom named fact_231_rev__finite__subset
% A new axiom: (forall (A_217:((hoare_1708887482_state->Prop)->Prop)) (B_144:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_144)->(((ord_le1728773982te_o_o A_217) B_144)->(finite1329924456tate_o A_217))))
% FOF formula (forall (A_217:(hoare_1708887482_state->Prop)) (B_144:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_144)->(((ord_le777019615tate_o A_217) B_144)->(finite1625599783_state A_217)))) of role axiom named fact_232_rev__finite__subset
% A new axiom: (forall (A_217:(hoare_1708887482_state->Prop)) (B_144:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_144)->(((ord_le777019615tate_o A_217) B_144)->(finite1625599783_state A_217))))
% FOF formula (forall (A_217:(pname->Prop)) (B_144:(pname->Prop)), ((finite_finite_pname B_144)->(((ord_less_eq_pname_o A_217) B_144)->(finite_finite_pname A_217)))) of role axiom named fact_233_rev__finite__subset
% A new axiom: (forall (A_217:(pname->Prop)) (B_144:(pname->Prop)), ((finite_finite_pname B_144)->(((ord_less_eq_pname_o A_217) B_144)->(finite_finite_pname A_217))))
% FOF formula (forall (A_216:pname) (C_62:(pname->Prop)) (D_6:(pname->Prop)), (((ord_less_eq_pname_o C_62) D_6)->((ord_less_eq_pname_o ((insert_pname A_216) C_62)) ((insert_pname A_216) D_6)))) of role axiom named fact_234_insert__mono
% A new axiom: (forall (A_216:pname) (C_62:(pname->Prop)) (D_6:(pname->Prop)), (((ord_less_eq_pname_o C_62) D_6)->((ord_less_eq_pname_o ((insert_pname A_216) C_62)) ((insert_pname A_216) D_6))))
% FOF formula (forall (A_216:com) (C_62:(com->Prop)) (D_6:(com->Prop)), (((ord_less_eq_com_o C_62) D_6)->((ord_less_eq_com_o ((insert_com A_216) C_62)) ((insert_com A_216) D_6)))) of role axiom named fact_235_insert__mono
% A new axiom: (forall (A_216:com) (C_62:(com->Prop)) (D_6:(com->Prop)), (((ord_less_eq_com_o C_62) D_6)->((ord_less_eq_com_o ((insert_com A_216) C_62)) ((insert_com A_216) D_6))))
% FOF formula (forall (A_216:hoare_1708887482_state) (C_62:(hoare_1708887482_state->Prop)) (D_6:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o C_62) D_6)->((ord_le777019615tate_o ((insert528405184_state A_216) C_62)) ((insert528405184_state A_216) D_6)))) of role axiom named fact_236_insert__mono
% A new axiom: (forall (A_216:hoare_1708887482_state) (C_62:(hoare_1708887482_state->Prop)) (D_6:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o C_62) D_6)->((ord_le777019615tate_o ((insert528405184_state A_216) C_62)) ((insert528405184_state A_216) D_6))))
% FOF formula (forall (X_106:com) (A_215:(com->Prop)), ((iff ((member_com X_106) A_215)) (A_215 X_106))) of role axiom named fact_237_mem__def
% A new axiom: (forall (X_106:com) (A_215:(com->Prop)), ((iff ((member_com X_106) A_215)) (A_215 X_106)))
% FOF formula (forall (X_106:hoare_1708887482_state) (A_215:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state X_106) A_215)) (A_215 X_106))) of role axiom named fact_238_mem__def
% A new axiom: (forall (X_106:hoare_1708887482_state) (A_215:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state X_106) A_215)) (A_215 X_106)))
% FOF formula (forall (X_106:pname) (A_215:(pname->Prop)), ((iff ((member_pname X_106) A_215)) (A_215 X_106))) of role axiom named fact_239_mem__def
% A new axiom: (forall (X_106:pname) (A_215:(pname->Prop)), ((iff ((member_pname X_106) A_215)) (A_215 X_106)))
% FOF formula (forall (P_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state P_40)) P_40)) of role axiom named fact_240_Collect__def
% A new axiom: (forall (P_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state P_40)) P_40))
% FOF formula (forall (P_40:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_40)) P_40)) of role axiom named fact_241_Collect__def
% A new axiom: (forall (P_40:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_40)) P_40))
% FOF formula (forall (P_40:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_40)) P_40)) of role axiom named fact_242_Collect__def
% A new axiom: (forall (P_40:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_40)) P_40))
% FOF formula (forall (P_40:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o P_40)) P_40)) of role axiom named fact_243_Collect__def
% A new axiom: (forall (P_40:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o P_40)) P_40))
% FOF formula (forall (B_143:pname) (A_214:(pname->Prop)) (B_142:(pname->Prop)), (((ord_less_eq_pname_o A_214) B_142)->((ord_less_eq_pname_o A_214) ((insert_pname B_143) B_142)))) of role axiom named fact_244_subset__insertI2
% A new axiom: (forall (B_143:pname) (A_214:(pname->Prop)) (B_142:(pname->Prop)), (((ord_less_eq_pname_o A_214) B_142)->((ord_less_eq_pname_o A_214) ((insert_pname B_143) B_142))))
% FOF formula (forall (B_143:com) (A_214:(com->Prop)) (B_142:(com->Prop)), (((ord_less_eq_com_o A_214) B_142)->((ord_less_eq_com_o A_214) ((insert_com B_143) B_142)))) of role axiom named fact_245_subset__insertI2
% A new axiom: (forall (B_143:com) (A_214:(com->Prop)) (B_142:(com->Prop)), (((ord_less_eq_com_o A_214) B_142)->((ord_less_eq_com_o A_214) ((insert_com B_143) B_142))))
% FOF formula (forall (B_143:hoare_1708887482_state) (A_214:(hoare_1708887482_state->Prop)) (B_142:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_214) B_142)->((ord_le777019615tate_o A_214) ((insert528405184_state B_143) B_142)))) of role axiom named fact_246_subset__insertI2
% A new axiom: (forall (B_143:hoare_1708887482_state) (A_214:(hoare_1708887482_state->Prop)) (B_142:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_214) B_142)->((ord_le777019615tate_o A_214) ((insert528405184_state B_143) B_142))))
% FOF formula (forall (B_141:(com->Prop)) (X_105:com) (A_213:(com->Prop)), ((((member_com X_105) A_213)->False)->((iff ((ord_less_eq_com_o A_213) ((insert_com X_105) B_141))) ((ord_less_eq_com_o A_213) B_141)))) of role axiom named fact_247_subset__insert
% A new axiom: (forall (B_141:(com->Prop)) (X_105:com) (A_213:(com->Prop)), ((((member_com X_105) A_213)->False)->((iff ((ord_less_eq_com_o A_213) ((insert_com X_105) B_141))) ((ord_less_eq_com_o A_213) B_141))))
% FOF formula (forall (B_141:(pname->Prop)) (X_105:pname) (A_213:(pname->Prop)), ((((member_pname X_105) A_213)->False)->((iff ((ord_less_eq_pname_o A_213) ((insert_pname X_105) B_141))) ((ord_less_eq_pname_o A_213) B_141)))) of role axiom named fact_248_subset__insert
% A new axiom: (forall (B_141:(pname->Prop)) (X_105:pname) (A_213:(pname->Prop)), ((((member_pname X_105) A_213)->False)->((iff ((ord_less_eq_pname_o A_213) ((insert_pname X_105) B_141))) ((ord_less_eq_pname_o A_213) B_141))))
% FOF formula (forall (B_141:(hoare_1708887482_state->Prop)) (X_105:hoare_1708887482_state) (A_213:(hoare_1708887482_state->Prop)), ((((member451959335_state X_105) A_213)->False)->((iff ((ord_le777019615tate_o A_213) ((insert528405184_state X_105) B_141))) ((ord_le777019615tate_o A_213) B_141)))) of role axiom named fact_249_subset__insert
% A new axiom: (forall (B_141:(hoare_1708887482_state->Prop)) (X_105:hoare_1708887482_state) (A_213:(hoare_1708887482_state->Prop)), ((((member451959335_state X_105) A_213)->False)->((iff ((ord_le777019615tate_o A_213) ((insert528405184_state X_105) B_141))) ((ord_le777019615tate_o A_213) B_141))))
% FOF formula (forall (X_104:com) (A_212:(com->Prop)) (B_140:(com->Prop)), ((iff ((ord_less_eq_com_o ((insert_com X_104) A_212)) B_140)) ((and ((member_com X_104) B_140)) ((ord_less_eq_com_o A_212) B_140)))) of role axiom named fact_250_insert__subset
% A new axiom: (forall (X_104:com) (A_212:(com->Prop)) (B_140:(com->Prop)), ((iff ((ord_less_eq_com_o ((insert_com X_104) A_212)) B_140)) ((and ((member_com X_104) B_140)) ((ord_less_eq_com_o A_212) B_140))))
% FOF formula (forall (X_104:pname) (A_212:(pname->Prop)) (B_140:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_104) A_212)) B_140)) ((and ((member_pname X_104) B_140)) ((ord_less_eq_pname_o A_212) B_140)))) of role axiom named fact_251_insert__subset
% A new axiom: (forall (X_104:pname) (A_212:(pname->Prop)) (B_140:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_104) A_212)) B_140)) ((and ((member_pname X_104) B_140)) ((ord_less_eq_pname_o A_212) B_140))))
% FOF formula (forall (X_104:hoare_1708887482_state) (A_212:(hoare_1708887482_state->Prop)) (B_140:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o ((insert528405184_state X_104) A_212)) B_140)) ((and ((member451959335_state X_104) B_140)) ((ord_le777019615tate_o A_212) B_140)))) of role axiom named fact_252_insert__subset
% A new axiom: (forall (X_104:hoare_1708887482_state) (A_212:(hoare_1708887482_state->Prop)) (B_140:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o ((insert528405184_state X_104) A_212)) B_140)) ((and ((member451959335_state X_104) B_140)) ((ord_le777019615tate_o A_212) B_140))))
% FOF formula (forall (B_139:(pname->Prop)) (A_211:pname), ((ord_less_eq_pname_o B_139) ((insert_pname A_211) B_139))) of role axiom named fact_253_subset__insertI
% A new axiom: (forall (B_139:(pname->Prop)) (A_211:pname), ((ord_less_eq_pname_o B_139) ((insert_pname A_211) B_139)))
% FOF formula (forall (B_139:(com->Prop)) (A_211:com), ((ord_less_eq_com_o B_139) ((insert_com A_211) B_139))) of role axiom named fact_254_subset__insertI
% A new axiom: (forall (B_139:(com->Prop)) (A_211:com), ((ord_less_eq_com_o B_139) ((insert_com A_211) B_139)))
% FOF formula (forall (B_139:(hoare_1708887482_state->Prop)) (A_211:hoare_1708887482_state), ((ord_le777019615tate_o B_139) ((insert528405184_state A_211) B_139))) of role axiom named fact_255_subset__insertI
% A new axiom: (forall (B_139:(hoare_1708887482_state->Prop)) (A_211:hoare_1708887482_state), ((ord_le777019615tate_o B_139) ((insert528405184_state A_211) B_139)))
% FOF formula (forall (F_78:(hoare_1708887482_state->pname)) (X_103:hoare_1708887482_state) (A_210:(hoare_1708887482_state->Prop)), (((member451959335_state X_103) A_210)->(((eq (pname->Prop)) ((insert_pname (F_78 X_103)) ((image_1509414295_pname F_78) A_210))) ((image_1509414295_pname F_78) A_210)))) of role axiom named fact_256_insert__image
% A new axiom: (forall (F_78:(hoare_1708887482_state->pname)) (X_103:hoare_1708887482_state) (A_210:(hoare_1708887482_state->Prop)), (((member451959335_state X_103) A_210)->(((eq (pname->Prop)) ((insert_pname (F_78 X_103)) ((image_1509414295_pname F_78) A_210))) ((image_1509414295_pname F_78) A_210))))
% FOF formula (forall (F_78:(hoare_1708887482_state->com)) (X_103:hoare_1708887482_state) (A_210:(hoare_1708887482_state->Prop)), (((member451959335_state X_103) A_210)->(((eq (com->Prop)) ((insert_com (F_78 X_103)) ((image_1604448413te_com F_78) A_210))) ((image_1604448413te_com F_78) A_210)))) of role axiom named fact_257_insert__image
% A new axiom: (forall (F_78:(hoare_1708887482_state->com)) (X_103:hoare_1708887482_state) (A_210:(hoare_1708887482_state->Prop)), (((member451959335_state X_103) A_210)->(((eq (com->Prop)) ((insert_com (F_78 X_103)) ((image_1604448413te_com F_78) A_210))) ((image_1604448413te_com F_78) A_210))))
% FOF formula (forall (F_78:(pname->pname)) (X_103:pname) (A_210:(pname->Prop)), (((member_pname X_103) A_210)->(((eq (pname->Prop)) ((insert_pname (F_78 X_103)) ((image_pname_pname F_78) A_210))) ((image_pname_pname F_78) A_210)))) of role axiom named fact_258_insert__image
% A new axiom: (forall (F_78:(pname->pname)) (X_103:pname) (A_210:(pname->Prop)), (((member_pname X_103) A_210)->(((eq (pname->Prop)) ((insert_pname (F_78 X_103)) ((image_pname_pname F_78) A_210))) ((image_pname_pname F_78) A_210))))
% FOF formula (forall (F_78:(pname->com)) (X_103:pname) (A_210:(pname->Prop)), (((member_pname X_103) A_210)->(((eq (com->Prop)) ((insert_com (F_78 X_103)) ((image_pname_com F_78) A_210))) ((image_pname_com F_78) A_210)))) of role axiom named fact_259_insert__image
% A new axiom: (forall (F_78:(pname->com)) (X_103:pname) (A_210:(pname->Prop)), (((member_pname X_103) A_210)->(((eq (com->Prop)) ((insert_com (F_78 X_103)) ((image_pname_com F_78) A_210))) ((image_pname_com F_78) A_210))))
% FOF formula (forall (F_78:(com->hoare_1708887482_state)) (X_103:com) (A_210:(com->Prop)), (((member_com X_103) A_210)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state (F_78 X_103)) ((image_934102463_state F_78) A_210))) ((image_934102463_state F_78) A_210)))) of role axiom named fact_260_insert__image
% A new axiom: (forall (F_78:(com->hoare_1708887482_state)) (X_103:com) (A_210:(com->Prop)), (((member_com X_103) A_210)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state (F_78 X_103)) ((image_934102463_state F_78) A_210))) ((image_934102463_state F_78) A_210))))
% FOF formula (forall (F_78:(pname->hoare_1708887482_state)) (X_103:pname) (A_210:(pname->Prop)), (((member_pname X_103) A_210)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state (F_78 X_103)) ((image_1116629049_state F_78) A_210))) ((image_1116629049_state F_78) A_210)))) of role axiom named fact_261_insert__image
% A new axiom: (forall (F_78:(pname->hoare_1708887482_state)) (X_103:pname) (A_210:(pname->Prop)), (((member_pname X_103) A_210)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state (F_78 X_103)) ((image_1116629049_state F_78) A_210))) ((image_1116629049_state F_78) A_210))))
% FOF formula (forall (F_77:(hoare_1708887482_state->pname)) (A_209:hoare_1708887482_state) (B_138:(hoare_1708887482_state->Prop)), (((eq (pname->Prop)) ((image_1509414295_pname F_77) ((insert528405184_state A_209) B_138))) ((insert_pname (F_77 A_209)) ((image_1509414295_pname F_77) B_138)))) of role axiom named fact_262_image__insert
% A new axiom: (forall (F_77:(hoare_1708887482_state->pname)) (A_209:hoare_1708887482_state) (B_138:(hoare_1708887482_state->Prop)), (((eq (pname->Prop)) ((image_1509414295_pname F_77) ((insert528405184_state A_209) B_138))) ((insert_pname (F_77 A_209)) ((image_1509414295_pname F_77) B_138))))
% FOF formula (forall (F_77:(hoare_1708887482_state->com)) (A_209:hoare_1708887482_state) (B_138:(hoare_1708887482_state->Prop)), (((eq (com->Prop)) ((image_1604448413te_com F_77) ((insert528405184_state A_209) B_138))) ((insert_com (F_77 A_209)) ((image_1604448413te_com F_77) B_138)))) of role axiom named fact_263_image__insert
% A new axiom: (forall (F_77:(hoare_1708887482_state->com)) (A_209:hoare_1708887482_state) (B_138:(hoare_1708887482_state->Prop)), (((eq (com->Prop)) ((image_1604448413te_com F_77) ((insert528405184_state A_209) B_138))) ((insert_com (F_77 A_209)) ((image_1604448413te_com F_77) B_138))))
% FOF formula (forall (F_77:(com->hoare_1708887482_state)) (A_209:com) (B_138:(com->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_934102463_state F_77) ((insert_com A_209) B_138))) ((insert528405184_state (F_77 A_209)) ((image_934102463_state F_77) B_138)))) of role axiom named fact_264_image__insert
% A new axiom: (forall (F_77:(com->hoare_1708887482_state)) (A_209:com) (B_138:(com->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_934102463_state F_77) ((insert_com A_209) B_138))) ((insert528405184_state (F_77 A_209)) ((image_934102463_state F_77) B_138))))
% FOF formula (forall (F_77:(pname->hoare_1708887482_state)) (A_209:pname) (B_138:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_77) ((insert_pname A_209) B_138))) ((insert528405184_state (F_77 A_209)) ((image_1116629049_state F_77) B_138)))) of role axiom named fact_265_image__insert
% A new axiom: (forall (F_77:(pname->hoare_1708887482_state)) (A_209:pname) (B_138:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_77) ((insert_pname A_209) B_138))) ((insert528405184_state (F_77 A_209)) ((image_1116629049_state F_77) B_138))))
% FOF formula (forall (F_76:(hoare_1708887482_state->pname)) (A_208:(hoare_1708887482_state->Prop)) (B_137:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_208) B_137)->((ord_less_eq_pname_o ((image_1509414295_pname F_76) A_208)) ((image_1509414295_pname F_76) B_137)))) of role axiom named fact_266_image__mono
% A new axiom: (forall (F_76:(hoare_1708887482_state->pname)) (A_208:(hoare_1708887482_state->Prop)) (B_137:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_208) B_137)->((ord_less_eq_pname_o ((image_1509414295_pname F_76) A_208)) ((image_1509414295_pname F_76) B_137))))
% FOF formula (forall (F_76:(pname->hoare_1708887482_state)) (A_208:(pname->Prop)) (B_137:(pname->Prop)), (((ord_less_eq_pname_o A_208) B_137)->((ord_le777019615tate_o ((image_1116629049_state F_76) A_208)) ((image_1116629049_state F_76) B_137)))) of role axiom named fact_267_image__mono
% A new axiom: (forall (F_76:(pname->hoare_1708887482_state)) (A_208:(pname->Prop)) (B_137:(pname->Prop)), (((ord_less_eq_pname_o A_208) B_137)->((ord_le777019615tate_o ((image_1116629049_state F_76) A_208)) ((image_1116629049_state F_76) B_137))))
% FOF formula (forall (B_136:(pname->Prop)) (F_75:(hoare_1708887482_state->pname)) (A_207:(hoare_1708887482_state->Prop)), ((iff ((ord_less_eq_pname_o B_136) ((image_1509414295_pname F_75) A_207))) ((ex (hoare_1708887482_state->Prop)) (fun (AA:(hoare_1708887482_state->Prop))=> ((and ((ord_le777019615tate_o AA) A_207)) (((eq (pname->Prop)) B_136) ((image_1509414295_pname F_75) AA))))))) of role axiom named fact_268_subset__image__iff
% A new axiom: (forall (B_136:(pname->Prop)) (F_75:(hoare_1708887482_state->pname)) (A_207:(hoare_1708887482_state->Prop)), ((iff ((ord_less_eq_pname_o B_136) ((image_1509414295_pname F_75) A_207))) ((ex (hoare_1708887482_state->Prop)) (fun (AA:(hoare_1708887482_state->Prop))=> ((and ((ord_le777019615tate_o AA) A_207)) (((eq (pname->Prop)) B_136) ((image_1509414295_pname F_75) AA)))))))
% FOF formula (forall (B_136:(hoare_1708887482_state->Prop)) (F_75:(pname->hoare_1708887482_state)) (A_207:(pname->Prop)), ((iff ((ord_le777019615tate_o B_136) ((image_1116629049_state F_75) A_207))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_207)) (((eq (hoare_1708887482_state->Prop)) B_136) ((image_1116629049_state F_75) AA))))))) of role axiom named fact_269_subset__image__iff
% A new axiom: (forall (B_136:(hoare_1708887482_state->Prop)) (F_75:(pname->hoare_1708887482_state)) (A_207:(pname->Prop)), ((iff ((ord_le777019615tate_o B_136) ((image_1116629049_state F_75) A_207))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_207)) (((eq (hoare_1708887482_state->Prop)) B_136) ((image_1116629049_state F_75) AA)))))))
% FOF formula (forall (M_5:(com->option_com)) (A_206:com) (B_135:com), ((((eq option_com) (M_5 A_206)) (some_com B_135))->((member_com A_206) (dom_com_com M_5)))) of role axiom named fact_270_domI
% A new axiom: (forall (M_5:(com->option_com)) (A_206:com) (B_135:com), ((((eq option_com) (M_5 A_206)) (some_com B_135))->((member_com A_206) (dom_com_com M_5))))
% FOF formula (forall (M_5:(hoare_1708887482_state->option_pname)) (A_206:hoare_1708887482_state) (B_135:pname), ((((eq option_pname) (M_5 A_206)) (some_pname B_135))->((member451959335_state A_206) (dom_Ho1805192458_pname M_5)))) of role axiom named fact_271_domI
% A new axiom: (forall (M_5:(hoare_1708887482_state->option_pname)) (A_206:hoare_1708887482_state) (B_135:pname), ((((eq option_pname) (M_5 A_206)) (some_pname B_135))->((member451959335_state A_206) (dom_Ho1805192458_pname M_5))))
% FOF formula (forall (M_5:(hoare_1708887482_state->option1624383643_state)) (A_206:hoare_1708887482_state) (B_135:hoare_1708887482_state), ((((eq option1624383643_state) (M_5 A_206)) (some_H1974565227_state B_135))->((member451959335_state A_206) (dom_Ho1703271284_state M_5)))) of role axiom named fact_272_domI
% A new axiom: (forall (M_5:(hoare_1708887482_state->option1624383643_state)) (A_206:hoare_1708887482_state) (B_135:hoare_1708887482_state), ((((eq option1624383643_state) (M_5 A_206)) (some_H1974565227_state B_135))->((member451959335_state A_206) (dom_Ho1703271284_state M_5))))
% FOF formula (forall (M_5:(pname->option_pname)) (A_206:pname) (B_135:pname), ((((eq option_pname) (M_5 A_206)) (some_pname B_135))->((member_pname A_206) (dom_pname_pname M_5)))) of role axiom named fact_273_domI
% A new axiom: (forall (M_5:(pname->option_pname)) (A_206:pname) (B_135:pname), ((((eq option_pname) (M_5 A_206)) (some_pname B_135))->((member_pname A_206) (dom_pname_pname M_5))))
% FOF formula (forall (M_5:(pname->option1624383643_state)) (A_206:pname) (B_135:hoare_1708887482_state), ((((eq option1624383643_state) (M_5 A_206)) (some_H1974565227_state B_135))->((member_pname A_206) (dom_pn1412407212_state M_5)))) of role axiom named fact_274_domI
% A new axiom: (forall (M_5:(pname->option1624383643_state)) (A_206:pname) (B_135:hoare_1708887482_state), ((((eq option1624383643_state) (M_5 A_206)) (some_H1974565227_state B_135))->((member_pname A_206) (dom_pn1412407212_state M_5))))
% FOF formula (forall (M_5:(pname->option_com)) (A_206:pname) (B_135:com), ((((eq option_com) (M_5 A_206)) (some_com B_135))->((member_pname A_206) (dom_pname_com M_5)))) of role axiom named fact_275_domI
% A new axiom: (forall (M_5:(pname->option_com)) (A_206:pname) (B_135:com), ((((eq option_com) (M_5 A_206)) (some_com B_135))->((member_pname A_206) (dom_pname_com M_5))))
% FOF formula (forall (P_39:(pname->Prop)) (A_205:pname), ((and ((P_39 A_205)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) X_3) A_205)) (P_39 X_3))))) ((insert_pname A_205) bot_bot_pname_o)))) (((P_39 A_205)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) X_3) A_205)) (P_39 X_3))))) bot_bot_pname_o)))) of role axiom named fact_276_Collect__conv__if
% A new axiom: (forall (P_39:(pname->Prop)) (A_205:pname), ((and ((P_39 A_205)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) X_3) A_205)) (P_39 X_3))))) ((insert_pname A_205) bot_bot_pname_o)))) (((P_39 A_205)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) X_3) A_205)) (P_39 X_3))))) bot_bot_pname_o))))
% FOF formula (forall (P_39:(com->Prop)) (A_205:com), ((and ((P_39 A_205)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) X_3) A_205)) (P_39 X_3))))) ((insert_com A_205) bot_bot_com_o)))) (((P_39 A_205)->False)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) X_3) A_205)) (P_39 X_3))))) bot_bot_com_o)))) of role axiom named fact_277_Collect__conv__if
% A new axiom: (forall (P_39:(com->Prop)) (A_205:com), ((and ((P_39 A_205)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) X_3) A_205)) (P_39 X_3))))) ((insert_com A_205) bot_bot_com_o)))) (((P_39 A_205)->False)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) X_3) A_205)) (P_39 X_3))))) bot_bot_com_o))))
% FOF formula (forall (P_39:((pname->Prop)->Prop)) (A_205:(pname->Prop)), ((and ((P_39 A_205)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) X_3) A_205)) (P_39 X_3))))) ((insert_pname_o A_205) bot_bot_pname_o_o)))) (((P_39 A_205)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) X_3) A_205)) (P_39 X_3))))) bot_bot_pname_o_o)))) of role axiom named fact_278_Collect__conv__if
% A new axiom: (forall (P_39:((pname->Prop)->Prop)) (A_205:(pname->Prop)), ((and ((P_39 A_205)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) X_3) A_205)) (P_39 X_3))))) ((insert_pname_o A_205) bot_bot_pname_o_o)))) (((P_39 A_205)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) X_3) A_205)) (P_39 X_3))))) bot_bot_pname_o_o))))
% FOF formula (forall (P_39:((hoare_1708887482_state->Prop)->Prop)) (A_205:(hoare_1708887482_state->Prop)), ((and ((P_39 A_205)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) X_3) A_205)) (P_39 X_3))))) ((insert949073679tate_o A_205) bot_bo1678742418te_o_o)))) (((P_39 A_205)->False)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) X_3) A_205)) (P_39 X_3))))) bot_bo1678742418te_o_o)))) of role axiom named fact_279_Collect__conv__if
% A new axiom: (forall (P_39:((hoare_1708887482_state->Prop)->Prop)) (A_205:(hoare_1708887482_state->Prop)), ((and ((P_39 A_205)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) X_3) A_205)) (P_39 X_3))))) ((insert949073679tate_o A_205) bot_bo1678742418te_o_o)))) (((P_39 A_205)->False)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) X_3) A_205)) (P_39 X_3))))) bot_bo1678742418te_o_o))))
% FOF formula (forall (P_39:(hoare_1708887482_state->Prop)) (A_205:hoare_1708887482_state), ((and ((P_39 A_205)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X_3) A_205)) (P_39 X_3))))) ((insert528405184_state A_205) bot_bo19817387tate_o)))) (((P_39 A_205)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X_3) A_205)) (P_39 X_3))))) bot_bo19817387tate_o)))) of role axiom named fact_280_Collect__conv__if
% A new axiom: (forall (P_39:(hoare_1708887482_state->Prop)) (A_205:hoare_1708887482_state), ((and ((P_39 A_205)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X_3) A_205)) (P_39 X_3))))) ((insert528405184_state A_205) bot_bo19817387tate_o)))) (((P_39 A_205)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X_3) A_205)) (P_39 X_3))))) bot_bo19817387tate_o))))
% FOF formula (forall (P_38:(pname->Prop)) (A_204:pname), ((and ((P_38 A_204)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) A_204) X_3)) (P_38 X_3))))) ((insert_pname A_204) bot_bot_pname_o)))) (((P_38 A_204)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) A_204) X_3)) (P_38 X_3))))) bot_bot_pname_o)))) of role axiom named fact_281_Collect__conv__if2
% A new axiom: (forall (P_38:(pname->Prop)) (A_204:pname), ((and ((P_38 A_204)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) A_204) X_3)) (P_38 X_3))))) ((insert_pname A_204) bot_bot_pname_o)))) (((P_38 A_204)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) A_204) X_3)) (P_38 X_3))))) bot_bot_pname_o))))
% FOF formula (forall (P_38:(com->Prop)) (A_204:com), ((and ((P_38 A_204)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) A_204) X_3)) (P_38 X_3))))) ((insert_com A_204) bot_bot_com_o)))) (((P_38 A_204)->False)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) A_204) X_3)) (P_38 X_3))))) bot_bot_com_o)))) of role axiom named fact_282_Collect__conv__if2
% A new axiom: (forall (P_38:(com->Prop)) (A_204:com), ((and ((P_38 A_204)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) A_204) X_3)) (P_38 X_3))))) ((insert_com A_204) bot_bot_com_o)))) (((P_38 A_204)->False)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) A_204) X_3)) (P_38 X_3))))) bot_bot_com_o))))
% FOF formula (forall (P_38:((pname->Prop)->Prop)) (A_204:(pname->Prop)), ((and ((P_38 A_204)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) A_204) X_3)) (P_38 X_3))))) ((insert_pname_o A_204) bot_bot_pname_o_o)))) (((P_38 A_204)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) A_204) X_3)) (P_38 X_3))))) bot_bot_pname_o_o)))) of role axiom named fact_283_Collect__conv__if2
% A new axiom: (forall (P_38:((pname->Prop)->Prop)) (A_204:(pname->Prop)), ((and ((P_38 A_204)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) A_204) X_3)) (P_38 X_3))))) ((insert_pname_o A_204) bot_bot_pname_o_o)))) (((P_38 A_204)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) A_204) X_3)) (P_38 X_3))))) bot_bot_pname_o_o))))
% FOF formula (forall (P_38:((hoare_1708887482_state->Prop)->Prop)) (A_204:(hoare_1708887482_state->Prop)), ((and ((P_38 A_204)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_204) X_3)) (P_38 X_3))))) ((insert949073679tate_o A_204) bot_bo1678742418te_o_o)))) (((P_38 A_204)->False)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_204) X_3)) (P_38 X_3))))) bot_bo1678742418te_o_o)))) of role axiom named fact_284_Collect__conv__if2
% A new axiom: (forall (P_38:((hoare_1708887482_state->Prop)->Prop)) (A_204:(hoare_1708887482_state->Prop)), ((and ((P_38 A_204)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_204) X_3)) (P_38 X_3))))) ((insert949073679tate_o A_204) bot_bo1678742418te_o_o)))) (((P_38 A_204)->False)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_204) X_3)) (P_38 X_3))))) bot_bo1678742418te_o_o))))
% FOF formula (forall (P_38:(hoare_1708887482_state->Prop)) (A_204:hoare_1708887482_state), ((and ((P_38 A_204)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_204) X_3)) (P_38 X_3))))) ((insert528405184_state A_204) bot_bo19817387tate_o)))) (((P_38 A_204)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_204) X_3)) (P_38 X_3))))) bot_bo19817387tate_o)))) of role axiom named fact_285_Collect__conv__if2
% A new axiom: (forall (P_38:(hoare_1708887482_state->Prop)) (A_204:hoare_1708887482_state), ((and ((P_38 A_204)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_204) X_3)) (P_38 X_3))))) ((insert528405184_state A_204) bot_bo19817387tate_o)))) (((P_38 A_204)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_204) X_3)) (P_38 X_3))))) bot_bo19817387tate_o))))
% FOF formula (forall (A_203:pname), (((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> (((eq pname) X_3) A_203)))) ((insert_pname A_203) bot_bot_pname_o))) of role axiom named fact_286_singleton__conv
% A new axiom: (forall (A_203:pname), (((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> (((eq pname) X_3) A_203)))) ((insert_pname A_203) bot_bot_pname_o)))
% FOF formula (forall (A_203:com), (((eq (com->Prop)) (collect_com (fun (X_3:com)=> (((eq com) X_3) A_203)))) ((insert_com A_203) bot_bot_com_o))) of role axiom named fact_287_singleton__conv
% A new axiom: (forall (A_203:com), (((eq (com->Prop)) (collect_com (fun (X_3:com)=> (((eq com) X_3) A_203)))) ((insert_com A_203) bot_bot_com_o)))
% FOF formula (forall (A_203:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> (((eq (pname->Prop)) X_3) A_203)))) ((insert_pname_o A_203) bot_bot_pname_o_o))) of role axiom named fact_288_singleton__conv
% A new axiom: (forall (A_203:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> (((eq (pname->Prop)) X_3) A_203)))) ((insert_pname_o A_203) bot_bot_pname_o_o)))
% FOF formula (forall (A_203:(hoare_1708887482_state->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> (((eq (hoare_1708887482_state->Prop)) X_3) A_203)))) ((insert949073679tate_o A_203) bot_bo1678742418te_o_o))) of role axiom named fact_289_singleton__conv
% A new axiom: (forall (A_203:(hoare_1708887482_state->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> (((eq (hoare_1708887482_state->Prop)) X_3) A_203)))) ((insert949073679tate_o A_203) bot_bo1678742418te_o_o)))
% FOF formula (forall (A_203:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X_3) A_203)))) ((insert528405184_state A_203) bot_bo19817387tate_o))) of role axiom named fact_290_singleton__conv
% A new axiom: (forall (A_203:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X_3) A_203)))) ((insert528405184_state A_203) bot_bo19817387tate_o)))
% FOF formula (forall (A_202:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_202))) ((insert_pname A_202) bot_bot_pname_o))) of role axiom named fact_291_singleton__conv2
% A new axiom: (forall (A_202:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_202))) ((insert_pname A_202) bot_bot_pname_o)))
% FOF formula (forall (A_202:com), (((eq (com->Prop)) (collect_com (fequal_com A_202))) ((insert_com A_202) bot_bot_com_o))) of role axiom named fact_292_singleton__conv2
% A new axiom: (forall (A_202:com), (((eq (com->Prop)) (collect_com (fequal_com A_202))) ((insert_com A_202) bot_bot_com_o)))
% FOF formula (forall (A_202:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fequal_pname_o A_202))) ((insert_pname_o A_202) bot_bot_pname_o_o))) of role axiom named fact_293_singleton__conv2
% A new axiom: (forall (A_202:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fequal_pname_o A_202))) ((insert_pname_o A_202) bot_bot_pname_o_o)))
% FOF formula (forall (A_202:(hoare_1708887482_state->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fequal1436017556tate_o A_202))) ((insert949073679tate_o A_202) bot_bo1678742418te_o_o))) of role axiom named fact_294_singleton__conv2
% A new axiom: (forall (A_202:(hoare_1708887482_state->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fequal1436017556tate_o A_202))) ((insert949073679tate_o A_202) bot_bo1678742418te_o_o)))
% FOF formula (forall (A_202:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fequal224822779_state A_202))) ((insert528405184_state A_202) bot_bo19817387tate_o))) of role axiom named fact_295_singleton__conv2
% A new axiom: (forall (A_202:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fequal224822779_state A_202))) ((insert528405184_state A_202) bot_bo19817387tate_o)))
% FOF formula (forall (C_34:com) (G_7:(hoare_1708887482_state->Prop)), (hoare_1160767572gleton->((forall (X_3:pname), (((member_pname X_3) (dom_pname_com body))->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT (body_1 X_3))) bot_bo19817387tate_o))))->((wt C_34)->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o)))))) of role axiom named fact_296_MGF__lemma1
% A new axiom: (forall (C_34:com) (G_7:(hoare_1708887482_state->Prop)), (hoare_1160767572gleton->((forall (X_3:pname), (((member_pname X_3) (dom_pname_com body))->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT (body_1 X_3))) bot_bo19817387tate_o))))->((wt C_34)->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o))))))
% FOF formula (forall (Pn_1:pname) (B_82:com), (wT_bodies->((((eq option_com) (body Pn_1)) (some_com B_82))->(wt B_82)))) of role axiom named fact_297_WT__bodiesD
% A new axiom: (forall (Pn_1:pname) (B_82:com), (wT_bodies->((((eq option_com) (body Pn_1)) (some_com B_82))->(wt B_82))))
% FOF formula (forall (B_134:hoare_1708887482_state) (F_74:(com->hoare_1708887482_state)) (A_201:(com->Prop)), (((member451959335_state B_134) ((image_934102463_state F_74) A_201))->((forall (X_3:com), ((((eq hoare_1708887482_state) B_134) (F_74 X_3))->(((member_com X_3) A_201)->False)))->False))) of role axiom named fact_298_imageE
% A new axiom: (forall (B_134:hoare_1708887482_state) (F_74:(com->hoare_1708887482_state)) (A_201:(com->Prop)), (((member451959335_state B_134) ((image_934102463_state F_74) A_201))->((forall (X_3:com), ((((eq hoare_1708887482_state) B_134) (F_74 X_3))->(((member_com X_3) A_201)->False)))->False)))
% FOF formula (forall (B_134:pname) (F_74:(com->pname)) (A_201:(com->Prop)), (((member_pname B_134) ((image_com_pname F_74) A_201))->((forall (X_3:com), ((((eq pname) B_134) (F_74 X_3))->(((member_com X_3) A_201)->False)))->False))) of role axiom named fact_299_imageE
% A new axiom: (forall (B_134:pname) (F_74:(com->pname)) (A_201:(com->Prop)), (((member_pname B_134) ((image_com_pname F_74) A_201))->((forall (X_3:com), ((((eq pname) B_134) (F_74 X_3))->(((member_com X_3) A_201)->False)))->False)))
% FOF formula (forall (B_134:com) (F_74:(hoare_1708887482_state->com)) (A_201:(hoare_1708887482_state->Prop)), (((member_com B_134) ((image_1604448413te_com F_74) A_201))->((forall (X_3:hoare_1708887482_state), ((((eq com) B_134) (F_74 X_3))->(((member451959335_state X_3) A_201)->False)))->False))) of role axiom named fact_300_imageE
% A new axiom: (forall (B_134:com) (F_74:(hoare_1708887482_state->com)) (A_201:(hoare_1708887482_state->Prop)), (((member_com B_134) ((image_1604448413te_com F_74) A_201))->((forall (X_3:hoare_1708887482_state), ((((eq com) B_134) (F_74 X_3))->(((member451959335_state X_3) A_201)->False)))->False)))
% FOF formula (forall (B_134:com) (F_74:(pname->com)) (A_201:(pname->Prop)), (((member_com B_134) ((image_pname_com F_74) A_201))->((forall (X_3:pname), ((((eq com) B_134) (F_74 X_3))->(((member_pname X_3) A_201)->False)))->False))) of role axiom named fact_301_imageE
% A new axiom: (forall (B_134:com) (F_74:(pname->com)) (A_201:(pname->Prop)), (((member_com B_134) ((image_pname_com F_74) A_201))->((forall (X_3:pname), ((((eq com) B_134) (F_74 X_3))->(((member_pname X_3) A_201)->False)))->False)))
% FOF formula (forall (B_134:hoare_1708887482_state) (F_74:(pname->hoare_1708887482_state)) (A_201:(pname->Prop)), (((member451959335_state B_134) ((image_1116629049_state F_74) A_201))->((forall (X_3:pname), ((((eq hoare_1708887482_state) B_134) (F_74 X_3))->(((member_pname X_3) A_201)->False)))->False))) of role axiom named fact_302_imageE
% A new axiom: (forall (B_134:hoare_1708887482_state) (F_74:(pname->hoare_1708887482_state)) (A_201:(pname->Prop)), (((member451959335_state B_134) ((image_1116629049_state F_74) A_201))->((forall (X_3:pname), ((((eq hoare_1708887482_state) B_134) (F_74 X_3))->(((member_pname X_3) A_201)->False)))->False)))
% FOF formula (forall (P_37:((com->Prop)->Prop)) (A_200:(com->Prop)) (F_73:(com->Prop)), ((finite_finite_com F_73)->(((ord_less_eq_com_o F_73) A_200)->((P_37 bot_bot_com_o)->((forall (A_6:com) (F_53:(com->Prop)), ((finite_finite_com F_53)->(((member_com A_6) A_200)->((((member_com A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert_com A_6) F_53)))))))->(P_37 F_73)))))) of role axiom named fact_303_finite__subset__induct
% A new axiom: (forall (P_37:((com->Prop)->Prop)) (A_200:(com->Prop)) (F_73:(com->Prop)), ((finite_finite_com F_73)->(((ord_less_eq_com_o F_73) A_200)->((P_37 bot_bot_com_o)->((forall (A_6:com) (F_53:(com->Prop)), ((finite_finite_com F_53)->(((member_com A_6) A_200)->((((member_com A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert_com A_6) F_53)))))))->(P_37 F_73))))))
% FOF formula (forall (P_37:(((pname->Prop)->Prop)->Prop)) (A_200:((pname->Prop)->Prop)) (F_73:((pname->Prop)->Prop)), ((finite297249702name_o F_73)->(((ord_le1205211808me_o_o F_73) A_200)->((P_37 bot_bot_pname_o_o)->((forall (A_6:(pname->Prop)) (F_53:((pname->Prop)->Prop)), ((finite297249702name_o F_53)->(((member_pname_o A_6) A_200)->((((member_pname_o A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert_pname_o A_6) F_53)))))))->(P_37 F_73)))))) of role axiom named fact_304_finite__subset__induct
% A new axiom: (forall (P_37:(((pname->Prop)->Prop)->Prop)) (A_200:((pname->Prop)->Prop)) (F_73:((pname->Prop)->Prop)), ((finite297249702name_o F_73)->(((ord_le1205211808me_o_o F_73) A_200)->((P_37 bot_bot_pname_o_o)->((forall (A_6:(pname->Prop)) (F_53:((pname->Prop)->Prop)), ((finite297249702name_o F_53)->(((member_pname_o A_6) A_200)->((((member_pname_o A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert_pname_o A_6) F_53)))))))->(P_37 F_73))))))
% FOF formula (forall (P_37:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (A_200:((hoare_1708887482_state->Prop)->Prop)) (F_73:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_73)->(((ord_le1728773982te_o_o F_73) A_200)->((P_37 bot_bo1678742418te_o_o)->((forall (A_6:(hoare_1708887482_state->Prop)) (F_53:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_53)->(((member814030440tate_o A_6) A_200)->((((member814030440tate_o A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert949073679tate_o A_6) F_53)))))))->(P_37 F_73)))))) of role axiom named fact_305_finite__subset__induct
% A new axiom: (forall (P_37:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (A_200:((hoare_1708887482_state->Prop)->Prop)) (F_73:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_73)->(((ord_le1728773982te_o_o F_73) A_200)->((P_37 bot_bo1678742418te_o_o)->((forall (A_6:(hoare_1708887482_state->Prop)) (F_53:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_53)->(((member814030440tate_o A_6) A_200)->((((member814030440tate_o A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert949073679tate_o A_6) F_53)))))))->(P_37 F_73))))))
% FOF formula (forall (P_37:((pname->Prop)->Prop)) (A_200:(pname->Prop)) (F_73:(pname->Prop)), ((finite_finite_pname F_73)->(((ord_less_eq_pname_o F_73) A_200)->((P_37 bot_bot_pname_o)->((forall (A_6:pname) (F_53:(pname->Prop)), ((finite_finite_pname F_53)->(((member_pname A_6) A_200)->((((member_pname A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert_pname A_6) F_53)))))))->(P_37 F_73)))))) of role axiom named fact_306_finite__subset__induct
% A new axiom: (forall (P_37:((pname->Prop)->Prop)) (A_200:(pname->Prop)) (F_73:(pname->Prop)), ((finite_finite_pname F_73)->(((ord_less_eq_pname_o F_73) A_200)->((P_37 bot_bot_pname_o)->((forall (A_6:pname) (F_53:(pname->Prop)), ((finite_finite_pname F_53)->(((member_pname A_6) A_200)->((((member_pname A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert_pname A_6) F_53)))))))->(P_37 F_73))))))
% FOF formula (forall (P_37:((hoare_1708887482_state->Prop)->Prop)) (A_200:(hoare_1708887482_state->Prop)) (F_73:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_73)->(((ord_le777019615tate_o F_73) A_200)->((P_37 bot_bo19817387tate_o)->((forall (A_6:hoare_1708887482_state) (F_53:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_53)->(((member451959335_state A_6) A_200)->((((member451959335_state A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert528405184_state A_6) F_53)))))))->(P_37 F_73)))))) of role axiom named fact_307_finite__subset__induct
% A new axiom: (forall (P_37:((hoare_1708887482_state->Prop)->Prop)) (A_200:(hoare_1708887482_state->Prop)) (F_73:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_73)->(((ord_le777019615tate_o F_73) A_200)->((P_37 bot_bo19817387tate_o)->((forall (A_6:hoare_1708887482_state) (F_53:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_53)->(((member451959335_state A_6) A_200)->((((member451959335_state A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert528405184_state A_6) F_53)))))))->(P_37 F_73))))))
% FOF formula (forall (P:pname), ((wt (body_1 P))->((forall (Y_4:com), (not (((eq option_com) (body P)) (some_com Y_4))))->False))) of role axiom named fact_308_WTs__elim__cases_I7_J
% A new axiom: (forall (P:pname), ((wt (body_1 P))->((forall (Y_4:com), (not (((eq option_com) (body P)) (some_com Y_4))))->False)))
% FOF formula (forall (B_133:(com->Prop)) (A_199:(com->Prop)), ((forall (X_3:com), (((member_com X_3) A_199)->((member_com X_3) B_133)))->((ord_less_eq_com_o A_199) B_133))) of role axiom named fact_309_subsetI
% A new axiom: (forall (B_133:(com->Prop)) (A_199:(com->Prop)), ((forall (X_3:com), (((member_com X_3) A_199)->((member_com X_3) B_133)))->((ord_less_eq_com_o A_199) B_133)))
% FOF formula (forall (B_133:(hoare_1708887482_state->Prop)) (A_199:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_199)->((member451959335_state X_3) B_133)))->((ord_le777019615tate_o A_199) B_133))) of role axiom named fact_310_subsetI
% A new axiom: (forall (B_133:(hoare_1708887482_state->Prop)) (A_199:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_199)->((member451959335_state X_3) B_133)))->((ord_le777019615tate_o A_199) B_133)))
% FOF formula (forall (B_133:(pname->Prop)) (A_199:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_199)->((member_pname X_3) B_133)))->((ord_less_eq_pname_o A_199) B_133))) of role axiom named fact_311_subsetI
% A new axiom: (forall (B_133:(pname->Prop)) (A_199:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_199)->((member_pname X_3) B_133)))->((ord_less_eq_pname_o A_199) B_133)))
% FOF formula (forall (F_72:((pname->Prop)->hoare_1708887482_state)) (A_198:((pname->Prop)->Prop)) (B_132:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_132)->(((ord_le777019615tate_o B_132) ((image_1922967206_state F_72) A_198))->((ex ((pname->Prop)->Prop)) (fun (C_61:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_61) A_198)) (finite297249702name_o C_61))) (((eq (hoare_1708887482_state->Prop)) B_132) ((image_1922967206_state F_72) C_61)))))))) of role axiom named fact_312_finite__subset__image
% A new axiom: (forall (F_72:((pname->Prop)->hoare_1708887482_state)) (A_198:((pname->Prop)->Prop)) (B_132:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_132)->(((ord_le777019615tate_o B_132) ((image_1922967206_state F_72) A_198))->((ex ((pname->Prop)->Prop)) (fun (C_61:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_61) A_198)) (finite297249702name_o C_61))) (((eq (hoare_1708887482_state->Prop)) B_132) ((image_1922967206_state F_72) C_61))))))))
% FOF formula (forall (F_72:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (A_198:((hoare_1708887482_state->Prop)->Prop)) (B_132:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_132)->(((ord_le777019615tate_o B_132) ((image_27005066_state F_72) A_198))->((ex ((hoare_1708887482_state->Prop)->Prop)) (fun (C_61:((hoare_1708887482_state->Prop)->Prop))=> ((and ((and ((ord_le1728773982te_o_o C_61) A_198)) (finite1329924456tate_o C_61))) (((eq (hoare_1708887482_state->Prop)) B_132) ((image_27005066_state F_72) C_61)))))))) of role axiom named fact_313_finite__subset__image
% A new axiom: (forall (F_72:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (A_198:((hoare_1708887482_state->Prop)->Prop)) (B_132:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_132)->(((ord_le777019615tate_o B_132) ((image_27005066_state F_72) A_198))->((ex ((hoare_1708887482_state->Prop)->Prop)) (fun (C_61:((hoare_1708887482_state->Prop)->Prop))=> ((and ((and ((ord_le1728773982te_o_o C_61) A_198)) (finite1329924456tate_o C_61))) (((eq (hoare_1708887482_state->Prop)) B_132) ((image_27005066_state F_72) C_61))))))))
% FOF formula (forall (F_72:((pname->Prop)->pname)) (A_198:((pname->Prop)->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_pname_o_pname F_72) A_198))->((ex ((pname->Prop)->Prop)) (fun (C_61:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_61) A_198)) (finite297249702name_o C_61))) (((eq (pname->Prop)) B_132) ((image_pname_o_pname F_72) C_61)))))))) of role axiom named fact_314_finite__subset__image
% A new axiom: (forall (F_72:((pname->Prop)->pname)) (A_198:((pname->Prop)->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_pname_o_pname F_72) A_198))->((ex ((pname->Prop)->Prop)) (fun (C_61:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_61) A_198)) (finite297249702name_o C_61))) (((eq (pname->Prop)) B_132) ((image_pname_o_pname F_72) C_61))))))))
% FOF formula (forall (F_72:((hoare_1708887482_state->Prop)->pname)) (A_198:((hoare_1708887482_state->Prop)->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_2051418740_pname F_72) A_198))->((ex ((hoare_1708887482_state->Prop)->Prop)) (fun (C_61:((hoare_1708887482_state->Prop)->Prop))=> ((and ((and ((ord_le1728773982te_o_o C_61) A_198)) (finite1329924456tate_o C_61))) (((eq (pname->Prop)) B_132) ((image_2051418740_pname F_72) C_61)))))))) of role axiom named fact_315_finite__subset__image
% A new axiom: (forall (F_72:((hoare_1708887482_state->Prop)->pname)) (A_198:((hoare_1708887482_state->Prop)->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_2051418740_pname F_72) A_198))->((ex ((hoare_1708887482_state->Prop)->Prop)) (fun (C_61:((hoare_1708887482_state->Prop)->Prop))=> ((and ((and ((ord_le1728773982te_o_o C_61) A_198)) (finite1329924456tate_o C_61))) (((eq (pname->Prop)) B_132) ((image_2051418740_pname F_72) C_61))))))))
% FOF formula (forall (F_72:(hoare_1708887482_state->(pname->Prop))) (A_198:(hoare_1708887482_state->Prop)) (B_132:((pname->Prop)->Prop)), ((finite297249702name_o B_132)->(((ord_le1205211808me_o_o B_132) ((image_1552895654name_o F_72) A_198))->((ex (hoare_1708887482_state->Prop)) (fun (C_61:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o C_61) A_198)) (finite1625599783_state C_61))) (((eq ((pname->Prop)->Prop)) B_132) ((image_1552895654name_o F_72) C_61)))))))) of role axiom named fact_316_finite__subset__image
% A new axiom: (forall (F_72:(hoare_1708887482_state->(pname->Prop))) (A_198:(hoare_1708887482_state->Prop)) (B_132:((pname->Prop)->Prop)), ((finite297249702name_o B_132)->(((ord_le1205211808me_o_o B_132) ((image_1552895654name_o F_72) A_198))->((ex (hoare_1708887482_state->Prop)) (fun (C_61:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o C_61) A_198)) (finite1625599783_state C_61))) (((eq ((pname->Prop)->Prop)) B_132) ((image_1552895654name_o F_72) C_61))))))))
% FOF formula (forall (F_72:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (A_198:(hoare_1708887482_state->Prop)) (B_132:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_132)->(((ord_le1728773982te_o_o B_132) ((image_1551509096tate_o F_72) A_198))->((ex (hoare_1708887482_state->Prop)) (fun (C_61:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o C_61) A_198)) (finite1625599783_state C_61))) (((eq ((hoare_1708887482_state->Prop)->Prop)) B_132) ((image_1551509096tate_o F_72) C_61)))))))) of role axiom named fact_317_finite__subset__image
% A new axiom: (forall (F_72:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (A_198:(hoare_1708887482_state->Prop)) (B_132:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_132)->(((ord_le1728773982te_o_o B_132) ((image_1551509096tate_o F_72) A_198))->((ex (hoare_1708887482_state->Prop)) (fun (C_61:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o C_61) A_198)) (finite1625599783_state C_61))) (((eq ((hoare_1708887482_state->Prop)->Prop)) B_132) ((image_1551509096tate_o F_72) C_61))))))))
% FOF formula (forall (F_72:(hoare_1708887482_state->pname)) (A_198:(hoare_1708887482_state->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_1509414295_pname F_72) A_198))->((ex (hoare_1708887482_state->Prop)) (fun (C_61:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o C_61) A_198)) (finite1625599783_state C_61))) (((eq (pname->Prop)) B_132) ((image_1509414295_pname F_72) C_61)))))))) of role axiom named fact_318_finite__subset__image
% A new axiom: (forall (F_72:(hoare_1708887482_state->pname)) (A_198:(hoare_1708887482_state->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_1509414295_pname F_72) A_198))->((ex (hoare_1708887482_state->Prop)) (fun (C_61:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o C_61) A_198)) (finite1625599783_state C_61))) (((eq (pname->Prop)) B_132) ((image_1509414295_pname F_72) C_61))))))))
% FOF formula (forall (F_72:(pname->(pname->Prop))) (A_198:(pname->Prop)) (B_132:((pname->Prop)->Prop)), ((finite297249702name_o B_132)->(((ord_le1205211808me_o_o B_132) ((image_pname_pname_o F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq ((pname->Prop)->Prop)) B_132) ((image_pname_pname_o F_72) C_61)))))))) of role axiom named fact_319_finite__subset__image
% A new axiom: (forall (F_72:(pname->(pname->Prop))) (A_198:(pname->Prop)) (B_132:((pname->Prop)->Prop)), ((finite297249702name_o B_132)->(((ord_le1205211808me_o_o B_132) ((image_pname_pname_o F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq ((pname->Prop)->Prop)) B_132) ((image_pname_pname_o F_72) C_61))))))))
% FOF formula (forall (F_72:(pname->(hoare_1708887482_state->Prop))) (A_198:(pname->Prop)) (B_132:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_132)->(((ord_le1728773982te_o_o B_132) ((image_425134806tate_o F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq ((hoare_1708887482_state->Prop)->Prop)) B_132) ((image_425134806tate_o F_72) C_61)))))))) of role axiom named fact_320_finite__subset__image
% A new axiom: (forall (F_72:(pname->(hoare_1708887482_state->Prop))) (A_198:(pname->Prop)) (B_132:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_132)->(((ord_le1728773982te_o_o B_132) ((image_425134806tate_o F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq ((hoare_1708887482_state->Prop)->Prop)) B_132) ((image_425134806tate_o F_72) C_61))))))))
% FOF formula (forall (F_72:(pname->pname)) (A_198:(pname->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_pname_pname F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq (pname->Prop)) B_132) ((image_pname_pname F_72) C_61)))))))) of role axiom named fact_321_finite__subset__image
% A new axiom: (forall (F_72:(pname->pname)) (A_198:(pname->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_pname_pname F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq (pname->Prop)) B_132) ((image_pname_pname F_72) C_61))))))))
% FOF formula (forall (F_72:(pname->hoare_1708887482_state)) (A_198:(pname->Prop)) (B_132:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_132)->(((ord_le777019615tate_o B_132) ((image_1116629049_state F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq (hoare_1708887482_state->Prop)) B_132) ((image_1116629049_state F_72) C_61)))))))) of role axiom named fact_322_finite__subset__image
% A new axiom: (forall (F_72:(pname->hoare_1708887482_state)) (A_198:(pname->Prop)) (B_132:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_132)->(((ord_le777019615tate_o B_132) ((image_1116629049_state F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq (hoare_1708887482_state->Prop)) B_132) ((image_1116629049_state F_72) C_61))))))))
% FOF formula (finite_finite_pname (dom_pname_com body)) of role axiom named fact_323_finite__dom__body
% A new axiom: (finite_finite_pname (dom_pname_com body))
% FOF formula (forall (P_36:((com->Prop)->Prop)) (F_71:(com->Prop)), ((finite_finite_com F_71)->((P_36 bot_bot_com_o)->((forall (X_3:com) (F_53:(com->Prop)), ((finite_finite_com F_53)->((((member_com X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert_com X_3) F_53))))))->(P_36 F_71))))) of role axiom named fact_324_finite__induct
% A new axiom: (forall (P_36:((com->Prop)->Prop)) (F_71:(com->Prop)), ((finite_finite_com F_71)->((P_36 bot_bot_com_o)->((forall (X_3:com) (F_53:(com->Prop)), ((finite_finite_com F_53)->((((member_com X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert_com X_3) F_53))))))->(P_36 F_71)))))
% FOF formula (forall (P_36:(((pname->Prop)->Prop)->Prop)) (F_71:((pname->Prop)->Prop)), ((finite297249702name_o F_71)->((P_36 bot_bot_pname_o_o)->((forall (X_3:(pname->Prop)) (F_53:((pname->Prop)->Prop)), ((finite297249702name_o F_53)->((((member_pname_o X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert_pname_o X_3) F_53))))))->(P_36 F_71))))) of role axiom named fact_325_finite__induct
% A new axiom: (forall (P_36:(((pname->Prop)->Prop)->Prop)) (F_71:((pname->Prop)->Prop)), ((finite297249702name_o F_71)->((P_36 bot_bot_pname_o_o)->((forall (X_3:(pname->Prop)) (F_53:((pname->Prop)->Prop)), ((finite297249702name_o F_53)->((((member_pname_o X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert_pname_o X_3) F_53))))))->(P_36 F_71)))))
% FOF formula (forall (P_36:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (F_71:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_71)->((P_36 bot_bo1678742418te_o_o)->((forall (X_3:(hoare_1708887482_state->Prop)) (F_53:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_53)->((((member814030440tate_o X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert949073679tate_o X_3) F_53))))))->(P_36 F_71))))) of role axiom named fact_326_finite__induct
% A new axiom: (forall (P_36:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (F_71:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_71)->((P_36 bot_bo1678742418te_o_o)->((forall (X_3:(hoare_1708887482_state->Prop)) (F_53:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_53)->((((member814030440tate_o X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert949073679tate_o X_3) F_53))))))->(P_36 F_71)))))
% FOF formula (forall (P_36:((pname->Prop)->Prop)) (F_71:(pname->Prop)), ((finite_finite_pname F_71)->((P_36 bot_bot_pname_o)->((forall (X_3:pname) (F_53:(pname->Prop)), ((finite_finite_pname F_53)->((((member_pname X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert_pname X_3) F_53))))))->(P_36 F_71))))) of role axiom named fact_327_finite__induct
% A new axiom: (forall (P_36:((pname->Prop)->Prop)) (F_71:(pname->Prop)), ((finite_finite_pname F_71)->((P_36 bot_bot_pname_o)->((forall (X_3:pname) (F_53:(pname->Prop)), ((finite_finite_pname F_53)->((((member_pname X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert_pname X_3) F_53))))))->(P_36 F_71)))))
% FOF formula (forall (P_36:((hoare_1708887482_state->Prop)->Prop)) (F_71:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_71)->((P_36 bot_bo19817387tate_o)->((forall (X_3:hoare_1708887482_state) (F_53:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_53)->((((member451959335_state X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert528405184_state X_3) F_53))))))->(P_36 F_71))))) of role axiom named fact_328_finite__induct
% A new axiom: (forall (P_36:((hoare_1708887482_state->Prop)->Prop)) (F_71:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_71)->((P_36 bot_bo19817387tate_o)->((forall (X_3:hoare_1708887482_state) (F_53:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_53)->((((member451959335_state X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert528405184_state X_3) F_53))))))->(P_36 F_71)))))
% FOF formula (forall (A_197:(com->Prop)), ((iff (finite_finite_com A_197)) ((or (((eq (com->Prop)) A_197) bot_bot_com_o)) ((ex (com->Prop)) (fun (A_39:(com->Prop))=> ((ex com) (fun (A_6:com)=> ((and (((eq (com->Prop)) A_197) ((insert_com A_6) A_39))) (finite_finite_com A_39))))))))) of role axiom named fact_329_finite_Osimps
% A new axiom: (forall (A_197:(com->Prop)), ((iff (finite_finite_com A_197)) ((or (((eq (com->Prop)) A_197) bot_bot_com_o)) ((ex (com->Prop)) (fun (A_39:(com->Prop))=> ((ex com) (fun (A_6:com)=> ((and (((eq (com->Prop)) A_197) ((insert_com A_6) A_39))) (finite_finite_com A_39)))))))))
% FOF formula (forall (A_197:((pname->Prop)->Prop)), ((iff (finite297249702name_o A_197)) ((or (((eq ((pname->Prop)->Prop)) A_197) bot_bot_pname_o_o)) ((ex ((pname->Prop)->Prop)) (fun (A_39:((pname->Prop)->Prop))=> ((ex (pname->Prop)) (fun (A_6:(pname->Prop))=> ((and (((eq ((pname->Prop)->Prop)) A_197) ((insert_pname_o A_6) A_39))) (finite297249702name_o A_39))))))))) of role axiom named fact_330_finite_Osimps
% A new axiom: (forall (A_197:((pname->Prop)->Prop)), ((iff (finite297249702name_o A_197)) ((or (((eq ((pname->Prop)->Prop)) A_197) bot_bot_pname_o_o)) ((ex ((pname->Prop)->Prop)) (fun (A_39:((pname->Prop)->Prop))=> ((ex (pname->Prop)) (fun (A_6:(pname->Prop))=> ((and (((eq ((pname->Prop)->Prop)) A_197) ((insert_pname_o A_6) A_39))) (finite297249702name_o A_39)))))))))
% FOF formula (forall (A_197:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o A_197)) ((or (((eq ((hoare_1708887482_state->Prop)->Prop)) A_197) bot_bo1678742418te_o_o)) ((ex ((hoare_1708887482_state->Prop)->Prop)) (fun (A_39:((hoare_1708887482_state->Prop)->Prop))=> ((ex (hoare_1708887482_state->Prop)) (fun (A_6:(hoare_1708887482_state->Prop))=> ((and (((eq ((hoare_1708887482_state->Prop)->Prop)) A_197) ((insert949073679tate_o A_6) A_39))) (finite1329924456tate_o A_39))))))))) of role axiom named fact_331_finite_Osimps
% A new axiom: (forall (A_197:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o A_197)) ((or (((eq ((hoare_1708887482_state->Prop)->Prop)) A_197) bot_bo1678742418te_o_o)) ((ex ((hoare_1708887482_state->Prop)->Prop)) (fun (A_39:((hoare_1708887482_state->Prop)->Prop))=> ((ex (hoare_1708887482_state->Prop)) (fun (A_6:(hoare_1708887482_state->Prop))=> ((and (((eq ((hoare_1708887482_state->Prop)->Prop)) A_197) ((insert949073679tate_o A_6) A_39))) (finite1329924456tate_o A_39)))))))))
% FOF formula (forall (A_197:(pname->Prop)), ((iff (finite_finite_pname A_197)) ((or (((eq (pname->Prop)) A_197) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_39:(pname->Prop))=> ((ex pname) (fun (A_6:pname)=> ((and (((eq (pname->Prop)) A_197) ((insert_pname A_6) A_39))) (finite_finite_pname A_39))))))))) of role axiom named fact_332_finite_Osimps
% A new axiom: (forall (A_197:(pname->Prop)), ((iff (finite_finite_pname A_197)) ((or (((eq (pname->Prop)) A_197) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_39:(pname->Prop))=> ((ex pname) (fun (A_6:pname)=> ((and (((eq (pname->Prop)) A_197) ((insert_pname A_6) A_39))) (finite_finite_pname A_39)))))))))
% FOF formula (forall (A_197:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state A_197)) ((or (((eq (hoare_1708887482_state->Prop)) A_197) bot_bo19817387tate_o)) ((ex (hoare_1708887482_state->Prop)) (fun (A_39:(hoare_1708887482_state->Prop))=> ((ex hoare_1708887482_state) (fun (A_6:hoare_1708887482_state)=> ((and (((eq (hoare_1708887482_state->Prop)) A_197) ((insert528405184_state A_6) A_39))) (finite1625599783_state A_39))))))))) of role axiom named fact_333_finite_Osimps
% A new axiom: (forall (A_197:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state A_197)) ((or (((eq (hoare_1708887482_state->Prop)) A_197) bot_bo19817387tate_o)) ((ex (hoare_1708887482_state->Prop)) (fun (A_39:(hoare_1708887482_state->Prop))=> ((ex hoare_1708887482_state) (fun (A_6:hoare_1708887482_state)=> ((and (((eq (hoare_1708887482_state->Prop)) A_197) ((insert528405184_state A_6) A_39))) (finite1625599783_state A_39)))))))))
% FOF formula (forall (F_70:(com->hoare_1708887482_state)) (A_196:(com->Prop)), (((finite_finite_com A_196)->False)->((finite1625599783_state ((image_934102463_state F_70) A_196))->((ex com) (fun (X_3:com)=> ((and ((member_com X_3) A_196)) ((finite_finite_com (collect_com (fun (A_6:com)=> ((and ((member_com A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_334_pigeonhole__infinite
% A new axiom: (forall (F_70:(com->hoare_1708887482_state)) (A_196:(com->Prop)), (((finite_finite_com A_196)->False)->((finite1625599783_state ((image_934102463_state F_70) A_196))->((ex com) (fun (X_3:com)=> ((and ((member_com X_3) A_196)) ((finite_finite_com (collect_com (fun (A_6:com)=> ((and ((member_com A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:(hoare_1708887482_state->hoare_1708887482_state)) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite1625599783_state ((image_757158439_state F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_335_pigeonhole__infinite
% A new axiom: (forall (F_70:(hoare_1708887482_state->hoare_1708887482_state)) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite1625599783_state ((image_757158439_state F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:((pname->Prop)->hoare_1708887482_state)) (A_196:((pname->Prop)->Prop)), (((finite297249702name_o A_196)->False)->((finite1625599783_state ((image_1922967206_state F_70) A_196))->((ex (pname->Prop)) (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_196)) ((finite297249702name_o (collect_pname_o (fun (A_6:(pname->Prop))=> ((and ((member_pname_o A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_336_pigeonhole__infinite
% A new axiom: (forall (F_70:((pname->Prop)->hoare_1708887482_state)) (A_196:((pname->Prop)->Prop)), (((finite297249702name_o A_196)->False)->((finite1625599783_state ((image_1922967206_state F_70) A_196))->((ex (pname->Prop)) (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_196)) ((finite297249702name_o (collect_pname_o (fun (A_6:(pname->Prop))=> ((and ((member_pname_o A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (A_196:((hoare_1708887482_state->Prop)->Prop)), (((finite1329924456tate_o A_196)->False)->((finite1625599783_state ((image_27005066_state F_70) A_196))->((ex (hoare_1708887482_state->Prop)) (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_196)) ((finite1329924456tate_o (collec219771562tate_o (fun (A_6:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_337_pigeonhole__infinite
% A new axiom: (forall (F_70:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (A_196:((hoare_1708887482_state->Prop)->Prop)), (((finite1329924456tate_o A_196)->False)->((finite1625599783_state ((image_27005066_state F_70) A_196))->((ex (hoare_1708887482_state->Prop)) (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_196)) ((finite1329924456tate_o (collec219771562tate_o (fun (A_6:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:(com->pname)) (A_196:(com->Prop)), (((finite_finite_com A_196)->False)->((finite_finite_pname ((image_com_pname F_70) A_196))->((ex com) (fun (X_3:com)=> ((and ((member_com X_3) A_196)) ((finite_finite_com (collect_com (fun (A_6:com)=> ((and ((member_com A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_338_pigeonhole__infinite
% A new axiom: (forall (F_70:(com->pname)) (A_196:(com->Prop)), (((finite_finite_com A_196)->False)->((finite_finite_pname ((image_com_pname F_70) A_196))->((ex com) (fun (X_3:com)=> ((and ((member_com X_3) A_196)) ((finite_finite_com (collect_com (fun (A_6:com)=> ((and ((member_com A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:(hoare_1708887482_state->pname)) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite_finite_pname ((image_1509414295_pname F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_339_pigeonhole__infinite
% A new axiom: (forall (F_70:(hoare_1708887482_state->pname)) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite_finite_pname ((image_1509414295_pname F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:(pname->pname)) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite_finite_pname ((image_pname_pname F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_340_pigeonhole__infinite
% A new axiom: (forall (F_70:(pname->pname)) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite_finite_pname ((image_pname_pname F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:((pname->Prop)->pname)) (A_196:((pname->Prop)->Prop)), (((finite297249702name_o A_196)->False)->((finite_finite_pname ((image_pname_o_pname F_70) A_196))->((ex (pname->Prop)) (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_196)) ((finite297249702name_o (collect_pname_o (fun (A_6:(pname->Prop))=> ((and ((member_pname_o A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_341_pigeonhole__infinite
% A new axiom: (forall (F_70:((pname->Prop)->pname)) (A_196:((pname->Prop)->Prop)), (((finite297249702name_o A_196)->False)->((finite_finite_pname ((image_pname_o_pname F_70) A_196))->((ex (pname->Prop)) (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_196)) ((finite297249702name_o (collect_pname_o (fun (A_6:(pname->Prop))=> ((and ((member_pname_o A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:((hoare_1708887482_state->Prop)->pname)) (A_196:((hoare_1708887482_state->Prop)->Prop)), (((finite1329924456tate_o A_196)->False)->((finite_finite_pname ((image_2051418740_pname F_70) A_196))->((ex (hoare_1708887482_state->Prop)) (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_196)) ((finite1329924456tate_o (collec219771562tate_o (fun (A_6:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_342_pigeonhole__infinite
% A new axiom: (forall (F_70:((hoare_1708887482_state->Prop)->pname)) (A_196:((hoare_1708887482_state->Prop)->Prop)), (((finite1329924456tate_o A_196)->False)->((finite_finite_pname ((image_2051418740_pname F_70) A_196))->((ex (hoare_1708887482_state->Prop)) (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_196)) ((finite1329924456tate_o (collec219771562tate_o (fun (A_6:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:(hoare_1708887482_state->(pname->Prop))) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite297249702name_o ((image_1552895654name_o F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq (pname->Prop)) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_343_pigeonhole__infinite
% A new axiom: (forall (F_70:(hoare_1708887482_state->(pname->Prop))) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite297249702name_o ((image_1552895654name_o F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq (pname->Prop)) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite1329924456tate_o ((image_1551509096tate_o F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq (hoare_1708887482_state->Prop)) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_344_pigeonhole__infinite
% A new axiom: (forall (F_70:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite1329924456tate_o ((image_1551509096tate_o F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq (hoare_1708887482_state->Prop)) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:(pname->(pname->Prop))) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite297249702name_o ((image_pname_pname_o F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq (pname->Prop)) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_345_pigeonhole__infinite
% A new axiom: (forall (F_70:(pname->(pname->Prop))) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite297249702name_o ((image_pname_pname_o F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq (pname->Prop)) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:(pname->(hoare_1708887482_state->Prop))) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite1329924456tate_o ((image_425134806tate_o F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq (hoare_1708887482_state->Prop)) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_346_pigeonhole__infinite
% A new axiom: (forall (F_70:(pname->(hoare_1708887482_state->Prop))) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite1329924456tate_o ((image_425134806tate_o F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq (hoare_1708887482_state->Prop)) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (F_70:(pname->hoare_1708887482_state)) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite1625599783_state ((image_1116629049_state F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False))))))) of role axiom named fact_347_pigeonhole__infinite
% A new axiom: (forall (F_70:(pname->hoare_1708887482_state)) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite1625599783_state ((image_1116629049_state F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False)))))))
% FOF formula (forall (Pname_1:pname) (Pname:pname), ((iff (((eq com) (body_1 Pname_1)) (body_1 Pname))) (((eq pname) Pname_1) Pname))) of role axiom named fact_348_com_Osimps_I6_J
% A new axiom: (forall (Pname_1:pname) (Pname:pname), ((iff (((eq com) (body_1 Pname_1)) (body_1 Pname))) (((eq pname) Pname_1) Pname)))
% FOF formula (forall (G_7:(hoare_1708887482_state->Prop)) (Procs_3:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_7) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3))) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) Procs_3))->((finite_finite_pname Procs_3)->((hoare_90032982_state G_7) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3))))) of role axiom named fact_349_MGT__Body
% A new axiom: (forall (G_7:(hoare_1708887482_state->Prop)) (Procs_3:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_7) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3))) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) Procs_3))->((finite_finite_pname Procs_3)->((hoare_90032982_state G_7) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3)))))
% FOF formula (forall (A_195:com) (M_4:(com->option_com)), (((member_com A_195) (dom_com_com M_4))->((ex com) (fun (B_131:com)=> (((eq option_com) (M_4 A_195)) (some_com B_131)))))) of role axiom named fact_350_domD
% A new axiom: (forall (A_195:com) (M_4:(com->option_com)), (((member_com A_195) (dom_com_com M_4))->((ex com) (fun (B_131:com)=> (((eq option_com) (M_4 A_195)) (some_com B_131))))))
% FOF formula (forall (A_195:hoare_1708887482_state) (M_4:(hoare_1708887482_state->option_pname)), (((member451959335_state A_195) (dom_Ho1805192458_pname M_4))->((ex pname) (fun (B_131:pname)=> (((eq option_pname) (M_4 A_195)) (some_pname B_131)))))) of role axiom named fact_351_domD
% A new axiom: (forall (A_195:hoare_1708887482_state) (M_4:(hoare_1708887482_state->option_pname)), (((member451959335_state A_195) (dom_Ho1805192458_pname M_4))->((ex pname) (fun (B_131:pname)=> (((eq option_pname) (M_4 A_195)) (some_pname B_131))))))
% FOF formula (forall (A_195:hoare_1708887482_state) (M_4:(hoare_1708887482_state->option1624383643_state)), (((member451959335_state A_195) (dom_Ho1703271284_state M_4))->((ex hoare_1708887482_state) (fun (B_131:hoare_1708887482_state)=> (((eq option1624383643_state) (M_4 A_195)) (some_H1974565227_state B_131)))))) of role axiom named fact_352_domD
% A new axiom: (forall (A_195:hoare_1708887482_state) (M_4:(hoare_1708887482_state->option1624383643_state)), (((member451959335_state A_195) (dom_Ho1703271284_state M_4))->((ex hoare_1708887482_state) (fun (B_131:hoare_1708887482_state)=> (((eq option1624383643_state) (M_4 A_195)) (some_H1974565227_state B_131))))))
% FOF formula (forall (A_195:pname) (M_4:(pname->option_pname)), (((member_pname A_195) (dom_pname_pname M_4))->((ex pname) (fun (B_131:pname)=> (((eq option_pname) (M_4 A_195)) (some_pname B_131)))))) of role axiom named fact_353_domD
% A new axiom: (forall (A_195:pname) (M_4:(pname->option_pname)), (((member_pname A_195) (dom_pname_pname M_4))->((ex pname) (fun (B_131:pname)=> (((eq option_pname) (M_4 A_195)) (some_pname B_131))))))
% FOF formula (forall (A_195:pname) (M_4:(pname->option1624383643_state)), (((member_pname A_195) (dom_pn1412407212_state M_4))->((ex hoare_1708887482_state) (fun (B_131:hoare_1708887482_state)=> (((eq option1624383643_state) (M_4 A_195)) (some_H1974565227_state B_131)))))) of role axiom named fact_354_domD
% A new axiom: (forall (A_195:pname) (M_4:(pname->option1624383643_state)), (((member_pname A_195) (dom_pn1412407212_state M_4))->((ex hoare_1708887482_state) (fun (B_131:hoare_1708887482_state)=> (((eq option1624383643_state) (M_4 A_195)) (some_H1974565227_state B_131))))))
% FOF formula (forall (A_195:pname) (M_4:(pname->option_com)), (((member_pname A_195) (dom_pname_com M_4))->((ex com) (fun (B_131:com)=> (((eq option_com) (M_4 A_195)) (some_com B_131)))))) of role axiom named fact_355_domD
% A new axiom: (forall (A_195:pname) (M_4:(pname->option_com)), (((member_pname A_195) (dom_pname_com M_4))->((ex com) (fun (B_131:com)=> (((eq option_com) (M_4 A_195)) (some_com B_131))))))
% FOF formula (forall (X_102:pname), (((eq pname) (the_elem_pname ((insert_pname X_102) bot_bot_pname_o))) X_102)) of role axiom named fact_356_the__elem__eq
% A new axiom: (forall (X_102:pname), (((eq pname) (the_elem_pname ((insert_pname X_102) bot_bot_pname_o))) X_102))
% FOF formula (forall (X_102:com), (((eq com) (the_elem_com ((insert_com X_102) bot_bot_com_o))) X_102)) of role axiom named fact_357_the__elem__eq
% A new axiom: (forall (X_102:com), (((eq com) (the_elem_com ((insert_com X_102) bot_bot_com_o))) X_102))
% FOF formula (forall (X_102:hoare_1708887482_state), (((eq hoare_1708887482_state) (the_el864710747_state ((insert528405184_state X_102) bot_bo19817387tate_o))) X_102)) of role axiom named fact_358_the__elem__eq
% A new axiom: (forall (X_102:hoare_1708887482_state), (((eq hoare_1708887482_state) (the_el864710747_state ((insert528405184_state X_102) bot_bo19817387tate_o))) X_102))
% FOF formula (forall (F_69:(hoare_1708887482_state->com)) (B_130:(com->Prop)) (A_194:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_194)->((member_com (F_69 X_3)) B_130)))->((ord_less_eq_com_o ((image_1604448413te_com F_69) A_194)) B_130))) of role axiom named fact_359_image__subsetI
% A new axiom: (forall (F_69:(hoare_1708887482_state->com)) (B_130:(com->Prop)) (A_194:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_194)->((member_com (F_69 X_3)) B_130)))->((ord_less_eq_com_o ((image_1604448413te_com F_69) A_194)) B_130)))
% FOF formula (forall (F_69:(hoare_1708887482_state->pname)) (B_130:(pname->Prop)) (A_194:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_194)->((member_pname (F_69 X_3)) B_130)))->((ord_less_eq_pname_o ((image_1509414295_pname F_69) A_194)) B_130))) of role axiom named fact_360_image__subsetI
% A new axiom: (forall (F_69:(hoare_1708887482_state->pname)) (B_130:(pname->Prop)) (A_194:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_194)->((member_pname (F_69 X_3)) B_130)))->((ord_less_eq_pname_o ((image_1509414295_pname F_69) A_194)) B_130)))
% FOF formula (forall (F_69:(pname->com)) (B_130:(com->Prop)) (A_194:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_194)->((member_com (F_69 X_3)) B_130)))->((ord_less_eq_com_o ((image_pname_com F_69) A_194)) B_130))) of role axiom named fact_361_image__subsetI
% A new axiom: (forall (F_69:(pname->com)) (B_130:(com->Prop)) (A_194:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_194)->((member_com (F_69 X_3)) B_130)))->((ord_less_eq_com_o ((image_pname_com F_69) A_194)) B_130)))
% FOF formula (forall (F_69:(pname->pname)) (B_130:(pname->Prop)) (A_194:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_194)->((member_pname (F_69 X_3)) B_130)))->((ord_less_eq_pname_o ((image_pname_pname F_69) A_194)) B_130))) of role axiom named fact_362_image__subsetI
% A new axiom: (forall (F_69:(pname->pname)) (B_130:(pname->Prop)) (A_194:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_194)->((member_pname (F_69 X_3)) B_130)))->((ord_less_eq_pname_o ((image_pname_pname F_69) A_194)) B_130)))
% FOF formula (forall (F_69:(com->hoare_1708887482_state)) (B_130:(hoare_1708887482_state->Prop)) (A_194:(com->Prop)), ((forall (X_3:com), (((member_com X_3) A_194)->((member451959335_state (F_69 X_3)) B_130)))->((ord_le777019615tate_o ((image_934102463_state F_69) A_194)) B_130))) of role axiom named fact_363_image__subsetI
% A new axiom: (forall (F_69:(com->hoare_1708887482_state)) (B_130:(hoare_1708887482_state->Prop)) (A_194:(com->Prop)), ((forall (X_3:com), (((member_com X_3) A_194)->((member451959335_state (F_69 X_3)) B_130)))->((ord_le777019615tate_o ((image_934102463_state F_69) A_194)) B_130)))
% FOF formula (forall (F_69:(com->pname)) (B_130:(pname->Prop)) (A_194:(com->Prop)), ((forall (X_3:com), (((member_com X_3) A_194)->((member_pname (F_69 X_3)) B_130)))->((ord_less_eq_pname_o ((image_com_pname F_69) A_194)) B_130))) of role axiom named fact_364_image__subsetI
% A new axiom: (forall (F_69:(com->pname)) (B_130:(pname->Prop)) (A_194:(com->Prop)), ((forall (X_3:com), (((member_com X_3) A_194)->((member_pname (F_69 X_3)) B_130)))->((ord_less_eq_pname_o ((image_com_pname F_69) A_194)) B_130)))
% FOF formula (forall (F_69:(pname->hoare_1708887482_state)) (B_130:(hoare_1708887482_state->Prop)) (A_194:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_194)->((member451959335_state (F_69 X_3)) B_130)))->((ord_le777019615tate_o ((image_1116629049_state F_69) A_194)) B_130))) of role axiom named fact_365_image__subsetI
% A new axiom: (forall (F_69:(pname->hoare_1708887482_state)) (B_130:(hoare_1708887482_state->Prop)) (A_194:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_194)->((member451959335_state (F_69 X_3)) B_130)))->((ord_le777019615tate_o ((image_1116629049_state F_69) A_194)) B_130)))
% FOF formula (forall (X_101:(pname->Prop)), ((ord_less_eq_pname_o X_101) X_101)) of role axiom named fact_366_order__refl
% A new axiom: (forall (X_101:(pname->Prop)), ((ord_less_eq_pname_o X_101) X_101))
% FOF formula (forall (X_101:Prop), ((ord_less_eq_o X_101) X_101)) of role axiom named fact_367_order__refl
% A new axiom: (forall (X_101:Prop), ((ord_less_eq_o X_101) X_101))
% FOF formula (forall (X_101:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o X_101) X_101)) of role axiom named fact_368_order__refl
% A new axiom: (forall (X_101:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o X_101) X_101))
% FOF formula (forall (A_193:(com->Prop)), ((iff (not (((eq (com->Prop)) A_193) bot_bot_com_o))) ((ex com) (fun (X_3:com)=> ((ex (com->Prop)) (fun (B_84:(com->Prop))=> ((and (((eq (com->Prop)) A_193) ((insert_com X_3) B_84))) (((member_com X_3) B_84)->False)))))))) of role axiom named fact_369_nonempty__iff
% A new axiom: (forall (A_193:(com->Prop)), ((iff (not (((eq (com->Prop)) A_193) bot_bot_com_o))) ((ex com) (fun (X_3:com)=> ((ex (com->Prop)) (fun (B_84:(com->Prop))=> ((and (((eq (com->Prop)) A_193) ((insert_com X_3) B_84))) (((member_com X_3) B_84)->False))))))))
% FOF formula (forall (A_193:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_193) bot_bot_pname_o))) ((ex pname) (fun (X_3:pname)=> ((ex (pname->Prop)) (fun (B_84:(pname->Prop))=> ((and (((eq (pname->Prop)) A_193) ((insert_pname X_3) B_84))) (((member_pname X_3) B_84)->False)))))))) of role axiom named fact_370_nonempty__iff
% A new axiom: (forall (A_193:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_193) bot_bot_pname_o))) ((ex pname) (fun (X_3:pname)=> ((ex (pname->Prop)) (fun (B_84:(pname->Prop))=> ((and (((eq (pname->Prop)) A_193) ((insert_pname X_3) B_84))) (((member_pname X_3) B_84)->False))))))))
% FOF formula (forall (A_193:(hoare_1708887482_state->Prop)), ((iff (not (((eq (hoare_1708887482_state->Prop)) A_193) bot_bo19817387tate_o))) ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((ex (hoare_1708887482_state->Prop)) (fun (B_84:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_193) ((insert528405184_state X_3) B_84))) (((member451959335_state X_3) B_84)->False)))))))) of role axiom named fact_371_nonempty__iff
% A new axiom: (forall (A_193:(hoare_1708887482_state->Prop)), ((iff (not (((eq (hoare_1708887482_state->Prop)) A_193) bot_bo19817387tate_o))) ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((ex (hoare_1708887482_state->Prop)) (fun (B_84:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_193) ((insert528405184_state X_3) B_84))) (((member451959335_state X_3) B_84)->False))))))))
% FOF formula (forall (X_100:pname), (((eq pname) (the_pname_1 (some_pname X_100))) X_100)) of role axiom named fact_372_the_Osimps
% A new axiom: (forall (X_100:pname), (((eq pname) (the_pname_1 (some_pname X_100))) X_100))
% FOF formula (forall (X_100:hoare_1708887482_state), (((eq hoare_1708887482_state) (the_Ho963921505_state (some_H1974565227_state X_100))) X_100)) of role axiom named fact_373_the_Osimps
% A new axiom: (forall (X_100:hoare_1708887482_state), (((eq hoare_1708887482_state) (the_Ho963921505_state (some_H1974565227_state X_100))) X_100))
% FOF formula (forall (X_100:com), (((eq com) (the_com (some_com X_100))) X_100)) of role axiom named fact_374_the_Osimps
% A new axiom: (forall (X_100:com), (((eq com) (the_com (some_com X_100))) X_100))
% FOF formula (forall (G_31:(hoare_1708887482_state->Prop)) (P_35:(state->(state->Prop))) (Pn_4:pname) (Q_24:(state->(state->Prop))), (((hoare_90032982_state G_31) ((insert528405184_state (((hoare_858012674_state P_35) (the_com (body Pn_4))) Q_24)) bot_bo19817387tate_o))->((hoare_90032982_state G_31) ((insert528405184_state (((hoare_858012674_state P_35) (body_1 Pn_4)) Q_24)) bot_bo19817387tate_o)))) of role axiom named fact_375_weak__Body
% A new axiom: (forall (G_31:(hoare_1708887482_state->Prop)) (P_35:(state->(state->Prop))) (Pn_4:pname) (Q_24:(state->(state->Prop))), (((hoare_90032982_state G_31) ((insert528405184_state (((hoare_858012674_state P_35) (the_com (body Pn_4))) Q_24)) bot_bo19817387tate_o))->((hoare_90032982_state G_31) ((insert528405184_state (((hoare_858012674_state P_35) (body_1 Pn_4)) Q_24)) bot_bo19817387tate_o))))
% FOF formula (forall (P_34:(state->(state->Prop))) (Pn_3:pname) (Q_23:(state->(state->Prop))) (G_30:(hoare_1708887482_state->Prop)), (((hoare_90032982_state ((insert528405184_state (((hoare_858012674_state P_34) (body_1 Pn_3)) Q_23)) G_30)) ((insert528405184_state (((hoare_858012674_state P_34) (the_com (body Pn_3))) Q_23)) bot_bo19817387tate_o))->((hoare_90032982_state G_30) ((insert528405184_state (((hoare_858012674_state P_34) (body_1 Pn_3)) Q_23)) bot_bo19817387tate_o)))) of role axiom named fact_376_BodyN
% A new axiom: (forall (P_34:(state->(state->Prop))) (Pn_3:pname) (Q_23:(state->(state->Prop))) (G_30:(hoare_1708887482_state->Prop)), (((hoare_90032982_state ((insert528405184_state (((hoare_858012674_state P_34) (body_1 Pn_3)) Q_23)) G_30)) ((insert528405184_state (((hoare_858012674_state P_34) (the_com (body Pn_3))) Q_23)) bot_bo19817387tate_o))->((hoare_90032982_state G_30) ((insert528405184_state (((hoare_858012674_state P_34) (body_1 Pn_3)) Q_23)) bot_bo19817387tate_o))))
% FOF formula ((iff hoare_1160767572gleton) ((ex state) (fun (S_2:state)=> ((ex state) (fun (T_1:state)=> (not (((eq state) S_2) T_1))))))) of role axiom named fact_377_state__not__singleton__def
% A new axiom: ((iff hoare_1160767572gleton) ((ex state) (fun (S_2:state)=> ((ex state) (fun (T_1:state)=> (not (((eq state) S_2) T_1)))))))
% FOF formula (forall (A_192:(com->Prop)) (C_60:com) (B_129:(com->Prop)), (((((member_com C_60) B_129)->False)->((member_com C_60) A_192))->((member_com C_60) ((semila1562558655_com_o A_192) B_129)))) of role axiom named fact_378_UnCI
% A new axiom: (forall (A_192:(com->Prop)) (C_60:com) (B_129:(com->Prop)), (((((member_com C_60) B_129)->False)->((member_com C_60) A_192))->((member_com C_60) ((semila1562558655_com_o A_192) B_129))))
% FOF formula (forall (A_192:(hoare_1708887482_state->Prop)) (C_60:hoare_1708887482_state) (B_129:(hoare_1708887482_state->Prop)), (((((member451959335_state C_60) B_129)->False)->((member451959335_state C_60) A_192))->((member451959335_state C_60) ((semila1122118281tate_o A_192) B_129)))) of role axiom named fact_379_UnCI
% A new axiom: (forall (A_192:(hoare_1708887482_state->Prop)) (C_60:hoare_1708887482_state) (B_129:(hoare_1708887482_state->Prop)), (((((member451959335_state C_60) B_129)->False)->((member451959335_state C_60) A_192))->((member451959335_state C_60) ((semila1122118281tate_o A_192) B_129))))
% FOF formula (forall (A_192:(pname->Prop)) (C_60:pname) (B_129:(pname->Prop)), (((((member_pname C_60) B_129)->False)->((member_pname C_60) A_192))->((member_pname C_60) ((semila1780557381name_o A_192) B_129)))) of role axiom named fact_380_UnCI
% A new axiom: (forall (A_192:(pname->Prop)) (C_60:pname) (B_129:(pname->Prop)), (((((member_pname C_60) B_129)->False)->((member_pname C_60) A_192))->((member_pname C_60) ((semila1780557381name_o A_192) B_129))))
% FOF formula (forall (C_59:com) (A_191:(com->Prop)) (B_128:(com->Prop)), (((member_com C_59) ((semila1562558655_com_o A_191) B_128))->((((member_com C_59) A_191)->False)->((member_com C_59) B_128)))) of role axiom named fact_381_UnE
% A new axiom: (forall (C_59:com) (A_191:(com->Prop)) (B_128:(com->Prop)), (((member_com C_59) ((semila1562558655_com_o A_191) B_128))->((((member_com C_59) A_191)->False)->((member_com C_59) B_128))))
% FOF formula (forall (C_59:hoare_1708887482_state) (A_191:(hoare_1708887482_state->Prop)) (B_128:(hoare_1708887482_state->Prop)), (((member451959335_state C_59) ((semila1122118281tate_o A_191) B_128))->((((member451959335_state C_59) A_191)->False)->((member451959335_state C_59) B_128)))) of role axiom named fact_382_UnE
% A new axiom: (forall (C_59:hoare_1708887482_state) (A_191:(hoare_1708887482_state->Prop)) (B_128:(hoare_1708887482_state->Prop)), (((member451959335_state C_59) ((semila1122118281tate_o A_191) B_128))->((((member451959335_state C_59) A_191)->False)->((member451959335_state C_59) B_128))))
% FOF formula (forall (C_59:pname) (A_191:(pname->Prop)) (B_128:(pname->Prop)), (((member_pname C_59) ((semila1780557381name_o A_191) B_128))->((((member_pname C_59) A_191)->False)->((member_pname C_59) B_128)))) of role axiom named fact_383_UnE
% A new axiom: (forall (C_59:pname) (A_191:(pname->Prop)) (B_128:(pname->Prop)), (((member_pname C_59) ((semila1780557381name_o A_191) B_128))->((((member_pname C_59) A_191)->False)->((member_pname C_59) B_128))))
% FOF formula (forall (Fun1_2:(state->(state->Prop))) (Com_4:com) (Fun2_2:(state->(state->Prop))) (Fun1_1:(state->(state->Prop))) (Com_3:com) (Fun2_1:(state->(state->Prop))), ((iff (((eq hoare_1708887482_state) (((hoare_858012674_state Fun1_2) Com_4) Fun2_2)) (((hoare_858012674_state Fun1_1) Com_3) Fun2_1))) ((and ((and (((eq (state->(state->Prop))) Fun1_2) Fun1_1)) (((eq com) Com_4) Com_3))) (((eq (state->(state->Prop))) Fun2_2) Fun2_1)))) of role axiom named fact_384_triple_Oinject
% A new axiom: (forall (Fun1_2:(state->(state->Prop))) (Com_4:com) (Fun2_2:(state->(state->Prop))) (Fun1_1:(state->(state->Prop))) (Com_3:com) (Fun2_1:(state->(state->Prop))), ((iff (((eq hoare_1708887482_state) (((hoare_858012674_state Fun1_2) Com_4) Fun2_2)) (((hoare_858012674_state Fun1_1) Com_3) Fun2_1))) ((and ((and (((eq (state->(state->Prop))) Fun1_2) Fun1_1)) (((eq com) Com_4) Com_3))) (((eq (state->(state->Prop))) Fun2_2) Fun2_1))))
% FOF formula (forall (A_190:(com->Prop)) (C_58:com) (B_127:(com->Prop)), (((member_com C_58) B_127)->((member_com C_58) ((semila1562558655_com_o A_190) B_127)))) of role axiom named fact_385_UnI2
% A new axiom: (forall (A_190:(com->Prop)) (C_58:com) (B_127:(com->Prop)), (((member_com C_58) B_127)->((member_com C_58) ((semila1562558655_com_o A_190) B_127))))
% FOF formula (forall (A_190:(hoare_1708887482_state->Prop)) (C_58:hoare_1708887482_state) (B_127:(hoare_1708887482_state->Prop)), (((member451959335_state C_58) B_127)->((member451959335_state C_58) ((semila1122118281tate_o A_190) B_127)))) of role axiom named fact_386_UnI2
% A new axiom: (forall (A_190:(hoare_1708887482_state->Prop)) (C_58:hoare_1708887482_state) (B_127:(hoare_1708887482_state->Prop)), (((member451959335_state C_58) B_127)->((member451959335_state C_58) ((semila1122118281tate_o A_190) B_127))))
% FOF formula (forall (A_190:(pname->Prop)) (C_58:pname) (B_127:(pname->Prop)), (((member_pname C_58) B_127)->((member_pname C_58) ((semila1780557381name_o A_190) B_127)))) of role axiom named fact_387_UnI2
% A new axiom: (forall (A_190:(pname->Prop)) (C_58:pname) (B_127:(pname->Prop)), (((member_pname C_58) B_127)->((member_pname C_58) ((semila1780557381name_o A_190) B_127))))
% FOF formula (forall (B_126:(com->Prop)) (C_57:com) (A_189:(com->Prop)), (((member_com C_57) A_189)->((member_com C_57) ((semila1562558655_com_o A_189) B_126)))) of role axiom named fact_388_UnI1
% A new axiom: (forall (B_126:(com->Prop)) (C_57:com) (A_189:(com->Prop)), (((member_com C_57) A_189)->((member_com C_57) ((semila1562558655_com_o A_189) B_126))))
% FOF formula (forall (B_126:(hoare_1708887482_state->Prop)) (C_57:hoare_1708887482_state) (A_189:(hoare_1708887482_state->Prop)), (((member451959335_state C_57) A_189)->((member451959335_state C_57) ((semila1122118281tate_o A_189) B_126)))) of role axiom named fact_389_UnI1
% A new axiom: (forall (B_126:(hoare_1708887482_state->Prop)) (C_57:hoare_1708887482_state) (A_189:(hoare_1708887482_state->Prop)), (((member451959335_state C_57) A_189)->((member451959335_state C_57) ((semila1122118281tate_o A_189) B_126))))
% FOF formula (forall (B_126:(pname->Prop)) (C_57:pname) (A_189:(pname->Prop)), (((member_pname C_57) A_189)->((member_pname C_57) ((semila1780557381name_o A_189) B_126)))) of role axiom named fact_390_UnI1
% A new axiom: (forall (B_126:(pname->Prop)) (C_57:pname) (A_189:(pname->Prop)), (((member_pname C_57) A_189)->((member_pname C_57) ((semila1780557381name_o A_189) B_126))))
% FOF formula (forall (P_33:(pname->Prop)) (A_188:(pname->Prop)) (B_125:(pname->Prop)), ((iff (forall (X_3:pname), (((member_pname X_3) ((semila1780557381name_o A_188) B_125))->(P_33 X_3)))) ((and (forall (X_3:pname), (((member_pname X_3) A_188)->(P_33 X_3)))) (forall (X_3:pname), (((member_pname X_3) B_125)->(P_33 X_3)))))) of role axiom named fact_391_ball__Un
% A new axiom: (forall (P_33:(pname->Prop)) (A_188:(pname->Prop)) (B_125:(pname->Prop)), ((iff (forall (X_3:pname), (((member_pname X_3) ((semila1780557381name_o A_188) B_125))->(P_33 X_3)))) ((and (forall (X_3:pname), (((member_pname X_3) A_188)->(P_33 X_3)))) (forall (X_3:pname), (((member_pname X_3) B_125)->(P_33 X_3))))))
% FOF formula (forall (P_33:(hoare_1708887482_state->Prop)) (A_188:(hoare_1708887482_state->Prop)) (B_125:(hoare_1708887482_state->Prop)), ((iff (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) ((semila1122118281tate_o A_188) B_125))->(P_33 X_3)))) ((and (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_188)->(P_33 X_3)))) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) B_125)->(P_33 X_3)))))) of role axiom named fact_392_ball__Un
% A new axiom: (forall (P_33:(hoare_1708887482_state->Prop)) (A_188:(hoare_1708887482_state->Prop)) (B_125:(hoare_1708887482_state->Prop)), ((iff (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) ((semila1122118281tate_o A_188) B_125))->(P_33 X_3)))) ((and (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_188)->(P_33 X_3)))) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) B_125)->(P_33 X_3))))))
% FOF formula (forall (P_32:(pname->Prop)) (A_187:(pname->Prop)) (B_124:(pname->Prop)), ((iff ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) ((semila1780557381name_o A_187) B_124))) (P_32 X_3))))) ((or ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_187)) (P_32 X_3))))) ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) B_124)) (P_32 X_3))))))) of role axiom named fact_393_bex__Un
% A new axiom: (forall (P_32:(pname->Prop)) (A_187:(pname->Prop)) (B_124:(pname->Prop)), ((iff ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) ((semila1780557381name_o A_187) B_124))) (P_32 X_3))))) ((or ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_187)) (P_32 X_3))))) ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) B_124)) (P_32 X_3)))))))
% FOF formula (forall (P_32:(hoare_1708887482_state->Prop)) (A_187:(hoare_1708887482_state->Prop)) (B_124:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) ((semila1122118281tate_o A_187) B_124))) (P_32 X_3))))) ((or ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_187)) (P_32 X_3))))) ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) B_124)) (P_32 X_3))))))) of role axiom named fact_394_bex__Un
% A new axiom: (forall (P_32:(hoare_1708887482_state->Prop)) (A_187:(hoare_1708887482_state->Prop)) (B_124:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) ((semila1122118281tate_o A_187) B_124))) (P_32 X_3))))) ((or ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_187)) (P_32 X_3))))) ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) B_124)) (P_32 X_3)))))))
% FOF formula (forall (A_186:(pname->Prop)) (B_123:(pname->Prop)) (C_56:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_186) B_123)) C_56)) ((semila1780557381name_o A_186) ((semila1780557381name_o B_123) C_56)))) of role axiom named fact_395_Un__assoc
% A new axiom: (forall (A_186:(pname->Prop)) (B_123:(pname->Prop)) (C_56:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_186) B_123)) C_56)) ((semila1780557381name_o A_186) ((semila1780557381name_o B_123) C_56))))
% FOF formula (forall (A_186:(hoare_1708887482_state->Prop)) (B_123:(hoare_1708887482_state->Prop)) (C_56:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_186) B_123)) C_56)) ((semila1122118281tate_o A_186) ((semila1122118281tate_o B_123) C_56)))) of role axiom named fact_396_Un__assoc
% A new axiom: (forall (A_186:(hoare_1708887482_state->Prop)) (B_123:(hoare_1708887482_state->Prop)) (C_56:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_186) B_123)) C_56)) ((semila1122118281tate_o A_186) ((semila1122118281tate_o B_123) C_56))))
% FOF formula (forall (C_55:com) (A_185:(com->Prop)) (B_122:(com->Prop)), ((iff ((member_com C_55) ((semila1562558655_com_o A_185) B_122))) ((or ((member_com C_55) A_185)) ((member_com C_55) B_122)))) of role axiom named fact_397_Un__iff
% A new axiom: (forall (C_55:com) (A_185:(com->Prop)) (B_122:(com->Prop)), ((iff ((member_com C_55) ((semila1562558655_com_o A_185) B_122))) ((or ((member_com C_55) A_185)) ((member_com C_55) B_122))))
% FOF formula (forall (C_55:hoare_1708887482_state) (A_185:(hoare_1708887482_state->Prop)) (B_122:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_55) ((semila1122118281tate_o A_185) B_122))) ((or ((member451959335_state C_55) A_185)) ((member451959335_state C_55) B_122)))) of role axiom named fact_398_Un__iff
% A new axiom: (forall (C_55:hoare_1708887482_state) (A_185:(hoare_1708887482_state->Prop)) (B_122:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_55) ((semila1122118281tate_o A_185) B_122))) ((or ((member451959335_state C_55) A_185)) ((member451959335_state C_55) B_122))))
% FOF formula (forall (C_55:pname) (A_185:(pname->Prop)) (B_122:(pname->Prop)), ((iff ((member_pname C_55) ((semila1780557381name_o A_185) B_122))) ((or ((member_pname C_55) A_185)) ((member_pname C_55) B_122)))) of role axiom named fact_399_Un__iff
% A new axiom: (forall (C_55:pname) (A_185:(pname->Prop)) (B_122:(pname->Prop)), ((iff ((member_pname C_55) ((semila1780557381name_o A_185) B_122))) ((or ((member_pname C_55) A_185)) ((member_pname C_55) B_122))))
% FOF formula (forall (A_184:(pname->Prop)) (B_121:(pname->Prop)) (C_54:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_184) ((semila1780557381name_o B_121) C_54))) ((semila1780557381name_o B_121) ((semila1780557381name_o A_184) C_54)))) of role axiom named fact_400_Un__left__commute
% A new axiom: (forall (A_184:(pname->Prop)) (B_121:(pname->Prop)) (C_54:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_184) ((semila1780557381name_o B_121) C_54))) ((semila1780557381name_o B_121) ((semila1780557381name_o A_184) C_54))))
% FOF formula (forall (A_184:(hoare_1708887482_state->Prop)) (B_121:(hoare_1708887482_state->Prop)) (C_54:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_184) ((semila1122118281tate_o B_121) C_54))) ((semila1122118281tate_o B_121) ((semila1122118281tate_o A_184) C_54)))) of role axiom named fact_401_Un__left__commute
% A new axiom: (forall (A_184:(hoare_1708887482_state->Prop)) (B_121:(hoare_1708887482_state->Prop)) (C_54:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_184) ((semila1122118281tate_o B_121) C_54))) ((semila1122118281tate_o B_121) ((semila1122118281tate_o A_184) C_54))))
% FOF formula (forall (A_183:(pname->Prop)) (B_120:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_183) ((semila1780557381name_o A_183) B_120))) ((semila1780557381name_o A_183) B_120))) of role axiom named fact_402_Un__left__absorb
% A new axiom: (forall (A_183:(pname->Prop)) (B_120:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_183) ((semila1780557381name_o A_183) B_120))) ((semila1780557381name_o A_183) B_120)))
% FOF formula (forall (A_183:(hoare_1708887482_state->Prop)) (B_120:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_183) ((semila1122118281tate_o A_183) B_120))) ((semila1122118281tate_o A_183) B_120))) of role axiom named fact_403_Un__left__absorb
% A new axiom: (forall (A_183:(hoare_1708887482_state->Prop)) (B_120:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_183) ((semila1122118281tate_o A_183) B_120))) ((semila1122118281tate_o A_183) B_120)))
% FOF formula (forall (A_182:(pname->Prop)) (B_119:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_182) B_119)) ((semila1780557381name_o B_119) A_182))) of role axiom named fact_404_Un__commute
% A new axiom: (forall (A_182:(pname->Prop)) (B_119:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_182) B_119)) ((semila1780557381name_o B_119) A_182)))
% FOF formula (forall (A_182:(hoare_1708887482_state->Prop)) (B_119:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_182) B_119)) ((semila1122118281tate_o B_119) A_182))) of role axiom named fact_405_Un__commute
% A new axiom: (forall (A_182:(hoare_1708887482_state->Prop)) (B_119:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_182) B_119)) ((semila1122118281tate_o B_119) A_182)))
% FOF formula (forall (A_181:(com->Prop)) (B_118:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o A_181) B_118)) (collect_com (fun (X_3:com)=> ((or ((member_com X_3) A_181)) ((member_com X_3) B_118)))))) of role axiom named fact_406_Un__def
% A new axiom: (forall (A_181:(com->Prop)) (B_118:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o A_181) B_118)) (collect_com (fun (X_3:com)=> ((or ((member_com X_3) A_181)) ((member_com X_3) B_118))))))
% FOF formula (forall (A_181:((pname->Prop)->Prop)) (B_118:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila181081674me_o_o A_181) B_118)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((or ((member_pname_o X_3) A_181)) ((member_pname_o X_3) B_118)))))) of role axiom named fact_407_Un__def
% A new axiom: (forall (A_181:((pname->Prop)->Prop)) (B_118:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila181081674me_o_o A_181) B_118)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((or ((member_pname_o X_3) A_181)) ((member_pname_o X_3) B_118))))))
% FOF formula (forall (A_181:((hoare_1708887482_state->Prop)->Prop)) (B_118:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila1853742644te_o_o A_181) B_118)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or ((member814030440tate_o X_3) A_181)) ((member814030440tate_o X_3) B_118)))))) of role axiom named fact_408_Un__def
% A new axiom: (forall (A_181:((hoare_1708887482_state->Prop)->Prop)) (B_118:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila1853742644te_o_o A_181) B_118)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or ((member814030440tate_o X_3) A_181)) ((member814030440tate_o X_3) B_118))))))
% FOF formula (forall (A_181:(hoare_1708887482_state->Prop)) (B_118:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_181) B_118)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or ((member451959335_state X_3) A_181)) ((member451959335_state X_3) B_118)))))) of role axiom named fact_409_Un__def
% A new axiom: (forall (A_181:(hoare_1708887482_state->Prop)) (B_118:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_181) B_118)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or ((member451959335_state X_3) A_181)) ((member451959335_state X_3) B_118))))))
% FOF formula (forall (A_181:(pname->Prop)) (B_118:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_181) B_118)) (collect_pname (fun (X_3:pname)=> ((or ((member_pname X_3) A_181)) ((member_pname X_3) B_118)))))) of role axiom named fact_410_Un__def
% A new axiom: (forall (A_181:(pname->Prop)) (B_118:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_181) B_118)) (collect_pname (fun (X_3:pname)=> ((or ((member_pname X_3) A_181)) ((member_pname X_3) B_118))))))
% FOF formula (forall (A_180:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_180) A_180)) A_180)) of role axiom named fact_411_Un__absorb
% A new axiom: (forall (A_180:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_180) A_180)) A_180))
% FOF formula (forall (A_180:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_180) A_180)) A_180)) of role axiom named fact_412_Un__absorb
% A new axiom: (forall (A_180:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_180) A_180)) A_180))
% FOF formula (forall (P_31:(pname->Prop)) (Q_22:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila1780557381name_o (collect_pname P_31)) (collect_pname Q_22)))) of role axiom named fact_413_Collect__disj__eq
% A new axiom: (forall (P_31:(pname->Prop)) (Q_22:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila1780557381name_o (collect_pname P_31)) (collect_pname Q_22))))
% FOF formula (forall (P_31:((pname->Prop)->Prop)) (Q_22:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila181081674me_o_o (collect_pname_o P_31)) (collect_pname_o Q_22)))) of role axiom named fact_414_Collect__disj__eq
% A new axiom: (forall (P_31:((pname->Prop)->Prop)) (Q_22:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila181081674me_o_o (collect_pname_o P_31)) (collect_pname_o Q_22))))
% FOF formula (forall (P_31:((hoare_1708887482_state->Prop)->Prop)) (Q_22:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila1853742644te_o_o (collec219771562tate_o P_31)) (collec219771562tate_o Q_22)))) of role axiom named fact_415_Collect__disj__eq
% A new axiom: (forall (P_31:((hoare_1708887482_state->Prop)->Prop)) (Q_22:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila1853742644te_o_o (collec219771562tate_o P_31)) (collec219771562tate_o Q_22))))
% FOF formula (forall (P_31:(hoare_1708887482_state->Prop)) (Q_22:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila1122118281tate_o (collec1568722789_state P_31)) (collec1568722789_state Q_22)))) of role axiom named fact_416_Collect__disj__eq
% A new axiom: (forall (P_31:(hoare_1708887482_state->Prop)) (Q_22:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila1122118281tate_o (collec1568722789_state P_31)) (collec1568722789_state Q_22))))
% FOF formula (forall (A_179:(pname->Prop)) (B_117:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_179) B_117)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_179) bot_bot_pname_o)) (((eq (pname->Prop)) B_117) bot_bot_pname_o)))) of role axiom named fact_417_Un__empty
% A new axiom: (forall (A_179:(pname->Prop)) (B_117:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_179) B_117)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_179) bot_bot_pname_o)) (((eq (pname->Prop)) B_117) bot_bot_pname_o))))
% FOF formula (forall (A_179:(com->Prop)) (B_117:(com->Prop)), ((iff (((eq (com->Prop)) ((semila1562558655_com_o A_179) B_117)) bot_bot_com_o)) ((and (((eq (com->Prop)) A_179) bot_bot_com_o)) (((eq (com->Prop)) B_117) bot_bot_com_o)))) of role axiom named fact_418_Un__empty
% A new axiom: (forall (A_179:(com->Prop)) (B_117:(com->Prop)), ((iff (((eq (com->Prop)) ((semila1562558655_com_o A_179) B_117)) bot_bot_com_o)) ((and (((eq (com->Prop)) A_179) bot_bot_com_o)) (((eq (com->Prop)) B_117) bot_bot_com_o))))
% FOF formula (forall (A_179:(hoare_1708887482_state->Prop)) (B_117:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_179) B_117)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) A_179) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) B_117) bot_bo19817387tate_o)))) of role axiom named fact_419_Un__empty
% A new axiom: (forall (A_179:(hoare_1708887482_state->Prop)) (B_117:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_179) B_117)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) A_179) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) B_117) bot_bo19817387tate_o))))
% FOF formula (forall (A_178:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_178) bot_bot_pname_o)) A_178)) of role axiom named fact_420_Un__empty__right
% A new axiom: (forall (A_178:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_178) bot_bot_pname_o)) A_178))
% FOF formula (forall (A_178:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o A_178) bot_bot_com_o)) A_178)) of role axiom named fact_421_Un__empty__right
% A new axiom: (forall (A_178:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o A_178) bot_bot_com_o)) A_178))
% FOF formula (forall (A_178:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_178) bot_bo19817387tate_o)) A_178)) of role axiom named fact_422_Un__empty__right
% A new axiom: (forall (A_178:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_178) bot_bo19817387tate_o)) A_178))
% FOF formula (forall (B_116:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_116)) B_116)) of role axiom named fact_423_Un__empty__left
% A new axiom: (forall (B_116:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_116)) B_116))
% FOF formula (forall (B_116:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o bot_bot_com_o) B_116)) B_116)) of role axiom named fact_424_Un__empty__left
% A new axiom: (forall (B_116:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o bot_bot_com_o) B_116)) B_116))
% FOF formula (forall (B_116:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_o) B_116)) B_116)) of role axiom named fact_425_Un__empty__left
% A new axiom: (forall (B_116:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_o) B_116)) B_116))
% FOF formula (forall (G_29:((pname->Prop)->Prop)) (F_68:((pname->Prop)->Prop)), ((finite297249702name_o F_68)->((finite297249702name_o G_29)->(finite297249702name_o ((semila181081674me_o_o F_68) G_29))))) of role axiom named fact_426_finite__UnI
% A new axiom: (forall (G_29:((pname->Prop)->Prop)) (F_68:((pname->Prop)->Prop)), ((finite297249702name_o F_68)->((finite297249702name_o G_29)->(finite297249702name_o ((semila181081674me_o_o F_68) G_29)))))
% FOF formula (forall (G_29:((hoare_1708887482_state->Prop)->Prop)) (F_68:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_68)->((finite1329924456tate_o G_29)->(finite1329924456tate_o ((semila1853742644te_o_o F_68) G_29))))) of role axiom named fact_427_finite__UnI
% A new axiom: (forall (G_29:((hoare_1708887482_state->Prop)->Prop)) (F_68:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_68)->((finite1329924456tate_o G_29)->(finite1329924456tate_o ((semila1853742644te_o_o F_68) G_29)))))
% FOF formula (forall (G_29:(hoare_1708887482_state->Prop)) (F_68:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_68)->((finite1625599783_state G_29)->(finite1625599783_state ((semila1122118281tate_o F_68) G_29))))) of role axiom named fact_428_finite__UnI
% A new axiom: (forall (G_29:(hoare_1708887482_state->Prop)) (F_68:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_68)->((finite1625599783_state G_29)->(finite1625599783_state ((semila1122118281tate_o F_68) G_29)))))
% FOF formula (forall (G_29:(pname->Prop)) (F_68:(pname->Prop)), ((finite_finite_pname F_68)->((finite_finite_pname G_29)->(finite_finite_pname ((semila1780557381name_o F_68) G_29))))) of role axiom named fact_429_finite__UnI
% A new axiom: (forall (G_29:(pname->Prop)) (F_68:(pname->Prop)), ((finite_finite_pname F_68)->((finite_finite_pname G_29)->(finite_finite_pname ((semila1780557381name_o F_68) G_29)))))
% FOF formula (forall (F_67:((pname->Prop)->Prop)) (G_28:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((semila181081674me_o_o F_67) G_28))) ((and (finite297249702name_o F_67)) (finite297249702name_o G_28)))) of role axiom named fact_430_finite__Un
% A new axiom: (forall (F_67:((pname->Prop)->Prop)) (G_28:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((semila181081674me_o_o F_67) G_28))) ((and (finite297249702name_o F_67)) (finite297249702name_o G_28))))
% FOF formula (forall (F_67:((hoare_1708887482_state->Prop)->Prop)) (G_28:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o ((semila1853742644te_o_o F_67) G_28))) ((and (finite1329924456tate_o F_67)) (finite1329924456tate_o G_28)))) of role axiom named fact_431_finite__Un
% A new axiom: (forall (F_67:((hoare_1708887482_state->Prop)->Prop)) (G_28:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o ((semila1853742644te_o_o F_67) G_28))) ((and (finite1329924456tate_o F_67)) (finite1329924456tate_o G_28))))
% FOF formula (forall (F_67:(hoare_1708887482_state->Prop)) (G_28:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((semila1122118281tate_o F_67) G_28))) ((and (finite1625599783_state F_67)) (finite1625599783_state G_28)))) of role axiom named fact_432_finite__Un
% A new axiom: (forall (F_67:(hoare_1708887482_state->Prop)) (G_28:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((semila1122118281tate_o F_67) G_28))) ((and (finite1625599783_state F_67)) (finite1625599783_state G_28))))
% FOF formula (forall (F_67:(pname->Prop)) (G_28:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_67) G_28))) ((and (finite_finite_pname F_67)) (finite_finite_pname G_28)))) of role axiom named fact_433_finite__Un
% A new axiom: (forall (F_67:(pname->Prop)) (G_28:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_67) G_28))) ((and (finite_finite_pname F_67)) (finite_finite_pname G_28))))
% FOF formula (forall (A_177:pname) (B_115:(pname->Prop)) (C_53:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_177) B_115)) C_53)) ((insert_pname A_177) ((semila1780557381name_o B_115) C_53)))) of role axiom named fact_434_Un__insert__left
% A new axiom: (forall (A_177:pname) (B_115:(pname->Prop)) (C_53:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_177) B_115)) C_53)) ((insert_pname A_177) ((semila1780557381name_o B_115) C_53))))
% FOF formula (forall (A_177:com) (B_115:(com->Prop)) (C_53:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o ((insert_com A_177) B_115)) C_53)) ((insert_com A_177) ((semila1562558655_com_o B_115) C_53)))) of role axiom named fact_435_Un__insert__left
% A new axiom: (forall (A_177:com) (B_115:(com->Prop)) (C_53:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o ((insert_com A_177) B_115)) C_53)) ((insert_com A_177) ((semila1562558655_com_o B_115) C_53))))
% FOF formula (forall (A_177:hoare_1708887482_state) (B_115:(hoare_1708887482_state->Prop)) (C_53:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((insert528405184_state A_177) B_115)) C_53)) ((insert528405184_state A_177) ((semila1122118281tate_o B_115) C_53)))) of role axiom named fact_436_Un__insert__left
% A new axiom: (forall (A_177:hoare_1708887482_state) (B_115:(hoare_1708887482_state->Prop)) (C_53:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((insert528405184_state A_177) B_115)) C_53)) ((insert528405184_state A_177) ((semila1122118281tate_o B_115) C_53))))
% FOF formula (forall (A_176:(pname->Prop)) (A_175:pname) (B_114:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_176) ((insert_pname A_175) B_114))) ((insert_pname A_175) ((semila1780557381name_o A_176) B_114)))) of role axiom named fact_437_Un__insert__right
% A new axiom: (forall (A_176:(pname->Prop)) (A_175:pname) (B_114:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_176) ((insert_pname A_175) B_114))) ((insert_pname A_175) ((semila1780557381name_o A_176) B_114))))
% FOF formula (forall (A_176:(com->Prop)) (A_175:com) (B_114:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o A_176) ((insert_com A_175) B_114))) ((insert_com A_175) ((semila1562558655_com_o A_176) B_114)))) of role axiom named fact_438_Un__insert__right
% A new axiom: (forall (A_176:(com->Prop)) (A_175:com) (B_114:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o A_176) ((insert_com A_175) B_114))) ((insert_com A_175) ((semila1562558655_com_o A_176) B_114))))
% FOF formula (forall (A_176:(hoare_1708887482_state->Prop)) (A_175:hoare_1708887482_state) (B_114:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_176) ((insert528405184_state A_175) B_114))) ((insert528405184_state A_175) ((semila1122118281tate_o A_176) B_114)))) of role axiom named fact_439_Un__insert__right
% A new axiom: (forall (A_176:(hoare_1708887482_state->Prop)) (A_175:hoare_1708887482_state) (B_114:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_176) ((insert528405184_state A_175) B_114))) ((insert528405184_state A_175) ((semila1122118281tate_o A_176) B_114))))
% FOF formula (forall (B_113:(pname->Prop)) (D_5:(pname->Prop)) (A_174:(pname->Prop)) (C_52:(pname->Prop)), (((ord_less_eq_pname_o A_174) C_52)->(((ord_less_eq_pname_o B_113) D_5)->((ord_less_eq_pname_o ((semila1780557381name_o A_174) B_113)) ((semila1780557381name_o C_52) D_5))))) of role axiom named fact_440_Un__mono
% A new axiom: (forall (B_113:(pname->Prop)) (D_5:(pname->Prop)) (A_174:(pname->Prop)) (C_52:(pname->Prop)), (((ord_less_eq_pname_o A_174) C_52)->(((ord_less_eq_pname_o B_113) D_5)->((ord_less_eq_pname_o ((semila1780557381name_o A_174) B_113)) ((semila1780557381name_o C_52) D_5)))))
% FOF formula (forall (B_113:(hoare_1708887482_state->Prop)) (D_5:(hoare_1708887482_state->Prop)) (A_174:(hoare_1708887482_state->Prop)) (C_52:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_174) C_52)->(((ord_le777019615tate_o B_113) D_5)->((ord_le777019615tate_o ((semila1122118281tate_o A_174) B_113)) ((semila1122118281tate_o C_52) D_5))))) of role axiom named fact_441_Un__mono
% A new axiom: (forall (B_113:(hoare_1708887482_state->Prop)) (D_5:(hoare_1708887482_state->Prop)) (A_174:(hoare_1708887482_state->Prop)) (C_52:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_174) C_52)->(((ord_le777019615tate_o B_113) D_5)->((ord_le777019615tate_o ((semila1122118281tate_o A_174) B_113)) ((semila1122118281tate_o C_52) D_5)))))
% FOF formula (forall (B_112:(pname->Prop)) (A_173:(pname->Prop)) (C_51:(pname->Prop)), (((ord_less_eq_pname_o A_173) C_51)->(((ord_less_eq_pname_o B_112) C_51)->((ord_less_eq_pname_o ((semila1780557381name_o A_173) B_112)) C_51)))) of role axiom named fact_442_Un__least
% A new axiom: (forall (B_112:(pname->Prop)) (A_173:(pname->Prop)) (C_51:(pname->Prop)), (((ord_less_eq_pname_o A_173) C_51)->(((ord_less_eq_pname_o B_112) C_51)->((ord_less_eq_pname_o ((semila1780557381name_o A_173) B_112)) C_51))))
% FOF formula (forall (B_112:(hoare_1708887482_state->Prop)) (A_173:(hoare_1708887482_state->Prop)) (C_51:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_173) C_51)->(((ord_le777019615tate_o B_112) C_51)->((ord_le777019615tate_o ((semila1122118281tate_o A_173) B_112)) C_51)))) of role axiom named fact_443_Un__least
% A new axiom: (forall (B_112:(hoare_1708887482_state->Prop)) (A_173:(hoare_1708887482_state->Prop)) (C_51:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_173) C_51)->(((ord_le777019615tate_o B_112) C_51)->((ord_le777019615tate_o ((semila1122118281tate_o A_173) B_112)) C_51))))
% FOF formula (forall (B_111:(pname->Prop)) (A_172:(pname->Prop)), (((ord_less_eq_pname_o B_111) A_172)->(((eq (pname->Prop)) ((semila1780557381name_o A_172) B_111)) A_172))) of role axiom named fact_444_Un__absorb2
% A new axiom: (forall (B_111:(pname->Prop)) (A_172:(pname->Prop)), (((ord_less_eq_pname_o B_111) A_172)->(((eq (pname->Prop)) ((semila1780557381name_o A_172) B_111)) A_172)))
% FOF formula (forall (B_111:(hoare_1708887482_state->Prop)) (A_172:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_111) A_172)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_172) B_111)) A_172))) of role axiom named fact_445_Un__absorb2
% A new axiom: (forall (B_111:(hoare_1708887482_state->Prop)) (A_172:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_111) A_172)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_172) B_111)) A_172)))
% FOF formula (forall (A_171:(pname->Prop)) (B_110:(pname->Prop)), (((ord_less_eq_pname_o A_171) B_110)->(((eq (pname->Prop)) ((semila1780557381name_o A_171) B_110)) B_110))) of role axiom named fact_446_Un__absorb1
% A new axiom: (forall (A_171:(pname->Prop)) (B_110:(pname->Prop)), (((ord_less_eq_pname_o A_171) B_110)->(((eq (pname->Prop)) ((semila1780557381name_o A_171) B_110)) B_110)))
% FOF formula (forall (A_171:(hoare_1708887482_state->Prop)) (B_110:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_171) B_110)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_171) B_110)) B_110))) of role axiom named fact_447_Un__absorb1
% A new axiom: (forall (A_171:(hoare_1708887482_state->Prop)) (B_110:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_171) B_110)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_171) B_110)) B_110)))
% FOF formula (forall (A_170:(pname->Prop)) (B_109:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_170) B_109)) (((eq (pname->Prop)) ((semila1780557381name_o A_170) B_109)) B_109))) of role axiom named fact_448_subset__Un__eq
% A new axiom: (forall (A_170:(pname->Prop)) (B_109:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_170) B_109)) (((eq (pname->Prop)) ((semila1780557381name_o A_170) B_109)) B_109)))
% FOF formula (forall (A_170:(hoare_1708887482_state->Prop)) (B_109:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_170) B_109)) (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_170) B_109)) B_109))) of role axiom named fact_449_subset__Un__eq
% A new axiom: (forall (A_170:(hoare_1708887482_state->Prop)) (B_109:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_170) B_109)) (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_170) B_109)) B_109)))
% FOF formula (forall (B_108:(pname->Prop)) (A_169:(pname->Prop)), ((ord_less_eq_pname_o B_108) ((semila1780557381name_o A_169) B_108))) of role axiom named fact_450_Un__upper2
% A new axiom: (forall (B_108:(pname->Prop)) (A_169:(pname->Prop)), ((ord_less_eq_pname_o B_108) ((semila1780557381name_o A_169) B_108)))
% FOF formula (forall (B_108:(hoare_1708887482_state->Prop)) (A_169:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o B_108) ((semila1122118281tate_o A_169) B_108))) of role axiom named fact_451_Un__upper2
% A new axiom: (forall (B_108:(hoare_1708887482_state->Prop)) (A_169:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o B_108) ((semila1122118281tate_o A_169) B_108)))
% FOF formula (forall (A_168:(pname->Prop)) (B_107:(pname->Prop)), ((ord_less_eq_pname_o A_168) ((semila1780557381name_o A_168) B_107))) of role axiom named fact_452_Un__upper1
% A new axiom: (forall (A_168:(pname->Prop)) (B_107:(pname->Prop)), ((ord_less_eq_pname_o A_168) ((semila1780557381name_o A_168) B_107)))
% FOF formula (forall (A_168:(hoare_1708887482_state->Prop)) (B_107:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o A_168) ((semila1122118281tate_o A_168) B_107))) of role axiom named fact_453_Un__upper1
% A new axiom: (forall (A_168:(hoare_1708887482_state->Prop)) (B_107:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o A_168) ((semila1122118281tate_o A_168) B_107)))
% FOF formula (forall (F_66:(hoare_1708887482_state->pname)) (A_167:(hoare_1708887482_state->Prop)) (B_106:(hoare_1708887482_state->Prop)), (((eq (pname->Prop)) ((image_1509414295_pname F_66) ((semila1122118281tate_o A_167) B_106))) ((semila1780557381name_o ((image_1509414295_pname F_66) A_167)) ((image_1509414295_pname F_66) B_106)))) of role axiom named fact_454_image__Un
% A new axiom: (forall (F_66:(hoare_1708887482_state->pname)) (A_167:(hoare_1708887482_state->Prop)) (B_106:(hoare_1708887482_state->Prop)), (((eq (pname->Prop)) ((image_1509414295_pname F_66) ((semila1122118281tate_o A_167) B_106))) ((semila1780557381name_o ((image_1509414295_pname F_66) A_167)) ((image_1509414295_pname F_66) B_106))))
% FOF formula (forall (F_66:(pname->hoare_1708887482_state)) (A_167:(pname->Prop)) (B_106:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_66) ((semila1780557381name_o A_167) B_106))) ((semila1122118281tate_o ((image_1116629049_state F_66) A_167)) ((image_1116629049_state F_66) B_106)))) of role axiom named fact_455_image__Un
% A new axiom: (forall (F_66:(pname->hoare_1708887482_state)) (A_167:(pname->Prop)) (B_106:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_66) ((semila1780557381name_o A_167) B_106))) ((semila1122118281tate_o ((image_1116629049_state F_66) A_167)) ((image_1116629049_state F_66) B_106))))
% FOF formula (forall (A_166:pname) (B_105:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_166) B_105)) ((semila1780557381name_o (collect_pname (fun (X_3:pname)=> (((eq pname) X_3) A_166)))) B_105))) of role axiom named fact_456_insert__def
% A new axiom: (forall (A_166:pname) (B_105:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_166) B_105)) ((semila1780557381name_o (collect_pname (fun (X_3:pname)=> (((eq pname) X_3) A_166)))) B_105)))
% FOF formula (forall (A_166:com) (B_105:(com->Prop)), (((eq (com->Prop)) ((insert_com A_166) B_105)) ((semila1562558655_com_o (collect_com (fun (X_3:com)=> (((eq com) X_3) A_166)))) B_105))) of role axiom named fact_457_insert__def
% A new axiom: (forall (A_166:com) (B_105:(com->Prop)), (((eq (com->Prop)) ((insert_com A_166) B_105)) ((semila1562558655_com_o (collect_com (fun (X_3:com)=> (((eq com) X_3) A_166)))) B_105)))
% FOF formula (forall (A_166:(pname->Prop)) (B_105:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_166) B_105)) ((semila181081674me_o_o (collect_pname_o (fun (X_3:(pname->Prop))=> (((eq (pname->Prop)) X_3) A_166)))) B_105))) of role axiom named fact_458_insert__def
% A new axiom: (forall (A_166:(pname->Prop)) (B_105:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_166) B_105)) ((semila181081674me_o_o (collect_pname_o (fun (X_3:(pname->Prop))=> (((eq (pname->Prop)) X_3) A_166)))) B_105)))
% FOF formula (forall (A_166:(hoare_1708887482_state->Prop)) (B_105:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o A_166) B_105)) ((semila1853742644te_o_o (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> (((eq (hoare_1708887482_state->Prop)) X_3) A_166)))) B_105))) of role axiom named fact_459_insert__def
% A new axiom: (forall (A_166:(hoare_1708887482_state->Prop)) (B_105:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o A_166) B_105)) ((semila1853742644te_o_o (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> (((eq (hoare_1708887482_state->Prop)) X_3) A_166)))) B_105)))
% FOF formula (forall (A_166:hoare_1708887482_state) (B_105:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_166) B_105)) ((semila1122118281tate_o (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X_3) A_166)))) B_105))) of role axiom named fact_460_insert__def
% A new axiom: (forall (A_166:hoare_1708887482_state) (B_105:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_166) B_105)) ((semila1122118281tate_o (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X_3) A_166)))) B_105)))
% FOF formula (forall (A_165:pname) (A_164:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_165) A_164)) ((semila1780557381name_o ((insert_pname A_165) bot_bot_pname_o)) A_164))) of role axiom named fact_461_insert__is__Un
% A new axiom: (forall (A_165:pname) (A_164:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_165) A_164)) ((semila1780557381name_o ((insert_pname A_165) bot_bot_pname_o)) A_164)))
% FOF formula (forall (A_165:com) (A_164:(com->Prop)), (((eq (com->Prop)) ((insert_com A_165) A_164)) ((semila1562558655_com_o ((insert_com A_165) bot_bot_com_o)) A_164))) of role axiom named fact_462_insert__is__Un
% A new axiom: (forall (A_165:com) (A_164:(com->Prop)), (((eq (com->Prop)) ((insert_com A_165) A_164)) ((semila1562558655_com_o ((insert_com A_165) bot_bot_com_o)) A_164)))
% FOF formula (forall (A_165:hoare_1708887482_state) (A_164:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_165) A_164)) ((semila1122118281tate_o ((insert528405184_state A_165) bot_bo19817387tate_o)) A_164))) of role axiom named fact_463_insert__is__Un
% A new axiom: (forall (A_165:hoare_1708887482_state) (A_164:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_165) A_164)) ((semila1122118281tate_o ((insert528405184_state A_165) bot_bo19817387tate_o)) A_164)))
% FOF formula (forall (G_27:(hoare_1708887482_state->Prop)) (P_30:(pname->(state->(state->Prop)))) (Q_21:(pname->(state->(state->Prop)))) (Procs_2:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_27) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_30 P_27)) (body_1 P_27)) (Q_21 P_27)))) Procs_2))) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_30 P_27)) (the_com (body P_27))) (Q_21 P_27)))) Procs_2))->((hoare_90032982_state G_27) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_30 P_27)) (body_1 P_27)) (Q_21 P_27)))) Procs_2)))) of role axiom named fact_464_hoare__derivs_OBody
% A new axiom: (forall (G_27:(hoare_1708887482_state->Prop)) (P_30:(pname->(state->(state->Prop)))) (Q_21:(pname->(state->(state->Prop)))) (Procs_2:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_27) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_30 P_27)) (body_1 P_27)) (Q_21 P_27)))) Procs_2))) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_30 P_27)) (the_com (body P_27))) (Q_21 P_27)))) Procs_2))->((hoare_90032982_state G_27) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_30 P_27)) (body_1 P_27)) (Q_21 P_27)))) Procs_2))))
% FOF formula (forall (Z_20:(pname->Prop)) (Y_50:(pname->Prop)) (X_99:(pname->Prop)), (((ord_less_eq_pname_o Y_50) X_99)->(((ord_less_eq_pname_o Z_20) Y_50)->((ord_less_eq_pname_o Z_20) X_99)))) of role axiom named fact_465_xt1_I6_J
% A new axiom: (forall (Z_20:(pname->Prop)) (Y_50:(pname->Prop)) (X_99:(pname->Prop)), (((ord_less_eq_pname_o Y_50) X_99)->(((ord_less_eq_pname_o Z_20) Y_50)->((ord_less_eq_pname_o Z_20) X_99))))
% FOF formula (forall (Z_20:Prop) (Y_50:Prop) (X_99:Prop), (((ord_less_eq_o Y_50) X_99)->(((ord_less_eq_o Z_20) Y_50)->((ord_less_eq_o Z_20) X_99)))) of role axiom named fact_466_xt1_I6_J
% A new axiom: (forall (Z_20:Prop) (Y_50:Prop) (X_99:Prop), (((ord_less_eq_o Y_50) X_99)->(((ord_less_eq_o Z_20) Y_50)->((ord_less_eq_o Z_20) X_99))))
% FOF formula (forall (Z_20:(hoare_1708887482_state->Prop)) (Y_50:(hoare_1708887482_state->Prop)) (X_99:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_50) X_99)->(((ord_le777019615tate_o Z_20) Y_50)->((ord_le777019615tate_o Z_20) X_99)))) of role axiom named fact_467_xt1_I6_J
% A new axiom: (forall (Z_20:(hoare_1708887482_state->Prop)) (Y_50:(hoare_1708887482_state->Prop)) (X_99:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_50) X_99)->(((ord_le777019615tate_o Z_20) Y_50)->((ord_le777019615tate_o Z_20) X_99))))
% FOF formula (forall (Y_49:(pname->Prop)) (X_98:(pname->Prop)), (((ord_less_eq_pname_o Y_49) X_98)->(((ord_less_eq_pname_o X_98) Y_49)->(((eq (pname->Prop)) X_98) Y_49)))) of role axiom named fact_468_xt1_I5_J
% A new axiom: (forall (Y_49:(pname->Prop)) (X_98:(pname->Prop)), (((ord_less_eq_pname_o Y_49) X_98)->(((ord_less_eq_pname_o X_98) Y_49)->(((eq (pname->Prop)) X_98) Y_49))))
% FOF formula (forall (Y_49:Prop) (X_98:Prop), (((ord_less_eq_o Y_49) X_98)->(((ord_less_eq_o X_98) Y_49)->((iff X_98) Y_49)))) of role axiom named fact_469_xt1_I5_J
% A new axiom: (forall (Y_49:Prop) (X_98:Prop), (((ord_less_eq_o Y_49) X_98)->(((ord_less_eq_o X_98) Y_49)->((iff X_98) Y_49))))
% FOF formula (forall (Y_49:(hoare_1708887482_state->Prop)) (X_98:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_49) X_98)->(((ord_le777019615tate_o X_98) Y_49)->(((eq (hoare_1708887482_state->Prop)) X_98) Y_49)))) of role axiom named fact_470_xt1_I5_J
% A new axiom: (forall (Y_49:(hoare_1708887482_state->Prop)) (X_98:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_49) X_98)->(((ord_le777019615tate_o X_98) Y_49)->(((eq (hoare_1708887482_state->Prop)) X_98) Y_49))))
% FOF formula (forall (Z_19:(pname->Prop)) (X_97:(pname->Prop)) (Y_48:(pname->Prop)), (((ord_less_eq_pname_o X_97) Y_48)->(((ord_less_eq_pname_o Y_48) Z_19)->((ord_less_eq_pname_o X_97) Z_19)))) of role axiom named fact_471_order__trans
% A new axiom: (forall (Z_19:(pname->Prop)) (X_97:(pname->Prop)) (Y_48:(pname->Prop)), (((ord_less_eq_pname_o X_97) Y_48)->(((ord_less_eq_pname_o Y_48) Z_19)->((ord_less_eq_pname_o X_97) Z_19))))
% FOF formula (forall (Z_19:Prop) (X_97:Prop) (Y_48:Prop), (((ord_less_eq_o X_97) Y_48)->(((ord_less_eq_o Y_48) Z_19)->((ord_less_eq_o X_97) Z_19)))) of role axiom named fact_472_order__trans
% A new axiom: (forall (Z_19:Prop) (X_97:Prop) (Y_48:Prop), (((ord_less_eq_o X_97) Y_48)->(((ord_less_eq_o Y_48) Z_19)->((ord_less_eq_o X_97) Z_19))))
% FOF formula (forall (Z_19:(hoare_1708887482_state->Prop)) (X_97:(hoare_1708887482_state->Prop)) (Y_48:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_97) Y_48)->(((ord_le777019615tate_o Y_48) Z_19)->((ord_le777019615tate_o X_97) Z_19)))) of role axiom named fact_473_order__trans
% A new axiom: (forall (Z_19:(hoare_1708887482_state->Prop)) (X_97:(hoare_1708887482_state->Prop)) (Y_48:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_97) Y_48)->(((ord_le777019615tate_o Y_48) Z_19)->((ord_le777019615tate_o X_97) Z_19))))
% FOF formula (forall (X_96:(pname->Prop)) (Y_47:(pname->Prop)), (((ord_less_eq_pname_o X_96) Y_47)->(((ord_less_eq_pname_o Y_47) X_96)->(((eq (pname->Prop)) X_96) Y_47)))) of role axiom named fact_474_order__antisym
% A new axiom: (forall (X_96:(pname->Prop)) (Y_47:(pname->Prop)), (((ord_less_eq_pname_o X_96) Y_47)->(((ord_less_eq_pname_o Y_47) X_96)->(((eq (pname->Prop)) X_96) Y_47))))
% FOF formula (forall (X_96:Prop) (Y_47:Prop), (((ord_less_eq_o X_96) Y_47)->(((ord_less_eq_o Y_47) X_96)->((iff X_96) Y_47)))) of role axiom named fact_475_order__antisym
% A new axiom: (forall (X_96:Prop) (Y_47:Prop), (((ord_less_eq_o X_96) Y_47)->(((ord_less_eq_o Y_47) X_96)->((iff X_96) Y_47))))
% FOF formula (forall (X_96:(hoare_1708887482_state->Prop)) (Y_47:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_96) Y_47)->(((ord_le777019615tate_o Y_47) X_96)->(((eq (hoare_1708887482_state->Prop)) X_96) Y_47)))) of role axiom named fact_476_order__antisym
% A new axiom: (forall (X_96:(hoare_1708887482_state->Prop)) (Y_47:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_96) Y_47)->(((ord_le777019615tate_o Y_47) X_96)->(((eq (hoare_1708887482_state->Prop)) X_96) Y_47))))
% FOF formula (forall (C_50:(pname->Prop)) (B_104:(pname->Prop)) (A_163:(pname->Prop)), (((ord_less_eq_pname_o B_104) A_163)->((((eq (pname->Prop)) B_104) C_50)->((ord_less_eq_pname_o C_50) A_163)))) of role axiom named fact_477_xt1_I4_J
% A new axiom: (forall (C_50:(pname->Prop)) (B_104:(pname->Prop)) (A_163:(pname->Prop)), (((ord_less_eq_pname_o B_104) A_163)->((((eq (pname->Prop)) B_104) C_50)->((ord_less_eq_pname_o C_50) A_163))))
% FOF formula (forall (C_50:Prop) (B_104:Prop) (A_163:Prop), (((ord_less_eq_o B_104) A_163)->(((iff B_104) C_50)->((ord_less_eq_o C_50) A_163)))) of role axiom named fact_478_xt1_I4_J
% A new axiom: (forall (C_50:Prop) (B_104:Prop) (A_163:Prop), (((ord_less_eq_o B_104) A_163)->(((iff B_104) C_50)->((ord_less_eq_o C_50) A_163))))
% FOF formula (forall (C_50:(hoare_1708887482_state->Prop)) (B_104:(hoare_1708887482_state->Prop)) (A_163:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_104) A_163)->((((eq (hoare_1708887482_state->Prop)) B_104) C_50)->((ord_le777019615tate_o C_50) A_163)))) of role axiom named fact_479_xt1_I4_J
% A new axiom: (forall (C_50:(hoare_1708887482_state->Prop)) (B_104:(hoare_1708887482_state->Prop)) (A_163:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_104) A_163)->((((eq (hoare_1708887482_state->Prop)) B_104) C_50)->((ord_le777019615tate_o C_50) A_163))))
% FOF formula (forall (C_49:(pname->Prop)) (A_162:(pname->Prop)) (B_103:(pname->Prop)), (((ord_less_eq_pname_o A_162) B_103)->((((eq (pname->Prop)) B_103) C_49)->((ord_less_eq_pname_o A_162) C_49)))) of role axiom named fact_480_ord__le__eq__trans
% A new axiom: (forall (C_49:(pname->Prop)) (A_162:(pname->Prop)) (B_103:(pname->Prop)), (((ord_less_eq_pname_o A_162) B_103)->((((eq (pname->Prop)) B_103) C_49)->((ord_less_eq_pname_o A_162) C_49))))
% FOF formula (forall (C_49:Prop) (A_162:Prop) (B_103:Prop), (((ord_less_eq_o A_162) B_103)->(((iff B_103) C_49)->((ord_less_eq_o A_162) C_49)))) of role axiom named fact_481_ord__le__eq__trans
% A new axiom: (forall (C_49:Prop) (A_162:Prop) (B_103:Prop), (((ord_less_eq_o A_162) B_103)->(((iff B_103) C_49)->((ord_less_eq_o A_162) C_49))))
% FOF formula (forall (C_49:(hoare_1708887482_state->Prop)) (A_162:(hoare_1708887482_state->Prop)) (B_103:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_162) B_103)->((((eq (hoare_1708887482_state->Prop)) B_103) C_49)->((ord_le777019615tate_o A_162) C_49)))) of role axiom named fact_482_ord__le__eq__trans
% A new axiom: (forall (C_49:(hoare_1708887482_state->Prop)) (A_162:(hoare_1708887482_state->Prop)) (B_103:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_162) B_103)->((((eq (hoare_1708887482_state->Prop)) B_103) C_49)->((ord_le777019615tate_o A_162) C_49))))
% FOF formula (forall (C_48:(pname->Prop)) (A_161:(pname->Prop)) (B_102:(pname->Prop)), ((((eq (pname->Prop)) A_161) B_102)->(((ord_less_eq_pname_o C_48) B_102)->((ord_less_eq_pname_o C_48) A_161)))) of role axiom named fact_483_xt1_I3_J
% A new axiom: (forall (C_48:(pname->Prop)) (A_161:(pname->Prop)) (B_102:(pname->Prop)), ((((eq (pname->Prop)) A_161) B_102)->(((ord_less_eq_pname_o C_48) B_102)->((ord_less_eq_pname_o C_48) A_161))))
% FOF formula (forall (C_48:Prop) (B_102:Prop) (A_161:Prop), (((iff A_161) B_102)->(((ord_less_eq_o C_48) B_102)->((ord_less_eq_o C_48) A_161)))) of role axiom named fact_484_xt1_I3_J
% A new axiom: (forall (C_48:Prop) (B_102:Prop) (A_161:Prop), (((iff A_161) B_102)->(((ord_less_eq_o C_48) B_102)->((ord_less_eq_o C_48) A_161))))
% FOF formula (forall (C_48:(hoare_1708887482_state->Prop)) (A_161:(hoare_1708887482_state->Prop)) (B_102:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_161) B_102)->(((ord_le777019615tate_o C_48) B_102)->((ord_le777019615tate_o C_48) A_161)))) of role axiom named fact_485_xt1_I3_J
% A new axiom: (forall (C_48:(hoare_1708887482_state->Prop)) (A_161:(hoare_1708887482_state->Prop)) (B_102:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_161) B_102)->(((ord_le777019615tate_o C_48) B_102)->((ord_le777019615tate_o C_48) A_161))))
% FOF formula (forall (C_47:(pname->Prop)) (A_160:(pname->Prop)) (B_101:(pname->Prop)), ((((eq (pname->Prop)) A_160) B_101)->(((ord_less_eq_pname_o B_101) C_47)->((ord_less_eq_pname_o A_160) C_47)))) of role axiom named fact_486_ord__eq__le__trans
% A new axiom: (forall (C_47:(pname->Prop)) (A_160:(pname->Prop)) (B_101:(pname->Prop)), ((((eq (pname->Prop)) A_160) B_101)->(((ord_less_eq_pname_o B_101) C_47)->((ord_less_eq_pname_o A_160) C_47))))
% FOF formula (forall (C_47:Prop) (B_101:Prop) (A_160:Prop), (((iff A_160) B_101)->(((ord_less_eq_o B_101) C_47)->((ord_less_eq_o A_160) C_47)))) of role axiom named fact_487_ord__eq__le__trans
% A new axiom: (forall (C_47:Prop) (B_101:Prop) (A_160:Prop), (((iff A_160) B_101)->(((ord_less_eq_o B_101) C_47)->((ord_less_eq_o A_160) C_47))))
% FOF formula (forall (C_47:(hoare_1708887482_state->Prop)) (A_160:(hoare_1708887482_state->Prop)) (B_101:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_160) B_101)->(((ord_le777019615tate_o B_101) C_47)->((ord_le777019615tate_o A_160) C_47)))) of role axiom named fact_488_ord__eq__le__trans
% A new axiom: (forall (C_47:(hoare_1708887482_state->Prop)) (A_160:(hoare_1708887482_state->Prop)) (B_101:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_160) B_101)->(((ord_le777019615tate_o B_101) C_47)->((ord_le777019615tate_o A_160) C_47))))
% FOF formula (forall (Y_46:(pname->Prop)) (X_95:(pname->Prop)), (((ord_less_eq_pname_o Y_46) X_95)->((iff ((ord_less_eq_pname_o X_95) Y_46)) (((eq (pname->Prop)) X_95) Y_46)))) of role axiom named fact_489_order__antisym__conv
% A new axiom: (forall (Y_46:(pname->Prop)) (X_95:(pname->Prop)), (((ord_less_eq_pname_o Y_46) X_95)->((iff ((ord_less_eq_pname_o X_95) Y_46)) (((eq (pname->Prop)) X_95) Y_46))))
% FOF formula (forall (Y_46:Prop) (X_95:Prop), (((ord_less_eq_o Y_46) X_95)->((iff ((ord_less_eq_o X_95) Y_46)) ((iff X_95) Y_46)))) of role axiom named fact_490_order__antisym__conv
% A new axiom: (forall (Y_46:Prop) (X_95:Prop), (((ord_less_eq_o Y_46) X_95)->((iff ((ord_less_eq_o X_95) Y_46)) ((iff X_95) Y_46))))
% FOF formula (forall (Y_46:(hoare_1708887482_state->Prop)) (X_95:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_46) X_95)->((iff ((ord_le777019615tate_o X_95) Y_46)) (((eq (hoare_1708887482_state->Prop)) X_95) Y_46)))) of role axiom named fact_491_order__antisym__conv
% A new axiom: (forall (Y_46:(hoare_1708887482_state->Prop)) (X_95:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_46) X_95)->((iff ((ord_le777019615tate_o X_95) Y_46)) (((eq (hoare_1708887482_state->Prop)) X_95) Y_46))))
% FOF formula (forall (X_94:(pname->Prop)) (Y_45:(pname->Prop)), ((((eq (pname->Prop)) X_94) Y_45)->((ord_less_eq_pname_o X_94) Y_45))) of role axiom named fact_492_order__eq__refl
% A new axiom: (forall (X_94:(pname->Prop)) (Y_45:(pname->Prop)), ((((eq (pname->Prop)) X_94) Y_45)->((ord_less_eq_pname_o X_94) Y_45)))
% FOF formula (forall (Y_45:Prop) (X_94:Prop), (((iff X_94) Y_45)->((ord_less_eq_o X_94) Y_45))) of role axiom named fact_493_order__eq__refl
% A new axiom: (forall (Y_45:Prop) (X_94:Prop), (((iff X_94) Y_45)->((ord_less_eq_o X_94) Y_45)))
% FOF formula (forall (X_94:(hoare_1708887482_state->Prop)) (Y_45:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) X_94) Y_45)->((ord_le777019615tate_o X_94) Y_45))) of role axiom named fact_494_order__eq__refl
% A new axiom: (forall (X_94:(hoare_1708887482_state->Prop)) (Y_45:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) X_94) Y_45)->((ord_le777019615tate_o X_94) Y_45)))
% FOF formula (forall (X_93:(pname->Prop)) (Y_44:(pname->Prop)), ((iff (((eq (pname->Prop)) X_93) Y_44)) ((and ((ord_less_eq_pname_o X_93) Y_44)) ((ord_less_eq_pname_o Y_44) X_93)))) of role axiom named fact_495_order__eq__iff
% A new axiom: (forall (X_93:(pname->Prop)) (Y_44:(pname->Prop)), ((iff (((eq (pname->Prop)) X_93) Y_44)) ((and ((ord_less_eq_pname_o X_93) Y_44)) ((ord_less_eq_pname_o Y_44) X_93))))
% FOF formula (forall (Y_44:Prop) (X_93:Prop), ((iff ((iff X_93) Y_44)) ((and ((ord_less_eq_o X_93) Y_44)) ((ord_less_eq_o Y_44) X_93)))) of role axiom named fact_496_order__eq__iff
% A new axiom: (forall (Y_44:Prop) (X_93:Prop), ((iff ((iff X_93) Y_44)) ((and ((ord_less_eq_o X_93) Y_44)) ((ord_less_eq_o Y_44) X_93))))
% FOF formula (forall (X_93:(hoare_1708887482_state->Prop)) (Y_44:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) X_93) Y_44)) ((and ((ord_le777019615tate_o X_93) Y_44)) ((ord_le777019615tate_o Y_44) X_93)))) of role axiom named fact_497_order__eq__iff
% A new axiom: (forall (X_93:(hoare_1708887482_state->Prop)) (Y_44:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) X_93) Y_44)) ((and ((ord_le777019615tate_o X_93) Y_44)) ((ord_le777019615tate_o Y_44) X_93))))
% FOF formula (forall (A_159:pname) (A_158:pname), ((iff (((eq option_pname) (some_pname A_159)) (some_pname A_158))) (((eq pname) A_159) A_158))) of role axiom named fact_498_option_Oinject
% A new axiom: (forall (A_159:pname) (A_158:pname), ((iff (((eq option_pname) (some_pname A_159)) (some_pname A_158))) (((eq pname) A_159) A_158)))
% FOF formula (forall (A_159:hoare_1708887482_state) (A_158:hoare_1708887482_state), ((iff (((eq option1624383643_state) (some_H1974565227_state A_159)) (some_H1974565227_state A_158))) (((eq hoare_1708887482_state) A_159) A_158))) of role axiom named fact_499_option_Oinject
% A new axiom: (forall (A_159:hoare_1708887482_state) (A_158:hoare_1708887482_state), ((iff (((eq option1624383643_state) (some_H1974565227_state A_159)) (some_H1974565227_state A_158))) (((eq hoare_1708887482_state) A_159) A_158)))
% FOF formula (forall (A_159:com) (A_158:com), ((iff (((eq option_com) (some_com A_159)) (some_com A_158))) (((eq com) A_159) A_158))) of role axiom named fact_500_option_Oinject
% A new axiom: (forall (A_159:com) (A_158:com), ((iff (((eq option_com) (some_com A_159)) (some_com A_158))) (((eq com) A_159) A_158)))
% FOF formula (forall (G_26:(hoare_1708887482_state->Prop)) (P_29:(state->(state->Prop))) (C_46:com) (Q_20:(state->(state->Prop))) (C_45:Prop), ((C_45->((hoare_90032982_state G_26) ((insert528405184_state (((hoare_858012674_state P_29) C_46) Q_20)) bot_bo19817387tate_o)))->((hoare_90032982_state G_26) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S_2:state)=> ((and ((P_29 Z_11) S_2)) C_45))) C_46) Q_20)) bot_bo19817387tate_o)))) of role axiom named fact_501_constant
% A new axiom: (forall (G_26:(hoare_1708887482_state->Prop)) (P_29:(state->(state->Prop))) (C_46:com) (Q_20:(state->(state->Prop))) (C_45:Prop), ((C_45->((hoare_90032982_state G_26) ((insert528405184_state (((hoare_858012674_state P_29) C_46) Q_20)) bot_bo19817387tate_o)))->((hoare_90032982_state G_26) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S_2:state)=> ((and ((P_29 Z_11) S_2)) C_45))) C_46) Q_20)) bot_bo19817387tate_o))))
% FOF formula (forall (Pn_2:pname) (G_25:(hoare_1708887482_state->Prop)) (P_28:(pname->(state->(state->Prop)))) (Q_19:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_25) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_28 P_27)) (body_1 P_27)) (Q_19 P_27)))) Procs_1))) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_28 P_27)) (the_com (body P_27))) (Q_19 P_27)))) Procs_1))->(((member_pname Pn_2) Procs_1)->((hoare_90032982_state G_25) ((insert528405184_state (((hoare_858012674_state (P_28 Pn_2)) (body_1 Pn_2)) (Q_19 Pn_2))) bot_bo19817387tate_o))))) of role axiom named fact_502_Body1
% A new axiom: (forall (Pn_2:pname) (G_25:(hoare_1708887482_state->Prop)) (P_28:(pname->(state->(state->Prop)))) (Q_19:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_25) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_28 P_27)) (body_1 P_27)) (Q_19 P_27)))) Procs_1))) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_28 P_27)) (the_com (body P_27))) (Q_19 P_27)))) Procs_1))->(((member_pname Pn_2) Procs_1)->((hoare_90032982_state G_25) ((insert528405184_state (((hoare_858012674_state (P_28 Pn_2)) (body_1 Pn_2)) (Q_19 Pn_2))) bot_bo19817387tate_o)))))
% FOF formula (forall (A_157:(pname->Prop)), (((ord_less_eq_pname_o A_157) bot_bot_pname_o)->(((eq (pname->Prop)) A_157) bot_bot_pname_o))) of role axiom named fact_503_le__bot
% A new axiom: (forall (A_157:(pname->Prop)), (((ord_less_eq_pname_o A_157) bot_bot_pname_o)->(((eq (pname->Prop)) A_157) bot_bot_pname_o)))
% FOF formula (forall (A_157:(com->Prop)), (((ord_less_eq_com_o A_157) bot_bot_com_o)->(((eq (com->Prop)) A_157) bot_bot_com_o))) of role axiom named fact_504_le__bot
% A new axiom: (forall (A_157:(com->Prop)), (((ord_less_eq_com_o A_157) bot_bot_com_o)->(((eq (com->Prop)) A_157) bot_bot_com_o)))
% FOF formula (forall (A_157:Prop), (((ord_less_eq_o A_157) bot_bot_o)->((iff A_157) bot_bot_o))) of role axiom named fact_505_le__bot
% A new axiom: (forall (A_157:Prop), (((ord_less_eq_o A_157) bot_bot_o)->((iff A_157) bot_bot_o)))
% FOF formula (forall (A_157:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_157) bot_bo19817387tate_o)->(((eq (hoare_1708887482_state->Prop)) A_157) bot_bo19817387tate_o))) of role axiom named fact_506_le__bot
% A new axiom: (forall (A_157:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_157) bot_bo19817387tate_o)->(((eq (hoare_1708887482_state->Prop)) A_157) bot_bo19817387tate_o)))
% FOF formula (forall (A_156:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_156) bot_bot_pname_o)) (((eq (pname->Prop)) A_156) bot_bot_pname_o))) of role axiom named fact_507_bot__unique
% A new axiom: (forall (A_156:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_156) bot_bot_pname_o)) (((eq (pname->Prop)) A_156) bot_bot_pname_o)))
% FOF formula (forall (A_156:(com->Prop)), ((iff ((ord_less_eq_com_o A_156) bot_bot_com_o)) (((eq (com->Prop)) A_156) bot_bot_com_o))) of role axiom named fact_508_bot__unique
% A new axiom: (forall (A_156:(com->Prop)), ((iff ((ord_less_eq_com_o A_156) bot_bot_com_o)) (((eq (com->Prop)) A_156) bot_bot_com_o)))
% FOF formula (forall (A_156:Prop), ((iff ((ord_less_eq_o A_156) bot_bot_o)) ((iff A_156) bot_bot_o))) of role axiom named fact_509_bot__unique
% A new axiom: (forall (A_156:Prop), ((iff ((ord_less_eq_o A_156) bot_bot_o)) ((iff A_156) bot_bot_o)))
% FOF formula (forall (A_156:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_156) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) A_156) bot_bo19817387tate_o))) of role axiom named fact_510_bot__unique
% A new axiom: (forall (A_156:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_156) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) A_156) bot_bo19817387tate_o)))
% FOF formula (forall (A_155:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_155)) of role axiom named fact_511_bot__least
% A new axiom: (forall (A_155:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_155))
% FOF formula (forall (A_155:(com->Prop)), ((ord_less_eq_com_o bot_bot_com_o) A_155)) of role axiom named fact_512_bot__least
% A new axiom: (forall (A_155:(com->Prop)), ((ord_less_eq_com_o bot_bot_com_o) A_155))
% FOF formula (forall (A_155:Prop), ((ord_less_eq_o bot_bot_o) A_155)) of role axiom named fact_513_bot__least
% A new axiom: (forall (A_155:Prop), ((ord_less_eq_o bot_bot_o) A_155))
% FOF formula (forall (A_155:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o bot_bo19817387tate_o) A_155)) of role axiom named fact_514_bot__least
% A new axiom: (forall (A_155:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o bot_bo19817387tate_o) A_155))
% FOF formula (forall (X_92:pname) (F_65:(pname->Prop)) (G_24:(pname->Prop)), (((ord_less_eq_pname_o F_65) G_24)->((ord_less_eq_o (F_65 X_92)) (G_24 X_92)))) of role axiom named fact_515_le__funE
% A new axiom: (forall (X_92:pname) (F_65:(pname->Prop)) (G_24:(pname->Prop)), (((ord_less_eq_pname_o F_65) G_24)->((ord_less_eq_o (F_65 X_92)) (G_24 X_92))))
% FOF formula (forall (X_92:hoare_1708887482_state) (F_65:(hoare_1708887482_state->Prop)) (G_24:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o F_65) G_24)->((ord_less_eq_o (F_65 X_92)) (G_24 X_92)))) of role axiom named fact_516_le__funE
% A new axiom: (forall (X_92:hoare_1708887482_state) (F_65:(hoare_1708887482_state->Prop)) (G_24:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o F_65) G_24)->((ord_less_eq_o (F_65 X_92)) (G_24 X_92))))
% FOF formula (forall (X_91:pname) (F_64:(pname->Prop)) (G_23:(pname->Prop)), (((ord_less_eq_pname_o F_64) G_23)->((ord_less_eq_o (F_64 X_91)) (G_23 X_91)))) of role axiom named fact_517_le__funD
% A new axiom: (forall (X_91:pname) (F_64:(pname->Prop)) (G_23:(pname->Prop)), (((ord_less_eq_pname_o F_64) G_23)->((ord_less_eq_o (F_64 X_91)) (G_23 X_91))))
% FOF formula (forall (X_91:hoare_1708887482_state) (F_64:(hoare_1708887482_state->Prop)) (G_23:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o F_64) G_23)->((ord_less_eq_o (F_64 X_91)) (G_23 X_91)))) of role axiom named fact_518_le__funD
% A new axiom: (forall (X_91:hoare_1708887482_state) (F_64:(hoare_1708887482_state->Prop)) (G_23:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o F_64) G_23)->((ord_less_eq_o (F_64 X_91)) (G_23 X_91))))
% FOF formula (forall (F_63:(pname->Prop)) (G_22:(pname->Prop)), ((iff ((ord_less_eq_pname_o F_63) G_22)) (forall (X_3:pname), ((ord_less_eq_o (F_63 X_3)) (G_22 X_3))))) of role axiom named fact_519_le__fun__def
% A new axiom: (forall (F_63:(pname->Prop)) (G_22:(pname->Prop)), ((iff ((ord_less_eq_pname_o F_63) G_22)) (forall (X_3:pname), ((ord_less_eq_o (F_63 X_3)) (G_22 X_3)))))
% FOF formula (forall (F_63:(hoare_1708887482_state->Prop)) (G_22:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o F_63) G_22)) (forall (X_3:hoare_1708887482_state), ((ord_less_eq_o (F_63 X_3)) (G_22 X_3))))) of role axiom named fact_520_le__fun__def
% A new axiom: (forall (F_63:(hoare_1708887482_state->Prop)) (G_22:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o F_63) G_22)) (forall (X_3:hoare_1708887482_state), ((ord_less_eq_o (F_63 X_3)) (G_22 X_3)))))
% FOF formula (forall (X_90:pname), ((iff (bot_bot_pname_o X_90)) bot_bot_o)) of role axiom named fact_521_bot__apply
% A new axiom: (forall (X_90:pname), ((iff (bot_bot_pname_o X_90)) bot_bot_o))
% FOF formula (forall (X_90:com), ((iff (bot_bot_com_o X_90)) bot_bot_o)) of role axiom named fact_522_bot__apply
% A new axiom: (forall (X_90:com), ((iff (bot_bot_com_o X_90)) bot_bot_o))
% FOF formula (forall (X_90:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X_90)) bot_bot_o)) of role axiom named fact_523_bot__apply
% A new axiom: (forall (X_90:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X_90)) bot_bot_o))
% FOF formula (forall (X_3:pname), ((iff (bot_bot_pname_o X_3)) bot_bot_o)) of role axiom named fact_524_bot__fun__def
% A new axiom: (forall (X_3:pname), ((iff (bot_bot_pname_o X_3)) bot_bot_o))
% FOF formula (forall (X_3:com), ((iff (bot_bot_com_o X_3)) bot_bot_o)) of role axiom named fact_525_bot__fun__def
% A new axiom: (forall (X_3:com), ((iff (bot_bot_com_o X_3)) bot_bot_o))
% FOF formula (forall (X_3:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X_3)) bot_bot_o)) of role axiom named fact_526_bot__fun__def
% A new axiom: (forall (X_3:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X_3)) bot_bot_o))
% FOF formula (forall (P_26:((pname->Prop)->(state->(state->Prop)))) (Q_18:((pname->Prop)->(state->(state->Prop)))) (G_21:(hoare_1708887482_state->Prop)) (P_25:((pname->Prop)->(state->(state->Prop)))) (C0_1:((pname->Prop)->com)) (Q_17:((pname->Prop)->(state->(state->Prop)))) (U_1:((pname->Prop)->Prop)), ((finite297249702name_o U_1)->((forall (P_27:(pname->Prop)), (((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27))) bot_bo19817387tate_o))->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_21) ((image_1922967206_state (fun (P_27:(pname->Prop))=> (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27)))) U_1))->((hoare_90032982_state G_21) ((image_1922967206_state (fun (P_27:(pname->Prop))=> (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27)))) U_1)))))) of role axiom named fact_527_finite__pointwise
% A new axiom: (forall (P_26:((pname->Prop)->(state->(state->Prop)))) (Q_18:((pname->Prop)->(state->(state->Prop)))) (G_21:(hoare_1708887482_state->Prop)) (P_25:((pname->Prop)->(state->(state->Prop)))) (C0_1:((pname->Prop)->com)) (Q_17:((pname->Prop)->(state->(state->Prop)))) (U_1:((pname->Prop)->Prop)), ((finite297249702name_o U_1)->((forall (P_27:(pname->Prop)), (((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27))) bot_bo19817387tate_o))->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_21) ((image_1922967206_state (fun (P_27:(pname->Prop))=> (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27)))) U_1))->((hoare_90032982_state G_21) ((image_1922967206_state (fun (P_27:(pname->Prop))=> (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27)))) U_1))))))
% FOF formula (forall (P_26:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (Q_18:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (G_21:(hoare_1708887482_state->Prop)) (P_25:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (C0_1:((hoare_1708887482_state->Prop)->com)) (Q_17:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (U_1:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o U_1)->((forall (P_27:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27))) bot_bo19817387tate_o))->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_21) ((image_27005066_state (fun (P_27:(hoare_1708887482_state->Prop))=> (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27)))) U_1))->((hoare_90032982_state G_21) ((image_27005066_state (fun (P_27:(hoare_1708887482_state->Prop))=> (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27)))) U_1)))))) of role axiom named fact_528_finite__pointwise
% A new axiom: (forall (P_26:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (Q_18:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (G_21:(hoare_1708887482_state->Prop)) (P_25:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (C0_1:((hoare_1708887482_state->Prop)->com)) (Q_17:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (U_1:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o U_1)->((forall (P_27:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27))) bot_bo19817387tate_o))->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_21) ((image_27005066_state (fun (P_27:(hoare_1708887482_state->Prop))=> (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27)))) U_1))->((hoare_90032982_state G_21) ((image_27005066_state (fun (P_27:(hoare_1708887482_state->Prop))=> (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27)))) U_1))))))
% FOF formula (forall (P_26:(pname->(state->(state->Prop)))) (Q_18:(pname->(state->(state->Prop)))) (G_21:(hoare_1708887482_state->Prop)) (P_25:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_17:(pname->(state->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_27:pname), (((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27))) bot_bo19817387tate_o))->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_21) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27)))) U_1))->((hoare_90032982_state G_21) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27)))) U_1)))))) of role axiom named fact_529_finite__pointwise
% A new axiom: (forall (P_26:(pname->(state->(state->Prop)))) (Q_18:(pname->(state->(state->Prop)))) (G_21:(hoare_1708887482_state->Prop)) (P_25:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_17:(pname->(state->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_27:pname), (((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27))) bot_bo19817387tate_o))->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_21) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27)))) U_1))->((hoare_90032982_state G_21) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27)))) U_1))))))
% FOF formula (forall (G_20:(hoare_1708887482_state->Prop)) (C_44:com) (Q_16:(state->(state->Prop))) (P_24:(state->(state->Prop))), ((forall (Z_11:state) (S_2:state), (((P_24 Z_11) S_2)->((hoare_90032982_state G_20) ((insert528405184_state (((hoare_858012674_state (fun (Za:state) (S_3:state)=> (((eq state) S_3) S_2))) C_44) (fun (Z_12:state)=> (Q_16 Z_11)))) bot_bo19817387tate_o))))->((hoare_90032982_state G_20) ((insert528405184_state (((hoare_858012674_state P_24) C_44) Q_16)) bot_bo19817387tate_o)))) of role axiom named fact_530_escape
% A new axiom: (forall (G_20:(hoare_1708887482_state->Prop)) (C_44:com) (Q_16:(state->(state->Prop))) (P_24:(state->(state->Prop))), ((forall (Z_11:state) (S_2:state), (((P_24 Z_11) S_2)->((hoare_90032982_state G_20) ((insert528405184_state (((hoare_858012674_state (fun (Za:state) (S_3:state)=> (((eq state) S_3) S_2))) C_44) (fun (Z_12:state)=> (Q_16 Z_11)))) bot_bo19817387tate_o))))->((hoare_90032982_state G_20) ((insert528405184_state (((hoare_858012674_state P_24) C_44) Q_16)) bot_bo19817387tate_o))))
% FOF formula (forall (G_19:(hoare_1708887482_state->Prop)) (P_23:(pname->(state->(state->Prop)))) (Q_15:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_496444244_state ((semila1122118281tate_o G_19) ((image_1116629049_state (fun (Pn:pname)=> (((hoare_858012674_state (P_23 Pn)) (body_1 Pn)) (Q_15 Pn)))) Procs))) ((image_1116629049_state (fun (Pn:pname)=> (((hoare_858012674_state (P_23 Pn)) (the_com (body Pn))) (Q_15 Pn)))) Procs))->((hoare_496444244_state G_19) ((image_1116629049_state (fun (Pn:pname)=> (((hoare_858012674_state (P_23 Pn)) (body_1 Pn)) (Q_15 Pn)))) Procs)))) of role axiom named fact_531_Body__sound__lemma
% A new axiom: (forall (G_19:(hoare_1708887482_state->Prop)) (P_23:(pname->(state->(state->Prop)))) (Q_15:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_496444244_state ((semila1122118281tate_o G_19) ((image_1116629049_state (fun (Pn:pname)=> (((hoare_858012674_state (P_23 Pn)) (body_1 Pn)) (Q_15 Pn)))) Procs))) ((image_1116629049_state (fun (Pn:pname)=> (((hoare_858012674_state (P_23 Pn)) (the_com (body Pn))) (Q_15 Pn)))) Procs))->((hoare_496444244_state G_19) ((image_1116629049_state (fun (Pn:pname)=> (((hoare_858012674_state (P_23 Pn)) (body_1 Pn)) (Q_15 Pn)))) Procs))))
% FOF formula (forall (P_22:(state->(state->Prop))) (G_18:(hoare_1708887482_state->Prop)) (P_21:(state->(state->Prop))) (C_43:com) (Q_14:(state->(state->Prop))), (((hoare_90032982_state G_18) ((insert528405184_state (((hoare_858012674_state P_21) C_43) Q_14)) bot_bo19817387tate_o))->((forall (Z_11:state) (S_2:state), (((P_22 Z_11) S_2)->((P_21 Z_11) S_2)))->((hoare_90032982_state G_18) ((insert528405184_state (((hoare_858012674_state P_22) C_43) Q_14)) bot_bo19817387tate_o))))) of role axiom named fact_532_conseq1
% A new axiom: (forall (P_22:(state->(state->Prop))) (G_18:(hoare_1708887482_state->Prop)) (P_21:(state->(state->Prop))) (C_43:com) (Q_14:(state->(state->Prop))), (((hoare_90032982_state G_18) ((insert528405184_state (((hoare_858012674_state P_21) C_43) Q_14)) bot_bo19817387tate_o))->((forall (Z_11:state) (S_2:state), (((P_22 Z_11) S_2)->((P_21 Z_11) S_2)))->((hoare_90032982_state G_18) ((insert528405184_state (((hoare_858012674_state P_22) C_43) Q_14)) bot_bo19817387tate_o)))))
% FOF formula (forall (Q_13:(state->(state->Prop))) (G_17:(hoare_1708887482_state->Prop)) (P_20:(state->(state->Prop))) (C_42:com) (Q_12:(state->(state->Prop))), (((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state P_20) C_42) Q_12)) bot_bo19817387tate_o))->((forall (Z_11:state) (S_2:state), (((Q_12 Z_11) S_2)->((Q_13 Z_11) S_2)))->((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state P_20) C_42) Q_13)) bot_bo19817387tate_o))))) of role axiom named fact_533_conseq2
% A new axiom: (forall (Q_13:(state->(state->Prop))) (G_17:(hoare_1708887482_state->Prop)) (P_20:(state->(state->Prop))) (C_42:com) (Q_12:(state->(state->Prop))), (((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state P_20) C_42) Q_12)) bot_bo19817387tate_o))->((forall (Z_11:state) (S_2:state), (((Q_12 Z_11) S_2)->((Q_13 Z_11) S_2)))->((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state P_20) C_42) Q_13)) bot_bo19817387tate_o)))))
% FOF formula (forall (P:(state->(state->Prop))) (Q_11:(state->(state->Prop))) (C_34:com), (((hoare_90032982_state bot_bo19817387tate_o) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o))->(((hoare_496444244_state bot_bo19817387tate_o) ((insert528405184_state (((hoare_858012674_state P) C_34) Q_11)) bot_bo19817387tate_o))->((hoare_90032982_state bot_bo19817387tate_o) ((insert528405184_state (((hoare_858012674_state P) C_34) Q_11)) bot_bo19817387tate_o))))) of role axiom named fact_534_MGF__complete
% A new axiom: (forall (P:(state->(state->Prop))) (Q_11:(state->(state->Prop))) (C_34:com), (((hoare_90032982_state bot_bo19817387tate_o) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o))->(((hoare_496444244_state bot_bo19817387tate_o) ((insert528405184_state (((hoare_858012674_state P) C_34) Q_11)) bot_bo19817387tate_o))->((hoare_90032982_state bot_bo19817387tate_o) ((insert528405184_state (((hoare_858012674_state P) C_34) Q_11)) bot_bo19817387tate_o)))))
% FOF formula (forall (A_154:(pname->Prop)) (B_100:(pname->Prop)) (X_89:pname), ((((semila1780557381name_o A_154) B_100) X_89)->(((A_154 X_89)->False)->(B_100 X_89)))) of role axiom named fact_535_sup1E
% A new axiom: (forall (A_154:(pname->Prop)) (B_100:(pname->Prop)) (X_89:pname), ((((semila1780557381name_o A_154) B_100) X_89)->(((A_154 X_89)->False)->(B_100 X_89))))
% FOF formula (forall (A_154:(hoare_1708887482_state->Prop)) (B_100:(hoare_1708887482_state->Prop)) (X_89:hoare_1708887482_state), ((((semila1122118281tate_o A_154) B_100) X_89)->(((A_154 X_89)->False)->(B_100 X_89)))) of role axiom named fact_536_sup1E
% A new axiom: (forall (A_154:(hoare_1708887482_state->Prop)) (B_100:(hoare_1708887482_state->Prop)) (X_89:hoare_1708887482_state), ((((semila1122118281tate_o A_154) B_100) X_89)->(((A_154 X_89)->False)->(B_100 X_89))))
% FOF formula (forall (A_153:(pname->Prop)) (B_99:(pname->Prop)) (X_88:pname), ((((B_99 X_88)->False)->(A_153 X_88))->(((semila1780557381name_o A_153) B_99) X_88))) of role axiom named fact_537_sup1CI
% A new axiom: (forall (A_153:(pname->Prop)) (B_99:(pname->Prop)) (X_88:pname), ((((B_99 X_88)->False)->(A_153 X_88))->(((semila1780557381name_o A_153) B_99) X_88)))
% FOF formula (forall (A_153:(hoare_1708887482_state->Prop)) (B_99:(hoare_1708887482_state->Prop)) (X_88:hoare_1708887482_state), ((((B_99 X_88)->False)->(A_153 X_88))->(((semila1122118281tate_o A_153) B_99) X_88))) of role axiom named fact_538_sup1CI
% A new axiom: (forall (A_153:(hoare_1708887482_state->Prop)) (B_99:(hoare_1708887482_state->Prop)) (X_88:hoare_1708887482_state), ((((B_99 X_88)->False)->(A_153 X_88))->(((semila1122118281tate_o A_153) B_99) X_88)))
% FOF formula (forall (Q_10:(state->(state->Prop))) (P_19:(state->(state->Prop))) (G_16:(hoare_1708887482_state->Prop)) (P_18:(state->(state->Prop))) (C_41:com) (Q_9:(state->(state->Prop))), (((hoare_90032982_state G_16) ((insert528405184_state (((hoare_858012674_state P_18) C_41) Q_9)) bot_bo19817387tate_o))->((forall (Z_11:state) (S_2:state), (((P_19 Z_11) S_2)->(forall (S_3:state), ((forall (Z_12:state), (((P_18 Z_12) S_2)->((Q_9 Z_12) S_3)))->((Q_10 Z_11) S_3)))))->((hoare_90032982_state G_16) ((insert528405184_state (((hoare_858012674_state P_19) C_41) Q_10)) bot_bo19817387tate_o))))) of role axiom named fact_539_conseq12
% A new axiom: (forall (Q_10:(state->(state->Prop))) (P_19:(state->(state->Prop))) (G_16:(hoare_1708887482_state->Prop)) (P_18:(state->(state->Prop))) (C_41:com) (Q_9:(state->(state->Prop))), (((hoare_90032982_state G_16) ((insert528405184_state (((hoare_858012674_state P_18) C_41) Q_9)) bot_bo19817387tate_o))->((forall (Z_11:state) (S_2:state), (((P_19 Z_11) S_2)->(forall (S_3:state), ((forall (Z_12:state), (((P_18 Z_12) S_2)->((Q_9 Z_12) S_3)))->((Q_10 Z_11) S_3)))))->((hoare_90032982_state G_16) ((insert528405184_state (((hoare_858012674_state P_19) C_41) Q_10)) bot_bo19817387tate_o)))))
% FOF formula (forall (G_15:(hoare_1708887482_state->Prop)) (Ts:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_15) Ts)->((hoare_496444244_state G_15) Ts))) of role axiom named fact_540_hoare__sound
% A new axiom: (forall (G_15:(hoare_1708887482_state->Prop)) (Ts:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_15) Ts)->((hoare_496444244_state G_15) Ts)))
% FOF formula (forall (X_3:com), ((iff (bot_bot_com_o X_3)) ((member_com X_3) bot_bot_com_o))) of role axiom named fact_541_bot__empty__eq
% A new axiom: (forall (X_3:com), ((iff (bot_bot_com_o X_3)) ((member_com X_3) bot_bot_com_o)))
% FOF formula (forall (X_3:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X_3)) ((member451959335_state X_3) bot_bo19817387tate_o))) of role axiom named fact_542_bot__empty__eq
% A new axiom: (forall (X_3:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X_3)) ((member451959335_state X_3) bot_bo19817387tate_o)))
% FOF formula (forall (X_3:pname), ((iff (bot_bot_pname_o X_3)) ((member_pname X_3) bot_bot_pname_o))) of role axiom named fact_543_bot__empty__eq
% A new axiom: (forall (X_3:pname), ((iff (bot_bot_pname_o X_3)) ((member_pname X_3) bot_bot_pname_o)))
% FOF formula (forall (Q_8:(pname->Prop)) (P_17:(pname->Prop)) (X_87:pname), ((P_17 X_87)->(((ord_less_eq_pname_o P_17) Q_8)->(Q_8 X_87)))) of role axiom named fact_544_rev__predicate1D
% A new axiom: (forall (Q_8:(pname->Prop)) (P_17:(pname->Prop)) (X_87:pname), ((P_17 X_87)->(((ord_less_eq_pname_o P_17) Q_8)->(Q_8 X_87))))
% FOF formula (forall (Q_8:(hoare_1708887482_state->Prop)) (P_17:(hoare_1708887482_state->Prop)) (X_87:hoare_1708887482_state), ((P_17 X_87)->(((ord_le777019615tate_o P_17) Q_8)->(Q_8 X_87)))) of role axiom named fact_545_rev__predicate1D
% A new axiom: (forall (Q_8:(hoare_1708887482_state->Prop)) (P_17:(hoare_1708887482_state->Prop)) (X_87:hoare_1708887482_state), ((P_17 X_87)->(((ord_le777019615tate_o P_17) Q_8)->(Q_8 X_87))))
% FOF formula (forall (X_86:pname) (P_16:(pname->Prop)) (Q_7:(pname->Prop)), (((ord_less_eq_pname_o P_16) Q_7)->((P_16 X_86)->(Q_7 X_86)))) of role axiom named fact_546_predicate1D
% A new axiom: (forall (X_86:pname) (P_16:(pname->Prop)) (Q_7:(pname->Prop)), (((ord_less_eq_pname_o P_16) Q_7)->((P_16 X_86)->(Q_7 X_86))))
% FOF formula (forall (X_86:hoare_1708887482_state) (P_16:(hoare_1708887482_state->Prop)) (Q_7:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o P_16) Q_7)->((P_16 X_86)->(Q_7 X_86)))) of role axiom named fact_547_predicate1D
% A new axiom: (forall (X_86:hoare_1708887482_state) (P_16:(hoare_1708887482_state->Prop)) (Q_7:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o P_16) Q_7)->((P_16 X_86)->(Q_7 X_86))))
% FOF formula (forall (A_152:(pname->Prop)) (B_98:(pname->Prop)) (X_85:pname), ((B_98 X_85)->(((semila1780557381name_o A_152) B_98) X_85))) of role axiom named fact_548_sup1I2
% A new axiom: (forall (A_152:(pname->Prop)) (B_98:(pname->Prop)) (X_85:pname), ((B_98 X_85)->(((semila1780557381name_o A_152) B_98) X_85)))
% FOF formula (forall (A_152:(hoare_1708887482_state->Prop)) (B_98:(hoare_1708887482_state->Prop)) (X_85:hoare_1708887482_state), ((B_98 X_85)->(((semila1122118281tate_o A_152) B_98) X_85))) of role axiom named fact_549_sup1I2
% A new axiom: (forall (A_152:(hoare_1708887482_state->Prop)) (B_98:(hoare_1708887482_state->Prop)) (X_85:hoare_1708887482_state), ((B_98 X_85)->(((semila1122118281tate_o A_152) B_98) X_85)))
% FOF formula (forall (B_97:(pname->Prop)) (A_151:(pname->Prop)) (X_84:pname), ((A_151 X_84)->(((semila1780557381name_o A_151) B_97) X_84))) of role axiom named fact_550_sup1I1
% A new axiom: (forall (B_97:(pname->Prop)) (A_151:(pname->Prop)) (X_84:pname), ((A_151 X_84)->(((semila1780557381name_o A_151) B_97) X_84)))
% FOF formula (forall (B_97:(hoare_1708887482_state->Prop)) (A_151:(hoare_1708887482_state->Prop)) (X_84:hoare_1708887482_state), ((A_151 X_84)->(((semila1122118281tate_o A_151) B_97) X_84))) of role axiom named fact_551_sup1I1
% A new axiom: (forall (B_97:(hoare_1708887482_state->Prop)) (A_151:(hoare_1708887482_state->Prop)) (X_84:hoare_1708887482_state), ((A_151 X_84)->(((semila1122118281tate_o A_151) B_97) X_84)))
% FOF formula (forall (R_3:(com->Prop)) (S_6:(com->Prop)), ((iff ((ord_less_eq_com_o (fun (X_3:com)=> ((member_com X_3) R_3))) (fun (X_3:com)=> ((member_com X_3) S_6)))) ((ord_less_eq_com_o R_3) S_6))) of role axiom named fact_552_pred__subset__eq
% A new axiom: (forall (R_3:(com->Prop)) (S_6:(com->Prop)), ((iff ((ord_less_eq_com_o (fun (X_3:com)=> ((member_com X_3) R_3))) (fun (X_3:com)=> ((member_com X_3) S_6)))) ((ord_less_eq_com_o R_3) S_6)))
% FOF formula (forall (R_3:(hoare_1708887482_state->Prop)) (S_6:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) R_3))) (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) S_6)))) ((ord_le777019615tate_o R_3) S_6))) of role axiom named fact_553_pred__subset__eq
% A new axiom: (forall (R_3:(hoare_1708887482_state->Prop)) (S_6:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) R_3))) (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) S_6)))) ((ord_le777019615tate_o R_3) S_6)))
% FOF formula (forall (R_3:(pname->Prop)) (S_6:(pname->Prop)), ((iff ((ord_less_eq_pname_o (fun (X_3:pname)=> ((member_pname X_3) R_3))) (fun (X_3:pname)=> ((member_pname X_3) S_6)))) ((ord_less_eq_pname_o R_3) S_6))) of role axiom named fact_554_pred__subset__eq
% A new axiom: (forall (R_3:(pname->Prop)) (S_6:(pname->Prop)), ((iff ((ord_less_eq_pname_o (fun (X_3:pname)=> ((member_pname X_3) R_3))) (fun (X_3:pname)=> ((member_pname X_3) S_6)))) ((ord_less_eq_pname_o R_3) S_6)))
% FOF formula (forall (R_2:(com->Prop)) (S_5:(com->Prop)) (X_3:com), ((iff (((semila1562558655_com_o (fun (Y_4:com)=> ((member_com Y_4) R_2))) (fun (Y_4:com)=> ((member_com Y_4) S_5))) X_3)) ((member_com X_3) ((semila1562558655_com_o R_2) S_5)))) of role axiom named fact_555_sup__Un__eq
% A new axiom: (forall (R_2:(com->Prop)) (S_5:(com->Prop)) (X_3:com), ((iff (((semila1562558655_com_o (fun (Y_4:com)=> ((member_com Y_4) R_2))) (fun (Y_4:com)=> ((member_com Y_4) S_5))) X_3)) ((member_com X_3) ((semila1562558655_com_o R_2) S_5))))
% FOF formula (forall (R_2:(hoare_1708887482_state->Prop)) (S_5:(hoare_1708887482_state->Prop)) (X_3:hoare_1708887482_state), ((iff (((semila1122118281tate_o (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) R_2))) (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) S_5))) X_3)) ((member451959335_state X_3) ((semila1122118281tate_o R_2) S_5)))) of role axiom named fact_556_sup__Un__eq
% A new axiom: (forall (R_2:(hoare_1708887482_state->Prop)) (S_5:(hoare_1708887482_state->Prop)) (X_3:hoare_1708887482_state), ((iff (((semila1122118281tate_o (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) R_2))) (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) S_5))) X_3)) ((member451959335_state X_3) ((semila1122118281tate_o R_2) S_5))))
% FOF formula (forall (R_2:(pname->Prop)) (S_5:(pname->Prop)) (X_3:pname), ((iff (((semila1780557381name_o (fun (Y_4:pname)=> ((member_pname Y_4) R_2))) (fun (Y_4:pname)=> ((member_pname Y_4) S_5))) X_3)) ((member_pname X_3) ((semila1780557381name_o R_2) S_5)))) of role axiom named fact_557_sup__Un__eq
% A new axiom: (forall (R_2:(pname->Prop)) (S_5:(pname->Prop)) (X_3:pname), ((iff (((semila1780557381name_o (fun (Y_4:pname)=> ((member_pname Y_4) R_2))) (fun (Y_4:pname)=> ((member_pname Y_4) S_5))) X_3)) ((member_pname X_3) ((semila1780557381name_o R_2) S_5))))
% FOF formula (forall (F_62:(pname->Prop)) (G_14:(pname->Prop)), ((forall (X_3:pname), ((ord_less_eq_o (F_62 X_3)) (G_14 X_3)))->((ord_less_eq_pname_o F_62) G_14))) of role axiom named fact_558_le__funI
% A new axiom: (forall (F_62:(pname->Prop)) (G_14:(pname->Prop)), ((forall (X_3:pname), ((ord_less_eq_o (F_62 X_3)) (G_14 X_3)))->((ord_less_eq_pname_o F_62) G_14)))
% FOF formula (forall (F_62:(hoare_1708887482_state->Prop)) (G_14:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), ((ord_less_eq_o (F_62 X_3)) (G_14 X_3)))->((ord_le777019615tate_o F_62) G_14))) of role axiom named fact_559_le__funI
% A new axiom: (forall (F_62:(hoare_1708887482_state->Prop)) (G_14:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), ((ord_less_eq_o (F_62 X_3)) (G_14 X_3)))->((ord_le777019615tate_o F_62) G_14)))
% FOF formula (forall (X_83:pname), (((eq (pname->Prop)) (set_pname (some_pname X_83))) ((insert_pname X_83) bot_bot_pname_o))) of role axiom named fact_560_Option_Oset_Osimps_I2_J
% A new axiom: (forall (X_83:pname), (((eq (pname->Prop)) (set_pname (some_pname X_83))) ((insert_pname X_83) bot_bot_pname_o)))
% FOF formula (forall (X_83:com), (((eq (com->Prop)) (set_com (some_com X_83))) ((insert_com X_83) bot_bot_com_o))) of role axiom named fact_561_Option_Oset_Osimps_I2_J
% A new axiom: (forall (X_83:com), (((eq (com->Prop)) (set_com (some_com X_83))) ((insert_com X_83) bot_bot_com_o)))
% FOF formula (forall (X_83:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (set_Ho525251890_state (some_H1974565227_state X_83))) ((insert528405184_state X_83) bot_bo19817387tate_o))) of role axiom named fact_562_Option_Oset_Osimps_I2_J
% A new axiom: (forall (X_83:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (set_Ho525251890_state (some_H1974565227_state X_83))) ((insert528405184_state X_83) bot_bo19817387tate_o)))
% FOF formula (forall (F_61:(pname->Prop)) (G_13:(pname->Prop)) (X_82:pname), ((iff (((semila1780557381name_o F_61) G_13) X_82)) ((semila10642723_sup_o (F_61 X_82)) (G_13 X_82)))) of role axiom named fact_563_sup__apply
% A new axiom: (forall (F_61:(pname->Prop)) (G_13:(pname->Prop)) (X_82:pname), ((iff (((semila1780557381name_o F_61) G_13) X_82)) ((semila10642723_sup_o (F_61 X_82)) (G_13 X_82))))
% FOF formula (forall (F_61:(hoare_1708887482_state->Prop)) (G_13:(hoare_1708887482_state->Prop)) (X_82:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_61) G_13) X_82)) ((semila10642723_sup_o (F_61 X_82)) (G_13 X_82)))) of role axiom named fact_564_sup__apply
% A new axiom: (forall (F_61:(hoare_1708887482_state->Prop)) (G_13:(hoare_1708887482_state->Prop)) (X_82:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_61) G_13) X_82)) ((semila10642723_sup_o (F_61 X_82)) (G_13 X_82))))
% FOF formula (forall (F_60:(pname->Prop)) (G_12:(pname->Prop)) (X_3:pname), ((iff (((semila1780557381name_o F_60) G_12) X_3)) ((semila10642723_sup_o (F_60 X_3)) (G_12 X_3)))) of role axiom named fact_565_sup__fun__def
% A new axiom: (forall (F_60:(pname->Prop)) (G_12:(pname->Prop)) (X_3:pname), ((iff (((semila1780557381name_o F_60) G_12) X_3)) ((semila10642723_sup_o (F_60 X_3)) (G_12 X_3))))
% FOF formula (forall (F_60:(hoare_1708887482_state->Prop)) (G_12:(hoare_1708887482_state->Prop)) (X_3:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_60) G_12) X_3)) ((semila10642723_sup_o (F_60 X_3)) (G_12 X_3)))) of role axiom named fact_566_sup__fun__def
% A new axiom: (forall (F_60:(hoare_1708887482_state->Prop)) (G_12:(hoare_1708887482_state->Prop)) (X_3:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_60) G_12) X_3)) ((semila10642723_sup_o (F_60 X_3)) (G_12 X_3))))
% FOF formula (hoare_1160767572gleton->(forall (T_1:state), ((forall (S_2:state), (((eq state) S_2) T_1))->False))) of role axiom named fact_567_single__stateE
% A new axiom: (hoare_1160767572gleton->(forall (T_1:state), ((forall (S_2:state), (((eq state) S_2) T_1))->False)))
% FOF formula (forall (X_81:(pname->Prop)) (Y_43:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_81) Y_43)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_81) bot_bot_pname_o)) (((eq (pname->Prop)) Y_43) bot_bot_pname_o)))) of role axiom named fact_568_sup__eq__bot__iff
% A new axiom: (forall (X_81:(pname->Prop)) (Y_43:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_81) Y_43)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_81) bot_bot_pname_o)) (((eq (pname->Prop)) Y_43) bot_bot_pname_o))))
% FOF formula (forall (X_81:(com->Prop)) (Y_43:(com->Prop)), ((iff (((eq (com->Prop)) ((semila1562558655_com_o X_81) Y_43)) bot_bot_com_o)) ((and (((eq (com->Prop)) X_81) bot_bot_com_o)) (((eq (com->Prop)) Y_43) bot_bot_com_o)))) of role axiom named fact_569_sup__eq__bot__iff
% A new axiom: (forall (X_81:(com->Prop)) (Y_43:(com->Prop)), ((iff (((eq (com->Prop)) ((semila1562558655_com_o X_81) Y_43)) bot_bot_com_o)) ((and (((eq (com->Prop)) X_81) bot_bot_com_o)) (((eq (com->Prop)) Y_43) bot_bot_com_o))))
% FOF formula (forall (X_81:Prop) (Y_43:Prop), ((iff ((iff ((semila10642723_sup_o X_81) Y_43)) bot_bot_o)) ((and ((iff X_81) bot_bot_o)) ((iff Y_43) bot_bot_o)))) of role axiom named fact_570_sup__eq__bot__iff
% A new axiom: (forall (X_81:Prop) (Y_43:Prop), ((iff ((iff ((semila10642723_sup_o X_81) Y_43)) bot_bot_o)) ((and ((iff X_81) bot_bot_o)) ((iff Y_43) bot_bot_o))))
% FOF formula (forall (X_81:(hoare_1708887482_state->Prop)) (Y_43:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_81) Y_43)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) X_81) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) Y_43) bot_bo19817387tate_o)))) of role axiom named fact_571_sup__eq__bot__iff
% A new axiom: (forall (X_81:(hoare_1708887482_state->Prop)) (Y_43:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_81) Y_43)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) X_81) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) Y_43) bot_bo19817387tate_o))))
% FOF formula (forall (X_80:com) (Xo_1:option_com), ((iff ((member_com X_80) (set_com Xo_1))) (((eq option_com) Xo_1) (some_com X_80)))) of role axiom named fact_572_elem__set
% A new axiom: (forall (X_80:com) (Xo_1:option_com), ((iff ((member_com X_80) (set_com Xo_1))) (((eq option_com) Xo_1) (some_com X_80))))
% FOF formula (forall (X_80:hoare_1708887482_state) (Xo_1:option1624383643_state), ((iff ((member451959335_state X_80) (set_Ho525251890_state Xo_1))) (((eq option1624383643_state) Xo_1) (some_H1974565227_state X_80)))) of role axiom named fact_573_elem__set
% A new axiom: (forall (X_80:hoare_1708887482_state) (Xo_1:option1624383643_state), ((iff ((member451959335_state X_80) (set_Ho525251890_state Xo_1))) (((eq option1624383643_state) Xo_1) (some_H1974565227_state X_80))))
% FOF formula (forall (X_80:pname) (Xo_1:option_pname), ((iff ((member_pname X_80) (set_pname Xo_1))) (((eq option_pname) Xo_1) (some_pname X_80)))) of role axiom named fact_574_elem__set
% A new axiom: (forall (X_80:pname) (Xo_1:option_pname), ((iff ((member_pname X_80) (set_pname Xo_1))) (((eq option_pname) Xo_1) (some_pname X_80))))
% FOF formula (forall (A_150:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_150) A_150)) A_150)) of role axiom named fact_575_sup_Oidem
% A new axiom: (forall (A_150:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_150) A_150)) A_150))
% FOF formula (forall (A_150:Prop), ((iff ((semila10642723_sup_o A_150) A_150)) A_150)) of role axiom named fact_576_sup_Oidem
% A new axiom: (forall (A_150:Prop), ((iff ((semila10642723_sup_o A_150) A_150)) A_150))
% FOF formula (forall (A_150:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_150) A_150)) A_150)) of role axiom named fact_577_sup_Oidem
% A new axiom: (forall (A_150:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_150) A_150)) A_150))
% FOF formula (forall (X_79:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_79) X_79)) X_79)) of role axiom named fact_578_sup__idem
% A new axiom: (forall (X_79:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_79) X_79)) X_79))
% FOF formula (forall (X_79:Prop), ((iff ((semila10642723_sup_o X_79) X_79)) X_79)) of role axiom named fact_579_sup__idem
% A new axiom: (forall (X_79:Prop), ((iff ((semila10642723_sup_o X_79) X_79)) X_79))
% FOF formula (forall (X_79:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_79) X_79)) X_79)) of role axiom named fact_580_sup__idem
% A new axiom: (forall (X_79:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_79) X_79)) X_79))
% FOF formula (forall (A_149:(pname->Prop)) (B_96:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_149) B_96)) ((semila1780557381name_o B_96) A_149))) of role axiom named fact_581_sup_Ocommute
% A new axiom: (forall (A_149:(pname->Prop)) (B_96:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_149) B_96)) ((semila1780557381name_o B_96) A_149)))
% FOF formula (forall (A_149:Prop) (B_96:Prop), ((iff ((semila10642723_sup_o A_149) B_96)) ((semila10642723_sup_o B_96) A_149))) of role axiom named fact_582_sup_Ocommute
% A new axiom: (forall (A_149:Prop) (B_96:Prop), ((iff ((semila10642723_sup_o A_149) B_96)) ((semila10642723_sup_o B_96) A_149)))
% FOF formula (forall (A_149:(hoare_1708887482_state->Prop)) (B_96:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_149) B_96)) ((semila1122118281tate_o B_96) A_149))) of role axiom named fact_583_sup_Ocommute
% A new axiom: (forall (A_149:(hoare_1708887482_state->Prop)) (B_96:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_149) B_96)) ((semila1122118281tate_o B_96) A_149)))
% FOF formula (forall (X_78:(pname->Prop)) (Y_42:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_78) Y_42)) ((semila1780557381name_o Y_42) X_78))) of role axiom named fact_584_inf__sup__aci_I5_J
% A new axiom: (forall (X_78:(pname->Prop)) (Y_42:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_78) Y_42)) ((semila1780557381name_o Y_42) X_78)))
% FOF formula (forall (X_78:Prop) (Y_42:Prop), ((iff ((semila10642723_sup_o X_78) Y_42)) ((semila10642723_sup_o Y_42) X_78))) of role axiom named fact_585_inf__sup__aci_I5_J
% A new axiom: (forall (X_78:Prop) (Y_42:Prop), ((iff ((semila10642723_sup_o X_78) Y_42)) ((semila10642723_sup_o Y_42) X_78)))
% FOF formula (forall (X_78:(hoare_1708887482_state->Prop)) (Y_42:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_78) Y_42)) ((semila1122118281tate_o Y_42) X_78))) of role axiom named fact_586_inf__sup__aci_I5_J
% A new axiom: (forall (X_78:(hoare_1708887482_state->Prop)) (Y_42:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_78) Y_42)) ((semila1122118281tate_o Y_42) X_78)))
% FOF formula (forall (X_77:(pname->Prop)) (Y_41:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_77) Y_41)) ((semila1780557381name_o Y_41) X_77))) of role axiom named fact_587_sup__commute
% A new axiom: (forall (X_77:(pname->Prop)) (Y_41:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_77) Y_41)) ((semila1780557381name_o Y_41) X_77)))
% FOF formula (forall (X_77:Prop) (Y_41:Prop), ((iff ((semila10642723_sup_o X_77) Y_41)) ((semila10642723_sup_o Y_41) X_77))) of role axiom named fact_588_sup__commute
% A new axiom: (forall (X_77:Prop) (Y_41:Prop), ((iff ((semila10642723_sup_o X_77) Y_41)) ((semila10642723_sup_o Y_41) X_77)))
% FOF formula (forall (X_77:(hoare_1708887482_state->Prop)) (Y_41:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_77) Y_41)) ((semila1122118281tate_o Y_41) X_77))) of role axiom named fact_589_sup__commute
% A new axiom: (forall (X_77:(hoare_1708887482_state->Prop)) (Y_41:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_77) Y_41)) ((semila1122118281tate_o Y_41) X_77)))
% FOF formula (forall (A_148:(pname->Prop)) (B_95:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_148) ((semila1780557381name_o A_148) B_95))) ((semila1780557381name_o A_148) B_95))) of role axiom named fact_590_sup_Oleft__idem
% A new axiom: (forall (A_148:(pname->Prop)) (B_95:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_148) ((semila1780557381name_o A_148) B_95))) ((semila1780557381name_o A_148) B_95)))
% FOF formula (forall (A_148:Prop) (B_95:Prop), ((iff ((semila10642723_sup_o A_148) ((semila10642723_sup_o A_148) B_95))) ((semila10642723_sup_o A_148) B_95))) of role axiom named fact_591_sup_Oleft__idem
% A new axiom: (forall (A_148:Prop) (B_95:Prop), ((iff ((semila10642723_sup_o A_148) ((semila10642723_sup_o A_148) B_95))) ((semila10642723_sup_o A_148) B_95)))
% FOF formula (forall (A_148:(hoare_1708887482_state->Prop)) (B_95:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_148) ((semila1122118281tate_o A_148) B_95))) ((semila1122118281tate_o A_148) B_95))) of role axiom named fact_592_sup_Oleft__idem
% A new axiom: (forall (A_148:(hoare_1708887482_state->Prop)) (B_95:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_148) ((semila1122118281tate_o A_148) B_95))) ((semila1122118281tate_o A_148) B_95)))
% FOF formula (forall (X_76:(pname->Prop)) (Y_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_76) ((semila1780557381name_o X_76) Y_40))) ((semila1780557381name_o X_76) Y_40))) of role axiom named fact_593_inf__sup__aci_I8_J
% A new axiom: (forall (X_76:(pname->Prop)) (Y_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_76) ((semila1780557381name_o X_76) Y_40))) ((semila1780557381name_o X_76) Y_40)))
% FOF formula (forall (X_76:Prop) (Y_40:Prop), ((iff ((semila10642723_sup_o X_76) ((semila10642723_sup_o X_76) Y_40))) ((semila10642723_sup_o X_76) Y_40))) of role axiom named fact_594_inf__sup__aci_I8_J
% A new axiom: (forall (X_76:Prop) (Y_40:Prop), ((iff ((semila10642723_sup_o X_76) ((semila10642723_sup_o X_76) Y_40))) ((semila10642723_sup_o X_76) Y_40)))
% FOF formula (forall (X_76:(hoare_1708887482_state->Prop)) (Y_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_76) ((semila1122118281tate_o X_76) Y_40))) ((semila1122118281tate_o X_76) Y_40))) of role axiom named fact_595_inf__sup__aci_I8_J
% A new axiom: (forall (X_76:(hoare_1708887482_state->Prop)) (Y_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_76) ((semila1122118281tate_o X_76) Y_40))) ((semila1122118281tate_o X_76) Y_40)))
% FOF formula (forall (X_75:(pname->Prop)) (Y_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_75) ((semila1780557381name_o X_75) Y_39))) ((semila1780557381name_o X_75) Y_39))) of role axiom named fact_596_sup__left__idem
% A new axiom: (forall (X_75:(pname->Prop)) (Y_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_75) ((semila1780557381name_o X_75) Y_39))) ((semila1780557381name_o X_75) Y_39)))
% FOF formula (forall (X_75:Prop) (Y_39:Prop), ((iff ((semila10642723_sup_o X_75) ((semila10642723_sup_o X_75) Y_39))) ((semila10642723_sup_o X_75) Y_39))) of role axiom named fact_597_sup__left__idem
% A new axiom: (forall (X_75:Prop) (Y_39:Prop), ((iff ((semila10642723_sup_o X_75) ((semila10642723_sup_o X_75) Y_39))) ((semila10642723_sup_o X_75) Y_39)))
% FOF formula (forall (X_75:(hoare_1708887482_state->Prop)) (Y_39:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_75) ((semila1122118281tate_o X_75) Y_39))) ((semila1122118281tate_o X_75) Y_39))) of role axiom named fact_598_sup__left__idem
% A new axiom: (forall (X_75:(hoare_1708887482_state->Prop)) (Y_39:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_75) ((semila1122118281tate_o X_75) Y_39))) ((semila1122118281tate_o X_75) Y_39)))
% FOF formula (forall (B_94:(pname->Prop)) (A_147:(pname->Prop)) (C_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_94) ((semila1780557381name_o A_147) C_40))) ((semila1780557381name_o A_147) ((semila1780557381name_o B_94) C_40)))) of role axiom named fact_599_sup_Oleft__commute
% A new axiom: (forall (B_94:(pname->Prop)) (A_147:(pname->Prop)) (C_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_94) ((semila1780557381name_o A_147) C_40))) ((semila1780557381name_o A_147) ((semila1780557381name_o B_94) C_40))))
% FOF formula (forall (B_94:Prop) (A_147:Prop) (C_40:Prop), ((iff ((semila10642723_sup_o B_94) ((semila10642723_sup_o A_147) C_40))) ((semila10642723_sup_o A_147) ((semila10642723_sup_o B_94) C_40)))) of role axiom named fact_600_sup_Oleft__commute
% A new axiom: (forall (B_94:Prop) (A_147:Prop) (C_40:Prop), ((iff ((semila10642723_sup_o B_94) ((semila10642723_sup_o A_147) C_40))) ((semila10642723_sup_o A_147) ((semila10642723_sup_o B_94) C_40))))
% FOF formula (forall (B_94:(hoare_1708887482_state->Prop)) (A_147:(hoare_1708887482_state->Prop)) (C_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o B_94) ((semila1122118281tate_o A_147) C_40))) ((semila1122118281tate_o A_147) ((semila1122118281tate_o B_94) C_40)))) of role axiom named fact_601_sup_Oleft__commute
% A new axiom: (forall (B_94:(hoare_1708887482_state->Prop)) (A_147:(hoare_1708887482_state->Prop)) (C_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o B_94) ((semila1122118281tate_o A_147) C_40))) ((semila1122118281tate_o A_147) ((semila1122118281tate_o B_94) C_40))))
% FOF formula (forall (X_74:(pname->Prop)) (Y_38:(pname->Prop)) (Z_18:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_74) ((semila1780557381name_o Y_38) Z_18))) ((semila1780557381name_o Y_38) ((semila1780557381name_o X_74) Z_18)))) of role axiom named fact_602_inf__sup__aci_I7_J
% A new axiom: (forall (X_74:(pname->Prop)) (Y_38:(pname->Prop)) (Z_18:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_74) ((semila1780557381name_o Y_38) Z_18))) ((semila1780557381name_o Y_38) ((semila1780557381name_o X_74) Z_18))))
% FOF formula (forall (X_74:Prop) (Y_38:Prop) (Z_18:Prop), ((iff ((semila10642723_sup_o X_74) ((semila10642723_sup_o Y_38) Z_18))) ((semila10642723_sup_o Y_38) ((semila10642723_sup_o X_74) Z_18)))) of role axiom named fact_603_inf__sup__aci_I7_J
% A new axiom: (forall (X_74:Prop) (Y_38:Prop) (Z_18:Prop), ((iff ((semila10642723_sup_o X_74) ((semila10642723_sup_o Y_38) Z_18))) ((semila10642723_sup_o Y_38) ((semila10642723_sup_o X_74) Z_18))))
% FOF formula (forall (X_74:(hoare_1708887482_state->Prop)) (Y_38:(hoare_1708887482_state->Prop)) (Z_18:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_74) ((semila1122118281tate_o Y_38) Z_18))) ((semila1122118281tate_o Y_38) ((semila1122118281tate_o X_74) Z_18)))) of role axiom named fact_604_inf__sup__aci_I7_J
% A new axiom: (forall (X_74:(hoare_1708887482_state->Prop)) (Y_38:(hoare_1708887482_state->Prop)) (Z_18:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_74) ((semila1122118281tate_o Y_38) Z_18))) ((semila1122118281tate_o Y_38) ((semila1122118281tate_o X_74) Z_18))))
% FOF formula (forall (X_73:(pname->Prop)) (Y_37:(pname->Prop)) (Z_17:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_73) ((semila1780557381name_o Y_37) Z_17))) ((semila1780557381name_o Y_37) ((semila1780557381name_o X_73) Z_17)))) of role axiom named fact_605_sup__left__commute
% A new axiom: (forall (X_73:(pname->Prop)) (Y_37:(pname->Prop)) (Z_17:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_73) ((semila1780557381name_o Y_37) Z_17))) ((semila1780557381name_o Y_37) ((semila1780557381name_o X_73) Z_17))))
% FOF formula (forall (X_73:Prop) (Y_37:Prop) (Z_17:Prop), ((iff ((semila10642723_sup_o X_73) ((semila10642723_sup_o Y_37) Z_17))) ((semila10642723_sup_o Y_37) ((semila10642723_sup_o X_73) Z_17)))) of role axiom named fact_606_sup__left__commute
% A new axiom: (forall (X_73:Prop) (Y_37:Prop) (Z_17:Prop), ((iff ((semila10642723_sup_o X_73) ((semila10642723_sup_o Y_37) Z_17))) ((semila10642723_sup_o Y_37) ((semila10642723_sup_o X_73) Z_17))))
% FOF formula (forall (X_73:(hoare_1708887482_state->Prop)) (Y_37:(hoare_1708887482_state->Prop)) (Z_17:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_73) ((semila1122118281tate_o Y_37) Z_17))) ((semila1122118281tate_o Y_37) ((semila1122118281tate_o X_73) Z_17)))) of role axiom named fact_607_sup__left__commute
% A new axiom: (forall (X_73:(hoare_1708887482_state->Prop)) (Y_37:(hoare_1708887482_state->Prop)) (Z_17:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_73) ((semila1122118281tate_o Y_37) Z_17))) ((semila1122118281tate_o Y_37) ((semila1122118281tate_o X_73) Z_17))))
% FOF formula (forall (A_146:(pname->Prop)) (B_93:(pname->Prop)) (C_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_146) B_93)) C_39)) ((semila1780557381name_o A_146) ((semila1780557381name_o B_93) C_39)))) of role axiom named fact_608_sup_Oassoc
% A new axiom: (forall (A_146:(pname->Prop)) (B_93:(pname->Prop)) (C_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_146) B_93)) C_39)) ((semila1780557381name_o A_146) ((semila1780557381name_o B_93) C_39))))
% FOF formula (forall (A_146:Prop) (B_93:Prop) (C_39:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_146) B_93)) C_39)) ((semila10642723_sup_o A_146) ((semila10642723_sup_o B_93) C_39)))) of role axiom named fact_609_sup_Oassoc
% A new axiom: (forall (A_146:Prop) (B_93:Prop) (C_39:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_146) B_93)) C_39)) ((semila10642723_sup_o A_146) ((semila10642723_sup_o B_93) C_39))))
% FOF formula (forall (A_146:(hoare_1708887482_state->Prop)) (B_93:(hoare_1708887482_state->Prop)) (C_39:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_146) B_93)) C_39)) ((semila1122118281tate_o A_146) ((semila1122118281tate_o B_93) C_39)))) of role axiom named fact_610_sup_Oassoc
% A new axiom: (forall (A_146:(hoare_1708887482_state->Prop)) (B_93:(hoare_1708887482_state->Prop)) (C_39:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_146) B_93)) C_39)) ((semila1122118281tate_o A_146) ((semila1122118281tate_o B_93) C_39))))
% FOF formula (forall (X_72:(pname->Prop)) (Y_36:(pname->Prop)) (Z_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_72) Y_36)) Z_16)) ((semila1780557381name_o X_72) ((semila1780557381name_o Y_36) Z_16)))) of role axiom named fact_611_inf__sup__aci_I6_J
% A new axiom: (forall (X_72:(pname->Prop)) (Y_36:(pname->Prop)) (Z_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_72) Y_36)) Z_16)) ((semila1780557381name_o X_72) ((semila1780557381name_o Y_36) Z_16))))
% FOF formula (forall (X_72:Prop) (Y_36:Prop) (Z_16:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_72) Y_36)) Z_16)) ((semila10642723_sup_o X_72) ((semila10642723_sup_o Y_36) Z_16)))) of role axiom named fact_612_inf__sup__aci_I6_J
% A new axiom: (forall (X_72:Prop) (Y_36:Prop) (Z_16:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_72) Y_36)) Z_16)) ((semila10642723_sup_o X_72) ((semila10642723_sup_o Y_36) Z_16))))
% FOF formula (forall (X_72:(hoare_1708887482_state->Prop)) (Y_36:(hoare_1708887482_state->Prop)) (Z_16:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_72) Y_36)) Z_16)) ((semila1122118281tate_o X_72) ((semila1122118281tate_o Y_36) Z_16)))) of role axiom named fact_613_inf__sup__aci_I6_J
% A new axiom: (forall (X_72:(hoare_1708887482_state->Prop)) (Y_36:(hoare_1708887482_state->Prop)) (Z_16:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_72) Y_36)) Z_16)) ((semila1122118281tate_o X_72) ((semila1122118281tate_o Y_36) Z_16))))
% FOF formula (forall (X_71:(pname->Prop)) (Y_35:(pname->Prop)) (Z_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_71) Y_35)) Z_15)) ((semila1780557381name_o X_71) ((semila1780557381name_o Y_35) Z_15)))) of role axiom named fact_614_sup__assoc
% A new axiom: (forall (X_71:(pname->Prop)) (Y_35:(pname->Prop)) (Z_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_71) Y_35)) Z_15)) ((semila1780557381name_o X_71) ((semila1780557381name_o Y_35) Z_15))))
% FOF formula (forall (X_71:Prop) (Y_35:Prop) (Z_15:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_71) Y_35)) Z_15)) ((semila10642723_sup_o X_71) ((semila10642723_sup_o Y_35) Z_15)))) of role axiom named fact_615_sup__assoc
% A new axiom: (forall (X_71:Prop) (Y_35:Prop) (Z_15:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_71) Y_35)) Z_15)) ((semila10642723_sup_o X_71) ((semila10642723_sup_o Y_35) Z_15))))
% FOF formula (forall (X_71:(hoare_1708887482_state->Prop)) (Y_35:(hoare_1708887482_state->Prop)) (Z_15:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_71) Y_35)) Z_15)) ((semila1122118281tate_o X_71) ((semila1122118281tate_o Y_35) Z_15)))) of role axiom named fact_616_sup__assoc
% A new axiom: (forall (X_71:(hoare_1708887482_state->Prop)) (Y_35:(hoare_1708887482_state->Prop)) (Z_15:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_71) Y_35)) Z_15)) ((semila1122118281tate_o X_71) ((semila1122118281tate_o Y_35) Z_15))))
% FOF formula (forall (X_70:(pname->Prop)) (Y_34:(pname->Prop)), ((ord_less_eq_pname_o X_70) ((semila1780557381name_o X_70) Y_34))) of role axiom named fact_617_inf__sup__ord_I3_J
% A new axiom: (forall (X_70:(pname->Prop)) (Y_34:(pname->Prop)), ((ord_less_eq_pname_o X_70) ((semila1780557381name_o X_70) Y_34)))
% FOF formula (forall (X_70:Prop) (Y_34:Prop), ((ord_less_eq_o X_70) ((semila10642723_sup_o X_70) Y_34))) of role axiom named fact_618_inf__sup__ord_I3_J
% A new axiom: (forall (X_70:Prop) (Y_34:Prop), ((ord_less_eq_o X_70) ((semila10642723_sup_o X_70) Y_34)))
% FOF formula (forall (X_70:(hoare_1708887482_state->Prop)) (Y_34:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o X_70) ((semila1122118281tate_o X_70) Y_34))) of role axiom named fact_619_inf__sup__ord_I3_J
% A new axiom: (forall (X_70:(hoare_1708887482_state->Prop)) (Y_34:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o X_70) ((semila1122118281tate_o X_70) Y_34)))
% FOF formula (forall (X_69:(pname->Prop)) (Y_33:(pname->Prop)), ((ord_less_eq_pname_o X_69) ((semila1780557381name_o X_69) Y_33))) of role axiom named fact_620_sup__ge1
% A new axiom: (forall (X_69:(pname->Prop)) (Y_33:(pname->Prop)), ((ord_less_eq_pname_o X_69) ((semila1780557381name_o X_69) Y_33)))
% FOF formula (forall (X_69:Prop) (Y_33:Prop), ((ord_less_eq_o X_69) ((semila10642723_sup_o X_69) Y_33))) of role axiom named fact_621_sup__ge1
% A new axiom: (forall (X_69:Prop) (Y_33:Prop), ((ord_less_eq_o X_69) ((semila10642723_sup_o X_69) Y_33)))
% FOF formula (forall (X_69:(hoare_1708887482_state->Prop)) (Y_33:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o X_69) ((semila1122118281tate_o X_69) Y_33))) of role axiom named fact_622_sup__ge1
% A new axiom: (forall (X_69:(hoare_1708887482_state->Prop)) (Y_33:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o X_69) ((semila1122118281tate_o X_69) Y_33)))
% FOF formula (forall (Y_32:(pname->Prop)) (X_68:(pname->Prop)), ((ord_less_eq_pname_o Y_32) ((semila1780557381name_o X_68) Y_32))) of role axiom named fact_623_inf__sup__ord_I4_J
% A new axiom: (forall (Y_32:(pname->Prop)) (X_68:(pname->Prop)), ((ord_less_eq_pname_o Y_32) ((semila1780557381name_o X_68) Y_32)))
% FOF formula (forall (Y_32:Prop) (X_68:Prop), ((ord_less_eq_o Y_32) ((semila10642723_sup_o X_68) Y_32))) of role axiom named fact_624_inf__sup__ord_I4_J
% A new axiom: (forall (Y_32:Prop) (X_68:Prop), ((ord_less_eq_o Y_32) ((semila10642723_sup_o X_68) Y_32)))
% FOF formula (forall (Y_32:(hoare_1708887482_state->Prop)) (X_68:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o Y_32) ((semila1122118281tate_o X_68) Y_32))) of role axiom named fact_625_inf__sup__ord_I4_J
% A new axiom: (forall (Y_32:(hoare_1708887482_state->Prop)) (X_68:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o Y_32) ((semila1122118281tate_o X_68) Y_32)))
% FOF formula (forall (Y_31:(pname->Prop)) (X_67:(pname->Prop)), ((ord_less_eq_pname_o Y_31) ((semila1780557381name_o X_67) Y_31))) of role axiom named fact_626_sup__ge2
% A new axiom: (forall (Y_31:(pname->Prop)) (X_67:(pname->Prop)), ((ord_less_eq_pname_o Y_31) ((semila1780557381name_o X_67) Y_31)))
% FOF formula (forall (Y_31:Prop) (X_67:Prop), ((ord_less_eq_o Y_31) ((semila10642723_sup_o X_67) Y_31))) of role axiom named fact_627_sup__ge2
% A new axiom: (forall (Y_31:Prop) (X_67:Prop), ((ord_less_eq_o Y_31) ((semila10642723_sup_o X_67) Y_31)))
% FOF formula (forall (Y_31:(hoare_1708887482_state->Prop)) (X_67:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o Y_31) ((semila1122118281tate_o X_67) Y_31))) of role axiom named fact_628_sup__ge2
% A new axiom: (forall (Y_31:(hoare_1708887482_state->Prop)) (X_67:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o Y_31) ((semila1122118281tate_o X_67) Y_31)))
% FOF formula (forall (X_66:(pname->Prop)) (Y_30:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_66) Y_30)) (((eq (pname->Prop)) ((semila1780557381name_o X_66) Y_30)) Y_30))) of role axiom named fact_629_le__iff__sup
% A new axiom: (forall (X_66:(pname->Prop)) (Y_30:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_66) Y_30)) (((eq (pname->Prop)) ((semila1780557381name_o X_66) Y_30)) Y_30)))
% FOF formula (forall (X_66:Prop) (Y_30:Prop), ((iff ((ord_less_eq_o X_66) Y_30)) ((iff ((semila10642723_sup_o X_66) Y_30)) Y_30))) of role axiom named fact_630_le__iff__sup
% A new axiom: (forall (X_66:Prop) (Y_30:Prop), ((iff ((ord_less_eq_o X_66) Y_30)) ((iff ((semila10642723_sup_o X_66) Y_30)) Y_30)))
% FOF formula (forall (X_66:(hoare_1708887482_state->Prop)) (Y_30:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o X_66) Y_30)) (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_66) Y_30)) Y_30))) of role axiom named fact_631_le__iff__sup
% A new axiom: (forall (X_66:(hoare_1708887482_state->Prop)) (Y_30:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o X_66) Y_30)) (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_66) Y_30)) Y_30)))
% FOF formula (forall (X_65:(pname->Prop)) (Y_29:(pname->Prop)) (Z_14:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((semila1780557381name_o X_65) Y_29)) Z_14)) ((and ((ord_less_eq_pname_o X_65) Z_14)) ((ord_less_eq_pname_o Y_29) Z_14)))) of role axiom named fact_632_le__sup__iff
% A new axiom: (forall (X_65:(pname->Prop)) (Y_29:(pname->Prop)) (Z_14:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((semila1780557381name_o X_65) Y_29)) Z_14)) ((and ((ord_less_eq_pname_o X_65) Z_14)) ((ord_less_eq_pname_o Y_29) Z_14))))
% FOF formula (forall (X_65:Prop) (Y_29:Prop) (Z_14:Prop), ((iff ((ord_less_eq_o ((semila10642723_sup_o X_65) Y_29)) Z_14)) ((and ((ord_less_eq_o X_65) Z_14)) ((ord_less_eq_o Y_29) Z_14)))) of role axiom named fact_633_le__sup__iff
% A new axiom: (forall (X_65:Prop) (Y_29:Prop) (Z_14:Prop), ((iff ((ord_less_eq_o ((semila10642723_sup_o X_65) Y_29)) Z_14)) ((and ((ord_less_eq_o X_65) Z_14)) ((ord_less_eq_o Y_29) Z_14))))
% FOF formula (forall (X_65:(hoare_1708887482_state->Prop)) (Y_29:(hoare_1708887482_state->Prop)) (Z_14:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o ((semila1122118281tate_o X_65) Y_29)) Z_14)) ((and ((ord_le777019615tate_o X_65) Z_14)) ((ord_le777019615tate_o Y_29) Z_14)))) of role axiom named fact_634_le__sup__iff
% A new axiom: (forall (X_65:(hoare_1708887482_state->Prop)) (Y_29:(hoare_1708887482_state->Prop)) (Z_14:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o ((semila1122118281tate_o X_65) Y_29)) Z_14)) ((and ((ord_le777019615tate_o X_65) Z_14)) ((ord_le777019615tate_o Y_29) Z_14))))
% FOF formula (forall (B_92:(pname->Prop)) (X_64:(pname->Prop)) (A_145:(pname->Prop)), (((ord_less_eq_pname_o X_64) A_145)->((ord_less_eq_pname_o X_64) ((semila1780557381name_o A_145) B_92)))) of role axiom named fact_635_le__supI1
% A new axiom: (forall (B_92:(pname->Prop)) (X_64:(pname->Prop)) (A_145:(pname->Prop)), (((ord_less_eq_pname_o X_64) A_145)->((ord_less_eq_pname_o X_64) ((semila1780557381name_o A_145) B_92))))
% FOF formula (forall (B_92:Prop) (X_64:Prop) (A_145:Prop), (((ord_less_eq_o X_64) A_145)->((ord_less_eq_o X_64) ((semila10642723_sup_o A_145) B_92)))) of role axiom named fact_636_le__supI1
% A new axiom: (forall (B_92:Prop) (X_64:Prop) (A_145:Prop), (((ord_less_eq_o X_64) A_145)->((ord_less_eq_o X_64) ((semila10642723_sup_o A_145) B_92))))
% FOF formula (forall (B_92:(hoare_1708887482_state->Prop)) (X_64:(hoare_1708887482_state->Prop)) (A_145:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_64) A_145)->((ord_le777019615tate_o X_64) ((semila1122118281tate_o A_145) B_92)))) of role axiom named fact_637_le__supI1
% A new axiom: (forall (B_92:(hoare_1708887482_state->Prop)) (X_64:(hoare_1708887482_state->Prop)) (A_145:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_64) A_145)->((ord_le777019615tate_o X_64) ((semila1122118281tate_o A_145) B_92))))
% FOF formula (forall (A_144:(pname->Prop)) (X_63:(pname->Prop)) (B_91:(pname->Prop)), (((ord_less_eq_pname_o X_63) B_91)->((ord_less_eq_pname_o X_63) ((semila1780557381name_o A_144) B_91)))) of role axiom named fact_638_le__supI2
% A new axiom: (forall (A_144:(pname->Prop)) (X_63:(pname->Prop)) (B_91:(pname->Prop)), (((ord_less_eq_pname_o X_63) B_91)->((ord_less_eq_pname_o X_63) ((semila1780557381name_o A_144) B_91))))
% FOF formula (forall (A_144:Prop) (X_63:Prop) (B_91:Prop), (((ord_less_eq_o X_63) B_91)->((ord_less_eq_o X_63) ((semila10642723_sup_o A_144) B_91)))) of role axiom named fact_639_le__supI2
% A new axiom: (forall (A_144:Prop) (X_63:Prop) (B_91:Prop), (((ord_less_eq_o X_63) B_91)->((ord_less_eq_o X_63) ((semila10642723_sup_o A_144) B_91))))
% FOF formula (forall (A_144:(hoare_1708887482_state->Prop)) (X_63:(hoare_1708887482_state->Prop)) (B_91:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_63) B_91)->((ord_le777019615tate_o X_63) ((semila1122118281tate_o A_144) B_91)))) of role axiom named fact_640_le__supI2
% A new axiom: (forall (A_144:(hoare_1708887482_state->Prop)) (X_63:(hoare_1708887482_state->Prop)) (B_91:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_63) B_91)->((ord_le777019615tate_o X_63) ((semila1122118281tate_o A_144) B_91))))
% FOF formula (forall (X_62:(pname->Prop)) (Y_28:(pname->Prop)), (((ord_less_eq_pname_o X_62) Y_28)->(((eq (pname->Prop)) ((semila1780557381name_o X_62) Y_28)) Y_28))) of role axiom named fact_641_sup__absorb2
% A new axiom: (forall (X_62:(pname->Prop)) (Y_28:(pname->Prop)), (((ord_less_eq_pname_o X_62) Y_28)->(((eq (pname->Prop)) ((semila1780557381name_o X_62) Y_28)) Y_28)))
% FOF formula (forall (X_62:Prop) (Y_28:Prop), (((ord_less_eq_o X_62) Y_28)->((iff ((semila10642723_sup_o X_62) Y_28)) Y_28))) of role axiom named fact_642_sup__absorb2
% A new axiom: (forall (X_62:Prop) (Y_28:Prop), (((ord_less_eq_o X_62) Y_28)->((iff ((semila10642723_sup_o X_62) Y_28)) Y_28)))
% FOF formula (forall (X_62:(hoare_1708887482_state->Prop)) (Y_28:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_62) Y_28)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_62) Y_28)) Y_28))) of role axiom named fact_643_sup__absorb2
% A new axiom: (forall (X_62:(hoare_1708887482_state->Prop)) (Y_28:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_62) Y_28)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_62) Y_28)) Y_28)))
% FOF formula (forall (Y_27:(pname->Prop)) (X_61:(pname->Prop)), (((ord_less_eq_pname_o Y_27) X_61)->(((eq (pname->Prop)) ((semila1780557381name_o X_61) Y_27)) X_61))) of role axiom named fact_644_sup__absorb1
% A new axiom: (forall (Y_27:(pname->Prop)) (X_61:(pname->Prop)), (((ord_less_eq_pname_o Y_27) X_61)->(((eq (pname->Prop)) ((semila1780557381name_o X_61) Y_27)) X_61)))
% FOF formula (forall (Y_27:Prop) (X_61:Prop), (((ord_less_eq_o Y_27) X_61)->((iff ((semila10642723_sup_o X_61) Y_27)) X_61))) of role axiom named fact_645_sup__absorb1
% A new axiom: (forall (Y_27:Prop) (X_61:Prop), (((ord_less_eq_o Y_27) X_61)->((iff ((semila10642723_sup_o X_61) Y_27)) X_61)))
% FOF formula (forall (Y_27:(hoare_1708887482_state->Prop)) (X_61:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_27) X_61)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_61) Y_27)) X_61))) of role axiom named fact_646_sup__absorb1
% A new axiom: (forall (Y_27:(hoare_1708887482_state->Prop)) (X_61:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_27) X_61)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_61) Y_27)) X_61)))
% FOF formula (forall (B_90:(pname->Prop)) (A_143:(pname->Prop)) (X_60:(pname->Prop)), (((ord_less_eq_pname_o A_143) X_60)->(((ord_less_eq_pname_o B_90) X_60)->((ord_less_eq_pname_o ((semila1780557381name_o A_143) B_90)) X_60)))) of role axiom named fact_647_le__supI
% A new axiom: (forall (B_90:(pname->Prop)) (A_143:(pname->Prop)) (X_60:(pname->Prop)), (((ord_less_eq_pname_o A_143) X_60)->(((ord_less_eq_pname_o B_90) X_60)->((ord_less_eq_pname_o ((semila1780557381name_o A_143) B_90)) X_60))))
% FOF formula (forall (B_90:Prop) (A_143:Prop) (X_60:Prop), (((ord_less_eq_o A_143) X_60)->(((ord_less_eq_o B_90) X_60)->((ord_less_eq_o ((semila10642723_sup_o A_143) B_90)) X_60)))) of role axiom named fact_648_le__supI
% A new axiom: (forall (B_90:Prop) (A_143:Prop) (X_60:Prop), (((ord_less_eq_o A_143) X_60)->(((ord_less_eq_o B_90) X_60)->((ord_less_eq_o ((semila10642723_sup_o A_143) B_90)) X_60))))
% FOF formula (forall (B_90:(hoare_1708887482_state->Prop)) (A_143:(hoare_1708887482_state->Prop)) (X_60:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_143) X_60)->(((ord_le777019615tate_o B_90) X_60)->((ord_le777019615tate_o ((semila1122118281tate_o A_143) B_90)) X_60)))) of role axiom named fact_649_le__supI
% A new axiom: (forall (B_90:(hoare_1708887482_state->Prop)) (A_143:(hoare_1708887482_state->Prop)) (X_60:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_143) X_60)->(((ord_le777019615tate_o B_90) X_60)->((ord_le777019615tate_o ((semila1122118281tate_o A_143) B_90)) X_60))))
% FOF formula (forall (Z_13:(pname->Prop)) (Y_26:(pname->Prop)) (X_59:(pname->Prop)), (((ord_less_eq_pname_o Y_26) X_59)->(((ord_less_eq_pname_o Z_13) X_59)->((ord_less_eq_pname_o ((semila1780557381name_o Y_26) Z_13)) X_59)))) of role axiom named fact_650_sup__least
% A new axiom: (forall (Z_13:(pname->Prop)) (Y_26:(pname->Prop)) (X_59:(pname->Prop)), (((ord_less_eq_pname_o Y_26) X_59)->(((ord_less_eq_pname_o Z_13) X_59)->((ord_less_eq_pname_o ((semila1780557381name_o Y_26) Z_13)) X_59))))
% FOF formula (forall (Z_13:Prop) (Y_26:Prop) (X_59:Prop), (((ord_less_eq_o Y_26) X_59)->(((ord_less_eq_o Z_13) X_59)->((ord_less_eq_o ((semila10642723_sup_o Y_26) Z_13)) X_59)))) of role axiom named fact_651_sup__least
% A new axiom: (forall (Z_13:Prop) (Y_26:Prop) (X_59:Prop), (((ord_less_eq_o Y_26) X_59)->(((ord_less_eq_o Z_13) X_59)->((ord_less_eq_o ((semila10642723_sup_o Y_26) Z_13)) X_59))))
% FOF formula (forall (Z_13:(hoare_1708887482_state->Prop)) (Y_26:(hoare_1708887482_state->Prop)) (X_59:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_26) X_59)->(((ord_le777019615tate_o Z_13) X_59)->((ord_le777019615tate_o ((semila1122118281tate_o Y_26) Z_13)) X_59)))) of role axiom named fact_652_sup__least
% A new axiom: (forall (Z_13:(hoare_1708887482_state->Prop)) (Y_26:(hoare_1708887482_state->Prop)) (X_59:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_26) X_59)->(((ord_le777019615tate_o Z_13) X_59)->((ord_le777019615tate_o ((semila1122118281tate_o Y_26) Z_13)) X_59))))
% FOF formula (forall (B_89:(pname->Prop)) (D_4:(pname->Prop)) (A_142:(pname->Prop)) (C_38:(pname->Prop)), (((ord_less_eq_pname_o A_142) C_38)->(((ord_less_eq_pname_o B_89) D_4)->((ord_less_eq_pname_o ((semila1780557381name_o A_142) B_89)) ((semila1780557381name_o C_38) D_4))))) of role axiom named fact_653_sup__mono
% A new axiom: (forall (B_89:(pname->Prop)) (D_4:(pname->Prop)) (A_142:(pname->Prop)) (C_38:(pname->Prop)), (((ord_less_eq_pname_o A_142) C_38)->(((ord_less_eq_pname_o B_89) D_4)->((ord_less_eq_pname_o ((semila1780557381name_o A_142) B_89)) ((semila1780557381name_o C_38) D_4)))))
% FOF formula (forall (B_89:Prop) (D_4:Prop) (A_142:Prop) (C_38:Prop), (((ord_less_eq_o A_142) C_38)->(((ord_less_eq_o B_89) D_4)->((ord_less_eq_o ((semila10642723_sup_o A_142) B_89)) ((semila10642723_sup_o C_38) D_4))))) of role axiom named fact_654_sup__mono
% A new axiom: (forall (B_89:Prop) (D_4:Prop) (A_142:Prop) (C_38:Prop), (((ord_less_eq_o A_142) C_38)->(((ord_less_eq_o B_89) D_4)->((ord_less_eq_o ((semila10642723_sup_o A_142) B_89)) ((semila10642723_sup_o C_38) D_4)))))
% FOF formula (forall (B_89:(hoare_1708887482_state->Prop)) (D_4:(hoare_1708887482_state->Prop)) (A_142:(hoare_1708887482_state->Prop)) (C_38:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_142) C_38)->(((ord_le777019615tate_o B_89) D_4)->((ord_le777019615tate_o ((semila1122118281tate_o A_142) B_89)) ((semila1122118281tate_o C_38) D_4))))) of role axiom named fact_655_sup__mono
% A new axiom: (forall (B_89:(hoare_1708887482_state->Prop)) (D_4:(hoare_1708887482_state->Prop)) (A_142:(hoare_1708887482_state->Prop)) (C_38:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_142) C_38)->(((ord_le777019615tate_o B_89) D_4)->((ord_le777019615tate_o ((semila1122118281tate_o A_142) B_89)) ((semila1122118281tate_o C_38) D_4)))))
% FOF formula (forall (A_141:(pname->Prop)) (B_88:(pname->Prop)) (X_58:(pname->Prop)), (((ord_less_eq_pname_o ((semila1780557381name_o A_141) B_88)) X_58)->((((ord_less_eq_pname_o A_141) X_58)->(((ord_less_eq_pname_o B_88) X_58)->False))->False))) of role axiom named fact_656_le__supE
% A new axiom: (forall (A_141:(pname->Prop)) (B_88:(pname->Prop)) (X_58:(pname->Prop)), (((ord_less_eq_pname_o ((semila1780557381name_o A_141) B_88)) X_58)->((((ord_less_eq_pname_o A_141) X_58)->(((ord_less_eq_pname_o B_88) X_58)->False))->False)))
% FOF formula (forall (A_141:Prop) (B_88:Prop) (X_58:Prop), (((ord_less_eq_o ((semila10642723_sup_o A_141) B_88)) X_58)->((((ord_less_eq_o A_141) X_58)->(((ord_less_eq_o B_88) X_58)->False))->False))) of role axiom named fact_657_le__supE
% A new axiom: (forall (A_141:Prop) (B_88:Prop) (X_58:Prop), (((ord_less_eq_o ((semila10642723_sup_o A_141) B_88)) X_58)->((((ord_less_eq_o A_141) X_58)->(((ord_less_eq_o B_88) X_58)->False))->False)))
% FOF formula (forall (A_141:(hoare_1708887482_state->Prop)) (B_88:(hoare_1708887482_state->Prop)) (X_58:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o ((semila1122118281tate_o A_141) B_88)) X_58)->((((ord_le777019615tate_o A_141) X_58)->(((ord_le777019615tate_o B_88) X_58)->False))->False))) of role axiom named fact_658_le__supE
% A new axiom: (forall (A_141:(hoare_1708887482_state->Prop)) (B_88:(hoare_1708887482_state->Prop)) (X_58:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o ((semila1122118281tate_o A_141) B_88)) X_58)->((((ord_le777019615tate_o A_141) X_58)->(((ord_le777019615tate_o B_88) X_58)->False))->False)))
% FOF formula (forall (X_57:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) X_57)) X_57)) of role axiom named fact_659_sup__bot__left
% A new axiom: (forall (X_57:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) X_57)) X_57))
% FOF formula (forall (X_57:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o bot_bot_com_o) X_57)) X_57)) of role axiom named fact_660_sup__bot__left
% A new axiom: (forall (X_57:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o bot_bot_com_o) X_57)) X_57))
% FOF formula (forall (X_57:Prop), ((iff ((semila10642723_sup_o bot_bot_o) X_57)) X_57)) of role axiom named fact_661_sup__bot__left
% A new axiom: (forall (X_57:Prop), ((iff ((semila10642723_sup_o bot_bot_o) X_57)) X_57))
% FOF formula (forall (X_57:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_o) X_57)) X_57)) of role axiom named fact_662_sup__bot__left
% A new axiom: (forall (X_57:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_o) X_57)) X_57))
% FOF formula (forall (X_56:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_56) bot_bot_pname_o)) X_56)) of role axiom named fact_663_sup__bot__right
% A new axiom: (forall (X_56:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_56) bot_bot_pname_o)) X_56))
% FOF formula (forall (X_56:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o X_56) bot_bot_com_o)) X_56)) of role axiom named fact_664_sup__bot__right
% A new axiom: (forall (X_56:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o X_56) bot_bot_com_o)) X_56))
% FOF formula (forall (X_56:Prop), ((iff ((semila10642723_sup_o X_56) bot_bot_o)) X_56)) of role axiom named fact_665_sup__bot__right
% A new axiom: (forall (X_56:Prop), ((iff ((semila10642723_sup_o X_56) bot_bot_o)) X_56))
% FOF formula (forall (X_56:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_56) bot_bo19817387tate_o)) X_56)) of role axiom named fact_666_sup__bot__right
% A new axiom: (forall (X_56:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_56) bot_bo19817387tate_o)) X_56))
% FOF formula (forall (X_55:pname) (P_15:(pname->Prop)) (A_140:option_pname), ((forall (X_3:pname), (((member_pname X_3) (set_pname A_140))->(P_15 X_3)))->((((eq option_pname) A_140) (some_pname X_55))->(P_15 X_55)))) of role axiom named fact_667_ospec
% A new axiom: (forall (X_55:pname) (P_15:(pname->Prop)) (A_140:option_pname), ((forall (X_3:pname), (((member_pname X_3) (set_pname A_140))->(P_15 X_3)))->((((eq option_pname) A_140) (some_pname X_55))->(P_15 X_55))))
% FOF formula (forall (X_55:hoare_1708887482_state) (P_15:(hoare_1708887482_state->Prop)) (A_140:option1624383643_state), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) (set_Ho525251890_state A_140))->(P_15 X_3)))->((((eq option1624383643_state) A_140) (some_H1974565227_state X_55))->(P_15 X_55)))) of role axiom named fact_668_ospec
% A new axiom: (forall (X_55:hoare_1708887482_state) (P_15:(hoare_1708887482_state->Prop)) (A_140:option1624383643_state), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) (set_Ho525251890_state A_140))->(P_15 X_3)))->((((eq option1624383643_state) A_140) (some_H1974565227_state X_55))->(P_15 X_55))))
% FOF formula (forall (X_55:com) (P_15:(com->Prop)) (A_140:option_com), ((forall (X_3:com), (((member_com X_3) (set_com A_140))->(P_15 X_3)))->((((eq option_com) A_140) (some_com X_55))->(P_15 X_55)))) of role axiom named fact_669_ospec
% A new axiom: (forall (X_55:com) (P_15:(com->Prop)) (A_140:option_com), ((forall (X_3:com), (((member_com X_3) (set_com A_140))->(P_15 X_3)))->((((eq option_com) A_140) (some_com X_55))->(P_15 X_55))))
% FOF formula (forall (B_87:((pname->Prop)->Prop)) (A_139:((pname->Prop)->Prop)) (F_59:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_58:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_59) F_58)->((finite297249702name_o A_139)->((not (((eq ((pname->Prop)->Prop)) A_139) bot_bot_pname_o_o))->((finite297249702name_o B_87)->((not (((eq ((pname->Prop)->Prop)) B_87) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_58 ((semila181081674me_o_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87))))))))) of role axiom named fact_670_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_87:((pname->Prop)->Prop)) (A_139:((pname->Prop)->Prop)) (F_59:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_58:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_59) F_58)->((finite297249702name_o A_139)->((not (((eq ((pname->Prop)->Prop)) A_139) bot_bot_pname_o_o))->((finite297249702name_o B_87)->((not (((eq ((pname->Prop)->Prop)) B_87) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_58 ((semila181081674me_o_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87)))))))))
% FOF formula (forall (B_87:((hoare_1708887482_state->Prop)->Prop)) (A_139:((hoare_1708887482_state->Prop)->Prop)) (F_59:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_58:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_59) F_58)->((finite1329924456tate_o A_139)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_139) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_87)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_87) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_58 ((semila1853742644te_o_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87))))))))) of role axiom named fact_671_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_87:((hoare_1708887482_state->Prop)->Prop)) (A_139:((hoare_1708887482_state->Prop)->Prop)) (F_59:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_58:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_59) F_58)->((finite1329924456tate_o A_139)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_139) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_87)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_87) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_58 ((semila1853742644te_o_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87)))))))))
% FOF formula (forall (B_87:(com->Prop)) (A_139:(com->Prop)) (F_59:(com->(com->com))) (F_58:((com->Prop)->com)), (((finite666746948em_com F_59) F_58)->((finite_finite_com A_139)->((not (((eq (com->Prop)) A_139) bot_bot_com_o))->((finite_finite_com B_87)->((not (((eq (com->Prop)) B_87) bot_bot_com_o))->(((eq com) (F_58 ((semila1562558655_com_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87))))))))) of role axiom named fact_672_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_87:(com->Prop)) (A_139:(com->Prop)) (F_59:(com->(com->com))) (F_58:((com->Prop)->com)), (((finite666746948em_com F_59) F_58)->((finite_finite_com A_139)->((not (((eq (com->Prop)) A_139) bot_bot_com_o))->((finite_finite_com B_87)->((not (((eq (com->Prop)) B_87) bot_bot_com_o))->(((eq com) (F_58 ((semila1562558655_com_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87)))))))))
% FOF formula (forall (B_87:(hoare_1708887482_state->Prop)) (A_139:(hoare_1708887482_state->Prop)) (F_59:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_58:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_59) F_58)->((finite1625599783_state A_139)->((not (((eq (hoare_1708887482_state->Prop)) A_139) bot_bo19817387tate_o))->((finite1625599783_state B_87)->((not (((eq (hoare_1708887482_state->Prop)) B_87) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_58 ((semila1122118281tate_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87))))))))) of role axiom named fact_673_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_87:(hoare_1708887482_state->Prop)) (A_139:(hoare_1708887482_state->Prop)) (F_59:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_58:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_59) F_58)->((finite1625599783_state A_139)->((not (((eq (hoare_1708887482_state->Prop)) A_139) bot_bo19817387tate_o))->((finite1625599783_state B_87)->((not (((eq (hoare_1708887482_state->Prop)) B_87) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_58 ((semila1122118281tate_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87)))))))))
% FOF formula (forall (B_87:(pname->Prop)) (A_139:(pname->Prop)) (F_59:(pname->(pname->pname))) (F_58:((pname->Prop)->pname)), (((finite89670078_pname F_59) F_58)->((finite_finite_pname A_139)->((not (((eq (pname->Prop)) A_139) bot_bot_pname_o))->((finite_finite_pname B_87)->((not (((eq (pname->Prop)) B_87) bot_bot_pname_o))->(((eq pname) (F_58 ((semila1780557381name_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87))))))))) of role axiom named fact_674_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_87:(pname->Prop)) (A_139:(pname->Prop)) (F_59:(pname->(pname->pname))) (F_58:((pname->Prop)->pname)), (((finite89670078_pname F_59) F_58)->((finite_finite_pname A_139)->((not (((eq (pname->Prop)) A_139) bot_bot_pname_o))->((finite_finite_pname B_87)->((not (((eq (pname->Prop)) B_87) bot_bot_pname_o))->(((eq pname) (F_58 ((semila1780557381name_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87)))))))))
% FOF formula (forall (B_86:((pname->Prop)->Prop)) (A_138:((pname->Prop)->Prop)) (F_57:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_56:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_57) F_56)->((finite297249702name_o A_138)->((not (((eq ((pname->Prop)->Prop)) B_86) bot_bot_pname_o_o))->(((ord_le1205211808me_o_o B_86) A_138)->(((eq (pname->Prop)) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138))))))) of role axiom named fact_675_folding__one__idem_Osubset__idem
% A new axiom: (forall (B_86:((pname->Prop)->Prop)) (A_138:((pname->Prop)->Prop)) (F_57:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_56:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_57) F_56)->((finite297249702name_o A_138)->((not (((eq ((pname->Prop)->Prop)) B_86) bot_bot_pname_o_o))->(((ord_le1205211808me_o_o B_86) A_138)->(((eq (pname->Prop)) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138)))))))
% FOF formula (forall (B_86:((hoare_1708887482_state->Prop)->Prop)) (A_138:((hoare_1708887482_state->Prop)->Prop)) (F_57:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_56:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_57) F_56)->((finite1329924456tate_o A_138)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_86) bot_bo1678742418te_o_o))->(((ord_le1728773982te_o_o B_86) A_138)->(((eq (hoare_1708887482_state->Prop)) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138))))))) of role axiom named fact_676_folding__one__idem_Osubset__idem
% A new axiom: (forall (B_86:((hoare_1708887482_state->Prop)->Prop)) (A_138:((hoare_1708887482_state->Prop)->Prop)) (F_57:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_56:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_57) F_56)->((finite1329924456tate_o A_138)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_86) bot_bo1678742418te_o_o))->(((ord_le1728773982te_o_o B_86) A_138)->(((eq (hoare_1708887482_state->Prop)) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138)))))))
% FOF formula (forall (B_86:(com->Prop)) (A_138:(com->Prop)) (F_57:(com->(com->com))) (F_56:((com->Prop)->com)), (((finite666746948em_com F_57) F_56)->((finite_finite_com A_138)->((not (((eq (com->Prop)) B_86) bot_bot_com_o))->(((ord_less_eq_com_o B_86) A_138)->(((eq com) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138))))))) of role axiom named fact_677_folding__one__idem_Osubset__idem
% A new axiom: (forall (B_86:(com->Prop)) (A_138:(com->Prop)) (F_57:(com->(com->com))) (F_56:((com->Prop)->com)), (((finite666746948em_com F_57) F_56)->((finite_finite_com A_138)->((not (((eq (com->Prop)) B_86) bot_bot_com_o))->(((ord_less_eq_com_o B_86) A_138)->(((eq com) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138)))))))
% FOF formula (forall (B_86:(hoare_1708887482_state->Prop)) (A_138:(hoare_1708887482_state->Prop)) (F_57:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_56:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_57) F_56)->((finite1625599783_state A_138)->((not (((eq (hoare_1708887482_state->Prop)) B_86) bot_bo19817387tate_o))->(((ord_le777019615tate_o B_86) A_138)->(((eq hoare_1708887482_state) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138))))))) of role axiom named fact_678_folding__one__idem_Osubset__idem
% A new axiom: (forall (B_86:(hoare_1708887482_state->Prop)) (A_138:(hoare_1708887482_state->Prop)) (F_57:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_56:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_57) F_56)->((finite1625599783_state A_138)->((not (((eq (hoare_1708887482_state->Prop)) B_86) bot_bo19817387tate_o))->(((ord_le777019615tate_o B_86) A_138)->(((eq hoare_1708887482_state) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138)))))))
% FOF formula (forall (B_86:(pname->Prop)) (A_138:(pname->Prop)) (F_57:(pname->(pname->pname))) (F_56:((pname->Prop)->pname)), (((finite89670078_pname F_57) F_56)->((finite_finite_pname A_138)->((not (((eq (pname->Prop)) B_86) bot_bot_pname_o))->(((ord_less_eq_pname_o B_86) A_138)->(((eq pname) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138))))))) of role axiom named fact_679_folding__one__idem_Osubset__idem
% A new axiom: (forall (B_86:(pname->Prop)) (A_138:(pname->Prop)) (F_57:(pname->(pname->pname))) (F_56:((pname->Prop)->pname)), (((finite89670078_pname F_57) F_56)->((finite_finite_pname A_138)->((not (((eq (pname->Prop)) B_86) bot_bot_pname_o))->(((ord_less_eq_pname_o B_86) A_138)->(((eq pname) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138)))))))
% FOF formula (forall (G_11:(hoare_1708887482_state->Prop)) (P_14:(state->(state->Prop))), ((hoare_90032982_state G_11) ((insert528405184_state (((hoare_858012674_state P_14) skip) P_14)) bot_bo19817387tate_o))) of role axiom named fact_680_hoare__derivs_OSkip
% A new axiom: (forall (G_11:(hoare_1708887482_state->Prop)) (P_14:(state->(state->Prop))), ((hoare_90032982_state G_11) ((insert528405184_state (((hoare_858012674_state P_14) skip) P_14)) bot_bo19817387tate_o)))
% FOF formula (forall (X_54:com) (A_137:(com->Prop)) (F_55:(com->(com->com))) (F_54:((com->Prop)->com)), (((finite666746948em_com F_55) F_54)->((finite_finite_com A_137)->((not (((eq (com->Prop)) A_137) bot_bot_com_o))->(((eq com) (F_54 ((insert_com X_54) A_137))) ((F_55 X_54) (F_54 A_137))))))) of role axiom named fact_681_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_54:com) (A_137:(com->Prop)) (F_55:(com->(com->com))) (F_54:((com->Prop)->com)), (((finite666746948em_com F_55) F_54)->((finite_finite_com A_137)->((not (((eq (com->Prop)) A_137) bot_bot_com_o))->(((eq com) (F_54 ((insert_com X_54) A_137))) ((F_55 X_54) (F_54 A_137)))))))
% FOF formula (forall (X_54:(pname->Prop)) (A_137:((pname->Prop)->Prop)) (F_55:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_54:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_55) F_54)->((finite297249702name_o A_137)->((not (((eq ((pname->Prop)->Prop)) A_137) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_54 ((insert_pname_o X_54) A_137))) ((F_55 X_54) (F_54 A_137))))))) of role axiom named fact_682_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_54:(pname->Prop)) (A_137:((pname->Prop)->Prop)) (F_55:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_54:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_55) F_54)->((finite297249702name_o A_137)->((not (((eq ((pname->Prop)->Prop)) A_137) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_54 ((insert_pname_o X_54) A_137))) ((F_55 X_54) (F_54 A_137)))))))
% FOF formula (forall (X_54:(hoare_1708887482_state->Prop)) (A_137:((hoare_1708887482_state->Prop)->Prop)) (F_55:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_54:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_55) F_54)->((finite1329924456tate_o A_137)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_137) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_54 ((insert949073679tate_o X_54) A_137))) ((F_55 X_54) (F_54 A_137))))))) of role axiom named fact_683_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_54:(hoare_1708887482_state->Prop)) (A_137:((hoare_1708887482_state->Prop)->Prop)) (F_55:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_54:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_55) F_54)->((finite1329924456tate_o A_137)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_137) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_54 ((insert949073679tate_o X_54) A_137))) ((F_55 X_54) (F_54 A_137)))))))
% FOF formula (forall (X_54:pname) (A_137:(pname->Prop)) (F_55:(pname->(pname->pname))) (F_54:((pname->Prop)->pname)), (((finite89670078_pname F_55) F_54)->((finite_finite_pname A_137)->((not (((eq (pname->Prop)) A_137) bot_bot_pname_o))->(((eq pname) (F_54 ((insert_pname X_54) A_137))) ((F_55 X_54) (F_54 A_137))))))) of role axiom named fact_684_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_54:pname) (A_137:(pname->Prop)) (F_55:(pname->(pname->pname))) (F_54:((pname->Prop)->pname)), (((finite89670078_pname F_55) F_54)->((finite_finite_pname A_137)->((not (((eq (pname->Prop)) A_137) bot_bot_pname_o))->(((eq pname) (F_54 ((insert_pname X_54) A_137))) ((F_55 X_54) (F_54 A_137)))))))
% FOF formula (forall (X_54:hoare_1708887482_state) (A_137:(hoare_1708887482_state->Prop)) (F_55:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_54:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_55) F_54)->((finite1625599783_state A_137)->((not (((eq (hoare_1708887482_state->Prop)) A_137) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_54 ((insert528405184_state X_54) A_137))) ((F_55 X_54) (F_54 A_137))))))) of role axiom named fact_685_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_54:hoare_1708887482_state) (A_137:(hoare_1708887482_state->Prop)) (F_55:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_54:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_55) F_54)->((finite1625599783_state A_137)->((not (((eq (hoare_1708887482_state->Prop)) A_137) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_54 ((insert528405184_state X_54) A_137))) ((F_55 X_54) (F_54 A_137)))))))
% FOF formula (forall (P_13:((com->Prop)->Prop)) (F_52:(com->Prop)), ((finite_finite_com F_52)->((not (((eq (com->Prop)) F_52) bot_bot_com_o))->((forall (X_3:com), (P_13 ((insert_com X_3) bot_bot_com_o)))->((forall (X_3:com) (F_53:(com->Prop)), ((finite_finite_com F_53)->((not (((eq (com->Prop)) F_53) bot_bot_com_o))->((((member_com X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert_com X_3) F_53)))))))->(P_13 F_52)))))) of role axiom named fact_686_finite__ne__induct
% A new axiom: (forall (P_13:((com->Prop)->Prop)) (F_52:(com->Prop)), ((finite_finite_com F_52)->((not (((eq (com->Prop)) F_52) bot_bot_com_o))->((forall (X_3:com), (P_13 ((insert_com X_3) bot_bot_com_o)))->((forall (X_3:com) (F_53:(com->Prop)), ((finite_finite_com F_53)->((not (((eq (com->Prop)) F_53) bot_bot_com_o))->((((member_com X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert_com X_3) F_53)))))))->(P_13 F_52))))))
% FOF formula (forall (P_13:(((pname->Prop)->Prop)->Prop)) (F_52:((pname->Prop)->Prop)), ((finite297249702name_o F_52)->((not (((eq ((pname->Prop)->Prop)) F_52) bot_bot_pname_o_o))->((forall (X_3:(pname->Prop)), (P_13 ((insert_pname_o X_3) bot_bot_pname_o_o)))->((forall (X_3:(pname->Prop)) (F_53:((pname->Prop)->Prop)), ((finite297249702name_o F_53)->((not (((eq ((pname->Prop)->Prop)) F_53) bot_bot_pname_o_o))->((((member_pname_o X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert_pname_o X_3) F_53)))))))->(P_13 F_52)))))) of role axiom named fact_687_finite__ne__induct
% A new axiom: (forall (P_13:(((pname->Prop)->Prop)->Prop)) (F_52:((pname->Prop)->Prop)), ((finite297249702name_o F_52)->((not (((eq ((pname->Prop)->Prop)) F_52) bot_bot_pname_o_o))->((forall (X_3:(pname->Prop)), (P_13 ((insert_pname_o X_3) bot_bot_pname_o_o)))->((forall (X_3:(pname->Prop)) (F_53:((pname->Prop)->Prop)), ((finite297249702name_o F_53)->((not (((eq ((pname->Prop)->Prop)) F_53) bot_bot_pname_o_o))->((((member_pname_o X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert_pname_o X_3) F_53)))))))->(P_13 F_52))))))
% FOF formula (forall (P_13:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (F_52:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_52)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) F_52) bot_bo1678742418te_o_o))->((forall (X_3:(hoare_1708887482_state->Prop)), (P_13 ((insert949073679tate_o X_3) bot_bo1678742418te_o_o)))->((forall (X_3:(hoare_1708887482_state->Prop)) (F_53:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_53)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) F_53) bot_bo1678742418te_o_o))->((((member814030440tate_o X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert949073679tate_o X_3) F_53)))))))->(P_13 F_52)))))) of role axiom named fact_688_finite__ne__induct
% A new axiom: (forall (P_13:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (F_52:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_52)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) F_52) bot_bo1678742418te_o_o))->((forall (X_3:(hoare_1708887482_state->Prop)), (P_13 ((insert949073679tate_o X_3) bot_bo1678742418te_o_o)))->((forall (X_3:(hoare_1708887482_state->Prop)) (F_53:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_53)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) F_53) bot_bo1678742418te_o_o))->((((member814030440tate_o X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert949073679tate_o X_3) F_53)))))))->(P_13 F_52))))))
% FOF formula (forall (P_13:((pname->Prop)->Prop)) (F_52:(pname->Prop)), ((finite_finite_pname F_52)->((not (((eq (pname->Prop)) F_52) bot_bot_pname_o))->((forall (X_3:pname), (P_13 ((insert_pname X_3) bot_bot_pname_o)))->((forall (X_3:pname) (F_53:(pname->Prop)), ((finite_finite_pname F_53)->((not (((eq (pname->Prop)) F_53) bot_bot_pname_o))->((((member_pname X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert_pname X_3) F_53)))))))->(P_13 F_52)))))) of role axiom named fact_689_finite__ne__induct
% A new axiom: (forall (P_13:((pname->Prop)->Prop)) (F_52:(pname->Prop)), ((finite_finite_pname F_52)->((not (((eq (pname->Prop)) F_52) bot_bot_pname_o))->((forall (X_3:pname), (P_13 ((insert_pname X_3) bot_bot_pname_o)))->((forall (X_3:pname) (F_53:(pname->Prop)), ((finite_finite_pname F_53)->((not (((eq (pname->Prop)) F_53) bot_bot_pname_o))->((((member_pname X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert_pname X_3) F_53)))))))->(P_13 F_52))))))
% FOF formula (forall (P_13:((hoare_1708887482_state->Prop)->Prop)) (F_52:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_52)->((not (((eq (hoare_1708887482_state->Prop)) F_52) bot_bo19817387tate_o))->((forall (X_3:hoare_1708887482_state), (P_13 ((insert528405184_state X_3) bot_bo19817387tate_o)))->((forall (X_3:hoare_1708887482_state) (F_53:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_53)->((not (((eq (hoare_1708887482_state->Prop)) F_53) bot_bo19817387tate_o))->((((member451959335_state X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert528405184_state X_3) F_53)))))))->(P_13 F_52)))))) of role axiom named fact_690_finite__ne__induct
% A new axiom: (forall (P_13:((hoare_1708887482_state->Prop)->Prop)) (F_52:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_52)->((not (((eq (hoare_1708887482_state->Prop)) F_52) bot_bo19817387tate_o))->((forall (X_3:hoare_1708887482_state), (P_13 ((insert528405184_state X_3) bot_bo19817387tate_o)))->((forall (X_3:hoare_1708887482_state) (F_53:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_53)->((not (((eq (hoare_1708887482_state->Prop)) F_53) bot_bo19817387tate_o))->((((member451959335_state X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert528405184_state X_3) F_53)))))))->(P_13 F_52))))))
% FOF formula (forall (G_10:(hoare_1708887482_state->Prop)) (P_12:(state->(state->Prop))) (B_85:(state->Prop)) (C_37:com), ((hoare_90032982_state G_10) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S_2:state)=> ((and ((P_12 Z_11) S_2)) (not (B_85 S_2))))) ((while B_85) C_37)) P_12)) bot_bo19817387tate_o))) of role axiom named fact_691_LoopF
% A new axiom: (forall (G_10:(hoare_1708887482_state->Prop)) (P_12:(state->(state->Prop))) (B_85:(state->Prop)) (C_37:com), ((hoare_90032982_state G_10) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S_2:state)=> ((and ((P_12 Z_11) S_2)) (not (B_85 S_2))))) ((while B_85) C_37)) P_12)) bot_bo19817387tate_o)))
% FOF formula (forall (D_3:com) (R_1:(state->(state->Prop))) (G_9:(hoare_1708887482_state->Prop)) (P_11:(state->(state->Prop))) (C_36:com) (Q_6:(state->(state->Prop))), (((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state P_11) C_36) Q_6)) bot_bo19817387tate_o))->(((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state Q_6) D_3) R_1)) bot_bo19817387tate_o))->((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state P_11) ((semi C_36) D_3)) R_1)) bot_bo19817387tate_o))))) of role axiom named fact_692_Comp
% A new axiom: (forall (D_3:com) (R_1:(state->(state->Prop))) (G_9:(hoare_1708887482_state->Prop)) (P_11:(state->(state->Prop))) (C_36:com) (Q_6:(state->(state->Prop))), (((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state P_11) C_36) Q_6)) bot_bo19817387tate_o))->(((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state Q_6) D_3) R_1)) bot_bo19817387tate_o))->((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state P_11) ((semi C_36) D_3)) R_1)) bot_bo19817387tate_o)))))
% FOF formula (forall (B_82:(state->Prop)) (C_34:com), ((wt ((while B_82) C_34))->(wt C_34))) of role axiom named fact_693_WTs__elim__cases_I6_J
% A new axiom: (forall (B_82:(state->Prop)) (C_34:com), ((wt ((while B_82) C_34))->(wt C_34)))
% FOF formula (forall (C1:com) (C2:com), ((wt ((semi C1) C2))->(((wt C1)->((wt C2)->False))->False))) of role axiom named fact_694_WTs__elim__cases_I4_J
% A new axiom: (forall (C1:com) (C2:com), ((wt ((semi C1) C2))->(((wt C1)->((wt C2)->False))->False)))
% FOF formula (forall (X_53:hoare_1708887482_state) (F_51:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_50:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_51) F_50)->(((eq hoare_1708887482_state) ((F_51 X_53) X_53)) X_53))) of role axiom named fact_695_folding__one__idem_Oidem
% A new axiom: (forall (X_53:hoare_1708887482_state) (F_51:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_50:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_51) F_50)->(((eq hoare_1708887482_state) ((F_51 X_53) X_53)) X_53)))
% FOF formula (forall (X_53:pname) (F_51:(pname->(pname->pname))) (F_50:((pname->Prop)->pname)), (((finite89670078_pname F_51) F_50)->(((eq pname) ((F_51 X_53) X_53)) X_53))) of role axiom named fact_696_folding__one__idem_Oidem
% A new axiom: (forall (X_53:pname) (F_51:(pname->(pname->pname))) (F_50:((pname->Prop)->pname)), (((finite89670078_pname F_51) F_50)->(((eq pname) ((F_51 X_53) X_53)) X_53)))
% FOF formula (forall (Com1_1:com) (Com2_1:com), (not (((eq com) skip) ((semi Com1_1) Com2_1)))) of role axiom named fact_697_com_Osimps_I12_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com), (not (((eq com) skip) ((semi Com1_1) Com2_1))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) skip) ((while Fun_1) Com_2)))) of role axiom named fact_698_com_Osimps_I16_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) skip) ((while Fun_1) Com_2))))
% FOF formula (forall (Com1_1:com) (Com2_1:com), (not (((eq com) ((semi Com1_1) Com2_1)) skip))) of role axiom named fact_699_com_Osimps_I13_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com), (not (((eq com) ((semi Com1_1) Com2_1)) skip)))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) ((while Fun_1) Com_2)) skip))) of role axiom named fact_700_com_Osimps_I17_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) ((while Fun_1) Com_2)) skip)))
% FOF formula (forall (Com1:com) (Com2:com) (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) ((semi Com1) Com2)) ((while Fun_1) Com_2)))) of role axiom named fact_701_com_Osimps_I46_J
% A new axiom: (forall (Com1:com) (Com2:com) (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) ((semi Com1) Com2)) ((while Fun_1) Com_2))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_2:com) (Com1:com) (Com2:com), (not (((eq com) ((while Fun_1) Com_2)) ((semi Com1) Com2)))) of role axiom named fact_702_com_Osimps_I47_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_2:com) (Com1:com) (Com2:com), (not (((eq com) ((while Fun_1) Com_2)) ((semi Com1) Com2))))
% FOF formula (forall (Com1:com) (Com2:com) (Com1_1:com) (Com2_1:com), ((iff (((eq com) ((semi Com1) Com2)) ((semi Com1_1) Com2_1))) ((and (((eq com) Com1) Com1_1)) (((eq com) Com2) Com2_1)))) of role axiom named fact_703_com_Osimps_I3_J
% A new axiom: (forall (Com1:com) (Com2:com) (Com1_1:com) (Com2_1:com), ((iff (((eq com) ((semi Com1) Com2)) ((semi Com1_1) Com2_1))) ((and (((eq com) Com1) Com1_1)) (((eq com) Com2) Com2_1))))
% FOF formula (forall (Fun:(state->Prop)) (Com_1:com) (Fun_1:(state->Prop)) (Com_2:com), ((iff (((eq com) ((while Fun) Com_1)) ((while Fun_1) Com_2))) ((and (((eq (state->Prop)) Fun) Fun_1)) (((eq com) Com_1) Com_2)))) of role axiom named fact_704_com_Osimps_I5_J
% A new axiom: (forall (Fun:(state->Prop)) (Com_1:com) (Fun_1:(state->Prop)) (Com_2:com), ((iff (((eq com) ((while Fun) Com_1)) ((while Fun_1) Com_2))) ((and (((eq (state->Prop)) Fun) Fun_1)) (((eq com) Com_1) Com_2))))
% FOF formula (forall (Pname:pname) (Fun:(state->Prop)) (Com_1:com), (not (((eq com) (body_1 Pname)) ((while Fun) Com_1)))) of role axiom named fact_705_com_Osimps_I59_J
% A new axiom: (forall (Pname:pname) (Fun:(state->Prop)) (Com_1:com), (not (((eq com) (body_1 Pname)) ((while Fun) Com_1))))
% FOF formula (forall (Fun:(state->Prop)) (Com_1:com) (Pname:pname), (not (((eq com) ((while Fun) Com_1)) (body_1 Pname)))) of role axiom named fact_706_com_Osimps_I58_J
% A new axiom: (forall (Fun:(state->Prop)) (Com_1:com) (Pname:pname), (not (((eq com) ((while Fun) Com_1)) (body_1 Pname))))
% FOF formula (forall (B_82:(state->Prop)) (C_34:com), ((wt C_34)->(wt ((while B_82) C_34)))) of role axiom named fact_707_While
% A new axiom: (forall (B_82:(state->Prop)) (C_34:com), ((wt C_34)->(wt ((while B_82) C_34))))
% FOF formula (forall (Pname:pname) (Com1:com) (Com2:com), (not (((eq com) (body_1 Pname)) ((semi Com1) Com2)))) of role axiom named fact_708_com_Osimps_I49_J
% A new axiom: (forall (Pname:pname) (Com1:com) (Com2:com), (not (((eq com) (body_1 Pname)) ((semi Com1) Com2))))
% FOF formula (forall (Com1:com) (Com2:com) (Pname:pname), (not (((eq com) ((semi Com1) Com2)) (body_1 Pname)))) of role axiom named fact_709_com_Osimps_I48_J
% A new axiom: (forall (Com1:com) (Com2:com) (Pname:pname), (not (((eq com) ((semi Com1) Com2)) (body_1 Pname))))
% FOF formula (forall (C1:com) (C0:com), ((wt C0)->((wt C1)->(wt ((semi C0) C1))))) of role axiom named fact_710_WT_OSemi
% A new axiom: (forall (C1:com) (C0:com), ((wt C0)->((wt C1)->(wt ((semi C0) C1)))))
% FOF formula (forall (Pname:pname), (not (((eq com) skip) (body_1 Pname)))) of role axiom named fact_711_com_Osimps_I18_J
% A new axiom: (forall (Pname:pname), (not (((eq com) skip) (body_1 Pname))))
% FOF formula (forall (Pname:pname), (not (((eq com) (body_1 Pname)) skip))) of role axiom named fact_712_com_Osimps_I19_J
% A new axiom: (forall (Pname:pname), (not (((eq com) (body_1 Pname)) skip)))
% FOF formula (wt skip) of role axiom named fact_713_WT_OSkip
% A new axiom: (wt skip)
% FOF formula (forall (X_52:com) (A_136:(com->Prop)) (F_49:(com->(com->com))) (F_48:((com->Prop)->com)), (((finite666746948em_com F_49) F_48)->((finite_finite_com A_136)->(((member_com X_52) A_136)->(((eq com) ((F_49 X_52) (F_48 A_136))) (F_48 A_136)))))) of role axiom named fact_714_folding__one__idem_Oin__idem
% A new axiom: (forall (X_52:com) (A_136:(com->Prop)) (F_49:(com->(com->com))) (F_48:((com->Prop)->com)), (((finite666746948em_com F_49) F_48)->((finite_finite_com A_136)->(((member_com X_52) A_136)->(((eq com) ((F_49 X_52) (F_48 A_136))) (F_48 A_136))))))
% FOF formula (forall (X_52:pname) (A_136:(pname->Prop)) (F_49:(pname->(pname->pname))) (F_48:((pname->Prop)->pname)), (((finite89670078_pname F_49) F_48)->((finite_finite_pname A_136)->(((member_pname X_52) A_136)->(((eq pname) ((F_49 X_52) (F_48 A_136))) (F_48 A_136)))))) of role axiom named fact_715_folding__one__idem_Oin__idem
% A new axiom: (forall (X_52:pname) (A_136:(pname->Prop)) (F_49:(pname->(pname->pname))) (F_48:((pname->Prop)->pname)), (((finite89670078_pname F_49) F_48)->((finite_finite_pname A_136)->(((member_pname X_52) A_136)->(((eq pname) ((F_49 X_52) (F_48 A_136))) (F_48 A_136))))))
% FOF formula (forall (X_52:hoare_1708887482_state) (A_136:(hoare_1708887482_state->Prop)) (F_49:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_48:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_49) F_48)->((finite1625599783_state A_136)->(((member451959335_state X_52) A_136)->(((eq hoare_1708887482_state) ((F_49 X_52) (F_48 A_136))) (F_48 A_136)))))) of role axiom named fact_716_folding__one__idem_Oin__idem
% A new axiom: (forall (X_52:hoare_1708887482_state) (A_136:(hoare_1708887482_state->Prop)) (F_49:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_48:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_49) F_48)->((finite1625599783_state A_136)->(((member451959335_state X_52) A_136)->(((eq hoare_1708887482_state) ((F_49 X_52) (F_48 A_136))) (F_48 A_136))))))
% FOF formula (forall (X_52:(pname->Prop)) (A_136:((pname->Prop)->Prop)) (F_49:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_48:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_49) F_48)->((finite297249702name_o A_136)->(((member_pname_o X_52) A_136)->(((eq (pname->Prop)) ((F_49 X_52) (F_48 A_136))) (F_48 A_136)))))) of role axiom named fact_717_folding__one__idem_Oin__idem
% A new axiom: (forall (X_52:(pname->Prop)) (A_136:((pname->Prop)->Prop)) (F_49:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_48:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_49) F_48)->((finite297249702name_o A_136)->(((member_pname_o X_52) A_136)->(((eq (pname->Prop)) ((F_49 X_52) (F_48 A_136))) (F_48 A_136))))))
% FOF formula (forall (X_52:(hoare_1708887482_state->Prop)) (A_136:((hoare_1708887482_state->Prop)->Prop)) (F_49:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_48:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_49) F_48)->((finite1329924456tate_o A_136)->(((member814030440tate_o X_52) A_136)->(((eq (hoare_1708887482_state->Prop)) ((F_49 X_52) (F_48 A_136))) (F_48 A_136)))))) of role axiom named fact_718_folding__one__idem_Oin__idem
% A new axiom: (forall (X_52:(hoare_1708887482_state->Prop)) (A_136:((hoare_1708887482_state->Prop)->Prop)) (F_49:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_48:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_49) F_48)->((finite1329924456tate_o A_136)->(((member814030440tate_o X_52) A_136)->(((eq (hoare_1708887482_state->Prop)) ((F_49 X_52) (F_48 A_136))) (F_48 A_136))))))
% FOF formula (forall (N_1:((pname->Prop)->Prop)) (H_1:((pname->Prop)->(pname->Prop))) (F_47:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_46:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_47) F_46)->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), (((eq (pname->Prop)) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite297249702name_o N_1)->((not (((eq ((pname->Prop)->Prop)) N_1) bot_bot_pname_o_o))->(((eq (pname->Prop)) (H_1 (F_46 N_1))) (F_46 ((image_1085733413name_o H_1) N_1)))))))) of role axiom named fact_719_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_1:((pname->Prop)->Prop)) (H_1:((pname->Prop)->(pname->Prop))) (F_47:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_46:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_47) F_46)->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), (((eq (pname->Prop)) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite297249702name_o N_1)->((not (((eq ((pname->Prop)->Prop)) N_1) bot_bot_pname_o_o))->(((eq (pname->Prop)) (H_1 (F_46 N_1))) (F_46 ((image_1085733413name_o H_1) N_1))))))))
% FOF formula (forall (N_1:((hoare_1708887482_state->Prop)->Prop)) (H_1:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (F_47:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_46:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_47) F_46)->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite1329924456tate_o N_1)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) N_1) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (H_1 (F_46 N_1))) (F_46 ((image_909543877tate_o H_1) N_1)))))))) of role axiom named fact_720_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_1:((hoare_1708887482_state->Prop)->Prop)) (H_1:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (F_47:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_46:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_47) F_46)->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite1329924456tate_o N_1)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) N_1) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (H_1 (F_46 N_1))) (F_46 ((image_909543877tate_o H_1) N_1))))))))
% FOF formula (forall (N_1:(pname->Prop)) (H_1:(pname->pname)) (F_47:(pname->(pname->pname))) (F_46:((pname->Prop)->pname)), (((finite89670078_pname F_47) F_46)->((forall (X_3:pname) (Y_4:pname), (((eq pname) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite_finite_pname N_1)->((not (((eq (pname->Prop)) N_1) bot_bot_pname_o))->(((eq pname) (H_1 (F_46 N_1))) (F_46 ((image_pname_pname H_1) N_1)))))))) of role axiom named fact_721_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_1:(pname->Prop)) (H_1:(pname->pname)) (F_47:(pname->(pname->pname))) (F_46:((pname->Prop)->pname)), (((finite89670078_pname F_47) F_46)->((forall (X_3:pname) (Y_4:pname), (((eq pname) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite_finite_pname N_1)->((not (((eq (pname->Prop)) N_1) bot_bot_pname_o))->(((eq pname) (H_1 (F_46 N_1))) (F_46 ((image_pname_pname H_1) N_1))))))))
% FOF formula (forall (N_1:(hoare_1708887482_state->Prop)) (H_1:(hoare_1708887482_state->hoare_1708887482_state)) (F_47:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_46:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_47) F_46)->((forall (X_3:hoare_1708887482_state) (Y_4:hoare_1708887482_state), (((eq hoare_1708887482_state) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite1625599783_state N_1)->((not (((eq (hoare_1708887482_state->Prop)) N_1) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (H_1 (F_46 N_1))) (F_46 ((image_757158439_state H_1) N_1)))))))) of role axiom named fact_722_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_1:(hoare_1708887482_state->Prop)) (H_1:(hoare_1708887482_state->hoare_1708887482_state)) (F_47:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_46:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_47) F_46)->((forall (X_3:hoare_1708887482_state) (Y_4:hoare_1708887482_state), (((eq hoare_1708887482_state) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite1625599783_state N_1)->((not (((eq (hoare_1708887482_state->Prop)) N_1) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (H_1 (F_46 N_1))) (F_46 ((image_757158439_state H_1) N_1))))))))
% FOF formula (forall (N_1:(com->Prop)) (H_1:(com->com)) (F_47:(com->(com->com))) (F_46:((com->Prop)->com)), (((finite666746948em_com F_47) F_46)->((forall (X_3:com) (Y_4:com), (((eq com) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite_finite_com N_1)->((not (((eq (com->Prop)) N_1) bot_bot_com_o))->(((eq com) (H_1 (F_46 N_1))) (F_46 ((image_com_com H_1) N_1)))))))) of role axiom named fact_723_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_1:(com->Prop)) (H_1:(com->com)) (F_47:(com->(com->com))) (F_46:((com->Prop)->com)), (((finite666746948em_com F_47) F_46)->((forall (X_3:com) (Y_4:com), (((eq com) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite_finite_com N_1)->((not (((eq (com->Prop)) N_1) bot_bot_com_o))->(((eq com) (H_1 (F_46 N_1))) (F_46 ((image_com_com H_1) N_1))))))))
% FOF formula (forall (X_51:(com->Prop)), (((eq com) (the_elem_com X_51)) (the_com_1 (fun (X_3:com)=> (((eq (com->Prop)) X_51) ((insert_com X_3) bot_bot_com_o)))))) of role axiom named fact_724_the__elem__def
% A new axiom: (forall (X_51:(com->Prop)), (((eq com) (the_elem_com X_51)) (the_com_1 (fun (X_3:com)=> (((eq (com->Prop)) X_51) ((insert_com X_3) bot_bot_com_o))))))
% FOF formula (forall (X_51:(pname->Prop)), (((eq pname) (the_elem_pname X_51)) (the_pname (fun (X_3:pname)=> (((eq (pname->Prop)) X_51) ((insert_pname X_3) bot_bot_pname_o)))))) of role axiom named fact_725_the__elem__def
% A new axiom: (forall (X_51:(pname->Prop)), (((eq pname) (the_elem_pname X_51)) (the_pname (fun (X_3:pname)=> (((eq (pname->Prop)) X_51) ((insert_pname X_3) bot_bot_pname_o))))))
% FOF formula (forall (X_51:(hoare_1708887482_state->Prop)), (((eq hoare_1708887482_state) (the_el864710747_state X_51)) (the_Ho851197897_state (fun (X_3:hoare_1708887482_state)=> (((eq (hoare_1708887482_state->Prop)) X_51) ((insert528405184_state X_3) bot_bo19817387tate_o)))))) of role axiom named fact_726_the__elem__def
% A new axiom: (forall (X_51:(hoare_1708887482_state->Prop)), (((eq hoare_1708887482_state) (the_el864710747_state X_51)) (the_Ho851197897_state (fun (X_3:hoare_1708887482_state)=> (((eq (hoare_1708887482_state->Prop)) X_51) ((insert528405184_state X_3) bot_bo19817387tate_o))))))
% FOF formula (forall (X_50:com) (A_135:(com->Prop)) (F_45:(com->(com->com))) (F_44:((com->Prop)->com)), (((finite860057415ne_com F_45) F_44)->((finite_finite_com A_135)->((((member_com X_50) A_135)->False)->((not (((eq (com->Prop)) A_135) bot_bot_com_o))->(((eq com) (F_44 ((insert_com X_50) A_135))) ((F_45 X_50) (F_44 A_135)))))))) of role axiom named fact_727_folding__one_Oinsert
% A new axiom: (forall (X_50:com) (A_135:(com->Prop)) (F_45:(com->(com->com))) (F_44:((com->Prop)->com)), (((finite860057415ne_com F_45) F_44)->((finite_finite_com A_135)->((((member_com X_50) A_135)->False)->((not (((eq (com->Prop)) A_135) bot_bot_com_o))->(((eq com) (F_44 ((insert_com X_50) A_135))) ((F_45 X_50) (F_44 A_135))))))))
% FOF formula (forall (X_50:pname) (A_135:(pname->Prop)) (F_45:(pname->(pname->pname))) (F_44:((pname->Prop)->pname)), (((finite1282449217_pname F_45) F_44)->((finite_finite_pname A_135)->((((member_pname X_50) A_135)->False)->((not (((eq (pname->Prop)) A_135) bot_bot_pname_o))->(((eq pname) (F_44 ((insert_pname X_50) A_135))) ((F_45 X_50) (F_44 A_135)))))))) of role axiom named fact_728_folding__one_Oinsert
% A new axiom: (forall (X_50:pname) (A_135:(pname->Prop)) (F_45:(pname->(pname->pname))) (F_44:((pname->Prop)->pname)), (((finite1282449217_pname F_45) F_44)->((finite_finite_pname A_135)->((((member_pname X_50) A_135)->False)->((not (((eq (pname->Prop)) A_135) bot_bot_pname_o))->(((eq pname) (F_44 ((insert_pname X_50) A_135))) ((F_45 X_50) (F_44 A_135))))))))
% FOF formula (forall (X_50:hoare_1708887482_state) (A_135:(hoare_1708887482_state->Prop)) (F_45:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_44:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_45) F_44)->((finite1625599783_state A_135)->((((member451959335_state X_50) A_135)->False)->((not (((eq (hoare_1708887482_state->Prop)) A_135) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_44 ((insert528405184_state X_50) A_135))) ((F_45 X_50) (F_44 A_135)))))))) of role axiom named fact_729_folding__one_Oinsert
% A new axiom: (forall (X_50:hoare_1708887482_state) (A_135:(hoare_1708887482_state->Prop)) (F_45:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_44:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_45) F_44)->((finite1625599783_state A_135)->((((member451959335_state X_50) A_135)->False)->((not (((eq (hoare_1708887482_state->Prop)) A_135) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_44 ((insert528405184_state X_50) A_135))) ((F_45 X_50) (F_44 A_135))))))))
% FOF formula (forall (X_50:(pname->Prop)) (A_135:((pname->Prop)->Prop)) (F_45:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_44:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_45) F_44)->((finite297249702name_o A_135)->((((member_pname_o X_50) A_135)->False)->((not (((eq ((pname->Prop)->Prop)) A_135) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_44 ((insert_pname_o X_50) A_135))) ((F_45 X_50) (F_44 A_135)))))))) of role axiom named fact_730_folding__one_Oinsert
% A new axiom: (forall (X_50:(pname->Prop)) (A_135:((pname->Prop)->Prop)) (F_45:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_44:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_45) F_44)->((finite297249702name_o A_135)->((((member_pname_o X_50) A_135)->False)->((not (((eq ((pname->Prop)->Prop)) A_135) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_44 ((insert_pname_o X_50) A_135))) ((F_45 X_50) (F_44 A_135))))))))
% FOF formula (forall (X_50:(hoare_1708887482_state->Prop)) (A_135:((hoare_1708887482_state->Prop)->Prop)) (F_45:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_44:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_45) F_44)->((finite1329924456tate_o A_135)->((((member814030440tate_o X_50) A_135)->False)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_135) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_44 ((insert949073679tate_o X_50) A_135))) ((F_45 X_50) (F_44 A_135)))))))) of role axiom named fact_731_folding__one_Oinsert
% A new axiom: (forall (X_50:(hoare_1708887482_state->Prop)) (A_135:((hoare_1708887482_state->Prop)->Prop)) (F_45:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_44:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_45) F_44)->((finite1329924456tate_o A_135)->((((member814030440tate_o X_50) A_135)->False)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_135) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_44 ((insert949073679tate_o X_50) A_135))) ((F_45 X_50) (F_44 A_135))))))))
% FOF formula (forall (Y_25:hoare_1708887482_state), ((forall (Fun1:(state->(state->Prop))) (Com:com) (Fun2:(state->(state->Prop))), (not (((eq hoare_1708887482_state) Y_25) (((hoare_858012674_state Fun1) Com) Fun2))))->False)) of role axiom named fact_732_triple_Oexhaust
% A new axiom: (forall (Y_25:hoare_1708887482_state), ((forall (Fun1:(state->(state->Prop))) (Com:com) (Fun2:(state->(state->Prop))), (not (((eq hoare_1708887482_state) Y_25) (((hoare_858012674_state Fun1) Com) Fun2))))->False))
% FOF formula (forall (X_49:com) (F_43:(com->(com->com))) (F_42:((com->Prop)->com)), (((finite860057415ne_com F_43) F_42)->(((eq com) (F_42 ((insert_com X_49) bot_bot_com_o))) X_49))) of role axiom named fact_733_folding__one_Osingleton
% A new axiom: (forall (X_49:com) (F_43:(com->(com->com))) (F_42:((com->Prop)->com)), (((finite860057415ne_com F_43) F_42)->(((eq com) (F_42 ((insert_com X_49) bot_bot_com_o))) X_49)))
% FOF formula (forall (X_49:pname) (F_43:(pname->(pname->pname))) (F_42:((pname->Prop)->pname)), (((finite1282449217_pname F_43) F_42)->(((eq pname) (F_42 ((insert_pname X_49) bot_bot_pname_o))) X_49))) of role axiom named fact_734_folding__one_Osingleton
% A new axiom: (forall (X_49:pname) (F_43:(pname->(pname->pname))) (F_42:((pname->Prop)->pname)), (((finite1282449217_pname F_43) F_42)->(((eq pname) (F_42 ((insert_pname X_49) bot_bot_pname_o))) X_49)))
% FOF formula (forall (X_49:hoare_1708887482_state) (F_43:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_42:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_43) F_42)->(((eq hoare_1708887482_state) (F_42 ((insert528405184_state X_49) bot_bo19817387tate_o))) X_49))) of role axiom named fact_735_folding__one_Osingleton
% A new axiom: (forall (X_49:hoare_1708887482_state) (F_43:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_42:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_43) F_42)->(((eq hoare_1708887482_state) (F_42 ((insert528405184_state X_49) bot_bo19817387tate_o))) X_49)))
% FOF formula (forall (A_134:(com->Prop)) (F_41:(com->(com->com))) (F_40:((com->Prop)->com)), (((finite860057415ne_com F_41) F_40)->((finite_finite_com A_134)->((not (((eq (com->Prop)) A_134) bot_bot_com_o))->((forall (X_3:com) (Y_4:com), ((member_com ((F_41 X_3) Y_4)) ((insert_com X_3) ((insert_com Y_4) bot_bot_com_o))))->((member_com (F_40 A_134)) A_134)))))) of role axiom named fact_736_folding__one_Oclosed
% A new axiom: (forall (A_134:(com->Prop)) (F_41:(com->(com->com))) (F_40:((com->Prop)->com)), (((finite860057415ne_com F_41) F_40)->((finite_finite_com A_134)->((not (((eq (com->Prop)) A_134) bot_bot_com_o))->((forall (X_3:com) (Y_4:com), ((member_com ((F_41 X_3) Y_4)) ((insert_com X_3) ((insert_com Y_4) bot_bot_com_o))))->((member_com (F_40 A_134)) A_134))))))
% FOF formula (forall (A_134:(pname->Prop)) (F_41:(pname->(pname->pname))) (F_40:((pname->Prop)->pname)), (((finite1282449217_pname F_41) F_40)->((finite_finite_pname A_134)->((not (((eq (pname->Prop)) A_134) bot_bot_pname_o))->((forall (X_3:pname) (Y_4:pname), ((member_pname ((F_41 X_3) Y_4)) ((insert_pname X_3) ((insert_pname Y_4) bot_bot_pname_o))))->((member_pname (F_40 A_134)) A_134)))))) of role axiom named fact_737_folding__one_Oclosed
% A new axiom: (forall (A_134:(pname->Prop)) (F_41:(pname->(pname->pname))) (F_40:((pname->Prop)->pname)), (((finite1282449217_pname F_41) F_40)->((finite_finite_pname A_134)->((not (((eq (pname->Prop)) A_134) bot_bot_pname_o))->((forall (X_3:pname) (Y_4:pname), ((member_pname ((F_41 X_3) Y_4)) ((insert_pname X_3) ((insert_pname Y_4) bot_bot_pname_o))))->((member_pname (F_40 A_134)) A_134))))))
% FOF formula (forall (A_134:(hoare_1708887482_state->Prop)) (F_41:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_40:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_41) F_40)->((finite1625599783_state A_134)->((not (((eq (hoare_1708887482_state->Prop)) A_134) bot_bo19817387tate_o))->((forall (X_3:hoare_1708887482_state) (Y_4:hoare_1708887482_state), ((member451959335_state ((F_41 X_3) Y_4)) ((insert528405184_state X_3) ((insert528405184_state Y_4) bot_bo19817387tate_o))))->((member451959335_state (F_40 A_134)) A_134)))))) of role axiom named fact_738_folding__one_Oclosed
% A new axiom: (forall (A_134:(hoare_1708887482_state->Prop)) (F_41:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_40:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_41) F_40)->((finite1625599783_state A_134)->((not (((eq (hoare_1708887482_state->Prop)) A_134) bot_bo19817387tate_o))->((forall (X_3:hoare_1708887482_state) (Y_4:hoare_1708887482_state), ((member451959335_state ((F_41 X_3) Y_4)) ((insert528405184_state X_3) ((insert528405184_state Y_4) bot_bo19817387tate_o))))->((member451959335_state (F_40 A_134)) A_134))))))
% FOF formula (forall (A_134:((pname->Prop)->Prop)) (F_41:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_40:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_41) F_40)->((finite297249702name_o A_134)->((not (((eq ((pname->Prop)->Prop)) A_134) bot_bot_pname_o_o))->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), ((member_pname_o ((F_41 X_3) Y_4)) ((insert_pname_o X_3) ((insert_pname_o Y_4) bot_bot_pname_o_o))))->((member_pname_o (F_40 A_134)) A_134)))))) of role axiom named fact_739_folding__one_Oclosed
% A new axiom: (forall (A_134:((pname->Prop)->Prop)) (F_41:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_40:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_41) F_40)->((finite297249702name_o A_134)->((not (((eq ((pname->Prop)->Prop)) A_134) bot_bot_pname_o_o))->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), ((member_pname_o ((F_41 X_3) Y_4)) ((insert_pname_o X_3) ((insert_pname_o Y_4) bot_bot_pname_o_o))))->((member_pname_o (F_40 A_134)) A_134))))))
% FOF formula (forall (A_134:((hoare_1708887482_state->Prop)->Prop)) (F_41:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_40:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_41) F_40)->((finite1329924456tate_o A_134)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_134) bot_bo1678742418te_o_o))->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), ((member814030440tate_o ((F_41 X_3) Y_4)) ((insert949073679tate_o X_3) ((insert949073679tate_o Y_4) bot_bo1678742418te_o_o))))->((member814030440tate_o (F_40 A_134)) A_134)))))) of role axiom named fact_740_folding__one_Oclosed
% A new axiom: (forall (A_134:((hoare_1708887482_state->Prop)->Prop)) (F_41:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_40:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_41) F_40)->((finite1329924456tate_o A_134)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_134) bot_bo1678742418te_o_o))->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), ((member814030440tate_o ((F_41 X_3) Y_4)) ((insert949073679tate_o X_3) ((insert949073679tate_o Y_4) bot_bo1678742418te_o_o))))->((member814030440tate_o (F_40 A_134)) A_134))))))
% FOF formula (forall (F_39:(pname->hoare_1708887482_state)) (G_8:(pname->hoare_1708887482_state)) (M_3:(pname->Prop)) (N:(pname->Prop)), ((((eq (pname->Prop)) M_3) N)->((forall (X_3:pname), (((member_pname X_3) N)->(((eq hoare_1708887482_state) (F_39 X_3)) (G_8 X_3))))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_39) M_3)) ((image_1116629049_state G_8) N))))) of role axiom named fact_741_image__cong
% A new axiom: (forall (F_39:(pname->hoare_1708887482_state)) (G_8:(pname->hoare_1708887482_state)) (M_3:(pname->Prop)) (N:(pname->Prop)), ((((eq (pname->Prop)) M_3) N)->((forall (X_3:pname), (((member_pname X_3) N)->(((eq hoare_1708887482_state) (F_39 X_3)) (G_8 X_3))))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_39) M_3)) ((image_1116629049_state G_8) N)))))
% FOF formula (forall (Q_5:(hoare_1708887482_state->Prop)) (P_10:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), ((P_10 X_3)->(Q_5 X_3)))->((ord_le777019615tate_o (collec1568722789_state P_10)) (collec1568722789_state Q_5)))) of role axiom named fact_742_Collect__mono
% A new axiom: (forall (Q_5:(hoare_1708887482_state->Prop)) (P_10:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), ((P_10 X_3)->(Q_5 X_3)))->((ord_le777019615tate_o (collec1568722789_state P_10)) (collec1568722789_state Q_5))))
% FOF formula (forall (Q_5:(pname->Prop)) (P_10:(pname->Prop)), ((forall (X_3:pname), ((P_10 X_3)->(Q_5 X_3)))->((ord_less_eq_pname_o (collect_pname P_10)) (collect_pname Q_5)))) of role axiom named fact_743_Collect__mono
% A new axiom: (forall (Q_5:(pname->Prop)) (P_10:(pname->Prop)), ((forall (X_3:pname), ((P_10 X_3)->(Q_5 X_3)))->((ord_less_eq_pname_o (collect_pname P_10)) (collect_pname Q_5))))
% FOF formula (forall (Q_5:((pname->Prop)->Prop)) (P_10:((pname->Prop)->Prop)), ((forall (X_3:(pname->Prop)), ((P_10 X_3)->(Q_5 X_3)))->((ord_le1205211808me_o_o (collect_pname_o P_10)) (collect_pname_o Q_5)))) of role axiom named fact_744_Collect__mono
% A new axiom: (forall (Q_5:((pname->Prop)->Prop)) (P_10:((pname->Prop)->Prop)), ((forall (X_3:(pname->Prop)), ((P_10 X_3)->(Q_5 X_3)))->((ord_le1205211808me_o_o (collect_pname_o P_10)) (collect_pname_o Q_5))))
% FOF formula (forall (Q_5:((hoare_1708887482_state->Prop)->Prop)) (P_10:((hoare_1708887482_state->Prop)->Prop)), ((forall (X_3:(hoare_1708887482_state->Prop)), ((P_10 X_3)->(Q_5 X_3)))->((ord_le1728773982te_o_o (collec219771562tate_o P_10)) (collec219771562tate_o Q_5)))) of role axiom named fact_745_Collect__mono
% A new axiom: (forall (Q_5:((hoare_1708887482_state->Prop)->Prop)) (P_10:((hoare_1708887482_state->Prop)->Prop)), ((forall (X_3:(hoare_1708887482_state->Prop)), ((P_10 X_3)->(Q_5 X_3)))->((ord_le1728773982te_o_o (collec219771562tate_o P_10)) (collec219771562tate_o Q_5))))
% FOF formula (forall (Q_4:(pname->Prop)) (P_9:(pname->Prop)), ((forall (X_3:pname), ((P_9 X_3)->(Q_4 X_3)))->((ord_less_eq_pname_o P_9) Q_4))) of role axiom named fact_746_predicate1I
% A new axiom: (forall (Q_4:(pname->Prop)) (P_9:(pname->Prop)), ((forall (X_3:pname), ((P_9 X_3)->(Q_4 X_3)))->((ord_less_eq_pname_o P_9) Q_4)))
% FOF formula (forall (Q_4:(hoare_1708887482_state->Prop)) (P_9:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), ((P_9 X_3)->(Q_4 X_3)))->((ord_le777019615tate_o P_9) Q_4))) of role axiom named fact_747_predicate1I
% A new axiom: (forall (Q_4:(hoare_1708887482_state->Prop)) (P_9:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), ((P_9 X_3)->(Q_4 X_3)))->((ord_le777019615tate_o P_9) Q_4)))
% FOF formula (forall (A_133:com) (A_132:(com->Prop)), (((member_com A_133) A_132)->((ex (com->Prop)) (fun (B_84:(com->Prop))=> ((and (((eq (com->Prop)) A_132) ((insert_com A_133) B_84))) (((member_com A_133) B_84)->False)))))) of role axiom named fact_748_mk__disjoint__insert
% A new axiom: (forall (A_133:com) (A_132:(com->Prop)), (((member_com A_133) A_132)->((ex (com->Prop)) (fun (B_84:(com->Prop))=> ((and (((eq (com->Prop)) A_132) ((insert_com A_133) B_84))) (((member_com A_133) B_84)->False))))))
% FOF formula (forall (A_133:pname) (A_132:(pname->Prop)), (((member_pname A_133) A_132)->((ex (pname->Prop)) (fun (B_84:(pname->Prop))=> ((and (((eq (pname->Prop)) A_132) ((insert_pname A_133) B_84))) (((member_pname A_133) B_84)->False)))))) of role axiom named fact_749_mk__disjoint__insert
% A new axiom: (forall (A_133:pname) (A_132:(pname->Prop)), (((member_pname A_133) A_132)->((ex (pname->Prop)) (fun (B_84:(pname->Prop))=> ((and (((eq (pname->Prop)) A_132) ((insert_pname A_133) B_84))) (((member_pname A_133) B_84)->False))))))
% FOF formula (forall (A_133:hoare_1708887482_state) (A_132:(hoare_1708887482_state->Prop)), (((member451959335_state A_133) A_132)->((ex (hoare_1708887482_state->Prop)) (fun (B_84:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_132) ((insert528405184_state A_133) B_84))) (((member451959335_state A_133) B_84)->False)))))) of role axiom named fact_750_mk__disjoint__insert
% A new axiom: (forall (A_133:hoare_1708887482_state) (A_132:(hoare_1708887482_state->Prop)), (((member451959335_state A_133) A_132)->((ex (hoare_1708887482_state->Prop)) (fun (B_84:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_132) ((insert528405184_state A_133) B_84))) (((member451959335_state A_133) B_84)->False))))))
% FOF formula (forall (X_48:com) (A_131:(com->Prop)), (((member_com X_48) A_131)->((forall (B_84:(com->Prop)), ((((eq (com->Prop)) A_131) ((insert_com X_48) B_84))->((member_com X_48) B_84)))->False))) of role axiom named fact_751_Set_Oset__insert
% A new axiom: (forall (X_48:com) (A_131:(com->Prop)), (((member_com X_48) A_131)->((forall (B_84:(com->Prop)), ((((eq (com->Prop)) A_131) ((insert_com X_48) B_84))->((member_com X_48) B_84)))->False)))
% FOF formula (forall (X_48:pname) (A_131:(pname->Prop)), (((member_pname X_48) A_131)->((forall (B_84:(pname->Prop)), ((((eq (pname->Prop)) A_131) ((insert_pname X_48) B_84))->((member_pname X_48) B_84)))->False))) of role axiom named fact_752_Set_Oset__insert
% A new axiom: (forall (X_48:pname) (A_131:(pname->Prop)), (((member_pname X_48) A_131)->((forall (B_84:(pname->Prop)), ((((eq (pname->Prop)) A_131) ((insert_pname X_48) B_84))->((member_pname X_48) B_84)))->False)))
% FOF formula (forall (X_48:hoare_1708887482_state) (A_131:(hoare_1708887482_state->Prop)), (((member451959335_state X_48) A_131)->((forall (B_84:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_131) ((insert528405184_state X_48) B_84))->((member451959335_state X_48) B_84)))->False))) of role axiom named fact_753_Set_Oset__insert
% A new axiom: (forall (X_48:hoare_1708887482_state) (A_131:(hoare_1708887482_state->Prop)), (((member451959335_state X_48) A_131)->((forall (B_84:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_131) ((insert528405184_state X_48) B_84))->((member451959335_state X_48) B_84)))->False)))
% FOF formula (forall (A_130:(com->Prop)), ((forall (Y_4:com), (((member_com Y_4) A_130)->False))->(((eq (com->Prop)) A_130) bot_bot_com_o))) of role axiom named fact_754_equals0I
% A new axiom: (forall (A_130:(com->Prop)), ((forall (Y_4:com), (((member_com Y_4) A_130)->False))->(((eq (com->Prop)) A_130) bot_bot_com_o)))
% FOF formula (forall (A_130:(pname->Prop)), ((forall (Y_4:pname), (((member_pname Y_4) A_130)->False))->(((eq (pname->Prop)) A_130) bot_bot_pname_o))) of role axiom named fact_755_equals0I
% A new axiom: (forall (A_130:(pname->Prop)), ((forall (Y_4:pname), (((member_pname Y_4) A_130)->False))->(((eq (pname->Prop)) A_130) bot_bot_pname_o)))
% FOF formula (forall (A_130:(hoare_1708887482_state->Prop)), ((forall (Y_4:hoare_1708887482_state), (((member451959335_state Y_4) A_130)->False))->(((eq (hoare_1708887482_state->Prop)) A_130) bot_bo19817387tate_o))) of role axiom named fact_756_equals0I
% A new axiom: (forall (A_130:(hoare_1708887482_state->Prop)), ((forall (Y_4:hoare_1708887482_state), (((member451959335_state Y_4) A_130)->False))->(((eq (hoare_1708887482_state->Prop)) A_130) bot_bo19817387tate_o)))
% FOF formula (forall (G_7:(hoare_1708887482_state->Prop)) (C_34:com), (hoare_1160767572gleton->(((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_34) S0_1) S1)) (((eq state) Z_11) S1))))) C_34) fequal_state)) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o))))) of role axiom named fact_757_MGT__alternD
% A new axiom: (forall (G_7:(hoare_1708887482_state->Prop)) (C_34:com), (hoare_1160767572gleton->(((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_34) S0_1) S1)) (((eq state) Z_11) S1))))) C_34) fequal_state)) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o)))))
% FOF formula (forall (C_35:Prop) (F_38:(Prop->Prop)) (B_83:Prop) (A_129:Prop), (((iff A_129) (F_38 B_83))->(((ord_less_eq_o C_35) B_83)->((forall (X_3:Prop) (Y_4:Prop), (((ord_less_eq_o Y_4) X_3)->((ord_less_eq_o (F_38 Y_4)) (F_38 X_3))))->((ord_less_eq_o (F_38 C_35)) A_129))))) of role axiom named fact_758_xt1_I15_J
% A new axiom: (forall (C_35:Prop) (F_38:(Prop->Prop)) (B_83:Prop) (A_129:Prop), (((iff A_129) (F_38 B_83))->(((ord_less_eq_o C_35) B_83)->((forall (X_3:Prop) (Y_4:Prop), (((ord_less_eq_o Y_4) X_3)->((ord_less_eq_o (F_38 Y_4)) (F_38 X_3))))->((ord_less_eq_o (F_38 C_35)) A_129)))))
% FOF formula (forall (C_35:(pname->Prop)) (A_129:(pname->Prop)) (F_38:((pname->Prop)->(pname->Prop))) (B_83:(pname->Prop)), ((((eq (pname->Prop)) A_129) (F_38 B_83))->(((ord_less_eq_pname_o C_35) B_83)->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), (((ord_less_eq_pname_o Y_4) X_3)->((ord_less_eq_pname_o (F_38 Y_4)) (F_38 X_3))))->((ord_less_eq_pname_o (F_38 C_35)) A_129))))) of role axiom named fact_759_xt1_I15_J
% A new axiom: (forall (C_35:(pname->Prop)) (A_129:(pname->Prop)) (F_38:((pname->Prop)->(pname->Prop))) (B_83:(pname->Prop)), ((((eq (pname->Prop)) A_129) (F_38 B_83))->(((ord_less_eq_pname_o C_35) B_83)->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), (((ord_less_eq_pname_o Y_4) X_3)->((ord_less_eq_pname_o (F_38 Y_4)) (F_38 X_3))))->((ord_less_eq_pname_o (F_38 C_35)) A_129)))))
% FOF formula (forall (C_35:(hoare_1708887482_state->Prop)) (A_129:(hoare_1708887482_state->Prop)) (F_38:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (B_83:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_129) (F_38 B_83))->(((ord_le777019615tate_o C_35) B_83)->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_4) X_3)->((ord_le777019615tate_o (F_38 Y_4)) (F_38 X_3))))->((ord_le777019615tate_o (F_38 C_35)) A_129))))) of role axiom named fact_760_xt1_I15_J
% A new axiom: (forall (C_35:(hoare_1708887482_state->Prop)) (A_129:(hoare_1708887482_state->Prop)) (F_38:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (B_83:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_129) (F_38 B_83))->(((ord_le777019615tate_o C_35) B_83)->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_4) X_3)->((ord_le777019615tate_o (F_38 Y_4)) (F_38 X_3))))->((ord_le777019615tate_o (F_38 C_35)) A_129)))))
% FOF formula (forall (G_7:(hoare_1708887482_state->Prop)) (C_34:com), (((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_34) S0_1) S1)) (((eq state) Z_11) S1))))) C_34) fequal_state)) bot_bo19817387tate_o)))) of role axiom named fact_761_MGT__alternI
% A new axiom: (forall (G_7:(hoare_1708887482_state->Prop)) (C_34:com), (((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_34) S0_1) S1)) (((eq state) Z_11) S1))))) C_34) fequal_state)) bot_bo19817387tate_o))))
% FOF formula (forall (C_34:com), (((eq hoare_1708887482_state) (hoare_Mirabelle_MGT C_34)) (((hoare_858012674_state fequal_state) C_34) (evalc C_34)))) of role axiom named fact_762_MGT__def
% A new axiom: (forall (C_34:com), (((eq hoare_1708887482_state) (hoare_Mirabelle_MGT C_34)) (((hoare_858012674_state fequal_state) C_34) (evalc C_34))))
% FOF formula (forall (P:pname) (S_4:state) (S1_1:state), ((((evalc (body_1 P)) S_4) S1_1)->(((evalc (the_com (body P))) S_4) S1_1))) of role axiom named fact_763_evalc__elim__cases_I6_J
% A new axiom: (forall (P:pname) (S_4:state) (S1_1:state), ((((evalc (body_1 P)) S_4) S1_1)->(((evalc (the_com (body P))) S_4) S1_1)))
% FOF formula (forall (Pn_1:pname) (S0:state) (S1_1:state), ((((evalc (the_com (body Pn_1))) S0) S1_1)->(((evalc (body_1 Pn_1)) S0) S1_1))) of role axiom named fact_764_evalc_OBody
% A new axiom: (forall (Pn_1:pname) (S0:state) (S1_1:state), ((((evalc (the_com (body Pn_1))) S0) S1_1)->(((evalc (body_1 Pn_1)) S0) S1_1)))
% FOF formula (forall (S_4:state) (T:state), ((((evalc skip) S_4) T)->(((eq state) T) S_4))) of role axiom named fact_765_evalc__elim__cases_I1_J
% A new axiom: (forall (S_4:state) (T:state), ((((evalc skip) S_4) T)->(((eq state) T) S_4)))
% FOF formula (forall (S_4:state), (((evalc skip) S_4) S_4)) of role axiom named fact_766_evalc_OSkip
% A new axiom: (forall (S_4:state), (((evalc skip) S_4) S_4))
% FOF formula (forall (C1:com) (S2:state) (C0:com) (S0:state) (S1_1:state), ((((evalc C0) S0) S1_1)->((((evalc C1) S1_1) S2)->(((evalc ((semi C0) C1)) S0) S2)))) of role axiom named fact_767_evalc_OSemi
% A new axiom: (forall (C1:com) (S2:state) (C0:com) (S0:state) (S1_1:state), ((((evalc C0) S0) S1_1)->((((evalc C1) S1_1) S2)->(((evalc ((semi C0) C1)) S0) S2))))
% FOF formula (forall (S2:state) (C_34:com) (S1_1:state) (B_82:(state->Prop)) (S0:state), ((B_82 S0)->((((evalc C_34) S0) S1_1)->((((evalc ((while B_82) C_34)) S1_1) S2)->(((evalc ((while B_82) C_34)) S0) S2))))) of role axiom named fact_768_evalc_OWhileTrue
% A new axiom: (forall (S2:state) (C_34:com) (S1_1:state) (B_82:(state->Prop)) (S0:state), ((B_82 S0)->((((evalc C_34) S0) S1_1)->((((evalc ((while B_82) C_34)) S1_1) S2)->(((evalc ((while B_82) C_34)) S0) S2)))))
% FOF formula (forall (C_34:com) (B_82:(state->Prop)) (S_4:state), (((B_82 S_4)->False)->(((evalc ((while B_82) C_34)) S_4) S_4))) of role axiom named fact_769_evalc_OWhileFalse
% A new axiom: (forall (C_34:com) (B_82:(state->Prop)) (S_4:state), (((B_82 S_4)->False)->(((evalc ((while B_82) C_34)) S_4) S_4)))
% FOF formula (forall (U:state) (C_34:com) (S_4:state) (T:state), ((((evalc C_34) S_4) T)->((((evalc C_34) S_4) U)->(((eq state) U) T)))) of role axiom named fact_770_com__det
% A new axiom: (forall (U:state) (C_34:com) (S_4:state) (T:state), ((((evalc C_34) S_4) T)->((((evalc C_34) S_4) U)->(((eq state) U) T))))
% FOF formula (forall (C1:com) (C2:com) (S_4:state) (T:state), ((((evalc ((semi C1) C2)) S_4) T)->((forall (S1:state), ((((evalc C1) S_4) S1)->((((evalc C2) S1) T)->False)))->False))) of role axiom named fact_771_evalc__elim__cases_I4_J
% A new axiom: (forall (C1:com) (C2:com) (S_4:state) (T:state), ((((evalc ((semi C1) C2)) S_4) T)->((forall (S1:state), ((((evalc C1) S_4) S1)->((((evalc C2) S1) T)->False)))->False)))
% FOF formula (forall (B_82:(state->Prop)) (C_34:com) (S_4:state) (T:state), ((((evalc ((while B_82) C_34)) S_4) T)->(((((eq state) T) S_4)->(B_82 S_4))->(((B_82 S_4)->(forall (S1:state), ((((evalc C_34) S_4) S1)->((((evalc ((while B_82) C_34)) S1) T)->False))))->False)))) of role axiom named fact_772_evalc__WHILE__case
% A new axiom: (forall (B_82:(state->Prop)) (C_34:com) (S_4:state) (T:state), ((((evalc ((while B_82) C_34)) S_4) T)->(((((eq state) T) S_4)->(B_82 S_4))->(((B_82 S_4)->(forall (S1:state), ((((evalc C_34) S_4) S1)->((((evalc ((while B_82) C_34)) S1) T)->False))))->False))))
% FOF formula (forall (C_33:Prop) (F_37:(Prop->Prop)) (B_81:Prop) (A_128:Prop), (((ord_less_eq_o B_81) A_128)->(((iff (F_37 B_81)) C_33)->((forall (X_3:Prop) (Y_4:Prop), (((ord_less_eq_o Y_4) X_3)->((ord_less_eq_o (F_37 Y_4)) (F_37 X_3))))->((ord_less_eq_o C_33) (F_37 A_128)))))) of role axiom named fact_773_xt1_I16_J
% A new axiom: (forall (C_33:Prop) (F_37:(Prop->Prop)) (B_81:Prop) (A_128:Prop), (((ord_less_eq_o B_81) A_128)->(((iff (F_37 B_81)) C_33)->((forall (X_3:Prop) (Y_4:Prop), (((ord_less_eq_o Y_4) X_3)->((ord_less_eq_o (F_37 Y_4)) (F_37 X_3))))->((ord_less_eq_o C_33) (F_37 A_128))))))
% FOF formula (forall (F_37:((pname->Prop)->(pname->Prop))) (C_33:(pname->Prop)) (B_81:(pname->Prop)) (A_128:(pname->Prop)), (((ord_less_eq_pname_o B_81) A_128)->((((eq (pname->Prop)) (F_37 B_81)) C_33)->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), (((ord_less_eq_pname_o Y_4) X_3)->((ord_less_eq_pname_o (F_37 Y_4)) (F_37 X_3))))->((ord_less_eq_pname_o C_33) (F_37 A_128)))))) of role axiom named fact_774_xt1_I16_J
% A new axiom: (forall (F_37:((pname->Prop)->(pname->Prop))) (C_33:(pname->Prop)) (B_81:(pname->Prop)) (A_128:(pname->Prop)), (((ord_less_eq_pname_o B_81) A_128)->((((eq (pname->Prop)) (F_37 B_81)) C_33)->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), (((ord_less_eq_pname_o Y_4) X_3)->((ord_less_eq_pname_o (F_37 Y_4)) (F_37 X_3))))->((ord_less_eq_pname_o C_33) (F_37 A_128))))))
% FOF formula (forall (F_37:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (C_33:(hoare_1708887482_state->Prop)) (B_81:(hoare_1708887482_state->Prop)) (A_128:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_81) A_128)->((((eq (hoare_1708887482_state->Prop)) (F_37 B_81)) C_33)->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_4) X_3)->((ord_le777019615tate_o (F_37 Y_4)) (F_37 X_3))))->((ord_le777019615tate_o C_33) (F_37 A_128)))))) of role axiom named fact_775_xt1_I16_J
% A new axiom: (forall (F_37:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (C_33:(hoare_1708887482_state->Prop)) (B_81:(hoare_1708887482_state->Prop)) (A_128:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_81) A_128)->((((eq (hoare_1708887482_state->Prop)) (F_37 B_81)) C_33)->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_4) X_3)->((ord_le777019615tate_o (F_37 Y_4)) (F_37 X_3))))->((ord_le777019615tate_o C_33) (F_37 A_128))))))
% FOF formula (forall (B_80:((pname->Prop)->Prop)) (A_127:((pname->Prop)->Prop)) (F_36:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_35:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_36) F_35)->((finite297249702name_o A_127)->((finite297249702name_o B_80)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_127) B_80)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((F_36 (F_35 ((semila181081674me_o_o A_127) B_80))) (F_35 ((semila2013987940me_o_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80)))))))) of role axiom named fact_776_folding__one_Ounion__inter
% A new axiom: (forall (B_80:((pname->Prop)->Prop)) (A_127:((pname->Prop)->Prop)) (F_36:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_35:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_36) F_35)->((finite297249702name_o A_127)->((finite297249702name_o B_80)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_127) B_80)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((F_36 (F_35 ((semila181081674me_o_o A_127) B_80))) (F_35 ((semila2013987940me_o_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80))))))))
% FOF formula (forall (B_80:((hoare_1708887482_state->Prop)->Prop)) (A_127:((hoare_1708887482_state->Prop)->Prop)) (F_36:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_35:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_36) F_35)->((finite1329924456tate_o A_127)->((finite1329924456tate_o B_80)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_127) B_80)) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) ((F_36 (F_35 ((semila1853742644te_o_o A_127) B_80))) (F_35 ((semila598060698te_o_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80)))))))) of role axiom named fact_777_folding__one_Ounion__inter
% A new axiom: (forall (B_80:((hoare_1708887482_state->Prop)->Prop)) (A_127:((hoare_1708887482_state->Prop)->Prop)) (F_36:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_35:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_36) F_35)->((finite1329924456tate_o A_127)->((finite1329924456tate_o B_80)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_127) B_80)) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) ((F_36 (F_35 ((semila1853742644te_o_o A_127) B_80))) (F_35 ((semila598060698te_o_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80))))))))
% FOF formula (forall (B_80:(pname->Prop)) (A_127:(pname->Prop)) (F_36:(pname->(pname->pname))) (F_35:((pname->Prop)->pname)), (((finite1282449217_pname F_36) F_35)->((finite_finite_pname A_127)->((finite_finite_pname B_80)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_127) B_80)) bot_bot_pname_o))->(((eq pname) ((F_36 (F_35 ((semila1780557381name_o A_127) B_80))) (F_35 ((semila1673364395name_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80)))))))) of role axiom named fact_778_folding__one_Ounion__inter
% A new axiom: (forall (B_80:(pname->Prop)) (A_127:(pname->Prop)) (F_36:(pname->(pname->pname))) (F_35:((pname->Prop)->pname)), (((finite1282449217_pname F_36) F_35)->((finite_finite_pname A_127)->((finite_finite_pname B_80)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_127) B_80)) bot_bot_pname_o))->(((eq pname) ((F_36 (F_35 ((semila1780557381name_o A_127) B_80))) (F_35 ((semila1673364395name_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80))))))))
% FOF formula (forall (B_80:(hoare_1708887482_state->Prop)) (A_127:(hoare_1708887482_state->Prop)) (F_36:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_35:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_36) F_35)->((finite1625599783_state A_127)->((finite1625599783_state B_80)->((not (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_127) B_80)) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) ((F_36 (F_35 ((semila1122118281tate_o A_127) B_80))) (F_35 ((semila129691299tate_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80)))))))) of role axiom named fact_779_folding__one_Ounion__inter
% A new axiom: (forall (B_80:(hoare_1708887482_state->Prop)) (A_127:(hoare_1708887482_state->Prop)) (F_36:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_35:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_36) F_35)->((finite1625599783_state A_127)->((finite1625599783_state B_80)->((not (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_127) B_80)) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) ((F_36 (F_35 ((semila1122118281tate_o A_127) B_80))) (F_35 ((semila129691299tate_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80))))))))
% FOF formula (forall (B_80:(com->Prop)) (A_127:(com->Prop)) (F_36:(com->(com->com))) (F_35:((com->Prop)->com)), (((finite860057415ne_com F_36) F_35)->((finite_finite_com A_127)->((finite_finite_com B_80)->((not (((eq (com->Prop)) ((semila513601829_com_o A_127) B_80)) bot_bot_com_o))->(((eq com) ((F_36 (F_35 ((semila1562558655_com_o A_127) B_80))) (F_35 ((semila513601829_com_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80)))))))) of role axiom named fact_780_folding__one_Ounion__inter
% A new axiom: (forall (B_80:(com->Prop)) (A_127:(com->Prop)) (F_36:(com->(com->com))) (F_35:((com->Prop)->com)), (((finite860057415ne_com F_36) F_35)->((finite_finite_com A_127)->((finite_finite_com B_80)->((not (((eq (com->Prop)) ((semila513601829_com_o A_127) B_80)) bot_bot_com_o))->(((eq com) ((F_36 (F_35 ((semila1562558655_com_o A_127) B_80))) (F_35 ((semila513601829_com_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80))))))))
% FOF formula (forall (B_79:((pname->Prop)->Prop)) (A_126:((pname->Prop)->Prop)) (F_34:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_33:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_34) F_33)->((finite297249702name_o A_126)->((not (((eq ((pname->Prop)->Prop)) A_126) bot_bot_pname_o_o))->((finite297249702name_o B_79)->((not (((eq ((pname->Prop)->Prop)) B_79) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_126) B_79)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_33 ((semila181081674me_o_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79)))))))))) of role axiom named fact_781_folding__one_Ounion__disjoint
% A new axiom: (forall (B_79:((pname->Prop)->Prop)) (A_126:((pname->Prop)->Prop)) (F_34:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_33:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_34) F_33)->((finite297249702name_o A_126)->((not (((eq ((pname->Prop)->Prop)) A_126) bot_bot_pname_o_o))->((finite297249702name_o B_79)->((not (((eq ((pname->Prop)->Prop)) B_79) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_126) B_79)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_33 ((semila181081674me_o_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79))))))))))
% FOF formula (forall (B_79:((hoare_1708887482_state->Prop)->Prop)) (A_126:((hoare_1708887482_state->Prop)->Prop)) (F_34:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_33:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_34) F_33)->((finite1329924456tate_o A_126)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_126) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_79)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_79) bot_bo1678742418te_o_o))->((((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_126) B_79)) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (F_33 ((semila1853742644te_o_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79)))))))))) of role axiom named fact_782_folding__one_Ounion__disjoint
% A new axiom: (forall (B_79:((hoare_1708887482_state->Prop)->Prop)) (A_126:((hoare_1708887482_state->Prop)->Prop)) (F_34:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_33:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_34) F_33)->((finite1329924456tate_o A_126)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_126) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_79)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_79) bot_bo1678742418te_o_o))->((((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_126) B_79)) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (F_33 ((semila1853742644te_o_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79))))))))))
% FOF formula (forall (B_79:(pname->Prop)) (A_126:(pname->Prop)) (F_34:(pname->(pname->pname))) (F_33:((pname->Prop)->pname)), (((finite1282449217_pname F_34) F_33)->((finite_finite_pname A_126)->((not (((eq (pname->Prop)) A_126) bot_bot_pname_o))->((finite_finite_pname B_79)->((not (((eq (pname->Prop)) B_79) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_126) B_79)) bot_bot_pname_o)->(((eq pname) (F_33 ((semila1780557381name_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79)))))))))) of role axiom named fact_783_folding__one_Ounion__disjoint
% A new axiom: (forall (B_79:(pname->Prop)) (A_126:(pname->Prop)) (F_34:(pname->(pname->pname))) (F_33:((pname->Prop)->pname)), (((finite1282449217_pname F_34) F_33)->((finite_finite_pname A_126)->((not (((eq (pname->Prop)) A_126) bot_bot_pname_o))->((finite_finite_pname B_79)->((not (((eq (pname->Prop)) B_79) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_126) B_79)) bot_bot_pname_o)->(((eq pname) (F_33 ((semila1780557381name_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79))))))))))
% FOF formula (forall (B_79:(hoare_1708887482_state->Prop)) (A_126:(hoare_1708887482_state->Prop)) (F_34:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_33:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_34) F_33)->((finite1625599783_state A_126)->((not (((eq (hoare_1708887482_state->Prop)) A_126) bot_bo19817387tate_o))->((finite1625599783_state B_79)->((not (((eq (hoare_1708887482_state->Prop)) B_79) bot_bo19817387tate_o))->((((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_126) B_79)) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_33 ((semila1122118281tate_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79)))))))))) of role axiom named fact_784_folding__one_Ounion__disjoint
% A new axiom: (forall (B_79:(hoare_1708887482_state->Prop)) (A_126:(hoare_1708887482_state->Prop)) (F_34:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_33:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_34) F_33)->((finite1625599783_state A_126)->((not (((eq (hoare_1708887482_state->Prop)) A_126) bot_bo19817387tate_o))->((finite1625599783_state B_79)->((not (((eq (hoare_1708887482_state->Prop)) B_79) bot_bo19817387tate_o))->((((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_126) B_79)) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_33 ((semila1122118281tate_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79))))))))))
% FOF formula (forall (B_79:(com->Prop)) (A_126:(com->Prop)) (F_34:(com->(com->com))) (F_33:((com->Prop)->com)), (((finite860057415ne_com F_34) F_33)->((finite_finite_com A_126)->((not (((eq (com->Prop)) A_126) bot_bot_com_o))->((finite_finite_com B_79)->((not (((eq (com->Prop)) B_79) bot_bot_com_o))->((((eq (com->Prop)) ((semila513601829_com_o A_126) B_79)) bot_bot_com_o)->(((eq com) (F_33 ((semila1562558655_com_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79)))))))))) of role axiom named fact_785_folding__one_Ounion__disjoint
% A new axiom: (forall (B_79:(com->Prop)) (A_126:(com->Prop)) (F_34:(com->(com->com))) (F_33:((com->Prop)->com)), (((finite860057415ne_com F_34) F_33)->((finite_finite_com A_126)->((not (((eq (com->Prop)) A_126) bot_bot_com_o))->((finite_finite_com B_79)->((not (((eq (com->Prop)) B_79) bot_bot_com_o))->((((eq (com->Prop)) ((semila513601829_com_o A_126) B_79)) bot_bot_com_o)->(((eq com) (F_33 ((semila1562558655_com_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79))))))))))
% FOF formula (forall (X_47:com) (A_125:(com->Prop)) (F_32:(com->(com->com))) (F_31:((com->Prop)->com)), (((finite860057415ne_com F_32) F_31)->((finite_finite_com A_125)->((and ((((eq (com->Prop)) ((minus_minus_com_o A_125) ((insert_com X_47) bot_bot_com_o))) bot_bot_com_o)->(((eq com) (F_31 ((insert_com X_47) A_125))) X_47))) ((not (((eq (com->Prop)) ((minus_minus_com_o A_125) ((insert_com X_47) bot_bot_com_o))) bot_bot_com_o))->(((eq com) (F_31 ((insert_com X_47) A_125))) ((F_32 X_47) (F_31 ((minus_minus_com_o A_125) ((insert_com X_47) bot_bot_com_o)))))))))) of role axiom named fact_786_folding__one_Oinsert__remove
% A new axiom: (forall (X_47:com) (A_125:(com->Prop)) (F_32:(com->(com->com))) (F_31:((com->Prop)->com)), (((finite860057415ne_com F_32) F_31)->((finite_finite_com A_125)->((and ((((eq (com->Prop)) ((minus_minus_com_o A_125) ((insert_com X_47) bot_bot_com_o))) bot_bot_com_o)->(((eq com) (F_31 ((insert_com X_47) A_125))) X_47))) ((not (((eq (com->Prop)) ((minus_minus_com_o A_125) ((insert_com X_47) bot_bot_com_o))) bot_bot_com_o))->(((eq com) (F_31 ((insert_com X_47) A_125))) ((F_32 X_47) (F_31 ((minus_minus_com_o A_125) ((insert_com X_47) bot_bot_com_o))))))))))
% FOF formula (forall (X_47:pname) (A_125:(pname->Prop)) (F_32:(pname->(pname->pname))) (F_31:((pname->Prop)->pname)), (((finite1282449217_pname F_32) F_31)->((finite_finite_pname A_125)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_125) ((insert_pname X_47) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_31 ((insert_pname X_47) A_125))) X_47))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_125) ((insert_pname X_47) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_31 ((insert_pname X_47) A_125))) ((F_32 X_47) (F_31 ((minus_minus_pname_o A_125) ((insert_pname X_47) bot_bot_pname_o)))))))))) of role axiom named fact_787_folding__one_Oinsert__remove
% A new axiom: (forall (X_47:pname) (A_125:(pname->Prop)) (F_32:(pname->(pname->pname))) (F_31:((pname->Prop)->pname)), (((finite1282449217_pname F_32) F_31)->((finite_finite_pname A_125)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_125) ((insert_pname X_47) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_31 ((insert_pname X_47) A_125))) X_47))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_125) ((insert_pname X_47) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_31 ((insert_pname X_47) A_125))) ((F_32 X_47) (F_31 ((minus_minus_pname_o A_125) ((insert_pname X_47) bot_bot_pname_o))))))))))
% FOF formula (forall (X_47:hoare_1708887482_state) (A_125:(hoare_1708887482_state->Prop)) (F_32:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_31:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_32) F_31)->((finite1625599783_state A_125)->((and ((((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_125) ((insert528405184_state X_47) bot_bo19817387tate_o))) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_31 ((insert528405184_state X_47) A_125))) X_47))) ((not (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_125) ((insert528405184_state X_47) bot_bo19817387tate_o))) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_31 ((insert528405184_state X_47) A_125))) ((F_32 X_47) (F_31 ((minus_2056855718tate_o A_125) ((insert528405184_state X_47) bot_bo19817387tate_o)))))))))) of role axiom named fact_788_folding__one_Oinsert__remove
% A new axiom: (forall (X_47:hoare_1708887482_state) (A_125:(hoare_1708887482_state->Prop)) (F_32:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_31:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_32) F_31)->((finite1625599783_state A_125)->((and ((((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_125) ((insert528405184_state X_47) bot_bo19817387tate_o))) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_31 ((insert528405184_state X_47) A_125))) X_47))) ((not (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_125) ((insert528405184_state X_47) bot_bo19817387tate_o))) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_31 ((insert528405184_state X_47) A_125))) ((F_32 X_47) (F_31 ((minus_2056855718tate_o A_125) ((insert528405184_state X_47) bot_bo19817387tate_o))))))))))
% FOF formula (forall (X_47:(pname->Prop)) (A_125:((pname->Prop)->Prop)) (F_32:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_31:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_32) F_31)->((finite297249702name_o A_125)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_125) ((insert_pname_o X_47) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_31 ((insert_pname_o X_47) A_125))) X_47))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_125) ((insert_pname_o X_47) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_31 ((insert_pname_o X_47) A_125))) ((F_32 X_47) (F_31 ((minus_1480864103me_o_o A_125) ((insert_pname_o X_47) bot_bot_pname_o_o)))))))))) of role axiom named fact_789_folding__one_Oinsert__remove
% A new axiom: (forall (X_47:(pname->Prop)) (A_125:((pname->Prop)->Prop)) (F_32:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_31:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_32) F_31)->((finite297249702name_o A_125)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_125) ((insert_pname_o X_47) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_31 ((insert_pname_o X_47) A_125))) X_47))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_125) ((insert_pname_o X_47) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_31 ((insert_pname_o X_47) A_125))) ((F_32 X_47) (F_31 ((minus_1480864103me_o_o A_125) ((insert_pname_o X_47) bot_bot_pname_o_o))))))))))
% FOF formula (forall (X_47:(hoare_1708887482_state->Prop)) (A_125:((hoare_1708887482_state->Prop)->Prop)) (F_32:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_31:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_32) F_31)->((finite1329924456tate_o A_125)->((and ((((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_125) ((insert949073679tate_o X_47) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (F_31 ((insert949073679tate_o X_47) A_125))) X_47))) ((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_125) ((insert949073679tate_o X_47) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_31 ((insert949073679tate_o X_47) A_125))) ((F_32 X_47) (F_31 ((minus_548038231te_o_o A_125) ((insert949073679tate_o X_47) bot_bo1678742418te_o_o)))))))))) of role axiom named fact_790_folding__one_Oinsert__remove
% A new axiom: (forall (X_47:(hoare_1708887482_state->Prop)) (A_125:((hoare_1708887482_state->Prop)->Prop)) (F_32:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_31:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_32) F_31)->((finite1329924456tate_o A_125)->((and ((((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_125) ((insert949073679tate_o X_47) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (F_31 ((insert949073679tate_o X_47) A_125))) X_47))) ((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_125) ((insert949073679tate_o X_47) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_31 ((insert949073679tate_o X_47) A_125))) ((F_32 X_47) (F_31 ((minus_548038231te_o_o A_125) ((insert949073679tate_o X_47) bot_bo1678742418te_o_o))))))))))
% FOF formula (forall (X_46:com) (A_124:(com->Prop)) (F_30:(com->(com->com))) (F_29:((com->Prop)->com)), (((finite860057415ne_com F_30) F_29)->((finite_finite_com A_124)->(((member_com X_46) A_124)->((and ((((eq (com->Prop)) ((minus_minus_com_o A_124) ((insert_com X_46) bot_bot_com_o))) bot_bot_com_o)->(((eq com) (F_29 A_124)) X_46))) ((not (((eq (com->Prop)) ((minus_minus_com_o A_124) ((insert_com X_46) bot_bot_com_o))) bot_bot_com_o))->(((eq com) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_minus_com_o A_124) ((insert_com X_46) bot_bot_com_o))))))))))) of role axiom named fact_791_folding__one_Oremove
% A new axiom: (forall (X_46:com) (A_124:(com->Prop)) (F_30:(com->(com->com))) (F_29:((com->Prop)->com)), (((finite860057415ne_com F_30) F_29)->((finite_finite_com A_124)->(((member_com X_46) A_124)->((and ((((eq (com->Prop)) ((minus_minus_com_o A_124) ((insert_com X_46) bot_bot_com_o))) bot_bot_com_o)->(((eq com) (F_29 A_124)) X_46))) ((not (((eq (com->Prop)) ((minus_minus_com_o A_124) ((insert_com X_46) bot_bot_com_o))) bot_bot_com_o))->(((eq com) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_minus_com_o A_124) ((insert_com X_46) bot_bot_com_o)))))))))))
% FOF formula (forall (X_46:pname) (A_124:(pname->Prop)) (F_30:(pname->(pname->pname))) (F_29:((pname->Prop)->pname)), (((finite1282449217_pname F_30) F_29)->((finite_finite_pname A_124)->(((member_pname X_46) A_124)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_124) ((insert_pname X_46) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_29 A_124)) X_46))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_124) ((insert_pname X_46) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_minus_pname_o A_124) ((insert_pname X_46) bot_bot_pname_o))))))))))) of role axiom named fact_792_folding__one_Oremove
% A new axiom: (forall (X_46:pname) (A_124:(pname->Prop)) (F_30:(pname->(pname->pname))) (F_29:((pname->Prop)->pname)), (((finite1282449217_pname F_30) F_29)->((finite_finite_pname A_124)->(((member_pname X_46) A_124)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_124) ((insert_pname X_46) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_29 A_124)) X_46))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_124) ((insert_pname X_46) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_minus_pname_o A_124) ((insert_pname X_46) bot_bot_pname_o)))))))))))
% FOF formula (forall (X_46:hoare_1708887482_state) (A_124:(hoare_1708887482_state->Prop)) (F_30:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_29:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_30) F_29)->((finite1625599783_state A_124)->(((member451959335_state X_46) A_124)->((and ((((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_124) ((insert528405184_state X_46) bot_bo19817387tate_o))) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_29 A_124)) X_46))) ((not (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_124) ((insert528405184_state X_46) bot_bo19817387tate_o))) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_2056855718tate_o A_124) ((insert528405184_state X_46) bot_bo19817387tate_o))))))))))) of role axiom named fact_793_folding__one_Oremove
% A new axiom: (forall (X_46:hoare_1708887482_state) (A_124:(hoare_1708887482_state->Prop)) (F_30:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_29:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_30) F_29)->((finite1625599783_state A_124)->(((member451959335_state X_46) A_124)->((and ((((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_124) ((insert528405184_state X_46) bot_bo19817387tate_o))) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_29 A_124)) X_46))) ((not (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_124) ((insert528405184_state X_46) bot_bo19817387tate_o))) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_2056855718tate_o A_124) ((insert528405184_state X_46) bot_bo19817387tate_o)))))))))))
% FOF formula (forall (X_46:(pname->Prop)) (A_124:((pname->Prop)->Prop)) (F_30:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_29:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_30) F_29)->((finite297249702name_o A_124)->(((member_pname_o X_46) A_124)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_124) ((insert_pname_o X_46) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_29 A_124)) X_46))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_124) ((insert_pname_o X_46) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_1480864103me_o_o A_124) ((insert_pname_o X_46) bot_bot_pname_o_o))))))))))) of role axiom named fact_794_folding__one_Oremove
% A new axiom: (forall (X_46:(pname->Prop)) (A_124:((pname->Prop)->Prop)) (F_30:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_29:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_30) F_29)->((finite297249702name_o A_124)->(((member_pname_o X_46) A_124)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_124) ((insert_pname_o X_46) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_29 A_124)) X_46))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_124) ((insert_pname_o X_46) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_1480864103me_o_o A_124) ((insert_pname_o X_46) bot_bot_pname_o_o)))))))))))
% FOF formula (forall (X_46:(hoare_1708887482_state->Prop)) (A_124:((hoare_1708887482_state->Prop)->Prop)) (F_30:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_29:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_30) F_29)->((finite1329924456tate_o A_124)->(((member814030440tate_o X_46) A_124)->((and ((((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_124) ((insert949073679tate_o X_46) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (F_29 A_124)) X_46))) ((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_124) ((insert949073679tate_o X_46) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_548038231te_o_o A_124) ((insert949073679tate_o X_46) bot_bo1678742418te_o_o))))))))))) of role axiom named fact_795_folding__one_Oremove
% A new axiom: (forall (X_46:(hoare_1708887482_state->Prop)) (A_124:((hoare_1708887482_state->Prop)->Prop)) (F_30:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_29:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_30) F_29)->((finite1329924456tate_o A_124)->(((member814030440tate_o X_46) A_124)->((and ((((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_124) ((insert949073679tate_o X_46) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (F_29 A_124)) X_46))) ((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_124) ((insert949073679tate_o X_46) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_548038231te_o_o A_124) ((insert949073679tate_o X_46) bot_bo1678742418te_o_o)))))))))))
% FOF formula (forall (X_45:pname), ((is_none_pname (some_pname X_45))->False)) of role axiom named fact_796_is__none__code_I2_J
% A new axiom: (forall (X_45:pname), ((is_none_pname (some_pname X_45))->False))
% FOF formula (forall (X_45:hoare_1708887482_state), ((is_non163157940_state (some_H1974565227_state X_45))->False)) of role axiom named fact_797_is__none__code_I2_J
% A new axiom: (forall (X_45:hoare_1708887482_state), ((is_non163157940_state (some_H1974565227_state X_45))->False))
% FOF formula (forall (X_45:com), ((is_none_com (some_com X_45))->False)) of role axiom named fact_798_is__none__code_I2_J
% A new axiom: (forall (X_45:com), ((is_none_com (some_com X_45))->False))
% FOF formula (forall (Q_2:(state->(state->Prop))) (G_6:(hoare_1708887482_state->Prop)) (C_32:com) (P_7:(state->(state->Prop))), ((forall (Z_11:state) (S_2:state), (((P_7 Z_11) S_2)->((ex (state->(state->Prop))) (fun (P_8:(state->(state->Prop)))=> ((ex (state->(state->Prop))) (fun (Q_3:(state->(state->Prop)))=> ((and ((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state P_8) C_32) Q_3)) bot_bo19817387tate_o))) (forall (S_3:state), ((forall (Z_12:state), (((P_8 Z_12) S_2)->((Q_3 Z_12) S_3)))->((Q_2 Z_11) S_3))))))))))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state P_7) C_32) Q_2)) bot_bo19817387tate_o)))) of role axiom named fact_799_conseq
% A new axiom: (forall (Q_2:(state->(state->Prop))) (G_6:(hoare_1708887482_state->Prop)) (C_32:com) (P_7:(state->(state->Prop))), ((forall (Z_11:state) (S_2:state), (((P_7 Z_11) S_2)->((ex (state->(state->Prop))) (fun (P_8:(state->(state->Prop)))=> ((ex (state->(state->Prop))) (fun (Q_3:(state->(state->Prop)))=> ((and ((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state P_8) C_32) Q_3)) bot_bo19817387tate_o))) (forall (S_3:state), ((forall (Z_12:state), (((P_8 Z_12) S_2)->((Q_3 Z_12) S_3)))->((Q_2 Z_11) S_3))))))))))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state P_7) C_32) Q_2)) bot_bo19817387tate_o))))
% FOF formula (forall (C_31:com) (A_123:(com->Prop)) (B_78:(com->Prop)), (((member_com C_31) ((semila513601829_com_o A_123) B_78))->((((member_com C_31) A_123)->(((member_com C_31) B_78)->False))->False))) of role axiom named fact_800_IntE
% A new axiom: (forall (C_31:com) (A_123:(com->Prop)) (B_78:(com->Prop)), (((member_com C_31) ((semila513601829_com_o A_123) B_78))->((((member_com C_31) A_123)->(((member_com C_31) B_78)->False))->False)))
% FOF formula (forall (C_31:pname) (A_123:(pname->Prop)) (B_78:(pname->Prop)), (((member_pname C_31) ((semila1673364395name_o A_123) B_78))->((((member_pname C_31) A_123)->(((member_pname C_31) B_78)->False))->False))) of role axiom named fact_801_IntE
% A new axiom: (forall (C_31:pname) (A_123:(pname->Prop)) (B_78:(pname->Prop)), (((member_pname C_31) ((semila1673364395name_o A_123) B_78))->((((member_pname C_31) A_123)->(((member_pname C_31) B_78)->False))->False)))
% FOF formula (forall (C_31:hoare_1708887482_state) (A_123:(hoare_1708887482_state->Prop)) (B_78:(hoare_1708887482_state->Prop)), (((member451959335_state C_31) ((semila129691299tate_o A_123) B_78))->((((member451959335_state C_31) A_123)->(((member451959335_state C_31) B_78)->False))->False))) of role axiom named fact_802_IntE
% A new axiom: (forall (C_31:hoare_1708887482_state) (A_123:(hoare_1708887482_state->Prop)) (B_78:(hoare_1708887482_state->Prop)), (((member451959335_state C_31) ((semila129691299tate_o A_123) B_78))->((((member451959335_state C_31) A_123)->(((member451959335_state C_31) B_78)->False))->False)))
% FOF formula (forall (B_77:(com->Prop)) (C_30:com) (A_122:(com->Prop)), (((member_com C_30) A_122)->(((member_com C_30) B_77)->((member_com C_30) ((semila513601829_com_o A_122) B_77))))) of role axiom named fact_803_IntI
% A new axiom: (forall (B_77:(com->Prop)) (C_30:com) (A_122:(com->Prop)), (((member_com C_30) A_122)->(((member_com C_30) B_77)->((member_com C_30) ((semila513601829_com_o A_122) B_77)))))
% FOF formula (forall (B_77:(pname->Prop)) (C_30:pname) (A_122:(pname->Prop)), (((member_pname C_30) A_122)->(((member_pname C_30) B_77)->((member_pname C_30) ((semila1673364395name_o A_122) B_77))))) of role axiom named fact_804_IntI
% A new axiom: (forall (B_77:(pname->Prop)) (C_30:pname) (A_122:(pname->Prop)), (((member_pname C_30) A_122)->(((member_pname C_30) B_77)->((member_pname C_30) ((semila1673364395name_o A_122) B_77)))))
% FOF formula (forall (B_77:(hoare_1708887482_state->Prop)) (C_30:hoare_1708887482_state) (A_122:(hoare_1708887482_state->Prop)), (((member451959335_state C_30) A_122)->(((member451959335_state C_30) B_77)->((member451959335_state C_30) ((semila129691299tate_o A_122) B_77))))) of role axiom named fact_805_IntI
% A new axiom: (forall (B_77:(hoare_1708887482_state->Prop)) (C_30:hoare_1708887482_state) (A_122:(hoare_1708887482_state->Prop)), (((member451959335_state C_30) A_122)->(((member451959335_state C_30) B_77)->((member451959335_state C_30) ((semila129691299tate_o A_122) B_77)))))
% FOF formula (forall (C_29:com) (A_121:(com->Prop)) (B_76:(com->Prop)), (((member_com C_29) ((minus_minus_com_o A_121) B_76))->((((member_com C_29) A_121)->((member_com C_29) B_76))->False))) of role axiom named fact_806_DiffE
% A new axiom: (forall (C_29:com) (A_121:(com->Prop)) (B_76:(com->Prop)), (((member_com C_29) ((minus_minus_com_o A_121) B_76))->((((member_com C_29) A_121)->((member_com C_29) B_76))->False)))
% FOF formula (forall (C_29:pname) (A_121:(pname->Prop)) (B_76:(pname->Prop)), (((member_pname C_29) ((minus_minus_pname_o A_121) B_76))->((((member_pname C_29) A_121)->((member_pname C_29) B_76))->False))) of role axiom named fact_807_DiffE
% A new axiom: (forall (C_29:pname) (A_121:(pname->Prop)) (B_76:(pname->Prop)), (((member_pname C_29) ((minus_minus_pname_o A_121) B_76))->((((member_pname C_29) A_121)->((member_pname C_29) B_76))->False)))
% FOF formula (forall (C_29:hoare_1708887482_state) (A_121:(hoare_1708887482_state->Prop)) (B_76:(hoare_1708887482_state->Prop)), (((member451959335_state C_29) ((minus_2056855718tate_o A_121) B_76))->((((member451959335_state C_29) A_121)->((member451959335_state C_29) B_76))->False))) of role axiom named fact_808_DiffE
% A new axiom: (forall (C_29:hoare_1708887482_state) (A_121:(hoare_1708887482_state->Prop)) (B_76:(hoare_1708887482_state->Prop)), (((member451959335_state C_29) ((minus_2056855718tate_o A_121) B_76))->((((member451959335_state C_29) A_121)->((member451959335_state C_29) B_76))->False)))
% FOF formula (forall (B_75:(com->Prop)) (C_28:com) (A_120:(com->Prop)), (((member_com C_28) A_120)->((((member_com C_28) B_75)->False)->((member_com C_28) ((minus_minus_com_o A_120) B_75))))) of role axiom named fact_809_DiffI
% A new axiom: (forall (B_75:(com->Prop)) (C_28:com) (A_120:(com->Prop)), (((member_com C_28) A_120)->((((member_com C_28) B_75)->False)->((member_com C_28) ((minus_minus_com_o A_120) B_75)))))
% FOF formula (forall (B_75:(pname->Prop)) (C_28:pname) (A_120:(pname->Prop)), (((member_pname C_28) A_120)->((((member_pname C_28) B_75)->False)->((member_pname C_28) ((minus_minus_pname_o A_120) B_75))))) of role axiom named fact_810_DiffI
% A new axiom: (forall (B_75:(pname->Prop)) (C_28:pname) (A_120:(pname->Prop)), (((member_pname C_28) A_120)->((((member_pname C_28) B_75)->False)->((member_pname C_28) ((minus_minus_pname_o A_120) B_75)))))
% FOF formula (forall (B_75:(hoare_1708887482_state->Prop)) (C_28:hoare_1708887482_state) (A_120:(hoare_1708887482_state->Prop)), (((member451959335_state C_28) A_120)->((((member451959335_state C_28) B_75)->False)->((member451959335_state C_28) ((minus_2056855718tate_o A_120) B_75))))) of role axiom named fact_811_DiffI
% A new axiom: (forall (B_75:(hoare_1708887482_state->Prop)) (C_28:hoare_1708887482_state) (A_120:(hoare_1708887482_state->Prop)), (((member451959335_state C_28) A_120)->((((member451959335_state C_28) B_75)->False)->((member451959335_state C_28) ((minus_2056855718tate_o A_120) B_75)))))
% FOF formula (forall (G_5:((pname->Prop)->Prop)) (F_28:((pname->Prop)->Prop)), (((or (finite297249702name_o F_28)) (finite297249702name_o G_5))->(finite297249702name_o ((semila2013987940me_o_o F_28) G_5)))) of role axiom named fact_812_finite__Int
% A new axiom: (forall (G_5:((pname->Prop)->Prop)) (F_28:((pname->Prop)->Prop)), (((or (finite297249702name_o F_28)) (finite297249702name_o G_5))->(finite297249702name_o ((semila2013987940me_o_o F_28) G_5))))
% FOF formula (forall (G_5:((hoare_1708887482_state->Prop)->Prop)) (F_28:((hoare_1708887482_state->Prop)->Prop)), (((or (finite1329924456tate_o F_28)) (finite1329924456tate_o G_5))->(finite1329924456tate_o ((semila598060698te_o_o F_28) G_5)))) of role axiom named fact_813_finite__Int
% A new axiom: (forall (G_5:((hoare_1708887482_state->Prop)->Prop)) (F_28:((hoare_1708887482_state->Prop)->Prop)), (((or (finite1329924456tate_o F_28)) (finite1329924456tate_o G_5))->(finite1329924456tate_o ((semila598060698te_o_o F_28) G_5))))
% FOF formula (forall (G_5:(pname->Prop)) (F_28:(pname->Prop)), (((or (finite_finite_pname F_28)) (finite_finite_pname G_5))->(finite_finite_pname ((semila1673364395name_o F_28) G_5)))) of role axiom named fact_814_finite__Int
% A new axiom: (forall (G_5:(pname->Prop)) (F_28:(pname->Prop)), (((or (finite_finite_pname F_28)) (finite_finite_pname G_5))->(finite_finite_pname ((semila1673364395name_o F_28) G_5))))
% FOF formula (forall (G_5:(hoare_1708887482_state->Prop)) (F_28:(hoare_1708887482_state->Prop)), (((or (finite1625599783_state F_28)) (finite1625599783_state G_5))->(finite1625599783_state ((semila129691299tate_o F_28) G_5)))) of role axiom named fact_815_finite__Int
% A new axiom: (forall (G_5:(hoare_1708887482_state->Prop)) (F_28:(hoare_1708887482_state->Prop)), (((or (finite1625599783_state F_28)) (finite1625599783_state G_5))->(finite1625599783_state ((semila129691299tate_o F_28) G_5))))
% FOF formula (forall (B_74:((pname->Prop)->Prop)) (A_119:((pname->Prop)->Prop)), ((finite297249702name_o A_119)->(finite297249702name_o ((minus_1480864103me_o_o A_119) B_74)))) of role axiom named fact_816_finite__Diff
% A new axiom: (forall (B_74:((pname->Prop)->Prop)) (A_119:((pname->Prop)->Prop)), ((finite297249702name_o A_119)->(finite297249702name_o ((minus_1480864103me_o_o A_119) B_74))))
% FOF formula (forall (B_74:((hoare_1708887482_state->Prop)->Prop)) (A_119:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_119)->(finite1329924456tate_o ((minus_548038231te_o_o A_119) B_74)))) of role axiom named fact_817_finite__Diff
% A new axiom: (forall (B_74:((hoare_1708887482_state->Prop)->Prop)) (A_119:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_119)->(finite1329924456tate_o ((minus_548038231te_o_o A_119) B_74))))
% FOF formula (forall (B_74:(pname->Prop)) (A_119:(pname->Prop)), ((finite_finite_pname A_119)->(finite_finite_pname ((minus_minus_pname_o A_119) B_74)))) of role axiom named fact_818_finite__Diff
% A new axiom: (forall (B_74:(pname->Prop)) (A_119:(pname->Prop)), ((finite_finite_pname A_119)->(finite_finite_pname ((minus_minus_pname_o A_119) B_74))))
% FOF formula (forall (B_74:(hoare_1708887482_state->Prop)) (A_119:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_119)->(finite1625599783_state ((minus_2056855718tate_o A_119) B_74)))) of role axiom named fact_819_finite__Diff
% A new axiom: (forall (B_74:(hoare_1708887482_state->Prop)) (A_119:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_119)->(finite1625599783_state ((minus_2056855718tate_o A_119) B_74))))
% FOF formula (forall (R:(com->Prop)) (S_1:(com->Prop)) (X_3:com), ((iff (((semila513601829_com_o (fun (Y_4:com)=> ((member_com Y_4) R))) (fun (Y_4:com)=> ((member_com Y_4) S_1))) X_3)) ((member_com X_3) ((semila513601829_com_o R) S_1)))) of role axiom named fact_820_inf__Int__eq
% A new axiom: (forall (R:(com->Prop)) (S_1:(com->Prop)) (X_3:com), ((iff (((semila513601829_com_o (fun (Y_4:com)=> ((member_com Y_4) R))) (fun (Y_4:com)=> ((member_com Y_4) S_1))) X_3)) ((member_com X_3) ((semila513601829_com_o R) S_1))))
% FOF formula (forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X_3:pname), ((iff (((semila1673364395name_o (fun (Y_4:pname)=> ((member_pname Y_4) R))) (fun (Y_4:pname)=> ((member_pname Y_4) S_1))) X_3)) ((member_pname X_3) ((semila1673364395name_o R) S_1)))) of role axiom named fact_821_inf__Int__eq
% A new axiom: (forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X_3:pname), ((iff (((semila1673364395name_o (fun (Y_4:pname)=> ((member_pname Y_4) R))) (fun (Y_4:pname)=> ((member_pname Y_4) S_1))) X_3)) ((member_pname X_3) ((semila1673364395name_o R) S_1))))
% FOF formula (forall (R:(hoare_1708887482_state->Prop)) (S_1:(hoare_1708887482_state->Prop)) (X_3:hoare_1708887482_state), ((iff (((semila129691299tate_o (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) R))) (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) S_1))) X_3)) ((member451959335_state X_3) ((semila129691299tate_o R) S_1)))) of role axiom named fact_822_inf__Int__eq
% A new axiom: (forall (R:(hoare_1708887482_state->Prop)) (S_1:(hoare_1708887482_state->Prop)) (X_3:hoare_1708887482_state), ((iff (((semila129691299tate_o (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) R))) (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) S_1))) X_3)) ((member451959335_state X_3) ((semila129691299tate_o R) S_1))))
% FOF formula (forall (A_118:(com->Prop)) (B_73:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o A_118) ((minus_minus_com_o B_73) A_118))) bot_bot_com_o)) of role axiom named fact_823_Diff__disjoint
% A new axiom: (forall (A_118:(com->Prop)) (B_73:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o A_118) ((minus_minus_com_o B_73) A_118))) bot_bot_com_o))
% FOF formula (forall (A_118:(pname->Prop)) (B_73:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_118) ((minus_minus_pname_o B_73) A_118))) bot_bot_pname_o)) of role axiom named fact_824_Diff__disjoint
% A new axiom: (forall (A_118:(pname->Prop)) (B_73:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_118) ((minus_minus_pname_o B_73) A_118))) bot_bot_pname_o))
% FOF formula (forall (A_118:(hoare_1708887482_state->Prop)) (B_73:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_118) ((minus_2056855718tate_o B_73) A_118))) bot_bo19817387tate_o)) of role axiom named fact_825_Diff__disjoint
% A new axiom: (forall (A_118:(hoare_1708887482_state->Prop)) (B_73:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_118) ((minus_2056855718tate_o B_73) A_118))) bot_bo19817387tate_o))
% FOF formula (forall (A_117:(com->Prop)) (B_72:(com->Prop)), ((((eq (com->Prop)) ((semila513601829_com_o A_117) B_72)) bot_bot_com_o)->(((eq (com->Prop)) ((minus_minus_com_o A_117) B_72)) A_117))) of role axiom named fact_826_Diff__triv
% A new axiom: (forall (A_117:(com->Prop)) (B_72:(com->Prop)), ((((eq (com->Prop)) ((semila513601829_com_o A_117) B_72)) bot_bot_com_o)->(((eq (com->Prop)) ((minus_minus_com_o A_117) B_72)) A_117)))
% FOF formula (forall (A_117:(pname->Prop)) (B_72:(pname->Prop)), ((((eq (pname->Prop)) ((semila1673364395name_o A_117) B_72)) bot_bot_pname_o)->(((eq (pname->Prop)) ((minus_minus_pname_o A_117) B_72)) A_117))) of role axiom named fact_827_Diff__triv
% A new axiom: (forall (A_117:(pname->Prop)) (B_72:(pname->Prop)), ((((eq (pname->Prop)) ((semila1673364395name_o A_117) B_72)) bot_bot_pname_o)->(((eq (pname->Prop)) ((minus_minus_pname_o A_117) B_72)) A_117)))
% FOF formula (forall (A_117:(hoare_1708887482_state->Prop)) (B_72:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_117) B_72)) bot_bo19817387tate_o)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_117) B_72)) A_117))) of role axiom named fact_828_Diff__triv
% A new axiom: (forall (A_117:(hoare_1708887482_state->Prop)) (B_72:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_117) B_72)) bot_bo19817387tate_o)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_117) B_72)) A_117)))
% FOF formula (forall (C_27:com) (A_116:(com->Prop)) (B_71:(com->Prop)), (((member_com C_27) ((minus_minus_com_o A_116) B_71))->(((member_com C_27) B_71)->False))) of role axiom named fact_829_DiffD2
% A new axiom: (forall (C_27:com) (A_116:(com->Prop)) (B_71:(com->Prop)), (((member_com C_27) ((minus_minus_com_o A_116) B_71))->(((member_com C_27) B_71)->False)))
% FOF formula (forall (C_27:pname) (A_116:(pname->Prop)) (B_71:(pname->Prop)), (((member_pname C_27) ((minus_minus_pname_o A_116) B_71))->(((member_pname C_27) B_71)->False))) of role axiom named fact_830_DiffD2
% A new axiom: (forall (C_27:pname) (A_116:(pname->Prop)) (B_71:(pname->Prop)), (((member_pname C_27) ((minus_minus_pname_o A_116) B_71))->(((member_pname C_27) B_71)->False)))
% FOF formula (forall (C_27:hoare_1708887482_state) (A_116:(hoare_1708887482_state->Prop)) (B_71:(hoare_1708887482_state->Prop)), (((member451959335_state C_27) ((minus_2056855718tate_o A_116) B_71))->(((member451959335_state C_27) B_71)->False))) of role axiom named fact_831_DiffD2
% A new axiom: (forall (C_27:hoare_1708887482_state) (A_116:(hoare_1708887482_state->Prop)) (B_71:(hoare_1708887482_state->Prop)), (((member451959335_state C_27) ((minus_2056855718tate_o A_116) B_71))->(((member451959335_state C_27) B_71)->False)))
% FOF formula (forall (C_26:com) (A_115:(com->Prop)) (B_70:(com->Prop)), (((member_com C_26) ((semila513601829_com_o A_115) B_70))->((member_com C_26) B_70))) of role axiom named fact_832_IntD2
% A new axiom: (forall (C_26:com) (A_115:(com->Prop)) (B_70:(com->Prop)), (((member_com C_26) ((semila513601829_com_o A_115) B_70))->((member_com C_26) B_70)))
% FOF formula (forall (C_26:pname) (A_115:(pname->Prop)) (B_70:(pname->Prop)), (((member_pname C_26) ((semila1673364395name_o A_115) B_70))->((member_pname C_26) B_70))) of role axiom named fact_833_IntD2
% A new axiom: (forall (C_26:pname) (A_115:(pname->Prop)) (B_70:(pname->Prop)), (((member_pname C_26) ((semila1673364395name_o A_115) B_70))->((member_pname C_26) B_70)))
% FOF formula (forall (C_26:hoare_1708887482_state) (A_115:(hoare_1708887482_state->Prop)) (B_70:(hoare_1708887482_state->Prop)), (((member451959335_state C_26) ((semila129691299tate_o A_115) B_70))->((member451959335_state C_26) B_70))) of role axiom named fact_834_IntD2
% A new axiom: (forall (C_26:hoare_1708887482_state) (A_115:(hoare_1708887482_state->Prop)) (B_70:(hoare_1708887482_state->Prop)), (((member451959335_state C_26) ((semila129691299tate_o A_115) B_70))->((member451959335_state C_26) B_70)))
% FOF formula (forall (C_25:com) (A_114:(com->Prop)) (B_69:(com->Prop)), (((member_com C_25) ((semila513601829_com_o A_114) B_69))->((member_com C_25) A_114))) of role axiom named fact_835_IntD1
% A new axiom: (forall (C_25:com) (A_114:(com->Prop)) (B_69:(com->Prop)), (((member_com C_25) ((semila513601829_com_o A_114) B_69))->((member_com C_25) A_114)))
% FOF formula (forall (C_25:pname) (A_114:(pname->Prop)) (B_69:(pname->Prop)), (((member_pname C_25) ((semila1673364395name_o A_114) B_69))->((member_pname C_25) A_114))) of role axiom named fact_836_IntD1
% A new axiom: (forall (C_25:pname) (A_114:(pname->Prop)) (B_69:(pname->Prop)), (((member_pname C_25) ((semila1673364395name_o A_114) B_69))->((member_pname C_25) A_114)))
% FOF formula (forall (C_25:hoare_1708887482_state) (A_114:(hoare_1708887482_state->Prop)) (B_69:(hoare_1708887482_state->Prop)), (((member451959335_state C_25) ((semila129691299tate_o A_114) B_69))->((member451959335_state C_25) A_114))) of role axiom named fact_837_IntD1
% A new axiom: (forall (C_25:hoare_1708887482_state) (A_114:(hoare_1708887482_state->Prop)) (B_69:(hoare_1708887482_state->Prop)), (((member451959335_state C_25) ((semila129691299tate_o A_114) B_69))->((member451959335_state C_25) A_114)))
% FOF formula (forall (C_24:com) (A_113:(com->Prop)) (B_68:(com->Prop)), (((member_com C_24) ((minus_minus_com_o A_113) B_68))->((member_com C_24) A_113))) of role axiom named fact_838_DiffD1
% A new axiom: (forall (C_24:com) (A_113:(com->Prop)) (B_68:(com->Prop)), (((member_com C_24) ((minus_minus_com_o A_113) B_68))->((member_com C_24) A_113)))
% FOF formula (forall (C_24:pname) (A_113:(pname->Prop)) (B_68:(pname->Prop)), (((member_pname C_24) ((minus_minus_pname_o A_113) B_68))->((member_pname C_24) A_113))) of role axiom named fact_839_DiffD1
% A new axiom: (forall (C_24:pname) (A_113:(pname->Prop)) (B_68:(pname->Prop)), (((member_pname C_24) ((minus_minus_pname_o A_113) B_68))->((member_pname C_24) A_113)))
% FOF formula (forall (C_24:hoare_1708887482_state) (A_113:(hoare_1708887482_state->Prop)) (B_68:(hoare_1708887482_state->Prop)), (((member451959335_state C_24) ((minus_2056855718tate_o A_113) B_68))->((member451959335_state C_24) A_113))) of role axiom named fact_840_DiffD1
% A new axiom: (forall (C_24:hoare_1708887482_state) (A_113:(hoare_1708887482_state->Prop)) (B_68:(hoare_1708887482_state->Prop)), (((member451959335_state C_24) ((minus_2056855718tate_o A_113) B_68))->((member451959335_state C_24) A_113)))
% FOF formula (forall (C_23:com) (A_112:(com->Prop)) (B_67:(com->Prop)), ((iff ((member_com C_23) ((semila513601829_com_o A_112) B_67))) ((and ((member_com C_23) A_112)) ((member_com C_23) B_67)))) of role axiom named fact_841_Int__iff
% A new axiom: (forall (C_23:com) (A_112:(com->Prop)) (B_67:(com->Prop)), ((iff ((member_com C_23) ((semila513601829_com_o A_112) B_67))) ((and ((member_com C_23) A_112)) ((member_com C_23) B_67))))
% FOF formula (forall (C_23:pname) (A_112:(pname->Prop)) (B_67:(pname->Prop)), ((iff ((member_pname C_23) ((semila1673364395name_o A_112) B_67))) ((and ((member_pname C_23) A_112)) ((member_pname C_23) B_67)))) of role axiom named fact_842_Int__iff
% A new axiom: (forall (C_23:pname) (A_112:(pname->Prop)) (B_67:(pname->Prop)), ((iff ((member_pname C_23) ((semila1673364395name_o A_112) B_67))) ((and ((member_pname C_23) A_112)) ((member_pname C_23) B_67))))
% FOF formula (forall (C_23:hoare_1708887482_state) (A_112:(hoare_1708887482_state->Prop)) (B_67:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_23) ((semila129691299tate_o A_112) B_67))) ((and ((member451959335_state C_23) A_112)) ((member451959335_state C_23) B_67)))) of role axiom named fact_843_Int__iff
% A new axiom: (forall (C_23:hoare_1708887482_state) (A_112:(hoare_1708887482_state->Prop)) (B_67:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_23) ((semila129691299tate_o A_112) B_67))) ((and ((member451959335_state C_23) A_112)) ((member451959335_state C_23) B_67))))
% FOF formula (forall (C_22:com) (A_111:(com->Prop)) (B_66:(com->Prop)), ((iff ((member_com C_22) ((minus_minus_com_o A_111) B_66))) ((and ((member_com C_22) A_111)) (((member_com C_22) B_66)->False)))) of role axiom named fact_844_Diff__iff
% A new axiom: (forall (C_22:com) (A_111:(com->Prop)) (B_66:(com->Prop)), ((iff ((member_com C_22) ((minus_minus_com_o A_111) B_66))) ((and ((member_com C_22) A_111)) (((member_com C_22) B_66)->False))))
% FOF formula (forall (C_22:pname) (A_111:(pname->Prop)) (B_66:(pname->Prop)), ((iff ((member_pname C_22) ((minus_minus_pname_o A_111) B_66))) ((and ((member_pname C_22) A_111)) (((member_pname C_22) B_66)->False)))) of role axiom named fact_845_Diff__iff
% A new axiom: (forall (C_22:pname) (A_111:(pname->Prop)) (B_66:(pname->Prop)), ((iff ((member_pname C_22) ((minus_minus_pname_o A_111) B_66))) ((and ((member_pname C_22) A_111)) (((member_pname C_22) B_66)->False))))
% FOF formula (forall (C_22:hoare_1708887482_state) (A_111:(hoare_1708887482_state->Prop)) (B_66:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_22) ((minus_2056855718tate_o A_111) B_66))) ((and ((member451959335_state C_22) A_111)) (((member451959335_state C_22) B_66)->False)))) of role axiom named fact_846_Diff__iff
% A new axiom: (forall (C_22:hoare_1708887482_state) (A_111:(hoare_1708887482_state->Prop)) (B_66:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_22) ((minus_2056855718tate_o A_111) B_66))) ((and ((member451959335_state C_22) A_111)) (((member451959335_state C_22) B_66)->False))))
% FOF formula (forall (A_110:(com->Prop)) (B_65:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o A_110) B_65)) (collect_com (fun (X_3:com)=> ((and ((member_com X_3) A_110)) ((member_com X_3) B_65)))))) of role axiom named fact_847_Int__def
% A new axiom: (forall (A_110:(com->Prop)) (B_65:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o A_110) B_65)) (collect_com (fun (X_3:com)=> ((and ((member_com X_3) A_110)) ((member_com X_3) B_65))))))
% FOF formula (forall (A_110:(pname->Prop)) (B_65:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_110) B_65)) (collect_pname (fun (X_3:pname)=> ((and ((member_pname X_3) A_110)) ((member_pname X_3) B_65)))))) of role axiom named fact_848_Int__def
% A new axiom: (forall (A_110:(pname->Prop)) (B_65:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_110) B_65)) (collect_pname (fun (X_3:pname)=> ((and ((member_pname X_3) A_110)) ((member_pname X_3) B_65))))))
% FOF formula (forall (A_110:(hoare_1708887482_state->Prop)) (B_65:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_110) B_65)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_110)) ((member451959335_state X_3) B_65)))))) of role axiom named fact_849_Int__def
% A new axiom: (forall (A_110:(hoare_1708887482_state->Prop)) (B_65:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_110) B_65)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_110)) ((member451959335_state X_3) B_65))))))
% FOF formula (forall (A_110:((pname->Prop)->Prop)) (B_65:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_110) B_65)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_110)) ((member_pname_o X_3) B_65)))))) of role axiom named fact_850_Int__def
% A new axiom: (forall (A_110:((pname->Prop)->Prop)) (B_65:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_110) B_65)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_110)) ((member_pname_o X_3) B_65))))))
% FOF formula (forall (A_110:((hoare_1708887482_state->Prop)->Prop)) (B_65:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_110) B_65)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_110)) ((member814030440tate_o X_3) B_65)))))) of role axiom named fact_851_Int__def
% A new axiom: (forall (A_110:((hoare_1708887482_state->Prop)->Prop)) (B_65:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_110) B_65)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_110)) ((member814030440tate_o X_3) B_65))))))
% FOF formula (forall (A_109:(com->Prop)) (B_64:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_109) B_64)) (collect_com (fun (X_3:com)=> ((and ((member_com X_3) A_109)) (not ((member_com X_3) B_64))))))) of role axiom named fact_852_set__diff__eq
% A new axiom: (forall (A_109:(com->Prop)) (B_64:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_109) B_64)) (collect_com (fun (X_3:com)=> ((and ((member_com X_3) A_109)) (not ((member_com X_3) B_64)))))))
% FOF formula (forall (A_109:(pname->Prop)) (B_64:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_109) B_64)) (collect_pname (fun (X_3:pname)=> ((and ((member_pname X_3) A_109)) (not ((member_pname X_3) B_64))))))) of role axiom named fact_853_set__diff__eq
% A new axiom: (forall (A_109:(pname->Prop)) (B_64:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_109) B_64)) (collect_pname (fun (X_3:pname)=> ((and ((member_pname X_3) A_109)) (not ((member_pname X_3) B_64)))))))
% FOF formula (forall (A_109:(hoare_1708887482_state->Prop)) (B_64:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_109) B_64)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_109)) (not ((member451959335_state X_3) B_64))))))) of role axiom named fact_854_set__diff__eq
% A new axiom: (forall (A_109:(hoare_1708887482_state->Prop)) (B_64:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_109) B_64)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_109)) (not ((member451959335_state X_3) B_64)))))))
% FOF formula (forall (A_109:((pname->Prop)->Prop)) (B_64:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_109) B_64)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_109)) (not ((member_pname_o X_3) B_64))))))) of role axiom named fact_855_set__diff__eq
% A new axiom: (forall (A_109:((pname->Prop)->Prop)) (B_64:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_109) B_64)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_109)) (not ((member_pname_o X_3) B_64)))))))
% FOF formula (forall (A_109:((hoare_1708887482_state->Prop)->Prop)) (B_64:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_109) B_64)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_109)) (not ((member814030440tate_o X_3) B_64))))))) of role axiom named fact_856_set__diff__eq
% A new axiom: (forall (A_109:((hoare_1708887482_state->Prop)->Prop)) (B_64:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_109) B_64)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_109)) (not ((member814030440tate_o X_3) B_64)))))))
% FOF formula (forall (X_44:com) (A_108:(com->Prop)) (P_6:(com->Prop)), ((iff ((member_com X_44) ((semila513601829_com_o A_108) (collect_com P_6)))) ((and ((member_com X_44) A_108)) (P_6 X_44)))) of role axiom named fact_857_Int__Collect
% A new axiom: (forall (X_44:com) (A_108:(com->Prop)) (P_6:(com->Prop)), ((iff ((member_com X_44) ((semila513601829_com_o A_108) (collect_com P_6)))) ((and ((member_com X_44) A_108)) (P_6 X_44))))
% FOF formula (forall (X_44:pname) (A_108:(pname->Prop)) (P_6:(pname->Prop)), ((iff ((member_pname X_44) ((semila1673364395name_o A_108) (collect_pname P_6)))) ((and ((member_pname X_44) A_108)) (P_6 X_44)))) of role axiom named fact_858_Int__Collect
% A new axiom: (forall (X_44:pname) (A_108:(pname->Prop)) (P_6:(pname->Prop)), ((iff ((member_pname X_44) ((semila1673364395name_o A_108) (collect_pname P_6)))) ((and ((member_pname X_44) A_108)) (P_6 X_44))))
% FOF formula (forall (X_44:hoare_1708887482_state) (A_108:(hoare_1708887482_state->Prop)) (P_6:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state X_44) ((semila129691299tate_o A_108) (collec1568722789_state P_6)))) ((and ((member451959335_state X_44) A_108)) (P_6 X_44)))) of role axiom named fact_859_Int__Collect
% A new axiom: (forall (X_44:hoare_1708887482_state) (A_108:(hoare_1708887482_state->Prop)) (P_6:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state X_44) ((semila129691299tate_o A_108) (collec1568722789_state P_6)))) ((and ((member451959335_state X_44) A_108)) (P_6 X_44))))
% FOF formula (forall (X_44:(pname->Prop)) (A_108:((pname->Prop)->Prop)) (P_6:((pname->Prop)->Prop)), ((iff ((member_pname_o X_44) ((semila2013987940me_o_o A_108) (collect_pname_o P_6)))) ((and ((member_pname_o X_44) A_108)) (P_6 X_44)))) of role axiom named fact_860_Int__Collect
% A new axiom: (forall (X_44:(pname->Prop)) (A_108:((pname->Prop)->Prop)) (P_6:((pname->Prop)->Prop)), ((iff ((member_pname_o X_44) ((semila2013987940me_o_o A_108) (collect_pname_o P_6)))) ((and ((member_pname_o X_44) A_108)) (P_6 X_44))))
% FOF formula (forall (X_44:(hoare_1708887482_state->Prop)) (A_108:((hoare_1708887482_state->Prop)->Prop)) (P_6:((hoare_1708887482_state->Prop)->Prop)), ((iff ((member814030440tate_o X_44) ((semila598060698te_o_o A_108) (collec219771562tate_o P_6)))) ((and ((member814030440tate_o X_44) A_108)) (P_6 X_44)))) of role axiom named fact_861_Int__Collect
% A new axiom: (forall (X_44:(hoare_1708887482_state->Prop)) (A_108:((hoare_1708887482_state->Prop)->Prop)) (P_6:((hoare_1708887482_state->Prop)->Prop)), ((iff ((member814030440tate_o X_44) ((semila598060698te_o_o A_108) (collec219771562tate_o P_6)))) ((and ((member814030440tate_o X_44) A_108)) (P_6 X_44))))
% FOF formula (forall (P_5:(hoare_1708887482_state->Prop)) (Q_1:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila129691299tate_o (collec1568722789_state P_5)) (collec1568722789_state Q_1)))) of role axiom named fact_862_Collect__conj__eq
% A new axiom: (forall (P_5:(hoare_1708887482_state->Prop)) (Q_1:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila129691299tate_o (collec1568722789_state P_5)) (collec1568722789_state Q_1))))
% FOF formula (forall (P_5:(pname->Prop)) (Q_1:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila1673364395name_o (collect_pname P_5)) (collect_pname Q_1)))) of role axiom named fact_863_Collect__conj__eq
% A new axiom: (forall (P_5:(pname->Prop)) (Q_1:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila1673364395name_o (collect_pname P_5)) (collect_pname Q_1))))
% FOF formula (forall (P_5:((pname->Prop)->Prop)) (Q_1:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila2013987940me_o_o (collect_pname_o P_5)) (collect_pname_o Q_1)))) of role axiom named fact_864_Collect__conj__eq
% A new axiom: (forall (P_5:((pname->Prop)->Prop)) (Q_1:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila2013987940me_o_o (collect_pname_o P_5)) (collect_pname_o Q_1))))
% FOF formula (forall (P_5:((hoare_1708887482_state->Prop)->Prop)) (Q_1:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila598060698te_o_o (collec219771562tate_o P_5)) (collec219771562tate_o Q_1)))) of role axiom named fact_865_Collect__conj__eq
% A new axiom: (forall (P_5:((hoare_1708887482_state->Prop)->Prop)) (Q_1:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila598060698te_o_o (collec219771562tate_o P_5)) (collec219771562tate_o Q_1))))
% FOF formula (forall (A_107:(pname->Prop)) (B_63:(pname->Prop)) (C_21:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_107) ((semila1673364395name_o B_63) C_21))) ((semila1780557381name_o ((minus_minus_pname_o A_107) B_63)) ((minus_minus_pname_o A_107) C_21)))) of role axiom named fact_866_Diff__Int
% A new axiom: (forall (A_107:(pname->Prop)) (B_63:(pname->Prop)) (C_21:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_107) ((semila1673364395name_o B_63) C_21))) ((semila1780557381name_o ((minus_minus_pname_o A_107) B_63)) ((minus_minus_pname_o A_107) C_21))))
% FOF formula (forall (A_107:(hoare_1708887482_state->Prop)) (B_63:(hoare_1708887482_state->Prop)) (C_21:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_107) ((semila129691299tate_o B_63) C_21))) ((semila1122118281tate_o ((minus_2056855718tate_o A_107) B_63)) ((minus_2056855718tate_o A_107) C_21)))) of role axiom named fact_867_Diff__Int
% A new axiom: (forall (A_107:(hoare_1708887482_state->Prop)) (B_63:(hoare_1708887482_state->Prop)) (C_21:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_107) ((semila129691299tate_o B_63) C_21))) ((semila1122118281tate_o ((minus_2056855718tate_o A_107) B_63)) ((minus_2056855718tate_o A_107) C_21))))
% FOF formula (forall (A_106:(pname->Prop)) (B_62:(pname->Prop)) (C_20:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_106) ((semila1780557381name_o B_62) C_20))) ((semila1673364395name_o ((minus_minus_pname_o A_106) B_62)) ((minus_minus_pname_o A_106) C_20)))) of role axiom named fact_868_Diff__Un
% A new axiom: (forall (A_106:(pname->Prop)) (B_62:(pname->Prop)) (C_20:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_106) ((semila1780557381name_o B_62) C_20))) ((semila1673364395name_o ((minus_minus_pname_o A_106) B_62)) ((minus_minus_pname_o A_106) C_20))))
% FOF formula (forall (A_106:(hoare_1708887482_state->Prop)) (B_62:(hoare_1708887482_state->Prop)) (C_20:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_106) ((semila1122118281tate_o B_62) C_20))) ((semila129691299tate_o ((minus_2056855718tate_o A_106) B_62)) ((minus_2056855718tate_o A_106) C_20)))) of role axiom named fact_869_Diff__Un
% A new axiom: (forall (A_106:(hoare_1708887482_state->Prop)) (B_62:(hoare_1708887482_state->Prop)) (C_20:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_106) ((semila1122118281tate_o B_62) C_20))) ((semila129691299tate_o ((minus_2056855718tate_o A_106) B_62)) ((minus_2056855718tate_o A_106) C_20))))
% FOF formula (forall (A_105:(pname->Prop)) (B_61:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o A_105) B_61)) ((semila1673364395name_o A_105) B_61))) A_105)) of role axiom named fact_870_Un__Diff__Int
% A new axiom: (forall (A_105:(pname->Prop)) (B_61:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o A_105) B_61)) ((semila1673364395name_o A_105) B_61))) A_105))
% FOF formula (forall (A_105:(hoare_1708887482_state->Prop)) (B_61:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((minus_2056855718tate_o A_105) B_61)) ((semila129691299tate_o A_105) B_61))) A_105)) of role axiom named fact_871_Un__Diff__Int
% A new axiom: (forall (A_105:(hoare_1708887482_state->Prop)) (B_61:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((minus_2056855718tate_o A_105) B_61)) ((semila129691299tate_o A_105) B_61))) A_105))
% FOF formula (forall (X_43:Prop) (Y_24:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_43) Y_24)) X_43)) of role axiom named fact_872_inf__sup__ord_I1_J
% A new axiom: (forall (X_43:Prop) (Y_24:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_43) Y_24)) X_43))
% FOF formula (forall (X_43:(pname->Prop)) (Y_24:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_43) Y_24)) X_43)) of role axiom named fact_873_inf__sup__ord_I1_J
% A new axiom: (forall (X_43:(pname->Prop)) (Y_24:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_43) Y_24)) X_43))
% FOF formula (forall (X_43:(hoare_1708887482_state->Prop)) (Y_24:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_43) Y_24)) X_43)) of role axiom named fact_874_inf__sup__ord_I1_J
% A new axiom: (forall (X_43:(hoare_1708887482_state->Prop)) (Y_24:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_43) Y_24)) X_43))
% FOF formula (forall (X_42:Prop) (Y_23:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_42) Y_23)) X_42)) of role axiom named fact_875_inf__le1
% A new axiom: (forall (X_42:Prop) (Y_23:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_42) Y_23)) X_42))
% FOF formula (forall (X_42:(pname->Prop)) (Y_23:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_42) Y_23)) X_42)) of role axiom named fact_876_inf__le1
% A new axiom: (forall (X_42:(pname->Prop)) (Y_23:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_42) Y_23)) X_42))
% FOF formula (forall (X_42:(hoare_1708887482_state->Prop)) (Y_23:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_42) Y_23)) X_42)) of role axiom named fact_877_inf__le1
% A new axiom: (forall (X_42:(hoare_1708887482_state->Prop)) (Y_23:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_42) Y_23)) X_42))
% FOF formula (forall (X_41:Prop) (Y_22:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_41) Y_22)) Y_22)) of role axiom named fact_878_inf__sup__ord_I2_J
% A new axiom: (forall (X_41:Prop) (Y_22:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_41) Y_22)) Y_22))
% FOF formula (forall (X_41:(pname->Prop)) (Y_22:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_41) Y_22)) Y_22)) of role axiom named fact_879_inf__sup__ord_I2_J
% A new axiom: (forall (X_41:(pname->Prop)) (Y_22:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_41) Y_22)) Y_22))
% FOF formula (forall (X_41:(hoare_1708887482_state->Prop)) (Y_22:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_41) Y_22)) Y_22)) of role axiom named fact_880_inf__sup__ord_I2_J
% A new axiom: (forall (X_41:(hoare_1708887482_state->Prop)) (Y_22:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_41) Y_22)) Y_22))
% FOF formula (forall (X_40:Prop) (Y_21:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_40) Y_21)) Y_21)) of role axiom named fact_881_inf__le2
% A new axiom: (forall (X_40:Prop) (Y_21:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_40) Y_21)) Y_21))
% FOF formula (forall (X_40:(pname->Prop)) (Y_21:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_40) Y_21)) Y_21)) of role axiom named fact_882_inf__le2
% A new axiom: (forall (X_40:(pname->Prop)) (Y_21:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_40) Y_21)) Y_21))
% FOF formula (forall (X_40:(hoare_1708887482_state->Prop)) (Y_21:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_40) Y_21)) Y_21)) of role axiom named fact_883_inf__le2
% A new axiom: (forall (X_40:(hoare_1708887482_state->Prop)) (Y_21:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_40) Y_21)) Y_21))
% FOF formula (forall (X_39:Prop) (Y_20:Prop), ((iff ((ord_less_eq_o X_39) Y_20)) ((iff ((semila854092349_inf_o X_39) Y_20)) X_39))) of role axiom named fact_884_le__iff__inf
% A new axiom: (forall (X_39:Prop) (Y_20:Prop), ((iff ((ord_less_eq_o X_39) Y_20)) ((iff ((semila854092349_inf_o X_39) Y_20)) X_39)))
% FOF formula (forall (X_39:(pname->Prop)) (Y_20:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_39) Y_20)) (((eq (pname->Prop)) ((semila1673364395name_o X_39) Y_20)) X_39))) of role axiom named fact_885_le__iff__inf
% A new axiom: (forall (X_39:(pname->Prop)) (Y_20:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_39) Y_20)) (((eq (pname->Prop)) ((semila1673364395name_o X_39) Y_20)) X_39)))
% FOF formula (forall (X_39:(hoare_1708887482_state->Prop)) (Y_20:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o X_39) Y_20)) (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_39) Y_20)) X_39))) of role axiom named fact_886_le__iff__inf
% A new axiom: (forall (X_39:(hoare_1708887482_state->Prop)) (Y_20:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o X_39) Y_20)) (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_39) Y_20)) X_39)))
% FOF formula (forall (X_38:Prop) (Y_19:Prop) (Z_10:Prop), ((iff ((ord_less_eq_o X_38) ((semila854092349_inf_o Y_19) Z_10))) ((and ((ord_less_eq_o X_38) Y_19)) ((ord_less_eq_o X_38) Z_10)))) of role axiom named fact_887_le__inf__iff
% A new axiom: (forall (X_38:Prop) (Y_19:Prop) (Z_10:Prop), ((iff ((ord_less_eq_o X_38) ((semila854092349_inf_o Y_19) Z_10))) ((and ((ord_less_eq_o X_38) Y_19)) ((ord_less_eq_o X_38) Z_10))))
% FOF formula (forall (X_38:(pname->Prop)) (Y_19:(pname->Prop)) (Z_10:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_38) ((semila1673364395name_o Y_19) Z_10))) ((and ((ord_less_eq_pname_o X_38) Y_19)) ((ord_less_eq_pname_o X_38) Z_10)))) of role axiom named fact_888_le__inf__iff
% A new axiom: (forall (X_38:(pname->Prop)) (Y_19:(pname->Prop)) (Z_10:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_38) ((semila1673364395name_o Y_19) Z_10))) ((and ((ord_less_eq_pname_o X_38) Y_19)) ((ord_less_eq_pname_o X_38) Z_10))))
% FOF formula (forall (X_38:(hoare_1708887482_state->Prop)) (Y_19:(hoare_1708887482_state->Prop)) (Z_10:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o X_38) ((semila129691299tate_o Y_19) Z_10))) ((and ((ord_le777019615tate_o X_38) Y_19)) ((ord_le777019615tate_o X_38) Z_10)))) of role axiom named fact_889_le__inf__iff
% A new axiom: (forall (X_38:(hoare_1708887482_state->Prop)) (Y_19:(hoare_1708887482_state->Prop)) (Z_10:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o X_38) ((semila129691299tate_o Y_19) Z_10))) ((and ((ord_le777019615tate_o X_38) Y_19)) ((ord_le777019615tate_o X_38) Z_10))))
% FOF formula (forall (B_60:Prop) (A_104:Prop) (X_37:Prop), (((ord_less_eq_o A_104) X_37)->((ord_less_eq_o ((semila854092349_inf_o A_104) B_60)) X_37))) of role axiom named fact_890_le__infI1
% A new axiom: (forall (B_60:Prop) (A_104:Prop) (X_37:Prop), (((ord_less_eq_o A_104) X_37)->((ord_less_eq_o ((semila854092349_inf_o A_104) B_60)) X_37)))
% FOF formula (forall (B_60:(pname->Prop)) (A_104:(pname->Prop)) (X_37:(pname->Prop)), (((ord_less_eq_pname_o A_104) X_37)->((ord_less_eq_pname_o ((semila1673364395name_o A_104) B_60)) X_37))) of role axiom named fact_891_le__infI1
% A new axiom: (forall (B_60:(pname->Prop)) (A_104:(pname->Prop)) (X_37:(pname->Prop)), (((ord_less_eq_pname_o A_104) X_37)->((ord_less_eq_pname_o ((semila1673364395name_o A_104) B_60)) X_37)))
% FOF formula (forall (B_60:(hoare_1708887482_state->Prop)) (A_104:(hoare_1708887482_state->Prop)) (X_37:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_104) X_37)->((ord_le777019615tate_o ((semila129691299tate_o A_104) B_60)) X_37))) of role axiom named fact_892_le__infI1
% A new axiom: (forall (B_60:(hoare_1708887482_state->Prop)) (A_104:(hoare_1708887482_state->Prop)) (X_37:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_104) X_37)->((ord_le777019615tate_o ((semila129691299tate_o A_104) B_60)) X_37)))
% FOF formula (forall (A_103:Prop) (B_59:Prop) (X_36:Prop), (((ord_less_eq_o B_59) X_36)->((ord_less_eq_o ((semila854092349_inf_o A_103) B_59)) X_36))) of role axiom named fact_893_le__infI2
% A new axiom: (forall (A_103:Prop) (B_59:Prop) (X_36:Prop), (((ord_less_eq_o B_59) X_36)->((ord_less_eq_o ((semila854092349_inf_o A_103) B_59)) X_36)))
% FOF formula (forall (A_103:(pname->Prop)) (B_59:(pname->Prop)) (X_36:(pname->Prop)), (((ord_less_eq_pname_o B_59) X_36)->((ord_less_eq_pname_o ((semila1673364395name_o A_103) B_59)) X_36))) of role axiom named fact_894_le__infI2
% A new axiom: (forall (A_103:(pname->Prop)) (B_59:(pname->Prop)) (X_36:(pname->Prop)), (((ord_less_eq_pname_o B_59) X_36)->((ord_less_eq_pname_o ((semila1673364395name_o A_103) B_59)) X_36)))
% FOF formula (forall (A_103:(hoare_1708887482_state->Prop)) (B_59:(hoare_1708887482_state->Prop)) (X_36:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_59) X_36)->((ord_le777019615tate_o ((semila129691299tate_o A_103) B_59)) X_36))) of role axiom named fact_895_le__infI2
% A new axiom: (forall (A_103:(hoare_1708887482_state->Prop)) (B_59:(hoare_1708887482_state->Prop)) (X_36:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_59) X_36)->((ord_le777019615tate_o ((semila129691299tate_o A_103) B_59)) X_36)))
% FOF formula (forall (X_35:Prop) (Y_18:Prop), (((ord_less_eq_o X_35) Y_18)->((iff ((semila854092349_inf_o X_35) Y_18)) X_35))) of role axiom named fact_896_inf__absorb1
% A new axiom: (forall (X_35:Prop) (Y_18:Prop), (((ord_less_eq_o X_35) Y_18)->((iff ((semila854092349_inf_o X_35) Y_18)) X_35)))
% FOF formula (forall (X_35:(pname->Prop)) (Y_18:(pname->Prop)), (((ord_less_eq_pname_o X_35) Y_18)->(((eq (pname->Prop)) ((semila1673364395name_o X_35) Y_18)) X_35))) of role axiom named fact_897_inf__absorb1
% A new axiom: (forall (X_35:(pname->Prop)) (Y_18:(pname->Prop)), (((ord_less_eq_pname_o X_35) Y_18)->(((eq (pname->Prop)) ((semila1673364395name_o X_35) Y_18)) X_35)))
% FOF formula (forall (X_35:(hoare_1708887482_state->Prop)) (Y_18:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_35) Y_18)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_35) Y_18)) X_35))) of role axiom named fact_898_inf__absorb1
% A new axiom: (forall (X_35:(hoare_1708887482_state->Prop)) (Y_18:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_35) Y_18)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_35) Y_18)) X_35)))
% FOF formula (forall (Y_17:Prop) (X_34:Prop), (((ord_less_eq_o Y_17) X_34)->((iff ((semila854092349_inf_o X_34) Y_17)) Y_17))) of role axiom named fact_899_inf__absorb2
% A new axiom: (forall (Y_17:Prop) (X_34:Prop), (((ord_less_eq_o Y_17) X_34)->((iff ((semila854092349_inf_o X_34) Y_17)) Y_17)))
% FOF formula (forall (Y_17:(pname->Prop)) (X_34:(pname->Prop)), (((ord_less_eq_pname_o Y_17) X_34)->(((eq (pname->Prop)) ((semila1673364395name_o X_34) Y_17)) Y_17))) of role axiom named fact_900_inf__absorb2
% A new axiom: (forall (Y_17:(pname->Prop)) (X_34:(pname->Prop)), (((ord_less_eq_pname_o Y_17) X_34)->(((eq (pname->Prop)) ((semila1673364395name_o X_34) Y_17)) Y_17)))
% FOF formula (forall (Y_17:(hoare_1708887482_state->Prop)) (X_34:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_17) X_34)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_34) Y_17)) Y_17))) of role axiom named fact_901_inf__absorb2
% A new axiom: (forall (Y_17:(hoare_1708887482_state->Prop)) (X_34:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_17) X_34)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_34) Y_17)) Y_17)))
% FOF formula (forall (B_58:Prop) (X_33:Prop) (A_102:Prop), (((ord_less_eq_o X_33) A_102)->(((ord_less_eq_o X_33) B_58)->((ord_less_eq_o X_33) ((semila854092349_inf_o A_102) B_58))))) of role axiom named fact_902_le__infI
% A new axiom: (forall (B_58:Prop) (X_33:Prop) (A_102:Prop), (((ord_less_eq_o X_33) A_102)->(((ord_less_eq_o X_33) B_58)->((ord_less_eq_o X_33) ((semila854092349_inf_o A_102) B_58)))))
% FOF formula (forall (B_58:(pname->Prop)) (X_33:(pname->Prop)) (A_102:(pname->Prop)), (((ord_less_eq_pname_o X_33) A_102)->(((ord_less_eq_pname_o X_33) B_58)->((ord_less_eq_pname_o X_33) ((semila1673364395name_o A_102) B_58))))) of role axiom named fact_903_le__infI
% A new axiom: (forall (B_58:(pname->Prop)) (X_33:(pname->Prop)) (A_102:(pname->Prop)), (((ord_less_eq_pname_o X_33) A_102)->(((ord_less_eq_pname_o X_33) B_58)->((ord_less_eq_pname_o X_33) ((semila1673364395name_o A_102) B_58)))))
% FOF formula (forall (B_58:(hoare_1708887482_state->Prop)) (X_33:(hoare_1708887482_state->Prop)) (A_102:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_33) A_102)->(((ord_le777019615tate_o X_33) B_58)->((ord_le777019615tate_o X_33) ((semila129691299tate_o A_102) B_58))))) of role axiom named fact_904_le__infI
% A new axiom: (forall (B_58:(hoare_1708887482_state->Prop)) (X_33:(hoare_1708887482_state->Prop)) (A_102:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_33) A_102)->(((ord_le777019615tate_o X_33) B_58)->((ord_le777019615tate_o X_33) ((semila129691299tate_o A_102) B_58)))))
% FOF formula (forall (Z_9:Prop) (X_32:Prop) (Y_16:Prop), (((ord_less_eq_o X_32) Y_16)->(((ord_less_eq_o X_32) Z_9)->((ord_less_eq_o X_32) ((semila854092349_inf_o Y_16) Z_9))))) of role axiom named fact_905_inf__greatest
% A new axiom: (forall (Z_9:Prop) (X_32:Prop) (Y_16:Prop), (((ord_less_eq_o X_32) Y_16)->(((ord_less_eq_o X_32) Z_9)->((ord_less_eq_o X_32) ((semila854092349_inf_o Y_16) Z_9)))))
% FOF formula (forall (Z_9:(pname->Prop)) (X_32:(pname->Prop)) (Y_16:(pname->Prop)), (((ord_less_eq_pname_o X_32) Y_16)->(((ord_less_eq_pname_o X_32) Z_9)->((ord_less_eq_pname_o X_32) ((semila1673364395name_o Y_16) Z_9))))) of role axiom named fact_906_inf__greatest
% A new axiom: (forall (Z_9:(pname->Prop)) (X_32:(pname->Prop)) (Y_16:(pname->Prop)), (((ord_less_eq_pname_o X_32) Y_16)->(((ord_less_eq_pname_o X_32) Z_9)->((ord_less_eq_pname_o X_32) ((semila1673364395name_o Y_16) Z_9)))))
% FOF formula (forall (Z_9:(hoare_1708887482_state->Prop)) (X_32:(hoare_1708887482_state->Prop)) (Y_16:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_32) Y_16)->(((ord_le777019615tate_o X_32) Z_9)->((ord_le777019615tate_o X_32) ((semila129691299tate_o Y_16) Z_9))))) of role axiom named fact_907_inf__greatest
% A new axiom: (forall (Z_9:(hoare_1708887482_state->Prop)) (X_32:(hoare_1708887482_state->Prop)) (Y_16:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_32) Y_16)->(((ord_le777019615tate_o X_32) Z_9)->((ord_le777019615tate_o X_32) ((semila129691299tate_o Y_16) Z_9)))))
% FOF formula (forall (B_57:Prop) (D_2:Prop) (A_101:Prop) (C_19:Prop), (((ord_less_eq_o A_101) C_19)->(((ord_less_eq_o B_57) D_2)->((ord_less_eq_o ((semila854092349_inf_o A_101) B_57)) ((semila854092349_inf_o C_19) D_2))))) of role axiom named fact_908_inf__mono
% A new axiom: (forall (B_57:Prop) (D_2:Prop) (A_101:Prop) (C_19:Prop), (((ord_less_eq_o A_101) C_19)->(((ord_less_eq_o B_57) D_2)->((ord_less_eq_o ((semila854092349_inf_o A_101) B_57)) ((semila854092349_inf_o C_19) D_2)))))
% FOF formula (forall (B_57:(pname->Prop)) (D_2:(pname->Prop)) (A_101:(pname->Prop)) (C_19:(pname->Prop)), (((ord_less_eq_pname_o A_101) C_19)->(((ord_less_eq_pname_o B_57) D_2)->((ord_less_eq_pname_o ((semila1673364395name_o A_101) B_57)) ((semila1673364395name_o C_19) D_2))))) of role axiom named fact_909_inf__mono
% A new axiom: (forall (B_57:(pname->Prop)) (D_2:(pname->Prop)) (A_101:(pname->Prop)) (C_19:(pname->Prop)), (((ord_less_eq_pname_o A_101) C_19)->(((ord_less_eq_pname_o B_57) D_2)->((ord_less_eq_pname_o ((semila1673364395name_o A_101) B_57)) ((semila1673364395name_o C_19) D_2)))))
% FOF formula (forall (B_57:(hoare_1708887482_state->Prop)) (D_2:(hoare_1708887482_state->Prop)) (A_101:(hoare_1708887482_state->Prop)) (C_19:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_101) C_19)->(((ord_le777019615tate_o B_57) D_2)->((ord_le777019615tate_o ((semila129691299tate_o A_101) B_57)) ((semila129691299tate_o C_19) D_2))))) of role axiom named fact_910_inf__mono
% A new axiom: (forall (B_57:(hoare_1708887482_state->Prop)) (D_2:(hoare_1708887482_state->Prop)) (A_101:(hoare_1708887482_state->Prop)) (C_19:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_101) C_19)->(((ord_le777019615tate_o B_57) D_2)->((ord_le777019615tate_o ((semila129691299tate_o A_101) B_57)) ((semila129691299tate_o C_19) D_2)))))
% FOF formula (forall (X_31:Prop) (A_100:Prop) (B_56:Prop), (((ord_less_eq_o X_31) ((semila854092349_inf_o A_100) B_56))->((((ord_less_eq_o X_31) A_100)->(((ord_less_eq_o X_31) B_56)->False))->False))) of role axiom named fact_911_le__infE
% A new axiom: (forall (X_31:Prop) (A_100:Prop) (B_56:Prop), (((ord_less_eq_o X_31) ((semila854092349_inf_o A_100) B_56))->((((ord_less_eq_o X_31) A_100)->(((ord_less_eq_o X_31) B_56)->False))->False)))
% FOF formula (forall (X_31:(pname->Prop)) (A_100:(pname->Prop)) (B_56:(pname->Prop)), (((ord_less_eq_pname_o X_31) ((semila1673364395name_o A_100) B_56))->((((ord_less_eq_pname_o X_31) A_100)->(((ord_less_eq_pname_o X_31) B_56)->False))->False))) of role axiom named fact_912_le__infE
% A new axiom: (forall (X_31:(pname->Prop)) (A_100:(pname->Prop)) (B_56:(pname->Prop)), (((ord_less_eq_pname_o X_31) ((semila1673364395name_o A_100) B_56))->((((ord_less_eq_pname_o X_31) A_100)->(((ord_less_eq_pname_o X_31) B_56)->False))->False)))
% FOF formula (forall (X_31:(hoare_1708887482_state->Prop)) (A_100:(hoare_1708887482_state->Prop)) (B_56:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_31) ((semila129691299tate_o A_100) B_56))->((((ord_le777019615tate_o X_31) A_100)->(((ord_le777019615tate_o X_31) B_56)->False))->False))) of role axiom named fact_913_le__infE
% A new axiom: (forall (X_31:(hoare_1708887482_state->Prop)) (A_100:(hoare_1708887482_state->Prop)) (B_56:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_31) ((semila129691299tate_o A_100) B_56))->((((ord_le777019615tate_o X_31) A_100)->(((ord_le777019615tate_o X_31) B_56)->False))->False)))
% FOF formula (forall (X_30:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o X_30) bot_bot_com_o)) bot_bot_com_o)) of role axiom named fact_914_inf__bot__right
% A new axiom: (forall (X_30:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o X_30) bot_bot_com_o)) bot_bot_com_o))
% FOF formula (forall (X_30:Prop), ((iff ((semila854092349_inf_o X_30) bot_bot_o)) bot_bot_o)) of role axiom named fact_915_inf__bot__right
% A new axiom: (forall (X_30:Prop), ((iff ((semila854092349_inf_o X_30) bot_bot_o)) bot_bot_o))
% FOF formula (forall (X_30:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_30) bot_bot_pname_o)) bot_bot_pname_o)) of role axiom named fact_916_inf__bot__right
% A new axiom: (forall (X_30:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_30) bot_bot_pname_o)) bot_bot_pname_o))
% FOF formula (forall (X_30:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_30) bot_bo19817387tate_o)) bot_bo19817387tate_o)) of role axiom named fact_917_inf__bot__right
% A new axiom: (forall (X_30:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_30) bot_bo19817387tate_o)) bot_bo19817387tate_o))
% FOF formula (forall (X_29:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o bot_bot_com_o) X_29)) bot_bot_com_o)) of role axiom named fact_918_inf__bot__left
% A new axiom: (forall (X_29:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o bot_bot_com_o) X_29)) bot_bot_com_o))
% FOF formula (forall (X_29:Prop), ((iff ((semila854092349_inf_o bot_bot_o) X_29)) bot_bot_o)) of role axiom named fact_919_inf__bot__left
% A new axiom: (forall (X_29:Prop), ((iff ((semila854092349_inf_o bot_bot_o) X_29)) bot_bot_o))
% FOF formula (forall (X_29:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) X_29)) bot_bot_pname_o)) of role axiom named fact_920_inf__bot__left
% A new axiom: (forall (X_29:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) X_29)) bot_bot_pname_o))
% FOF formula (forall (X_29:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o bot_bo19817387tate_o) X_29)) bot_bo19817387tate_o)) of role axiom named fact_921_inf__bot__left
% A new axiom: (forall (X_29:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o bot_bo19817387tate_o) X_29)) bot_bo19817387tate_o))
% FOF formula (forall (X_28:Prop) (Y_15:Prop), ((iff ((semila854092349_inf_o X_28) ((semila10642723_sup_o X_28) Y_15))) X_28)) of role axiom named fact_922_inf__sup__absorb
% A new axiom: (forall (X_28:Prop) (Y_15:Prop), ((iff ((semila854092349_inf_o X_28) ((semila10642723_sup_o X_28) Y_15))) X_28))
% FOF formula (forall (X_28:(pname->Prop)) (Y_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_28) ((semila1780557381name_o X_28) Y_15))) X_28)) of role axiom named fact_923_inf__sup__absorb
% A new axiom: (forall (X_28:(pname->Prop)) (Y_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_28) ((semila1780557381name_o X_28) Y_15))) X_28))
% FOF formula (forall (X_28:(hoare_1708887482_state->Prop)) (Y_15:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_28) ((semila1122118281tate_o X_28) Y_15))) X_28)) of role axiom named fact_924_inf__sup__absorb
% A new axiom: (forall (X_28:(hoare_1708887482_state->Prop)) (Y_15:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_28) ((semila1122118281tate_o X_28) Y_15))) X_28))
% FOF formula (forall (X_27:Prop) (Y_14:Prop), ((iff ((semila10642723_sup_o X_27) ((semila854092349_inf_o X_27) Y_14))) X_27)) of role axiom named fact_925_sup__inf__absorb
% A new axiom: (forall (X_27:Prop) (Y_14:Prop), ((iff ((semila10642723_sup_o X_27) ((semila854092349_inf_o X_27) Y_14))) X_27))
% FOF formula (forall (X_27:(pname->Prop)) (Y_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_27) ((semila1673364395name_o X_27) Y_14))) X_27)) of role axiom named fact_926_sup__inf__absorb
% A new axiom: (forall (X_27:(pname->Prop)) (Y_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_27) ((semila1673364395name_o X_27) Y_14))) X_27))
% FOF formula (forall (X_27:(hoare_1708887482_state->Prop)) (Y_14:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_27) ((semila129691299tate_o X_27) Y_14))) X_27)) of role axiom named fact_927_sup__inf__absorb
% A new axiom: (forall (X_27:(hoare_1708887482_state->Prop)) (Y_14:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_27) ((semila129691299tate_o X_27) Y_14))) X_27))
% FOF formula (forall (X_26:Prop) (Y_13:Prop) (Z_8:Prop), ((iff ((semila854092349_inf_o X_26) ((semila10642723_sup_o Y_13) Z_8))) ((semila10642723_sup_o ((semila854092349_inf_o X_26) Y_13)) ((semila854092349_inf_o X_26) Z_8)))) of role axiom named fact_928_inf__sup__distrib1
% A new axiom: (forall (X_26:Prop) (Y_13:Prop) (Z_8:Prop), ((iff ((semila854092349_inf_o X_26) ((semila10642723_sup_o Y_13) Z_8))) ((semila10642723_sup_o ((semila854092349_inf_o X_26) Y_13)) ((semila854092349_inf_o X_26) Z_8))))
% FOF formula (forall (X_26:(pname->Prop)) (Y_13:(pname->Prop)) (Z_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_26) ((semila1780557381name_o Y_13) Z_8))) ((semila1780557381name_o ((semila1673364395name_o X_26) Y_13)) ((semila1673364395name_o X_26) Z_8)))) of role axiom named fact_929_inf__sup__distrib1
% A new axiom: (forall (X_26:(pname->Prop)) (Y_13:(pname->Prop)) (Z_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_26) ((semila1780557381name_o Y_13) Z_8))) ((semila1780557381name_o ((semila1673364395name_o X_26) Y_13)) ((semila1673364395name_o X_26) Z_8))))
% FOF formula (forall (X_26:(hoare_1708887482_state->Prop)) (Y_13:(hoare_1708887482_state->Prop)) (Z_8:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_26) ((semila1122118281tate_o Y_13) Z_8))) ((semila1122118281tate_o ((semila129691299tate_o X_26) Y_13)) ((semila129691299tate_o X_26) Z_8)))) of role axiom named fact_930_inf__sup__distrib1
% A new axiom: (forall (X_26:(hoare_1708887482_state->Prop)) (Y_13:(hoare_1708887482_state->Prop)) (Z_8:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_26) ((semila1122118281tate_o Y_13) Z_8))) ((semila1122118281tate_o ((semila129691299tate_o X_26) Y_13)) ((semila129691299tate_o X_26) Z_8))))
% FOF formula (forall (X_25:Prop) (Y_12:Prop) (Z_7:Prop), ((iff ((semila10642723_sup_o X_25) ((semila854092349_inf_o Y_12) Z_7))) ((semila854092349_inf_o ((semila10642723_sup_o X_25) Y_12)) ((semila10642723_sup_o X_25) Z_7)))) of role axiom named fact_931_sup__inf__distrib1
% A new axiom: (forall (X_25:Prop) (Y_12:Prop) (Z_7:Prop), ((iff ((semila10642723_sup_o X_25) ((semila854092349_inf_o Y_12) Z_7))) ((semila854092349_inf_o ((semila10642723_sup_o X_25) Y_12)) ((semila10642723_sup_o X_25) Z_7))))
% FOF formula (forall (X_25:(pname->Prop)) (Y_12:(pname->Prop)) (Z_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_25) ((semila1673364395name_o Y_12) Z_7))) ((semila1673364395name_o ((semila1780557381name_o X_25) Y_12)) ((semila1780557381name_o X_25) Z_7)))) of role axiom named fact_932_sup__inf__distrib1
% A new axiom: (forall (X_25:(pname->Prop)) (Y_12:(pname->Prop)) (Z_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_25) ((semila1673364395name_o Y_12) Z_7))) ((semila1673364395name_o ((semila1780557381name_o X_25) Y_12)) ((semila1780557381name_o X_25) Z_7))))
% FOF formula (forall (X_25:(hoare_1708887482_state->Prop)) (Y_12:(hoare_1708887482_state->Prop)) (Z_7:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_25) ((semila129691299tate_o Y_12) Z_7))) ((semila129691299tate_o ((semila1122118281tate_o X_25) Y_12)) ((semila1122118281tate_o X_25) Z_7)))) of role axiom named fact_933_sup__inf__distrib1
% A new axiom: (forall (X_25:(hoare_1708887482_state->Prop)) (Y_12:(hoare_1708887482_state->Prop)) (Z_7:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_25) ((semila129691299tate_o Y_12) Z_7))) ((semila129691299tate_o ((semila1122118281tate_o X_25) Y_12)) ((semila1122118281tate_o X_25) Z_7))))
% FOF formula (forall (Y_11:Prop) (Z_6:Prop) (X_24:Prop), ((iff ((semila854092349_inf_o ((semila10642723_sup_o Y_11) Z_6)) X_24)) ((semila10642723_sup_o ((semila854092349_inf_o Y_11) X_24)) ((semila854092349_inf_o Z_6) X_24)))) of role axiom named fact_934_inf__sup__distrib2
% A new axiom: (forall (Y_11:Prop) (Z_6:Prop) (X_24:Prop), ((iff ((semila854092349_inf_o ((semila10642723_sup_o Y_11) Z_6)) X_24)) ((semila10642723_sup_o ((semila854092349_inf_o Y_11) X_24)) ((semila854092349_inf_o Z_6) X_24))))
% FOF formula (forall (Y_11:(pname->Prop)) (Z_6:(pname->Prop)) (X_24:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o Y_11) Z_6)) X_24)) ((semila1780557381name_o ((semila1673364395name_o Y_11) X_24)) ((semila1673364395name_o Z_6) X_24)))) of role axiom named fact_935_inf__sup__distrib2
% A new axiom: (forall (Y_11:(pname->Prop)) (Z_6:(pname->Prop)) (X_24:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o Y_11) Z_6)) X_24)) ((semila1780557381name_o ((semila1673364395name_o Y_11) X_24)) ((semila1673364395name_o Z_6) X_24))))
% FOF formula (forall (Y_11:(hoare_1708887482_state->Prop)) (Z_6:(hoare_1708887482_state->Prop)) (X_24:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((semila1122118281tate_o Y_11) Z_6)) X_24)) ((semila1122118281tate_o ((semila129691299tate_o Y_11) X_24)) ((semila129691299tate_o Z_6) X_24)))) of role axiom named fact_936_inf__sup__distrib2
% A new axiom: (forall (Y_11:(hoare_1708887482_state->Prop)) (Z_6:(hoare_1708887482_state->Prop)) (X_24:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((semila1122118281tate_o Y_11) Z_6)) X_24)) ((semila1122118281tate_o ((semila129691299tate_o Y_11) X_24)) ((semila129691299tate_o Z_6) X_24))))
% FOF formula (forall (Y_10:Prop) (Z_5:Prop) (X_23:Prop), ((iff ((semila10642723_sup_o ((semila854092349_inf_o Y_10) Z_5)) X_23)) ((semila854092349_inf_o ((semila10642723_sup_o Y_10) X_23)) ((semila10642723_sup_o Z_5) X_23)))) of role axiom named fact_937_sup__inf__distrib2
% A new axiom: (forall (Y_10:Prop) (Z_5:Prop) (X_23:Prop), ((iff ((semila10642723_sup_o ((semila854092349_inf_o Y_10) Z_5)) X_23)) ((semila854092349_inf_o ((semila10642723_sup_o Y_10) X_23)) ((semila10642723_sup_o Z_5) X_23))))
% FOF formula (forall (Y_10:(pname->Prop)) (Z_5:(pname->Prop)) (X_23:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o Y_10) Z_5)) X_23)) ((semila1673364395name_o ((semila1780557381name_o Y_10) X_23)) ((semila1780557381name_o Z_5) X_23)))) of role axiom named fact_938_sup__inf__distrib2
% A new axiom: (forall (Y_10:(pname->Prop)) (Z_5:(pname->Prop)) (X_23:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o Y_10) Z_5)) X_23)) ((semila1673364395name_o ((semila1780557381name_o Y_10) X_23)) ((semila1780557381name_o Z_5) X_23))))
% FOF formula (forall (Y_10:(hoare_1708887482_state->Prop)) (Z_5:(hoare_1708887482_state->Prop)) (X_23:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila129691299tate_o Y_10) Z_5)) X_23)) ((semila129691299tate_o ((semila1122118281tate_o Y_10) X_23)) ((semila1122118281tate_o Z_5) X_23)))) of role axiom named fact_939_sup__inf__distrib2
% A new axiom: (forall (Y_10:(hoare_1708887482_state->Prop)) (Z_5:(hoare_1708887482_state->Prop)) (X_23:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila129691299tate_o Y_10) Z_5)) X_23)) ((semila129691299tate_o ((semila1122118281tate_o Y_10) X_23)) ((semila1122118281tate_o Z_5) X_23))))
% FOF formula (forall (A_99:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_99) A_99)) bot_bot_com_o)) of role axiom named fact_940_Diff__cancel
% A new axiom: (forall (A_99:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_99) A_99)) bot_bot_com_o))
% FOF formula (forall (A_99:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_99) A_99)) bot_bot_pname_o)) of role axiom named fact_941_Diff__cancel
% A new axiom: (forall (A_99:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_99) A_99)) bot_bot_pname_o))
% FOF formula (forall (A_99:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_99) A_99)) bot_bo19817387tate_o)) of role axiom named fact_942_Diff__cancel
% A new axiom: (forall (A_99:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_99) A_99)) bot_bo19817387tate_o))
% FOF formula (forall (A_98:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_98) bot_bot_com_o)) A_98)) of role axiom named fact_943_Diff__empty
% A new axiom: (forall (A_98:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_98) bot_bot_com_o)) A_98))
% FOF formula (forall (A_98:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_98) bot_bot_pname_o)) A_98)) of role axiom named fact_944_Diff__empty
% A new axiom: (forall (A_98:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_98) bot_bot_pname_o)) A_98))
% FOF formula (forall (A_98:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_98) bot_bo19817387tate_o)) A_98)) of role axiom named fact_945_Diff__empty
% A new axiom: (forall (A_98:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_98) bot_bo19817387tate_o)) A_98))
% FOF formula (forall (A_97:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o bot_bot_com_o) A_97)) bot_bot_com_o)) of role axiom named fact_946_empty__Diff
% A new axiom: (forall (A_97:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o bot_bot_com_o) A_97)) bot_bot_com_o))
% FOF formula (forall (A_97:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o bot_bot_pname_o) A_97)) bot_bot_pname_o)) of role axiom named fact_947_empty__Diff
% A new axiom: (forall (A_97:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o bot_bot_pname_o) A_97)) bot_bot_pname_o))
% FOF formula (forall (A_97:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o bot_bo19817387tate_o) A_97)) bot_bo19817387tate_o)) of role axiom named fact_948_empty__Diff
% A new axiom: (forall (A_97:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o bot_bo19817387tate_o) A_97)) bot_bo19817387tate_o))
% FOF formula (forall (A_96:((pname->Prop)->Prop)) (B_55:((pname->Prop)->Prop)), ((finite297249702name_o B_55)->((iff (finite297249702name_o ((minus_1480864103me_o_o A_96) B_55))) (finite297249702name_o A_96)))) of role axiom named fact_949_finite__Diff2
% A new axiom: (forall (A_96:((pname->Prop)->Prop)) (B_55:((pname->Prop)->Prop)), ((finite297249702name_o B_55)->((iff (finite297249702name_o ((minus_1480864103me_o_o A_96) B_55))) (finite297249702name_o A_96))))
% FOF formula (forall (A_96:((hoare_1708887482_state->Prop)->Prop)) (B_55:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_55)->((iff (finite1329924456tate_o ((minus_548038231te_o_o A_96) B_55))) (finite1329924456tate_o A_96)))) of role axiom named fact_950_finite__Diff2
% A new axiom: (forall (A_96:((hoare_1708887482_state->Prop)->Prop)) (B_55:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_55)->((iff (finite1329924456tate_o ((minus_548038231te_o_o A_96) B_55))) (finite1329924456tate_o A_96))))
% FOF formula (forall (A_96:(pname->Prop)) (B_55:(pname->Prop)), ((finite_finite_pname B_55)->((iff (finite_finite_pname ((minus_minus_pname_o A_96) B_55))) (finite_finite_pname A_96)))) of role axiom named fact_951_finite__Diff2
% A new axiom: (forall (A_96:(pname->Prop)) (B_55:(pname->Prop)), ((finite_finite_pname B_55)->((iff (finite_finite_pname ((minus_minus_pname_o A_96) B_55))) (finite_finite_pname A_96))))
% FOF formula (forall (A_96:(hoare_1708887482_state->Prop)) (B_55:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_55)->((iff (finite1625599783_state ((minus_2056855718tate_o A_96) B_55))) (finite1625599783_state A_96)))) of role axiom named fact_952_finite__Diff2
% A new axiom: (forall (A_96:(hoare_1708887482_state->Prop)) (B_55:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_55)->((iff (finite1625599783_state ((minus_2056855718tate_o A_96) B_55))) (finite1625599783_state A_96))))
% FOF formula (forall (A_95:(com->Prop)) (X_22:com) (B_54:(com->Prop)), (((member_com X_22) B_54)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_22) A_95)) B_54)) ((minus_minus_com_o A_95) B_54)))) of role axiom named fact_953_insert__Diff1
% A new axiom: (forall (A_95:(com->Prop)) (X_22:com) (B_54:(com->Prop)), (((member_com X_22) B_54)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_22) A_95)) B_54)) ((minus_minus_com_o A_95) B_54))))
% FOF formula (forall (A_95:(pname->Prop)) (X_22:pname) (B_54:(pname->Prop)), (((member_pname X_22) B_54)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_22) A_95)) B_54)) ((minus_minus_pname_o A_95) B_54)))) of role axiom named fact_954_insert__Diff1
% A new axiom: (forall (A_95:(pname->Prop)) (X_22:pname) (B_54:(pname->Prop)), (((member_pname X_22) B_54)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_22) A_95)) B_54)) ((minus_minus_pname_o A_95) B_54))))
% FOF formula (forall (A_95:(hoare_1708887482_state->Prop)) (X_22:hoare_1708887482_state) (B_54:(hoare_1708887482_state->Prop)), (((member451959335_state X_22) B_54)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_22) A_95)) B_54)) ((minus_2056855718tate_o A_95) B_54)))) of role axiom named fact_955_insert__Diff1
% A new axiom: (forall (A_95:(hoare_1708887482_state->Prop)) (X_22:hoare_1708887482_state) (B_54:(hoare_1708887482_state->Prop)), (((member451959335_state X_22) B_54)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_22) A_95)) B_54)) ((minus_2056855718tate_o A_95) B_54))))
% FOF formula (forall (A_94:(com->Prop)) (X_21:com) (B_53:(com->Prop)), ((and (((member_com X_21) B_53)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_21) A_94)) B_53)) ((minus_minus_com_o A_94) B_53)))) ((((member_com X_21) B_53)->False)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_21) A_94)) B_53)) ((insert_com X_21) ((minus_minus_com_o A_94) B_53)))))) of role axiom named fact_956_insert__Diff__if
% A new axiom: (forall (A_94:(com->Prop)) (X_21:com) (B_53:(com->Prop)), ((and (((member_com X_21) B_53)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_21) A_94)) B_53)) ((minus_minus_com_o A_94) B_53)))) ((((member_com X_21) B_53)->False)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_21) A_94)) B_53)) ((insert_com X_21) ((minus_minus_com_o A_94) B_53))))))
% FOF formula (forall (A_94:(pname->Prop)) (X_21:pname) (B_53:(pname->Prop)), ((and (((member_pname X_21) B_53)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_21) A_94)) B_53)) ((minus_minus_pname_o A_94) B_53)))) ((((member_pname X_21) B_53)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_21) A_94)) B_53)) ((insert_pname X_21) ((minus_minus_pname_o A_94) B_53)))))) of role axiom named fact_957_insert__Diff__if
% A new axiom: (forall (A_94:(pname->Prop)) (X_21:pname) (B_53:(pname->Prop)), ((and (((member_pname X_21) B_53)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_21) A_94)) B_53)) ((minus_minus_pname_o A_94) B_53)))) ((((member_pname X_21) B_53)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_21) A_94)) B_53)) ((insert_pname X_21) ((minus_minus_pname_o A_94) B_53))))))
% FOF formula (forall (A_94:(hoare_1708887482_state->Prop)) (X_21:hoare_1708887482_state) (B_53:(hoare_1708887482_state->Prop)), ((and (((member451959335_state X_21) B_53)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_21) A_94)) B_53)) ((minus_2056855718tate_o A_94) B_53)))) ((((member451959335_state X_21) B_53)->False)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_21) A_94)) B_53)) ((insert528405184_state X_21) ((minus_2056855718tate_o A_94) B_53)))))) of role axiom named fact_958_insert__Diff__if
% A new axiom: (forall (A_94:(hoare_1708887482_state->Prop)) (X_21:hoare_1708887482_state) (B_53:(hoare_1708887482_state->Prop)), ((and (((member451959335_state X_21) B_53)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_21) A_94)) B_53)) ((minus_2056855718tate_o A_94) B_53)))) ((((member451959335_state X_21) B_53)->False)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_21) A_94)) B_53)) ((insert528405184_state X_21) ((minus_2056855718tate_o A_94) B_53))))))
% FOF formula (forall (A_93:(com->Prop)) (B_52:(com->Prop)), ((iff (((eq (com->Prop)) ((semila513601829_com_o A_93) B_52)) bot_bot_com_o)) (forall (X_3:com), (((member_com X_3) A_93)->(forall (Xa:com), (((member_com Xa) B_52)->(not (((eq com) X_3) Xa)))))))) of role axiom named fact_959_disjoint__iff__not__equal
% A new axiom: (forall (A_93:(com->Prop)) (B_52:(com->Prop)), ((iff (((eq (com->Prop)) ((semila513601829_com_o A_93) B_52)) bot_bot_com_o)) (forall (X_3:com), (((member_com X_3) A_93)->(forall (Xa:com), (((member_com Xa) B_52)->(not (((eq com) X_3) Xa))))))))
% FOF formula (forall (A_93:(pname->Prop)) (B_52:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1673364395name_o A_93) B_52)) bot_bot_pname_o)) (forall (X_3:pname), (((member_pname X_3) A_93)->(forall (Xa:pname), (((member_pname Xa) B_52)->(not (((eq pname) X_3) Xa)))))))) of role axiom named fact_960_disjoint__iff__not__equal
% A new axiom: (forall (A_93:(pname->Prop)) (B_52:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1673364395name_o A_93) B_52)) bot_bot_pname_o)) (forall (X_3:pname), (((member_pname X_3) A_93)->(forall (Xa:pname), (((member_pname Xa) B_52)->(not (((eq pname) X_3) Xa))))))))
% FOF formula (forall (A_93:(hoare_1708887482_state->Prop)) (B_52:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_93) B_52)) bot_bo19817387tate_o)) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_93)->(forall (Xa:hoare_1708887482_state), (((member451959335_state Xa) B_52)->(not (((eq hoare_1708887482_state) X_3) Xa)))))))) of role axiom named fact_961_disjoint__iff__not__equal
% A new axiom: (forall (A_93:(hoare_1708887482_state->Prop)) (B_52:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_93) B_52)) bot_bo19817387tate_o)) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_93)->(forall (Xa:hoare_1708887482_state), (((member451959335_state Xa) B_52)->(not (((eq hoare_1708887482_state) X_3) Xa))))))))
% FOF formula (forall (A_92:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o A_92) bot_bot_com_o)) bot_bot_com_o)) of role axiom named fact_962_Int__empty__right
% A new axiom: (forall (A_92:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o A_92) bot_bot_com_o)) bot_bot_com_o))
% FOF formula (forall (A_92:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_92) bot_bot_pname_o)) bot_bot_pname_o)) of role axiom named fact_963_Int__empty__right
% A new axiom: (forall (A_92:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_92) bot_bot_pname_o)) bot_bot_pname_o))
% FOF formula (forall (A_92:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_92) bot_bo19817387tate_o)) bot_bo19817387tate_o)) of role axiom named fact_964_Int__empty__right
% A new axiom: (forall (A_92:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_92) bot_bo19817387tate_o)) bot_bo19817387tate_o))
% FOF formula (forall (B_51:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o bot_bot_com_o) B_51)) bot_bot_com_o)) of role axiom named fact_965_Int__empty__left
% A new axiom: (forall (B_51:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o bot_bot_com_o) B_51)) bot_bot_com_o))
% FOF formula (forall (B_51:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) B_51)) bot_bot_pname_o)) of role axiom named fact_966_Int__empty__left
% A new axiom: (forall (B_51:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) B_51)) bot_bot_pname_o))
% FOF formula (forall (B_51:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o bot_bo19817387tate_o) B_51)) bot_bo19817387tate_o)) of role axiom named fact_967_Int__empty__left
% A new axiom: (forall (B_51:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o bot_bo19817387tate_o) B_51)) bot_bo19817387tate_o))
% FOF formula (forall (C_18:(pname->Prop)) (A_91:(pname->Prop)) (B_50:(pname->Prop)), (((ord_less_eq_pname_o A_91) B_50)->(((ord_less_eq_pname_o B_50) C_18)->(((eq (pname->Prop)) ((minus_minus_pname_o B_50) ((minus_minus_pname_o C_18) A_91))) A_91)))) of role axiom named fact_968_double__diff
% A new axiom: (forall (C_18:(pname->Prop)) (A_91:(pname->Prop)) (B_50:(pname->Prop)), (((ord_less_eq_pname_o A_91) B_50)->(((ord_less_eq_pname_o B_50) C_18)->(((eq (pname->Prop)) ((minus_minus_pname_o B_50) ((minus_minus_pname_o C_18) A_91))) A_91))))
% FOF formula (forall (C_18:(hoare_1708887482_state->Prop)) (A_91:(hoare_1708887482_state->Prop)) (B_50:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_91) B_50)->(((ord_le777019615tate_o B_50) C_18)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o B_50) ((minus_2056855718tate_o C_18) A_91))) A_91)))) of role axiom named fact_969_double__diff
% A new axiom: (forall (C_18:(hoare_1708887482_state->Prop)) (A_91:(hoare_1708887482_state->Prop)) (B_50:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_91) B_50)->(((ord_le777019615tate_o B_50) C_18)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o B_50) ((minus_2056855718tate_o C_18) A_91))) A_91))))
% FOF formula (forall (D_1:(pname->Prop)) (B_49:(pname->Prop)) (A_90:(pname->Prop)) (C_17:(pname->Prop)), (((ord_less_eq_pname_o A_90) C_17)->(((ord_less_eq_pname_o D_1) B_49)->((ord_less_eq_pname_o ((minus_minus_pname_o A_90) B_49)) ((minus_minus_pname_o C_17) D_1))))) of role axiom named fact_970_Diff__mono
% A new axiom: (forall (D_1:(pname->Prop)) (B_49:(pname->Prop)) (A_90:(pname->Prop)) (C_17:(pname->Prop)), (((ord_less_eq_pname_o A_90) C_17)->(((ord_less_eq_pname_o D_1) B_49)->((ord_less_eq_pname_o ((minus_minus_pname_o A_90) B_49)) ((minus_minus_pname_o C_17) D_1)))))
% FOF formula (forall (D_1:(hoare_1708887482_state->Prop)) (B_49:(hoare_1708887482_state->Prop)) (A_90:(hoare_1708887482_state->Prop)) (C_17:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_90) C_17)->(((ord_le777019615tate_o D_1) B_49)->((ord_le777019615tate_o ((minus_2056855718tate_o A_90) B_49)) ((minus_2056855718tate_o C_17) D_1))))) of role axiom named fact_971_Diff__mono
% A new axiom: (forall (D_1:(hoare_1708887482_state->Prop)) (B_49:(hoare_1708887482_state->Prop)) (A_90:(hoare_1708887482_state->Prop)) (C_17:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_90) C_17)->(((ord_le777019615tate_o D_1) B_49)->((ord_le777019615tate_o ((minus_2056855718tate_o A_90) B_49)) ((minus_2056855718tate_o C_17) D_1)))))
% FOF formula (forall (A_89:(pname->Prop)) (B_48:(pname->Prop)), ((ord_less_eq_pname_o ((minus_minus_pname_o A_89) B_48)) A_89)) of role axiom named fact_972_Diff__subset
% A new axiom: (forall (A_89:(pname->Prop)) (B_48:(pname->Prop)), ((ord_less_eq_pname_o ((minus_minus_pname_o A_89) B_48)) A_89))
% FOF formula (forall (A_89:(hoare_1708887482_state->Prop)) (B_48:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((minus_2056855718tate_o A_89) B_48)) A_89)) of role axiom named fact_973_Diff__subset
% A new axiom: (forall (A_89:(hoare_1708887482_state->Prop)) (B_48:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((minus_2056855718tate_o A_89) B_48)) A_89))
% FOF formula (forall (A_88:(pname->Prop)) (B_47:(pname->Prop)) (C_16:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o ((semila1780557381name_o A_88) B_47)) C_16)) ((semila1780557381name_o ((minus_minus_pname_o A_88) C_16)) ((minus_minus_pname_o B_47) C_16)))) of role axiom named fact_974_Un__Diff
% A new axiom: (forall (A_88:(pname->Prop)) (B_47:(pname->Prop)) (C_16:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o ((semila1780557381name_o A_88) B_47)) C_16)) ((semila1780557381name_o ((minus_minus_pname_o A_88) C_16)) ((minus_minus_pname_o B_47) C_16))))
% FOF formula (forall (A_88:(hoare_1708887482_state->Prop)) (B_47:(hoare_1708887482_state->Prop)) (C_16:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((semila1122118281tate_o A_88) B_47)) C_16)) ((semila1122118281tate_o ((minus_2056855718tate_o A_88) C_16)) ((minus_2056855718tate_o B_47) C_16)))) of role axiom named fact_975_Un__Diff
% A new axiom: (forall (A_88:(hoare_1708887482_state->Prop)) (B_47:(hoare_1708887482_state->Prop)) (C_16:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((semila1122118281tate_o A_88) B_47)) C_16)) ((semila1122118281tate_o ((minus_2056855718tate_o A_88) C_16)) ((minus_2056855718tate_o B_47) C_16))))
% FOF formula (forall (B_46:(pname->Prop)) (A_87:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o B_46) A_87)) A_87)) ((semila1780557381name_o B_46) A_87))) of role axiom named fact_976_Un__Diff__cancel2
% A new axiom: (forall (B_46:(pname->Prop)) (A_87:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o B_46) A_87)) A_87)) ((semila1780557381name_o B_46) A_87)))
% FOF formula (forall (B_46:(hoare_1708887482_state->Prop)) (A_87:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((minus_2056855718tate_o B_46) A_87)) A_87)) ((semila1122118281tate_o B_46) A_87))) of role axiom named fact_977_Un__Diff__cancel2
% A new axiom: (forall (B_46:(hoare_1708887482_state->Prop)) (A_87:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((minus_2056855718tate_o B_46) A_87)) A_87)) ((semila1122118281tate_o B_46) A_87)))
% FOF formula (forall (A_86:(pname->Prop)) (B_45:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_86) ((minus_minus_pname_o B_45) A_86))) ((semila1780557381name_o A_86) B_45))) of role axiom named fact_978_Un__Diff__cancel
% A new axiom: (forall (A_86:(pname->Prop)) (B_45:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_86) ((minus_minus_pname_o B_45) A_86))) ((semila1780557381name_o A_86) B_45)))
% FOF formula (forall (A_86:(hoare_1708887482_state->Prop)) (B_45:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_86) ((minus_2056855718tate_o B_45) A_86))) ((semila1122118281tate_o A_86) B_45))) of role axiom named fact_979_Un__Diff__cancel
% A new axiom: (forall (A_86:(hoare_1708887482_state->Prop)) (B_45:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_86) ((minus_2056855718tate_o B_45) A_86))) ((semila1122118281tate_o A_86) B_45)))
% FOF formula (forall (B_44:(com->Prop)) (A_85:com) (C_15:(com->Prop)), (((member_com A_85) C_15)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_85) B_44)) C_15)) ((insert_com A_85) ((semila513601829_com_o B_44) C_15))))) of role axiom named fact_980_Int__insert__left__if1
% A new axiom: (forall (B_44:(com->Prop)) (A_85:com) (C_15:(com->Prop)), (((member_com A_85) C_15)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_85) B_44)) C_15)) ((insert_com A_85) ((semila513601829_com_o B_44) C_15)))))
% FOF formula (forall (B_44:(pname->Prop)) (A_85:pname) (C_15:(pname->Prop)), (((member_pname A_85) C_15)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_85) B_44)) C_15)) ((insert_pname A_85) ((semila1673364395name_o B_44) C_15))))) of role axiom named fact_981_Int__insert__left__if1
% A new axiom: (forall (B_44:(pname->Prop)) (A_85:pname) (C_15:(pname->Prop)), (((member_pname A_85) C_15)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_85) B_44)) C_15)) ((insert_pname A_85) ((semila1673364395name_o B_44) C_15)))))
% FOF formula (forall (B_44:(hoare_1708887482_state->Prop)) (A_85:hoare_1708887482_state) (C_15:(hoare_1708887482_state->Prop)), (((member451959335_state A_85) C_15)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_85) B_44)) C_15)) ((insert528405184_state A_85) ((semila129691299tate_o B_44) C_15))))) of role axiom named fact_982_Int__insert__left__if1
% A new axiom: (forall (B_44:(hoare_1708887482_state->Prop)) (A_85:hoare_1708887482_state) (C_15:(hoare_1708887482_state->Prop)), (((member451959335_state A_85) C_15)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_85) B_44)) C_15)) ((insert528405184_state A_85) ((semila129691299tate_o B_44) C_15)))))
% FOF formula (forall (B_43:(com->Prop)) (A_84:com) (A_83:(com->Prop)), (((member_com A_84) A_83)->(((eq (com->Prop)) ((semila513601829_com_o A_83) ((insert_com A_84) B_43))) ((insert_com A_84) ((semila513601829_com_o A_83) B_43))))) of role axiom named fact_983_Int__insert__right__if1
% A new axiom: (forall (B_43:(com->Prop)) (A_84:com) (A_83:(com->Prop)), (((member_com A_84) A_83)->(((eq (com->Prop)) ((semila513601829_com_o A_83) ((insert_com A_84) B_43))) ((insert_com A_84) ((semila513601829_com_o A_83) B_43)))))
% FOF formula (forall (B_43:(pname->Prop)) (A_84:pname) (A_83:(pname->Prop)), (((member_pname A_84) A_83)->(((eq (pname->Prop)) ((semila1673364395name_o A_83) ((insert_pname A_84) B_43))) ((insert_pname A_84) ((semila1673364395name_o A_83) B_43))))) of role axiom named fact_984_Int__insert__right__if1
% A new axiom: (forall (B_43:(pname->Prop)) (A_84:pname) (A_83:(pname->Prop)), (((member_pname A_84) A_83)->(((eq (pname->Prop)) ((semila1673364395name_o A_83) ((insert_pname A_84) B_43))) ((insert_pname A_84) ((semila1673364395name_o A_83) B_43)))))
% FOF formula (forall (B_43:(hoare_1708887482_state->Prop)) (A_84:hoare_1708887482_state) (A_83:(hoare_1708887482_state->Prop)), (((member451959335_state A_84) A_83)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_83) ((insert528405184_state A_84) B_43))) ((insert528405184_state A_84) ((semila129691299tate_o A_83) B_43))))) of role axiom named fact_985_Int__insert__right__if1
% A new axiom: (forall (B_43:(hoare_1708887482_state->Prop)) (A_84:hoare_1708887482_state) (A_83:(hoare_1708887482_state->Prop)), (((member451959335_state A_84) A_83)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_83) ((insert528405184_state A_84) B_43))) ((insert528405184_state A_84) ((semila129691299tate_o A_83) B_43)))))
% FOF formula (forall (B_42:(com->Prop)) (A_82:com) (C_14:(com->Prop)), ((((member_com A_82) C_14)->False)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_82) B_42)) C_14)) ((semila513601829_com_o B_42) C_14)))) of role axiom named fact_986_Int__insert__left__if0
% A new axiom: (forall (B_42:(com->Prop)) (A_82:com) (C_14:(com->Prop)), ((((member_com A_82) C_14)->False)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_82) B_42)) C_14)) ((semila513601829_com_o B_42) C_14))))
% FOF formula (forall (B_42:(pname->Prop)) (A_82:pname) (C_14:(pname->Prop)), ((((member_pname A_82) C_14)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_82) B_42)) C_14)) ((semila1673364395name_o B_42) C_14)))) of role axiom named fact_987_Int__insert__left__if0
% A new axiom: (forall (B_42:(pname->Prop)) (A_82:pname) (C_14:(pname->Prop)), ((((member_pname A_82) C_14)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_82) B_42)) C_14)) ((semila1673364395name_o B_42) C_14))))
% FOF formula (forall (B_42:(hoare_1708887482_state->Prop)) (A_82:hoare_1708887482_state) (C_14:(hoare_1708887482_state->Prop)), ((((member451959335_state A_82) C_14)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_82) B_42)) C_14)) ((semila129691299tate_o B_42) C_14)))) of role axiom named fact_988_Int__insert__left__if0
% A new axiom: (forall (B_42:(hoare_1708887482_state->Prop)) (A_82:hoare_1708887482_state) (C_14:(hoare_1708887482_state->Prop)), ((((member451959335_state A_82) C_14)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_82) B_42)) C_14)) ((semila129691299tate_o B_42) C_14))))
% FOF formula (forall (B_41:(com->Prop)) (A_81:com) (A_80:(com->Prop)), ((((member_com A_81) A_80)->False)->(((eq (com->Prop)) ((semila513601829_com_o A_80) ((insert_com A_81) B_41))) ((semila513601829_com_o A_80) B_41)))) of role axiom named fact_989_Int__insert__right__if0
% A new axiom: (forall (B_41:(com->Prop)) (A_81:com) (A_80:(com->Prop)), ((((member_com A_81) A_80)->False)->(((eq (com->Prop)) ((semila513601829_com_o A_80) ((insert_com A_81) B_41))) ((semila513601829_com_o A_80) B_41))))
% FOF formula (forall (B_41:(pname->Prop)) (A_81:pname) (A_80:(pname->Prop)), ((((member_pname A_81) A_80)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_80) ((insert_pname A_81) B_41))) ((semila1673364395name_o A_80) B_41)))) of role axiom named fact_990_Int__insert__right__if0
% A new axiom: (forall (B_41:(pname->Prop)) (A_81:pname) (A_80:(pname->Prop)), ((((member_pname A_81) A_80)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_80) ((insert_pname A_81) B_41))) ((semila1673364395name_o A_80) B_41))))
% FOF formula (forall (B_41:(hoare_1708887482_state->Prop)) (A_81:hoare_1708887482_state) (A_80:(hoare_1708887482_state->Prop)), ((((member451959335_state A_81) A_80)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_80) ((insert528405184_state A_81) B_41))) ((semila129691299tate_o A_80) B_41)))) of role axiom named fact_991_Int__insert__right__if0
% A new axiom: (forall (B_41:(hoare_1708887482_state->Prop)) (A_81:hoare_1708887482_state) (A_80:(hoare_1708887482_state->Prop)), ((((member451959335_state A_81) A_80)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_80) ((insert528405184_state A_81) B_41))) ((semila129691299tate_o A_80) B_41))))
% FOF formula (forall (A_79:com) (A_78:(com->Prop)) (B_40:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_79) A_78)) ((insert_com A_79) B_40))) ((insert_com A_79) ((semila513601829_com_o A_78) B_40)))) of role axiom named fact_992_insert__inter__insert
% A new axiom: (forall (A_79:com) (A_78:(com->Prop)) (B_40:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_79) A_78)) ((insert_com A_79) B_40))) ((insert_com A_79) ((semila513601829_com_o A_78) B_40))))
% FOF formula (forall (A_79:pname) (A_78:(pname->Prop)) (B_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_79) A_78)) ((insert_pname A_79) B_40))) ((insert_pname A_79) ((semila1673364395name_o A_78) B_40)))) of role axiom named fact_993_insert__inter__insert
% A new axiom: (forall (A_79:pname) (A_78:(pname->Prop)) (B_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_79) A_78)) ((insert_pname A_79) B_40))) ((insert_pname A_79) ((semila1673364395name_o A_78) B_40))))
% FOF formula (forall (A_79:hoare_1708887482_state) (A_78:(hoare_1708887482_state->Prop)) (B_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_79) A_78)) ((insert528405184_state A_79) B_40))) ((insert528405184_state A_79) ((semila129691299tate_o A_78) B_40)))) of role axiom named fact_994_insert__inter__insert
% A new axiom: (forall (A_79:hoare_1708887482_state) (A_78:(hoare_1708887482_state->Prop)) (B_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_79) A_78)) ((insert528405184_state A_79) B_40))) ((insert528405184_state A_79) ((semila129691299tate_o A_78) B_40))))
% FOF formula (forall (B_39:(com->Prop)) (A_77:com) (C_13:(com->Prop)), ((and (((member_com A_77) C_13)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_77) B_39)) C_13)) ((insert_com A_77) ((semila513601829_com_o B_39) C_13))))) ((((member_com A_77) C_13)->False)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_77) B_39)) C_13)) ((semila513601829_com_o B_39) C_13))))) of role axiom named fact_995_Int__insert__left
% A new axiom: (forall (B_39:(com->Prop)) (A_77:com) (C_13:(com->Prop)), ((and (((member_com A_77) C_13)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_77) B_39)) C_13)) ((insert_com A_77) ((semila513601829_com_o B_39) C_13))))) ((((member_com A_77) C_13)->False)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_77) B_39)) C_13)) ((semila513601829_com_o B_39) C_13)))))
% FOF formula (forall (B_39:(pname->Prop)) (A_77:pname) (C_13:(pname->Prop)), ((and (((member_pname A_77) C_13)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_77) B_39)) C_13)) ((insert_pname A_77) ((semila1673364395name_o B_39) C_13))))) ((((member_pname A_77) C_13)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_77) B_39)) C_13)) ((semila1673364395name_o B_39) C_13))))) of role axiom named fact_996_Int__insert__left
% A new axiom: (forall (B_39:(pname->Prop)) (A_77:pname) (C_13:(pname->Prop)), ((and (((member_pname A_77) C_13)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_77) B_39)) C_13)) ((insert_pname A_77) ((semila1673364395name_o B_39) C_13))))) ((((member_pname A_77) C_13)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_77) B_39)) C_13)) ((semila1673364395name_o B_39) C_13)))))
% FOF formula (forall (B_39:(hoare_1708887482_state->Prop)) (A_77:hoare_1708887482_state) (C_13:(hoare_1708887482_state->Prop)), ((and (((member451959335_state A_77) C_13)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_77) B_39)) C_13)) ((insert528405184_state A_77) ((semila129691299tate_o B_39) C_13))))) ((((member451959335_state A_77) C_13)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_77) B_39)) C_13)) ((semila129691299tate_o B_39) C_13))))) of role axiom named fact_997_Int__insert__left
% A new axiom: (forall (B_39:(hoare_1708887482_state->Prop)) (A_77:hoare_1708887482_state) (C_13:(hoare_1708887482_state->Prop)), ((and (((member451959335_state A_77) C_13)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_77) B_39)) C_13)) ((insert528405184_state A_77) ((semila129691299tate_o B_39) C_13))))) ((((member451959335_state A_77) C_13)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_77) B_39)) C_13)) ((semila129691299tate_o B_39) C_13)))))
% FOF formula (forall (B_38:(com->Prop)) (A_76:com) (A_75:(com->Prop)), ((and (((member_com A_76) A_75)->(((eq (com->Prop)) ((semila513601829_com_o A_75) ((insert_com A_76) B_38))) ((insert_com A_76) ((semila513601829_com_o A_75) B_38))))) ((((member_com A_76) A_75)->False)->(((eq (com->Prop)) ((semila513601829_com_o A_75) ((insert_com A_76) B_38))) ((semila513601829_com_o A_75) B_38))))) of role axiom named fact_998_Int__insert__right
% A new axiom: (forall (B_38:(com->Prop)) (A_76:com) (A_75:(com->Prop)), ((and (((member_com A_76) A_75)->(((eq (com->Prop)) ((semila513601829_com_o A_75) ((insert_com A_76) B_38))) ((insert_com A_76) ((semila513601829_com_o A_75) B_38))))) ((((member_com A_76) A_75)->False)->(((eq (com->Prop)) ((semila513601829_com_o A_75) ((insert_com A_76) B_38))) ((semila513601829_com_o A_75) B_38)))))
% FOF formula (forall (B_38:(pname->Prop)) (A_76:pname) (A_75:(pname->Prop)), ((and (((member_pname A_76) A_75)->(((eq (pname->Prop)) ((semila1673364395name_o A_75) ((insert_pname A_76) B_38))) ((insert_pname A_76) ((semila1673364395name_o A_75) B_38))))) ((((member_pname A_76) A_75)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_75) ((insert_pname A_76) B_38))) ((semila1673364395name_o A_75) B_38))))) of role axiom named fact_999_Int__insert__right
% A new axiom: (forall (B_38:(pname->Prop)) (A_76:pname) (A_75:(pname->Prop)), ((and (((member_pname A_76) A_75)->(((eq (pname->Prop)) ((semila1673364395name_o A_75) ((insert_pname A_76) B_38))) ((insert_pname A_76) ((semila1673364395name_o A_75) B_38))))) ((((member_pname A_76) A_75)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_75) ((insert_pname A_76) B_38))) ((semila1673364395name_o A_75) B_38)))))
% FOF formula (forall (B_38:(hoare_1708887482_state->Prop)) (A_76:hoare_1708887482_state) (A_75:(hoare_1708887482_state->Prop)), ((and (((member451959335_state A_76) A_75)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_75) ((insert528405184_state A_76) B_38))) ((insert528405184_state A_76) ((semila129691299tate_o A_75) B_38))))) ((((member451959335_state A_76) A_75)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_75) ((insert528405184_state A_76) B_38))) ((semila129691299tate_o A_75) B_38))))) of role axiom named fact_1000_Int__insert__right
% A new axiom: (forall (B_38:(hoare_1708887482_state->Prop)) (A_76:hoare_1708887482_state) (A_75:(hoare_1708887482_state->Prop)), ((and (((member451959335_state A_76) A_75)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_75) ((insert528405184_state A_76) B_38))) ((insert528405184_state A_76) ((semila129691299tate_o A_75) B_38))))) ((((member451959335_state A_76) A_75)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_75) ((insert528405184_state A_76) B_38))) ((semila129691299tate_o A_75) B_38)))))
% FOF formula (forall (B_37:(pname->Prop)) (D:(pname->Prop)) (A_74:(pname->Prop)) (C_12:(pname->Prop)), (((ord_less_eq_pname_o A_74) C_12)->(((ord_less_eq_pname_o B_37) D)->((ord_less_eq_pname_o ((semila1673364395name_o A_74) B_37)) ((semila1673364395name_o C_12) D))))) of role axiom named fact_1001_Int__mono
% A new axiom: (forall (B_37:(pname->Prop)) (D:(pname->Prop)) (A_74:(pname->Prop)) (C_12:(pname->Prop)), (((ord_less_eq_pname_o A_74) C_12)->(((ord_less_eq_pname_o B_37) D)->((ord_less_eq_pname_o ((semila1673364395name_o A_74) B_37)) ((semila1673364395name_o C_12) D)))))
% FOF formula (forall (B_37:(hoare_1708887482_state->Prop)) (D:(hoare_1708887482_state->Prop)) (A_74:(hoare_1708887482_state->Prop)) (C_12:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_74) C_12)->(((ord_le777019615tate_o B_37) D)->((ord_le777019615tate_o ((semila129691299tate_o A_74) B_37)) ((semila129691299tate_o C_12) D))))) of role axiom named fact_1002_Int__mono
% A new axiom: (forall (B_37:(hoare_1708887482_state->Prop)) (D:(hoare_1708887482_state->Prop)) (A_74:(hoare_1708887482_state->Prop)) (C_12:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_74) C_12)->(((ord_le777019615tate_o B_37) D)->((ord_le777019615tate_o ((semila129691299tate_o A_74) B_37)) ((semila129691299tate_o C_12) D)))))
% FOF formula (forall (B_36:(pname->Prop)) (C_11:(pname->Prop)) (A_73:(pname->Prop)), (((ord_less_eq_pname_o C_11) A_73)->(((ord_less_eq_pname_o C_11) B_36)->((ord_less_eq_pname_o C_11) ((semila1673364395name_o A_73) B_36))))) of role axiom named fact_1003_Int__greatest
% A new axiom: (forall (B_36:(pname->Prop)) (C_11:(pname->Prop)) (A_73:(pname->Prop)), (((ord_less_eq_pname_o C_11) A_73)->(((ord_less_eq_pname_o C_11) B_36)->((ord_less_eq_pname_o C_11) ((semila1673364395name_o A_73) B_36)))))
% FOF formula (forall (B_36:(hoare_1708887482_state->Prop)) (C_11:(hoare_1708887482_state->Prop)) (A_73:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o C_11) A_73)->(((ord_le777019615tate_o C_11) B_36)->((ord_le777019615tate_o C_11) ((semila129691299tate_o A_73) B_36))))) of role axiom named fact_1004_Int__greatest
% A new axiom: (forall (B_36:(hoare_1708887482_state->Prop)) (C_11:(hoare_1708887482_state->Prop)) (A_73:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o C_11) A_73)->(((ord_le777019615tate_o C_11) B_36)->((ord_le777019615tate_o C_11) ((semila129691299tate_o A_73) B_36)))))
% FOF formula (forall (B_35:(pname->Prop)) (A_72:(pname->Prop)), (((ord_less_eq_pname_o B_35) A_72)->(((eq (pname->Prop)) ((semila1673364395name_o A_72) B_35)) B_35))) of role axiom named fact_1005_Int__absorb1
% A new axiom: (forall (B_35:(pname->Prop)) (A_72:(pname->Prop)), (((ord_less_eq_pname_o B_35) A_72)->(((eq (pname->Prop)) ((semila1673364395name_o A_72) B_35)) B_35)))
% FOF formula (forall (B_35:(hoare_1708887482_state->Prop)) (A_72:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_35) A_72)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_72) B_35)) B_35))) of role axiom named fact_1006_Int__absorb1
% A new axiom: (forall (B_35:(hoare_1708887482_state->Prop)) (A_72:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_35) A_72)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_72) B_35)) B_35)))
% FOF formula (forall (A_71:(pname->Prop)) (B_34:(pname->Prop)), (((ord_less_eq_pname_o A_71) B_34)->(((eq (pname->Prop)) ((semila1673364395name_o A_71) B_34)) A_71))) of role axiom named fact_1007_Int__absorb2
% A new axiom: (forall (A_71:(pname->Prop)) (B_34:(pname->Prop)), (((ord_less_eq_pname_o A_71) B_34)->(((eq (pname->Prop)) ((semila1673364395name_o A_71) B_34)) A_71)))
% FOF formula (forall (A_71:(hoare_1708887482_state->Prop)) (B_34:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_71) B_34)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_71) B_34)) A_71))) of role axiom named fact_1008_Int__absorb2
% A new axiom: (forall (A_71:(hoare_1708887482_state->Prop)) (B_34:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_71) B_34)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_71) B_34)) A_71)))
% FOF formula (forall (A_70:(pname->Prop)) (B_33:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_70) B_33)) B_33)) of role axiom named fact_1009_Int__lower2
% A new axiom: (forall (A_70:(pname->Prop)) (B_33:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_70) B_33)) B_33))
% FOF formula (forall (A_70:(hoare_1708887482_state->Prop)) (B_33:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o A_70) B_33)) B_33)) of role axiom named fact_1010_Int__lower2
% A new axiom: (forall (A_70:(hoare_1708887482_state->Prop)) (B_33:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o A_70) B_33)) B_33))
% FOF formula (forall (A_69:(pname->Prop)) (B_32:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_69) B_32)) A_69)) of role axiom named fact_1011_Int__lower1
% A new axiom: (forall (A_69:(pname->Prop)) (B_32:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_69) B_32)) A_69))
% FOF formula (forall (A_69:(hoare_1708887482_state->Prop)) (B_32:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o A_69) B_32)) A_69)) of role axiom named fact_1012_Int__lower1
% A new axiom: (forall (A_69:(hoare_1708887482_state->Prop)) (B_32:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o A_69) B_32)) A_69))
% FOF formula (forall (A_68:(pname->Prop)) (B_31:(pname->Prop)) (C_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o ((semila1673364395name_o A_68) B_31)) ((semila1673364395name_o B_31) C_10))) ((semila1673364395name_o C_10) A_68))) ((semila1673364395name_o ((semila1673364395name_o ((semila1780557381name_o A_68) B_31)) ((semila1780557381name_o B_31) C_10))) ((semila1780557381name_o C_10) A_68)))) of role axiom named fact_1013_Un__Int__crazy
% A new axiom: (forall (A_68:(pname->Prop)) (B_31:(pname->Prop)) (C_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o ((semila1673364395name_o A_68) B_31)) ((semila1673364395name_o B_31) C_10))) ((semila1673364395name_o C_10) A_68))) ((semila1673364395name_o ((semila1673364395name_o ((semila1780557381name_o A_68) B_31)) ((semila1780557381name_o B_31) C_10))) ((semila1780557381name_o C_10) A_68))))
% FOF formula (forall (A_68:(hoare_1708887482_state->Prop)) (B_31:(hoare_1708887482_state->Prop)) (C_10:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o ((semila129691299tate_o A_68) B_31)) ((semila129691299tate_o B_31) C_10))) ((semila129691299tate_o C_10) A_68))) ((semila129691299tate_o ((semila129691299tate_o ((semila1122118281tate_o A_68) B_31)) ((semila1122118281tate_o B_31) C_10))) ((semila1122118281tate_o C_10) A_68)))) of role axiom named fact_1014_Un__Int__crazy
% A new axiom: (forall (A_68:(hoare_1708887482_state->Prop)) (B_31:(hoare_1708887482_state->Prop)) (C_10:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o ((semila129691299tate_o A_68) B_31)) ((semila129691299tate_o B_31) C_10))) ((semila129691299tate_o C_10) A_68))) ((semila129691299tate_o ((semila129691299tate_o ((semila1122118281tate_o A_68) B_31)) ((semila1122118281tate_o B_31) C_10))) ((semila1122118281tate_o C_10) A_68))))
% FOF formula (forall (B_30:(pname->Prop)) (C_9:(pname->Prop)) (A_67:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o B_30) C_9)) A_67)) ((semila1673364395name_o ((semila1780557381name_o B_30) A_67)) ((semila1780557381name_o C_9) A_67)))) of role axiom named fact_1015_Un__Int__distrib2
% A new axiom: (forall (B_30:(pname->Prop)) (C_9:(pname->Prop)) (A_67:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o B_30) C_9)) A_67)) ((semila1673364395name_o ((semila1780557381name_o B_30) A_67)) ((semila1780557381name_o C_9) A_67))))
% FOF formula (forall (B_30:(hoare_1708887482_state->Prop)) (C_9:(hoare_1708887482_state->Prop)) (A_67:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila129691299tate_o B_30) C_9)) A_67)) ((semila129691299tate_o ((semila1122118281tate_o B_30) A_67)) ((semila1122118281tate_o C_9) A_67)))) of role axiom named fact_1016_Un__Int__distrib2
% A new axiom: (forall (B_30:(hoare_1708887482_state->Prop)) (C_9:(hoare_1708887482_state->Prop)) (A_67:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila129691299tate_o B_30) C_9)) A_67)) ((semila129691299tate_o ((semila1122118281tate_o B_30) A_67)) ((semila1122118281tate_o C_9) A_67))))
% FOF formula (forall (B_29:(pname->Prop)) (C_8:(pname->Prop)) (A_66:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o B_29) C_8)) A_66)) ((semila1780557381name_o ((semila1673364395name_o B_29) A_66)) ((semila1673364395name_o C_8) A_66)))) of role axiom named fact_1017_Int__Un__distrib2
% A new axiom: (forall (B_29:(pname->Prop)) (C_8:(pname->Prop)) (A_66:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o B_29) C_8)) A_66)) ((semila1780557381name_o ((semila1673364395name_o B_29) A_66)) ((semila1673364395name_o C_8) A_66))))
% FOF formula (forall (B_29:(hoare_1708887482_state->Prop)) (C_8:(hoare_1708887482_state->Prop)) (A_66:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((semila1122118281tate_o B_29) C_8)) A_66)) ((semila1122118281tate_o ((semila129691299tate_o B_29) A_66)) ((semila129691299tate_o C_8) A_66)))) of role axiom named fact_1018_Int__Un__distrib2
% A new axiom: (forall (B_29:(hoare_1708887482_state->Prop)) (C_8:(hoare_1708887482_state->Prop)) (A_66:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((semila1122118281tate_o B_29) C_8)) A_66)) ((semila1122118281tate_o ((semila129691299tate_o B_29) A_66)) ((semila129691299tate_o C_8) A_66))))
% FOF formula (forall (A_65:(pname->Prop)) (B_28:(pname->Prop)) (C_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_65) ((semila1673364395name_o B_28) C_7))) ((semila1673364395name_o ((semila1780557381name_o A_65) B_28)) ((semila1780557381name_o A_65) C_7)))) of role axiom named fact_1019_Un__Int__distrib
% A new axiom: (forall (A_65:(pname->Prop)) (B_28:(pname->Prop)) (C_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_65) ((semila1673364395name_o B_28) C_7))) ((semila1673364395name_o ((semila1780557381name_o A_65) B_28)) ((semila1780557381name_o A_65) C_7))))
% FOF formula (forall (A_65:(hoare_1708887482_state->Prop)) (B_28:(hoare_1708887482_state->Prop)) (C_7:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_65) ((semila129691299tate_o B_28) C_7))) ((semila129691299tate_o ((semila1122118281tate_o A_65) B_28)) ((semila1122118281tate_o A_65) C_7)))) of role axiom named fact_1020_Un__Int__distrib
% A new axiom: (forall (A_65:(hoare_1708887482_state->Prop)) (B_28:(hoare_1708887482_state->Prop)) (C_7:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_65) ((semila129691299tate_o B_28) C_7))) ((semila129691299tate_o ((semila1122118281tate_o A_65) B_28)) ((semila1122118281tate_o A_65) C_7))))
% FOF formula (forall (A_64:(pname->Prop)) (B_27:(pname->Prop)) (C_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_64) ((semila1780557381name_o B_27) C_6))) ((semila1780557381name_o ((semila1673364395name_o A_64) B_27)) ((semila1673364395name_o A_64) C_6)))) of role axiom named fact_1021_Int__Un__distrib
% A new axiom: (forall (A_64:(pname->Prop)) (B_27:(pname->Prop)) (C_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_64) ((semila1780557381name_o B_27) C_6))) ((semila1780557381name_o ((semila1673364395name_o A_64) B_27)) ((semila1673364395name_o A_64) C_6))))
% FOF formula (forall (A_64:(hoare_1708887482_state->Prop)) (B_27:(hoare_1708887482_state->Prop)) (C_6:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_64) ((semila1122118281tate_o B_27) C_6))) ((semila1122118281tate_o ((semila129691299tate_o A_64) B_27)) ((semila129691299tate_o A_64) C_6)))) of role axiom named fact_1022_Int__Un__distrib
% A new axiom: (forall (A_64:(hoare_1708887482_state->Prop)) (B_27:(hoare_1708887482_state->Prop)) (C_6:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_64) ((semila1122118281tate_o B_27) C_6))) ((semila1122118281tate_o ((semila129691299tate_o A_64) B_27)) ((semila129691299tate_o A_64) C_6))))
% FOF formula (forall (X_20:Prop) (Y_9:Prop) (Z_4:Prop), ((ord_less_eq_o ((semila10642723_sup_o ((semila854092349_inf_o X_20) Y_9)) ((semila854092349_inf_o X_20) Z_4))) ((semila854092349_inf_o X_20) ((semila10642723_sup_o Y_9) Z_4)))) of role axiom named fact_1023_distrib__inf__le
% A new axiom: (forall (X_20:Prop) (Y_9:Prop) (Z_4:Prop), ((ord_less_eq_o ((semila10642723_sup_o ((semila854092349_inf_o X_20) Y_9)) ((semila854092349_inf_o X_20) Z_4))) ((semila854092349_inf_o X_20) ((semila10642723_sup_o Y_9) Z_4))))
% FOF formula (forall (X_20:(pname->Prop)) (Y_9:(pname->Prop)) (Z_4:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o ((semila1673364395name_o X_20) Y_9)) ((semila1673364395name_o X_20) Z_4))) ((semila1673364395name_o X_20) ((semila1780557381name_o Y_9) Z_4)))) of role axiom named fact_1024_distrib__inf__le
% A new axiom: (forall (X_20:(pname->Prop)) (Y_9:(pname->Prop)) (Z_4:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o ((semila1673364395name_o X_20) Y_9)) ((semila1673364395name_o X_20) Z_4))) ((semila1673364395name_o X_20) ((semila1780557381name_o Y_9) Z_4))))
% FOF formula (forall (X_20:(hoare_1708887482_state->Prop)) (Y_9:(hoare_1708887482_state->Prop)) (Z_4:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila1122118281tate_o ((semila129691299tate_o X_20) Y_9)) ((semila129691299tate_o X_20) Z_4))) ((semila129691299tate_o X_20) ((semila1122118281tate_o Y_9) Z_4)))) of role axiom named fact_1025_distrib__inf__le
% A new axiom: (forall (X_20:(hoare_1708887482_state->Prop)) (Y_9:(hoare_1708887482_state->Prop)) (Z_4:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila1122118281tate_o ((semila129691299tate_o X_20) Y_9)) ((semila129691299tate_o X_20) Z_4))) ((semila129691299tate_o X_20) ((semila1122118281tate_o Y_9) Z_4))))
% FOF formula (forall (X_19:Prop) (Y_8:Prop) (Z_3:Prop), ((ord_less_eq_o ((semila10642723_sup_o X_19) ((semila854092349_inf_o Y_8) Z_3))) ((semila854092349_inf_o ((semila10642723_sup_o X_19) Y_8)) ((semila10642723_sup_o X_19) Z_3)))) of role axiom named fact_1026_distrib__sup__le
% A new axiom: (forall (X_19:Prop) (Y_8:Prop) (Z_3:Prop), ((ord_less_eq_o ((semila10642723_sup_o X_19) ((semila854092349_inf_o Y_8) Z_3))) ((semila854092349_inf_o ((semila10642723_sup_o X_19) Y_8)) ((semila10642723_sup_o X_19) Z_3))))
% FOF formula (forall (X_19:(pname->Prop)) (Y_8:(pname->Prop)) (Z_3:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o X_19) ((semila1673364395name_o Y_8) Z_3))) ((semila1673364395name_o ((semila1780557381name_o X_19) Y_8)) ((semila1780557381name_o X_19) Z_3)))) of role axiom named fact_1027_distrib__sup__le
% A new axiom: (forall (X_19:(pname->Prop)) (Y_8:(pname->Prop)) (Z_3:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o X_19) ((semila1673364395name_o Y_8) Z_3))) ((semila1673364395name_o ((semila1780557381name_o X_19) Y_8)) ((semila1780557381name_o X_19) Z_3))))
% FOF formula (forall (X_19:(hoare_1708887482_state->Prop)) (Y_8:(hoare_1708887482_state->Prop)) (Z_3:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila1122118281tate_o X_19) ((semila129691299tate_o Y_8) Z_3))) ((semila129691299tate_o ((semila1122118281tate_o X_19) Y_8)) ((semila1122118281tate_o X_19) Z_3)))) of role axiom named fact_1028_distrib__sup__le
% A new axiom: (forall (X_19:(hoare_1708887482_state->Prop)) (Y_8:(hoare_1708887482_state->Prop)) (Z_3:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila1122118281tate_o X_19) ((semila129691299tate_o Y_8) Z_3))) ((semila129691299tate_o ((semila1122118281tate_o X_19) Y_8)) ((semila1122118281tate_o X_19) Z_3))))
% FOF formula (forall (A_63:com) (A_62:(com->Prop)), (((member_com A_63) A_62)->(((eq (com->Prop)) ((insert_com A_63) ((minus_minus_com_o A_62) ((insert_com A_63) bot_bot_com_o)))) A_62))) of role axiom named fact_1029_insert__Diff
% A new axiom: (forall (A_63:com) (A_62:(com->Prop)), (((member_com A_63) A_62)->(((eq (com->Prop)) ((insert_com A_63) ((minus_minus_com_o A_62) ((insert_com A_63) bot_bot_com_o)))) A_62)))
% FOF formula (forall (A_63:pname) (A_62:(pname->Prop)), (((member_pname A_63) A_62)->(((eq (pname->Prop)) ((insert_pname A_63) ((minus_minus_pname_o A_62) ((insert_pname A_63) bot_bot_pname_o)))) A_62))) of role axiom named fact_1030_insert__Diff
% A new axiom: (forall (A_63:pname) (A_62:(pname->Prop)), (((member_pname A_63) A_62)->(((eq (pname->Prop)) ((insert_pname A_63) ((minus_minus_pname_o A_62) ((insert_pname A_63) bot_bot_pname_o)))) A_62)))
% FOF formula (forall (A_63:hoare_1708887482_state) (A_62:(hoare_1708887482_state->Prop)), (((member451959335_state A_63) A_62)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_63) ((minus_2056855718tate_o A_62) ((insert528405184_state A_63) bot_bo19817387tate_o)))) A_62))) of role axiom named fact_1031_insert__Diff
% A new axiom: (forall (A_63:hoare_1708887482_state) (A_62:(hoare_1708887482_state->Prop)), (((member451959335_state A_63) A_62)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_63) ((minus_2056855718tate_o A_62) ((insert528405184_state A_63) bot_bo19817387tate_o)))) A_62)))
% FOF formula (forall (X_18:com) (A_61:(com->Prop)), ((((member_com X_18) A_61)->False)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_18) A_61)) ((insert_com X_18) bot_bot_com_o))) A_61))) of role axiom named fact_1032_Diff__insert__absorb
% A new axiom: (forall (X_18:com) (A_61:(com->Prop)), ((((member_com X_18) A_61)->False)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_18) A_61)) ((insert_com X_18) bot_bot_com_o))) A_61)))
% FOF formula (forall (X_18:pname) (A_61:(pname->Prop)), ((((member_pname X_18) A_61)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_18) A_61)) ((insert_pname X_18) bot_bot_pname_o))) A_61))) of role axiom named fact_1033_Diff__insert__absorb
% A new axiom: (forall (X_18:pname) (A_61:(pname->Prop)), ((((member_pname X_18) A_61)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_18) A_61)) ((insert_pname X_18) bot_bot_pname_o))) A_61)))
% FOF formula (forall (X_18:hoare_1708887482_state) (A_61:(hoare_1708887482_state->Prop)), ((((member451959335_state X_18) A_61)->False)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_18) A_61)) ((insert528405184_state X_18) bot_bo19817387tate_o))) A_61))) of role axiom named fact_1034_Diff__insert__absorb
% A new axiom: (forall (X_18:hoare_1708887482_state) (A_61:(hoare_1708887482_state->Prop)), ((((member451959335_state X_18) A_61)->False)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_18) A_61)) ((insert528405184_state X_18) bot_bo19817387tate_o))) A_61)))
% FOF formula (forall (A_60:com) (A_59:(com->Prop)), (((eq (com->Prop)) ((insert_com A_60) ((minus_minus_com_o A_59) ((insert_com A_60) bot_bot_com_o)))) ((insert_com A_60) A_59))) of role axiom named fact_1035_insert__Diff__single
% A new axiom: (forall (A_60:com) (A_59:(com->Prop)), (((eq (com->Prop)) ((insert_com A_60) ((minus_minus_com_o A_59) ((insert_com A_60) bot_bot_com_o)))) ((insert_com A_60) A_59)))
% FOF formula (forall (A_60:pname) (A_59:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_60) ((minus_minus_pname_o A_59) ((insert_pname A_60) bot_bot_pname_o)))) ((insert_pname A_60) A_59))) of role axiom named fact_1036_insert__Diff__single
% A new axiom: (forall (A_60:pname) (A_59:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_60) ((minus_minus_pname_o A_59) ((insert_pname A_60) bot_bot_pname_o)))) ((insert_pname A_60) A_59)))
% FOF formula (forall (A_60:hoare_1708887482_state) (A_59:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_60) ((minus_2056855718tate_o A_59) ((insert528405184_state A_60) bot_bo19817387tate_o)))) ((insert528405184_state A_60) A_59))) of role axiom named fact_1037_insert__Diff__single
% A new axiom: (forall (A_60:hoare_1708887482_state) (A_59:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_60) ((minus_2056855718tate_o A_59) ((insert528405184_state A_60) bot_bo19817387tate_o)))) ((insert528405184_state A_60) A_59)))
% FOF formula (forall (A_58:(com->Prop)) (A_57:com) (B_26:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_58) ((insert_com A_57) B_26))) ((minus_minus_com_o ((minus_minus_com_o A_58) ((insert_com A_57) bot_bot_com_o))) B_26))) of role axiom named fact_1038_Diff__insert2
% A new axiom: (forall (A_58:(com->Prop)) (A_57:com) (B_26:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_58) ((insert_com A_57) B_26))) ((minus_minus_com_o ((minus_minus_com_o A_58) ((insert_com A_57) bot_bot_com_o))) B_26)))
% FOF formula (forall (A_58:(pname->Prop)) (A_57:pname) (B_26:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_58) ((insert_pname A_57) B_26))) ((minus_minus_pname_o ((minus_minus_pname_o A_58) ((insert_pname A_57) bot_bot_pname_o))) B_26))) of role axiom named fact_1039_Diff__insert2
% A new axiom: (forall (A_58:(pname->Prop)) (A_57:pname) (B_26:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_58) ((insert_pname A_57) B_26))) ((minus_minus_pname_o ((minus_minus_pname_o A_58) ((insert_pname A_57) bot_bot_pname_o))) B_26)))
% FOF formula (forall (A_58:(hoare_1708887482_state->Prop)) (A_57:hoare_1708887482_state) (B_26:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_58) ((insert528405184_state A_57) B_26))) ((minus_2056855718tate_o ((minus_2056855718tate_o A_58) ((insert528405184_state A_57) bot_bo19817387tate_o))) B_26))) of role axiom named fact_1040_Diff__insert2
% A new axiom: (forall (A_58:(hoare_1708887482_state->Prop)) (A_57:hoare_1708887482_state) (B_26:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_58) ((insert528405184_state A_57) B_26))) ((minus_2056855718tate_o ((minus_2056855718tate_o A_58) ((insert528405184_state A_57) bot_bo19817387tate_o))) B_26)))
% FOF formula (forall (A_56:(com->Prop)) (A_55:com) (B_25:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_56) ((insert_com A_55) B_25))) ((minus_minus_com_o ((minus_minus_com_o A_56) B_25)) ((insert_com A_55) bot_bot_com_o)))) of role axiom named fact_1041_Diff__insert
% A new axiom: (forall (A_56:(com->Prop)) (A_55:com) (B_25:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_56) ((insert_com A_55) B_25))) ((minus_minus_com_o ((minus_minus_com_o A_56) B_25)) ((insert_com A_55) bot_bot_com_o))))
% FOF formula (forall (A_56:(pname->Prop)) (A_55:pname) (B_25:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_56) ((insert_pname A_55) B_25))) ((minus_minus_pname_o ((minus_minus_pname_o A_56) B_25)) ((insert_pname A_55) bot_bot_pname_o)))) of role axiom named fact_1042_Diff__insert
% A new axiom: (forall (A_56:(pname->Prop)) (A_55:pname) (B_25:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_56) ((insert_pname A_55) B_25))) ((minus_minus_pname_o ((minus_minus_pname_o A_56) B_25)) ((insert_pname A_55) bot_bot_pname_o))))
% FOF formula (forall (A_56:(hoare_1708887482_state->Prop)) (A_55:hoare_1708887482_state) (B_25:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_56) ((insert528405184_state A_55) B_25))) ((minus_2056855718tate_o ((minus_2056855718tate_o A_56) B_25)) ((insert528405184_state A_55) bot_bo19817387tate_o)))) of role axiom named fact_1043_Diff__insert
% A new axiom: (forall (A_56:(hoare_1708887482_state->Prop)) (A_55:hoare_1708887482_state) (B_25:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_56) ((insert528405184_state A_55) B_25))) ((minus_2056855718tate_o ((minus_2056855718tate_o A_56) B_25)) ((insert528405184_state A_55) bot_bo19817387tate_o))))
% FOF formula (forall (A_54:(com->Prop)) (A_53:com) (B_24:(com->Prop)), ((iff (finite_finite_com ((minus_minus_com_o A_54) ((insert_com A_53) B_24)))) (finite_finite_com ((minus_minus_com_o A_54) B_24)))) of role axiom named fact_1044_finite__Diff__insert
% A new axiom: (forall (A_54:(com->Prop)) (A_53:com) (B_24:(com->Prop)), ((iff (finite_finite_com ((minus_minus_com_o A_54) ((insert_com A_53) B_24)))) (finite_finite_com ((minus_minus_com_o A_54) B_24))))
% FOF formula (forall (A_54:(pname->Prop)) (A_53:pname) (B_24:(pname->Prop)), ((iff (finite_finite_pname ((minus_minus_pname_o A_54) ((insert_pname A_53) B_24)))) (finite_finite_pname ((minus_minus_pname_o A_54) B_24)))) of role axiom named fact_1045_finite__Diff__insert
% A new axiom: (forall (A_54:(pname->Prop)) (A_53:pname) (B_24:(pname->Prop)), ((iff (finite_finite_pname ((minus_minus_pname_o A_54) ((insert_pname A_53) B_24)))) (finite_finite_pname ((minus_minus_pname_o A_54) B_24))))
% FOF formula (forall (A_54:(hoare_1708887482_state->Prop)) (A_53:hoare_1708887482_state) (B_24:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((minus_2056855718tate_o A_54) ((insert528405184_state A_53) B_24)))) (finite1625599783_state ((minus_2056855718tate_o A_54) B_24)))) of role axiom named fact_1046_finite__Diff__insert
% A new axiom: (forall (A_54:(hoare_1708887482_state->Prop)) (A_53:hoare_1708887482_state) (B_24:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((minus_2056855718tate_o A_54) ((insert528405184_state A_53) B_24)))) (finite1625599783_state ((minus_2056855718tate_o A_54) B_24))))
% FOF formula (forall (A_54:((pname->Prop)->Prop)) (A_53:(pname->Prop)) (B_24:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((minus_1480864103me_o_o A_54) ((insert_pname_o A_53) B_24)))) (finite297249702name_o ((minus_1480864103me_o_o A_54) B_24)))) of role axiom named fact_1047_finite__Diff__insert
% A new axiom: (forall (A_54:((pname->Prop)->Prop)) (A_53:(pname->Prop)) (B_24:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((minus_1480864103me_o_o A_54) ((insert_pname_o A_53) B_24)))) (finite297249702name_o ((minus_1480864103me_o_o A_54) B_24))))
% FOF formula (forall (A_54:((hoare_1708887482_state->Prop)->Prop)) (A_53:(hoare_1708887482_state->Prop)) (B_24:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o ((minus_548038231te_o_o A_54) ((insert949073679tate_o A_53) B_24)))) (finite1329924456tate_o ((minus_548038231te_o_o A_54) B_24)))) of role axiom named fact_1048_finite__Diff__insert
% A new axiom: (forall (A_54:((hoare_1708887482_state->Prop)->Prop)) (A_53:(hoare_1708887482_state->Prop)) (B_24:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o ((minus_548038231te_o_o A_54) ((insert949073679tate_o A_53) B_24)))) (finite1329924456tate_o ((minus_548038231te_o_o A_54) B_24))))
% FOF formula (forall (F_27:(pname->hoare_1708887482_state)) (A_52:(pname->Prop)) (B_23:(pname->Prop)), ((ord_le777019615tate_o ((minus_2056855718tate_o ((image_1116629049_state F_27) A_52)) ((image_1116629049_state F_27) B_23))) ((image_1116629049_state F_27) ((minus_minus_pname_o A_52) B_23)))) of role axiom named fact_1049_image__diff__subset
% A new axiom: (forall (F_27:(pname->hoare_1708887482_state)) (A_52:(pname->Prop)) (B_23:(pname->Prop)), ((ord_le777019615tate_o ((minus_2056855718tate_o ((image_1116629049_state F_27) A_52)) ((image_1116629049_state F_27) B_23))) ((image_1116629049_state F_27) ((minus_minus_pname_o A_52) B_23))))
% FOF formula (forall (A_51:(pname->Prop)) (B_22:(pname->Prop)), (((ord_less_eq_pname_o A_51) B_22)->(((eq (pname->Prop)) ((semila1780557381name_o A_51) ((minus_minus_pname_o B_22) A_51))) B_22))) of role axiom named fact_1050_Diff__partition
% A new axiom: (forall (A_51:(pname->Prop)) (B_22:(pname->Prop)), (((ord_less_eq_pname_o A_51) B_22)->(((eq (pname->Prop)) ((semila1780557381name_o A_51) ((minus_minus_pname_o B_22) A_51))) B_22)))
% FOF formula (forall (A_51:(hoare_1708887482_state->Prop)) (B_22:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_51) B_22)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_51) ((minus_2056855718tate_o B_22) A_51))) B_22))) of role axiom named fact_1051_Diff__partition
% A new axiom: (forall (A_51:(hoare_1708887482_state->Prop)) (B_22:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_51) B_22)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_51) ((minus_2056855718tate_o B_22) A_51))) B_22)))
% FOF formula (forall (A_50:(pname->Prop)) (B_21:(pname->Prop)) (C_5:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((minus_minus_pname_o A_50) B_21)) C_5)) ((ord_less_eq_pname_o A_50) ((semila1780557381name_o B_21) C_5)))) of role axiom named fact_1052_Diff__subset__conv
% A new axiom: (forall (A_50:(pname->Prop)) (B_21:(pname->Prop)) (C_5:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((minus_minus_pname_o A_50) B_21)) C_5)) ((ord_less_eq_pname_o A_50) ((semila1780557381name_o B_21) C_5))))
% FOF formula (forall (A_50:(hoare_1708887482_state->Prop)) (B_21:(hoare_1708887482_state->Prop)) (C_5:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o ((minus_2056855718tate_o A_50) B_21)) C_5)) ((ord_le777019615tate_o A_50) ((semila1122118281tate_o B_21) C_5)))) of role axiom named fact_1053_Diff__subset__conv
% A new axiom: (forall (A_50:(hoare_1708887482_state->Prop)) (B_21:(hoare_1708887482_state->Prop)) (C_5:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o ((minus_2056855718tate_o A_50) B_21)) C_5)) ((ord_le777019615tate_o A_50) ((semila1122118281tate_o B_21) C_5))))
% FOF formula (forall (F_26:(pname->hoare_1708887482_state)) (A_49:(pname->Prop)) (B_20:(pname->Prop)), ((ord_le777019615tate_o ((image_1116629049_state F_26) ((semila1673364395name_o A_49) B_20))) ((semila129691299tate_o ((image_1116629049_state F_26) A_49)) ((image_1116629049_state F_26) B_20)))) of role axiom named fact_1054_image__Int__subset
% A new axiom: (forall (F_26:(pname->hoare_1708887482_state)) (A_49:(pname->Prop)) (B_20:(pname->Prop)), ((ord_le777019615tate_o ((image_1116629049_state F_26) ((semila1673364395name_o A_49) B_20))) ((semila129691299tate_o ((image_1116629049_state F_26) A_49)) ((image_1116629049_state F_26) B_20))))
% FOF formula (forall (A_48:(pname->Prop)) (B_19:(pname->Prop)) (C_4:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o A_48) B_19)) C_4)) ((semila1673364395name_o A_48) ((semila1780557381name_o B_19) C_4)))) ((ord_less_eq_pname_o C_4) A_48))) of role axiom named fact_1055_Un__Int__assoc__eq
% A new axiom: (forall (A_48:(pname->Prop)) (B_19:(pname->Prop)) (C_4:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o A_48) B_19)) C_4)) ((semila1673364395name_o A_48) ((semila1780557381name_o B_19) C_4)))) ((ord_less_eq_pname_o C_4) A_48)))
% FOF formula (forall (A_48:(hoare_1708887482_state->Prop)) (B_19:(hoare_1708887482_state->Prop)) (C_4:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila129691299tate_o A_48) B_19)) C_4)) ((semila129691299tate_o A_48) ((semila1122118281tate_o B_19) C_4)))) ((ord_le777019615tate_o C_4) A_48))) of role axiom named fact_1056_Un__Int__assoc__eq
% A new axiom: (forall (A_48:(hoare_1708887482_state->Prop)) (B_19:(hoare_1708887482_state->Prop)) (C_4:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila129691299tate_o A_48) B_19)) C_4)) ((semila129691299tate_o A_48) ((semila1122118281tate_o B_19) C_4)))) ((ord_le777019615tate_o C_4) A_48)))
% FOF formula (forall (P_4:(pname->Prop)) (F_25:(pname->hoare_1708887482_state)) (G_4:(pname->hoare_1708887482_state)) (S:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> (((if_Hoa1374726218_state (P_4 X_3)) (F_25 X_3)) (G_4 X_3)))) S)) ((semila1122118281tate_o ((image_1116629049_state F_25) ((semila1673364395name_o S) (collect_pname P_4)))) ((image_1116629049_state G_4) ((semila1673364395name_o S) (collect_pname (fun (X_3:pname)=> (not (P_4 X_3))))))))) of role axiom named fact_1057_if__image__distrib
% A new axiom: (forall (P_4:(pname->Prop)) (F_25:(pname->hoare_1708887482_state)) (G_4:(pname->hoare_1708887482_state)) (S:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> (((if_Hoa1374726218_state (P_4 X_3)) (F_25 X_3)) (G_4 X_3)))) S)) ((semila1122118281tate_o ((image_1116629049_state F_25) ((semila1673364395name_o S) (collect_pname P_4)))) ((image_1116629049_state G_4) ((semila1673364395name_o S) (collect_pname (fun (X_3:pname)=> (not (P_4 X_3)))))))))
% FOF formula (forall (P_3:(pname->Prop)) (F_24:(pname->option_com)) (G_3:(pname->option_com)), (((eq (pname->Prop)) (dom_pname_com (fun (X_3:pname)=> (((if_option_com (P_3 X_3)) (F_24 X_3)) (G_3 X_3))))) ((semila1780557381name_o ((semila1673364395name_o (dom_pname_com F_24)) (collect_pname P_3))) ((semila1673364395name_o (dom_pname_com G_3)) (collect_pname (fun (X_3:pname)=> (not (P_3 X_3)))))))) of role axiom named fact_1058_dom__if
% A new axiom: (forall (P_3:(pname->Prop)) (F_24:(pname->option_com)) (G_3:(pname->option_com)), (((eq (pname->Prop)) (dom_pname_com (fun (X_3:pname)=> (((if_option_com (P_3 X_3)) (F_24 X_3)) (G_3 X_3))))) ((semila1780557381name_o ((semila1673364395name_o (dom_pname_com F_24)) (collect_pname P_3))) ((semila1673364395name_o (dom_pname_com G_3)) (collect_pname (fun (X_3:pname)=> (not (P_3 X_3))))))))
% FOF formula (forall (A_47:(com->Prop)) (X_17:com) (B_18:(com->Prop)), (((ord_less_eq_com_o ((minus_minus_com_o A_47) ((insert_com X_17) bot_bot_com_o))) B_18)->(((member_com X_17) A_47)->((ord_less_eq_com_o A_47) ((insert_com X_17) B_18))))) of role axiom named fact_1059_diff__single__insert
% A new axiom: (forall (A_47:(com->Prop)) (X_17:com) (B_18:(com->Prop)), (((ord_less_eq_com_o ((minus_minus_com_o A_47) ((insert_com X_17) bot_bot_com_o))) B_18)->(((member_com X_17) A_47)->((ord_less_eq_com_o A_47) ((insert_com X_17) B_18)))))
% FOF formula (forall (A_47:(pname->Prop)) (X_17:pname) (B_18:(pname->Prop)), (((ord_less_eq_pname_o ((minus_minus_pname_o A_47) ((insert_pname X_17) bot_bot_pname_o))) B_18)->(((member_pname X_17) A_47)->((ord_less_eq_pname_o A_47) ((insert_pname X_17) B_18))))) of role axiom named fact_1060_diff__single__insert
% A new axiom: (forall (A_47:(pname->Prop)) (X_17:pname) (B_18:(pname->Prop)), (((ord_less_eq_pname_o ((minus_minus_pname_o A_47) ((insert_pname X_17) bot_bot_pname_o))) B_18)->(((member_pname X_17) A_47)->((ord_less_eq_pname_o A_47) ((insert_pname X_17) B_18)))))
% FOF formula (forall (A_47:(hoare_1708887482_state->Prop)) (X_17:hoare_1708887482_state) (B_18:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o ((minus_2056855718tate_o A_47) ((insert528405184_state X_17) bot_bo19817387tate_o))) B_18)->(((member451959335_state X_17) A_47)->((ord_le777019615tate_o A_47) ((insert528405184_state X_17) B_18))))) of role axiom named fact_1061_diff__single__insert
% A new axiom: (forall (A_47:(hoare_1708887482_state->Prop)) (X_17:hoare_1708887482_state) (B_18:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o ((minus_2056855718tate_o A_47) ((insert528405184_state X_17) bot_bo19817387tate_o))) B_18)->(((member451959335_state X_17) A_47)->((ord_le777019615tate_o A_47) ((insert528405184_state X_17) B_18)))))
% FOF formula (forall (A_46:(com->Prop)) (X_16:com) (B_17:(com->Prop)), ((iff ((ord_less_eq_com_o A_46) ((insert_com X_16) B_17))) ((and (((member_com X_16) A_46)->((ord_less_eq_com_o ((minus_minus_com_o A_46) ((insert_com X_16) bot_bot_com_o))) B_17))) ((((member_com X_16) A_46)->False)->((ord_less_eq_com_o A_46) B_17))))) of role axiom named fact_1062_subset__insert__iff
% A new axiom: (forall (A_46:(com->Prop)) (X_16:com) (B_17:(com->Prop)), ((iff ((ord_less_eq_com_o A_46) ((insert_com X_16) B_17))) ((and (((member_com X_16) A_46)->((ord_less_eq_com_o ((minus_minus_com_o A_46) ((insert_com X_16) bot_bot_com_o))) B_17))) ((((member_com X_16) A_46)->False)->((ord_less_eq_com_o A_46) B_17)))))
% FOF formula (forall (A_46:(pname->Prop)) (X_16:pname) (B_17:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_46) ((insert_pname X_16) B_17))) ((and (((member_pname X_16) A_46)->((ord_less_eq_pname_o ((minus_minus_pname_o A_46) ((insert_pname X_16) bot_bot_pname_o))) B_17))) ((((member_pname X_16) A_46)->False)->((ord_less_eq_pname_o A_46) B_17))))) of role axiom named fact_1063_subset__insert__iff
% A new axiom: (forall (A_46:(pname->Prop)) (X_16:pname) (B_17:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_46) ((insert_pname X_16) B_17))) ((and (((member_pname X_16) A_46)->((ord_less_eq_pname_o ((minus_minus_pname_o A_46) ((insert_pname X_16) bot_bot_pname_o))) B_17))) ((((member_pname X_16) A_46)->False)->((ord_less_eq_pname_o A_46) B_17)))))
% FOF formula (forall (A_46:(hoare_1708887482_state->Prop)) (X_16:hoare_1708887482_state) (B_17:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_46) ((insert528405184_state X_16) B_17))) ((and (((member451959335_state X_16) A_46)->((ord_le777019615tate_o ((minus_2056855718tate_o A_46) ((insert528405184_state X_16) bot_bo19817387tate_o))) B_17))) ((((member451959335_state X_16) A_46)->False)->((ord_le777019615tate_o A_46) B_17))))) of role axiom named fact_1064_subset__insert__iff
% A new axiom: (forall (A_46:(hoare_1708887482_state->Prop)) (X_16:hoare_1708887482_state) (B_17:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_46) ((insert528405184_state X_16) B_17))) ((and (((member451959335_state X_16) A_46)->((ord_le777019615tate_o ((minus_2056855718tate_o A_46) ((insert528405184_state X_16) bot_bo19817387tate_o))) B_17))) ((((member451959335_state X_16) A_46)->False)->((ord_le777019615tate_o A_46) B_17)))))
% FOF formula (forall (P_2:((com->Prop)->Prop)) (A_45:(com->Prop)), ((finite_finite_com A_45)->((P_2 A_45)->((forall (A_6:com) (A_39:(com->Prop)), ((finite_finite_com A_39)->(((member_com A_6) A_39)->((P_2 A_39)->(P_2 ((minus_minus_com_o A_39) ((insert_com A_6) bot_bot_com_o)))))))->(P_2 bot_bot_com_o))))) of role axiom named fact_1065_finite__empty__induct
% A new axiom: (forall (P_2:((com->Prop)->Prop)) (A_45:(com->Prop)), ((finite_finite_com A_45)->((P_2 A_45)->((forall (A_6:com) (A_39:(com->Prop)), ((finite_finite_com A_39)->(((member_com A_6) A_39)->((P_2 A_39)->(P_2 ((minus_minus_com_o A_39) ((insert_com A_6) bot_bot_com_o)))))))->(P_2 bot_bot_com_o)))))
% FOF formula (forall (P_2:((pname->Prop)->Prop)) (A_45:(pname->Prop)), ((finite_finite_pname A_45)->((P_2 A_45)->((forall (A_6:pname) (A_39:(pname->Prop)), ((finite_finite_pname A_39)->(((member_pname A_6) A_39)->((P_2 A_39)->(P_2 ((minus_minus_pname_o A_39) ((insert_pname A_6) bot_bot_pname_o)))))))->(P_2 bot_bot_pname_o))))) of role axiom named fact_1066_finite__empty__induct
% A new axiom: (forall (P_2:((pname->Prop)->Prop)) (A_45:(pname->Prop)), ((finite_finite_pname A_45)->((P_2 A_45)->((forall (A_6:pname) (A_39:(pname->Prop)), ((finite_finite_pname A_39)->(((member_pname A_6) A_39)->((P_2 A_39)->(P_2 ((minus_minus_pname_o A_39) ((insert_pname A_6) bot_bot_pname_o)))))))->(P_2 bot_bot_pname_o)))))
% FOF formula (forall (P_2:((hoare_1708887482_state->Prop)->Prop)) (A_45:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_45)->((P_2 A_45)->((forall (A_6:hoare_1708887482_state) (A_39:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_39)->(((member451959335_state A_6) A_39)->((P_2 A_39)->(P_2 ((minus_2056855718tate_o A_39) ((insert528405184_state A_6) bot_bo19817387tate_o)))))))->(P_2 bot_bo19817387tate_o))))) of role axiom named fact_1067_finite__empty__induct
% A new axiom: (forall (P_2:((hoare_1708887482_state->Prop)->Prop)) (A_45:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_45)->((P_2 A_45)->((forall (A_6:hoare_1708887482_state) (A_39:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_39)->(((member451959335_state A_6) A_39)->((P_2 A_39)->(P_2 ((minus_2056855718tate_o A_39) ((insert528405184_state A_6) bot_bo19817387tate_o)))))))->(P_2 bot_bo19817387tate_o)))))
% FOF formula (forall (P_2:(((pname->Prop)->Prop)->Prop)) (A_45:((pname->Prop)->Prop)), ((finite297249702name_o A_45)->((P_2 A_45)->((forall (A_6:(pname->Prop)) (A_39:((pname->Prop)->Prop)), ((finite297249702name_o A_39)->(((member_pname_o A_6) A_39)->((P_2 A_39)->(P_2 ((minus_1480864103me_o_o A_39) ((insert_pname_o A_6) bot_bot_pname_o_o)))))))->(P_2 bot_bot_pname_o_o))))) of role axiom named fact_1068_finite__empty__induct
% A new axiom: (forall (P_2:(((pname->Prop)->Prop)->Prop)) (A_45:((pname->Prop)->Prop)), ((finite297249702name_o A_45)->((P_2 A_45)->((forall (A_6:(pname->Prop)) (A_39:((pname->Prop)->Prop)), ((finite297249702name_o A_39)->(((member_pname_o A_6) A_39)->((P_2 A_39)->(P_2 ((minus_1480864103me_o_o A_39) ((insert_pname_o A_6) bot_bot_pname_o_o)))))))->(P_2 bot_bot_pname_o_o)))))
% FOF formula (forall (P_2:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (A_45:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_45)->((P_2 A_45)->((forall (A_6:(hoare_1708887482_state->Prop)) (A_39:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_39)->(((member814030440tate_o A_6) A_39)->((P_2 A_39)->(P_2 ((minus_548038231te_o_o A_39) ((insert949073679tate_o A_6) bot_bo1678742418te_o_o)))))))->(P_2 bot_bo1678742418te_o_o))))) of role axiom named fact_1069_finite__empty__induct
% A new axiom: (forall (P_2:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (A_45:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_45)->((P_2 A_45)->((forall (A_6:(hoare_1708887482_state->Prop)) (A_39:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_39)->(((member814030440tate_o A_6) A_39)->((P_2 A_39)->(P_2 ((minus_548038231te_o_o A_39) ((insert949073679tate_o A_6) bot_bo1678742418te_o_o)))))))->(P_2 bot_bo1678742418te_o_o)))))
% FOF formula (forall (F_23:(pname->option_com)) (G_2:(pname->option_com)) (A_44:(pname->Prop)), (((eq (pname->Prop)) (dom_pname_com (((overri1496249029on_com F_23) G_2) A_44))) ((semila1780557381name_o ((minus_minus_pname_o (dom_pname_com F_23)) (collect_pname (fun (A_6:pname)=> ((member_pname A_6) ((minus_minus_pname_o A_44) (dom_pname_com G_2))))))) (collect_pname (fun (A_6:pname)=> ((member_pname A_6) ((semila1673364395name_o A_44) (dom_pname_com G_2)))))))) of role axiom named fact_1070_dom__override__on
% A new axiom: (forall (F_23:(pname->option_com)) (G_2:(pname->option_com)) (A_44:(pname->Prop)), (((eq (pname->Prop)) (dom_pname_com (((overri1496249029on_com F_23) G_2) A_44))) ((semila1780557381name_o ((minus_minus_pname_o (dom_pname_com F_23)) (collect_pname (fun (A_6:pname)=> ((member_pname A_6) ((minus_minus_pname_o A_44) (dom_pname_com G_2))))))) (collect_pname (fun (A_6:pname)=> ((member_pname A_6) ((semila1673364395name_o A_44) (dom_pname_com G_2))))))))
% FOF formula (forall (Q:(com->Prop)) (P_1:(com->Prop)) (A_43:(com->Prop)) (B_16:(com->Prop)), (((ord_less_eq_com_o A_43) B_16)->((forall (X_3:com), (((member_com X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_less_eq_com_o ((semila513601829_com_o A_43) (collect_com P_1))) ((semila513601829_com_o B_16) (collect_com Q)))))) of role axiom named fact_1071_Int__Collect__mono
% A new axiom: (forall (Q:(com->Prop)) (P_1:(com->Prop)) (A_43:(com->Prop)) (B_16:(com->Prop)), (((ord_less_eq_com_o A_43) B_16)->((forall (X_3:com), (((member_com X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_less_eq_com_o ((semila513601829_com_o A_43) (collect_com P_1))) ((semila513601829_com_o B_16) (collect_com Q))))))
% FOF formula (forall (Q:(pname->Prop)) (P_1:(pname->Prop)) (A_43:(pname->Prop)) (B_16:(pname->Prop)), (((ord_less_eq_pname_o A_43) B_16)->((forall (X_3:pname), (((member_pname X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_less_eq_pname_o ((semila1673364395name_o A_43) (collect_pname P_1))) ((semila1673364395name_o B_16) (collect_pname Q)))))) of role axiom named fact_1072_Int__Collect__mono
% A new axiom: (forall (Q:(pname->Prop)) (P_1:(pname->Prop)) (A_43:(pname->Prop)) (B_16:(pname->Prop)), (((ord_less_eq_pname_o A_43) B_16)->((forall (X_3:pname), (((member_pname X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_less_eq_pname_o ((semila1673364395name_o A_43) (collect_pname P_1))) ((semila1673364395name_o B_16) (collect_pname Q))))))
% FOF formula (forall (Q:(hoare_1708887482_state->Prop)) (P_1:(hoare_1708887482_state->Prop)) (A_43:(hoare_1708887482_state->Prop)) (B_16:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_43) B_16)->((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_le777019615tate_o ((semila129691299tate_o A_43) (collec1568722789_state P_1))) ((semila129691299tate_o B_16) (collec1568722789_state Q)))))) of role axiom named fact_1073_Int__Collect__mono
% A new axiom: (forall (Q:(hoare_1708887482_state->Prop)) (P_1:(hoare_1708887482_state->Prop)) (A_43:(hoare_1708887482_state->Prop)) (B_16:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_43) B_16)->((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_le777019615tate_o ((semila129691299tate_o A_43) (collec1568722789_state P_1))) ((semila129691299tate_o B_16) (collec1568722789_state Q))))))
% FOF formula (forall (Q:((pname->Prop)->Prop)) (P_1:((pname->Prop)->Prop)) (A_43:((pname->Prop)->Prop)) (B_16:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_43) B_16)->((forall (X_3:(pname->Prop)), (((member_pname_o X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_le1205211808me_o_o ((semila2013987940me_o_o A_43) (collect_pname_o P_1))) ((semila2013987940me_o_o B_16) (collect_pname_o Q)))))) of role axiom named fact_1074_Int__Collect__mono
% A new axiom: (forall (Q:((pname->Prop)->Prop)) (P_1:((pname->Prop)->Prop)) (A_43:((pname->Prop)->Prop)) (B_16:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_43) B_16)->((forall (X_3:(pname->Prop)), (((member_pname_o X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_le1205211808me_o_o ((semila2013987940me_o_o A_43) (collect_pname_o P_1))) ((semila2013987940me_o_o B_16) (collect_pname_o Q))))))
% FOF formula (forall (Q:((hoare_1708887482_state->Prop)->Prop)) (P_1:((hoare_1708887482_state->Prop)->Prop)) (A_43:((hoare_1708887482_state->Prop)->Prop)) (B_16:((hoare_1708887482_state->Prop)->Prop)), (((ord_le1728773982te_o_o A_43) B_16)->((forall (X_3:(hoare_1708887482_state->Prop)), (((member814030440tate_o X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_le1728773982te_o_o ((semila598060698te_o_o A_43) (collec219771562tate_o P_1))) ((semila598060698te_o_o B_16) (collec219771562tate_o Q)))))) of role axiom named fact_1075_Int__Collect__mono
% A new axiom: (forall (Q:((hoare_1708887482_state->Prop)->Prop)) (P_1:((hoare_1708887482_state->Prop)->Prop)) (A_43:((hoare_1708887482_state->Prop)->Prop)) (B_16:((hoare_1708887482_state->Prop)->Prop)), (((ord_le1728773982te_o_o A_43) B_16)->((forall (X_3:(hoare_1708887482_state->Prop)), (((member814030440tate_o X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_le1728773982te_o_o ((semila598060698te_o_o A_43) (collec219771562tate_o P_1))) ((semila598060698te_o_o B_16) (collec219771562tate_o Q))))))
% FOF formula (forall (X_15:Prop) (Y_7:Prop) (Z_2:Prop), ((forall (X_3:Prop) (Y_4:Prop) (Z_1:Prop), ((iff ((semila10642723_sup_o X_3) ((semila854092349_inf_o Y_4) Z_1))) ((semila854092349_inf_o ((semila10642723_sup_o X_3) Y_4)) ((semila10642723_sup_o X_3) Z_1))))->((iff ((semila854092349_inf_o X_15) ((semila10642723_sup_o Y_7) Z_2))) ((semila10642723_sup_o ((semila854092349_inf_o X_15) Y_7)) ((semila854092349_inf_o X_15) Z_2))))) of role axiom named fact_1076_distrib__imp2
% A new axiom: (forall (X_15:Prop) (Y_7:Prop) (Z_2:Prop), ((forall (X_3:Prop) (Y_4:Prop) (Z_1:Prop), ((iff ((semila10642723_sup_o X_3) ((semila854092349_inf_o Y_4) Z_1))) ((semila854092349_inf_o ((semila10642723_sup_o X_3) Y_4)) ((semila10642723_sup_o X_3) Z_1))))->((iff ((semila854092349_inf_o X_15) ((semila10642723_sup_o Y_7) Z_2))) ((semila10642723_sup_o ((semila854092349_inf_o X_15) Y_7)) ((semila854092349_inf_o X_15) Z_2)))))
% FOF formula (forall (X_15:(pname->Prop)) (Y_7:(pname->Prop)) (Z_2:(pname->Prop)), ((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_3) ((semila1673364395name_o Y_4) Z_1))) ((semila1673364395name_o ((semila1780557381name_o X_3) Y_4)) ((semila1780557381name_o X_3) Z_1))))->(((eq (pname->Prop)) ((semila1673364395name_o X_15) ((semila1780557381name_o Y_7) Z_2))) ((semila1780557381name_o ((semila1673364395name_o X_15) Y_7)) ((semila1673364395name_o X_15) Z_2))))) of role axiom named fact_1077_distrib__imp2
% A new axiom: (forall (X_15:(pname->Prop)) (Y_7:(pname->Prop)) (Z_2:(pname->Prop)), ((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_3) ((semila1673364395name_o Y_4) Z_1))) ((semila1673364395name_o ((semila1780557381name_o X_3) Y_4)) ((semila1780557381name_o X_3) Z_1))))->(((eq (pname->Prop)) ((semila1673364395name_o X_15) ((semila1780557381name_o Y_7) Z_2))) ((semila1780557381name_o ((semila1673364395name_o X_15) Y_7)) ((semila1673364395name_o X_15) Z_2)))))
% FOF formula (forall (X_15:(hoare_1708887482_state->Prop)) (Y_7:(hoare_1708887482_state->Prop)) (Z_2:(hoare_1708887482_state->Prop)), ((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)) (Z_1:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_3) ((semila129691299tate_o Y_4) Z_1))) ((semila129691299tate_o ((semila1122118281tate_o X_3) Y_4)) ((semila1122118281tate_o X_3) Z_1))))->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_15) ((semila1122118281tate_o Y_7) Z_2))) ((semila1122118281tate_o ((semila129691299tate_o X_15) Y_7)) ((semila129691299tate_o X_15) Z_2))))) of role axiom named fact_1078_distrib__imp2
% A new axiom: (forall (X_15:(hoare_1708887482_state->Prop)) (Y_7:(hoare_1708887482_state->Prop)) (Z_2:(hoare_1708887482_state->Prop)), ((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)) (Z_1:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_3) ((semila129691299tate_o Y_4) Z_1))) ((semila129691299tate_o ((semila1122118281tate_o X_3) Y_4)) ((semila1122118281tate_o X_3) Z_1))))->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_15) ((semila1122118281tate_o Y_7) Z_2))) ((semila1122118281tate_o ((semila129691299tate_o X_15) Y_7)) ((semila129691299tate_o X_15) Z_2)))))
% FOF formula (forall (X_14:Prop) (Y_6:Prop) (Z:Prop), ((forall (X_3:Prop) (Y_4:Prop) (Z_1:Prop), ((iff ((semila854092349_inf_o X_3) ((semila10642723_sup_o Y_4) Z_1))) ((semila10642723_sup_o ((semila854092349_inf_o X_3) Y_4)) ((semila854092349_inf_o X_3) Z_1))))->((iff ((semila10642723_sup_o X_14) ((semila854092349_inf_o Y_6) Z))) ((semila854092349_inf_o ((semila10642723_sup_o X_14) Y_6)) ((semila10642723_sup_o X_14) Z))))) of role axiom named fact_1079_distrib__imp1
% A new axiom: (forall (X_14:Prop) (Y_6:Prop) (Z:Prop), ((forall (X_3:Prop) (Y_4:Prop) (Z_1:Prop), ((iff ((semila854092349_inf_o X_3) ((semila10642723_sup_o Y_4) Z_1))) ((semila10642723_sup_o ((semila854092349_inf_o X_3) Y_4)) ((semila854092349_inf_o X_3) Z_1))))->((iff ((semila10642723_sup_o X_14) ((semila854092349_inf_o Y_6) Z))) ((semila854092349_inf_o ((semila10642723_sup_o X_14) Y_6)) ((semila10642723_sup_o X_14) Z)))))
% FOF formula (forall (X_14:(pname->Prop)) (Y_6:(pname->Prop)) (Z:(pname->Prop)), ((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_3) ((semila1780557381name_o Y_4) Z_1))) ((semila1780557381name_o ((semila1673364395name_o X_3) Y_4)) ((semila1673364395name_o X_3) Z_1))))->(((eq (pname->Prop)) ((semila1780557381name_o X_14) ((semila1673364395name_o Y_6) Z))) ((semila1673364395name_o ((semila1780557381name_o X_14) Y_6)) ((semila1780557381name_o X_14) Z))))) of role axiom named fact_1080_distrib__imp1
% A new axiom: (forall (X_14:(pname->Prop)) (Y_6:(pname->Prop)) (Z:(pname->Prop)), ((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_3) ((semila1780557381name_o Y_4) Z_1))) ((semila1780557381name_o ((semila1673364395name_o X_3) Y_4)) ((semila1673364395name_o X_3) Z_1))))->(((eq (pname->Prop)) ((semila1780557381name_o X_14) ((semila1673364395name_o Y_6) Z))) ((semila1673364395name_o ((semila1780557381name_o X_14) Y_6)) ((semila1780557381name_o X_14) Z)))))
% FOF formula (forall (X_14:(hoare_1708887482_state->Prop)) (Y_6:(hoare_1708887482_state->Prop)) (Z:(hoare_1708887482_state->Prop)), ((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)) (Z_1:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_3) ((semila1122118281tate_o Y_4) Z_1))) ((semila1122118281tate_o ((semila129691299tate_o X_3) Y_4)) ((semila129691299tate_o X_3) Z_1))))->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_14) ((semila129691299tate_o Y_6) Z))) ((semila129691299tate_o ((semila1122118281tate_o X_14) Y_6)) ((semila1122118281tate_o X_14) Z))))) of role axiom named fact_1081_distrib__imp1
% A new axiom: (forall (X_14:(hoare_1708887482_state->Prop)) (Y_6:(hoare_1708887482_state->Prop)) (Z:(hoare_1708887482_state->Prop)), ((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)) (Z_1:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_3) ((semila1122118281tate_o Y_4) Z_1))) ((semila1122118281tate_o ((semila129691299tate_o X_3) Y_4)) ((semila129691299tate_o X_3) Z_1))))->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_14) ((semila129691299tate_o Y_6) Z))) ((semila129691299tate_o ((semila1122118281tate_o X_14) Y_6)) ((semila1122118281tate_o X_14) Z)))))
% FOF formula (forall (A_42:(com->Prop)) (B_15:com), ((and (((ord_less_eq_com_o A_42) ((insert_com B_15) bot_bot_com_o))->(((eq com) ((partial_flat_lub_com B_15) A_42)) B_15))) ((((ord_less_eq_com_o A_42) ((insert_com B_15) bot_bot_com_o))->False)->(((eq com) ((partial_flat_lub_com B_15) A_42)) (the_com_1 (fun (X_3:com)=> ((member_com X_3) ((minus_minus_com_o A_42) ((insert_com B_15) bot_bot_com_o))))))))) of role axiom named fact_1082_flat__lub__def
% A new axiom: (forall (A_42:(com->Prop)) (B_15:com), ((and (((ord_less_eq_com_o A_42) ((insert_com B_15) bot_bot_com_o))->(((eq com) ((partial_flat_lub_com B_15) A_42)) B_15))) ((((ord_less_eq_com_o A_42) ((insert_com B_15) bot_bot_com_o))->False)->(((eq com) ((partial_flat_lub_com B_15) A_42)) (the_com_1 (fun (X_3:com)=> ((member_com X_3) ((minus_minus_com_o A_42) ((insert_com B_15) bot_bot_com_o)))))))))
% FOF formula (forall (A_42:(pname->Prop)) (B_15:pname), ((and (((ord_less_eq_pname_o A_42) ((insert_pname B_15) bot_bot_pname_o))->(((eq pname) ((partia752020666_pname B_15) A_42)) B_15))) ((((ord_less_eq_pname_o A_42) ((insert_pname B_15) bot_bot_pname_o))->False)->(((eq pname) ((partia752020666_pname B_15) A_42)) (the_pname (fun (X_3:pname)=> ((member_pname X_3) ((minus_minus_pname_o A_42) ((insert_pname B_15) bot_bot_pname_o))))))))) of role axiom named fact_1083_flat__lub__def
% A new axiom: (forall (A_42:(pname->Prop)) (B_15:pname), ((and (((ord_less_eq_pname_o A_42) ((insert_pname B_15) bot_bot_pname_o))->(((eq pname) ((partia752020666_pname B_15) A_42)) B_15))) ((((ord_less_eq_pname_o A_42) ((insert_pname B_15) bot_bot_pname_o))->False)->(((eq pname) ((partia752020666_pname B_15) A_42)) (the_pname (fun (X_3:pname)=> ((member_pname X_3) ((minus_minus_pname_o A_42) ((insert_pname B_15) bot_bot_pname_o)))))))))
% FOF formula (forall (A_42:(hoare_1708887482_state->Prop)) (B_15:hoare_1708887482_state), ((and (((ord_le777019615tate_o A_42) ((insert528405184_state B_15) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) ((partia1256728516_state B_15) A_42)) B_15))) ((((ord_le777019615tate_o A_42) ((insert528405184_state B_15) bot_bo19817387tate_o))->False)->(((eq hoare_1708887482_state) ((partia1256728516_state B_15) A_42)) (the_Ho851197897_state (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) ((minus_2056855718tate_o A_42) ((insert528405184_state B_15) bot_bo19817387tate_o))))))))) of role axiom named fact_1084_flat__lub__def
% A new axiom: (forall (A_42:(hoare_1708887482_state->Prop)) (B_15:hoare_1708887482_state), ((and (((ord_le777019615tate_o A_42) ((insert528405184_state B_15) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) ((partia1256728516_state B_15) A_42)) B_15))) ((((ord_le777019615tate_o A_42) ((insert528405184_state B_15) bot_bo19817387tate_o))->False)->(((eq hoare_1708887482_state) ((partia1256728516_state B_15) A_42)) (the_Ho851197897_state (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) ((minus_2056855718tate_o A_42) ((insert528405184_state B_15) bot_bo19817387tate_o)))))))))
% FOF formula (finite567462577_com_o (fun (X_3:com) (A_39:(com->Prop))=> ((minus_minus_com_o A_39) ((insert_com X_3) bot_bot_com_o)))) of role axiom named fact_1085_comp__fun__idem__remove
% A new axiom: (finite567462577_com_o (fun (X_3:com) (A_39:(com->Prop))=> ((minus_minus_com_o A_39) ((insert_com X_3) bot_bot_com_o))))
% FOF formula (finite1123817265name_o (fun (X_3:pname) (A_39:(pname->Prop))=> ((minus_minus_pname_o A_39) ((insert_pname X_3) bot_bot_pname_o)))) of role axiom named fact_1086_comp__fun__idem__remove
% A new axiom: (finite1123817265name_o (fun (X_3:pname) (A_39:(pname->Prop))=> ((minus_minus_pname_o A_39) ((insert_pname X_3) bot_bot_pname_o))))
% FOF formula (finite662762081tate_o (fun (X_3:hoare_1708887482_state) (A_39:(hoare_1708887482_state->Prop))=> ((minus_2056855718tate_o A_39) ((insert528405184_state X_3) bot_bo19817387tate_o)))) of role axiom named fact_1087_comp__fun__idem__remove
% A new axiom: (finite662762081tate_o (fun (X_3:hoare_1708887482_state) (A_39:(hoare_1708887482_state->Prop))=> ((minus_2056855718tate_o A_39) ((insert528405184_state X_3) bot_bo19817387tate_o))))
% FOF formula (forall (F_22:(pname->hoare_1708887482_state)) (Y_5:hoare_1708887482_state) (X_13:pname) (A_41:(pname->Prop)), ((and (((member_pname X_13) A_41)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (((fun_up1986763201_state F_22) X_13) Y_5)) A_41)) ((insert528405184_state Y_5) ((image_1116629049_state F_22) ((minus_minus_pname_o A_41) ((insert_pname X_13) bot_bot_pname_o))))))) ((((member_pname X_13) A_41)->False)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (((fun_up1986763201_state F_22) X_13) Y_5)) A_41)) ((image_1116629049_state F_22) A_41))))) of role axiom named fact_1088_fun__upd__image
% A new axiom: (forall (F_22:(pname->hoare_1708887482_state)) (Y_5:hoare_1708887482_state) (X_13:pname) (A_41:(pname->Prop)), ((and (((member_pname X_13) A_41)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (((fun_up1986763201_state F_22) X_13) Y_5)) A_41)) ((insert528405184_state Y_5) ((image_1116629049_state F_22) ((minus_minus_pname_o A_41) ((insert_pname X_13) bot_bot_pname_o))))))) ((((member_pname X_13) A_41)->False)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (((fun_up1986763201_state F_22) X_13) Y_5)) A_41)) ((image_1116629049_state F_22) A_41)))))
% FOF formula (finite567462577_com_o insert_com) of role axiom named fact_1089_comp__fun__idem__insert
% A new axiom: (finite567462577_com_o insert_com)
% FOF formula (finite1123817265name_o insert_pname) of role axiom named fact_1090_comp__fun__idem__insert
% A new axiom: (finite1123817265name_o insert_pname)
% FOF formula (finite662762081tate_o insert528405184_state) of role axiom named fact_1091_comp__fun__idem__insert
% A new axiom: (finite662762081tate_o insert528405184_state)
% FOF formula (finite2048025996em_o_o semila10642723_sup_o) of role axiom named fact_1092_comp__fun__idem__sup
% A new axiom: (finite2048025996em_o_o semila10642723_sup_o)
% FOF formula (finite138924780name_o semila1780557381name_o) of role axiom named fact_1093_comp__fun__idem__sup
% A new axiom: (finite138924780name_o semila1780557381name_o)
% FOF formula (finite2034616076tate_o semila1122118281tate_o) of role axiom named fact_1094_comp__fun__idem__sup
% A new axiom: (finite2034616076tate_o semila1122118281tate_o)
% FOF formula (forall (F_21:(pname->hoare_1708887482_state)) (A_40:(pname->Prop)) (B_14:(pname->Prop)), ((iff ((inj_on1553129421_state F_21) ((semila1780557381name_o A_40) B_14))) ((and ((and ((inj_on1553129421_state F_21) A_40)) ((inj_on1553129421_state F_21) B_14))) (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((image_1116629049_state F_21) ((minus_minus_pname_o A_40) B_14))) ((image_1116629049_state F_21) ((minus_minus_pname_o B_14) A_40)))) bot_bo19817387tate_o)))) of role axiom named fact_1095_inj__on__Un
% A new axiom: (forall (F_21:(pname->hoare_1708887482_state)) (A_40:(pname->Prop)) (B_14:(pname->Prop)), ((iff ((inj_on1553129421_state F_21) ((semila1780557381name_o A_40) B_14))) ((and ((and ((inj_on1553129421_state F_21) A_40)) ((inj_on1553129421_state F_21) B_14))) (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((image_1116629049_state F_21) ((minus_minus_pname_o A_40) B_14))) ((image_1116629049_state F_21) ((minus_minus_pname_o B_14) A_40)))) bot_bo19817387tate_o))))
% FOF formula (forall (F_20:(pname->option_com)) (X_12:pname), ((iff (((eq (pname->Prop)) (dom_pname_com F_20)) ((insert_pname X_12) bot_bot_pname_o))) ((ex com) (fun (V:com)=> (((eq (pname->option_com)) F_20) (((fun_up879233478on_com (fun (X_3:pname)=> none_com)) X_12) (some_com V))))))) of role axiom named fact_1096_dom__eq__singleton__conv
% A new axiom: (forall (F_20:(pname->option_com)) (X_12:pname), ((iff (((eq (pname->Prop)) (dom_pname_com F_20)) ((insert_pname X_12) bot_bot_pname_o))) ((ex com) (fun (V:com)=> (((eq (pname->option_com)) F_20) (((fun_up879233478on_com (fun (X_3:pname)=> none_com)) X_12) (some_com V)))))))
% FOF formula (forall (B_13:(com->Prop)) (A_38:(com->Prop)), ((finite_finite_com A_38)->(((eq (com->Prop)) ((minus_minus_com_o B_13) A_38)) (((finite504235573_com_o (fun (X_3:com) (A_39:(com->Prop))=> ((minus_minus_com_o A_39) ((insert_com X_3) bot_bot_com_o)))) B_13) A_38)))) of role axiom named fact_1097_minus__fold__remove
% A new axiom: (forall (B_13:(com->Prop)) (A_38:(com->Prop)), ((finite_finite_com A_38)->(((eq (com->Prop)) ((minus_minus_com_o B_13) A_38)) (((finite504235573_com_o (fun (X_3:com) (A_39:(com->Prop))=> ((minus_minus_com_o A_39) ((insert_com X_3) bot_bot_com_o)))) B_13) A_38))))
% FOF formula (forall (B_13:(pname->Prop)) (A_38:(pname->Prop)), ((finite_finite_pname A_38)->(((eq (pname->Prop)) ((minus_minus_pname_o B_13) A_38)) (((finite603803317name_o (fun (X_3:pname) (A_39:(pname->Prop))=> ((minus_minus_pname_o A_39) ((insert_pname X_3) bot_bot_pname_o)))) B_13) A_38)))) of role axiom named fact_1098_minus__fold__remove
% A new axiom: (forall (B_13:(pname->Prop)) (A_38:(pname->Prop)), ((finite_finite_pname A_38)->(((eq (pname->Prop)) ((minus_minus_pname_o B_13) A_38)) (((finite603803317name_o (fun (X_3:pname) (A_39:(pname->Prop))=> ((minus_minus_pname_o A_39) ((insert_pname X_3) bot_bot_pname_o)))) B_13) A_38))))
% FOF formula (forall (B_13:(hoare_1708887482_state->Prop)) (A_38:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_38)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o B_13) A_38)) (((finite96880613tate_o (fun (X_3:hoare_1708887482_state) (A_39:(hoare_1708887482_state->Prop))=> ((minus_2056855718tate_o A_39) ((insert528405184_state X_3) bot_bo19817387tate_o)))) B_13) A_38)))) of role axiom named fact_1099_minus__fold__remove
% A new axiom: (forall (B_13:(hoare_1708887482_state->Prop)) (A_38:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_38)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o B_13) A_38)) (((finite96880613tate_o (fun (X_3:hoare_1708887482_state) (A_39:(hoare_1708887482_state->Prop))=> ((minus_2056855718tate_o A_39) ((insert528405184_state X_3) bot_bo19817387tate_o)))) B_13) A_38))))
% FOF formula (forall (B_13:((pname->Prop)->Prop)) (A_38:((pname->Prop)->Prop)), ((finite297249702name_o A_38)->(((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o B_13) A_38)) (((finite1849951719me_o_o (fun (X_3:(pname->Prop)) (A_39:((pname->Prop)->Prop))=> ((minus_1480864103me_o_o A_39) ((insert_pname_o X_3) bot_bot_pname_o_o)))) B_13) A_38)))) of role axiom named fact_1100_minus__fold__remove
% A new axiom: (forall (B_13:((pname->Prop)->Prop)) (A_38:((pname->Prop)->Prop)), ((finite297249702name_o A_38)->(((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o B_13) A_38)) (((finite1849951719me_o_o (fun (X_3:(pname->Prop)) (A_39:((pname->Prop)->Prop))=> ((minus_1480864103me_o_o A_39) ((insert_pname_o X_3) bot_bot_pname_o_o)))) B_13) A_38))))
% FOF formula (forall (B_13:((hoare_1708887482_state->Prop)->Prop)) (A_38:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_38)->(((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o B_13) A_38)) (((finite463603445te_o_o (fun (X_3:(hoare_1708887482_state->Prop)) (A_39:((hoare_1708887482_state->Prop)->Prop))=> ((minus_548038231te_o_o A_39) ((insert949073679tate_o X_3) bot_bo1678742418te_o_o)))) B_13) A_38)))) of role axiom named fact_1101_minus__fold__remove
% A new axiom: (forall (B_13:((hoare_1708887482_state->Prop)->Prop)) (A_38:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_38)->(((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o B_13) A_38)) (((finite463603445te_o_o (fun (X_3:(hoare_1708887482_state->Prop)) (A_39:((hoare_1708887482_state->Prop)->Prop))=> ((minus_548038231te_o_o A_39) ((insert949073679tate_o X_3) bot_bo1678742418te_o_o)))) B_13) A_38))))
% FOF formula (forall (F_19:(pname->hoare_1708887482_state)) (A_37:(pname->Prop)), ((finite_finite_pname A_37)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_19) A_37)) ((((finite2139561282_pname semila1122118281tate_o) (fun (X_3:pname)=> ((insert528405184_state (F_19 X_3)) bot_bo19817387tate_o))) bot_bo19817387tate_o) A_37)))) of role axiom named fact_1102_image__eq__fold__image
% A new axiom: (forall (F_19:(pname->hoare_1708887482_state)) (A_37:(pname->Prop)), ((finite_finite_pname A_37)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_19) A_37)) ((((finite2139561282_pname semila1122118281tate_o) (fun (X_3:pname)=> ((insert528405184_state (F_19 X_3)) bot_bo19817387tate_o))) bot_bo19817387tate_o) A_37))))
% FOF formula (forall (A_36:(pname->Prop)), ((inj_on737724108_pname some_pname) A_36)) of role axiom named fact_1103_inj__Some
% A new axiom: (forall (A_36:(pname->Prop)), ((inj_on737724108_pname some_pname) A_36))
% FOF formula (forall (A_36:(hoare_1708887482_state->Prop)), ((inj_on945311362_state some_H1974565227_state) A_36)) of role axiom named fact_1104_inj__Some
% A new axiom: (forall (A_36:(hoare_1708887482_state->Prop)), ((inj_on945311362_state some_H1974565227_state) A_36))
% FOF formula (forall (A_36:(com->Prop)), ((inj_on11367768on_com some_com) A_36)) of role axiom named fact_1105_inj__Some
% A new axiom: (forall (A_36:(com->Prop)), ((inj_on11367768on_com some_com) A_36))
% FOF formula (forall (A_35:com), (not (((eq option_com) none_com) (some_com A_35)))) of role axiom named fact_1106_option_Osimps_I2_J
% A new axiom: (forall (A_35:com), (not (((eq option_com) none_com) (some_com A_35))))
% FOF formula (forall (A_35:pname), (not (((eq option_pname) none_pname) (some_pname A_35)))) of role axiom named fact_1107_option_Osimps_I2_J
% A new axiom: (forall (A_35:pname), (not (((eq option_pname) none_pname) (some_pname A_35))))
% FOF formula (forall (A_35:hoare_1708887482_state), (not (((eq option1624383643_state) none_H1106584047_state) (some_H1974565227_state A_35)))) of role axiom named fact_1108_option_Osimps_I2_J
% A new axiom: (forall (A_35:hoare_1708887482_state), (not (((eq option1624383643_state) none_H1106584047_state) (some_H1974565227_state A_35))))
% FOF formula (forall (A_34:com), (not (((eq option_com) (some_com A_34)) none_com))) of role axiom named fact_1109_option_Osimps_I3_J
% A new axiom: (forall (A_34:com), (not (((eq option_com) (some_com A_34)) none_com)))
% FOF formula (forall (A_34:pname), (not (((eq option_pname) (some_pname A_34)) none_pname))) of role axiom named fact_1110_option_Osimps_I3_J
% A new axiom: (forall (A_34:pname), (not (((eq option_pname) (some_pname A_34)) none_pname)))
% FOF formula (forall (A_34:hoare_1708887482_state), (not (((eq option1624383643_state) (some_H1974565227_state A_34)) none_H1106584047_state))) of role axiom named fact_1111_option_Osimps_I3_J
% A new axiom: (forall (A_34:hoare_1708887482_state), (not (((eq option1624383643_state) (some_H1974565227_state A_34)) none_H1106584047_state)))
% FOF formula (forall (X_11:option_com), ((iff (forall (Y_4:com), (not (((eq option_com) X_11) (some_com Y_4))))) (((eq option_com) X_11) none_com))) of role axiom named fact_1112_not__Some__eq
% A new axiom: (forall (X_11:option_com), ((iff (forall (Y_4:com), (not (((eq option_com) X_11) (some_com Y_4))))) (((eq option_com) X_11) none_com)))
% FOF formula (forall (X_11:option_pname), ((iff (forall (Y_4:pname), (not (((eq option_pname) X_11) (some_pname Y_4))))) (((eq option_pname) X_11) none_pname))) of role axiom named fact_1113_not__Some__eq
% A new axiom: (forall (X_11:option_pname), ((iff (forall (Y_4:pname), (not (((eq option_pname) X_11) (some_pname Y_4))))) (((eq option_pname) X_11) none_pname)))
% FOF formula (forall (X_11:option1624383643_state), ((iff (forall (Y_4:hoare_1708887482_state), (not (((eq option1624383643_state) X_11) (some_H1974565227_state Y_4))))) (((eq option1624383643_state) X_11) none_H1106584047_state))) of role axiom named fact_1114_not__Some__eq
% A new axiom: (forall (X_11:option1624383643_state), ((iff (forall (Y_4:hoare_1708887482_state), (not (((eq option1624383643_state) X_11) (some_H1974565227_state Y_4))))) (((eq option1624383643_state) X_11) none_H1106584047_state)))
% FOF formula (forall (X_10:option_com), ((iff (not (((eq option_com) X_10) none_com))) ((ex com) (fun (Y_4:com)=> (((eq option_com) X_10) (some_com Y_4)))))) of role axiom named fact_1115_not__None__eq
% A new axiom: (forall (X_10:option_com), ((iff (not (((eq option_com) X_10) none_com))) ((ex com) (fun (Y_4:com)=> (((eq option_com) X_10) (some_com Y_4))))))
% FOF formula (forall (X_10:option_pname), ((iff (not (((eq option_pname) X_10) none_pname))) ((ex pname) (fun (Y_4:pname)=> (((eq option_pname) X_10) (some_pname Y_4)))))) of role axiom named fact_1116_not__None__eq
% A new axiom: (forall (X_10:option_pname), ((iff (not (((eq option_pname) X_10) none_pname))) ((ex pname) (fun (Y_4:pname)=> (((eq option_pname) X_10) (some_pname Y_4))))))
% FOF formula (forall (X_10:option1624383643_state), ((iff (not (((eq option1624383643_state) X_10) none_H1106584047_state))) ((ex hoare_1708887482_state) (fun (Y_4:hoare_1708887482_state)=> (((eq option1624383643_state) X_10) (some_H1974565227_state Y_4)))))) of role axiom named fact_1117_not__None__eq
% A new axiom: (forall (X_10:option1624383643_state), ((iff (not (((eq option1624383643_state) X_10) none_H1106584047_state))) ((ex hoare_1708887482_state) (fun (Y_4:hoare_1708887482_state)=> (((eq option1624383643_state) X_10) (some_H1974565227_state Y_4))))))
% FOF formula (forall (M_2:(pname->option_com)), (((eq (pname->Prop)) (dom_pname_com M_2)) (collect_pname (fun (A_6:pname)=> (not (((eq option_com) (M_2 A_6)) none_com)))))) of role axiom named fact_1118_dom__def
% A new axiom: (forall (M_2:(pname->option_com)), (((eq (pname->Prop)) (dom_pname_com M_2)) (collect_pname (fun (A_6:pname)=> (not (((eq option_com) (M_2 A_6)) none_com))))))
% FOF formula (forall (A_33:pname) (M_1:(pname->option_com)), ((iff ((member_pname A_33) (dom_pname_com M_1))) (not (((eq option_com) (M_1 A_33)) none_com)))) of role axiom named fact_1119_domIff
% A new axiom: (forall (A_33:pname) (M_1:(pname->option_com)), ((iff ((member_pname A_33) (dom_pname_com M_1))) (not (((eq option_com) (M_1 A_33)) none_com))))
% FOF formula (forall (F_18:(pname->hoare_1708887482_state)) (A_32:(pname->Prop)), ((finite1625599783_state ((image_1116629049_state F_18) A_32))->(((inj_on1553129421_state F_18) A_32)->(finite_finite_pname A_32)))) of role axiom named fact_1120_finite__imageD
% A new axiom: (forall (F_18:(pname->hoare_1708887482_state)) (A_32:(pname->Prop)), ((finite1625599783_state ((image_1116629049_state F_18) A_32))->(((inj_on1553129421_state F_18) A_32)->(finite_finite_pname A_32))))
% FOF formula (forall (F_17:(pname->hoare_1708887482_state)) (A_31:(pname->Prop)) (B_12:(pname->Prop)), (((inj_on1553129421_state F_17) ((semila1780557381name_o A_31) B_12))->((iff (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_17) A_31)) ((image_1116629049_state F_17) B_12))) (((eq (pname->Prop)) A_31) B_12)))) of role axiom named fact_1121_inj__on__Un__image__eq__iff
% A new axiom: (forall (F_17:(pname->hoare_1708887482_state)) (A_31:(pname->Prop)) (B_12:(pname->Prop)), (((inj_on1553129421_state F_17) ((semila1780557381name_o A_31) B_12))->((iff (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_17) A_31)) ((image_1116629049_state F_17) B_12))) (((eq (pname->Prop)) A_31) B_12))))
% FOF formula (forall (X_9:option_com), ((iff (is_none_com X_9)) (((eq option_com) X_9) none_com))) of role axiom named fact_1122_is__none__def
% A new axiom: (forall (X_9:option_com), ((iff (is_none_com X_9)) (((eq option_com) X_9) none_com)))
% FOF formula (is_none_com none_com) of role axiom named fact_1123_is__none__code_I1_J
% A new axiom: (is_none_com none_com)
% FOF formula (forall (X_8:pname) (Y_3:hoare_1708887482_state) (F_16:(pname->hoare_1708887482_state)) (A_30:(pname->Prop)), (((inj_on1553129421_state F_16) A_30)->((((member451959335_state Y_3) ((image_1116629049_state F_16) A_30))->False)->((inj_on1553129421_state (((fun_up1986763201_state F_16) X_8) Y_3)) A_30)))) of role axiom named fact_1124_inj__on__fun__updI
% A new axiom: (forall (X_8:pname) (Y_3:hoare_1708887482_state) (F_16:(pname->hoare_1708887482_state)) (A_30:(pname->Prop)), (((inj_on1553129421_state F_16) A_30)->((((member451959335_state Y_3) ((image_1116629049_state F_16) A_30))->False)->((inj_on1553129421_state (((fun_up1986763201_state F_16) X_8) Y_3)) A_30))))
% FOF formula (forall (B_11:(pname->Prop)) (A_29:(pname->Prop)) (A_28:((pname->Prop)->Prop)), ((finite297249702name_o A_28)->(((member_pname_o A_29) A_28)->((ord_less_eq_pname_o ((semila1780557381name_o A_29) B_11)) (((finite472615016name_o semila1780557381name_o) B_11) A_28))))) of role axiom named fact_1125_sup__le__fold__sup
% A new axiom: (forall (B_11:(pname->Prop)) (A_29:(pname->Prop)) (A_28:((pname->Prop)->Prop)), ((finite297249702name_o A_28)->(((member_pname_o A_29) A_28)->((ord_less_eq_pname_o ((semila1780557381name_o A_29) B_11)) (((finite472615016name_o semila1780557381name_o) B_11) A_28)))))
% FOF formula (forall (B_11:(hoare_1708887482_state->Prop)) (A_29:(hoare_1708887482_state->Prop)) (A_28:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_28)->(((member814030440tate_o A_29) A_28)->((ord_le777019615tate_o ((semila1122118281tate_o A_29) B_11)) (((finite822533768tate_o semila1122118281tate_o) B_11) A_28))))) of role axiom named fact_1126_sup__le__fold__sup
% A new axiom: (forall (B_11:(hoare_1708887482_state->Prop)) (A_29:(hoare_1708887482_state->Prop)) (A_28:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_28)->(((member814030440tate_o A_29) A_28)->((ord_le777019615tate_o ((semila1122118281tate_o A_29) B_11)) (((finite822533768tate_o semila1122118281tate_o) B_11) A_28)))))
% FOF formula (forall (B_11:Prop) (A_29:Prop) (A_28:(Prop->Prop)), ((finite_finite_o A_28)->(((member_o A_29) A_28)->((ord_less_eq_o ((semila10642723_sup_o A_29) B_11)) (((finite_fold_o_o semila10642723_sup_o) B_11) A_28))))) of role axiom named fact_1127_sup__le__fold__sup
% A new axiom: (forall (B_11:Prop) (A_29:Prop) (A_28:(Prop->Prop)), ((finite_finite_o A_28)->(((member_o A_29) A_28)->((ord_less_eq_o ((semila10642723_sup_o A_29) B_11)) (((finite_fold_o_o semila10642723_sup_o) B_11) A_28)))))
% FOF formula (forall (B_10:(pname->Prop)) (A_27:(pname->Prop)) (A_26:((pname->Prop)->Prop)), ((finite297249702name_o A_26)->(((member_pname_o A_27) A_26)->((ord_less_eq_pname_o (((finite472615016name_o semila1673364395name_o) B_10) A_26)) ((semila1673364395name_o A_27) B_10))))) of role axiom named fact_1128_fold__inf__le__inf
% A new axiom: (forall (B_10:(pname->Prop)) (A_27:(pname->Prop)) (A_26:((pname->Prop)->Prop)), ((finite297249702name_o A_26)->(((member_pname_o A_27) A_26)->((ord_less_eq_pname_o (((finite472615016name_o semila1673364395name_o) B_10) A_26)) ((semila1673364395name_o A_27) B_10)))))
% FOF formula (forall (B_10:(hoare_1708887482_state->Prop)) (A_27:(hoare_1708887482_state->Prop)) (A_26:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_26)->(((member814030440tate_o A_27) A_26)->((ord_le777019615tate_o (((finite822533768tate_o semila129691299tate_o) B_10) A_26)) ((semila129691299tate_o A_27) B_10))))) of role axiom named fact_1129_fold__inf__le__inf
% A new axiom: (forall (B_10:(hoare_1708887482_state->Prop)) (A_27:(hoare_1708887482_state->Prop)) (A_26:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_26)->(((member814030440tate_o A_27) A_26)->((ord_le777019615tate_o (((finite822533768tate_o semila129691299tate_o) B_10) A_26)) ((semila129691299tate_o A_27) B_10)))))
% FOF formula (forall (B_10:Prop) (A_27:Prop) (A_26:(Prop->Prop)), ((finite_finite_o A_26)->(((member_o A_27) A_26)->((ord_less_eq_o (((finite_fold_o_o semila854092349_inf_o) B_10) A_26)) ((semila854092349_inf_o A_27) B_10))))) of role axiom named fact_1130_fold__inf__le__inf
% A new axiom: (forall (B_10:Prop) (A_27:Prop) (A_26:(Prop->Prop)), ((finite_finite_o A_26)->(((member_o A_27) A_26)->((ord_less_eq_o (((finite_fold_o_o semila854092349_inf_o) B_10) A_26)) ((semila854092349_inf_o A_27) B_10)))))
% FOF formula (forall (B_9:(pname->Prop)) (A_25:(pname->Prop)) (A_24:((pname->Prop)->Prop)), ((finite297249702name_o A_24)->(((eq (pname->Prop)) (((finite472615016name_o semila1780557381name_o) B_9) ((insert_pname_o A_25) A_24))) ((semila1780557381name_o A_25) (((finite472615016name_o semila1780557381name_o) B_9) A_24))))) of role axiom named fact_1131_fold__sup__insert
% A new axiom: (forall (B_9:(pname->Prop)) (A_25:(pname->Prop)) (A_24:((pname->Prop)->Prop)), ((finite297249702name_o A_24)->(((eq (pname->Prop)) (((finite472615016name_o semila1780557381name_o) B_9) ((insert_pname_o A_25) A_24))) ((semila1780557381name_o A_25) (((finite472615016name_o semila1780557381name_o) B_9) A_24)))))
% FOF formula (forall (B_9:(hoare_1708887482_state->Prop)) (A_25:(hoare_1708887482_state->Prop)) (A_24:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_24)->(((eq (hoare_1708887482_state->Prop)) (((finite822533768tate_o semila1122118281tate_o) B_9) ((insert949073679tate_o A_25) A_24))) ((semila1122118281tate_o A_25) (((finite822533768tate_o semila1122118281tate_o) B_9) A_24))))) of role axiom named fact_1132_fold__sup__insert
% A new axiom: (forall (B_9:(hoare_1708887482_state->Prop)) (A_25:(hoare_1708887482_state->Prop)) (A_24:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_24)->(((eq (hoare_1708887482_state->Prop)) (((finite822533768tate_o semila1122118281tate_o) B_9) ((insert949073679tate_o A_25) A_24))) ((semila1122118281tate_o A_25) (((finite822533768tate_o semila1122118281tate_o) B_9) A_24)))))
% FOF formula (forall (B_9:Prop) (A_25:Prop) (A_24:(Prop->Prop)), ((finite_finite_o A_24)->((iff (((finite_fold_o_o semila10642723_sup_o) B_9) ((insert_o A_25) A_24))) ((semila10642723_sup_o A_25) (((finite_fold_o_o semila10642723_sup_o) B_9) A_24))))) of role axiom named fact_1133_fold__sup__insert
% A new axiom: (forall (B_9:Prop) (A_25:Prop) (A_24:(Prop->Prop)), ((finite_finite_o A_24)->((iff (((finite_fold_o_o semila10642723_sup_o) B_9) ((insert_o A_25) A_24))) ((semila10642723_sup_o A_25) (((finite_fold_o_o semila10642723_sup_o) B_9) A_24)))))
% FOF formula (forall (B_8:(pname->Prop)) (A_23:(pname->Prop)) (A_22:((pname->Prop)->Prop)), ((finite297249702name_o A_22)->(((eq (pname->Prop)) (((finite472615016name_o semila1673364395name_o) B_8) ((insert_pname_o A_23) A_22))) ((semila1673364395name_o A_23) (((finite472615016name_o semila1673364395name_o) B_8) A_22))))) of role axiom named fact_1134_fold__inf__insert
% A new axiom: (forall (B_8:(pname->Prop)) (A_23:(pname->Prop)) (A_22:((pname->Prop)->Prop)), ((finite297249702name_o A_22)->(((eq (pname->Prop)) (((finite472615016name_o semila1673364395name_o) B_8) ((insert_pname_o A_23) A_22))) ((semila1673364395name_o A_23) (((finite472615016name_o semila1673364395name_o) B_8) A_22)))))
% FOF formula (forall (B_8:(hoare_1708887482_state->Prop)) (A_23:(hoare_1708887482_state->Prop)) (A_22:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_22)->(((eq (hoare_1708887482_state->Prop)) (((finite822533768tate_o semila129691299tate_o) B_8) ((insert949073679tate_o A_23) A_22))) ((semila129691299tate_o A_23) (((finite822533768tate_o semila129691299tate_o) B_8) A_22))))) of role axiom named fact_1135_fold__inf__insert
% A new axiom: (forall (B_8:(hoare_1708887482_state->Prop)) (A_23:(hoare_1708887482_state->Prop)) (A_22:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_22)->(((eq (hoare_1708887482_state->Prop)) (((finite822533768tate_o semila129691299tate_o) B_8) ((insert949073679tate_o A_23) A_22))) ((semila129691299tate_o A_23) (((finite822533768tate_o semila129691299tate_o) B_8) A_22)))))
% FOF formula (forall (F_15:(pname->option_com)), ((iff (((eq (pname->Prop)) (dom_pname_com F_15)) bot_bot_pname_o)) (forall (X_3:pname), (((eq option_com) (F_15 X_3)) none_com)))) of role axiom named fact_1136_dom__eq__empty__conv
% A new axiom: (forall (F_15:(pname->option_com)), ((iff (((eq (pname->Prop)) (dom_pname_com F_15)) bot_bot_pname_o)) (forall (X_3:pname), (((eq option_com) (F_15 X_3)) none_com))))
% FOF formula (((eq (pname->Prop)) (dom_pname_com (fun (X_3:pname)=> none_com))) bot_bot_pname_o) of role axiom named fact_1137_dom__empty
% A new axiom: (((eq (pname->Prop)) (dom_pname_com (fun (X_3:pname)=> none_com))) bot_bot_pname_o)
% FOF formula (((eq (com->Prop)) (set_com none_com)) bot_bot_com_o) of role axiom named fact_1138_Option_Oset_Osimps_I1_J
% A new axiom: (((eq (com->Prop)) (set_com none_com)) bot_bot_com_o)
% FOF formula (((eq (pname->Prop)) (set_pname none_pname)) bot_bot_pname_o) of role axiom named fact_1139_Option_Oset_Osimps_I1_J
% A new axiom: (((eq (pname->Prop)) (set_pname none_pname)) bot_bot_pname_o)
% FOF formula (((eq (hoare_1708887482_state->Prop)) (set_Ho525251890_state none_H1106584047_state)) bot_bo19817387tate_o) of role axiom named fact_1140_Option_Oset_Osimps_I1_J
% A new axiom: (((eq (hoare_1708887482_state->Prop)) (set_Ho525251890_state none_H1106584047_state)) bot_bo19817387tate_o)
% FOF formula (forall (Xo:option_com), ((iff (((eq (com->Prop)) (set_com Xo)) bot_bot_com_o)) (((eq option_com) Xo) none_com))) of role axiom named fact_1141_set__empty__eq
% A new axiom: (forall (Xo:option_com), ((iff (((eq (com->Prop)) (set_com Xo)) bot_bot_com_o)) (((eq option_com) Xo) none_com)))
% FOF formula (forall (Xo:option_pname), ((iff (((eq (pname->Prop)) (set_pname Xo)) bot_bot_pname_o)) (((eq option_pname) Xo) none_pname))) of role axiom named fact_1142_set__empty__eq
% A new axiom: (forall (Xo:option_pname), ((iff (((eq (pname->Prop)) (set_pname Xo)) bot_bot_pname_o)) (((eq option_pname) Xo) none_pname)))
% FOF formula (forall (Xo:option1624383643_state), ((iff (((eq (hoare_1708887482_state->Prop)) (set_Ho525251890_state Xo)) bot_bo19817387tate_o)) (((eq option1624383643_state) Xo) none_H1106584047_state))) of role axiom named fact_1143_set__empty__eq
% A new axiom: (forall (Xo:option1624383643_state), ((iff (((eq (hoare_1708887482_state->Prop)) (set_Ho525251890_state Xo)) bot_bo19817387tate_o)) (((eq option1624383643_state) Xo) none_H1106584047_state)))
% FOF formula (forall (F_14:((pname->Prop)->(pname->Prop))) (A_21:((pname->Prop)->Prop)), ((finite297249702name_o A_21)->(((ord_le1205211808me_o_o ((image_1085733413name_o F_14) A_21)) A_21)->(((inj_on691924881name_o F_14) A_21)->(((eq ((pname->Prop)->Prop)) ((image_1085733413name_o F_14) A_21)) A_21))))) of role axiom named fact_1144_endo__inj__surj
% A new axiom: (forall (F_14:((pname->Prop)->(pname->Prop))) (A_21:((pname->Prop)->Prop)), ((finite297249702name_o A_21)->(((ord_le1205211808me_o_o ((image_1085733413name_o F_14) A_21)) A_21)->(((inj_on691924881name_o F_14) A_21)->(((eq ((pname->Prop)->Prop)) ((image_1085733413name_o F_14) A_21)) A_21)))))
% FOF formula (forall (F_14:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (A_21:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_21)->(((ord_le1728773982te_o_o ((image_909543877tate_o F_14) A_21)) A_21)->(((inj_on176908593tate_o F_14) A_21)->(((eq ((hoare_1708887482_state->Prop)->Prop)) ((image_909543877tate_o F_14) A_21)) A_21))))) of role axiom named fact_1145_endo__inj__surj
% A new axiom: (forall (F_14:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (A_21:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_21)->(((ord_le1728773982te_o_o ((image_909543877tate_o F_14) A_21)) A_21)->(((inj_on176908593tate_o F_14) A_21)->(((eq ((hoare_1708887482_state->Prop)->Prop)) ((image_909543877tate_o F_14) A_21)) A_21)))))
% FOF formula (forall (F_14:(pname->pname)) (A_21:(pname->Prop)), ((finite_finite_pname A_21)->(((ord_less_eq_pname_o ((image_pname_pname F_14) A_21)) A_21)->(((inj_on_pname_pname F_14) A_21)->(((eq (pname->Prop)) ((image_pname_pname F_14) A_21)) A_21))))) of role axiom named fact_1146_endo__inj__surj
% A new axiom: (forall (F_14:(pname->pname)) (A_21:(pname->Prop)), ((finite_finite_pname A_21)->(((ord_less_eq_pname_o ((image_pname_pname F_14) A_21)) A_21)->(((inj_on_pname_pname F_14) A_21)->(((eq (pname->Prop)) ((image_pname_pname F_14) A_21)) A_21)))))
% FOF formula (forall (F_14:(hoare_1708887482_state->hoare_1708887482_state)) (A_21:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_21)->(((ord_le777019615tate_o ((image_757158439_state F_14) A_21)) A_21)->(((inj_on632008595_state F_14) A_21)->(((eq (hoare_1708887482_state->Prop)) ((image_757158439_state F_14) A_21)) A_21))))) of role axiom named fact_1147_endo__inj__surj
% A new axiom: (forall (F_14:(hoare_1708887482_state->hoare_1708887482_state)) (A_21:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_21)->(((ord_le777019615tate_o ((image_757158439_state F_14) A_21)) A_21)->(((inj_on632008595_state F_14) A_21)->(((eq (hoare_1708887482_state->Prop)) ((image_757158439_state F_14) A_21)) A_21)))))
% FOF formula (forall (F_13:((pname->Prop)->(pname->Prop))) (A_20:((pname->Prop)->Prop)), ((finite297249702name_o A_20)->(((ord_le1205211808me_o_o A_20) ((image_1085733413name_o F_13) A_20))->((inj_on691924881name_o F_13) A_20)))) of role axiom named fact_1148_finite__surj__inj
% A new axiom: (forall (F_13:((pname->Prop)->(pname->Prop))) (A_20:((pname->Prop)->Prop)), ((finite297249702name_o A_20)->(((ord_le1205211808me_o_o A_20) ((image_1085733413name_o F_13) A_20))->((inj_on691924881name_o F_13) A_20))))
% FOF formula (forall (F_13:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (A_20:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_20)->(((ord_le1728773982te_o_o A_20) ((image_909543877tate_o F_13) A_20))->((inj_on176908593tate_o F_13) A_20)))) of role axiom named fact_1149_finite__surj__inj
% A new axiom: (forall (F_13:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (A_20:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_20)->(((ord_le1728773982te_o_o A_20) ((image_909543877tate_o F_13) A_20))->((inj_on176908593tate_o F_13) A_20))))
% FOF formula (forall (F_13:(pname->pname)) (A_20:(pname->Prop)), ((finite_finite_pname A_20)->(((ord_less_eq_pname_o A_20) ((image_pname_pname F_13) A_20))->((inj_on_pname_pname F_13) A_20)))) of role axiom named fact_1150_finite__surj__inj
% A new axiom: (forall (F_13:(pname->pname)) (A_20:(pname->Prop)), ((finite_finite_pname A_20)->(((ord_less_eq_pname_o A_20) ((image_pname_pname F_13) A_20))->((inj_on_pname_pname F_13) A_20))))
% FOF formula (forall (F_13:(hoare_1708887482_state->hoare_1708887482_state)) (A_20:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_20)->(((ord_le777019615tate_o A_20) ((image_757158439_state F_13) A_20))->((inj_on632008595_state F_13) A_20)))) of role axiom named fact_1151_finite__surj__inj
% A new axiom: (forall (F_13:(hoare_1708887482_state->hoare_1708887482_state)) (A_20:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_20)->(((ord_le777019615tate_o A_20) ((image_757158439_state F_13) A_20))->((inj_on632008595_state F_13) A_20))))
% FOF formula (forall (B_7:(pname->Prop)) (A_19:(pname->Prop)) (F_12:(pname->hoare_1708887482_state)) (C_3:(pname->Prop)), (((inj_on1553129421_state F_12) C_3)->(((ord_less_eq_pname_o A_19) C_3)->(((ord_less_eq_pname_o B_7) C_3)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_12) ((semila1673364395name_o A_19) B_7))) ((semila129691299tate_o ((image_1116629049_state F_12) A_19)) ((image_1116629049_state F_12) B_7))))))) of role axiom named fact_1152_inj__on__image__Int
% A new axiom: (forall (B_7:(pname->Prop)) (A_19:(pname->Prop)) (F_12:(pname->hoare_1708887482_state)) (C_3:(pname->Prop)), (((inj_on1553129421_state F_12) C_3)->(((ord_less_eq_pname_o A_19) C_3)->(((ord_less_eq_pname_o B_7) C_3)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_12) ((semila1673364395name_o A_19) B_7))) ((semila129691299tate_o ((image_1116629049_state F_12) A_19)) ((image_1116629049_state F_12) B_7)))))))
% FOF formula (forall (B_6:(pname->Prop)) (A_18:(pname->Prop)) (F_11:(pname->hoare_1708887482_state)) (C_2:(pname->Prop)), (((inj_on1553129421_state F_11) C_2)->(((ord_less_eq_pname_o A_18) C_2)->(((ord_less_eq_pname_o B_6) C_2)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_11) ((minus_minus_pname_o A_18) B_6))) ((minus_2056855718tate_o ((image_1116629049_state F_11) A_18)) ((image_1116629049_state F_11) B_6))))))) of role axiom named fact_1153_inj__on__image__set__diff
% A new axiom: (forall (B_6:(pname->Prop)) (A_18:(pname->Prop)) (F_11:(pname->hoare_1708887482_state)) (C_2:(pname->Prop)), (((inj_on1553129421_state F_11) C_2)->(((ord_less_eq_pname_o A_18) C_2)->(((ord_less_eq_pname_o B_6) C_2)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_11) ((minus_minus_pname_o A_18) B_6))) ((minus_2056855718tate_o ((image_1116629049_state F_11) A_18)) ((image_1116629049_state F_11) B_6)))))))
% FOF formula (forall (B_5:(com->Prop)) (A_17:(com->Prop)), ((finite_finite_com A_17)->(((eq (com->Prop)) ((semila1562558655_com_o A_17) B_5)) (((finite504235573_com_o insert_com) B_5) A_17)))) of role axiom named fact_1154_union__fold__insert
% A new axiom: (forall (B_5:(com->Prop)) (A_17:(com->Prop)), ((finite_finite_com A_17)->(((eq (com->Prop)) ((semila1562558655_com_o A_17) B_5)) (((finite504235573_com_o insert_com) B_5) A_17))))
% FOF formula (forall (B_5:(pname->Prop)) (A_17:(pname->Prop)), ((finite_finite_pname A_17)->(((eq (pname->Prop)) ((semila1780557381name_o A_17) B_5)) (((finite603803317name_o insert_pname) B_5) A_17)))) of role axiom named fact_1155_union__fold__insert
% A new axiom: (forall (B_5:(pname->Prop)) (A_17:(pname->Prop)), ((finite_finite_pname A_17)->(((eq (pname->Prop)) ((semila1780557381name_o A_17) B_5)) (((finite603803317name_o insert_pname) B_5) A_17))))
% FOF formula (forall (B_5:(hoare_1708887482_state->Prop)) (A_17:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_17)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_17) B_5)) (((finite96880613tate_o insert528405184_state) B_5) A_17)))) of role axiom named fact_1156_union__fold__insert
% A new axiom: (forall (B_5:(hoare_1708887482_state->Prop)) (A_17:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_17)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_17) B_5)) (((finite96880613tate_o insert528405184_state) B_5) A_17))))
% FOF formula (forall (B_5:((pname->Prop)->Prop)) (A_17:((pname->Prop)->Prop)), ((finite297249702name_o A_17)->(((eq ((pname->Prop)->Prop)) ((semila181081674me_o_o A_17) B_5)) (((finite1849951719me_o_o insert_pname_o) B_5) A_17)))) of role axiom named fact_1157_union__fold__insert
% A new axiom: (forall (B_5:((pname->Prop)->Prop)) (A_17:((pname->Prop)->Prop)), ((finite297249702name_o A_17)->(((eq ((pname->Prop)->Prop)) ((semila181081674me_o_o A_17) B_5)) (((finite1849951719me_o_o insert_pname_o) B_5) A_17))))
% FOF formula (forall (B_5:((hoare_1708887482_state->Prop)->Prop)) (A_17:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_17)->(((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila1853742644te_o_o A_17) B_5)) (((finite463603445te_o_o insert949073679tate_o) B_5) A_17)))) of role axiom named fact_1158_union__fold__insert
% A new axiom: (forall (B_5:((hoare_1708887482_state->Prop)->Prop)) (A_17:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_17)->(((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila1853742644te_o_o A_17) B_5)) (((finite463603445te_o_o insert949073679tate_o) B_5) A_17))))
% FOF formula (forall (A_16:(pname->Prop)) (F_10:(pname->option_com)) (X_7:pname), ((((eq option_com) (F_10 X_7)) none_com)->(((eq (pname->Prop)) ((minus_minus_pname_o (dom_pname_com F_10)) ((insert_pname X_7) A_16))) ((minus_minus_pname_o (dom_pname_com F_10)) A_16)))) of role axiom named fact_1159_dom__minus
% A new axiom: (forall (A_16:(pname->Prop)) (F_10:(pname->option_com)) (X_7:pname), ((((eq option_com) (F_10 X_7)) none_com)->(((eq (pname->Prop)) ((minus_minus_pname_o (dom_pname_com F_10)) ((insert_pname X_7) A_16))) ((minus_minus_pname_o (dom_pname_com F_10)) A_16))))
% FOF formula (forall (X_6:Prop), ((iff ((semila10642723_sup_o X_6) X_6)) X_6)) of role axiom named fact_1160_Sup__fin_Oidem
% A new axiom: (forall (X_6:Prop), ((iff ((semila10642723_sup_o X_6) X_6)) X_6))
% FOF formula (forall (X_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_6) X_6)) X_6)) of role axiom named fact_1161_Sup__fin_Oidem
% A new axiom: (forall (X_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_6) X_6)) X_6))
% FOF formula (forall (X_6:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_6) X_6)) X_6)) of role axiom named fact_1162_Sup__fin_Oidem
% A new axiom: (forall (X_6:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_6) X_6)) X_6))
% FOF formula (forall (X_5:com) (A_15:(com->Prop)) (F_9:(com->(com->com))) (F_8:((com->Prop)->com)), (((finite860057415ne_com F_9) F_8)->((finite_finite_com A_15)->((((member_com X_5) A_15)->False)->(((eq com) (F_8 ((insert_com X_5) A_15))) (((finite_fold_com_com F_9) X_5) A_15)))))) of role axiom named fact_1163_folding__one_Oeq__fold_H
% A new axiom: (forall (X_5:com) (A_15:(com->Prop)) (F_9:(com->(com->com))) (F_8:((com->Prop)->com)), (((finite860057415ne_com F_9) F_8)->((finite_finite_com A_15)->((((member_com X_5) A_15)->False)->(((eq com) (F_8 ((insert_com X_5) A_15))) (((finite_fold_com_com F_9) X_5) A_15))))))
% FOF formula (forall (X_5:pname) (A_15:(pname->Prop)) (F_9:(pname->(pname->pname))) (F_8:((pname->Prop)->pname)), (((finite1282449217_pname F_9) F_8)->((finite_finite_pname A_15)->((((member_pname X_5) A_15)->False)->(((eq pname) (F_8 ((insert_pname X_5) A_15))) (((finite1657623752_pname F_9) X_5) A_15)))))) of role axiom named fact_1164_folding__one_Oeq__fold_H
% A new axiom: (forall (X_5:pname) (A_15:(pname->Prop)) (F_9:(pname->(pname->pname))) (F_8:((pname->Prop)->pname)), (((finite1282449217_pname F_9) F_8)->((finite_finite_pname A_15)->((((member_pname X_5) A_15)->False)->(((eq pname) (F_8 ((insert_pname X_5) A_15))) (((finite1657623752_pname F_9) X_5) A_15))))))
% FOF formula (forall (X_5:hoare_1708887482_state) (A_15:(hoare_1708887482_state->Prop)) (F_9:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_8:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_9) F_8)->((finite1625599783_state A_15)->((((member451959335_state X_5) A_15)->False)->(((eq hoare_1708887482_state) (F_8 ((insert528405184_state X_5) A_15))) (((finite309095018_state F_9) X_5) A_15)))))) of role axiom named fact_1165_folding__one_Oeq__fold_H
% A new axiom: (forall (X_5:hoare_1708887482_state) (A_15:(hoare_1708887482_state->Prop)) (F_9:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_8:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_9) F_8)->((finite1625599783_state A_15)->((((member451959335_state X_5) A_15)->False)->(((eq hoare_1708887482_state) (F_8 ((insert528405184_state X_5) A_15))) (((finite309095018_state F_9) X_5) A_15))))))
% FOF formula (forall (X_5:(pname->Prop)) (A_15:((pname->Prop)->Prop)) (F_9:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_8:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_9) F_8)->((finite297249702name_o A_15)->((((member_pname_o X_5) A_15)->False)->(((eq (pname->Prop)) (F_8 ((insert_pname_o X_5) A_15))) (((finite472615016name_o F_9) X_5) A_15)))))) of role axiom named fact_1166_folding__one_Oeq__fold_H
% A new axiom: (forall (X_5:(pname->Prop)) (A_15:((pname->Prop)->Prop)) (F_9:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_8:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_9) F_8)->((finite297249702name_o A_15)->((((member_pname_o X_5) A_15)->False)->(((eq (pname->Prop)) (F_8 ((insert_pname_o X_5) A_15))) (((finite472615016name_o F_9) X_5) A_15))))))
% FOF formula (forall (X_5:(hoare_1708887482_state->Prop)) (A_15:((hoare_1708887482_state->Prop)->Prop)) (F_9:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_8:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_9) F_8)->((finite1329924456tate_o A_15)->((((member814030440tate_o X_5) A_15)->False)->(((eq (hoare_1708887482_state->Prop)) (F_8 ((insert949073679tate_o X_5) A_15))) (((finite822533768tate_o F_9) X_5) A_15)))))) of role axiom named fact_1167_folding__one_Oeq__fold_H
% A new axiom: (forall (X_5:(hoare_1708887482_state->Prop)) (A_15:((hoare_1708887482_state->Prop)->Prop)) (F_9:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_8:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_9) F_8)->((finite1329924456tate_o A_15)->((((member814030440tate_o X_5) A_15)->False)->(((eq (hoare_1708887482_state->Prop)) (F_8 ((insert949073679tate_o X_5) A_15))) (((finite822533768tate_o F_9) X_5) A_15))))))
% FOF formula (forall (A_14:com) (A_13:(com->Prop)) (F_7:(com->(com->com))) (F_6:((com->Prop)->com)), (((finite666746948em_com F_7) F_6)->((finite_finite_com A_13)->(((eq com) (F_6 ((insert_com A_14) A_13))) (((finite_fold_com_com F_7) A_14) A_13))))) of role axiom named fact_1168_folding__one__idem_Oeq__fold__idem_H
% A new axiom: (forall (A_14:com) (A_13:(com->Prop)) (F_7:(com->(com->com))) (F_6:((com->Prop)->com)), (((finite666746948em_com F_7) F_6)->((finite_finite_com A_13)->(((eq com) (F_6 ((insert_com A_14) A_13))) (((finite_fold_com_com F_7) A_14) A_13)))))
% FOF formula (forall (A_14:pname) (A_13:(pname->Prop)) (F_7:(pname->(pname->pname))) (F_6:((pname->Prop)->pname)), (((finite89670078_pname F_7) F_6)->((finite_finite_pname A_13)->(((eq pname) (F_6 ((insert_pname A_14) A_13))) (((finite1657623752_pname F_7) A_14) A_13))))) of role axiom named fact_1169_folding__one__idem_Oeq__fold__idem_H
% A new axiom: (forall (A_14:pname) (A_13:(pname->Prop)) (F_7:(pname->(pname->pname))) (F_6:((pname->Prop)->pname)), (((finite89670078_pname F_7) F_6)->((finite_finite_pname A_13)->(((eq pname) (F_6 ((insert_pname A_14) A_13))) (((finite1657623752_pname F_7) A_14) A_13)))))
% FOF formula (forall (A_14:hoare_1708887482_state) (A_13:(hoare_1708887482_state->Prop)) (F_7:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_6:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_7) F_6)->((finite1625599783_state A_13)->(((eq hoare_1708887482_state) (F_6 ((insert528405184_state A_14) A_13))) (((finite309095018_state F_7) A_14) A_13))))) of role axiom named fact_1170_folding__one__idem_Oeq__fold__idem_H
% A new axiom: (forall (A_14:hoare_1708887482_state) (A_13:(hoare_1708887482_state->Prop)) (F_7:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_6:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_7) F_6)->((finite1625599783_state A_13)->(((eq hoare_1708887482_state) (F_6 ((insert528405184_state A_14) A_13))) (((finite309095018_state F_7) A_14) A_13)))))
% FOF formula (forall (A_14:(pname->Prop)) (A_13:((pname->Prop)->Prop)) (F_7:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_6:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_7) F_6)->((finite297249702name_o A_13)->(((eq (pname->Prop)) (F_6 ((insert_pname_o A_14) A_13))) (((finite472615016name_o F_7) A_14) A_13))))) of role axiom named fact_1171_folding__one__idem_Oeq__fold__idem_H
% A new axiom: (forall (A_14:(pname->Prop)) (A_13:((pname->Prop)->Prop)) (F_7:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_6:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_7) F_6)->((finite297249702name_o A_13)->(((eq (pname->Prop)) (F_6 ((insert_pname_o A_14) A_13))) (((finite472615016name_o F_7) A_14) A_13)))))
% FOF formula (forall (A_14:(hoare_1708887482_state->Prop)) (A_13:((hoare_1708887482_state->Prop)->Prop)) (F_7:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_6:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_7) F_6)->((finite1329924456tate_o A_13)->(((eq (hoare_1708887482_state->Prop)) (F_6 ((insert949073679tate_o A_14) A_13))) (((finite822533768tate_o F_7) A_14) A_13))))) of role axiom named fact_1172_folding__one__idem_Oeq__fold__idem_H
% A new axiom: (forall (A_14:(hoare_1708887482_state->Prop)) (A_13:((hoare_1708887482_state->Prop)->Prop)) (F_7:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_6:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_7) F_6)->((finite1329924456tate_o A_13)->(((eq (hoare_1708887482_state->Prop)) (F_6 ((insert949073679tate_o A_14) A_13))) (((finite822533768tate_o F_7) A_14) A_13)))))
% FOF formula (forall (Pn_1:pname), ((not (((eq option_com) (body Pn_1)) none_com))->(wt (body_1 Pn_1)))) of role axiom named fact_1173_WT_OBody
% A new axiom: (forall (Pn_1:pname), ((not (((eq option_com) (body Pn_1)) none_com))->(wt (body_1 Pn_1))))
% FOF formula (forall (F_5:(pname->hoare_1708887482_state)) (A_12:pname) (A_11:(pname->Prop)), ((iff ((inj_on1553129421_state F_5) ((insert_pname A_12) A_11))) ((and ((inj_on1553129421_state F_5) A_11)) (((member451959335_state (F_5 A_12)) ((image_1116629049_state F_5) ((minus_minus_pname_o A_11) ((insert_pname A_12) bot_bot_pname_o))))->False)))) of role axiom named fact_1174_inj__on__insert
% A new axiom: (forall (F_5:(pname->hoare_1708887482_state)) (A_12:pname) (A_11:(pname->Prop)), ((iff ((inj_on1553129421_state F_5) ((insert_pname A_12) A_11))) ((and ((inj_on1553129421_state F_5) A_11)) (((member451959335_state (F_5 A_12)) ((image_1116629049_state F_5) ((minus_minus_pname_o A_11) ((insert_pname A_12) bot_bot_pname_o))))->False))))
% FOF formula (forall (F_4:(pname->option_com)) (X_4:pname) (Y_2:option_com), ((and ((((eq option_com) Y_2) none_com)->(((eq (pname->Prop)) (dom_pname_com (((fun_up879233478on_com F_4) X_4) Y_2))) ((minus_minus_pname_o (dom_pname_com F_4)) ((insert_pname X_4) bot_bot_pname_o))))) ((not (((eq option_com) Y_2) none_com))->(((eq (pname->Prop)) (dom_pname_com (((fun_up879233478on_com F_4) X_4) Y_2))) ((insert_pname X_4) (dom_pname_com F_4)))))) of role axiom named fact_1175_dom__fun__upd
% A new axiom: (forall (F_4:(pname->option_com)) (X_4:pname) (Y_2:option_com), ((and ((((eq option_com) Y_2) none_com)->(((eq (pname->Prop)) (dom_pname_com (((fun_up879233478on_com F_4) X_4) Y_2))) ((minus_minus_pname_o (dom_pname_com F_4)) ((insert_pname X_4) bot_bot_pname_o))))) ((not (((eq option_com) Y_2) none_com))->(((eq (pname->Prop)) (dom_pname_com (((fun_up879233478on_com F_4) X_4) Y_2))) ((insert_pname X_4) (dom_pname_com F_4))))))
% FOF formula (forall (C_1:(pname->Prop)) (B_4:(pname->Prop)) (A_10:((pname->Prop)->Prop)), ((finite297249702name_o A_10)->((forall (X_3:(pname->Prop)), (((member_pname_o X_3) A_10)->((ord_less_eq_pname_o B_4) X_3)))->((ord_less_eq_pname_o ((semila1673364395name_o B_4) C_1)) (((finite472615016name_o semila1673364395name_o) C_1) A_10))))) of role axiom named fact_1176_inf__le__fold__inf
% A new axiom: (forall (C_1:(pname->Prop)) (B_4:(pname->Prop)) (A_10:((pname->Prop)->Prop)), ((finite297249702name_o A_10)->((forall (X_3:(pname->Prop)), (((member_pname_o X_3) A_10)->((ord_less_eq_pname_o B_4) X_3)))->((ord_less_eq_pname_o ((semila1673364395name_o B_4) C_1)) (((finite472615016name_o semila1673364395name_o) C_1) A_10)))))
% FOF formula (forall (C_1:(hoare_1708887482_state->Prop)) (B_4:(hoare_1708887482_state->Prop)) (A_10:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_10)->((forall (X_3:(hoare_1708887482_state->Prop)), (((member814030440tate_o X_3) A_10)->((ord_le777019615tate_o B_4) X_3)))->((ord_le777019615tate_o ((semila129691299tate_o B_4) C_1)) (((finite822533768tate_o semila129691299tate_o) C_1) A_10))))) of role axiom named fact_1177_inf__le__fold__inf
% A new axiom: (forall (C_1:(hoare_1708887482_state->Prop)) (B_4:(hoare_1708887482_state->Prop)) (A_10:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_10)->((forall (X_3:(hoare_1708887482_state->Prop)), (((member814030440tate_o X_3) A_10)->((ord_le777019615tate_o B_4) X_3)))->((ord_le777019615tate_o ((semila129691299tate_o B_4) C_1)) (((finite822533768tate_o semila129691299tate_o) C_1) A_10)))))
% FOF formula (forall (C_1:Prop) (B_4:Prop) (A_10:(Prop->Prop)), ((finite_finite_o A_10)->((forall (X_3:Prop), (((member_o X_3) A_10)->((ord_less_eq_o B_4) X_3)))->((ord_less_eq_o ((semila854092349_inf_o B_4) C_1)) (((finite_fold_o_o semila854092349_inf_o) C_1) A_10))))) of role axiom named fact_1178_inf__le__fold__inf
% A new axiom: (forall (C_1:Prop) (B_4:Prop) (A_10:(Prop->Prop)), ((finite_finite_o A_10)->((forall (X_3:Prop), (((member_o X_3) A_10)->((ord_less_eq_o B_4) X_3)))->((ord_less_eq_o ((semila854092349_inf_o B_4) C_1)) (((finite_fold_o_o semila854092349_inf_o) C_1) A_10)))))
% FOF formula (forall (C:(pname->Prop)) (B_3:(pname->Prop)) (A_9:((pname->Prop)->Prop)), ((finite297249702name_o A_9)->((forall (X_3:(pname->Prop)), (((member_pname_o X_3) A_9)->((ord_less_eq_pname_o X_3) B_3)))->((ord_less_eq_pname_o (((finite472615016name_o semila1780557381name_o) C) A_9)) ((semila1780557381name_o B_3) C))))) of role axiom named fact_1179_fold__sup__le__sup
% A new axiom: (forall (C:(pname->Prop)) (B_3:(pname->Prop)) (A_9:((pname->Prop)->Prop)), ((finite297249702name_o A_9)->((forall (X_3:(pname->Prop)), (((member_pname_o X_3) A_9)->((ord_less_eq_pname_o X_3) B_3)))->((ord_less_eq_pname_o (((finite472615016name_o semila1780557381name_o) C) A_9)) ((semila1780557381name_o B_3) C)))))
% FOF formula (forall (C:(hoare_1708887482_state->Prop)) (B_3:(hoare_1708887482_state->Prop)) (A_9:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_9)->((forall (X_3:(hoare_1708887482_state->Prop)), (((member814030440tate_o X_3) A_9)->((ord_le777019615tate_o X_3) B_3)))->((ord_le777019615tate_o (((finite822533768tate_o semila1122118281tate_o) C) A_9)) ((semila1122118281tate_o B_3) C))))) of role axiom named fact_1180_fold__sup__le__sup
% A new axiom: (forall (C:(hoare_1708887482_state->Prop)) (B_3:(hoare_1708887482_state->Prop)) (A_9:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_9)->((forall (X_3:(hoare_1708887482_state->Prop)), (((member814030440tate_o X_3) A_9)->((ord_le777019615tate_o X_3) B_3)))->((ord_le777019615tate_o (((finite822533768tate_o semila1122118281tate_o) C) A_9)) ((semila1122118281tate_o B_3) C)))))
% FOF formula (forall (C:Prop) (B_3:Prop) (A_9:(Prop->Prop)), ((finite_finite_o A_9)->((forall (X_3:Prop), (((member_o X_3) A_9)->((ord_less_eq_o X_3) B_3)))->((ord_less_eq_o (((finite_fold_o_o semila10642723_sup_o) C) A_9)) ((semila10642723_sup_o B_3) C))))) of role axiom named fact_1181_fold__sup__le__sup
% A new axiom: (forall (C:Prop) (B_3:Prop) (A_9:(Prop->Prop)), ((finite_finite_o A_9)->((forall (X_3:Prop), (((member_o X_3) A_9)->((ord_less_eq_o X_3) B_3)))->((ord_less_eq_o (((finite_fold_o_o semila10642723_sup_o) C) A_9)) ((semila10642723_sup_o B_3) C)))))
% FOF formula (forall (A_8:(pname->Prop)) (A_7:(hoare_1708887482_state->Prop)), ((not (((eq (hoare_1708887482_state->Prop)) A_7) bot_bo19817387tate_o))->((iff ((ex (hoare_1708887482_state->pname)) (fun (F_3:(hoare_1708887482_state->pname))=> ((and ((inj_on1945914667_pname F_3) A_7)) ((ord_less_eq_pname_o ((image_1509414295_pname F_3) A_7)) A_8))))) ((ex (pname->hoare_1708887482_state)) (fun (G_1:(pname->hoare_1708887482_state))=> (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state G_1) A_8)) A_7)))))) of role axiom named fact_1182_inj__on__iff__surj
% A new axiom: (forall (A_8:(pname->Prop)) (A_7:(hoare_1708887482_state->Prop)), ((not (((eq (hoare_1708887482_state->Prop)) A_7) bot_bo19817387tate_o))->((iff ((ex (hoare_1708887482_state->pname)) (fun (F_3:(hoare_1708887482_state->pname))=> ((and ((inj_on1945914667_pname F_3) A_7)) ((ord_less_eq_pname_o ((image_1509414295_pname F_3) A_7)) A_8))))) ((ex (pname->hoare_1708887482_state)) (fun (G_1:(pname->hoare_1708887482_state))=> (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state G_1) A_8)) A_7))))))
% FOF formula (forall (A_8:(hoare_1708887482_state->Prop)) (A_7:(pname->Prop)), ((not (((eq (pname->Prop)) A_7) bot_bot_pname_o))->((iff ((ex (pname->hoare_1708887482_state)) (fun (F_3:(pname->hoare_1708887482_state))=> ((and ((inj_on1553129421_state F_3) A_7)) ((ord_le777019615tate_o ((image_1116629049_state F_3) A_7)) A_8))))) ((ex (hoare_1708887482_state->pname)) (fun (G_1:(hoare_1708887482_state->pname))=> (((eq (pname->Prop)) ((image_1509414295_pname G_1) A_8)) A_7)))))) of role axiom named fact_1183_inj__on__iff__surj
% A new axiom: (forall (A_8:(hoare_1708887482_state->Prop)) (A_7:(pname->Prop)), ((not (((eq (pname->Prop)) A_7) bot_bot_pname_o))->((iff ((ex (pname->hoare_1708887482_state)) (fun (F_3:(pname->hoare_1708887482_state))=> ((and ((inj_on1553129421_state F_3) A_7)) ((ord_le777019615tate_o ((image_1116629049_state F_3) A_7)) A_8))))) ((ex (hoare_1708887482_state->pname)) (fun (G_1:(hoare_1708887482_state->pname))=> (((eq (pname->Prop)) ((image_1509414295_pname G_1) A_8)) A_7))))))
% FOF formula (forall (Y_1:option_com), ((not (((eq option_com) Y_1) none_com))->((forall (A_6:com), (not (((eq option_com) Y_1) (some_com A_6))))->False))) of role axiom named fact_1184_option_Oexhaust
% A new axiom: (forall (Y_1:option_com), ((not (((eq option_com) Y_1) none_com))->((forall (A_6:com), (not (((eq option_com) Y_1) (some_com A_6))))->False)))
% FOF formula (forall (Y_1:option_pname), ((not (((eq option_pname) Y_1) none_pname))->((forall (A_6:pname), (not (((eq option_pname) Y_1) (some_pname A_6))))->False))) of role axiom named fact_1185_option_Oexhaust
% A new axiom: (forall (Y_1:option_pname), ((not (((eq option_pname) Y_1) none_pname))->((forall (A_6:pname), (not (((eq option_pname) Y_1) (some_pname A_6))))->False)))
% FOF formula (forall (Y_1:option1624383643_state), ((not (((eq option1624383643_state) Y_1) none_H1106584047_state))->((forall (A_6:hoare_1708887482_state), (not (((eq option1624383643_state) Y_1) (some_H1974565227_state A_6))))->False))) of role axiom named fact_1186_option_Oexhaust
% A new axiom: (forall (Y_1:option1624383643_state), ((not (((eq option1624383643_state) Y_1) none_H1106584047_state))->((forall (A_6:hoare_1708887482_state), (not (((eq option1624383643_state) Y_1) (some_H1974565227_state A_6))))->False)))
% FOF formula (forall (G:(hoare_1708887482_state->pname)) (B_2:(hoare_1708887482_state->Prop)) (F_2:(pname->hoare_1708887482_state)) (A_4:(pname->Prop)), ((ex (pname->Prop)) (fun (A_5:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o A_5) A_4)) (forall (X_3:pname), (((member_pname X_3) A_5)->(((member_pname X_3) ((image_1509414295_pname G) ((minus_2056855718tate_o B_2) ((image_1116629049_state F_2) A_5))))->False))))) ((ex (pname->hoare_1708887482_state)) (fun (H:(pname->hoare_1708887482_state))=> ((and (forall (X_3:pname), (((member_pname X_3) A_5)->(((eq hoare_1708887482_state) (H X_3)) (F_2 X_3))))) (forall (X_3:pname), (((member_pname X_3) ((minus_minus_pname_o A_4) A_5))->((and ((member451959335_state (H X_3)) ((minus_2056855718tate_o B_2) ((image_1116629049_state F_2) A_5)))) (((eq pname) X_3) (G (H X_3))))))))))))) of role axiom named fact_1187_Cantor__Bernstein__aux
% A new axiom: (forall (G:(hoare_1708887482_state->pname)) (B_2:(hoare_1708887482_state->Prop)) (F_2:(pname->hoare_1708887482_state)) (A_4:(pname->Prop)), ((ex (pname->Prop)) (fun (A_5:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o A_5) A_4)) (forall (X_3:pname), (((member_pname X_3) A_5)->(((member_pname X_3) ((image_1509414295_pname G) ((minus_2056855718tate_o B_2) ((image_1116629049_state F_2) A_5))))->False))))) ((ex (pname->hoare_1708887482_state)) (fun (H:(pname->hoare_1708887482_state))=> ((and (forall (X_3:pname), (((member_pname X_3) A_5)->(((eq hoare_1708887482_state) (H X_3)) (F_2 X_3))))) (forall (X_3:pname), (((member_pname X_3) ((minus_minus_pname_o A_4) A_5))->((and ((member451959335_state (H X_3)) ((minus_2056855718tate_o B_2) ((image_1116629049_state F_2) A_5)))) (((eq pname) X_3) (G (H X_3)))))))))))))
% FOF formula (forall (G:(pname->hoare_1708887482_state)) (B_2:(pname->Prop)) (F_2:(hoare_1708887482_state->pname)) (A_4:(hoare_1708887482_state->Prop)), ((ex (hoare_1708887482_state->Prop)) (fun (A_5:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o A_5) A_4)) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_5)->(((member451959335_state X_3) ((image_1116629049_state G) ((minus_minus_pname_o B_2) ((image_1509414295_pname F_2) A_5))))->False))))) ((ex (hoare_1708887482_state->pname)) (fun (H:(hoare_1708887482_state->pname))=> ((and (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_5)->(((eq pname) (H X_3)) (F_2 X_3))))) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) ((minus_2056855718tate_o A_4) A_5))->((and ((member_pname (H X_3)) ((minus_minus_pname_o B_2) ((image_1509414295_pname F_2) A_5)))) (((eq hoare_1708887482_state) X_3) (G (H X_3))))))))))))) of role axiom named fact_1188_Cantor__Bernstein__aux
% A new axiom: (forall (G:(pname->hoare_1708887482_state)) (B_2:(pname->Prop)) (F_2:(hoare_1708887482_state->pname)) (A_4:(hoare_1708887482_state->Prop)), ((ex (hoare_1708887482_state->Prop)) (fun (A_5:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o A_5) A_4)) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_5)->(((member451959335_state X_3) ((image_1116629049_state G) ((minus_minus_pname_o B_2) ((image_1509414295_pname F_2) A_5))))->False))))) ((ex (hoare_1708887482_state->pname)) (fun (H:(hoare_1708887482_state->pname))=> ((and (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_5)->(((eq pname) (H X_3)) (F_2 X_3))))) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) ((minus_2056855718tate_o A_4) A_5))->((and ((member_pname (H X_3)) ((minus_minus_pname_o B_2) ((image_1509414295_pname F_2) A_5)))) (((eq hoare_1708887482_state) X_3) (G (H X_3)))))))))))))
% FOF formula (forall (F_1:(pname->hoare_1708887482_state)) (A_3:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((image_1116629049_state F_1) ((vimage1943311875_state F_1) A_3))) A_3)) of role axiom named fact_1189_image__vimage__subset
% A new axiom: (forall (F_1:(pname->hoare_1708887482_state)) (A_3:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((image_1116629049_state F_1) ((vimage1943311875_state F_1) A_3))) A_3))
% FOF formula (forall (M:(pname->option_com)) (A_2:(pname->Prop)), (((eq (pname->Prop)) (dom_pname_com ((restri1382200118me_com M) A_2))) ((semila1673364395name_o (dom_pname_com M)) A_2))) of role axiom named fact_1190_dom__restrict
% A new axiom: (forall (M:(pname->option_com)) (A_2:(pname->Prop)), (((eq (pname->Prop)) (dom_pname_com ((restri1382200118me_com M) A_2))) ((semila1673364395name_o (dom_pname_com M)) A_2)))
% FOF formula (forall (B_1:((pname->Prop)->Prop)) (A_1:((pname->Prop)->Prop)), ((finite297249702name_o A_1)->((not (((eq ((pname->Prop)->Prop)) A_1) bot_bot_pname_o_o))->((finite297249702name_o B_1)->((not (((eq ((pname->Prop)->Prop)) B_1) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_1) B_1)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (big_la1126801287name_o ((semila181081674me_o_o A_1) B_1))) ((semila1673364395name_o (big_la1126801287name_o A_1)) (big_la1126801287name_o B_1))))))))) of role axiom named fact_1191_Inf__fin_Ounion__disjoint
% A new axiom: (forall (B_1:((pname->Prop)->Prop)) (A_1:((pname->Prop)->Prop)), ((finite297249702name_o A_1)->((not (((eq ((pname->Prop)->Prop)) A_1) bot_bot_pname_o_o))->((finite297249702name_o B_1)->((not (((eq ((pname->Prop)->Prop)) B_1) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_1) B_1)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (big_la1126801287name_o ((semila181081674me_o_o A_1) B_1))) ((semila1673364395name_o (big_la1126801287name_o A_1)) (big_la1126801287name_o B_1)))))))))
% FOF formula (forall (B_1:((hoare_1708887482_state->Prop)->Prop)) (A_1:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_1)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_1) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_1)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_1) bot_bo1678742418te_o_o))->((((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_1) B_1)) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (big_la781588935tate_o ((semila1853742644te_o_o A_1) B_1))) ((semila129691299tate_o (big_la781588935tate_o A_1)) (big_la781588935tate_o B_1))))))))) of role axiom named fact_1192_Inf__fin_Ounion__disjoint
% A new axiom: (forall (B_1:((hoare_1708887482_state->Prop)->Prop)) (A_1:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_1)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_1) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_1)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_1) bot_bo1678742418te_o_o))->((((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_1) B_1)) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (big_la781588935tate_o ((semila1853742644te_o_o A_1) B_1))) ((semila129691299tate_o (big_la781588935tate_o A_1)) (big_la781588935tate_o B_1)))))))))
% FOF formula (forall (B:((pname->Prop)->Prop)) (A:((pname->Prop)->Prop)), ((finite297249702name_o A)->((finite297249702name_o B)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A) B)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((semila1673364395name_o (big_la1126801287name_o ((semila181081674me_o_o A) B))) (big_la1126801287name_o ((semila2013987940me_o_o A) B)))) ((semila1673364395name_o (big_la1126801287name_o A)) (big_la1126801287name_o B))))))) of role axiom named fact_1193_Inf__fin_Ounion__inter
% A new axiom: (forall (B:((pname->Prop)->Prop)) (A:((pname->Prop)->Prop)), ((finite297249702name_o A)->((finite297249702name_o B)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A) B)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((semila1673364395name_o (big_la1126801287name_o ((semila181081674me_o_o A) B))) (big_la1126801287name_o ((semila2013987940me_o_o A) B)))) ((semila1673364395name_o (big_la1126801287name_o A)) (big_la1126801287name_o B)))))))
% FOF formula (forall (B:((hoare_1708887482_state->Prop)->Prop)) (A:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A)->((finite1329924456tate_o B)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A) B)) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o (big_la781588935tate_o ((semila1853742644te_o_o A) B))) (big_la781588935tate_o ((semila598060698te_o_o A) B)))) ((semila129691299tate_o (big_la781588935tate_o A)) (big_la781588935tate_o B))))))) of role axiom named fact_1194_Inf__fin_Ounion__inter
% A new axiom: (forall (B:((hoare_1708887482_state->Prop)->Prop)) (A:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A)->((finite1329924456tate_o B)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A) B)) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o (big_la781588935tate_o ((semila1853742644te_o_o A) B))) (big_la781588935tate_o ((semila598060698te_o_o A) B)))) ((semila129691299tate_o (big_la781588935tate_o A)) (big_la781588935tate_o B)))))))
% FOF formula (forall (X_2:com), ((member_com X_2) top_top_com_o)) of role axiom named fact_1195_UNIV__I
% A new axiom: (forall (X_2:com), ((member_com X_2) top_top_com_o))
% FOF formula (forall (X_2:pname), ((member_pname X_2) top_top_pname_o)) of role axiom named fact_1196_UNIV__I
% A new axiom: (forall (X_2:pname), ((member_pname X_2) top_top_pname_o))
% FOF formula (forall (X_2:hoare_1708887482_state), ((member451959335_state X_2) top_to832624271tate_o)) of role axiom named fact_1197_UNIV__I
% A new axiom: (forall (X_2:hoare_1708887482_state), ((member451959335_state X_2) top_to832624271tate_o))
% FOF formula (forall (F:(pname->hoare_1708887482_state)) (X_1:pname), ((member451959335_state (F X_1)) ((image_1116629049_state F) top_top_pname_o))) of role axiom named fact_1198_rangeI
% A new axiom: (forall (F:(pname->hoare_1708887482_state)) (X_1:pname), ((member451959335_state (F X_1)) ((image_1116629049_state F) top_top_pname_o)))
% FOF formula (forall (X:com) (Y:com), ((or (((fequal_com X) Y)->False)) (((eq com) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Com__Ocom_T
% A new axiom: (forall (X:com) (Y:com), ((or (((fequal_com X) Y)->False)) (((eq com) X) Y)))
% FOF formula (forall (X:com) (Y:com), ((or (not (((eq com) X) Y))) ((fequal_com X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Com__Ocom_T
% A new axiom: (forall (X:com) (Y:com), ((or (not (((eq com) X) Y))) ((fequal_com X) Y)))
% FOF formula (forall (X:pname) (Y:pname), ((or (((fequal_pname X) Y)->False)) (((eq pname) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Com__Opname_T
% A new axiom: (forall (X:pname) (Y:pname), ((or (((fequal_pname X) Y)->False)) (((eq pname) X) Y)))
% FOF formula (forall (X:pname) (Y:pname), ((or (not (((eq pname) X) Y))) ((fequal_pname X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Com__Opname_T
% A new axiom: (forall (X:pname) (Y:pname), ((or (not (((eq pname) X) Y))) ((fequal_pname X) Y)))
% FOF formula (forall (X:state) (Y:state), ((or (((fequal_state X) Y)->False)) (((eq state) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Com__Ostate_T
% A new axiom: (forall (X:state) (Y:state), ((or (((fequal_state X) Y)->False)) (((eq state) X) Y)))
% FOF formula (forall (X:state) (Y:state), ((or (not (((eq state) X) Y))) ((fequal_state X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Com__Ostate_T
% A new axiom: (forall (X:state) (Y:state), ((or (not (((eq state) X) Y))) ((fequal_state X) Y)))
% FOF formula (forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (((fequal_pname_o X) Y)->False)) (((eq (pname->Prop)) X) Y))) of role axiom named help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T
% A new axiom: (forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (((fequal_pname_o X) Y)->False)) (((eq (pname->Prop)) X) Y)))
% FOF formula (forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (not (((eq (pname->Prop)) X) Y))) ((fequal_pname_o X) Y))) of role axiom named help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T
% A new axiom: (forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (not (((eq (pname->Prop)) X) Y))) ((fequal_pname_o X) Y)))
% FOF formula (forall (X:option_com) (Y:option_com), (((eq option_com) (((if_option_com True) X) Y)) X)) of role axiom named help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T
% A new axiom: (forall (X:option_com) (Y:option_com), (((eq option_com) (((if_option_com True) X) Y)) X))
% FOF formula (forall (X:option_com) (Y:option_com), (((eq option_com) (((if_option_com False) X) Y)) Y)) of role axiom named help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T
% A new axiom: (forall (X:option_com) (Y:option_com), (((eq option_com) (((if_option_com False) X) Y)) Y))
% FOF formula (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))) of role axiom named help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T
% A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False)))
% FOF formula (forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), (((eq hoare_1708887482_state) (((if_Hoa1374726218_state True) X) Y)) X)) of role axiom named help_If_1_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate
% A new axiom: (forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), (((eq hoare_1708887482_state) (((if_Hoa1374726218_state True) X) Y)) X))
% FOF formula (forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), (((eq hoare_1708887482_state) (((if_Hoa1374726218_state False) X) Y)) Y)) of role axiom named help_If_2_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate
% A new axiom: (forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), (((eq hoare_1708887482_state) (((if_Hoa1374726218_state False) X) Y)) Y))
% FOF formula (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))) of role axiom named help_If_3_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate
% A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False)))
% FOF formula (forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), ((or (((fequal224822779_state X) Y)->False)) (((eq hoare_1708887482_state) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com
% A new axiom: (forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), ((or (((fequal224822779_state X) Y)->False)) (((eq hoare_1708887482_state) X) Y)))
% FOF formula (forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), ((or (not (((eq hoare_1708887482_state) X) Y))) ((fequal224822779_state X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com
% A new axiom: (forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), ((or (not (((eq hoare_1708887482_state) X) Y))) ((fequal224822779_state X) Y)))
% FOF formula (forall (X:(hoare_1708887482_state->Prop)) (Y:(hoare_1708887482_state->Prop)), ((or (((fequal1436017556tate_o X) Y)->False)) (((eq (hoare_1708887482_state->Prop)) X) Y))) of role axiom named help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It
% A new axiom: (forall (X:(hoare_1708887482_state->Prop)) (Y:(hoare_1708887482_state->Prop)), ((or (((fequal1436017556tate_o X) Y)->False)) (((eq (hoare_1708887482_state->Prop)) X) Y)))
% FOF formula (forall (X:(hoare_1708887482_state->Prop)) (Y:(hoare_1708887482_state->Prop)), ((or (not (((eq (hoare_1708887482_state->Prop)) X) Y))) ((fequal1436017556tate_o X) Y))) of role axiom named help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It
% A new axiom: (forall (X:(hoare_1708887482_state->Prop)) (Y:(hoare_1708887482_state->Prop)), ((or (not (((eq (hoare_1708887482_state->Prop)) X) Y))) ((fequal1436017556tate_o X) Y)))
% FOF formula hoare_1160767572gleton of role hypothesis named conj_0
% A new axiom: hoare_1160767572gleton
% FOF formula wT_bodies of role hypothesis named conj_1
% A new axiom: wT_bodies
% FOF formula (finite1625599783_state fa) of role hypothesis named conj_2
% A new axiom: (finite1625599783_state fa)
% FOF formula (((member451959335_state (hoare_Mirabelle_MGT y)) fa)->False) of role hypothesis named conj_3
% A new axiom: (((member451959335_state (hoare_Mirabelle_MGT y)) fa)->False)
% FOF formula ((ord_le777019615tate_o fa) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) (dom_pname_com body))) of role hypothesis named conj_4
% A new axiom: ((ord_le777019615tate_o fa) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) (dom_pname_com body)))
% FOF formula (((eq option_com) (body pn)) (some_com y)) of role hypothesis named conj_5
% A new axiom: (((eq option_com) (body pn)) (some_com y))
% FOF formula ((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) of role hypothesis named conj_6
% A new axiom: ((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa)
% FOF formula ((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert528405184_state (hoare_Mirabelle_MGT y)) bot_bo19817387tate_o)) of role conjecture named conj_7
% Conjecture to prove = ((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert528405184_state (hoare_Mirabelle_MGT y)) bot_bo19817387tate_o)):Prop
% Parameter state_DUMMY:state.
% Parameter hoare_1708887482_state_DUMMY:hoare_1708887482_state.
% We need to prove ['((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert528405184_state (hoare_Mirabelle_MGT y)) bot_bo19817387tate_o))']
% Parameter com:Type.
% Parameter pname:Type.
% Parameter state:Type.
% Parameter hoare_1708887482_state:Type.
% Parameter option_com:Type.
% Parameter option_pname:Type.
% Parameter option1624383643_state:Type.
% Parameter big_la1126801287name_o:(((pname->Prop)->Prop)->(pname->Prop)).
% Parameter big_la781588935tate_o:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop)).
% Parameter wt:(com->Prop).
% Parameter wT_bodies:Prop.
% Parameter body:(pname->option_com).
% Parameter body_1:(pname->com).
% Parameter skip:com.
% Parameter semi:(com->(com->com)).
% Parameter while:((state->Prop)->(com->com)).
% Parameter finite138924780name_o:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->Prop).
% Parameter finite2034616076tate_o:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->Prop).
% Parameter finite2048025996em_o_o:((Prop->(Prop->Prop))->Prop).
% Parameter finite567462577_com_o:((com->((com->Prop)->(com->Prop)))->Prop).
% Parameter finite1123817265name_o:((pname->((pname->Prop)->(pname->Prop)))->Prop).
% Parameter finite662762081tate_o:((hoare_1708887482_state->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->Prop).
% Parameter finite1066544169me_o_o:((((pname->Prop)->Prop)->Prop)->Prop).
% Parameter finite1019950101te_o_o:((((hoare_1708887482_state->Prop)->Prop)->Prop)->Prop).
% Parameter finite297249702name_o:(((pname->Prop)->Prop)->Prop).
% Parameter finite1329924456tate_o:(((hoare_1708887482_state->Prop)->Prop)->Prop).
% Parameter finite_finite_o:((Prop->Prop)->Prop).
% Parameter finite_finite_com:((com->Prop)->Prop).
% Parameter finite_finite_pname:((pname->Prop)->Prop).
% Parameter finite1625599783_state:((hoare_1708887482_state->Prop)->Prop).
% Parameter finite1849951719me_o_o:(((pname->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop)))->(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop)))).
% Parameter finite472615016name_o:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->((pname->Prop)->(((pname->Prop)->Prop)->(pname->Prop)))).
% Parameter finite463603445te_o_o:(((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop)))->(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop)))).
% Parameter finite822533768tate_o:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop)))).
% Parameter finite_fold_o_o:((Prop->(Prop->Prop))->(Prop->((Prop->Prop)->Prop))).
% Parameter finite504235573_com_o:((com->((com->Prop)->(com->Prop)))->((com->Prop)->((com->Prop)->(com->Prop)))).
% Parameter finite_fold_com_com:((com->(com->com))->(com->((com->Prop)->com))).
% Parameter finite603803317name_o:((pname->((pname->Prop)->(pname->Prop)))->((pname->Prop)->((pname->Prop)->(pname->Prop)))).
% Parameter finite1657623752_pname:((pname->(pname->pname))->(pname->((pname->Prop)->pname))).
% Parameter finite96880613tate_o:((hoare_1708887482_state->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))).
% Parameter finite309095018_state:((hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))->(hoare_1708887482_state->((hoare_1708887482_state->Prop)->hoare_1708887482_state))).
% Parameter finite2139561282_pname:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((pname->(hoare_1708887482_state->Prop))->((hoare_1708887482_state->Prop)->((pname->Prop)->(hoare_1708887482_state->Prop))))).
% Parameter finite349908348name_o:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->((((pname->Prop)->Prop)->(pname->Prop))->Prop)).
% Parameter finite928843026tate_o:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))->Prop)).
% Parameter finite860057415ne_com:((com->(com->com))->(((com->Prop)->com)->Prop)).
% Parameter finite1282449217_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)).
% Parameter finite1615457021_state:((hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))->(((hoare_1708887482_state->Prop)->hoare_1708887482_state)->Prop)).
% Parameter finite697516351name_o:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->((((pname->Prop)->Prop)->(pname->Prop))->Prop)).
% Parameter finite621643279tate_o:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))->Prop)).
% Parameter finite666746948em_com:((com->(com->com))->(((com->Prop)->com)->Prop)).
% Parameter finite89670078_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)).
% Parameter finite1347568576_state:((hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))->(((hoare_1708887482_state->Prop)->hoare_1708887482_state)->Prop)).
% Parameter fun_up1986763201_state:((pname->hoare_1708887482_state)->(pname->(hoare_1708887482_state->(pname->hoare_1708887482_state)))).
% Parameter fun_up879233478on_com:((pname->option_com)->(pname->(option_com->(pname->option_com)))).
% Parameter inj_on691924881name_o:(((pname->Prop)->(pname->Prop))->(((pname->Prop)->Prop)->Prop)).
% Parameter inj_on176908593tate_o:(((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))->(((hoare_1708887482_state->Prop)->Prop)->Prop)).
% Parameter inj_on11367768on_com:((com->option_com)->((com->Prop)->Prop)).
% Parameter inj_on_pname_pname:((pname->pname)->((pname->Prop)->Prop)).
% Parameter inj_on1553129421_state:((pname->hoare_1708887482_state)->((pname->Prop)->Prop)).
% Parameter inj_on737724108_pname:((pname->option_pname)->((pname->Prop)->Prop)).
% Parameter inj_on1945914667_pname:((hoare_1708887482_state->pname)->((hoare_1708887482_state->Prop)->Prop)).
% Parameter inj_on632008595_state:((hoare_1708887482_state->hoare_1708887482_state)->((hoare_1708887482_state->Prop)->Prop)).
% Parameter inj_on945311362_state:((hoare_1708887482_state->option1624383643_state)->((hoare_1708887482_state->Prop)->Prop)).
% Parameter overri1496249029on_com:((pname->option_com)->((pname->option_com)->((pname->Prop)->(pname->option_com)))).
% Parameter minus_1480864103me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter minus_548038231te_o_o:(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop))).
% Parameter minus_minus_com_o:((com->Prop)->((com->Prop)->(com->Prop))).
% Parameter minus_minus_pname_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter minus_2056855718tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))).
% Parameter the_com_1:((com->Prop)->com).
% Parameter the_pname:((pname->Prop)->pname).
% Parameter the_Ho851197897_state:((hoare_1708887482_state->Prop)->hoare_1708887482_state).
% Parameter hoare_Mirabelle_MGT:(com->hoare_1708887482_state).
% Parameter hoare_90032982_state:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop)).
% Parameter hoare_496444244_state:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop)).
% Parameter hoare_1160767572gleton:Prop.
% Parameter hoare_858012674_state:((state->(state->Prop))->(com->((state->(state->Prop))->hoare_1708887482_state))).
% Parameter if_Hoa1374726218_state:(Prop->(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))).
% Parameter if_option_com:(Prop->(option_com->(option_com->option_com))).
% Parameter semila2013987940me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter semila598060698te_o_o:(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop))).
% Parameter semila513601829_com_o:((com->Prop)->((com->Prop)->(com->Prop))).
% Parameter semila1673364395name_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter semila129691299tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))).
% Parameter semila854092349_inf_o:(Prop->(Prop->Prop)).
% Parameter semila181081674me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter semila1853742644te_o_o:(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop))).
% Parameter semila1562558655_com_o:((com->Prop)->((com->Prop)->(com->Prop))).
% Parameter semila1780557381name_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter semila1122118281tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))).
% Parameter semila10642723_sup_o:(Prop->(Prop->Prop)).
% Parameter dom_com_com:((com->option_com)->(com->Prop)).
% Parameter dom_pname_com:((pname->option_com)->(pname->Prop)).
% Parameter dom_pname_pname:((pname->option_pname)->(pname->Prop)).
% Parameter dom_pn1412407212_state:((pname->option1624383643_state)->(pname->Prop)).
% Parameter dom_Ho1805192458_pname:((hoare_1708887482_state->option_pname)->(hoare_1708887482_state->Prop)).
% Parameter dom_Ho1703271284_state:((hoare_1708887482_state->option1624383643_state)->(hoare_1708887482_state->Prop)).
% Parameter restri1382200118me_com:((pname->option_com)->((pname->Prop)->(pname->option_com))).
% Parameter evalc:(com->(state->(state->Prop))).
% Parameter is_none_com:(option_com->Prop).
% Parameter is_none_pname:(option_pname->Prop).
% Parameter is_non163157940_state:(option1624383643_state->Prop).
% Parameter none_com:option_com.
% Parameter none_pname:option_pname.
% Parameter none_H1106584047_state:option1624383643_state.
% Parameter some_com:(com->option_com).
% Parameter some_pname:(pname->option_pname).
% Parameter some_H1974565227_state:(hoare_1708887482_state->option1624383643_state).
% Parameter set_com:(option_com->(com->Prop)).
% Parameter set_pname:(option_pname->(pname->Prop)).
% Parameter set_Ho525251890_state:(option1624383643_state->(hoare_1708887482_state->Prop)).
% Parameter the_com:(option_com->com).
% Parameter the_pname_1:(option_pname->pname).
% Parameter the_Ho963921505_state:(option1624383643_state->hoare_1708887482_state).
% Parameter bot_bot_pname_o_o:((pname->Prop)->Prop).
% Parameter bot_bo1678742418te_o_o:((hoare_1708887482_state->Prop)->Prop).
% Parameter bot_bot_com_o:(com->Prop).
% Parameter bot_bot_pname_o:(pname->Prop).
% Parameter bot_bo19817387tate_o:(hoare_1708887482_state->Prop).
% Parameter bot_bot_o:Prop.
% Parameter ord_le1205211808me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)).
% Parameter ord_le1728773982te_o_o:(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->Prop)).
% Parameter ord_less_eq_com_o:((com->Prop)->((com->Prop)->Prop)).
% Parameter ord_less_eq_pname_o:((pname->Prop)->((pname->Prop)->Prop)).
% Parameter ord_le777019615tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop)).
% Parameter ord_less_eq_o:(Prop->(Prop->Prop)).
% Parameter top_top_com_o:(com->Prop).
% Parameter top_top_pname_o:(pname->Prop).
% Parameter top_to832624271tate_o:(hoare_1708887482_state->Prop).
% Parameter partial_flat_lub_com:(com->((com->Prop)->com)).
% Parameter partia752020666_pname:(pname->((pname->Prop)->pname)).
% Parameter partia1256728516_state:(hoare_1708887482_state->((hoare_1708887482_state->Prop)->hoare_1708887482_state)).
% Parameter collect_pname_o_o:((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)).
% Parameter collec58007891te_o_o:((((hoare_1708887482_state->Prop)->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->Prop)).
% Parameter collect_pname_o:(((pname->Prop)->Prop)->((pname->Prop)->Prop)).
% Parameter collec219771562tate_o:(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop)).
% Parameter collect_com:((com->Prop)->(com->Prop)).
% Parameter collect_pname:((pname->Prop)->(pname->Prop)).
% Parameter collec1568722789_state:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)).
% Parameter image_1085733413name_o:(((pname->Prop)->(pname->Prop))->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter image_pname_o_pname:(((pname->Prop)->pname)->(((pname->Prop)->Prop)->(pname->Prop))).
% Parameter image_1922967206_state:(((pname->Prop)->hoare_1708887482_state)->(((pname->Prop)->Prop)->(hoare_1708887482_state->Prop))).
% Parameter image_909543877tate_o:(((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop))).
% Parameter image_2051418740_pname:(((hoare_1708887482_state->Prop)->pname)->(((hoare_1708887482_state->Prop)->Prop)->(pname->Prop))).
% Parameter image_27005066_state:(((hoare_1708887482_state->Prop)->hoare_1708887482_state)->(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))).
% Parameter image_com_com:((com->com)->((com->Prop)->(com->Prop))).
% Parameter image_com_pname:((com->pname)->((com->Prop)->(pname->Prop))).
% Parameter image_934102463_state:((com->hoare_1708887482_state)->((com->Prop)->(hoare_1708887482_state->Prop))).
% Parameter image_pname_pname_o:((pname->(pname->Prop))->((pname->Prop)->((pname->Prop)->Prop))).
% Parameter image_425134806tate_o:((pname->(hoare_1708887482_state->Prop))->((pname->Prop)->((hoare_1708887482_state->Prop)->Prop))).
% Parameter image_pname_com:((pname->com)->((pname->Prop)->(com->Prop))).
% Parameter image_pname_pname:((pname->pname)->((pname->Prop)->(pname->Prop))).
% Parameter image_1116629049_state:((pname->hoare_1708887482_state)->((pname->Prop)->(hoare_1708887482_state->Prop))).
% Parameter image_1552895654name_o:((hoare_1708887482_state->(pname->Prop))->((hoare_1708887482_state->Prop)->((pname->Prop)->Prop))).
% Parameter image_1551509096tate_o:((hoare_1708887482_state->(hoare_1708887482_state->Prop))->((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop))).
% Parameter image_1604448413te_com:((hoare_1708887482_state->com)->((hoare_1708887482_state->Prop)->(com->Prop))).
% Parameter image_1509414295_pname:((hoare_1708887482_state->pname)->((hoare_1708887482_state->Prop)->(pname->Prop))).
% Parameter image_757158439_state:((hoare_1708887482_state->hoare_1708887482_state)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))).
% Parameter insert_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter insert949073679tate_o:((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop))).
% Parameter insert_o:(Prop->((Prop->Prop)->(Prop->Prop))).
% Parameter insert_com:(com->((com->Prop)->(com->Prop))).
% Parameter insert_pname:(pname->((pname->Prop)->(pname->Prop))).
% Parameter insert528405184_state:(hoare_1708887482_state->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))).
% Parameter the_elem_com:((com->Prop)->com).
% Parameter the_elem_pname:((pname->Prop)->pname).
% Parameter the_el864710747_state:((hoare_1708887482_state->Prop)->hoare_1708887482_state).
% Parameter vimage1943311875_state:((pname->hoare_1708887482_state)->((hoare_1708887482_state->Prop)->(pname->Prop))).
% Parameter fequal_pname_o:((pname->Prop)->((pname->Prop)->Prop)).
% Parameter fequal1436017556tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop)).
% Parameter fequal_com:(com->(com->Prop)).
% Parameter fequal_pname:(pname->(pname->Prop)).
% Parameter fequal_state:(state->(state->Prop)).
% Parameter fequal224822779_state:(hoare_1708887482_state->(hoare_1708887482_state->Prop)).
% Parameter member_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->Prop)).
% Parameter member814030440tate_o:((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->Prop)).
% Parameter member_o:(Prop->((Prop->Prop)->Prop)).
% Parameter member_com:(com->((com->Prop)->Prop)).
% Parameter member_pname:(pname->((pname->Prop)->Prop)).
% Parameter member451959335_state:(hoare_1708887482_state->((hoare_1708887482_state->Prop)->Prop)).
% Parameter fa:(hoare_1708887482_state->Prop).
% Parameter pn:pname.
% Parameter y:com.
% Axiom fact_0_empty:(forall (G_7:(hoare_1708887482_state->Prop)), ((hoare_90032982_state G_7) bot_bo19817387tate_o)).
% Axiom fact_1_asm:(forall (Ts_7:(hoare_1708887482_state->Prop)) (G_39:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Ts_7) G_39)->((hoare_90032982_state G_39) Ts_7))).
% Axiom fact_2_weaken:(forall (Ts_6:(hoare_1708887482_state->Prop)) (G_38:(hoare_1708887482_state->Prop)) (Ts_5:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_38) Ts_5)->(((ord_le777019615tate_o Ts_6) Ts_5)->((hoare_90032982_state G_38) Ts_6)))).
% Axiom fact_3_thin:(forall (G_37:(hoare_1708887482_state->Prop)) (G_36:(hoare_1708887482_state->Prop)) (Ts_4:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_36) Ts_4)->(((ord_le777019615tate_o G_36) G_37)->((hoare_90032982_state G_37) Ts_4)))).
% Axiom fact_4_cut:(forall (G_35:(hoare_1708887482_state->Prop)) (G_34:(hoare_1708887482_state->Prop)) (Ts_3:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_34) Ts_3)->(((hoare_90032982_state G_35) G_34)->((hoare_90032982_state G_35) Ts_3)))).
% Axiom fact_5_hoare__derivs_Oinsert:(forall (Ts_2:(hoare_1708887482_state->Prop)) (G_33:(hoare_1708887482_state->Prop)) (T_3:hoare_1708887482_state), (((hoare_90032982_state G_33) ((insert528405184_state T_3) bot_bo19817387tate_o))->(((hoare_90032982_state G_33) Ts_2)->((hoare_90032982_state G_33) ((insert528405184_state T_3) Ts_2))))).
% Axiom fact_6_derivs__insertD:(forall (G_32:(hoare_1708887482_state->Prop)) (T_2:hoare_1708887482_state) (Ts_1:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_32) ((insert528405184_state T_2) Ts_1))->((and ((hoare_90032982_state G_32) ((insert528405184_state T_2) bot_bo19817387tate_o))) ((hoare_90032982_state G_32) Ts_1)))).
% Axiom fact_7_MGT__BodyN:(forall (Pn_1:pname) (G_7:(hoare_1708887482_state->Prop)), (((hoare_90032982_state ((insert528405184_state (hoare_Mirabelle_MGT (body_1 Pn_1))) G_7)) ((insert528405184_state (hoare_Mirabelle_MGT (the_com (body Pn_1)))) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT (body_1 Pn_1))) bot_bo19817387tate_o)))).
% Axiom fact_8_finite__Collect__subsets:(forall (A_274:((pname->Prop)->Prop)), ((finite297249702name_o A_274)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_84:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_84) A_274)))))).
% Axiom fact_9_finite__Collect__subsets:(forall (A_274:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_274)->(finite1019950101te_o_o (collec58007891te_o_o (fun (B_84:((hoare_1708887482_state->Prop)->Prop))=> ((ord_le1728773982te_o_o B_84) A_274)))))).
% Axiom fact_10_finite__Collect__subsets:(forall (A_274:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_274)->(finite1329924456tate_o (collec219771562tate_o (fun (B_84:(hoare_1708887482_state->Prop))=> ((ord_le777019615tate_o B_84) A_274)))))).
% Axiom fact_11_finite__Collect__subsets:(forall (A_274:(pname->Prop)), ((finite_finite_pname A_274)->(finite297249702name_o (collect_pname_o (fun (B_84:(pname->Prop))=> ((ord_less_eq_pname_o B_84) A_274)))))).
% Axiom fact_12_finite__imageI:(forall (H_2:(hoare_1708887482_state->(pname->Prop))) (F_88:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_88)->(finite297249702name_o ((image_1552895654name_o H_2) F_88)))).
% Axiom fact_13_finite__imageI:(forall (H_2:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (F_88:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_88)->(finite1329924456tate_o ((image_1551509096tate_o H_2) F_88)))).
% Axiom fact_14_finite__imageI:(forall (H_2:(pname->(pname->Prop))) (F_88:(pname->Prop)), ((finite_finite_pname F_88)->(finite297249702name_o ((image_pname_pname_o H_2) F_88)))).
% Axiom fact_15_finite__imageI:(forall (H_2:(pname->(hoare_1708887482_state->Prop))) (F_88:(pname->Prop)), ((finite_finite_pname F_88)->(finite1329924456tate_o ((image_425134806tate_o H_2) F_88)))).
% Axiom fact_16_finite__imageI:(forall (H_2:((pname->Prop)->hoare_1708887482_state)) (F_88:((pname->Prop)->Prop)), ((finite297249702name_o F_88)->(finite1625599783_state ((image_1922967206_state H_2) F_88)))).
% Axiom fact_17_finite__imageI:(forall (H_2:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (F_88:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_88)->(finite1625599783_state ((image_27005066_state H_2) F_88)))).
% Axiom fact_18_finite__imageI:(forall (H_2:((pname->Prop)->pname)) (F_88:((pname->Prop)->Prop)), ((finite297249702name_o F_88)->(finite_finite_pname ((image_pname_o_pname H_2) F_88)))).
% Axiom fact_19_finite__imageI:(forall (H_2:((hoare_1708887482_state->Prop)->pname)) (F_88:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_88)->(finite_finite_pname ((image_2051418740_pname H_2) F_88)))).
% Axiom fact_20_finite__imageI:(forall (H_2:(pname->hoare_1708887482_state)) (F_88:(pname->Prop)), ((finite_finite_pname F_88)->(finite1625599783_state ((image_1116629049_state H_2) F_88)))).
% Axiom fact_21_empty__subsetI:(forall (A_273:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_273)).
% Axiom fact_22_empty__subsetI:(forall (A_273:(com->Prop)), ((ord_less_eq_com_o bot_bot_com_o) A_273)).
% Axiom fact_23_empty__subsetI:(forall (A_273:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o bot_bo19817387tate_o) A_273)).
% Axiom fact_24_finite_OinsertI:(forall (A_272:com) (A_271:(com->Prop)), ((finite_finite_com A_271)->(finite_finite_com ((insert_com A_272) A_271)))).
% Axiom fact_25_finite_OinsertI:(forall (A_272:(pname->Prop)) (A_271:((pname->Prop)->Prop)), ((finite297249702name_o A_271)->(finite297249702name_o ((insert_pname_o A_272) A_271)))).
% Axiom fact_26_finite_OinsertI:(forall (A_272:(hoare_1708887482_state->Prop)) (A_271:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_271)->(finite1329924456tate_o ((insert949073679tate_o A_272) A_271)))).
% Axiom fact_27_finite_OinsertI:(forall (A_272:pname) (A_271:(pname->Prop)), ((finite_finite_pname A_271)->(finite_finite_pname ((insert_pname A_272) A_271)))).
% Axiom fact_28_finite_OinsertI:(forall (A_272:hoare_1708887482_state) (A_271:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_271)->(finite1625599783_state ((insert528405184_state A_272) A_271)))).
% Axiom fact_29_finite_OemptyI:(finite297249702name_o bot_bot_pname_o_o).
% Axiom fact_30_finite_OemptyI:(finite1329924456tate_o bot_bo1678742418te_o_o).
% Axiom fact_31_finite_OemptyI:(finite_finite_com bot_bot_com_o).
% Axiom fact_32_finite_OemptyI:(finite1625599783_state bot_bo19817387tate_o).
% Axiom fact_33_finite_OemptyI:(finite_finite_pname bot_bot_pname_o).
% Axiom fact_34_finite__Collect__conjI:(forall (Q_26:((pname->Prop)->Prop)) (P_45:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_45))) (finite297249702name_o (collect_pname_o Q_26)))->(finite297249702name_o (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (P_45 X_3)) (Q_26 X_3))))))).
% Axiom fact_35_finite__Collect__conjI:(forall (Q_26:((hoare_1708887482_state->Prop)->Prop)) (P_45:((hoare_1708887482_state->Prop)->Prop)), (((or (finite1329924456tate_o (collec219771562tate_o P_45))) (finite1329924456tate_o (collec219771562tate_o Q_26)))->(finite1329924456tate_o (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (P_45 X_3)) (Q_26 X_3))))))).
% Axiom fact_36_finite__Collect__conjI:(forall (Q_26:(hoare_1708887482_state->Prop)) (P_45:(hoare_1708887482_state->Prop)), (((or (finite1625599783_state (collec1568722789_state P_45))) (finite1625599783_state (collec1568722789_state Q_26)))->(finite1625599783_state (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (P_45 X_3)) (Q_26 X_3))))))).
% Axiom fact_37_finite__Collect__conjI:(forall (Q_26:(pname->Prop)) (P_45:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_45))) (finite_finite_pname (collect_pname Q_26)))->(finite_finite_pname (collect_pname (fun (X_3:pname)=> ((and (P_45 X_3)) (Q_26 X_3))))))).
% Axiom fact_38_image__constant__conv:(forall (C_68:pname) (A_270:(hoare_1708887482_state->Prop)), ((and ((((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o)->(((eq (pname->Prop)) ((image_1509414295_pname (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) bot_bot_pname_o))) ((not (((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o))->(((eq (pname->Prop)) ((image_1509414295_pname (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) ((insert_pname C_68) bot_bot_pname_o))))).
% Axiom fact_39_image__constant__conv:(forall (C_68:com) (A_270:(hoare_1708887482_state->Prop)), ((and ((((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o)->(((eq (com->Prop)) ((image_1604448413te_com (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) bot_bot_com_o))) ((not (((eq (hoare_1708887482_state->Prop)) A_270) bot_bo19817387tate_o))->(((eq (com->Prop)) ((image_1604448413te_com (fun (X_3:hoare_1708887482_state)=> C_68)) A_270)) ((insert_com C_68) bot_bot_com_o))))).
% Axiom fact_40_image__constant__conv:(forall (C_68:hoare_1708887482_state) (A_270:(com->Prop)), ((and ((((eq (com->Prop)) A_270) bot_bot_com_o)->(((eq (hoare_1708887482_state->Prop)) ((image_934102463_state (fun (X_3:com)=> C_68)) A_270)) bot_bo19817387tate_o))) ((not (((eq (com->Prop)) A_270) bot_bot_com_o))->(((eq (hoare_1708887482_state->Prop)) ((image_934102463_state (fun (X_3:com)=> C_68)) A_270)) ((insert528405184_state C_68) bot_bo19817387tate_o))))).
% Axiom fact_41_image__constant__conv:(forall (C_68:hoare_1708887482_state) (A_270:(pname->Prop)), ((and ((((eq (pname->Prop)) A_270) bot_bot_pname_o)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> C_68)) A_270)) bot_bo19817387tate_o))) ((not (((eq (pname->Prop)) A_270) bot_bot_pname_o))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> C_68)) A_270)) ((insert528405184_state C_68) bot_bo19817387tate_o))))).
% Axiom fact_42_image__constant:(forall (C_67:pname) (X_119:hoare_1708887482_state) (A_269:(hoare_1708887482_state->Prop)), (((member451959335_state X_119) A_269)->(((eq (pname->Prop)) ((image_1509414295_pname (fun (X_3:hoare_1708887482_state)=> C_67)) A_269)) ((insert_pname C_67) bot_bot_pname_o)))).
% Axiom fact_43_image__constant:(forall (C_67:com) (X_119:hoare_1708887482_state) (A_269:(hoare_1708887482_state->Prop)), (((member451959335_state X_119) A_269)->(((eq (com->Prop)) ((image_1604448413te_com (fun (X_3:hoare_1708887482_state)=> C_67)) A_269)) ((insert_com C_67) bot_bot_com_o)))).
% Axiom fact_44_image__constant:(forall (C_67:pname) (X_119:pname) (A_269:(pname->Prop)), (((member_pname X_119) A_269)->(((eq (pname->Prop)) ((image_pname_pname (fun (X_3:pname)=> C_67)) A_269)) ((insert_pname C_67) bot_bot_pname_o)))).
% Axiom fact_45_image__constant:(forall (C_67:com) (X_119:pname) (A_269:(pname->Prop)), (((member_pname X_119) A_269)->(((eq (com->Prop)) ((image_pname_com (fun (X_3:pname)=> C_67)) A_269)) ((insert_com C_67) bot_bot_com_o)))).
% Axiom fact_46_image__constant:(forall (C_67:hoare_1708887482_state) (X_119:com) (A_269:(com->Prop)), (((member_com X_119) A_269)->(((eq (hoare_1708887482_state->Prop)) ((image_934102463_state (fun (X_3:com)=> C_67)) A_269)) ((insert528405184_state C_67) bot_bo19817387tate_o)))).
% Axiom fact_47_image__constant:(forall (C_67:hoare_1708887482_state) (X_119:pname) (A_269:(pname->Prop)), (((member_pname X_119) A_269)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> C_67)) A_269)) ((insert528405184_state C_67) bot_bo19817387tate_o)))).
% Axiom fact_48_insert__dom:(forall (F_87:(com->option_com)) (X_118:com) (Y_53:com), ((((eq option_com) (F_87 X_118)) (some_com Y_53))->(((eq (com->Prop)) ((insert_com X_118) (dom_com_com F_87))) (dom_com_com F_87)))).
% Axiom fact_49_insert__dom:(forall (F_87:(hoare_1708887482_state->option_pname)) (X_118:hoare_1708887482_state) (Y_53:pname), ((((eq option_pname) (F_87 X_118)) (some_pname Y_53))->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_118) (dom_Ho1805192458_pname F_87))) (dom_Ho1805192458_pname F_87)))).
% Axiom fact_50_insert__dom:(forall (F_87:(hoare_1708887482_state->option1624383643_state)) (X_118:hoare_1708887482_state) (Y_53:hoare_1708887482_state), ((((eq option1624383643_state) (F_87 X_118)) (some_H1974565227_state Y_53))->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_118) (dom_Ho1703271284_state F_87))) (dom_Ho1703271284_state F_87)))).
% Axiom fact_51_insert__dom:(forall (F_87:(pname->option_com)) (X_118:pname) (Y_53:com), ((((eq option_com) (F_87 X_118)) (some_com Y_53))->(((eq (pname->Prop)) ((insert_pname X_118) (dom_pname_com F_87))) (dom_pname_com F_87)))).
% Axiom fact_52_finite__surj:(forall (B_171:((pname->Prop)->Prop)) (F_86:(hoare_1708887482_state->(pname->Prop))) (A_268:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_268)->(((ord_le1205211808me_o_o B_171) ((image_1552895654name_o F_86) A_268))->(finite297249702name_o B_171)))).
% Axiom fact_53_finite__surj:(forall (B_171:((hoare_1708887482_state->Prop)->Prop)) (F_86:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (A_268:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_268)->(((ord_le1728773982te_o_o B_171) ((image_1551509096tate_o F_86) A_268))->(finite1329924456tate_o B_171)))).
% Axiom fact_54_finite__surj:(forall (B_171:(pname->Prop)) (F_86:(hoare_1708887482_state->pname)) (A_268:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_268)->(((ord_less_eq_pname_o B_171) ((image_1509414295_pname F_86) A_268))->(finite_finite_pname B_171)))).
% Axiom fact_55_finite__surj:(forall (B_171:((pname->Prop)->Prop)) (F_86:(pname->(pname->Prop))) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_le1205211808me_o_o B_171) ((image_pname_pname_o F_86) A_268))->(finite297249702name_o B_171)))).
% Axiom fact_56_finite__surj:(forall (B_171:((hoare_1708887482_state->Prop)->Prop)) (F_86:(pname->(hoare_1708887482_state->Prop))) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_le1728773982te_o_o B_171) ((image_425134806tate_o F_86) A_268))->(finite1329924456tate_o B_171)))).
% Axiom fact_57_finite__surj:(forall (B_171:(pname->Prop)) (F_86:(pname->pname)) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_less_eq_pname_o B_171) ((image_pname_pname F_86) A_268))->(finite_finite_pname B_171)))).
% Axiom fact_58_finite__surj:(forall (B_171:(hoare_1708887482_state->Prop)) (F_86:((pname->Prop)->hoare_1708887482_state)) (A_268:((pname->Prop)->Prop)), ((finite297249702name_o A_268)->(((ord_le777019615tate_o B_171) ((image_1922967206_state F_86) A_268))->(finite1625599783_state B_171)))).
% Axiom fact_59_finite__surj:(forall (B_171:(hoare_1708887482_state->Prop)) (F_86:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (A_268:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_268)->(((ord_le777019615tate_o B_171) ((image_27005066_state F_86) A_268))->(finite1625599783_state B_171)))).
% Axiom fact_60_finite__surj:(forall (B_171:(pname->Prop)) (F_86:((pname->Prop)->pname)) (A_268:((pname->Prop)->Prop)), ((finite297249702name_o A_268)->(((ord_less_eq_pname_o B_171) ((image_pname_o_pname F_86) A_268))->(finite_finite_pname B_171)))).
% Axiom fact_61_finite__surj:(forall (B_171:(pname->Prop)) (F_86:((hoare_1708887482_state->Prop)->pname)) (A_268:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_268)->(((ord_less_eq_pname_o B_171) ((image_2051418740_pname F_86) A_268))->(finite_finite_pname B_171)))).
% Axiom fact_62_finite__surj:(forall (B_171:(hoare_1708887482_state->Prop)) (F_86:(pname->hoare_1708887482_state)) (A_268:(pname->Prop)), ((finite_finite_pname A_268)->(((ord_le777019615tate_o B_171) ((image_1116629049_state F_86) A_268))->(finite1625599783_state B_171)))).
% Axiom fact_63_subset__singletonD:(forall (A_267:(pname->Prop)) (X_117:pname), (((ord_less_eq_pname_o A_267) ((insert_pname X_117) bot_bot_pname_o))->((or (((eq (pname->Prop)) A_267) bot_bot_pname_o)) (((eq (pname->Prop)) A_267) ((insert_pname X_117) bot_bot_pname_o))))).
% Axiom fact_64_subset__singletonD:(forall (A_267:(com->Prop)) (X_117:com), (((ord_less_eq_com_o A_267) ((insert_com X_117) bot_bot_com_o))->((or (((eq (com->Prop)) A_267) bot_bot_com_o)) (((eq (com->Prop)) A_267) ((insert_com X_117) bot_bot_com_o))))).
% Axiom fact_65_subset__singletonD:(forall (A_267:(hoare_1708887482_state->Prop)) (X_117:hoare_1708887482_state), (((ord_le777019615tate_o A_267) ((insert528405184_state X_117) bot_bo19817387tate_o))->((or (((eq (hoare_1708887482_state->Prop)) A_267) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) A_267) ((insert528405184_state X_117) bot_bo19817387tate_o))))).
% Axiom fact_66_MGF:(forall (C_34:com), (hoare_1160767572gleton->(wT_bodies->((wt C_34)->((hoare_90032982_state bot_bo19817387tate_o) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o)))))).
% Axiom fact_67_emptyE:(forall (A_266:com), (((member_com A_266) bot_bot_com_o)->False)).
% Axiom fact_68_emptyE:(forall (A_266:hoare_1708887482_state), (((member451959335_state A_266) bot_bo19817387tate_o)->False)).
% Axiom fact_69_emptyE:(forall (A_266:pname), (((member_pname A_266) bot_bot_pname_o)->False)).
% Axiom fact_70_insertCI:(forall (B_170:com) (A_265:com) (B_169:(com->Prop)), (((((member_com A_265) B_169)->False)->(((eq com) A_265) B_170))->((member_com A_265) ((insert_com B_170) B_169)))).
% Axiom fact_71_insertCI:(forall (B_170:pname) (A_265:pname) (B_169:(pname->Prop)), (((((member_pname A_265) B_169)->False)->(((eq pname) A_265) B_170))->((member_pname A_265) ((insert_pname B_170) B_169)))).
% Axiom fact_72_insertCI:(forall (B_170:hoare_1708887482_state) (A_265:hoare_1708887482_state) (B_169:(hoare_1708887482_state->Prop)), (((((member451959335_state A_265) B_169)->False)->(((eq hoare_1708887482_state) A_265) B_170))->((member451959335_state A_265) ((insert528405184_state B_170) B_169)))).
% Axiom fact_73_insertE:(forall (A_264:com) (B_168:com) (A_263:(com->Prop)), (((member_com A_264) ((insert_com B_168) A_263))->((not (((eq com) A_264) B_168))->((member_com A_264) A_263)))).
% Axiom fact_74_insertE:(forall (A_264:pname) (B_168:pname) (A_263:(pname->Prop)), (((member_pname A_264) ((insert_pname B_168) A_263))->((not (((eq pname) A_264) B_168))->((member_pname A_264) A_263)))).
% Axiom fact_75_insertE:(forall (A_264:hoare_1708887482_state) (B_168:hoare_1708887482_state) (A_263:(hoare_1708887482_state->Prop)), (((member451959335_state A_264) ((insert528405184_state B_168) A_263))->((not (((eq hoare_1708887482_state) A_264) B_168))->((member451959335_state A_264) A_263)))).
% Axiom fact_76_equalityI:(forall (A_262:(pname->Prop)) (B_167:(pname->Prop)), (((ord_less_eq_pname_o A_262) B_167)->(((ord_less_eq_pname_o B_167) A_262)->(((eq (pname->Prop)) A_262) B_167)))).
% Axiom fact_77_equalityI:(forall (A_262:(hoare_1708887482_state->Prop)) (B_167:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_262) B_167)->(((ord_le777019615tate_o B_167) A_262)->(((eq (hoare_1708887482_state->Prop)) A_262) B_167)))).
% Axiom fact_78_subsetD:(forall (C_66:com) (A_261:(com->Prop)) (B_166:(com->Prop)), (((ord_less_eq_com_o A_261) B_166)->(((member_com C_66) A_261)->((member_com C_66) B_166)))).
% Axiom fact_79_subsetD:(forall (C_66:hoare_1708887482_state) (A_261:(hoare_1708887482_state->Prop)) (B_166:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_261) B_166)->(((member451959335_state C_66) A_261)->((member451959335_state C_66) B_166)))).
% Axiom fact_80_subsetD:(forall (C_66:pname) (A_261:(pname->Prop)) (B_166:(pname->Prop)), (((ord_less_eq_pname_o A_261) B_166)->(((member_pname C_66) A_261)->((member_pname C_66) B_166)))).
% Axiom fact_81_image__eqI:(forall (A_260:(hoare_1708887482_state->Prop)) (B_165:com) (F_85:(hoare_1708887482_state->com)) (X_116:hoare_1708887482_state), ((((eq com) B_165) (F_85 X_116))->(((member451959335_state X_116) A_260)->((member_com B_165) ((image_1604448413te_com F_85) A_260))))).
% Axiom fact_82_image__eqI:(forall (A_260:(pname->Prop)) (B_165:com) (F_85:(pname->com)) (X_116:pname), ((((eq com) B_165) (F_85 X_116))->(((member_pname X_116) A_260)->((member_com B_165) ((image_pname_com F_85) A_260))))).
% Axiom fact_83_image__eqI:(forall (A_260:(com->Prop)) (B_165:hoare_1708887482_state) (F_85:(com->hoare_1708887482_state)) (X_116:com), ((((eq hoare_1708887482_state) B_165) (F_85 X_116))->(((member_com X_116) A_260)->((member451959335_state B_165) ((image_934102463_state F_85) A_260))))).
% Axiom fact_84_image__eqI:(forall (A_260:(com->Prop)) (B_165:pname) (F_85:(com->pname)) (X_116:com), ((((eq pname) B_165) (F_85 X_116))->(((member_com X_116) A_260)->((member_pname B_165) ((image_com_pname F_85) A_260))))).
% Axiom fact_85_image__eqI:(forall (A_260:(pname->Prop)) (B_165:hoare_1708887482_state) (F_85:(pname->hoare_1708887482_state)) (X_116:pname), ((((eq hoare_1708887482_state) B_165) (F_85 X_116))->(((member_pname X_116) A_260)->((member451959335_state B_165) ((image_1116629049_state F_85) A_260))))).
% Axiom fact_86_equals0D:(forall (A_259:com) (A_258:(com->Prop)), ((((eq (com->Prop)) A_258) bot_bot_com_o)->(((member_com A_259) A_258)->False))).
% Axiom fact_87_equals0D:(forall (A_259:hoare_1708887482_state) (A_258:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_258) bot_bo19817387tate_o)->(((member451959335_state A_259) A_258)->False))).
% Axiom fact_88_equals0D:(forall (A_259:pname) (A_258:(pname->Prop)), ((((eq (pname->Prop)) A_258) bot_bot_pname_o)->(((member_pname A_259) A_258)->False))).
% Axiom fact_89_Collect__empty__eq:(forall (P_44:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_44)) bot_bot_pname_o)) (forall (X_3:pname), ((P_44 X_3)->False)))).
% Axiom fact_90_Collect__empty__eq:(forall (P_44:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) (collect_pname_o P_44)) bot_bot_pname_o_o)) (forall (X_3:(pname->Prop)), ((P_44 X_3)->False)))).
% Axiom fact_91_Collect__empty__eq:(forall (P_44:((hoare_1708887482_state->Prop)->Prop)), ((iff (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o P_44)) bot_bo1678742418te_o_o)) (forall (X_3:(hoare_1708887482_state->Prop)), ((P_44 X_3)->False)))).
% Axiom fact_92_Collect__empty__eq:(forall (P_44:(com->Prop)), ((iff (((eq (com->Prop)) (collect_com P_44)) bot_bot_com_o)) (forall (X_3:com), ((P_44 X_3)->False)))).
% Axiom fact_93_Collect__empty__eq:(forall (P_44:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state P_44)) bot_bo19817387tate_o)) (forall (X_3:hoare_1708887482_state), ((P_44 X_3)->False)))).
% Axiom fact_94_empty__iff:(forall (C_65:com), (((member_com C_65) bot_bot_com_o)->False)).
% Axiom fact_95_empty__iff:(forall (C_65:hoare_1708887482_state), (((member451959335_state C_65) bot_bo19817387tate_o)->False)).
% Axiom fact_96_empty__iff:(forall (C_65:pname), (((member_pname C_65) bot_bot_pname_o)->False)).
% Axiom fact_97_empty__Collect__eq:(forall (P_43:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_43))) (forall (X_3:pname), ((P_43 X_3)->False)))).
% Axiom fact_98_empty__Collect__eq:(forall (P_43:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o P_43))) (forall (X_3:(pname->Prop)), ((P_43 X_3)->False)))).
% Axiom fact_99_empty__Collect__eq:(forall (P_43:((hoare_1708887482_state->Prop)->Prop)), ((iff (((eq ((hoare_1708887482_state->Prop)->Prop)) bot_bo1678742418te_o_o) (collec219771562tate_o P_43))) (forall (X_3:(hoare_1708887482_state->Prop)), ((P_43 X_3)->False)))).
% Axiom fact_100_empty__Collect__eq:(forall (P_43:(com->Prop)), ((iff (((eq (com->Prop)) bot_bot_com_o) (collect_com P_43))) (forall (X_3:com), ((P_43 X_3)->False)))).
% Axiom fact_101_empty__Collect__eq:(forall (P_43:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state P_43))) (forall (X_3:hoare_1708887482_state), ((P_43 X_3)->False)))).
% Axiom fact_102_ex__in__conv:(forall (A_257:(com->Prop)), ((iff ((ex com) (fun (X_3:com)=> ((member_com X_3) A_257)))) (not (((eq (com->Prop)) A_257) bot_bot_com_o)))).
% Axiom fact_103_ex__in__conv:(forall (A_257:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) A_257)))) (not (((eq (hoare_1708887482_state->Prop)) A_257) bot_bo19817387tate_o)))).
% Axiom fact_104_ex__in__conv:(forall (A_257:(pname->Prop)), ((iff ((ex pname) (fun (X_3:pname)=> ((member_pname X_3) A_257)))) (not (((eq (pname->Prop)) A_257) bot_bot_pname_o)))).
% Axiom fact_105_all__not__in__conv:(forall (A_256:(com->Prop)), ((iff (forall (X_3:com), (((member_com X_3) A_256)->False))) (((eq (com->Prop)) A_256) bot_bot_com_o))).
% Axiom fact_106_all__not__in__conv:(forall (A_256:(hoare_1708887482_state->Prop)), ((iff (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_256)->False))) (((eq (hoare_1708887482_state->Prop)) A_256) bot_bo19817387tate_o))).
% Axiom fact_107_all__not__in__conv:(forall (A_256:(pname->Prop)), ((iff (forall (X_3:pname), (((member_pname X_3) A_256)->False))) (((eq (pname->Prop)) A_256) bot_bot_pname_o))).
% Axiom fact_108_empty__def:(((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X_3:pname)=> False))).
% Axiom fact_109_empty__def:(((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o (fun (X_3:(pname->Prop))=> False))).
% Axiom fact_110_empty__def:(((eq ((hoare_1708887482_state->Prop)->Prop)) bot_bo1678742418te_o_o) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> False))).
% Axiom fact_111_empty__def:(((eq (com->Prop)) bot_bot_com_o) (collect_com (fun (X_3:com)=> False))).
% Axiom fact_112_empty__def:(((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> False))).
% Axiom fact_113_insert__absorb:(forall (A_255:com) (A_254:(com->Prop)), (((member_com A_255) A_254)->(((eq (com->Prop)) ((insert_com A_255) A_254)) A_254))).
% Axiom fact_114_insert__absorb:(forall (A_255:pname) (A_254:(pname->Prop)), (((member_pname A_255) A_254)->(((eq (pname->Prop)) ((insert_pname A_255) A_254)) A_254))).
% Axiom fact_115_insert__absorb:(forall (A_255:hoare_1708887482_state) (A_254:(hoare_1708887482_state->Prop)), (((member451959335_state A_255) A_254)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_255) A_254)) A_254))).
% Axiom fact_116_insertI2:(forall (B_164:com) (A_253:com) (B_163:(com->Prop)), (((member_com A_253) B_163)->((member_com A_253) ((insert_com B_164) B_163)))).
% Axiom fact_117_insertI2:(forall (B_164:pname) (A_253:pname) (B_163:(pname->Prop)), (((member_pname A_253) B_163)->((member_pname A_253) ((insert_pname B_164) B_163)))).
% Axiom fact_118_insertI2:(forall (B_164:hoare_1708887482_state) (A_253:hoare_1708887482_state) (B_163:(hoare_1708887482_state->Prop)), (((member451959335_state A_253) B_163)->((member451959335_state A_253) ((insert528405184_state B_164) B_163)))).
% Axiom fact_119_insert__ident:(forall (B_162:(com->Prop)) (X_115:com) (A_252:(com->Prop)), ((((member_com X_115) A_252)->False)->((((member_com X_115) B_162)->False)->((iff (((eq (com->Prop)) ((insert_com X_115) A_252)) ((insert_com X_115) B_162))) (((eq (com->Prop)) A_252) B_162))))).
% Axiom fact_120_insert__ident:(forall (B_162:(pname->Prop)) (X_115:pname) (A_252:(pname->Prop)), ((((member_pname X_115) A_252)->False)->((((member_pname X_115) B_162)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_115) A_252)) ((insert_pname X_115) B_162))) (((eq (pname->Prop)) A_252) B_162))))).
% Axiom fact_121_insert__ident:(forall (B_162:(hoare_1708887482_state->Prop)) (X_115:hoare_1708887482_state) (A_252:(hoare_1708887482_state->Prop)), ((((member451959335_state X_115) A_252)->False)->((((member451959335_state X_115) B_162)->False)->((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_115) A_252)) ((insert528405184_state X_115) B_162))) (((eq (hoare_1708887482_state->Prop)) A_252) B_162))))).
% Axiom fact_122_insert__code:(forall (Y_52:pname) (A_251:(pname->Prop)) (X_114:pname), ((iff (((insert_pname Y_52) A_251) X_114)) ((or (((eq pname) Y_52) X_114)) (A_251 X_114)))).
% Axiom fact_123_insert__code:(forall (Y_52:com) (A_251:(com->Prop)) (X_114:com), ((iff (((insert_com Y_52) A_251) X_114)) ((or (((eq com) Y_52) X_114)) (A_251 X_114)))).
% Axiom fact_124_insert__code:(forall (Y_52:hoare_1708887482_state) (A_251:(hoare_1708887482_state->Prop)) (X_114:hoare_1708887482_state), ((iff (((insert528405184_state Y_52) A_251) X_114)) ((or (((eq hoare_1708887482_state) Y_52) X_114)) (A_251 X_114)))).
% Axiom fact_125_insert__iff:(forall (A_250:com) (B_161:com) (A_249:(com->Prop)), ((iff ((member_com A_250) ((insert_com B_161) A_249))) ((or (((eq com) A_250) B_161)) ((member_com A_250) A_249)))).
% Axiom fact_126_insert__iff:(forall (A_250:pname) (B_161:pname) (A_249:(pname->Prop)), ((iff ((member_pname A_250) ((insert_pname B_161) A_249))) ((or (((eq pname) A_250) B_161)) ((member_pname A_250) A_249)))).
% Axiom fact_127_insert__iff:(forall (A_250:hoare_1708887482_state) (B_161:hoare_1708887482_state) (A_249:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state A_250) ((insert528405184_state B_161) A_249))) ((or (((eq hoare_1708887482_state) A_250) B_161)) ((member451959335_state A_250) A_249)))).
% Axiom fact_128_insert__commute:(forall (X_113:pname) (Y_51:pname) (A_248:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_113) ((insert_pname Y_51) A_248))) ((insert_pname Y_51) ((insert_pname X_113) A_248)))).
% Axiom fact_129_insert__commute:(forall (X_113:com) (Y_51:com) (A_248:(com->Prop)), (((eq (com->Prop)) ((insert_com X_113) ((insert_com Y_51) A_248))) ((insert_com Y_51) ((insert_com X_113) A_248)))).
% Axiom fact_130_insert__commute:(forall (X_113:hoare_1708887482_state) (Y_51:hoare_1708887482_state) (A_248:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_113) ((insert528405184_state Y_51) A_248))) ((insert528405184_state Y_51) ((insert528405184_state X_113) A_248)))).
% Axiom fact_131_insert__absorb2:(forall (X_112:pname) (A_247:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_112) ((insert_pname X_112) A_247))) ((insert_pname X_112) A_247))).
% Axiom fact_132_insert__absorb2:(forall (X_112:com) (A_247:(com->Prop)), (((eq (com->Prop)) ((insert_com X_112) ((insert_com X_112) A_247))) ((insert_com X_112) A_247))).
% Axiom fact_133_insert__absorb2:(forall (X_112:hoare_1708887482_state) (A_247:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_112) ((insert528405184_state X_112) A_247))) ((insert528405184_state X_112) A_247))).
% Axiom fact_134_insert__Collect:(forall (A_246:pname) (P_42:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_246) (collect_pname P_42))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_246))) (P_42 U_2)))))).
% Axiom fact_135_insert__Collect:(forall (A_246:com) (P_42:(com->Prop)), (((eq (com->Prop)) ((insert_com A_246) (collect_com P_42))) (collect_com (fun (U_2:com)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq com) U_2) A_246))) (P_42 U_2)))))).
% Axiom fact_136_insert__Collect:(forall (A_246:(pname->Prop)) (P_42:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_246) (collect_pname_o P_42))) (collect_pname_o (fun (U_2:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U_2) A_246))) (P_42 U_2)))))).
% Axiom fact_137_insert__Collect:(forall (A_246:(hoare_1708887482_state->Prop)) (P_42:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o A_246) (collec219771562tate_o P_42))) (collec219771562tate_o (fun (U_2:(hoare_1708887482_state->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_1708887482_state->Prop)) U_2) A_246))) (P_42 U_2)))))).
% Axiom fact_138_insert__Collect:(forall (A_246:hoare_1708887482_state) (P_42:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_246) (collec1568722789_state P_42))) (collec1568722789_state (fun (U_2:hoare_1708887482_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1708887482_state) U_2) A_246))) (P_42 U_2)))))).
% Axiom fact_139_insert__compr:(forall (A_245:com) (B_160:(com->Prop)), (((eq (com->Prop)) ((insert_com A_245) B_160)) (collect_com (fun (X_3:com)=> ((or (((eq com) X_3) A_245)) ((member_com X_3) B_160)))))).
% Axiom fact_140_insert__compr:(forall (A_245:(pname->Prop)) (B_160:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_245) B_160)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((or (((eq (pname->Prop)) X_3) A_245)) ((member_pname_o X_3) B_160)))))).
% Axiom fact_141_insert__compr:(forall (A_245:(hoare_1708887482_state->Prop)) (B_160:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o A_245) B_160)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or (((eq (hoare_1708887482_state->Prop)) X_3) A_245)) ((member814030440tate_o X_3) B_160)))))).
% Axiom fact_142_insert__compr:(forall (A_245:pname) (B_160:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_245) B_160)) (collect_pname (fun (X_3:pname)=> ((or (((eq pname) X_3) A_245)) ((member_pname X_3) B_160)))))).
% Axiom fact_143_insert__compr:(forall (A_245:hoare_1708887482_state) (B_160:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_245) B_160)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) X_3) A_245)) ((member451959335_state X_3) B_160)))))).
% Axiom fact_144_insertI1:(forall (A_244:com) (B_159:(com->Prop)), ((member_com A_244) ((insert_com A_244) B_159))).
% Axiom fact_145_insertI1:(forall (A_244:pname) (B_159:(pname->Prop)), ((member_pname A_244) ((insert_pname A_244) B_159))).
% Axiom fact_146_insertI1:(forall (A_244:hoare_1708887482_state) (B_159:(hoare_1708887482_state->Prop)), ((member451959335_state A_244) ((insert528405184_state A_244) B_159))).
% Axiom fact_147_equalityE:(forall (A_243:(pname->Prop)) (B_158:(pname->Prop)), ((((eq (pname->Prop)) A_243) B_158)->((((ord_less_eq_pname_o A_243) B_158)->(((ord_less_eq_pname_o B_158) A_243)->False))->False))).
% Axiom fact_148_equalityE:(forall (A_243:(hoare_1708887482_state->Prop)) (B_158:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_243) B_158)->((((ord_le777019615tate_o A_243) B_158)->(((ord_le777019615tate_o B_158) A_243)->False))->False))).
% Axiom fact_149_subset__trans:(forall (C_64:(pname->Prop)) (A_242:(pname->Prop)) (B_157:(pname->Prop)), (((ord_less_eq_pname_o A_242) B_157)->(((ord_less_eq_pname_o B_157) C_64)->((ord_less_eq_pname_o A_242) C_64)))).
% Axiom fact_150_subset__trans:(forall (C_64:(hoare_1708887482_state->Prop)) (A_242:(hoare_1708887482_state->Prop)) (B_157:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_242) B_157)->(((ord_le777019615tate_o B_157) C_64)->((ord_le777019615tate_o A_242) C_64)))).
% Axiom fact_151_set__mp:(forall (X_111:com) (A_241:(com->Prop)) (B_156:(com->Prop)), (((ord_less_eq_com_o A_241) B_156)->(((member_com X_111) A_241)->((member_com X_111) B_156)))).
% Axiom fact_152_set__mp:(forall (X_111:hoare_1708887482_state) (A_241:(hoare_1708887482_state->Prop)) (B_156:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_241) B_156)->(((member451959335_state X_111) A_241)->((member451959335_state X_111) B_156)))).
% Axiom fact_153_set__mp:(forall (X_111:pname) (A_241:(pname->Prop)) (B_156:(pname->Prop)), (((ord_less_eq_pname_o A_241) B_156)->(((member_pname X_111) A_241)->((member_pname X_111) B_156)))).
% Axiom fact_154_set__rev__mp:(forall (B_155:(com->Prop)) (X_110:com) (A_240:(com->Prop)), (((member_com X_110) A_240)->(((ord_less_eq_com_o A_240) B_155)->((member_com X_110) B_155)))).
% Axiom fact_155_set__rev__mp:(forall (B_155:(hoare_1708887482_state->Prop)) (X_110:hoare_1708887482_state) (A_240:(hoare_1708887482_state->Prop)), (((member451959335_state X_110) A_240)->(((ord_le777019615tate_o A_240) B_155)->((member451959335_state X_110) B_155)))).
% Axiom fact_156_set__rev__mp:(forall (B_155:(pname->Prop)) (X_110:pname) (A_240:(pname->Prop)), (((member_pname X_110) A_240)->(((ord_less_eq_pname_o A_240) B_155)->((member_pname X_110) B_155)))).
% Axiom fact_157_in__mono:(forall (X_109:com) (A_239:(com->Prop)) (B_154:(com->Prop)), (((ord_less_eq_com_o A_239) B_154)->(((member_com X_109) A_239)->((member_com X_109) B_154)))).
% Axiom fact_158_in__mono:(forall (X_109:hoare_1708887482_state) (A_239:(hoare_1708887482_state->Prop)) (B_154:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_239) B_154)->(((member451959335_state X_109) A_239)->((member451959335_state X_109) B_154)))).
% Axiom fact_159_in__mono:(forall (X_109:pname) (A_239:(pname->Prop)) (B_154:(pname->Prop)), (((ord_less_eq_pname_o A_239) B_154)->(((member_pname X_109) A_239)->((member_pname X_109) B_154)))).
% Axiom fact_160_equalityD2:(forall (A_238:(pname->Prop)) (B_153:(pname->Prop)), ((((eq (pname->Prop)) A_238) B_153)->((ord_less_eq_pname_o B_153) A_238))).
% Axiom fact_161_equalityD2:(forall (A_238:(hoare_1708887482_state->Prop)) (B_153:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_238) B_153)->((ord_le777019615tate_o B_153) A_238))).
% Axiom fact_162_equalityD1:(forall (A_237:(pname->Prop)) (B_152:(pname->Prop)), ((((eq (pname->Prop)) A_237) B_152)->((ord_less_eq_pname_o A_237) B_152))).
% Axiom fact_163_equalityD1:(forall (A_237:(hoare_1708887482_state->Prop)) (B_152:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_237) B_152)->((ord_le777019615tate_o A_237) B_152))).
% Axiom fact_164_set__eq__subset:(forall (A_236:(pname->Prop)) (B_151:(pname->Prop)), ((iff (((eq (pname->Prop)) A_236) B_151)) ((and ((ord_less_eq_pname_o A_236) B_151)) ((ord_less_eq_pname_o B_151) A_236)))).
% Axiom fact_165_set__eq__subset:(forall (A_236:(hoare_1708887482_state->Prop)) (B_151:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) A_236) B_151)) ((and ((ord_le777019615tate_o A_236) B_151)) ((ord_le777019615tate_o B_151) A_236)))).
% Axiom fact_166_subset__refl:(forall (A_235:(pname->Prop)), ((ord_less_eq_pname_o A_235) A_235)).
% Axiom fact_167_subset__refl:(forall (A_235:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o A_235) A_235)).
% Axiom fact_168_rev__image__eqI:(forall (B_150:com) (F_84:(hoare_1708887482_state->com)) (X_108:hoare_1708887482_state) (A_234:(hoare_1708887482_state->Prop)), (((member451959335_state X_108) A_234)->((((eq com) B_150) (F_84 X_108))->((member_com B_150) ((image_1604448413te_com F_84) A_234))))).
% Axiom fact_169_rev__image__eqI:(forall (B_150:com) (F_84:(pname->com)) (X_108:pname) (A_234:(pname->Prop)), (((member_pname X_108) A_234)->((((eq com) B_150) (F_84 X_108))->((member_com B_150) ((image_pname_com F_84) A_234))))).
% Axiom fact_170_rev__image__eqI:(forall (B_150:hoare_1708887482_state) (F_84:(com->hoare_1708887482_state)) (X_108:com) (A_234:(com->Prop)), (((member_com X_108) A_234)->((((eq hoare_1708887482_state) B_150) (F_84 X_108))->((member451959335_state B_150) ((image_934102463_state F_84) A_234))))).
% Axiom fact_171_rev__image__eqI:(forall (B_150:pname) (F_84:(com->pname)) (X_108:com) (A_234:(com->Prop)), (((member_com X_108) A_234)->((((eq pname) B_150) (F_84 X_108))->((member_pname B_150) ((image_com_pname F_84) A_234))))).
% Axiom fact_172_rev__image__eqI:(forall (B_150:hoare_1708887482_state) (F_84:(pname->hoare_1708887482_state)) (X_108:pname) (A_234:(pname->Prop)), (((member_pname X_108) A_234)->((((eq hoare_1708887482_state) B_150) (F_84 X_108))->((member451959335_state B_150) ((image_1116629049_state F_84) A_234))))).
% Axiom fact_173_imageI:(forall (F_83:(hoare_1708887482_state->com)) (X_107:hoare_1708887482_state) (A_233:(hoare_1708887482_state->Prop)), (((member451959335_state X_107) A_233)->((member_com (F_83 X_107)) ((image_1604448413te_com F_83) A_233)))).
% Axiom fact_174_imageI:(forall (F_83:(pname->com)) (X_107:pname) (A_233:(pname->Prop)), (((member_pname X_107) A_233)->((member_com (F_83 X_107)) ((image_pname_com F_83) A_233)))).
% Axiom fact_175_imageI:(forall (F_83:(com->hoare_1708887482_state)) (X_107:com) (A_233:(com->Prop)), (((member_com X_107) A_233)->((member451959335_state (F_83 X_107)) ((image_934102463_state F_83) A_233)))).
% Axiom fact_176_imageI:(forall (F_83:(com->pname)) (X_107:com) (A_233:(com->Prop)), (((member_com X_107) A_233)->((member_pname (F_83 X_107)) ((image_com_pname F_83) A_233)))).
% Axiom fact_177_imageI:(forall (F_83:(pname->hoare_1708887482_state)) (X_107:pname) (A_233:(pname->Prop)), (((member_pname X_107) A_233)->((member451959335_state (F_83 X_107)) ((image_1116629049_state F_83) A_233)))).
% Axiom fact_178_image__iff:(forall (Z_21:hoare_1708887482_state) (F_82:(pname->hoare_1708887482_state)) (A_232:(pname->Prop)), ((iff ((member451959335_state Z_21) ((image_1116629049_state F_82) A_232))) ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_232)) (((eq hoare_1708887482_state) Z_21) (F_82 X_3))))))).
% Axiom fact_179_finite__Collect__disjI:(forall (P_41:((pname->Prop)->Prop)) (Q_25:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_3:(pname->Prop))=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite297249702name_o (collect_pname_o P_41))) (finite297249702name_o (collect_pname_o Q_25))))).
% Axiom fact_180_finite__Collect__disjI:(forall (P_41:((hoare_1708887482_state->Prop)->Prop)) (Q_25:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite1329924456tate_o (collec219771562tate_o P_41))) (finite1329924456tate_o (collec219771562tate_o Q_25))))).
% Axiom fact_181_finite__Collect__disjI:(forall (P_41:(hoare_1708887482_state->Prop)) (Q_25:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite1625599783_state (collec1568722789_state P_41))) (finite1625599783_state (collec1568722789_state Q_25))))).
% Axiom fact_182_finite__Collect__disjI:(forall (P_41:(pname->Prop)) (Q_25:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_3:pname)=> ((or (P_41 X_3)) (Q_25 X_3)))))) ((and (finite_finite_pname (collect_pname P_41))) (finite_finite_pname (collect_pname Q_25))))).
% Axiom fact_183_insert__compr__raw:(forall (X_3:com) (Xa:(com->Prop)), (((eq (com->Prop)) ((insert_com X_3) Xa)) (collect_com (fun (Y_4:com)=> ((or (((eq com) Y_4) X_3)) ((member_com Y_4) Xa)))))).
% Axiom fact_184_insert__compr__raw:(forall (X_3:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X_3) Xa)) (collect_pname_o (fun (Y_4:(pname->Prop))=> ((or (((eq (pname->Prop)) Y_4) X_3)) ((member_pname_o Y_4) Xa)))))).
% Axiom fact_185_insert__compr__raw:(forall (X_3:(hoare_1708887482_state->Prop)) (Xa:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o X_3) Xa)) (collec219771562tate_o (fun (Y_4:(hoare_1708887482_state->Prop))=> ((or (((eq (hoare_1708887482_state->Prop)) Y_4) X_3)) ((member814030440tate_o Y_4) Xa)))))).
% Axiom fact_186_insert__compr__raw:(forall (X_3:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_3) Xa)) (collect_pname (fun (Y_4:pname)=> ((or (((eq pname) Y_4) X_3)) ((member_pname Y_4) Xa)))))).
% Axiom fact_187_insert__compr__raw:(forall (X_3:hoare_1708887482_state) (Xa:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_3) Xa)) (collec1568722789_state (fun (Y_4:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) Y_4) X_3)) ((member451959335_state Y_4) Xa)))))).
% Axiom fact_188_singleton__inject:(forall (A_231:pname) (B_149:pname), ((((eq (pname->Prop)) ((insert_pname A_231) bot_bot_pname_o)) ((insert_pname B_149) bot_bot_pname_o))->(((eq pname) A_231) B_149))).
% Axiom fact_189_singleton__inject:(forall (A_231:com) (B_149:com), ((((eq (com->Prop)) ((insert_com A_231) bot_bot_com_o)) ((insert_com B_149) bot_bot_com_o))->(((eq com) A_231) B_149))).
% Axiom fact_190_singleton__inject:(forall (A_231:hoare_1708887482_state) (B_149:hoare_1708887482_state), ((((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_231) bot_bo19817387tate_o)) ((insert528405184_state B_149) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) A_231) B_149))).
% Axiom fact_191_singletonE:(forall (B_148:com) (A_230:com), (((member_com B_148) ((insert_com A_230) bot_bot_com_o))->(((eq com) B_148) A_230))).
% Axiom fact_192_singletonE:(forall (B_148:pname) (A_230:pname), (((member_pname B_148) ((insert_pname A_230) bot_bot_pname_o))->(((eq pname) B_148) A_230))).
% Axiom fact_193_singletonE:(forall (B_148:hoare_1708887482_state) (A_230:hoare_1708887482_state), (((member451959335_state B_148) ((insert528405184_state A_230) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) B_148) A_230))).
% Axiom fact_194_doubleton__eq__iff:(forall (A_229:pname) (B_147:pname) (C_63:pname) (D_7:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_229) ((insert_pname B_147) bot_bot_pname_o))) ((insert_pname C_63) ((insert_pname D_7) bot_bot_pname_o)))) ((or ((and (((eq pname) A_229) C_63)) (((eq pname) B_147) D_7))) ((and (((eq pname) A_229) D_7)) (((eq pname) B_147) C_63))))).
% Axiom fact_195_doubleton__eq__iff:(forall (A_229:com) (B_147:com) (C_63:com) (D_7:com), ((iff (((eq (com->Prop)) ((insert_com A_229) ((insert_com B_147) bot_bot_com_o))) ((insert_com C_63) ((insert_com D_7) bot_bot_com_o)))) ((or ((and (((eq com) A_229) C_63)) (((eq com) B_147) D_7))) ((and (((eq com) A_229) D_7)) (((eq com) B_147) C_63))))).
% Axiom fact_196_doubleton__eq__iff:(forall (A_229:hoare_1708887482_state) (B_147:hoare_1708887482_state) (C_63:hoare_1708887482_state) (D_7:hoare_1708887482_state), ((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_229) ((insert528405184_state B_147) bot_bo19817387tate_o))) ((insert528405184_state C_63) ((insert528405184_state D_7) bot_bo19817387tate_o)))) ((or ((and (((eq hoare_1708887482_state) A_229) C_63)) (((eq hoare_1708887482_state) B_147) D_7))) ((and (((eq hoare_1708887482_state) A_229) D_7)) (((eq hoare_1708887482_state) B_147) C_63))))).
% Axiom fact_197_singleton__iff:(forall (B_146:com) (A_228:com), ((iff ((member_com B_146) ((insert_com A_228) bot_bot_com_o))) (((eq com) B_146) A_228))).
% Axiom fact_198_singleton__iff:(forall (B_146:pname) (A_228:pname), ((iff ((member_pname B_146) ((insert_pname A_228) bot_bot_pname_o))) (((eq pname) B_146) A_228))).
% Axiom fact_199_singleton__iff:(forall (B_146:hoare_1708887482_state) (A_228:hoare_1708887482_state), ((iff ((member451959335_state B_146) ((insert528405184_state A_228) bot_bo19817387tate_o))) (((eq hoare_1708887482_state) B_146) A_228))).
% Axiom fact_200_insert__not__empty:(forall (A_227:pname) (A_226:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_227) A_226)) bot_bot_pname_o))).
% Axiom fact_201_insert__not__empty:(forall (A_227:com) (A_226:(com->Prop)), (not (((eq (com->Prop)) ((insert_com A_227) A_226)) bot_bot_com_o))).
% Axiom fact_202_insert__not__empty:(forall (A_227:hoare_1708887482_state) (A_226:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_227) A_226)) bot_bo19817387tate_o))).
% Axiom fact_203_empty__not__insert:(forall (A_225:pname) (A_224:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_225) A_224)))).
% Axiom fact_204_empty__not__insert:(forall (A_225:com) (A_224:(com->Prop)), (not (((eq (com->Prop)) bot_bot_com_o) ((insert_com A_225) A_224)))).
% Axiom fact_205_empty__not__insert:(forall (A_225:hoare_1708887482_state) (A_224:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((insert528405184_state A_225) A_224)))).
% Axiom fact_206_finite__insert:(forall (A_223:com) (A_222:(com->Prop)), ((iff (finite_finite_com ((insert_com A_223) A_222))) (finite_finite_com A_222))).
% Axiom fact_207_finite__insert:(forall (A_223:(pname->Prop)) (A_222:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_223) A_222))) (finite297249702name_o A_222))).
% Axiom fact_208_finite__insert:(forall (A_223:(hoare_1708887482_state->Prop)) (A_222:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o ((insert949073679tate_o A_223) A_222))) (finite1329924456tate_o A_222))).
% Axiom fact_209_finite__insert:(forall (A_223:pname) (A_222:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_223) A_222))) (finite_finite_pname A_222))).
% Axiom fact_210_finite__insert:(forall (A_223:hoare_1708887482_state) (A_222:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((insert528405184_state A_223) A_222))) (finite1625599783_state A_222))).
% Axiom fact_211_subset__empty:(forall (A_221:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_221) bot_bot_pname_o)) (((eq (pname->Prop)) A_221) bot_bot_pname_o))).
% Axiom fact_212_subset__empty:(forall (A_221:(com->Prop)), ((iff ((ord_less_eq_com_o A_221) bot_bot_com_o)) (((eq (com->Prop)) A_221) bot_bot_com_o))).
% Axiom fact_213_subset__empty:(forall (A_221:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_221) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) A_221) bot_bo19817387tate_o))).
% Axiom fact_214_image__is__empty:(forall (F_81:(com->hoare_1708887482_state)) (A_220:(com->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((image_934102463_state F_81) A_220)) bot_bo19817387tate_o)) (((eq (com->Prop)) A_220) bot_bot_com_o))).
% Axiom fact_215_image__is__empty:(forall (F_81:(hoare_1708887482_state->pname)) (A_220:(hoare_1708887482_state->Prop)), ((iff (((eq (pname->Prop)) ((image_1509414295_pname F_81) A_220)) bot_bot_pname_o)) (((eq (hoare_1708887482_state->Prop)) A_220) bot_bo19817387tate_o))).
% Axiom fact_216_image__is__empty:(forall (F_81:(hoare_1708887482_state->com)) (A_220:(hoare_1708887482_state->Prop)), ((iff (((eq (com->Prop)) ((image_1604448413te_com F_81) A_220)) bot_bot_com_o)) (((eq (hoare_1708887482_state->Prop)) A_220) bot_bo19817387tate_o))).
% Axiom fact_217_image__is__empty:(forall (F_81:(pname->hoare_1708887482_state)) (A_220:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_81) A_220)) bot_bo19817387tate_o)) (((eq (pname->Prop)) A_220) bot_bot_pname_o))).
% Axiom fact_218_image__empty:(forall (F_80:(hoare_1708887482_state->pname)), (((eq (pname->Prop)) ((image_1509414295_pname F_80) bot_bo19817387tate_o)) bot_bot_pname_o)).
% Axiom fact_219_image__empty:(forall (F_80:(hoare_1708887482_state->com)), (((eq (com->Prop)) ((image_1604448413te_com F_80) bot_bo19817387tate_o)) bot_bot_com_o)).
% Axiom fact_220_image__empty:(forall (F_80:(com->hoare_1708887482_state)), (((eq (hoare_1708887482_state->Prop)) ((image_934102463_state F_80) bot_bot_com_o)) bot_bo19817387tate_o)).
% Axiom fact_221_image__empty:(forall (F_80:(pname->hoare_1708887482_state)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_80) bot_bot_pname_o)) bot_bo19817387tate_o)).
% Axiom fact_222_empty__is__image:(forall (F_79:(com->hoare_1708887482_state)) (A_219:(com->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((image_934102463_state F_79) A_219))) (((eq (com->Prop)) A_219) bot_bot_com_o))).
% Axiom fact_223_empty__is__image:(forall (F_79:(hoare_1708887482_state->pname)) (A_219:(hoare_1708887482_state->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) ((image_1509414295_pname F_79) A_219))) (((eq (hoare_1708887482_state->Prop)) A_219) bot_bo19817387tate_o))).
% Axiom fact_224_empty__is__image:(forall (F_79:(hoare_1708887482_state->com)) (A_219:(hoare_1708887482_state->Prop)), ((iff (((eq (com->Prop)) bot_bot_com_o) ((image_1604448413te_com F_79) A_219))) (((eq (hoare_1708887482_state->Prop)) A_219) bot_bo19817387tate_o))).
% Axiom fact_225_empty__is__image:(forall (F_79:(pname->hoare_1708887482_state)) (A_219:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((image_1116629049_state F_79) A_219))) (((eq (pname->Prop)) A_219) bot_bot_pname_o))).
% Axiom fact_226_finite__subset:(forall (A_218:((pname->Prop)->Prop)) (B_145:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_218) B_145)->((finite297249702name_o B_145)->(finite297249702name_o A_218)))).
% Axiom fact_227_finite__subset:(forall (A_218:((hoare_1708887482_state->Prop)->Prop)) (B_145:((hoare_1708887482_state->Prop)->Prop)), (((ord_le1728773982te_o_o A_218) B_145)->((finite1329924456tate_o B_145)->(finite1329924456tate_o A_218)))).
% Axiom fact_228_finite__subset:(forall (A_218:(hoare_1708887482_state->Prop)) (B_145:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_218) B_145)->((finite1625599783_state B_145)->(finite1625599783_state A_218)))).
% Axiom fact_229_finite__subset:(forall (A_218:(pname->Prop)) (B_145:(pname->Prop)), (((ord_less_eq_pname_o A_218) B_145)->((finite_finite_pname B_145)->(finite_finite_pname A_218)))).
% Axiom fact_230_rev__finite__subset:(forall (A_217:((pname->Prop)->Prop)) (B_144:((pname->Prop)->Prop)), ((finite297249702name_o B_144)->(((ord_le1205211808me_o_o A_217) B_144)->(finite297249702name_o A_217)))).
% Axiom fact_231_rev__finite__subset:(forall (A_217:((hoare_1708887482_state->Prop)->Prop)) (B_144:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_144)->(((ord_le1728773982te_o_o A_217) B_144)->(finite1329924456tate_o A_217)))).
% Axiom fact_232_rev__finite__subset:(forall (A_217:(hoare_1708887482_state->Prop)) (B_144:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_144)->(((ord_le777019615tate_o A_217) B_144)->(finite1625599783_state A_217)))).
% Axiom fact_233_rev__finite__subset:(forall (A_217:(pname->Prop)) (B_144:(pname->Prop)), ((finite_finite_pname B_144)->(((ord_less_eq_pname_o A_217) B_144)->(finite_finite_pname A_217)))).
% Axiom fact_234_insert__mono:(forall (A_216:pname) (C_62:(pname->Prop)) (D_6:(pname->Prop)), (((ord_less_eq_pname_o C_62) D_6)->((ord_less_eq_pname_o ((insert_pname A_216) C_62)) ((insert_pname A_216) D_6)))).
% Axiom fact_235_insert__mono:(forall (A_216:com) (C_62:(com->Prop)) (D_6:(com->Prop)), (((ord_less_eq_com_o C_62) D_6)->((ord_less_eq_com_o ((insert_com A_216) C_62)) ((insert_com A_216) D_6)))).
% Axiom fact_236_insert__mono:(forall (A_216:hoare_1708887482_state) (C_62:(hoare_1708887482_state->Prop)) (D_6:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o C_62) D_6)->((ord_le777019615tate_o ((insert528405184_state A_216) C_62)) ((insert528405184_state A_216) D_6)))).
% Axiom fact_237_mem__def:(forall (X_106:com) (A_215:(com->Prop)), ((iff ((member_com X_106) A_215)) (A_215 X_106))).
% Axiom fact_238_mem__def:(forall (X_106:hoare_1708887482_state) (A_215:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state X_106) A_215)) (A_215 X_106))).
% Axiom fact_239_mem__def:(forall (X_106:pname) (A_215:(pname->Prop)), ((iff ((member_pname X_106) A_215)) (A_215 X_106))).
% Axiom fact_240_Collect__def:(forall (P_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state P_40)) P_40)).
% Axiom fact_241_Collect__def:(forall (P_40:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_40)) P_40)).
% Axiom fact_242_Collect__def:(forall (P_40:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_40)) P_40)).
% Axiom fact_243_Collect__def:(forall (P_40:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o P_40)) P_40)).
% Axiom fact_244_subset__insertI2:(forall (B_143:pname) (A_214:(pname->Prop)) (B_142:(pname->Prop)), (((ord_less_eq_pname_o A_214) B_142)->((ord_less_eq_pname_o A_214) ((insert_pname B_143) B_142)))).
% Axiom fact_245_subset__insertI2:(forall (B_143:com) (A_214:(com->Prop)) (B_142:(com->Prop)), (((ord_less_eq_com_o A_214) B_142)->((ord_less_eq_com_o A_214) ((insert_com B_143) B_142)))).
% Axiom fact_246_subset__insertI2:(forall (B_143:hoare_1708887482_state) (A_214:(hoare_1708887482_state->Prop)) (B_142:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_214) B_142)->((ord_le777019615tate_o A_214) ((insert528405184_state B_143) B_142)))).
% Axiom fact_247_subset__insert:(forall (B_141:(com->Prop)) (X_105:com) (A_213:(com->Prop)), ((((member_com X_105) A_213)->False)->((iff ((ord_less_eq_com_o A_213) ((insert_com X_105) B_141))) ((ord_less_eq_com_o A_213) B_141)))).
% Axiom fact_248_subset__insert:(forall (B_141:(pname->Prop)) (X_105:pname) (A_213:(pname->Prop)), ((((member_pname X_105) A_213)->False)->((iff ((ord_less_eq_pname_o A_213) ((insert_pname X_105) B_141))) ((ord_less_eq_pname_o A_213) B_141)))).
% Axiom fact_249_subset__insert:(forall (B_141:(hoare_1708887482_state->Prop)) (X_105:hoare_1708887482_state) (A_213:(hoare_1708887482_state->Prop)), ((((member451959335_state X_105) A_213)->False)->((iff ((ord_le777019615tate_o A_213) ((insert528405184_state X_105) B_141))) ((ord_le777019615tate_o A_213) B_141)))).
% Axiom fact_250_insert__subset:(forall (X_104:com) (A_212:(com->Prop)) (B_140:(com->Prop)), ((iff ((ord_less_eq_com_o ((insert_com X_104) A_212)) B_140)) ((and ((member_com X_104) B_140)) ((ord_less_eq_com_o A_212) B_140)))).
% Axiom fact_251_insert__subset:(forall (X_104:pname) (A_212:(pname->Prop)) (B_140:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_104) A_212)) B_140)) ((and ((member_pname X_104) B_140)) ((ord_less_eq_pname_o A_212) B_140)))).
% Axiom fact_252_insert__subset:(forall (X_104:hoare_1708887482_state) (A_212:(hoare_1708887482_state->Prop)) (B_140:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o ((insert528405184_state X_104) A_212)) B_140)) ((and ((member451959335_state X_104) B_140)) ((ord_le777019615tate_o A_212) B_140)))).
% Axiom fact_253_subset__insertI:(forall (B_139:(pname->Prop)) (A_211:pname), ((ord_less_eq_pname_o B_139) ((insert_pname A_211) B_139))).
% Axiom fact_254_subset__insertI:(forall (B_139:(com->Prop)) (A_211:com), ((ord_less_eq_com_o B_139) ((insert_com A_211) B_139))).
% Axiom fact_255_subset__insertI:(forall (B_139:(hoare_1708887482_state->Prop)) (A_211:hoare_1708887482_state), ((ord_le777019615tate_o B_139) ((insert528405184_state A_211) B_139))).
% Axiom fact_256_insert__image:(forall (F_78:(hoare_1708887482_state->pname)) (X_103:hoare_1708887482_state) (A_210:(hoare_1708887482_state->Prop)), (((member451959335_state X_103) A_210)->(((eq (pname->Prop)) ((insert_pname (F_78 X_103)) ((image_1509414295_pname F_78) A_210))) ((image_1509414295_pname F_78) A_210)))).
% Axiom fact_257_insert__image:(forall (F_78:(hoare_1708887482_state->com)) (X_103:hoare_1708887482_state) (A_210:(hoare_1708887482_state->Prop)), (((member451959335_state X_103) A_210)->(((eq (com->Prop)) ((insert_com (F_78 X_103)) ((image_1604448413te_com F_78) A_210))) ((image_1604448413te_com F_78) A_210)))).
% Axiom fact_258_insert__image:(forall (F_78:(pname->pname)) (X_103:pname) (A_210:(pname->Prop)), (((member_pname X_103) A_210)->(((eq (pname->Prop)) ((insert_pname (F_78 X_103)) ((image_pname_pname F_78) A_210))) ((image_pname_pname F_78) A_210)))).
% Axiom fact_259_insert__image:(forall (F_78:(pname->com)) (X_103:pname) (A_210:(pname->Prop)), (((member_pname X_103) A_210)->(((eq (com->Prop)) ((insert_com (F_78 X_103)) ((image_pname_com F_78) A_210))) ((image_pname_com F_78) A_210)))).
% Axiom fact_260_insert__image:(forall (F_78:(com->hoare_1708887482_state)) (X_103:com) (A_210:(com->Prop)), (((member_com X_103) A_210)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state (F_78 X_103)) ((image_934102463_state F_78) A_210))) ((image_934102463_state F_78) A_210)))).
% Axiom fact_261_insert__image:(forall (F_78:(pname->hoare_1708887482_state)) (X_103:pname) (A_210:(pname->Prop)), (((member_pname X_103) A_210)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state (F_78 X_103)) ((image_1116629049_state F_78) A_210))) ((image_1116629049_state F_78) A_210)))).
% Axiom fact_262_image__insert:(forall (F_77:(hoare_1708887482_state->pname)) (A_209:hoare_1708887482_state) (B_138:(hoare_1708887482_state->Prop)), (((eq (pname->Prop)) ((image_1509414295_pname F_77) ((insert528405184_state A_209) B_138))) ((insert_pname (F_77 A_209)) ((image_1509414295_pname F_77) B_138)))).
% Axiom fact_263_image__insert:(forall (F_77:(hoare_1708887482_state->com)) (A_209:hoare_1708887482_state) (B_138:(hoare_1708887482_state->Prop)), (((eq (com->Prop)) ((image_1604448413te_com F_77) ((insert528405184_state A_209) B_138))) ((insert_com (F_77 A_209)) ((image_1604448413te_com F_77) B_138)))).
% Axiom fact_264_image__insert:(forall (F_77:(com->hoare_1708887482_state)) (A_209:com) (B_138:(com->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_934102463_state F_77) ((insert_com A_209) B_138))) ((insert528405184_state (F_77 A_209)) ((image_934102463_state F_77) B_138)))).
% Axiom fact_265_image__insert:(forall (F_77:(pname->hoare_1708887482_state)) (A_209:pname) (B_138:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_77) ((insert_pname A_209) B_138))) ((insert528405184_state (F_77 A_209)) ((image_1116629049_state F_77) B_138)))).
% Axiom fact_266_image__mono:(forall (F_76:(hoare_1708887482_state->pname)) (A_208:(hoare_1708887482_state->Prop)) (B_137:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_208) B_137)->((ord_less_eq_pname_o ((image_1509414295_pname F_76) A_208)) ((image_1509414295_pname F_76) B_137)))).
% Axiom fact_267_image__mono:(forall (F_76:(pname->hoare_1708887482_state)) (A_208:(pname->Prop)) (B_137:(pname->Prop)), (((ord_less_eq_pname_o A_208) B_137)->((ord_le777019615tate_o ((image_1116629049_state F_76) A_208)) ((image_1116629049_state F_76) B_137)))).
% Axiom fact_268_subset__image__iff:(forall (B_136:(pname->Prop)) (F_75:(hoare_1708887482_state->pname)) (A_207:(hoare_1708887482_state->Prop)), ((iff ((ord_less_eq_pname_o B_136) ((image_1509414295_pname F_75) A_207))) ((ex (hoare_1708887482_state->Prop)) (fun (AA:(hoare_1708887482_state->Prop))=> ((and ((ord_le777019615tate_o AA) A_207)) (((eq (pname->Prop)) B_136) ((image_1509414295_pname F_75) AA))))))).
% Axiom fact_269_subset__image__iff:(forall (B_136:(hoare_1708887482_state->Prop)) (F_75:(pname->hoare_1708887482_state)) (A_207:(pname->Prop)), ((iff ((ord_le777019615tate_o B_136) ((image_1116629049_state F_75) A_207))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_207)) (((eq (hoare_1708887482_state->Prop)) B_136) ((image_1116629049_state F_75) AA))))))).
% Axiom fact_270_domI:(forall (M_5:(com->option_com)) (A_206:com) (B_135:com), ((((eq option_com) (M_5 A_206)) (some_com B_135))->((member_com A_206) (dom_com_com M_5)))).
% Axiom fact_271_domI:(forall (M_5:(hoare_1708887482_state->option_pname)) (A_206:hoare_1708887482_state) (B_135:pname), ((((eq option_pname) (M_5 A_206)) (some_pname B_135))->((member451959335_state A_206) (dom_Ho1805192458_pname M_5)))).
% Axiom fact_272_domI:(forall (M_5:(hoare_1708887482_state->option1624383643_state)) (A_206:hoare_1708887482_state) (B_135:hoare_1708887482_state), ((((eq option1624383643_state) (M_5 A_206)) (some_H1974565227_state B_135))->((member451959335_state A_206) (dom_Ho1703271284_state M_5)))).
% Axiom fact_273_domI:(forall (M_5:(pname->option_pname)) (A_206:pname) (B_135:pname), ((((eq option_pname) (M_5 A_206)) (some_pname B_135))->((member_pname A_206) (dom_pname_pname M_5)))).
% Axiom fact_274_domI:(forall (M_5:(pname->option1624383643_state)) (A_206:pname) (B_135:hoare_1708887482_state), ((((eq option1624383643_state) (M_5 A_206)) (some_H1974565227_state B_135))->((member_pname A_206) (dom_pn1412407212_state M_5)))).
% Axiom fact_275_domI:(forall (M_5:(pname->option_com)) (A_206:pname) (B_135:com), ((((eq option_com) (M_5 A_206)) (some_com B_135))->((member_pname A_206) (dom_pname_com M_5)))).
% Axiom fact_276_Collect__conv__if:(forall (P_39:(pname->Prop)) (A_205:pname), ((and ((P_39 A_205)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) X_3) A_205)) (P_39 X_3))))) ((insert_pname A_205) bot_bot_pname_o)))) (((P_39 A_205)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) X_3) A_205)) (P_39 X_3))))) bot_bot_pname_o)))).
% Axiom fact_277_Collect__conv__if:(forall (P_39:(com->Prop)) (A_205:com), ((and ((P_39 A_205)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) X_3) A_205)) (P_39 X_3))))) ((insert_com A_205) bot_bot_com_o)))) (((P_39 A_205)->False)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) X_3) A_205)) (P_39 X_3))))) bot_bot_com_o)))).
% Axiom fact_278_Collect__conv__if:(forall (P_39:((pname->Prop)->Prop)) (A_205:(pname->Prop)), ((and ((P_39 A_205)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) X_3) A_205)) (P_39 X_3))))) ((insert_pname_o A_205) bot_bot_pname_o_o)))) (((P_39 A_205)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) X_3) A_205)) (P_39 X_3))))) bot_bot_pname_o_o)))).
% Axiom fact_279_Collect__conv__if:(forall (P_39:((hoare_1708887482_state->Prop)->Prop)) (A_205:(hoare_1708887482_state->Prop)), ((and ((P_39 A_205)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) X_3) A_205)) (P_39 X_3))))) ((insert949073679tate_o A_205) bot_bo1678742418te_o_o)))) (((P_39 A_205)->False)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) X_3) A_205)) (P_39 X_3))))) bot_bo1678742418te_o_o)))).
% Axiom fact_280_Collect__conv__if:(forall (P_39:(hoare_1708887482_state->Prop)) (A_205:hoare_1708887482_state), ((and ((P_39 A_205)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X_3) A_205)) (P_39 X_3))))) ((insert528405184_state A_205) bot_bo19817387tate_o)))) (((P_39 A_205)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X_3) A_205)) (P_39 X_3))))) bot_bo19817387tate_o)))).
% Axiom fact_281_Collect__conv__if2:(forall (P_38:(pname->Prop)) (A_204:pname), ((and ((P_38 A_204)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) A_204) X_3)) (P_38 X_3))))) ((insert_pname A_204) bot_bot_pname_o)))) (((P_38 A_204)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (((eq pname) A_204) X_3)) (P_38 X_3))))) bot_bot_pname_o)))).
% Axiom fact_282_Collect__conv__if2:(forall (P_38:(com->Prop)) (A_204:com), ((and ((P_38 A_204)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) A_204) X_3)) (P_38 X_3))))) ((insert_com A_204) bot_bot_com_o)))) (((P_38 A_204)->False)->(((eq (com->Prop)) (collect_com (fun (X_3:com)=> ((and (((eq com) A_204) X_3)) (P_38 X_3))))) bot_bot_com_o)))).
% Axiom fact_283_Collect__conv__if2:(forall (P_38:((pname->Prop)->Prop)) (A_204:(pname->Prop)), ((and ((P_38 A_204)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) A_204) X_3)) (P_38 X_3))))) ((insert_pname_o A_204) bot_bot_pname_o_o)))) (((P_38 A_204)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (((eq (pname->Prop)) A_204) X_3)) (P_38 X_3))))) bot_bot_pname_o_o)))).
% Axiom fact_284_Collect__conv__if2:(forall (P_38:((hoare_1708887482_state->Prop)->Prop)) (A_204:(hoare_1708887482_state->Prop)), ((and ((P_38 A_204)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_204) X_3)) (P_38 X_3))))) ((insert949073679tate_o A_204) bot_bo1678742418te_o_o)))) (((P_38 A_204)->False)->(((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_204) X_3)) (P_38 X_3))))) bot_bo1678742418te_o_o)))).
% Axiom fact_285_Collect__conv__if2:(forall (P_38:(hoare_1708887482_state->Prop)) (A_204:hoare_1708887482_state), ((and ((P_38 A_204)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_204) X_3)) (P_38 X_3))))) ((insert528405184_state A_204) bot_bo19817387tate_o)))) (((P_38 A_204)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_204) X_3)) (P_38 X_3))))) bot_bo19817387tate_o)))).
% Axiom fact_286_singleton__conv:(forall (A_203:pname), (((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> (((eq pname) X_3) A_203)))) ((insert_pname A_203) bot_bot_pname_o))).
% Axiom fact_287_singleton__conv:(forall (A_203:com), (((eq (com->Prop)) (collect_com (fun (X_3:com)=> (((eq com) X_3) A_203)))) ((insert_com A_203) bot_bot_com_o))).
% Axiom fact_288_singleton__conv:(forall (A_203:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> (((eq (pname->Prop)) X_3) A_203)))) ((insert_pname_o A_203) bot_bot_pname_o_o))).
% Axiom fact_289_singleton__conv:(forall (A_203:(hoare_1708887482_state->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> (((eq (hoare_1708887482_state->Prop)) X_3) A_203)))) ((insert949073679tate_o A_203) bot_bo1678742418te_o_o))).
% Axiom fact_290_singleton__conv:(forall (A_203:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X_3) A_203)))) ((insert528405184_state A_203) bot_bo19817387tate_o))).
% Axiom fact_291_singleton__conv2:(forall (A_202:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_202))) ((insert_pname A_202) bot_bot_pname_o))).
% Axiom fact_292_singleton__conv2:(forall (A_202:com), (((eq (com->Prop)) (collect_com (fequal_com A_202))) ((insert_com A_202) bot_bot_com_o))).
% Axiom fact_293_singleton__conv2:(forall (A_202:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fequal_pname_o A_202))) ((insert_pname_o A_202) bot_bot_pname_o_o))).
% Axiom fact_294_singleton__conv2:(forall (A_202:(hoare_1708887482_state->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fequal1436017556tate_o A_202))) ((insert949073679tate_o A_202) bot_bo1678742418te_o_o))).
% Axiom fact_295_singleton__conv2:(forall (A_202:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fequal224822779_state A_202))) ((insert528405184_state A_202) bot_bo19817387tate_o))).
% Axiom fact_296_MGF__lemma1:(forall (C_34:com) (G_7:(hoare_1708887482_state->Prop)), (hoare_1160767572gleton->((forall (X_3:pname), (((member_pname X_3) (dom_pname_com body))->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT (body_1 X_3))) bot_bo19817387tate_o))))->((wt C_34)->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o)))))).
% Axiom fact_297_WT__bodiesD:(forall (Pn_1:pname) (B_82:com), (wT_bodies->((((eq option_com) (body Pn_1)) (some_com B_82))->(wt B_82)))).
% Axiom fact_298_imageE:(forall (B_134:hoare_1708887482_state) (F_74:(com->hoare_1708887482_state)) (A_201:(com->Prop)), (((member451959335_state B_134) ((image_934102463_state F_74) A_201))->((forall (X_3:com), ((((eq hoare_1708887482_state) B_134) (F_74 X_3))->(((member_com X_3) A_201)->False)))->False))).
% Axiom fact_299_imageE:(forall (B_134:pname) (F_74:(com->pname)) (A_201:(com->Prop)), (((member_pname B_134) ((image_com_pname F_74) A_201))->((forall (X_3:com), ((((eq pname) B_134) (F_74 X_3))->(((member_com X_3) A_201)->False)))->False))).
% Axiom fact_300_imageE:(forall (B_134:com) (F_74:(hoare_1708887482_state->com)) (A_201:(hoare_1708887482_state->Prop)), (((member_com B_134) ((image_1604448413te_com F_74) A_201))->((forall (X_3:hoare_1708887482_state), ((((eq com) B_134) (F_74 X_3))->(((member451959335_state X_3) A_201)->False)))->False))).
% Axiom fact_301_imageE:(forall (B_134:com) (F_74:(pname->com)) (A_201:(pname->Prop)), (((member_com B_134) ((image_pname_com F_74) A_201))->((forall (X_3:pname), ((((eq com) B_134) (F_74 X_3))->(((member_pname X_3) A_201)->False)))->False))).
% Axiom fact_302_imageE:(forall (B_134:hoare_1708887482_state) (F_74:(pname->hoare_1708887482_state)) (A_201:(pname->Prop)), (((member451959335_state B_134) ((image_1116629049_state F_74) A_201))->((forall (X_3:pname), ((((eq hoare_1708887482_state) B_134) (F_74 X_3))->(((member_pname X_3) A_201)->False)))->False))).
% Axiom fact_303_finite__subset__induct:(forall (P_37:((com->Prop)->Prop)) (A_200:(com->Prop)) (F_73:(com->Prop)), ((finite_finite_com F_73)->(((ord_less_eq_com_o F_73) A_200)->((P_37 bot_bot_com_o)->((forall (A_6:com) (F_53:(com->Prop)), ((finite_finite_com F_53)->(((member_com A_6) A_200)->((((member_com A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert_com A_6) F_53)))))))->(P_37 F_73)))))).
% Axiom fact_304_finite__subset__induct:(forall (P_37:(((pname->Prop)->Prop)->Prop)) (A_200:((pname->Prop)->Prop)) (F_73:((pname->Prop)->Prop)), ((finite297249702name_o F_73)->(((ord_le1205211808me_o_o F_73) A_200)->((P_37 bot_bot_pname_o_o)->((forall (A_6:(pname->Prop)) (F_53:((pname->Prop)->Prop)), ((finite297249702name_o F_53)->(((member_pname_o A_6) A_200)->((((member_pname_o A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert_pname_o A_6) F_53)))))))->(P_37 F_73)))))).
% Axiom fact_305_finite__subset__induct:(forall (P_37:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (A_200:((hoare_1708887482_state->Prop)->Prop)) (F_73:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_73)->(((ord_le1728773982te_o_o F_73) A_200)->((P_37 bot_bo1678742418te_o_o)->((forall (A_6:(hoare_1708887482_state->Prop)) (F_53:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_53)->(((member814030440tate_o A_6) A_200)->((((member814030440tate_o A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert949073679tate_o A_6) F_53)))))))->(P_37 F_73)))))).
% Axiom fact_306_finite__subset__induct:(forall (P_37:((pname->Prop)->Prop)) (A_200:(pname->Prop)) (F_73:(pname->Prop)), ((finite_finite_pname F_73)->(((ord_less_eq_pname_o F_73) A_200)->((P_37 bot_bot_pname_o)->((forall (A_6:pname) (F_53:(pname->Prop)), ((finite_finite_pname F_53)->(((member_pname A_6) A_200)->((((member_pname A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert_pname A_6) F_53)))))))->(P_37 F_73)))))).
% Axiom fact_307_finite__subset__induct:(forall (P_37:((hoare_1708887482_state->Prop)->Prop)) (A_200:(hoare_1708887482_state->Prop)) (F_73:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_73)->(((ord_le777019615tate_o F_73) A_200)->((P_37 bot_bo19817387tate_o)->((forall (A_6:hoare_1708887482_state) (F_53:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_53)->(((member451959335_state A_6) A_200)->((((member451959335_state A_6) F_53)->False)->((P_37 F_53)->(P_37 ((insert528405184_state A_6) F_53)))))))->(P_37 F_73)))))).
% Axiom fact_308_WTs__elim__cases_I7_J:(forall (P:pname), ((wt (body_1 P))->((forall (Y_4:com), (not (((eq option_com) (body P)) (some_com Y_4))))->False))).
% Axiom fact_309_subsetI:(forall (B_133:(com->Prop)) (A_199:(com->Prop)), ((forall (X_3:com), (((member_com X_3) A_199)->((member_com X_3) B_133)))->((ord_less_eq_com_o A_199) B_133))).
% Axiom fact_310_subsetI:(forall (B_133:(hoare_1708887482_state->Prop)) (A_199:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_199)->((member451959335_state X_3) B_133)))->((ord_le777019615tate_o A_199) B_133))).
% Axiom fact_311_subsetI:(forall (B_133:(pname->Prop)) (A_199:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_199)->((member_pname X_3) B_133)))->((ord_less_eq_pname_o A_199) B_133))).
% Axiom fact_312_finite__subset__image:(forall (F_72:((pname->Prop)->hoare_1708887482_state)) (A_198:((pname->Prop)->Prop)) (B_132:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_132)->(((ord_le777019615tate_o B_132) ((image_1922967206_state F_72) A_198))->((ex ((pname->Prop)->Prop)) (fun (C_61:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_61) A_198)) (finite297249702name_o C_61))) (((eq (hoare_1708887482_state->Prop)) B_132) ((image_1922967206_state F_72) C_61)))))))).
% Axiom fact_313_finite__subset__image:(forall (F_72:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (A_198:((hoare_1708887482_state->Prop)->Prop)) (B_132:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_132)->(((ord_le777019615tate_o B_132) ((image_27005066_state F_72) A_198))->((ex ((hoare_1708887482_state->Prop)->Prop)) (fun (C_61:((hoare_1708887482_state->Prop)->Prop))=> ((and ((and ((ord_le1728773982te_o_o C_61) A_198)) (finite1329924456tate_o C_61))) (((eq (hoare_1708887482_state->Prop)) B_132) ((image_27005066_state F_72) C_61)))))))).
% Axiom fact_314_finite__subset__image:(forall (F_72:((pname->Prop)->pname)) (A_198:((pname->Prop)->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_pname_o_pname F_72) A_198))->((ex ((pname->Prop)->Prop)) (fun (C_61:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_61) A_198)) (finite297249702name_o C_61))) (((eq (pname->Prop)) B_132) ((image_pname_o_pname F_72) C_61)))))))).
% Axiom fact_315_finite__subset__image:(forall (F_72:((hoare_1708887482_state->Prop)->pname)) (A_198:((hoare_1708887482_state->Prop)->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_2051418740_pname F_72) A_198))->((ex ((hoare_1708887482_state->Prop)->Prop)) (fun (C_61:((hoare_1708887482_state->Prop)->Prop))=> ((and ((and ((ord_le1728773982te_o_o C_61) A_198)) (finite1329924456tate_o C_61))) (((eq (pname->Prop)) B_132) ((image_2051418740_pname F_72) C_61)))))))).
% Axiom fact_316_finite__subset__image:(forall (F_72:(hoare_1708887482_state->(pname->Prop))) (A_198:(hoare_1708887482_state->Prop)) (B_132:((pname->Prop)->Prop)), ((finite297249702name_o B_132)->(((ord_le1205211808me_o_o B_132) ((image_1552895654name_o F_72) A_198))->((ex (hoare_1708887482_state->Prop)) (fun (C_61:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o C_61) A_198)) (finite1625599783_state C_61))) (((eq ((pname->Prop)->Prop)) B_132) ((image_1552895654name_o F_72) C_61)))))))).
% Axiom fact_317_finite__subset__image:(forall (F_72:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (A_198:(hoare_1708887482_state->Prop)) (B_132:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_132)->(((ord_le1728773982te_o_o B_132) ((image_1551509096tate_o F_72) A_198))->((ex (hoare_1708887482_state->Prop)) (fun (C_61:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o C_61) A_198)) (finite1625599783_state C_61))) (((eq ((hoare_1708887482_state->Prop)->Prop)) B_132) ((image_1551509096tate_o F_72) C_61)))))))).
% Axiom fact_318_finite__subset__image:(forall (F_72:(hoare_1708887482_state->pname)) (A_198:(hoare_1708887482_state->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_1509414295_pname F_72) A_198))->((ex (hoare_1708887482_state->Prop)) (fun (C_61:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o C_61) A_198)) (finite1625599783_state C_61))) (((eq (pname->Prop)) B_132) ((image_1509414295_pname F_72) C_61)))))))).
% Axiom fact_319_finite__subset__image:(forall (F_72:(pname->(pname->Prop))) (A_198:(pname->Prop)) (B_132:((pname->Prop)->Prop)), ((finite297249702name_o B_132)->(((ord_le1205211808me_o_o B_132) ((image_pname_pname_o F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq ((pname->Prop)->Prop)) B_132) ((image_pname_pname_o F_72) C_61)))))))).
% Axiom fact_320_finite__subset__image:(forall (F_72:(pname->(hoare_1708887482_state->Prop))) (A_198:(pname->Prop)) (B_132:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_132)->(((ord_le1728773982te_o_o B_132) ((image_425134806tate_o F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq ((hoare_1708887482_state->Prop)->Prop)) B_132) ((image_425134806tate_o F_72) C_61)))))))).
% Axiom fact_321_finite__subset__image:(forall (F_72:(pname->pname)) (A_198:(pname->Prop)) (B_132:(pname->Prop)), ((finite_finite_pname B_132)->(((ord_less_eq_pname_o B_132) ((image_pname_pname F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq (pname->Prop)) B_132) ((image_pname_pname F_72) C_61)))))))).
% Axiom fact_322_finite__subset__image:(forall (F_72:(pname->hoare_1708887482_state)) (A_198:(pname->Prop)) (B_132:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_132)->(((ord_le777019615tate_o B_132) ((image_1116629049_state F_72) A_198))->((ex (pname->Prop)) (fun (C_61:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_61) A_198)) (finite_finite_pname C_61))) (((eq (hoare_1708887482_state->Prop)) B_132) ((image_1116629049_state F_72) C_61)))))))).
% Axiom fact_323_finite__dom__body:(finite_finite_pname (dom_pname_com body)).
% Axiom fact_324_finite__induct:(forall (P_36:((com->Prop)->Prop)) (F_71:(com->Prop)), ((finite_finite_com F_71)->((P_36 bot_bot_com_o)->((forall (X_3:com) (F_53:(com->Prop)), ((finite_finite_com F_53)->((((member_com X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert_com X_3) F_53))))))->(P_36 F_71))))).
% Axiom fact_325_finite__induct:(forall (P_36:(((pname->Prop)->Prop)->Prop)) (F_71:((pname->Prop)->Prop)), ((finite297249702name_o F_71)->((P_36 bot_bot_pname_o_o)->((forall (X_3:(pname->Prop)) (F_53:((pname->Prop)->Prop)), ((finite297249702name_o F_53)->((((member_pname_o X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert_pname_o X_3) F_53))))))->(P_36 F_71))))).
% Axiom fact_326_finite__induct:(forall (P_36:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (F_71:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_71)->((P_36 bot_bo1678742418te_o_o)->((forall (X_3:(hoare_1708887482_state->Prop)) (F_53:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_53)->((((member814030440tate_o X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert949073679tate_o X_3) F_53))))))->(P_36 F_71))))).
% Axiom fact_327_finite__induct:(forall (P_36:((pname->Prop)->Prop)) (F_71:(pname->Prop)), ((finite_finite_pname F_71)->((P_36 bot_bot_pname_o)->((forall (X_3:pname) (F_53:(pname->Prop)), ((finite_finite_pname F_53)->((((member_pname X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert_pname X_3) F_53))))))->(P_36 F_71))))).
% Axiom fact_328_finite__induct:(forall (P_36:((hoare_1708887482_state->Prop)->Prop)) (F_71:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_71)->((P_36 bot_bo19817387tate_o)->((forall (X_3:hoare_1708887482_state) (F_53:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_53)->((((member451959335_state X_3) F_53)->False)->((P_36 F_53)->(P_36 ((insert528405184_state X_3) F_53))))))->(P_36 F_71))))).
% Axiom fact_329_finite_Osimps:(forall (A_197:(com->Prop)), ((iff (finite_finite_com A_197)) ((or (((eq (com->Prop)) A_197) bot_bot_com_o)) ((ex (com->Prop)) (fun (A_39:(com->Prop))=> ((ex com) (fun (A_6:com)=> ((and (((eq (com->Prop)) A_197) ((insert_com A_6) A_39))) (finite_finite_com A_39))))))))).
% Axiom fact_330_finite_Osimps:(forall (A_197:((pname->Prop)->Prop)), ((iff (finite297249702name_o A_197)) ((or (((eq ((pname->Prop)->Prop)) A_197) bot_bot_pname_o_o)) ((ex ((pname->Prop)->Prop)) (fun (A_39:((pname->Prop)->Prop))=> ((ex (pname->Prop)) (fun (A_6:(pname->Prop))=> ((and (((eq ((pname->Prop)->Prop)) A_197) ((insert_pname_o A_6) A_39))) (finite297249702name_o A_39))))))))).
% Axiom fact_331_finite_Osimps:(forall (A_197:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o A_197)) ((or (((eq ((hoare_1708887482_state->Prop)->Prop)) A_197) bot_bo1678742418te_o_o)) ((ex ((hoare_1708887482_state->Prop)->Prop)) (fun (A_39:((hoare_1708887482_state->Prop)->Prop))=> ((ex (hoare_1708887482_state->Prop)) (fun (A_6:(hoare_1708887482_state->Prop))=> ((and (((eq ((hoare_1708887482_state->Prop)->Prop)) A_197) ((insert949073679tate_o A_6) A_39))) (finite1329924456tate_o A_39))))))))).
% Axiom fact_332_finite_Osimps:(forall (A_197:(pname->Prop)), ((iff (finite_finite_pname A_197)) ((or (((eq (pname->Prop)) A_197) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_39:(pname->Prop))=> ((ex pname) (fun (A_6:pname)=> ((and (((eq (pname->Prop)) A_197) ((insert_pname A_6) A_39))) (finite_finite_pname A_39))))))))).
% Axiom fact_333_finite_Osimps:(forall (A_197:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state A_197)) ((or (((eq (hoare_1708887482_state->Prop)) A_197) bot_bo19817387tate_o)) ((ex (hoare_1708887482_state->Prop)) (fun (A_39:(hoare_1708887482_state->Prop))=> ((ex hoare_1708887482_state) (fun (A_6:hoare_1708887482_state)=> ((and (((eq (hoare_1708887482_state->Prop)) A_197) ((insert528405184_state A_6) A_39))) (finite1625599783_state A_39))))))))).
% Axiom fact_334_pigeonhole__infinite:(forall (F_70:(com->hoare_1708887482_state)) (A_196:(com->Prop)), (((finite_finite_com A_196)->False)->((finite1625599783_state ((image_934102463_state F_70) A_196))->((ex com) (fun (X_3:com)=> ((and ((member_com X_3) A_196)) ((finite_finite_com (collect_com (fun (A_6:com)=> ((and ((member_com A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_335_pigeonhole__infinite:(forall (F_70:(hoare_1708887482_state->hoare_1708887482_state)) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite1625599783_state ((image_757158439_state F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_336_pigeonhole__infinite:(forall (F_70:((pname->Prop)->hoare_1708887482_state)) (A_196:((pname->Prop)->Prop)), (((finite297249702name_o A_196)->False)->((finite1625599783_state ((image_1922967206_state F_70) A_196))->((ex (pname->Prop)) (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_196)) ((finite297249702name_o (collect_pname_o (fun (A_6:(pname->Prop))=> ((and ((member_pname_o A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_337_pigeonhole__infinite:(forall (F_70:((hoare_1708887482_state->Prop)->hoare_1708887482_state)) (A_196:((hoare_1708887482_state->Prop)->Prop)), (((finite1329924456tate_o A_196)->False)->((finite1625599783_state ((image_27005066_state F_70) A_196))->((ex (hoare_1708887482_state->Prop)) (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_196)) ((finite1329924456tate_o (collec219771562tate_o (fun (A_6:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_338_pigeonhole__infinite:(forall (F_70:(com->pname)) (A_196:(com->Prop)), (((finite_finite_com A_196)->False)->((finite_finite_pname ((image_com_pname F_70) A_196))->((ex com) (fun (X_3:com)=> ((and ((member_com X_3) A_196)) ((finite_finite_com (collect_com (fun (A_6:com)=> ((and ((member_com A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_339_pigeonhole__infinite:(forall (F_70:(hoare_1708887482_state->pname)) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite_finite_pname ((image_1509414295_pname F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_340_pigeonhole__infinite:(forall (F_70:(pname->pname)) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite_finite_pname ((image_pname_pname F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_341_pigeonhole__infinite:(forall (F_70:((pname->Prop)->pname)) (A_196:((pname->Prop)->Prop)), (((finite297249702name_o A_196)->False)->((finite_finite_pname ((image_pname_o_pname F_70) A_196))->((ex (pname->Prop)) (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_196)) ((finite297249702name_o (collect_pname_o (fun (A_6:(pname->Prop))=> ((and ((member_pname_o A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_342_pigeonhole__infinite:(forall (F_70:((hoare_1708887482_state->Prop)->pname)) (A_196:((hoare_1708887482_state->Prop)->Prop)), (((finite1329924456tate_o A_196)->False)->((finite_finite_pname ((image_2051418740_pname F_70) A_196))->((ex (hoare_1708887482_state->Prop)) (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_196)) ((finite1329924456tate_o (collec219771562tate_o (fun (A_6:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o A_6) A_196)) (((eq pname) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_343_pigeonhole__infinite:(forall (F_70:(hoare_1708887482_state->(pname->Prop))) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite297249702name_o ((image_1552895654name_o F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq (pname->Prop)) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_344_pigeonhole__infinite:(forall (F_70:(hoare_1708887482_state->(hoare_1708887482_state->Prop))) (A_196:(hoare_1708887482_state->Prop)), (((finite1625599783_state A_196)->False)->((finite1329924456tate_o ((image_1551509096tate_o F_70) A_196))->((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_196)) ((finite1625599783_state (collec1568722789_state (fun (A_6:hoare_1708887482_state)=> ((and ((member451959335_state A_6) A_196)) (((eq (hoare_1708887482_state->Prop)) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_345_pigeonhole__infinite:(forall (F_70:(pname->(pname->Prop))) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite297249702name_o ((image_pname_pname_o F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq (pname->Prop)) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_346_pigeonhole__infinite:(forall (F_70:(pname->(hoare_1708887482_state->Prop))) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite1329924456tate_o ((image_425134806tate_o F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq (hoare_1708887482_state->Prop)) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_347_pigeonhole__infinite:(forall (F_70:(pname->hoare_1708887482_state)) (A_196:(pname->Prop)), (((finite_finite_pname A_196)->False)->((finite1625599783_state ((image_1116629049_state F_70) A_196))->((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_196)) ((finite_finite_pname (collect_pname (fun (A_6:pname)=> ((and ((member_pname A_6) A_196)) (((eq hoare_1708887482_state) (F_70 A_6)) (F_70 X_3))))))->False))))))).
% Axiom fact_348_com_Osimps_I6_J:(forall (Pname_1:pname) (Pname:pname), ((iff (((eq com) (body_1 Pname_1)) (body_1 Pname))) (((eq pname) Pname_1) Pname))).
% Axiom fact_349_MGT__Body:(forall (G_7:(hoare_1708887482_state->Prop)) (Procs_3:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_7) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3))) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) Procs_3))->((finite_finite_pname Procs_3)->((hoare_90032982_state G_7) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3))))).
% Axiom fact_350_domD:(forall (A_195:com) (M_4:(com->option_com)), (((member_com A_195) (dom_com_com M_4))->((ex com) (fun (B_131:com)=> (((eq option_com) (M_4 A_195)) (some_com B_131)))))).
% Axiom fact_351_domD:(forall (A_195:hoare_1708887482_state) (M_4:(hoare_1708887482_state->option_pname)), (((member451959335_state A_195) (dom_Ho1805192458_pname M_4))->((ex pname) (fun (B_131:pname)=> (((eq option_pname) (M_4 A_195)) (some_pname B_131)))))).
% Axiom fact_352_domD:(forall (A_195:hoare_1708887482_state) (M_4:(hoare_1708887482_state->option1624383643_state)), (((member451959335_state A_195) (dom_Ho1703271284_state M_4))->((ex hoare_1708887482_state) (fun (B_131:hoare_1708887482_state)=> (((eq option1624383643_state) (M_4 A_195)) (some_H1974565227_state B_131)))))).
% Axiom fact_353_domD:(forall (A_195:pname) (M_4:(pname->option_pname)), (((member_pname A_195) (dom_pname_pname M_4))->((ex pname) (fun (B_131:pname)=> (((eq option_pname) (M_4 A_195)) (some_pname B_131)))))).
% Axiom fact_354_domD:(forall (A_195:pname) (M_4:(pname->option1624383643_state)), (((member_pname A_195) (dom_pn1412407212_state M_4))->((ex hoare_1708887482_state) (fun (B_131:hoare_1708887482_state)=> (((eq option1624383643_state) (M_4 A_195)) (some_H1974565227_state B_131)))))).
% Axiom fact_355_domD:(forall (A_195:pname) (M_4:(pname->option_com)), (((member_pname A_195) (dom_pname_com M_4))->((ex com) (fun (B_131:com)=> (((eq option_com) (M_4 A_195)) (some_com B_131)))))).
% Axiom fact_356_the__elem__eq:(forall (X_102:pname), (((eq pname) (the_elem_pname ((insert_pname X_102) bot_bot_pname_o))) X_102)).
% Axiom fact_357_the__elem__eq:(forall (X_102:com), (((eq com) (the_elem_com ((insert_com X_102) bot_bot_com_o))) X_102)).
% Axiom fact_358_the__elem__eq:(forall (X_102:hoare_1708887482_state), (((eq hoare_1708887482_state) (the_el864710747_state ((insert528405184_state X_102) bot_bo19817387tate_o))) X_102)).
% Axiom fact_359_image__subsetI:(forall (F_69:(hoare_1708887482_state->com)) (B_130:(com->Prop)) (A_194:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_194)->((member_com (F_69 X_3)) B_130)))->((ord_less_eq_com_o ((image_1604448413te_com F_69) A_194)) B_130))).
% Axiom fact_360_image__subsetI:(forall (F_69:(hoare_1708887482_state->pname)) (B_130:(pname->Prop)) (A_194:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_194)->((member_pname (F_69 X_3)) B_130)))->((ord_less_eq_pname_o ((image_1509414295_pname F_69) A_194)) B_130))).
% Axiom fact_361_image__subsetI:(forall (F_69:(pname->com)) (B_130:(com->Prop)) (A_194:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_194)->((member_com (F_69 X_3)) B_130)))->((ord_less_eq_com_o ((image_pname_com F_69) A_194)) B_130))).
% Axiom fact_362_image__subsetI:(forall (F_69:(pname->pname)) (B_130:(pname->Prop)) (A_194:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_194)->((member_pname (F_69 X_3)) B_130)))->((ord_less_eq_pname_o ((image_pname_pname F_69) A_194)) B_130))).
% Axiom fact_363_image__subsetI:(forall (F_69:(com->hoare_1708887482_state)) (B_130:(hoare_1708887482_state->Prop)) (A_194:(com->Prop)), ((forall (X_3:com), (((member_com X_3) A_194)->((member451959335_state (F_69 X_3)) B_130)))->((ord_le777019615tate_o ((image_934102463_state F_69) A_194)) B_130))).
% Axiom fact_364_image__subsetI:(forall (F_69:(com->pname)) (B_130:(pname->Prop)) (A_194:(com->Prop)), ((forall (X_3:com), (((member_com X_3) A_194)->((member_pname (F_69 X_3)) B_130)))->((ord_less_eq_pname_o ((image_com_pname F_69) A_194)) B_130))).
% Axiom fact_365_image__subsetI:(forall (F_69:(pname->hoare_1708887482_state)) (B_130:(hoare_1708887482_state->Prop)) (A_194:(pname->Prop)), ((forall (X_3:pname), (((member_pname X_3) A_194)->((member451959335_state (F_69 X_3)) B_130)))->((ord_le777019615tate_o ((image_1116629049_state F_69) A_194)) B_130))).
% Axiom fact_366_order__refl:(forall (X_101:(pname->Prop)), ((ord_less_eq_pname_o X_101) X_101)).
% Axiom fact_367_order__refl:(forall (X_101:Prop), ((ord_less_eq_o X_101) X_101)).
% Axiom fact_368_order__refl:(forall (X_101:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o X_101) X_101)).
% Axiom fact_369_nonempty__iff:(forall (A_193:(com->Prop)), ((iff (not (((eq (com->Prop)) A_193) bot_bot_com_o))) ((ex com) (fun (X_3:com)=> ((ex (com->Prop)) (fun (B_84:(com->Prop))=> ((and (((eq (com->Prop)) A_193) ((insert_com X_3) B_84))) (((member_com X_3) B_84)->False)))))))).
% Axiom fact_370_nonempty__iff:(forall (A_193:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_193) bot_bot_pname_o))) ((ex pname) (fun (X_3:pname)=> ((ex (pname->Prop)) (fun (B_84:(pname->Prop))=> ((and (((eq (pname->Prop)) A_193) ((insert_pname X_3) B_84))) (((member_pname X_3) B_84)->False)))))))).
% Axiom fact_371_nonempty__iff:(forall (A_193:(hoare_1708887482_state->Prop)), ((iff (not (((eq (hoare_1708887482_state->Prop)) A_193) bot_bo19817387tate_o))) ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((ex (hoare_1708887482_state->Prop)) (fun (B_84:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_193) ((insert528405184_state X_3) B_84))) (((member451959335_state X_3) B_84)->False)))))))).
% Axiom fact_372_the_Osimps:(forall (X_100:pname), (((eq pname) (the_pname_1 (some_pname X_100))) X_100)).
% Axiom fact_373_the_Osimps:(forall (X_100:hoare_1708887482_state), (((eq hoare_1708887482_state) (the_Ho963921505_state (some_H1974565227_state X_100))) X_100)).
% Axiom fact_374_the_Osimps:(forall (X_100:com), (((eq com) (the_com (some_com X_100))) X_100)).
% Axiom fact_375_weak__Body:(forall (G_31:(hoare_1708887482_state->Prop)) (P_35:(state->(state->Prop))) (Pn_4:pname) (Q_24:(state->(state->Prop))), (((hoare_90032982_state G_31) ((insert528405184_state (((hoare_858012674_state P_35) (the_com (body Pn_4))) Q_24)) bot_bo19817387tate_o))->((hoare_90032982_state G_31) ((insert528405184_state (((hoare_858012674_state P_35) (body_1 Pn_4)) Q_24)) bot_bo19817387tate_o)))).
% Axiom fact_376_BodyN:(forall (P_34:(state->(state->Prop))) (Pn_3:pname) (Q_23:(state->(state->Prop))) (G_30:(hoare_1708887482_state->Prop)), (((hoare_90032982_state ((insert528405184_state (((hoare_858012674_state P_34) (body_1 Pn_3)) Q_23)) G_30)) ((insert528405184_state (((hoare_858012674_state P_34) (the_com (body Pn_3))) Q_23)) bot_bo19817387tate_o))->((hoare_90032982_state G_30) ((insert528405184_state (((hoare_858012674_state P_34) (body_1 Pn_3)) Q_23)) bot_bo19817387tate_o)))).
% Axiom fact_377_state__not__singleton__def:((iff hoare_1160767572gleton) ((ex state) (fun (S_2:state)=> ((ex state) (fun (T_1:state)=> (not (((eq state) S_2) T_1))))))).
% Axiom fact_378_UnCI:(forall (A_192:(com->Prop)) (C_60:com) (B_129:(com->Prop)), (((((member_com C_60) B_129)->False)->((member_com C_60) A_192))->((member_com C_60) ((semila1562558655_com_o A_192) B_129)))).
% Axiom fact_379_UnCI:(forall (A_192:(hoare_1708887482_state->Prop)) (C_60:hoare_1708887482_state) (B_129:(hoare_1708887482_state->Prop)), (((((member451959335_state C_60) B_129)->False)->((member451959335_state C_60) A_192))->((member451959335_state C_60) ((semila1122118281tate_o A_192) B_129)))).
% Axiom fact_380_UnCI:(forall (A_192:(pname->Prop)) (C_60:pname) (B_129:(pname->Prop)), (((((member_pname C_60) B_129)->False)->((member_pname C_60) A_192))->((member_pname C_60) ((semila1780557381name_o A_192) B_129)))).
% Axiom fact_381_UnE:(forall (C_59:com) (A_191:(com->Prop)) (B_128:(com->Prop)), (((member_com C_59) ((semila1562558655_com_o A_191) B_128))->((((member_com C_59) A_191)->False)->((member_com C_59) B_128)))).
% Axiom fact_382_UnE:(forall (C_59:hoare_1708887482_state) (A_191:(hoare_1708887482_state->Prop)) (B_128:(hoare_1708887482_state->Prop)), (((member451959335_state C_59) ((semila1122118281tate_o A_191) B_128))->((((member451959335_state C_59) A_191)->False)->((member451959335_state C_59) B_128)))).
% Axiom fact_383_UnE:(forall (C_59:pname) (A_191:(pname->Prop)) (B_128:(pname->Prop)), (((member_pname C_59) ((semila1780557381name_o A_191) B_128))->((((member_pname C_59) A_191)->False)->((member_pname C_59) B_128)))).
% Axiom fact_384_triple_Oinject:(forall (Fun1_2:(state->(state->Prop))) (Com_4:com) (Fun2_2:(state->(state->Prop))) (Fun1_1:(state->(state->Prop))) (Com_3:com) (Fun2_1:(state->(state->Prop))), ((iff (((eq hoare_1708887482_state) (((hoare_858012674_state Fun1_2) Com_4) Fun2_2)) (((hoare_858012674_state Fun1_1) Com_3) Fun2_1))) ((and ((and (((eq (state->(state->Prop))) Fun1_2) Fun1_1)) (((eq com) Com_4) Com_3))) (((eq (state->(state->Prop))) Fun2_2) Fun2_1)))).
% Axiom fact_385_UnI2:(forall (A_190:(com->Prop)) (C_58:com) (B_127:(com->Prop)), (((member_com C_58) B_127)->((member_com C_58) ((semila1562558655_com_o A_190) B_127)))).
% Axiom fact_386_UnI2:(forall (A_190:(hoare_1708887482_state->Prop)) (C_58:hoare_1708887482_state) (B_127:(hoare_1708887482_state->Prop)), (((member451959335_state C_58) B_127)->((member451959335_state C_58) ((semila1122118281tate_o A_190) B_127)))).
% Axiom fact_387_UnI2:(forall (A_190:(pname->Prop)) (C_58:pname) (B_127:(pname->Prop)), (((member_pname C_58) B_127)->((member_pname C_58) ((semila1780557381name_o A_190) B_127)))).
% Axiom fact_388_UnI1:(forall (B_126:(com->Prop)) (C_57:com) (A_189:(com->Prop)), (((member_com C_57) A_189)->((member_com C_57) ((semila1562558655_com_o A_189) B_126)))).
% Axiom fact_389_UnI1:(forall (B_126:(hoare_1708887482_state->Prop)) (C_57:hoare_1708887482_state) (A_189:(hoare_1708887482_state->Prop)), (((member451959335_state C_57) A_189)->((member451959335_state C_57) ((semila1122118281tate_o A_189) B_126)))).
% Axiom fact_390_UnI1:(forall (B_126:(pname->Prop)) (C_57:pname) (A_189:(pname->Prop)), (((member_pname C_57) A_189)->((member_pname C_57) ((semila1780557381name_o A_189) B_126)))).
% Axiom fact_391_ball__Un:(forall (P_33:(pname->Prop)) (A_188:(pname->Prop)) (B_125:(pname->Prop)), ((iff (forall (X_3:pname), (((member_pname X_3) ((semila1780557381name_o A_188) B_125))->(P_33 X_3)))) ((and (forall (X_3:pname), (((member_pname X_3) A_188)->(P_33 X_3)))) (forall (X_3:pname), (((member_pname X_3) B_125)->(P_33 X_3)))))).
% Axiom fact_392_ball__Un:(forall (P_33:(hoare_1708887482_state->Prop)) (A_188:(hoare_1708887482_state->Prop)) (B_125:(hoare_1708887482_state->Prop)), ((iff (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) ((semila1122118281tate_o A_188) B_125))->(P_33 X_3)))) ((and (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_188)->(P_33 X_3)))) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) B_125)->(P_33 X_3)))))).
% Axiom fact_393_bex__Un:(forall (P_32:(pname->Prop)) (A_187:(pname->Prop)) (B_124:(pname->Prop)), ((iff ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) ((semila1780557381name_o A_187) B_124))) (P_32 X_3))))) ((or ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) A_187)) (P_32 X_3))))) ((ex pname) (fun (X_3:pname)=> ((and ((member_pname X_3) B_124)) (P_32 X_3))))))).
% Axiom fact_394_bex__Un:(forall (P_32:(hoare_1708887482_state->Prop)) (A_187:(hoare_1708887482_state->Prop)) (B_124:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) ((semila1122118281tate_o A_187) B_124))) (P_32 X_3))))) ((or ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_187)) (P_32 X_3))))) ((ex hoare_1708887482_state) (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) B_124)) (P_32 X_3))))))).
% Axiom fact_395_Un__assoc:(forall (A_186:(pname->Prop)) (B_123:(pname->Prop)) (C_56:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_186) B_123)) C_56)) ((semila1780557381name_o A_186) ((semila1780557381name_o B_123) C_56)))).
% Axiom fact_396_Un__assoc:(forall (A_186:(hoare_1708887482_state->Prop)) (B_123:(hoare_1708887482_state->Prop)) (C_56:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_186) B_123)) C_56)) ((semila1122118281tate_o A_186) ((semila1122118281tate_o B_123) C_56)))).
% Axiom fact_397_Un__iff:(forall (C_55:com) (A_185:(com->Prop)) (B_122:(com->Prop)), ((iff ((member_com C_55) ((semila1562558655_com_o A_185) B_122))) ((or ((member_com C_55) A_185)) ((member_com C_55) B_122)))).
% Axiom fact_398_Un__iff:(forall (C_55:hoare_1708887482_state) (A_185:(hoare_1708887482_state->Prop)) (B_122:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_55) ((semila1122118281tate_o A_185) B_122))) ((or ((member451959335_state C_55) A_185)) ((member451959335_state C_55) B_122)))).
% Axiom fact_399_Un__iff:(forall (C_55:pname) (A_185:(pname->Prop)) (B_122:(pname->Prop)), ((iff ((member_pname C_55) ((semila1780557381name_o A_185) B_122))) ((or ((member_pname C_55) A_185)) ((member_pname C_55) B_122)))).
% Axiom fact_400_Un__left__commute:(forall (A_184:(pname->Prop)) (B_121:(pname->Prop)) (C_54:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_184) ((semila1780557381name_o B_121) C_54))) ((semila1780557381name_o B_121) ((semila1780557381name_o A_184) C_54)))).
% Axiom fact_401_Un__left__commute:(forall (A_184:(hoare_1708887482_state->Prop)) (B_121:(hoare_1708887482_state->Prop)) (C_54:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_184) ((semila1122118281tate_o B_121) C_54))) ((semila1122118281tate_o B_121) ((semila1122118281tate_o A_184) C_54)))).
% Axiom fact_402_Un__left__absorb:(forall (A_183:(pname->Prop)) (B_120:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_183) ((semila1780557381name_o A_183) B_120))) ((semila1780557381name_o A_183) B_120))).
% Axiom fact_403_Un__left__absorb:(forall (A_183:(hoare_1708887482_state->Prop)) (B_120:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_183) ((semila1122118281tate_o A_183) B_120))) ((semila1122118281tate_o A_183) B_120))).
% Axiom fact_404_Un__commute:(forall (A_182:(pname->Prop)) (B_119:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_182) B_119)) ((semila1780557381name_o B_119) A_182))).
% Axiom fact_405_Un__commute:(forall (A_182:(hoare_1708887482_state->Prop)) (B_119:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_182) B_119)) ((semila1122118281tate_o B_119) A_182))).
% Axiom fact_406_Un__def:(forall (A_181:(com->Prop)) (B_118:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o A_181) B_118)) (collect_com (fun (X_3:com)=> ((or ((member_com X_3) A_181)) ((member_com X_3) B_118)))))).
% Axiom fact_407_Un__def:(forall (A_181:((pname->Prop)->Prop)) (B_118:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila181081674me_o_o A_181) B_118)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((or ((member_pname_o X_3) A_181)) ((member_pname_o X_3) B_118)))))).
% Axiom fact_408_Un__def:(forall (A_181:((hoare_1708887482_state->Prop)->Prop)) (B_118:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila1853742644te_o_o A_181) B_118)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or ((member814030440tate_o X_3) A_181)) ((member814030440tate_o X_3) B_118)))))).
% Axiom fact_409_Un__def:(forall (A_181:(hoare_1708887482_state->Prop)) (B_118:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_181) B_118)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or ((member451959335_state X_3) A_181)) ((member451959335_state X_3) B_118)))))).
% Axiom fact_410_Un__def:(forall (A_181:(pname->Prop)) (B_118:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_181) B_118)) (collect_pname (fun (X_3:pname)=> ((or ((member_pname X_3) A_181)) ((member_pname X_3) B_118)))))).
% Axiom fact_411_Un__absorb:(forall (A_180:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_180) A_180)) A_180)).
% Axiom fact_412_Un__absorb:(forall (A_180:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_180) A_180)) A_180)).
% Axiom fact_413_Collect__disj__eq:(forall (P_31:(pname->Prop)) (Q_22:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila1780557381name_o (collect_pname P_31)) (collect_pname Q_22)))).
% Axiom fact_414_Collect__disj__eq:(forall (P_31:((pname->Prop)->Prop)) (Q_22:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila181081674me_o_o (collect_pname_o P_31)) (collect_pname_o Q_22)))).
% Axiom fact_415_Collect__disj__eq:(forall (P_31:((hoare_1708887482_state->Prop)->Prop)) (Q_22:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila1853742644te_o_o (collec219771562tate_o P_31)) (collec219771562tate_o Q_22)))).
% Axiom fact_416_Collect__disj__eq:(forall (P_31:(hoare_1708887482_state->Prop)) (Q_22:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((or (P_31 X_3)) (Q_22 X_3))))) ((semila1122118281tate_o (collec1568722789_state P_31)) (collec1568722789_state Q_22)))).
% Axiom fact_417_Un__empty:(forall (A_179:(pname->Prop)) (B_117:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_179) B_117)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_179) bot_bot_pname_o)) (((eq (pname->Prop)) B_117) bot_bot_pname_o)))).
% Axiom fact_418_Un__empty:(forall (A_179:(com->Prop)) (B_117:(com->Prop)), ((iff (((eq (com->Prop)) ((semila1562558655_com_o A_179) B_117)) bot_bot_com_o)) ((and (((eq (com->Prop)) A_179) bot_bot_com_o)) (((eq (com->Prop)) B_117) bot_bot_com_o)))).
% Axiom fact_419_Un__empty:(forall (A_179:(hoare_1708887482_state->Prop)) (B_117:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_179) B_117)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) A_179) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) B_117) bot_bo19817387tate_o)))).
% Axiom fact_420_Un__empty__right:(forall (A_178:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_178) bot_bot_pname_o)) A_178)).
% Axiom fact_421_Un__empty__right:(forall (A_178:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o A_178) bot_bot_com_o)) A_178)).
% Axiom fact_422_Un__empty__right:(forall (A_178:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_178) bot_bo19817387tate_o)) A_178)).
% Axiom fact_423_Un__empty__left:(forall (B_116:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_116)) B_116)).
% Axiom fact_424_Un__empty__left:(forall (B_116:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o bot_bot_com_o) B_116)) B_116)).
% Axiom fact_425_Un__empty__left:(forall (B_116:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_o) B_116)) B_116)).
% Axiom fact_426_finite__UnI:(forall (G_29:((pname->Prop)->Prop)) (F_68:((pname->Prop)->Prop)), ((finite297249702name_o F_68)->((finite297249702name_o G_29)->(finite297249702name_o ((semila181081674me_o_o F_68) G_29))))).
% Axiom fact_427_finite__UnI:(forall (G_29:((hoare_1708887482_state->Prop)->Prop)) (F_68:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_68)->((finite1329924456tate_o G_29)->(finite1329924456tate_o ((semila1853742644te_o_o F_68) G_29))))).
% Axiom fact_428_finite__UnI:(forall (G_29:(hoare_1708887482_state->Prop)) (F_68:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_68)->((finite1625599783_state G_29)->(finite1625599783_state ((semila1122118281tate_o F_68) G_29))))).
% Axiom fact_429_finite__UnI:(forall (G_29:(pname->Prop)) (F_68:(pname->Prop)), ((finite_finite_pname F_68)->((finite_finite_pname G_29)->(finite_finite_pname ((semila1780557381name_o F_68) G_29))))).
% Axiom fact_430_finite__Un:(forall (F_67:((pname->Prop)->Prop)) (G_28:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((semila181081674me_o_o F_67) G_28))) ((and (finite297249702name_o F_67)) (finite297249702name_o G_28)))).
% Axiom fact_431_finite__Un:(forall (F_67:((hoare_1708887482_state->Prop)->Prop)) (G_28:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o ((semila1853742644te_o_o F_67) G_28))) ((and (finite1329924456tate_o F_67)) (finite1329924456tate_o G_28)))).
% Axiom fact_432_finite__Un:(forall (F_67:(hoare_1708887482_state->Prop)) (G_28:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((semila1122118281tate_o F_67) G_28))) ((and (finite1625599783_state F_67)) (finite1625599783_state G_28)))).
% Axiom fact_433_finite__Un:(forall (F_67:(pname->Prop)) (G_28:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_67) G_28))) ((and (finite_finite_pname F_67)) (finite_finite_pname G_28)))).
% Axiom fact_434_Un__insert__left:(forall (A_177:pname) (B_115:(pname->Prop)) (C_53:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_177) B_115)) C_53)) ((insert_pname A_177) ((semila1780557381name_o B_115) C_53)))).
% Axiom fact_435_Un__insert__left:(forall (A_177:com) (B_115:(com->Prop)) (C_53:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o ((insert_com A_177) B_115)) C_53)) ((insert_com A_177) ((semila1562558655_com_o B_115) C_53)))).
% Axiom fact_436_Un__insert__left:(forall (A_177:hoare_1708887482_state) (B_115:(hoare_1708887482_state->Prop)) (C_53:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((insert528405184_state A_177) B_115)) C_53)) ((insert528405184_state A_177) ((semila1122118281tate_o B_115) C_53)))).
% Axiom fact_437_Un__insert__right:(forall (A_176:(pname->Prop)) (A_175:pname) (B_114:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_176) ((insert_pname A_175) B_114))) ((insert_pname A_175) ((semila1780557381name_o A_176) B_114)))).
% Axiom fact_438_Un__insert__right:(forall (A_176:(com->Prop)) (A_175:com) (B_114:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o A_176) ((insert_com A_175) B_114))) ((insert_com A_175) ((semila1562558655_com_o A_176) B_114)))).
% Axiom fact_439_Un__insert__right:(forall (A_176:(hoare_1708887482_state->Prop)) (A_175:hoare_1708887482_state) (B_114:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_176) ((insert528405184_state A_175) B_114))) ((insert528405184_state A_175) ((semila1122118281tate_o A_176) B_114)))).
% Axiom fact_440_Un__mono:(forall (B_113:(pname->Prop)) (D_5:(pname->Prop)) (A_174:(pname->Prop)) (C_52:(pname->Prop)), (((ord_less_eq_pname_o A_174) C_52)->(((ord_less_eq_pname_o B_113) D_5)->((ord_less_eq_pname_o ((semila1780557381name_o A_174) B_113)) ((semila1780557381name_o C_52) D_5))))).
% Axiom fact_441_Un__mono:(forall (B_113:(hoare_1708887482_state->Prop)) (D_5:(hoare_1708887482_state->Prop)) (A_174:(hoare_1708887482_state->Prop)) (C_52:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_174) C_52)->(((ord_le777019615tate_o B_113) D_5)->((ord_le777019615tate_o ((semila1122118281tate_o A_174) B_113)) ((semila1122118281tate_o C_52) D_5))))).
% Axiom fact_442_Un__least:(forall (B_112:(pname->Prop)) (A_173:(pname->Prop)) (C_51:(pname->Prop)), (((ord_less_eq_pname_o A_173) C_51)->(((ord_less_eq_pname_o B_112) C_51)->((ord_less_eq_pname_o ((semila1780557381name_o A_173) B_112)) C_51)))).
% Axiom fact_443_Un__least:(forall (B_112:(hoare_1708887482_state->Prop)) (A_173:(hoare_1708887482_state->Prop)) (C_51:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_173) C_51)->(((ord_le777019615tate_o B_112) C_51)->((ord_le777019615tate_o ((semila1122118281tate_o A_173) B_112)) C_51)))).
% Axiom fact_444_Un__absorb2:(forall (B_111:(pname->Prop)) (A_172:(pname->Prop)), (((ord_less_eq_pname_o B_111) A_172)->(((eq (pname->Prop)) ((semila1780557381name_o A_172) B_111)) A_172))).
% Axiom fact_445_Un__absorb2:(forall (B_111:(hoare_1708887482_state->Prop)) (A_172:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_111) A_172)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_172) B_111)) A_172))).
% Axiom fact_446_Un__absorb1:(forall (A_171:(pname->Prop)) (B_110:(pname->Prop)), (((ord_less_eq_pname_o A_171) B_110)->(((eq (pname->Prop)) ((semila1780557381name_o A_171) B_110)) B_110))).
% Axiom fact_447_Un__absorb1:(forall (A_171:(hoare_1708887482_state->Prop)) (B_110:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_171) B_110)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_171) B_110)) B_110))).
% Axiom fact_448_subset__Un__eq:(forall (A_170:(pname->Prop)) (B_109:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_170) B_109)) (((eq (pname->Prop)) ((semila1780557381name_o A_170) B_109)) B_109))).
% Axiom fact_449_subset__Un__eq:(forall (A_170:(hoare_1708887482_state->Prop)) (B_109:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_170) B_109)) (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_170) B_109)) B_109))).
% Axiom fact_450_Un__upper2:(forall (B_108:(pname->Prop)) (A_169:(pname->Prop)), ((ord_less_eq_pname_o B_108) ((semila1780557381name_o A_169) B_108))).
% Axiom fact_451_Un__upper2:(forall (B_108:(hoare_1708887482_state->Prop)) (A_169:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o B_108) ((semila1122118281tate_o A_169) B_108))).
% Axiom fact_452_Un__upper1:(forall (A_168:(pname->Prop)) (B_107:(pname->Prop)), ((ord_less_eq_pname_o A_168) ((semila1780557381name_o A_168) B_107))).
% Axiom fact_453_Un__upper1:(forall (A_168:(hoare_1708887482_state->Prop)) (B_107:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o A_168) ((semila1122118281tate_o A_168) B_107))).
% Axiom fact_454_image__Un:(forall (F_66:(hoare_1708887482_state->pname)) (A_167:(hoare_1708887482_state->Prop)) (B_106:(hoare_1708887482_state->Prop)), (((eq (pname->Prop)) ((image_1509414295_pname F_66) ((semila1122118281tate_o A_167) B_106))) ((semila1780557381name_o ((image_1509414295_pname F_66) A_167)) ((image_1509414295_pname F_66) B_106)))).
% Axiom fact_455_image__Un:(forall (F_66:(pname->hoare_1708887482_state)) (A_167:(pname->Prop)) (B_106:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_66) ((semila1780557381name_o A_167) B_106))) ((semila1122118281tate_o ((image_1116629049_state F_66) A_167)) ((image_1116629049_state F_66) B_106)))).
% Axiom fact_456_insert__def:(forall (A_166:pname) (B_105:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_166) B_105)) ((semila1780557381name_o (collect_pname (fun (X_3:pname)=> (((eq pname) X_3) A_166)))) B_105))).
% Axiom fact_457_insert__def:(forall (A_166:com) (B_105:(com->Prop)), (((eq (com->Prop)) ((insert_com A_166) B_105)) ((semila1562558655_com_o (collect_com (fun (X_3:com)=> (((eq com) X_3) A_166)))) B_105))).
% Axiom fact_458_insert__def:(forall (A_166:(pname->Prop)) (B_105:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_166) B_105)) ((semila181081674me_o_o (collect_pname_o (fun (X_3:(pname->Prop))=> (((eq (pname->Prop)) X_3) A_166)))) B_105))).
% Axiom fact_459_insert__def:(forall (A_166:(hoare_1708887482_state->Prop)) (B_105:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((insert949073679tate_o A_166) B_105)) ((semila1853742644te_o_o (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> (((eq (hoare_1708887482_state->Prop)) X_3) A_166)))) B_105))).
% Axiom fact_460_insert__def:(forall (A_166:hoare_1708887482_state) (B_105:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_166) B_105)) ((semila1122118281tate_o (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X_3) A_166)))) B_105))).
% Axiom fact_461_insert__is__Un:(forall (A_165:pname) (A_164:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_165) A_164)) ((semila1780557381name_o ((insert_pname A_165) bot_bot_pname_o)) A_164))).
% Axiom fact_462_insert__is__Un:(forall (A_165:com) (A_164:(com->Prop)), (((eq (com->Prop)) ((insert_com A_165) A_164)) ((semila1562558655_com_o ((insert_com A_165) bot_bot_com_o)) A_164))).
% Axiom fact_463_insert__is__Un:(forall (A_165:hoare_1708887482_state) (A_164:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_165) A_164)) ((semila1122118281tate_o ((insert528405184_state A_165) bot_bo19817387tate_o)) A_164))).
% Axiom fact_464_hoare__derivs_OBody:(forall (G_27:(hoare_1708887482_state->Prop)) (P_30:(pname->(state->(state->Prop)))) (Q_21:(pname->(state->(state->Prop)))) (Procs_2:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_27) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_30 P_27)) (body_1 P_27)) (Q_21 P_27)))) Procs_2))) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_30 P_27)) (the_com (body P_27))) (Q_21 P_27)))) Procs_2))->((hoare_90032982_state G_27) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_30 P_27)) (body_1 P_27)) (Q_21 P_27)))) Procs_2)))).
% Axiom fact_465_xt1_I6_J:(forall (Z_20:(pname->Prop)) (Y_50:(pname->Prop)) (X_99:(pname->Prop)), (((ord_less_eq_pname_o Y_50) X_99)->(((ord_less_eq_pname_o Z_20) Y_50)->((ord_less_eq_pname_o Z_20) X_99)))).
% Axiom fact_466_xt1_I6_J:(forall (Z_20:Prop) (Y_50:Prop) (X_99:Prop), (((ord_less_eq_o Y_50) X_99)->(((ord_less_eq_o Z_20) Y_50)->((ord_less_eq_o Z_20) X_99)))).
% Axiom fact_467_xt1_I6_J:(forall (Z_20:(hoare_1708887482_state->Prop)) (Y_50:(hoare_1708887482_state->Prop)) (X_99:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_50) X_99)->(((ord_le777019615tate_o Z_20) Y_50)->((ord_le777019615tate_o Z_20) X_99)))).
% Axiom fact_468_xt1_I5_J:(forall (Y_49:(pname->Prop)) (X_98:(pname->Prop)), (((ord_less_eq_pname_o Y_49) X_98)->(((ord_less_eq_pname_o X_98) Y_49)->(((eq (pname->Prop)) X_98) Y_49)))).
% Axiom fact_469_xt1_I5_J:(forall (Y_49:Prop) (X_98:Prop), (((ord_less_eq_o Y_49) X_98)->(((ord_less_eq_o X_98) Y_49)->((iff X_98) Y_49)))).
% Axiom fact_470_xt1_I5_J:(forall (Y_49:(hoare_1708887482_state->Prop)) (X_98:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_49) X_98)->(((ord_le777019615tate_o X_98) Y_49)->(((eq (hoare_1708887482_state->Prop)) X_98) Y_49)))).
% Axiom fact_471_order__trans:(forall (Z_19:(pname->Prop)) (X_97:(pname->Prop)) (Y_48:(pname->Prop)), (((ord_less_eq_pname_o X_97) Y_48)->(((ord_less_eq_pname_o Y_48) Z_19)->((ord_less_eq_pname_o X_97) Z_19)))).
% Axiom fact_472_order__trans:(forall (Z_19:Prop) (X_97:Prop) (Y_48:Prop), (((ord_less_eq_o X_97) Y_48)->(((ord_less_eq_o Y_48) Z_19)->((ord_less_eq_o X_97) Z_19)))).
% Axiom fact_473_order__trans:(forall (Z_19:(hoare_1708887482_state->Prop)) (X_97:(hoare_1708887482_state->Prop)) (Y_48:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_97) Y_48)->(((ord_le777019615tate_o Y_48) Z_19)->((ord_le777019615tate_o X_97) Z_19)))).
% Axiom fact_474_order__antisym:(forall (X_96:(pname->Prop)) (Y_47:(pname->Prop)), (((ord_less_eq_pname_o X_96) Y_47)->(((ord_less_eq_pname_o Y_47) X_96)->(((eq (pname->Prop)) X_96) Y_47)))).
% Axiom fact_475_order__antisym:(forall (X_96:Prop) (Y_47:Prop), (((ord_less_eq_o X_96) Y_47)->(((ord_less_eq_o Y_47) X_96)->((iff X_96) Y_47)))).
% Axiom fact_476_order__antisym:(forall (X_96:(hoare_1708887482_state->Prop)) (Y_47:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_96) Y_47)->(((ord_le777019615tate_o Y_47) X_96)->(((eq (hoare_1708887482_state->Prop)) X_96) Y_47)))).
% Axiom fact_477_xt1_I4_J:(forall (C_50:(pname->Prop)) (B_104:(pname->Prop)) (A_163:(pname->Prop)), (((ord_less_eq_pname_o B_104) A_163)->((((eq (pname->Prop)) B_104) C_50)->((ord_less_eq_pname_o C_50) A_163)))).
% Axiom fact_478_xt1_I4_J:(forall (C_50:Prop) (B_104:Prop) (A_163:Prop), (((ord_less_eq_o B_104) A_163)->(((iff B_104) C_50)->((ord_less_eq_o C_50) A_163)))).
% Axiom fact_479_xt1_I4_J:(forall (C_50:(hoare_1708887482_state->Prop)) (B_104:(hoare_1708887482_state->Prop)) (A_163:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_104) A_163)->((((eq (hoare_1708887482_state->Prop)) B_104) C_50)->((ord_le777019615tate_o C_50) A_163)))).
% Axiom fact_480_ord__le__eq__trans:(forall (C_49:(pname->Prop)) (A_162:(pname->Prop)) (B_103:(pname->Prop)), (((ord_less_eq_pname_o A_162) B_103)->((((eq (pname->Prop)) B_103) C_49)->((ord_less_eq_pname_o A_162) C_49)))).
% Axiom fact_481_ord__le__eq__trans:(forall (C_49:Prop) (A_162:Prop) (B_103:Prop), (((ord_less_eq_o A_162) B_103)->(((iff B_103) C_49)->((ord_less_eq_o A_162) C_49)))).
% Axiom fact_482_ord__le__eq__trans:(forall (C_49:(hoare_1708887482_state->Prop)) (A_162:(hoare_1708887482_state->Prop)) (B_103:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_162) B_103)->((((eq (hoare_1708887482_state->Prop)) B_103) C_49)->((ord_le777019615tate_o A_162) C_49)))).
% Axiom fact_483_xt1_I3_J:(forall (C_48:(pname->Prop)) (A_161:(pname->Prop)) (B_102:(pname->Prop)), ((((eq (pname->Prop)) A_161) B_102)->(((ord_less_eq_pname_o C_48) B_102)->((ord_less_eq_pname_o C_48) A_161)))).
% Axiom fact_484_xt1_I3_J:(forall (C_48:Prop) (B_102:Prop) (A_161:Prop), (((iff A_161) B_102)->(((ord_less_eq_o C_48) B_102)->((ord_less_eq_o C_48) A_161)))).
% Axiom fact_485_xt1_I3_J:(forall (C_48:(hoare_1708887482_state->Prop)) (A_161:(hoare_1708887482_state->Prop)) (B_102:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_161) B_102)->(((ord_le777019615tate_o C_48) B_102)->((ord_le777019615tate_o C_48) A_161)))).
% Axiom fact_486_ord__eq__le__trans:(forall (C_47:(pname->Prop)) (A_160:(pname->Prop)) (B_101:(pname->Prop)), ((((eq (pname->Prop)) A_160) B_101)->(((ord_less_eq_pname_o B_101) C_47)->((ord_less_eq_pname_o A_160) C_47)))).
% Axiom fact_487_ord__eq__le__trans:(forall (C_47:Prop) (B_101:Prop) (A_160:Prop), (((iff A_160) B_101)->(((ord_less_eq_o B_101) C_47)->((ord_less_eq_o A_160) C_47)))).
% Axiom fact_488_ord__eq__le__trans:(forall (C_47:(hoare_1708887482_state->Prop)) (A_160:(hoare_1708887482_state->Prop)) (B_101:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_160) B_101)->(((ord_le777019615tate_o B_101) C_47)->((ord_le777019615tate_o A_160) C_47)))).
% Axiom fact_489_order__antisym__conv:(forall (Y_46:(pname->Prop)) (X_95:(pname->Prop)), (((ord_less_eq_pname_o Y_46) X_95)->((iff ((ord_less_eq_pname_o X_95) Y_46)) (((eq (pname->Prop)) X_95) Y_46)))).
% Axiom fact_490_order__antisym__conv:(forall (Y_46:Prop) (X_95:Prop), (((ord_less_eq_o Y_46) X_95)->((iff ((ord_less_eq_o X_95) Y_46)) ((iff X_95) Y_46)))).
% Axiom fact_491_order__antisym__conv:(forall (Y_46:(hoare_1708887482_state->Prop)) (X_95:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_46) X_95)->((iff ((ord_le777019615tate_o X_95) Y_46)) (((eq (hoare_1708887482_state->Prop)) X_95) Y_46)))).
% Axiom fact_492_order__eq__refl:(forall (X_94:(pname->Prop)) (Y_45:(pname->Prop)), ((((eq (pname->Prop)) X_94) Y_45)->((ord_less_eq_pname_o X_94) Y_45))).
% Axiom fact_493_order__eq__refl:(forall (Y_45:Prop) (X_94:Prop), (((iff X_94) Y_45)->((ord_less_eq_o X_94) Y_45))).
% Axiom fact_494_order__eq__refl:(forall (X_94:(hoare_1708887482_state->Prop)) (Y_45:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) X_94) Y_45)->((ord_le777019615tate_o X_94) Y_45))).
% Axiom fact_495_order__eq__iff:(forall (X_93:(pname->Prop)) (Y_44:(pname->Prop)), ((iff (((eq (pname->Prop)) X_93) Y_44)) ((and ((ord_less_eq_pname_o X_93) Y_44)) ((ord_less_eq_pname_o Y_44) X_93)))).
% Axiom fact_496_order__eq__iff:(forall (Y_44:Prop) (X_93:Prop), ((iff ((iff X_93) Y_44)) ((and ((ord_less_eq_o X_93) Y_44)) ((ord_less_eq_o Y_44) X_93)))).
% Axiom fact_497_order__eq__iff:(forall (X_93:(hoare_1708887482_state->Prop)) (Y_44:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) X_93) Y_44)) ((and ((ord_le777019615tate_o X_93) Y_44)) ((ord_le777019615tate_o Y_44) X_93)))).
% Axiom fact_498_option_Oinject:(forall (A_159:pname) (A_158:pname), ((iff (((eq option_pname) (some_pname A_159)) (some_pname A_158))) (((eq pname) A_159) A_158))).
% Axiom fact_499_option_Oinject:(forall (A_159:hoare_1708887482_state) (A_158:hoare_1708887482_state), ((iff (((eq option1624383643_state) (some_H1974565227_state A_159)) (some_H1974565227_state A_158))) (((eq hoare_1708887482_state) A_159) A_158))).
% Axiom fact_500_option_Oinject:(forall (A_159:com) (A_158:com), ((iff (((eq option_com) (some_com A_159)) (some_com A_158))) (((eq com) A_159) A_158))).
% Axiom fact_501_constant:(forall (G_26:(hoare_1708887482_state->Prop)) (P_29:(state->(state->Prop))) (C_46:com) (Q_20:(state->(state->Prop))) (C_45:Prop), ((C_45->((hoare_90032982_state G_26) ((insert528405184_state (((hoare_858012674_state P_29) C_46) Q_20)) bot_bo19817387tate_o)))->((hoare_90032982_state G_26) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S_2:state)=> ((and ((P_29 Z_11) S_2)) C_45))) C_46) Q_20)) bot_bo19817387tate_o)))).
% Axiom fact_502_Body1:(forall (Pn_2:pname) (G_25:(hoare_1708887482_state->Prop)) (P_28:(pname->(state->(state->Prop)))) (Q_19:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_25) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_28 P_27)) (body_1 P_27)) (Q_19 P_27)))) Procs_1))) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_28 P_27)) (the_com (body P_27))) (Q_19 P_27)))) Procs_1))->(((member_pname Pn_2) Procs_1)->((hoare_90032982_state G_25) ((insert528405184_state (((hoare_858012674_state (P_28 Pn_2)) (body_1 Pn_2)) (Q_19 Pn_2))) bot_bo19817387tate_o))))).
% Axiom fact_503_le__bot:(forall (A_157:(pname->Prop)), (((ord_less_eq_pname_o A_157) bot_bot_pname_o)->(((eq (pname->Prop)) A_157) bot_bot_pname_o))).
% Axiom fact_504_le__bot:(forall (A_157:(com->Prop)), (((ord_less_eq_com_o A_157) bot_bot_com_o)->(((eq (com->Prop)) A_157) bot_bot_com_o))).
% Axiom fact_505_le__bot:(forall (A_157:Prop), (((ord_less_eq_o A_157) bot_bot_o)->((iff A_157) bot_bot_o))).
% Axiom fact_506_le__bot:(forall (A_157:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_157) bot_bo19817387tate_o)->(((eq (hoare_1708887482_state->Prop)) A_157) bot_bo19817387tate_o))).
% Axiom fact_507_bot__unique:(forall (A_156:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_156) bot_bot_pname_o)) (((eq (pname->Prop)) A_156) bot_bot_pname_o))).
% Axiom fact_508_bot__unique:(forall (A_156:(com->Prop)), ((iff ((ord_less_eq_com_o A_156) bot_bot_com_o)) (((eq (com->Prop)) A_156) bot_bot_com_o))).
% Axiom fact_509_bot__unique:(forall (A_156:Prop), ((iff ((ord_less_eq_o A_156) bot_bot_o)) ((iff A_156) bot_bot_o))).
% Axiom fact_510_bot__unique:(forall (A_156:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_156) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) A_156) bot_bo19817387tate_o))).
% Axiom fact_511_bot__least:(forall (A_155:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_155)).
% Axiom fact_512_bot__least:(forall (A_155:(com->Prop)), ((ord_less_eq_com_o bot_bot_com_o) A_155)).
% Axiom fact_513_bot__least:(forall (A_155:Prop), ((ord_less_eq_o bot_bot_o) A_155)).
% Axiom fact_514_bot__least:(forall (A_155:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o bot_bo19817387tate_o) A_155)).
% Axiom fact_515_le__funE:(forall (X_92:pname) (F_65:(pname->Prop)) (G_24:(pname->Prop)), (((ord_less_eq_pname_o F_65) G_24)->((ord_less_eq_o (F_65 X_92)) (G_24 X_92)))).
% Axiom fact_516_le__funE:(forall (X_92:hoare_1708887482_state) (F_65:(hoare_1708887482_state->Prop)) (G_24:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o F_65) G_24)->((ord_less_eq_o (F_65 X_92)) (G_24 X_92)))).
% Axiom fact_517_le__funD:(forall (X_91:pname) (F_64:(pname->Prop)) (G_23:(pname->Prop)), (((ord_less_eq_pname_o F_64) G_23)->((ord_less_eq_o (F_64 X_91)) (G_23 X_91)))).
% Axiom fact_518_le__funD:(forall (X_91:hoare_1708887482_state) (F_64:(hoare_1708887482_state->Prop)) (G_23:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o F_64) G_23)->((ord_less_eq_o (F_64 X_91)) (G_23 X_91)))).
% Axiom fact_519_le__fun__def:(forall (F_63:(pname->Prop)) (G_22:(pname->Prop)), ((iff ((ord_less_eq_pname_o F_63) G_22)) (forall (X_3:pname), ((ord_less_eq_o (F_63 X_3)) (G_22 X_3))))).
% Axiom fact_520_le__fun__def:(forall (F_63:(hoare_1708887482_state->Prop)) (G_22:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o F_63) G_22)) (forall (X_3:hoare_1708887482_state), ((ord_less_eq_o (F_63 X_3)) (G_22 X_3))))).
% Axiom fact_521_bot__apply:(forall (X_90:pname), ((iff (bot_bot_pname_o X_90)) bot_bot_o)).
% Axiom fact_522_bot__apply:(forall (X_90:com), ((iff (bot_bot_com_o X_90)) bot_bot_o)).
% Axiom fact_523_bot__apply:(forall (X_90:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X_90)) bot_bot_o)).
% Axiom fact_524_bot__fun__def:(forall (X_3:pname), ((iff (bot_bot_pname_o X_3)) bot_bot_o)).
% Axiom fact_525_bot__fun__def:(forall (X_3:com), ((iff (bot_bot_com_o X_3)) bot_bot_o)).
% Axiom fact_526_bot__fun__def:(forall (X_3:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X_3)) bot_bot_o)).
% Axiom fact_527_finite__pointwise:(forall (P_26:((pname->Prop)->(state->(state->Prop)))) (Q_18:((pname->Prop)->(state->(state->Prop)))) (G_21:(hoare_1708887482_state->Prop)) (P_25:((pname->Prop)->(state->(state->Prop)))) (C0_1:((pname->Prop)->com)) (Q_17:((pname->Prop)->(state->(state->Prop)))) (U_1:((pname->Prop)->Prop)), ((finite297249702name_o U_1)->((forall (P_27:(pname->Prop)), (((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27))) bot_bo19817387tate_o))->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_21) ((image_1922967206_state (fun (P_27:(pname->Prop))=> (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27)))) U_1))->((hoare_90032982_state G_21) ((image_1922967206_state (fun (P_27:(pname->Prop))=> (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27)))) U_1)))))).
% Axiom fact_528_finite__pointwise:(forall (P_26:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (Q_18:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (G_21:(hoare_1708887482_state->Prop)) (P_25:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (C0_1:((hoare_1708887482_state->Prop)->com)) (Q_17:((hoare_1708887482_state->Prop)->(state->(state->Prop)))) (U_1:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o U_1)->((forall (P_27:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27))) bot_bo19817387tate_o))->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_21) ((image_27005066_state (fun (P_27:(hoare_1708887482_state->Prop))=> (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27)))) U_1))->((hoare_90032982_state G_21) ((image_27005066_state (fun (P_27:(hoare_1708887482_state->Prop))=> (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27)))) U_1)))))).
% Axiom fact_529_finite__pointwise:(forall (P_26:(pname->(state->(state->Prop)))) (Q_18:(pname->(state->(state->Prop)))) (G_21:(hoare_1708887482_state->Prop)) (P_25:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_17:(pname->(state->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_27:pname), (((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27))) bot_bo19817387tate_o))->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_21) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_25 P_27)) (C0_1 P_27)) (Q_17 P_27)))) U_1))->((hoare_90032982_state G_21) ((image_1116629049_state (fun (P_27:pname)=> (((hoare_858012674_state (P_26 P_27)) (C0_1 P_27)) (Q_18 P_27)))) U_1)))))).
% Axiom fact_530_escape:(forall (G_20:(hoare_1708887482_state->Prop)) (C_44:com) (Q_16:(state->(state->Prop))) (P_24:(state->(state->Prop))), ((forall (Z_11:state) (S_2:state), (((P_24 Z_11) S_2)->((hoare_90032982_state G_20) ((insert528405184_state (((hoare_858012674_state (fun (Za:state) (S_3:state)=> (((eq state) S_3) S_2))) C_44) (fun (Z_12:state)=> (Q_16 Z_11)))) bot_bo19817387tate_o))))->((hoare_90032982_state G_20) ((insert528405184_state (((hoare_858012674_state P_24) C_44) Q_16)) bot_bo19817387tate_o)))).
% Axiom fact_531_Body__sound__lemma:(forall (G_19:(hoare_1708887482_state->Prop)) (P_23:(pname->(state->(state->Prop)))) (Q_15:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_496444244_state ((semila1122118281tate_o G_19) ((image_1116629049_state (fun (Pn:pname)=> (((hoare_858012674_state (P_23 Pn)) (body_1 Pn)) (Q_15 Pn)))) Procs))) ((image_1116629049_state (fun (Pn:pname)=> (((hoare_858012674_state (P_23 Pn)) (the_com (body Pn))) (Q_15 Pn)))) Procs))->((hoare_496444244_state G_19) ((image_1116629049_state (fun (Pn:pname)=> (((hoare_858012674_state (P_23 Pn)) (body_1 Pn)) (Q_15 Pn)))) Procs)))).
% Axiom fact_532_conseq1:(forall (P_22:(state->(state->Prop))) (G_18:(hoare_1708887482_state->Prop)) (P_21:(state->(state->Prop))) (C_43:com) (Q_14:(state->(state->Prop))), (((hoare_90032982_state G_18) ((insert528405184_state (((hoare_858012674_state P_21) C_43) Q_14)) bot_bo19817387tate_o))->((forall (Z_11:state) (S_2:state), (((P_22 Z_11) S_2)->((P_21 Z_11) S_2)))->((hoare_90032982_state G_18) ((insert528405184_state (((hoare_858012674_state P_22) C_43) Q_14)) bot_bo19817387tate_o))))).
% Axiom fact_533_conseq2:(forall (Q_13:(state->(state->Prop))) (G_17:(hoare_1708887482_state->Prop)) (P_20:(state->(state->Prop))) (C_42:com) (Q_12:(state->(state->Prop))), (((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state P_20) C_42) Q_12)) bot_bo19817387tate_o))->((forall (Z_11:state) (S_2:state), (((Q_12 Z_11) S_2)->((Q_13 Z_11) S_2)))->((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state P_20) C_42) Q_13)) bot_bo19817387tate_o))))).
% Axiom fact_534_MGF__complete:(forall (P:(state->(state->Prop))) (Q_11:(state->(state->Prop))) (C_34:com), (((hoare_90032982_state bot_bo19817387tate_o) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o))->(((hoare_496444244_state bot_bo19817387tate_o) ((insert528405184_state (((hoare_858012674_state P) C_34) Q_11)) bot_bo19817387tate_o))->((hoare_90032982_state bot_bo19817387tate_o) ((insert528405184_state (((hoare_858012674_state P) C_34) Q_11)) bot_bo19817387tate_o))))).
% Axiom fact_535_sup1E:(forall (A_154:(pname->Prop)) (B_100:(pname->Prop)) (X_89:pname), ((((semila1780557381name_o A_154) B_100) X_89)->(((A_154 X_89)->False)->(B_100 X_89)))).
% Axiom fact_536_sup1E:(forall (A_154:(hoare_1708887482_state->Prop)) (B_100:(hoare_1708887482_state->Prop)) (X_89:hoare_1708887482_state), ((((semila1122118281tate_o A_154) B_100) X_89)->(((A_154 X_89)->False)->(B_100 X_89)))).
% Axiom fact_537_sup1CI:(forall (A_153:(pname->Prop)) (B_99:(pname->Prop)) (X_88:pname), ((((B_99 X_88)->False)->(A_153 X_88))->(((semila1780557381name_o A_153) B_99) X_88))).
% Axiom fact_538_sup1CI:(forall (A_153:(hoare_1708887482_state->Prop)) (B_99:(hoare_1708887482_state->Prop)) (X_88:hoare_1708887482_state), ((((B_99 X_88)->False)->(A_153 X_88))->(((semila1122118281tate_o A_153) B_99) X_88))).
% Axiom fact_539_conseq12:(forall (Q_10:(state->(state->Prop))) (P_19:(state->(state->Prop))) (G_16:(hoare_1708887482_state->Prop)) (P_18:(state->(state->Prop))) (C_41:com) (Q_9:(state->(state->Prop))), (((hoare_90032982_state G_16) ((insert528405184_state (((hoare_858012674_state P_18) C_41) Q_9)) bot_bo19817387tate_o))->((forall (Z_11:state) (S_2:state), (((P_19 Z_11) S_2)->(forall (S_3:state), ((forall (Z_12:state), (((P_18 Z_12) S_2)->((Q_9 Z_12) S_3)))->((Q_10 Z_11) S_3)))))->((hoare_90032982_state G_16) ((insert528405184_state (((hoare_858012674_state P_19) C_41) Q_10)) bot_bo19817387tate_o))))).
% Axiom fact_540_hoare__sound:(forall (G_15:(hoare_1708887482_state->Prop)) (Ts:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_15) Ts)->((hoare_496444244_state G_15) Ts))).
% Axiom fact_541_bot__empty__eq:(forall (X_3:com), ((iff (bot_bot_com_o X_3)) ((member_com X_3) bot_bot_com_o))).
% Axiom fact_542_bot__empty__eq:(forall (X_3:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X_3)) ((member451959335_state X_3) bot_bo19817387tate_o))).
% Axiom fact_543_bot__empty__eq:(forall (X_3:pname), ((iff (bot_bot_pname_o X_3)) ((member_pname X_3) bot_bot_pname_o))).
% Axiom fact_544_rev__predicate1D:(forall (Q_8:(pname->Prop)) (P_17:(pname->Prop)) (X_87:pname), ((P_17 X_87)->(((ord_less_eq_pname_o P_17) Q_8)->(Q_8 X_87)))).
% Axiom fact_545_rev__predicate1D:(forall (Q_8:(hoare_1708887482_state->Prop)) (P_17:(hoare_1708887482_state->Prop)) (X_87:hoare_1708887482_state), ((P_17 X_87)->(((ord_le777019615tate_o P_17) Q_8)->(Q_8 X_87)))).
% Axiom fact_546_predicate1D:(forall (X_86:pname) (P_16:(pname->Prop)) (Q_7:(pname->Prop)), (((ord_less_eq_pname_o P_16) Q_7)->((P_16 X_86)->(Q_7 X_86)))).
% Axiom fact_547_predicate1D:(forall (X_86:hoare_1708887482_state) (P_16:(hoare_1708887482_state->Prop)) (Q_7:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o P_16) Q_7)->((P_16 X_86)->(Q_7 X_86)))).
% Axiom fact_548_sup1I2:(forall (A_152:(pname->Prop)) (B_98:(pname->Prop)) (X_85:pname), ((B_98 X_85)->(((semila1780557381name_o A_152) B_98) X_85))).
% Axiom fact_549_sup1I2:(forall (A_152:(hoare_1708887482_state->Prop)) (B_98:(hoare_1708887482_state->Prop)) (X_85:hoare_1708887482_state), ((B_98 X_85)->(((semila1122118281tate_o A_152) B_98) X_85))).
% Axiom fact_550_sup1I1:(forall (B_97:(pname->Prop)) (A_151:(pname->Prop)) (X_84:pname), ((A_151 X_84)->(((semila1780557381name_o A_151) B_97) X_84))).
% Axiom fact_551_sup1I1:(forall (B_97:(hoare_1708887482_state->Prop)) (A_151:(hoare_1708887482_state->Prop)) (X_84:hoare_1708887482_state), ((A_151 X_84)->(((semila1122118281tate_o A_151) B_97) X_84))).
% Axiom fact_552_pred__subset__eq:(forall (R_3:(com->Prop)) (S_6:(com->Prop)), ((iff ((ord_less_eq_com_o (fun (X_3:com)=> ((member_com X_3) R_3))) (fun (X_3:com)=> ((member_com X_3) S_6)))) ((ord_less_eq_com_o R_3) S_6))).
% Axiom fact_553_pred__subset__eq:(forall (R_3:(hoare_1708887482_state->Prop)) (S_6:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) R_3))) (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) S_6)))) ((ord_le777019615tate_o R_3) S_6))).
% Axiom fact_554_pred__subset__eq:(forall (R_3:(pname->Prop)) (S_6:(pname->Prop)), ((iff ((ord_less_eq_pname_o (fun (X_3:pname)=> ((member_pname X_3) R_3))) (fun (X_3:pname)=> ((member_pname X_3) S_6)))) ((ord_less_eq_pname_o R_3) S_6))).
% Axiom fact_555_sup__Un__eq:(forall (R_2:(com->Prop)) (S_5:(com->Prop)) (X_3:com), ((iff (((semila1562558655_com_o (fun (Y_4:com)=> ((member_com Y_4) R_2))) (fun (Y_4:com)=> ((member_com Y_4) S_5))) X_3)) ((member_com X_3) ((semila1562558655_com_o R_2) S_5)))).
% Axiom fact_556_sup__Un__eq:(forall (R_2:(hoare_1708887482_state->Prop)) (S_5:(hoare_1708887482_state->Prop)) (X_3:hoare_1708887482_state), ((iff (((semila1122118281tate_o (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) R_2))) (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) S_5))) X_3)) ((member451959335_state X_3) ((semila1122118281tate_o R_2) S_5)))).
% Axiom fact_557_sup__Un__eq:(forall (R_2:(pname->Prop)) (S_5:(pname->Prop)) (X_3:pname), ((iff (((semila1780557381name_o (fun (Y_4:pname)=> ((member_pname Y_4) R_2))) (fun (Y_4:pname)=> ((member_pname Y_4) S_5))) X_3)) ((member_pname X_3) ((semila1780557381name_o R_2) S_5)))).
% Axiom fact_558_le__funI:(forall (F_62:(pname->Prop)) (G_14:(pname->Prop)), ((forall (X_3:pname), ((ord_less_eq_o (F_62 X_3)) (G_14 X_3)))->((ord_less_eq_pname_o F_62) G_14))).
% Axiom fact_559_le__funI:(forall (F_62:(hoare_1708887482_state->Prop)) (G_14:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), ((ord_less_eq_o (F_62 X_3)) (G_14 X_3)))->((ord_le777019615tate_o F_62) G_14))).
% Axiom fact_560_Option_Oset_Osimps_I2_J:(forall (X_83:pname), (((eq (pname->Prop)) (set_pname (some_pname X_83))) ((insert_pname X_83) bot_bot_pname_o))).
% Axiom fact_561_Option_Oset_Osimps_I2_J:(forall (X_83:com), (((eq (com->Prop)) (set_com (some_com X_83))) ((insert_com X_83) bot_bot_com_o))).
% Axiom fact_562_Option_Oset_Osimps_I2_J:(forall (X_83:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (set_Ho525251890_state (some_H1974565227_state X_83))) ((insert528405184_state X_83) bot_bo19817387tate_o))).
% Axiom fact_563_sup__apply:(forall (F_61:(pname->Prop)) (G_13:(pname->Prop)) (X_82:pname), ((iff (((semila1780557381name_o F_61) G_13) X_82)) ((semila10642723_sup_o (F_61 X_82)) (G_13 X_82)))).
% Axiom fact_564_sup__apply:(forall (F_61:(hoare_1708887482_state->Prop)) (G_13:(hoare_1708887482_state->Prop)) (X_82:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_61) G_13) X_82)) ((semila10642723_sup_o (F_61 X_82)) (G_13 X_82)))).
% Axiom fact_565_sup__fun__def:(forall (F_60:(pname->Prop)) (G_12:(pname->Prop)) (X_3:pname), ((iff (((semila1780557381name_o F_60) G_12) X_3)) ((semila10642723_sup_o (F_60 X_3)) (G_12 X_3)))).
% Axiom fact_566_sup__fun__def:(forall (F_60:(hoare_1708887482_state->Prop)) (G_12:(hoare_1708887482_state->Prop)) (X_3:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_60) G_12) X_3)) ((semila10642723_sup_o (F_60 X_3)) (G_12 X_3)))).
% Axiom fact_567_single__stateE:(hoare_1160767572gleton->(forall (T_1:state), ((forall (S_2:state), (((eq state) S_2) T_1))->False))).
% Axiom fact_568_sup__eq__bot__iff:(forall (X_81:(pname->Prop)) (Y_43:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_81) Y_43)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_81) bot_bot_pname_o)) (((eq (pname->Prop)) Y_43) bot_bot_pname_o)))).
% Axiom fact_569_sup__eq__bot__iff:(forall (X_81:(com->Prop)) (Y_43:(com->Prop)), ((iff (((eq (com->Prop)) ((semila1562558655_com_o X_81) Y_43)) bot_bot_com_o)) ((and (((eq (com->Prop)) X_81) bot_bot_com_o)) (((eq (com->Prop)) Y_43) bot_bot_com_o)))).
% Axiom fact_570_sup__eq__bot__iff:(forall (X_81:Prop) (Y_43:Prop), ((iff ((iff ((semila10642723_sup_o X_81) Y_43)) bot_bot_o)) ((and ((iff X_81) bot_bot_o)) ((iff Y_43) bot_bot_o)))).
% Axiom fact_571_sup__eq__bot__iff:(forall (X_81:(hoare_1708887482_state->Prop)) (Y_43:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_81) Y_43)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) X_81) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) Y_43) bot_bo19817387tate_o)))).
% Axiom fact_572_elem__set:(forall (X_80:com) (Xo_1:option_com), ((iff ((member_com X_80) (set_com Xo_1))) (((eq option_com) Xo_1) (some_com X_80)))).
% Axiom fact_573_elem__set:(forall (X_80:hoare_1708887482_state) (Xo_1:option1624383643_state), ((iff ((member451959335_state X_80) (set_Ho525251890_state Xo_1))) (((eq option1624383643_state) Xo_1) (some_H1974565227_state X_80)))).
% Axiom fact_574_elem__set:(forall (X_80:pname) (Xo_1:option_pname), ((iff ((member_pname X_80) (set_pname Xo_1))) (((eq option_pname) Xo_1) (some_pname X_80)))).
% Axiom fact_575_sup_Oidem:(forall (A_150:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_150) A_150)) A_150)).
% Axiom fact_576_sup_Oidem:(forall (A_150:Prop), ((iff ((semila10642723_sup_o A_150) A_150)) A_150)).
% Axiom fact_577_sup_Oidem:(forall (A_150:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_150) A_150)) A_150)).
% Axiom fact_578_sup__idem:(forall (X_79:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_79) X_79)) X_79)).
% Axiom fact_579_sup__idem:(forall (X_79:Prop), ((iff ((semila10642723_sup_o X_79) X_79)) X_79)).
% Axiom fact_580_sup__idem:(forall (X_79:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_79) X_79)) X_79)).
% Axiom fact_581_sup_Ocommute:(forall (A_149:(pname->Prop)) (B_96:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_149) B_96)) ((semila1780557381name_o B_96) A_149))).
% Axiom fact_582_sup_Ocommute:(forall (A_149:Prop) (B_96:Prop), ((iff ((semila10642723_sup_o A_149) B_96)) ((semila10642723_sup_o B_96) A_149))).
% Axiom fact_583_sup_Ocommute:(forall (A_149:(hoare_1708887482_state->Prop)) (B_96:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_149) B_96)) ((semila1122118281tate_o B_96) A_149))).
% Axiom fact_584_inf__sup__aci_I5_J:(forall (X_78:(pname->Prop)) (Y_42:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_78) Y_42)) ((semila1780557381name_o Y_42) X_78))).
% Axiom fact_585_inf__sup__aci_I5_J:(forall (X_78:Prop) (Y_42:Prop), ((iff ((semila10642723_sup_o X_78) Y_42)) ((semila10642723_sup_o Y_42) X_78))).
% Axiom fact_586_inf__sup__aci_I5_J:(forall (X_78:(hoare_1708887482_state->Prop)) (Y_42:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_78) Y_42)) ((semila1122118281tate_o Y_42) X_78))).
% Axiom fact_587_sup__commute:(forall (X_77:(pname->Prop)) (Y_41:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_77) Y_41)) ((semila1780557381name_o Y_41) X_77))).
% Axiom fact_588_sup__commute:(forall (X_77:Prop) (Y_41:Prop), ((iff ((semila10642723_sup_o X_77) Y_41)) ((semila10642723_sup_o Y_41) X_77))).
% Axiom fact_589_sup__commute:(forall (X_77:(hoare_1708887482_state->Prop)) (Y_41:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_77) Y_41)) ((semila1122118281tate_o Y_41) X_77))).
% Axiom fact_590_sup_Oleft__idem:(forall (A_148:(pname->Prop)) (B_95:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_148) ((semila1780557381name_o A_148) B_95))) ((semila1780557381name_o A_148) B_95))).
% Axiom fact_591_sup_Oleft__idem:(forall (A_148:Prop) (B_95:Prop), ((iff ((semila10642723_sup_o A_148) ((semila10642723_sup_o A_148) B_95))) ((semila10642723_sup_o A_148) B_95))).
% Axiom fact_592_sup_Oleft__idem:(forall (A_148:(hoare_1708887482_state->Prop)) (B_95:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_148) ((semila1122118281tate_o A_148) B_95))) ((semila1122118281tate_o A_148) B_95))).
% Axiom fact_593_inf__sup__aci_I8_J:(forall (X_76:(pname->Prop)) (Y_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_76) ((semila1780557381name_o X_76) Y_40))) ((semila1780557381name_o X_76) Y_40))).
% Axiom fact_594_inf__sup__aci_I8_J:(forall (X_76:Prop) (Y_40:Prop), ((iff ((semila10642723_sup_o X_76) ((semila10642723_sup_o X_76) Y_40))) ((semila10642723_sup_o X_76) Y_40))).
% Axiom fact_595_inf__sup__aci_I8_J:(forall (X_76:(hoare_1708887482_state->Prop)) (Y_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_76) ((semila1122118281tate_o X_76) Y_40))) ((semila1122118281tate_o X_76) Y_40))).
% Axiom fact_596_sup__left__idem:(forall (X_75:(pname->Prop)) (Y_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_75) ((semila1780557381name_o X_75) Y_39))) ((semila1780557381name_o X_75) Y_39))).
% Axiom fact_597_sup__left__idem:(forall (X_75:Prop) (Y_39:Prop), ((iff ((semila10642723_sup_o X_75) ((semila10642723_sup_o X_75) Y_39))) ((semila10642723_sup_o X_75) Y_39))).
% Axiom fact_598_sup__left__idem:(forall (X_75:(hoare_1708887482_state->Prop)) (Y_39:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_75) ((semila1122118281tate_o X_75) Y_39))) ((semila1122118281tate_o X_75) Y_39))).
% Axiom fact_599_sup_Oleft__commute:(forall (B_94:(pname->Prop)) (A_147:(pname->Prop)) (C_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_94) ((semila1780557381name_o A_147) C_40))) ((semila1780557381name_o A_147) ((semila1780557381name_o B_94) C_40)))).
% Axiom fact_600_sup_Oleft__commute:(forall (B_94:Prop) (A_147:Prop) (C_40:Prop), ((iff ((semila10642723_sup_o B_94) ((semila10642723_sup_o A_147) C_40))) ((semila10642723_sup_o A_147) ((semila10642723_sup_o B_94) C_40)))).
% Axiom fact_601_sup_Oleft__commute:(forall (B_94:(hoare_1708887482_state->Prop)) (A_147:(hoare_1708887482_state->Prop)) (C_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o B_94) ((semila1122118281tate_o A_147) C_40))) ((semila1122118281tate_o A_147) ((semila1122118281tate_o B_94) C_40)))).
% Axiom fact_602_inf__sup__aci_I7_J:(forall (X_74:(pname->Prop)) (Y_38:(pname->Prop)) (Z_18:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_74) ((semila1780557381name_o Y_38) Z_18))) ((semila1780557381name_o Y_38) ((semila1780557381name_o X_74) Z_18)))).
% Axiom fact_603_inf__sup__aci_I7_J:(forall (X_74:Prop) (Y_38:Prop) (Z_18:Prop), ((iff ((semila10642723_sup_o X_74) ((semila10642723_sup_o Y_38) Z_18))) ((semila10642723_sup_o Y_38) ((semila10642723_sup_o X_74) Z_18)))).
% Axiom fact_604_inf__sup__aci_I7_J:(forall (X_74:(hoare_1708887482_state->Prop)) (Y_38:(hoare_1708887482_state->Prop)) (Z_18:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_74) ((semila1122118281tate_o Y_38) Z_18))) ((semila1122118281tate_o Y_38) ((semila1122118281tate_o X_74) Z_18)))).
% Axiom fact_605_sup__left__commute:(forall (X_73:(pname->Prop)) (Y_37:(pname->Prop)) (Z_17:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_73) ((semila1780557381name_o Y_37) Z_17))) ((semila1780557381name_o Y_37) ((semila1780557381name_o X_73) Z_17)))).
% Axiom fact_606_sup__left__commute:(forall (X_73:Prop) (Y_37:Prop) (Z_17:Prop), ((iff ((semila10642723_sup_o X_73) ((semila10642723_sup_o Y_37) Z_17))) ((semila10642723_sup_o Y_37) ((semila10642723_sup_o X_73) Z_17)))).
% Axiom fact_607_sup__left__commute:(forall (X_73:(hoare_1708887482_state->Prop)) (Y_37:(hoare_1708887482_state->Prop)) (Z_17:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_73) ((semila1122118281tate_o Y_37) Z_17))) ((semila1122118281tate_o Y_37) ((semila1122118281tate_o X_73) Z_17)))).
% Axiom fact_608_sup_Oassoc:(forall (A_146:(pname->Prop)) (B_93:(pname->Prop)) (C_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_146) B_93)) C_39)) ((semila1780557381name_o A_146) ((semila1780557381name_o B_93) C_39)))).
% Axiom fact_609_sup_Oassoc:(forall (A_146:Prop) (B_93:Prop) (C_39:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_146) B_93)) C_39)) ((semila10642723_sup_o A_146) ((semila10642723_sup_o B_93) C_39)))).
% Axiom fact_610_sup_Oassoc:(forall (A_146:(hoare_1708887482_state->Prop)) (B_93:(hoare_1708887482_state->Prop)) (C_39:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_146) B_93)) C_39)) ((semila1122118281tate_o A_146) ((semila1122118281tate_o B_93) C_39)))).
% Axiom fact_611_inf__sup__aci_I6_J:(forall (X_72:(pname->Prop)) (Y_36:(pname->Prop)) (Z_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_72) Y_36)) Z_16)) ((semila1780557381name_o X_72) ((semila1780557381name_o Y_36) Z_16)))).
% Axiom fact_612_inf__sup__aci_I6_J:(forall (X_72:Prop) (Y_36:Prop) (Z_16:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_72) Y_36)) Z_16)) ((semila10642723_sup_o X_72) ((semila10642723_sup_o Y_36) Z_16)))).
% Axiom fact_613_inf__sup__aci_I6_J:(forall (X_72:(hoare_1708887482_state->Prop)) (Y_36:(hoare_1708887482_state->Prop)) (Z_16:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_72) Y_36)) Z_16)) ((semila1122118281tate_o X_72) ((semila1122118281tate_o Y_36) Z_16)))).
% Axiom fact_614_sup__assoc:(forall (X_71:(pname->Prop)) (Y_35:(pname->Prop)) (Z_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_71) Y_35)) Z_15)) ((semila1780557381name_o X_71) ((semila1780557381name_o Y_35) Z_15)))).
% Axiom fact_615_sup__assoc:(forall (X_71:Prop) (Y_35:Prop) (Z_15:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_71) Y_35)) Z_15)) ((semila10642723_sup_o X_71) ((semila10642723_sup_o Y_35) Z_15)))).
% Axiom fact_616_sup__assoc:(forall (X_71:(hoare_1708887482_state->Prop)) (Y_35:(hoare_1708887482_state->Prop)) (Z_15:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_71) Y_35)) Z_15)) ((semila1122118281tate_o X_71) ((semila1122118281tate_o Y_35) Z_15)))).
% Axiom fact_617_inf__sup__ord_I3_J:(forall (X_70:(pname->Prop)) (Y_34:(pname->Prop)), ((ord_less_eq_pname_o X_70) ((semila1780557381name_o X_70) Y_34))).
% Axiom fact_618_inf__sup__ord_I3_J:(forall (X_70:Prop) (Y_34:Prop), ((ord_less_eq_o X_70) ((semila10642723_sup_o X_70) Y_34))).
% Axiom fact_619_inf__sup__ord_I3_J:(forall (X_70:(hoare_1708887482_state->Prop)) (Y_34:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o X_70) ((semila1122118281tate_o X_70) Y_34))).
% Axiom fact_620_sup__ge1:(forall (X_69:(pname->Prop)) (Y_33:(pname->Prop)), ((ord_less_eq_pname_o X_69) ((semila1780557381name_o X_69) Y_33))).
% Axiom fact_621_sup__ge1:(forall (X_69:Prop) (Y_33:Prop), ((ord_less_eq_o X_69) ((semila10642723_sup_o X_69) Y_33))).
% Axiom fact_622_sup__ge1:(forall (X_69:(hoare_1708887482_state->Prop)) (Y_33:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o X_69) ((semila1122118281tate_o X_69) Y_33))).
% Axiom fact_623_inf__sup__ord_I4_J:(forall (Y_32:(pname->Prop)) (X_68:(pname->Prop)), ((ord_less_eq_pname_o Y_32) ((semila1780557381name_o X_68) Y_32))).
% Axiom fact_624_inf__sup__ord_I4_J:(forall (Y_32:Prop) (X_68:Prop), ((ord_less_eq_o Y_32) ((semila10642723_sup_o X_68) Y_32))).
% Axiom fact_625_inf__sup__ord_I4_J:(forall (Y_32:(hoare_1708887482_state->Prop)) (X_68:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o Y_32) ((semila1122118281tate_o X_68) Y_32))).
% Axiom fact_626_sup__ge2:(forall (Y_31:(pname->Prop)) (X_67:(pname->Prop)), ((ord_less_eq_pname_o Y_31) ((semila1780557381name_o X_67) Y_31))).
% Axiom fact_627_sup__ge2:(forall (Y_31:Prop) (X_67:Prop), ((ord_less_eq_o Y_31) ((semila10642723_sup_o X_67) Y_31))).
% Axiom fact_628_sup__ge2:(forall (Y_31:(hoare_1708887482_state->Prop)) (X_67:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o Y_31) ((semila1122118281tate_o X_67) Y_31))).
% Axiom fact_629_le__iff__sup:(forall (X_66:(pname->Prop)) (Y_30:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_66) Y_30)) (((eq (pname->Prop)) ((semila1780557381name_o X_66) Y_30)) Y_30))).
% Axiom fact_630_le__iff__sup:(forall (X_66:Prop) (Y_30:Prop), ((iff ((ord_less_eq_o X_66) Y_30)) ((iff ((semila10642723_sup_o X_66) Y_30)) Y_30))).
% Axiom fact_631_le__iff__sup:(forall (X_66:(hoare_1708887482_state->Prop)) (Y_30:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o X_66) Y_30)) (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_66) Y_30)) Y_30))).
% Axiom fact_632_le__sup__iff:(forall (X_65:(pname->Prop)) (Y_29:(pname->Prop)) (Z_14:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((semila1780557381name_o X_65) Y_29)) Z_14)) ((and ((ord_less_eq_pname_o X_65) Z_14)) ((ord_less_eq_pname_o Y_29) Z_14)))).
% Axiom fact_633_le__sup__iff:(forall (X_65:Prop) (Y_29:Prop) (Z_14:Prop), ((iff ((ord_less_eq_o ((semila10642723_sup_o X_65) Y_29)) Z_14)) ((and ((ord_less_eq_o X_65) Z_14)) ((ord_less_eq_o Y_29) Z_14)))).
% Axiom fact_634_le__sup__iff:(forall (X_65:(hoare_1708887482_state->Prop)) (Y_29:(hoare_1708887482_state->Prop)) (Z_14:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o ((semila1122118281tate_o X_65) Y_29)) Z_14)) ((and ((ord_le777019615tate_o X_65) Z_14)) ((ord_le777019615tate_o Y_29) Z_14)))).
% Axiom fact_635_le__supI1:(forall (B_92:(pname->Prop)) (X_64:(pname->Prop)) (A_145:(pname->Prop)), (((ord_less_eq_pname_o X_64) A_145)->((ord_less_eq_pname_o X_64) ((semila1780557381name_o A_145) B_92)))).
% Axiom fact_636_le__supI1:(forall (B_92:Prop) (X_64:Prop) (A_145:Prop), (((ord_less_eq_o X_64) A_145)->((ord_less_eq_o X_64) ((semila10642723_sup_o A_145) B_92)))).
% Axiom fact_637_le__supI1:(forall (B_92:(hoare_1708887482_state->Prop)) (X_64:(hoare_1708887482_state->Prop)) (A_145:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_64) A_145)->((ord_le777019615tate_o X_64) ((semila1122118281tate_o A_145) B_92)))).
% Axiom fact_638_le__supI2:(forall (A_144:(pname->Prop)) (X_63:(pname->Prop)) (B_91:(pname->Prop)), (((ord_less_eq_pname_o X_63) B_91)->((ord_less_eq_pname_o X_63) ((semila1780557381name_o A_144) B_91)))).
% Axiom fact_639_le__supI2:(forall (A_144:Prop) (X_63:Prop) (B_91:Prop), (((ord_less_eq_o X_63) B_91)->((ord_less_eq_o X_63) ((semila10642723_sup_o A_144) B_91)))).
% Axiom fact_640_le__supI2:(forall (A_144:(hoare_1708887482_state->Prop)) (X_63:(hoare_1708887482_state->Prop)) (B_91:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_63) B_91)->((ord_le777019615tate_o X_63) ((semila1122118281tate_o A_144) B_91)))).
% Axiom fact_641_sup__absorb2:(forall (X_62:(pname->Prop)) (Y_28:(pname->Prop)), (((ord_less_eq_pname_o X_62) Y_28)->(((eq (pname->Prop)) ((semila1780557381name_o X_62) Y_28)) Y_28))).
% Axiom fact_642_sup__absorb2:(forall (X_62:Prop) (Y_28:Prop), (((ord_less_eq_o X_62) Y_28)->((iff ((semila10642723_sup_o X_62) Y_28)) Y_28))).
% Axiom fact_643_sup__absorb2:(forall (X_62:(hoare_1708887482_state->Prop)) (Y_28:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_62) Y_28)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_62) Y_28)) Y_28))).
% Axiom fact_644_sup__absorb1:(forall (Y_27:(pname->Prop)) (X_61:(pname->Prop)), (((ord_less_eq_pname_o Y_27) X_61)->(((eq (pname->Prop)) ((semila1780557381name_o X_61) Y_27)) X_61))).
% Axiom fact_645_sup__absorb1:(forall (Y_27:Prop) (X_61:Prop), (((ord_less_eq_o Y_27) X_61)->((iff ((semila10642723_sup_o X_61) Y_27)) X_61))).
% Axiom fact_646_sup__absorb1:(forall (Y_27:(hoare_1708887482_state->Prop)) (X_61:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_27) X_61)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_61) Y_27)) X_61))).
% Axiom fact_647_le__supI:(forall (B_90:(pname->Prop)) (A_143:(pname->Prop)) (X_60:(pname->Prop)), (((ord_less_eq_pname_o A_143) X_60)->(((ord_less_eq_pname_o B_90) X_60)->((ord_less_eq_pname_o ((semila1780557381name_o A_143) B_90)) X_60)))).
% Axiom fact_648_le__supI:(forall (B_90:Prop) (A_143:Prop) (X_60:Prop), (((ord_less_eq_o A_143) X_60)->(((ord_less_eq_o B_90) X_60)->((ord_less_eq_o ((semila10642723_sup_o A_143) B_90)) X_60)))).
% Axiom fact_649_le__supI:(forall (B_90:(hoare_1708887482_state->Prop)) (A_143:(hoare_1708887482_state->Prop)) (X_60:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_143) X_60)->(((ord_le777019615tate_o B_90) X_60)->((ord_le777019615tate_o ((semila1122118281tate_o A_143) B_90)) X_60)))).
% Axiom fact_650_sup__least:(forall (Z_13:(pname->Prop)) (Y_26:(pname->Prop)) (X_59:(pname->Prop)), (((ord_less_eq_pname_o Y_26) X_59)->(((ord_less_eq_pname_o Z_13) X_59)->((ord_less_eq_pname_o ((semila1780557381name_o Y_26) Z_13)) X_59)))).
% Axiom fact_651_sup__least:(forall (Z_13:Prop) (Y_26:Prop) (X_59:Prop), (((ord_less_eq_o Y_26) X_59)->(((ord_less_eq_o Z_13) X_59)->((ord_less_eq_o ((semila10642723_sup_o Y_26) Z_13)) X_59)))).
% Axiom fact_652_sup__least:(forall (Z_13:(hoare_1708887482_state->Prop)) (Y_26:(hoare_1708887482_state->Prop)) (X_59:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_26) X_59)->(((ord_le777019615tate_o Z_13) X_59)->((ord_le777019615tate_o ((semila1122118281tate_o Y_26) Z_13)) X_59)))).
% Axiom fact_653_sup__mono:(forall (B_89:(pname->Prop)) (D_4:(pname->Prop)) (A_142:(pname->Prop)) (C_38:(pname->Prop)), (((ord_less_eq_pname_o A_142) C_38)->(((ord_less_eq_pname_o B_89) D_4)->((ord_less_eq_pname_o ((semila1780557381name_o A_142) B_89)) ((semila1780557381name_o C_38) D_4))))).
% Axiom fact_654_sup__mono:(forall (B_89:Prop) (D_4:Prop) (A_142:Prop) (C_38:Prop), (((ord_less_eq_o A_142) C_38)->(((ord_less_eq_o B_89) D_4)->((ord_less_eq_o ((semila10642723_sup_o A_142) B_89)) ((semila10642723_sup_o C_38) D_4))))).
% Axiom fact_655_sup__mono:(forall (B_89:(hoare_1708887482_state->Prop)) (D_4:(hoare_1708887482_state->Prop)) (A_142:(hoare_1708887482_state->Prop)) (C_38:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_142) C_38)->(((ord_le777019615tate_o B_89) D_4)->((ord_le777019615tate_o ((semila1122118281tate_o A_142) B_89)) ((semila1122118281tate_o C_38) D_4))))).
% Axiom fact_656_le__supE:(forall (A_141:(pname->Prop)) (B_88:(pname->Prop)) (X_58:(pname->Prop)), (((ord_less_eq_pname_o ((semila1780557381name_o A_141) B_88)) X_58)->((((ord_less_eq_pname_o A_141) X_58)->(((ord_less_eq_pname_o B_88) X_58)->False))->False))).
% Axiom fact_657_le__supE:(forall (A_141:Prop) (B_88:Prop) (X_58:Prop), (((ord_less_eq_o ((semila10642723_sup_o A_141) B_88)) X_58)->((((ord_less_eq_o A_141) X_58)->(((ord_less_eq_o B_88) X_58)->False))->False))).
% Axiom fact_658_le__supE:(forall (A_141:(hoare_1708887482_state->Prop)) (B_88:(hoare_1708887482_state->Prop)) (X_58:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o ((semila1122118281tate_o A_141) B_88)) X_58)->((((ord_le777019615tate_o A_141) X_58)->(((ord_le777019615tate_o B_88) X_58)->False))->False))).
% Axiom fact_659_sup__bot__left:(forall (X_57:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) X_57)) X_57)).
% Axiom fact_660_sup__bot__left:(forall (X_57:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o bot_bot_com_o) X_57)) X_57)).
% Axiom fact_661_sup__bot__left:(forall (X_57:Prop), ((iff ((semila10642723_sup_o bot_bot_o) X_57)) X_57)).
% Axiom fact_662_sup__bot__left:(forall (X_57:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_o) X_57)) X_57)).
% Axiom fact_663_sup__bot__right:(forall (X_56:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_56) bot_bot_pname_o)) X_56)).
% Axiom fact_664_sup__bot__right:(forall (X_56:(com->Prop)), (((eq (com->Prop)) ((semila1562558655_com_o X_56) bot_bot_com_o)) X_56)).
% Axiom fact_665_sup__bot__right:(forall (X_56:Prop), ((iff ((semila10642723_sup_o X_56) bot_bot_o)) X_56)).
% Axiom fact_666_sup__bot__right:(forall (X_56:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_56) bot_bo19817387tate_o)) X_56)).
% Axiom fact_667_ospec:(forall (X_55:pname) (P_15:(pname->Prop)) (A_140:option_pname), ((forall (X_3:pname), (((member_pname X_3) (set_pname A_140))->(P_15 X_3)))->((((eq option_pname) A_140) (some_pname X_55))->(P_15 X_55)))).
% Axiom fact_668_ospec:(forall (X_55:hoare_1708887482_state) (P_15:(hoare_1708887482_state->Prop)) (A_140:option1624383643_state), ((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) (set_Ho525251890_state A_140))->(P_15 X_3)))->((((eq option1624383643_state) A_140) (some_H1974565227_state X_55))->(P_15 X_55)))).
% Axiom fact_669_ospec:(forall (X_55:com) (P_15:(com->Prop)) (A_140:option_com), ((forall (X_3:com), (((member_com X_3) (set_com A_140))->(P_15 X_3)))->((((eq option_com) A_140) (some_com X_55))->(P_15 X_55)))).
% Axiom fact_670_folding__one__idem_Ounion__idem:(forall (B_87:((pname->Prop)->Prop)) (A_139:((pname->Prop)->Prop)) (F_59:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_58:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_59) F_58)->((finite297249702name_o A_139)->((not (((eq ((pname->Prop)->Prop)) A_139) bot_bot_pname_o_o))->((finite297249702name_o B_87)->((not (((eq ((pname->Prop)->Prop)) B_87) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_58 ((semila181081674me_o_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87))))))))).
% Axiom fact_671_folding__one__idem_Ounion__idem:(forall (B_87:((hoare_1708887482_state->Prop)->Prop)) (A_139:((hoare_1708887482_state->Prop)->Prop)) (F_59:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_58:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_59) F_58)->((finite1329924456tate_o A_139)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_139) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_87)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_87) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_58 ((semila1853742644te_o_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87))))))))).
% Axiom fact_672_folding__one__idem_Ounion__idem:(forall (B_87:(com->Prop)) (A_139:(com->Prop)) (F_59:(com->(com->com))) (F_58:((com->Prop)->com)), (((finite666746948em_com F_59) F_58)->((finite_finite_com A_139)->((not (((eq (com->Prop)) A_139) bot_bot_com_o))->((finite_finite_com B_87)->((not (((eq (com->Prop)) B_87) bot_bot_com_o))->(((eq com) (F_58 ((semila1562558655_com_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87))))))))).
% Axiom fact_673_folding__one__idem_Ounion__idem:(forall (B_87:(hoare_1708887482_state->Prop)) (A_139:(hoare_1708887482_state->Prop)) (F_59:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_58:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_59) F_58)->((finite1625599783_state A_139)->((not (((eq (hoare_1708887482_state->Prop)) A_139) bot_bo19817387tate_o))->((finite1625599783_state B_87)->((not (((eq (hoare_1708887482_state->Prop)) B_87) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_58 ((semila1122118281tate_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87))))))))).
% Axiom fact_674_folding__one__idem_Ounion__idem:(forall (B_87:(pname->Prop)) (A_139:(pname->Prop)) (F_59:(pname->(pname->pname))) (F_58:((pname->Prop)->pname)), (((finite89670078_pname F_59) F_58)->((finite_finite_pname A_139)->((not (((eq (pname->Prop)) A_139) bot_bot_pname_o))->((finite_finite_pname B_87)->((not (((eq (pname->Prop)) B_87) bot_bot_pname_o))->(((eq pname) (F_58 ((semila1780557381name_o A_139) B_87))) ((F_59 (F_58 A_139)) (F_58 B_87))))))))).
% Axiom fact_675_folding__one__idem_Osubset__idem:(forall (B_86:((pname->Prop)->Prop)) (A_138:((pname->Prop)->Prop)) (F_57:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_56:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_57) F_56)->((finite297249702name_o A_138)->((not (((eq ((pname->Prop)->Prop)) B_86) bot_bot_pname_o_o))->(((ord_le1205211808me_o_o B_86) A_138)->(((eq (pname->Prop)) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138))))))).
% Axiom fact_676_folding__one__idem_Osubset__idem:(forall (B_86:((hoare_1708887482_state->Prop)->Prop)) (A_138:((hoare_1708887482_state->Prop)->Prop)) (F_57:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_56:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_57) F_56)->((finite1329924456tate_o A_138)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_86) bot_bo1678742418te_o_o))->(((ord_le1728773982te_o_o B_86) A_138)->(((eq (hoare_1708887482_state->Prop)) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138))))))).
% Axiom fact_677_folding__one__idem_Osubset__idem:(forall (B_86:(com->Prop)) (A_138:(com->Prop)) (F_57:(com->(com->com))) (F_56:((com->Prop)->com)), (((finite666746948em_com F_57) F_56)->((finite_finite_com A_138)->((not (((eq (com->Prop)) B_86) bot_bot_com_o))->(((ord_less_eq_com_o B_86) A_138)->(((eq com) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138))))))).
% Axiom fact_678_folding__one__idem_Osubset__idem:(forall (B_86:(hoare_1708887482_state->Prop)) (A_138:(hoare_1708887482_state->Prop)) (F_57:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_56:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_57) F_56)->((finite1625599783_state A_138)->((not (((eq (hoare_1708887482_state->Prop)) B_86) bot_bo19817387tate_o))->(((ord_le777019615tate_o B_86) A_138)->(((eq hoare_1708887482_state) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138))))))).
% Axiom fact_679_folding__one__idem_Osubset__idem:(forall (B_86:(pname->Prop)) (A_138:(pname->Prop)) (F_57:(pname->(pname->pname))) (F_56:((pname->Prop)->pname)), (((finite89670078_pname F_57) F_56)->((finite_finite_pname A_138)->((not (((eq (pname->Prop)) B_86) bot_bot_pname_o))->(((ord_less_eq_pname_o B_86) A_138)->(((eq pname) ((F_57 (F_56 B_86)) (F_56 A_138))) (F_56 A_138))))))).
% Axiom fact_680_hoare__derivs_OSkip:(forall (G_11:(hoare_1708887482_state->Prop)) (P_14:(state->(state->Prop))), ((hoare_90032982_state G_11) ((insert528405184_state (((hoare_858012674_state P_14) skip) P_14)) bot_bo19817387tate_o))).
% Axiom fact_681_folding__one__idem_Oinsert__idem:(forall (X_54:com) (A_137:(com->Prop)) (F_55:(com->(com->com))) (F_54:((com->Prop)->com)), (((finite666746948em_com F_55) F_54)->((finite_finite_com A_137)->((not (((eq (com->Prop)) A_137) bot_bot_com_o))->(((eq com) (F_54 ((insert_com X_54) A_137))) ((F_55 X_54) (F_54 A_137))))))).
% Axiom fact_682_folding__one__idem_Oinsert__idem:(forall (X_54:(pname->Prop)) (A_137:((pname->Prop)->Prop)) (F_55:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_54:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_55) F_54)->((finite297249702name_o A_137)->((not (((eq ((pname->Prop)->Prop)) A_137) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_54 ((insert_pname_o X_54) A_137))) ((F_55 X_54) (F_54 A_137))))))).
% Axiom fact_683_folding__one__idem_Oinsert__idem:(forall (X_54:(hoare_1708887482_state->Prop)) (A_137:((hoare_1708887482_state->Prop)->Prop)) (F_55:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_54:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_55) F_54)->((finite1329924456tate_o A_137)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_137) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_54 ((insert949073679tate_o X_54) A_137))) ((F_55 X_54) (F_54 A_137))))))).
% Axiom fact_684_folding__one__idem_Oinsert__idem:(forall (X_54:pname) (A_137:(pname->Prop)) (F_55:(pname->(pname->pname))) (F_54:((pname->Prop)->pname)), (((finite89670078_pname F_55) F_54)->((finite_finite_pname A_137)->((not (((eq (pname->Prop)) A_137) bot_bot_pname_o))->(((eq pname) (F_54 ((insert_pname X_54) A_137))) ((F_55 X_54) (F_54 A_137))))))).
% Axiom fact_685_folding__one__idem_Oinsert__idem:(forall (X_54:hoare_1708887482_state) (A_137:(hoare_1708887482_state->Prop)) (F_55:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_54:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_55) F_54)->((finite1625599783_state A_137)->((not (((eq (hoare_1708887482_state->Prop)) A_137) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_54 ((insert528405184_state X_54) A_137))) ((F_55 X_54) (F_54 A_137))))))).
% Axiom fact_686_finite__ne__induct:(forall (P_13:((com->Prop)->Prop)) (F_52:(com->Prop)), ((finite_finite_com F_52)->((not (((eq (com->Prop)) F_52) bot_bot_com_o))->((forall (X_3:com), (P_13 ((insert_com X_3) bot_bot_com_o)))->((forall (X_3:com) (F_53:(com->Prop)), ((finite_finite_com F_53)->((not (((eq (com->Prop)) F_53) bot_bot_com_o))->((((member_com X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert_com X_3) F_53)))))))->(P_13 F_52)))))).
% Axiom fact_687_finite__ne__induct:(forall (P_13:(((pname->Prop)->Prop)->Prop)) (F_52:((pname->Prop)->Prop)), ((finite297249702name_o F_52)->((not (((eq ((pname->Prop)->Prop)) F_52) bot_bot_pname_o_o))->((forall (X_3:(pname->Prop)), (P_13 ((insert_pname_o X_3) bot_bot_pname_o_o)))->((forall (X_3:(pname->Prop)) (F_53:((pname->Prop)->Prop)), ((finite297249702name_o F_53)->((not (((eq ((pname->Prop)->Prop)) F_53) bot_bot_pname_o_o))->((((member_pname_o X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert_pname_o X_3) F_53)))))))->(P_13 F_52)))))).
% Axiom fact_688_finite__ne__induct:(forall (P_13:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (F_52:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_52)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) F_52) bot_bo1678742418te_o_o))->((forall (X_3:(hoare_1708887482_state->Prop)), (P_13 ((insert949073679tate_o X_3) bot_bo1678742418te_o_o)))->((forall (X_3:(hoare_1708887482_state->Prop)) (F_53:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o F_53)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) F_53) bot_bo1678742418te_o_o))->((((member814030440tate_o X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert949073679tate_o X_3) F_53)))))))->(P_13 F_52)))))).
% Axiom fact_689_finite__ne__induct:(forall (P_13:((pname->Prop)->Prop)) (F_52:(pname->Prop)), ((finite_finite_pname F_52)->((not (((eq (pname->Prop)) F_52) bot_bot_pname_o))->((forall (X_3:pname), (P_13 ((insert_pname X_3) bot_bot_pname_o)))->((forall (X_3:pname) (F_53:(pname->Prop)), ((finite_finite_pname F_53)->((not (((eq (pname->Prop)) F_53) bot_bot_pname_o))->((((member_pname X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert_pname X_3) F_53)))))))->(P_13 F_52)))))).
% Axiom fact_690_finite__ne__induct:(forall (P_13:((hoare_1708887482_state->Prop)->Prop)) (F_52:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_52)->((not (((eq (hoare_1708887482_state->Prop)) F_52) bot_bo19817387tate_o))->((forall (X_3:hoare_1708887482_state), (P_13 ((insert528405184_state X_3) bot_bo19817387tate_o)))->((forall (X_3:hoare_1708887482_state) (F_53:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_53)->((not (((eq (hoare_1708887482_state->Prop)) F_53) bot_bo19817387tate_o))->((((member451959335_state X_3) F_53)->False)->((P_13 F_53)->(P_13 ((insert528405184_state X_3) F_53)))))))->(P_13 F_52)))))).
% Axiom fact_691_LoopF:(forall (G_10:(hoare_1708887482_state->Prop)) (P_12:(state->(state->Prop))) (B_85:(state->Prop)) (C_37:com), ((hoare_90032982_state G_10) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S_2:state)=> ((and ((P_12 Z_11) S_2)) (not (B_85 S_2))))) ((while B_85) C_37)) P_12)) bot_bo19817387tate_o))).
% Axiom fact_692_Comp:(forall (D_3:com) (R_1:(state->(state->Prop))) (G_9:(hoare_1708887482_state->Prop)) (P_11:(state->(state->Prop))) (C_36:com) (Q_6:(state->(state->Prop))), (((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state P_11) C_36) Q_6)) bot_bo19817387tate_o))->(((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state Q_6) D_3) R_1)) bot_bo19817387tate_o))->((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state P_11) ((semi C_36) D_3)) R_1)) bot_bo19817387tate_o))))).
% Axiom fact_693_WTs__elim__cases_I6_J:(forall (B_82:(state->Prop)) (C_34:com), ((wt ((while B_82) C_34))->(wt C_34))).
% Axiom fact_694_WTs__elim__cases_I4_J:(forall (C1:com) (C2:com), ((wt ((semi C1) C2))->(((wt C1)->((wt C2)->False))->False))).
% Axiom fact_695_folding__one__idem_Oidem:(forall (X_53:hoare_1708887482_state) (F_51:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_50:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_51) F_50)->(((eq hoare_1708887482_state) ((F_51 X_53) X_53)) X_53))).
% Axiom fact_696_folding__one__idem_Oidem:(forall (X_53:pname) (F_51:(pname->(pname->pname))) (F_50:((pname->Prop)->pname)), (((finite89670078_pname F_51) F_50)->(((eq pname) ((F_51 X_53) X_53)) X_53))).
% Axiom fact_697_com_Osimps_I12_J:(forall (Com1_1:com) (Com2_1:com), (not (((eq com) skip) ((semi Com1_1) Com2_1)))).
% Axiom fact_698_com_Osimps_I16_J:(forall (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) skip) ((while Fun_1) Com_2)))).
% Axiom fact_699_com_Osimps_I13_J:(forall (Com1_1:com) (Com2_1:com), (not (((eq com) ((semi Com1_1) Com2_1)) skip))).
% Axiom fact_700_com_Osimps_I17_J:(forall (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) ((while Fun_1) Com_2)) skip))).
% Axiom fact_701_com_Osimps_I46_J:(forall (Com1:com) (Com2:com) (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) ((semi Com1) Com2)) ((while Fun_1) Com_2)))).
% Axiom fact_702_com_Osimps_I47_J:(forall (Fun_1:(state->Prop)) (Com_2:com) (Com1:com) (Com2:com), (not (((eq com) ((while Fun_1) Com_2)) ((semi Com1) Com2)))).
% Axiom fact_703_com_Osimps_I3_J:(forall (Com1:com) (Com2:com) (Com1_1:com) (Com2_1:com), ((iff (((eq com) ((semi Com1) Com2)) ((semi Com1_1) Com2_1))) ((and (((eq com) Com1) Com1_1)) (((eq com) Com2) Com2_1)))).
% Axiom fact_704_com_Osimps_I5_J:(forall (Fun:(state->Prop)) (Com_1:com) (Fun_1:(state->Prop)) (Com_2:com), ((iff (((eq com) ((while Fun) Com_1)) ((while Fun_1) Com_2))) ((and (((eq (state->Prop)) Fun) Fun_1)) (((eq com) Com_1) Com_2)))).
% Axiom fact_705_com_Osimps_I59_J:(forall (Pname:pname) (Fun:(state->Prop)) (Com_1:com), (not (((eq com) (body_1 Pname)) ((while Fun) Com_1)))).
% Axiom fact_706_com_Osimps_I58_J:(forall (Fun:(state->Prop)) (Com_1:com) (Pname:pname), (not (((eq com) ((while Fun) Com_1)) (body_1 Pname)))).
% Axiom fact_707_While:(forall (B_82:(state->Prop)) (C_34:com), ((wt C_34)->(wt ((while B_82) C_34)))).
% Axiom fact_708_com_Osimps_I49_J:(forall (Pname:pname) (Com1:com) (Com2:com), (not (((eq com) (body_1 Pname)) ((semi Com1) Com2)))).
% Axiom fact_709_com_Osimps_I48_J:(forall (Com1:com) (Com2:com) (Pname:pname), (not (((eq com) ((semi Com1) Com2)) (body_1 Pname)))).
% Axiom fact_710_WT_OSemi:(forall (C1:com) (C0:com), ((wt C0)->((wt C1)->(wt ((semi C0) C1))))).
% Axiom fact_711_com_Osimps_I18_J:(forall (Pname:pname), (not (((eq com) skip) (body_1 Pname)))).
% Axiom fact_712_com_Osimps_I19_J:(forall (Pname:pname), (not (((eq com) (body_1 Pname)) skip))).
% Axiom fact_713_WT_OSkip:(wt skip).
% Axiom fact_714_folding__one__idem_Oin__idem:(forall (X_52:com) (A_136:(com->Prop)) (F_49:(com->(com->com))) (F_48:((com->Prop)->com)), (((finite666746948em_com F_49) F_48)->((finite_finite_com A_136)->(((member_com X_52) A_136)->(((eq com) ((F_49 X_52) (F_48 A_136))) (F_48 A_136)))))).
% Axiom fact_715_folding__one__idem_Oin__idem:(forall (X_52:pname) (A_136:(pname->Prop)) (F_49:(pname->(pname->pname))) (F_48:((pname->Prop)->pname)), (((finite89670078_pname F_49) F_48)->((finite_finite_pname A_136)->(((member_pname X_52) A_136)->(((eq pname) ((F_49 X_52) (F_48 A_136))) (F_48 A_136)))))).
% Axiom fact_716_folding__one__idem_Oin__idem:(forall (X_52:hoare_1708887482_state) (A_136:(hoare_1708887482_state->Prop)) (F_49:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_48:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_49) F_48)->((finite1625599783_state A_136)->(((member451959335_state X_52) A_136)->(((eq hoare_1708887482_state) ((F_49 X_52) (F_48 A_136))) (F_48 A_136)))))).
% Axiom fact_717_folding__one__idem_Oin__idem:(forall (X_52:(pname->Prop)) (A_136:((pname->Prop)->Prop)) (F_49:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_48:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_49) F_48)->((finite297249702name_o A_136)->(((member_pname_o X_52) A_136)->(((eq (pname->Prop)) ((F_49 X_52) (F_48 A_136))) (F_48 A_136)))))).
% Axiom fact_718_folding__one__idem_Oin__idem:(forall (X_52:(hoare_1708887482_state->Prop)) (A_136:((hoare_1708887482_state->Prop)->Prop)) (F_49:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_48:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_49) F_48)->((finite1329924456tate_o A_136)->(((member814030440tate_o X_52) A_136)->(((eq (hoare_1708887482_state->Prop)) ((F_49 X_52) (F_48 A_136))) (F_48 A_136)))))).
% Axiom fact_719_folding__one__idem_Ohom__commute:(forall (N_1:((pname->Prop)->Prop)) (H_1:((pname->Prop)->(pname->Prop))) (F_47:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_46:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_47) F_46)->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), (((eq (pname->Prop)) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite297249702name_o N_1)->((not (((eq ((pname->Prop)->Prop)) N_1) bot_bot_pname_o_o))->(((eq (pname->Prop)) (H_1 (F_46 N_1))) (F_46 ((image_1085733413name_o H_1) N_1)))))))).
% Axiom fact_720_folding__one__idem_Ohom__commute:(forall (N_1:((hoare_1708887482_state->Prop)->Prop)) (H_1:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (F_47:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_46:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_47) F_46)->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite1329924456tate_o N_1)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) N_1) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (H_1 (F_46 N_1))) (F_46 ((image_909543877tate_o H_1) N_1)))))))).
% Axiom fact_721_folding__one__idem_Ohom__commute:(forall (N_1:(pname->Prop)) (H_1:(pname->pname)) (F_47:(pname->(pname->pname))) (F_46:((pname->Prop)->pname)), (((finite89670078_pname F_47) F_46)->((forall (X_3:pname) (Y_4:pname), (((eq pname) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite_finite_pname N_1)->((not (((eq (pname->Prop)) N_1) bot_bot_pname_o))->(((eq pname) (H_1 (F_46 N_1))) (F_46 ((image_pname_pname H_1) N_1)))))))).
% Axiom fact_722_folding__one__idem_Ohom__commute:(forall (N_1:(hoare_1708887482_state->Prop)) (H_1:(hoare_1708887482_state->hoare_1708887482_state)) (F_47:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_46:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_47) F_46)->((forall (X_3:hoare_1708887482_state) (Y_4:hoare_1708887482_state), (((eq hoare_1708887482_state) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite1625599783_state N_1)->((not (((eq (hoare_1708887482_state->Prop)) N_1) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (H_1 (F_46 N_1))) (F_46 ((image_757158439_state H_1) N_1)))))))).
% Axiom fact_723_folding__one__idem_Ohom__commute:(forall (N_1:(com->Prop)) (H_1:(com->com)) (F_47:(com->(com->com))) (F_46:((com->Prop)->com)), (((finite666746948em_com F_47) F_46)->((forall (X_3:com) (Y_4:com), (((eq com) (H_1 ((F_47 X_3) Y_4))) ((F_47 (H_1 X_3)) (H_1 Y_4))))->((finite_finite_com N_1)->((not (((eq (com->Prop)) N_1) bot_bot_com_o))->(((eq com) (H_1 (F_46 N_1))) (F_46 ((image_com_com H_1) N_1)))))))).
% Axiom fact_724_the__elem__def:(forall (X_51:(com->Prop)), (((eq com) (the_elem_com X_51)) (the_com_1 (fun (X_3:com)=> (((eq (com->Prop)) X_51) ((insert_com X_3) bot_bot_com_o)))))).
% Axiom fact_725_the__elem__def:(forall (X_51:(pname->Prop)), (((eq pname) (the_elem_pname X_51)) (the_pname (fun (X_3:pname)=> (((eq (pname->Prop)) X_51) ((insert_pname X_3) bot_bot_pname_o)))))).
% Axiom fact_726_the__elem__def:(forall (X_51:(hoare_1708887482_state->Prop)), (((eq hoare_1708887482_state) (the_el864710747_state X_51)) (the_Ho851197897_state (fun (X_3:hoare_1708887482_state)=> (((eq (hoare_1708887482_state->Prop)) X_51) ((insert528405184_state X_3) bot_bo19817387tate_o)))))).
% Axiom fact_727_folding__one_Oinsert:(forall (X_50:com) (A_135:(com->Prop)) (F_45:(com->(com->com))) (F_44:((com->Prop)->com)), (((finite860057415ne_com F_45) F_44)->((finite_finite_com A_135)->((((member_com X_50) A_135)->False)->((not (((eq (com->Prop)) A_135) bot_bot_com_o))->(((eq com) (F_44 ((insert_com X_50) A_135))) ((F_45 X_50) (F_44 A_135)))))))).
% Axiom fact_728_folding__one_Oinsert:(forall (X_50:pname) (A_135:(pname->Prop)) (F_45:(pname->(pname->pname))) (F_44:((pname->Prop)->pname)), (((finite1282449217_pname F_45) F_44)->((finite_finite_pname A_135)->((((member_pname X_50) A_135)->False)->((not (((eq (pname->Prop)) A_135) bot_bot_pname_o))->(((eq pname) (F_44 ((insert_pname X_50) A_135))) ((F_45 X_50) (F_44 A_135)))))))).
% Axiom fact_729_folding__one_Oinsert:(forall (X_50:hoare_1708887482_state) (A_135:(hoare_1708887482_state->Prop)) (F_45:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_44:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_45) F_44)->((finite1625599783_state A_135)->((((member451959335_state X_50) A_135)->False)->((not (((eq (hoare_1708887482_state->Prop)) A_135) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_44 ((insert528405184_state X_50) A_135))) ((F_45 X_50) (F_44 A_135)))))))).
% Axiom fact_730_folding__one_Oinsert:(forall (X_50:(pname->Prop)) (A_135:((pname->Prop)->Prop)) (F_45:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_44:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_45) F_44)->((finite297249702name_o A_135)->((((member_pname_o X_50) A_135)->False)->((not (((eq ((pname->Prop)->Prop)) A_135) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_44 ((insert_pname_o X_50) A_135))) ((F_45 X_50) (F_44 A_135)))))))).
% Axiom fact_731_folding__one_Oinsert:(forall (X_50:(hoare_1708887482_state->Prop)) (A_135:((hoare_1708887482_state->Prop)->Prop)) (F_45:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_44:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_45) F_44)->((finite1329924456tate_o A_135)->((((member814030440tate_o X_50) A_135)->False)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_135) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_44 ((insert949073679tate_o X_50) A_135))) ((F_45 X_50) (F_44 A_135)))))))).
% Axiom fact_732_triple_Oexhaust:(forall (Y_25:hoare_1708887482_state), ((forall (Fun1:(state->(state->Prop))) (Com:com) (Fun2:(state->(state->Prop))), (not (((eq hoare_1708887482_state) Y_25) (((hoare_858012674_state Fun1) Com) Fun2))))->False)).
% Axiom fact_733_folding__one_Osingleton:(forall (X_49:com) (F_43:(com->(com->com))) (F_42:((com->Prop)->com)), (((finite860057415ne_com F_43) F_42)->(((eq com) (F_42 ((insert_com X_49) bot_bot_com_o))) X_49))).
% Axiom fact_734_folding__one_Osingleton:(forall (X_49:pname) (F_43:(pname->(pname->pname))) (F_42:((pname->Prop)->pname)), (((finite1282449217_pname F_43) F_42)->(((eq pname) (F_42 ((insert_pname X_49) bot_bot_pname_o))) X_49))).
% Axiom fact_735_folding__one_Osingleton:(forall (X_49:hoare_1708887482_state) (F_43:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_42:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_43) F_42)->(((eq hoare_1708887482_state) (F_42 ((insert528405184_state X_49) bot_bo19817387tate_o))) X_49))).
% Axiom fact_736_folding__one_Oclosed:(forall (A_134:(com->Prop)) (F_41:(com->(com->com))) (F_40:((com->Prop)->com)), (((finite860057415ne_com F_41) F_40)->((finite_finite_com A_134)->((not (((eq (com->Prop)) A_134) bot_bot_com_o))->((forall (X_3:com) (Y_4:com), ((member_com ((F_41 X_3) Y_4)) ((insert_com X_3) ((insert_com Y_4) bot_bot_com_o))))->((member_com (F_40 A_134)) A_134)))))).
% Axiom fact_737_folding__one_Oclosed:(forall (A_134:(pname->Prop)) (F_41:(pname->(pname->pname))) (F_40:((pname->Prop)->pname)), (((finite1282449217_pname F_41) F_40)->((finite_finite_pname A_134)->((not (((eq (pname->Prop)) A_134) bot_bot_pname_o))->((forall (X_3:pname) (Y_4:pname), ((member_pname ((F_41 X_3) Y_4)) ((insert_pname X_3) ((insert_pname Y_4) bot_bot_pname_o))))->((member_pname (F_40 A_134)) A_134)))))).
% Axiom fact_738_folding__one_Oclosed:(forall (A_134:(hoare_1708887482_state->Prop)) (F_41:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_40:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_41) F_40)->((finite1625599783_state A_134)->((not (((eq (hoare_1708887482_state->Prop)) A_134) bot_bo19817387tate_o))->((forall (X_3:hoare_1708887482_state) (Y_4:hoare_1708887482_state), ((member451959335_state ((F_41 X_3) Y_4)) ((insert528405184_state X_3) ((insert528405184_state Y_4) bot_bo19817387tate_o))))->((member451959335_state (F_40 A_134)) A_134)))))).
% Axiom fact_739_folding__one_Oclosed:(forall (A_134:((pname->Prop)->Prop)) (F_41:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_40:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_41) F_40)->((finite297249702name_o A_134)->((not (((eq ((pname->Prop)->Prop)) A_134) bot_bot_pname_o_o))->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), ((member_pname_o ((F_41 X_3) Y_4)) ((insert_pname_o X_3) ((insert_pname_o Y_4) bot_bot_pname_o_o))))->((member_pname_o (F_40 A_134)) A_134)))))).
% Axiom fact_740_folding__one_Oclosed:(forall (A_134:((hoare_1708887482_state->Prop)->Prop)) (F_41:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_40:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_41) F_40)->((finite1329924456tate_o A_134)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_134) bot_bo1678742418te_o_o))->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), ((member814030440tate_o ((F_41 X_3) Y_4)) ((insert949073679tate_o X_3) ((insert949073679tate_o Y_4) bot_bo1678742418te_o_o))))->((member814030440tate_o (F_40 A_134)) A_134)))))).
% Axiom fact_741_image__cong:(forall (F_39:(pname->hoare_1708887482_state)) (G_8:(pname->hoare_1708887482_state)) (M_3:(pname->Prop)) (N:(pname->Prop)), ((((eq (pname->Prop)) M_3) N)->((forall (X_3:pname), (((member_pname X_3) N)->(((eq hoare_1708887482_state) (F_39 X_3)) (G_8 X_3))))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_39) M_3)) ((image_1116629049_state G_8) N))))).
% Axiom fact_742_Collect__mono:(forall (Q_5:(hoare_1708887482_state->Prop)) (P_10:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), ((P_10 X_3)->(Q_5 X_3)))->((ord_le777019615tate_o (collec1568722789_state P_10)) (collec1568722789_state Q_5)))).
% Axiom fact_743_Collect__mono:(forall (Q_5:(pname->Prop)) (P_10:(pname->Prop)), ((forall (X_3:pname), ((P_10 X_3)->(Q_5 X_3)))->((ord_less_eq_pname_o (collect_pname P_10)) (collect_pname Q_5)))).
% Axiom fact_744_Collect__mono:(forall (Q_5:((pname->Prop)->Prop)) (P_10:((pname->Prop)->Prop)), ((forall (X_3:(pname->Prop)), ((P_10 X_3)->(Q_5 X_3)))->((ord_le1205211808me_o_o (collect_pname_o P_10)) (collect_pname_o Q_5)))).
% Axiom fact_745_Collect__mono:(forall (Q_5:((hoare_1708887482_state->Prop)->Prop)) (P_10:((hoare_1708887482_state->Prop)->Prop)), ((forall (X_3:(hoare_1708887482_state->Prop)), ((P_10 X_3)->(Q_5 X_3)))->((ord_le1728773982te_o_o (collec219771562tate_o P_10)) (collec219771562tate_o Q_5)))).
% Axiom fact_746_predicate1I:(forall (Q_4:(pname->Prop)) (P_9:(pname->Prop)), ((forall (X_3:pname), ((P_9 X_3)->(Q_4 X_3)))->((ord_less_eq_pname_o P_9) Q_4))).
% Axiom fact_747_predicate1I:(forall (Q_4:(hoare_1708887482_state->Prop)) (P_9:(hoare_1708887482_state->Prop)), ((forall (X_3:hoare_1708887482_state), ((P_9 X_3)->(Q_4 X_3)))->((ord_le777019615tate_o P_9) Q_4))).
% Axiom fact_748_mk__disjoint__insert:(forall (A_133:com) (A_132:(com->Prop)), (((member_com A_133) A_132)->((ex (com->Prop)) (fun (B_84:(com->Prop))=> ((and (((eq (com->Prop)) A_132) ((insert_com A_133) B_84))) (((member_com A_133) B_84)->False)))))).
% Axiom fact_749_mk__disjoint__insert:(forall (A_133:pname) (A_132:(pname->Prop)), (((member_pname A_133) A_132)->((ex (pname->Prop)) (fun (B_84:(pname->Prop))=> ((and (((eq (pname->Prop)) A_132) ((insert_pname A_133) B_84))) (((member_pname A_133) B_84)->False)))))).
% Axiom fact_750_mk__disjoint__insert:(forall (A_133:hoare_1708887482_state) (A_132:(hoare_1708887482_state->Prop)), (((member451959335_state A_133) A_132)->((ex (hoare_1708887482_state->Prop)) (fun (B_84:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_132) ((insert528405184_state A_133) B_84))) (((member451959335_state A_133) B_84)->False)))))).
% Axiom fact_751_Set_Oset__insert:(forall (X_48:com) (A_131:(com->Prop)), (((member_com X_48) A_131)->((forall (B_84:(com->Prop)), ((((eq (com->Prop)) A_131) ((insert_com X_48) B_84))->((member_com X_48) B_84)))->False))).
% Axiom fact_752_Set_Oset__insert:(forall (X_48:pname) (A_131:(pname->Prop)), (((member_pname X_48) A_131)->((forall (B_84:(pname->Prop)), ((((eq (pname->Prop)) A_131) ((insert_pname X_48) B_84))->((member_pname X_48) B_84)))->False))).
% Axiom fact_753_Set_Oset__insert:(forall (X_48:hoare_1708887482_state) (A_131:(hoare_1708887482_state->Prop)), (((member451959335_state X_48) A_131)->((forall (B_84:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_131) ((insert528405184_state X_48) B_84))->((member451959335_state X_48) B_84)))->False))).
% Axiom fact_754_equals0I:(forall (A_130:(com->Prop)), ((forall (Y_4:com), (((member_com Y_4) A_130)->False))->(((eq (com->Prop)) A_130) bot_bot_com_o))).
% Axiom fact_755_equals0I:(forall (A_130:(pname->Prop)), ((forall (Y_4:pname), (((member_pname Y_4) A_130)->False))->(((eq (pname->Prop)) A_130) bot_bot_pname_o))).
% Axiom fact_756_equals0I:(forall (A_130:(hoare_1708887482_state->Prop)), ((forall (Y_4:hoare_1708887482_state), (((member451959335_state Y_4) A_130)->False))->(((eq (hoare_1708887482_state->Prop)) A_130) bot_bo19817387tate_o))).
% Axiom fact_757_MGT__alternD:(forall (G_7:(hoare_1708887482_state->Prop)) (C_34:com), (hoare_1160767572gleton->(((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_34) S0_1) S1)) (((eq state) Z_11) S1))))) C_34) fequal_state)) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o))))).
% Axiom fact_758_xt1_I15_J:(forall (C_35:Prop) (F_38:(Prop->Prop)) (B_83:Prop) (A_129:Prop), (((iff A_129) (F_38 B_83))->(((ord_less_eq_o C_35) B_83)->((forall (X_3:Prop) (Y_4:Prop), (((ord_less_eq_o Y_4) X_3)->((ord_less_eq_o (F_38 Y_4)) (F_38 X_3))))->((ord_less_eq_o (F_38 C_35)) A_129))))).
% Axiom fact_759_xt1_I15_J:(forall (C_35:(pname->Prop)) (A_129:(pname->Prop)) (F_38:((pname->Prop)->(pname->Prop))) (B_83:(pname->Prop)), ((((eq (pname->Prop)) A_129) (F_38 B_83))->(((ord_less_eq_pname_o C_35) B_83)->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), (((ord_less_eq_pname_o Y_4) X_3)->((ord_less_eq_pname_o (F_38 Y_4)) (F_38 X_3))))->((ord_less_eq_pname_o (F_38 C_35)) A_129))))).
% Axiom fact_760_xt1_I15_J:(forall (C_35:(hoare_1708887482_state->Prop)) (A_129:(hoare_1708887482_state->Prop)) (F_38:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (B_83:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_129) (F_38 B_83))->(((ord_le777019615tate_o C_35) B_83)->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_4) X_3)->((ord_le777019615tate_o (F_38 Y_4)) (F_38 X_3))))->((ord_le777019615tate_o (F_38 C_35)) A_129))))).
% Axiom fact_761_MGT__alternI:(forall (G_7:(hoare_1708887482_state->Prop)) (C_34:com), (((hoare_90032982_state G_7) ((insert528405184_state (hoare_Mirabelle_MGT C_34)) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_34) S0_1) S1)) (((eq state) Z_11) S1))))) C_34) fequal_state)) bot_bo19817387tate_o)))).
% Axiom fact_762_MGT__def:(forall (C_34:com), (((eq hoare_1708887482_state) (hoare_Mirabelle_MGT C_34)) (((hoare_858012674_state fequal_state) C_34) (evalc C_34)))).
% Axiom fact_763_evalc__elim__cases_I6_J:(forall (P:pname) (S_4:state) (S1_1:state), ((((evalc (body_1 P)) S_4) S1_1)->(((evalc (the_com (body P))) S_4) S1_1))).
% Axiom fact_764_evalc_OBody:(forall (Pn_1:pname) (S0:state) (S1_1:state), ((((evalc (the_com (body Pn_1))) S0) S1_1)->(((evalc (body_1 Pn_1)) S0) S1_1))).
% Axiom fact_765_evalc__elim__cases_I1_J:(forall (S_4:state) (T:state), ((((evalc skip) S_4) T)->(((eq state) T) S_4))).
% Axiom fact_766_evalc_OSkip:(forall (S_4:state), (((evalc skip) S_4) S_4)).
% Axiom fact_767_evalc_OSemi:(forall (C1:com) (S2:state) (C0:com) (S0:state) (S1_1:state), ((((evalc C0) S0) S1_1)->((((evalc C1) S1_1) S2)->(((evalc ((semi C0) C1)) S0) S2)))).
% Axiom fact_768_evalc_OWhileTrue:(forall (S2:state) (C_34:com) (S1_1:state) (B_82:(state->Prop)) (S0:state), ((B_82 S0)->((((evalc C_34) S0) S1_1)->((((evalc ((while B_82) C_34)) S1_1) S2)->(((evalc ((while B_82) C_34)) S0) S2))))).
% Axiom fact_769_evalc_OWhileFalse:(forall (C_34:com) (B_82:(state->Prop)) (S_4:state), (((B_82 S_4)->False)->(((evalc ((while B_82) C_34)) S_4) S_4))).
% Axiom fact_770_com__det:(forall (U:state) (C_34:com) (S_4:state) (T:state), ((((evalc C_34) S_4) T)->((((evalc C_34) S_4) U)->(((eq state) U) T)))).
% Axiom fact_771_evalc__elim__cases_I4_J:(forall (C1:com) (C2:com) (S_4:state) (T:state), ((((evalc ((semi C1) C2)) S_4) T)->((forall (S1:state), ((((evalc C1) S_4) S1)->((((evalc C2) S1) T)->False)))->False))).
% Axiom fact_772_evalc__WHILE__case:(forall (B_82:(state->Prop)) (C_34:com) (S_4:state) (T:state), ((((evalc ((while B_82) C_34)) S_4) T)->(((((eq state) T) S_4)->(B_82 S_4))->(((B_82 S_4)->(forall (S1:state), ((((evalc C_34) S_4) S1)->((((evalc ((while B_82) C_34)) S1) T)->False))))->False)))).
% Axiom fact_773_xt1_I16_J:(forall (C_33:Prop) (F_37:(Prop->Prop)) (B_81:Prop) (A_128:Prop), (((ord_less_eq_o B_81) A_128)->(((iff (F_37 B_81)) C_33)->((forall (X_3:Prop) (Y_4:Prop), (((ord_less_eq_o Y_4) X_3)->((ord_less_eq_o (F_37 Y_4)) (F_37 X_3))))->((ord_less_eq_o C_33) (F_37 A_128)))))).
% Axiom fact_774_xt1_I16_J:(forall (F_37:((pname->Prop)->(pname->Prop))) (C_33:(pname->Prop)) (B_81:(pname->Prop)) (A_128:(pname->Prop)), (((ord_less_eq_pname_o B_81) A_128)->((((eq (pname->Prop)) (F_37 B_81)) C_33)->((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)), (((ord_less_eq_pname_o Y_4) X_3)->((ord_less_eq_pname_o (F_37 Y_4)) (F_37 X_3))))->((ord_less_eq_pname_o C_33) (F_37 A_128)))))).
% Axiom fact_775_xt1_I16_J:(forall (F_37:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (C_33:(hoare_1708887482_state->Prop)) (B_81:(hoare_1708887482_state->Prop)) (A_128:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_81) A_128)->((((eq (hoare_1708887482_state->Prop)) (F_37 B_81)) C_33)->((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_4) X_3)->((ord_le777019615tate_o (F_37 Y_4)) (F_37 X_3))))->((ord_le777019615tate_o C_33) (F_37 A_128)))))).
% Axiom fact_776_folding__one_Ounion__inter:(forall (B_80:((pname->Prop)->Prop)) (A_127:((pname->Prop)->Prop)) (F_36:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_35:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_36) F_35)->((finite297249702name_o A_127)->((finite297249702name_o B_80)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_127) B_80)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((F_36 (F_35 ((semila181081674me_o_o A_127) B_80))) (F_35 ((semila2013987940me_o_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80)))))))).
% Axiom fact_777_folding__one_Ounion__inter:(forall (B_80:((hoare_1708887482_state->Prop)->Prop)) (A_127:((hoare_1708887482_state->Prop)->Prop)) (F_36:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_35:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_36) F_35)->((finite1329924456tate_o A_127)->((finite1329924456tate_o B_80)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_127) B_80)) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) ((F_36 (F_35 ((semila1853742644te_o_o A_127) B_80))) (F_35 ((semila598060698te_o_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80)))))))).
% Axiom fact_778_folding__one_Ounion__inter:(forall (B_80:(pname->Prop)) (A_127:(pname->Prop)) (F_36:(pname->(pname->pname))) (F_35:((pname->Prop)->pname)), (((finite1282449217_pname F_36) F_35)->((finite_finite_pname A_127)->((finite_finite_pname B_80)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_127) B_80)) bot_bot_pname_o))->(((eq pname) ((F_36 (F_35 ((semila1780557381name_o A_127) B_80))) (F_35 ((semila1673364395name_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80)))))))).
% Axiom fact_779_folding__one_Ounion__inter:(forall (B_80:(hoare_1708887482_state->Prop)) (A_127:(hoare_1708887482_state->Prop)) (F_36:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_35:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_36) F_35)->((finite1625599783_state A_127)->((finite1625599783_state B_80)->((not (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_127) B_80)) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) ((F_36 (F_35 ((semila1122118281tate_o A_127) B_80))) (F_35 ((semila129691299tate_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80)))))))).
% Axiom fact_780_folding__one_Ounion__inter:(forall (B_80:(com->Prop)) (A_127:(com->Prop)) (F_36:(com->(com->com))) (F_35:((com->Prop)->com)), (((finite860057415ne_com F_36) F_35)->((finite_finite_com A_127)->((finite_finite_com B_80)->((not (((eq (com->Prop)) ((semila513601829_com_o A_127) B_80)) bot_bot_com_o))->(((eq com) ((F_36 (F_35 ((semila1562558655_com_o A_127) B_80))) (F_35 ((semila513601829_com_o A_127) B_80)))) ((F_36 (F_35 A_127)) (F_35 B_80)))))))).
% Axiom fact_781_folding__one_Ounion__disjoint:(forall (B_79:((pname->Prop)->Prop)) (A_126:((pname->Prop)->Prop)) (F_34:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_33:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_34) F_33)->((finite297249702name_o A_126)->((not (((eq ((pname->Prop)->Prop)) A_126) bot_bot_pname_o_o))->((finite297249702name_o B_79)->((not (((eq ((pname->Prop)->Prop)) B_79) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_126) B_79)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_33 ((semila181081674me_o_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79)))))))))).
% Axiom fact_782_folding__one_Ounion__disjoint:(forall (B_79:((hoare_1708887482_state->Prop)->Prop)) (A_126:((hoare_1708887482_state->Prop)->Prop)) (F_34:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_33:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_34) F_33)->((finite1329924456tate_o A_126)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_126) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_79)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_79) bot_bo1678742418te_o_o))->((((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_126) B_79)) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (F_33 ((semila1853742644te_o_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79)))))))))).
% Axiom fact_783_folding__one_Ounion__disjoint:(forall (B_79:(pname->Prop)) (A_126:(pname->Prop)) (F_34:(pname->(pname->pname))) (F_33:((pname->Prop)->pname)), (((finite1282449217_pname F_34) F_33)->((finite_finite_pname A_126)->((not (((eq (pname->Prop)) A_126) bot_bot_pname_o))->((finite_finite_pname B_79)->((not (((eq (pname->Prop)) B_79) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_126) B_79)) bot_bot_pname_o)->(((eq pname) (F_33 ((semila1780557381name_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79)))))))))).
% Axiom fact_784_folding__one_Ounion__disjoint:(forall (B_79:(hoare_1708887482_state->Prop)) (A_126:(hoare_1708887482_state->Prop)) (F_34:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_33:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_34) F_33)->((finite1625599783_state A_126)->((not (((eq (hoare_1708887482_state->Prop)) A_126) bot_bo19817387tate_o))->((finite1625599783_state B_79)->((not (((eq (hoare_1708887482_state->Prop)) B_79) bot_bo19817387tate_o))->((((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_126) B_79)) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_33 ((semila1122118281tate_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79)))))))))).
% Axiom fact_785_folding__one_Ounion__disjoint:(forall (B_79:(com->Prop)) (A_126:(com->Prop)) (F_34:(com->(com->com))) (F_33:((com->Prop)->com)), (((finite860057415ne_com F_34) F_33)->((finite_finite_com A_126)->((not (((eq (com->Prop)) A_126) bot_bot_com_o))->((finite_finite_com B_79)->((not (((eq (com->Prop)) B_79) bot_bot_com_o))->((((eq (com->Prop)) ((semila513601829_com_o A_126) B_79)) bot_bot_com_o)->(((eq com) (F_33 ((semila1562558655_com_o A_126) B_79))) ((F_34 (F_33 A_126)) (F_33 B_79)))))))))).
% Axiom fact_786_folding__one_Oinsert__remove:(forall (X_47:com) (A_125:(com->Prop)) (F_32:(com->(com->com))) (F_31:((com->Prop)->com)), (((finite860057415ne_com F_32) F_31)->((finite_finite_com A_125)->((and ((((eq (com->Prop)) ((minus_minus_com_o A_125) ((insert_com X_47) bot_bot_com_o))) bot_bot_com_o)->(((eq com) (F_31 ((insert_com X_47) A_125))) X_47))) ((not (((eq (com->Prop)) ((minus_minus_com_o A_125) ((insert_com X_47) bot_bot_com_o))) bot_bot_com_o))->(((eq com) (F_31 ((insert_com X_47) A_125))) ((F_32 X_47) (F_31 ((minus_minus_com_o A_125) ((insert_com X_47) bot_bot_com_o)))))))))).
% Axiom fact_787_folding__one_Oinsert__remove:(forall (X_47:pname) (A_125:(pname->Prop)) (F_32:(pname->(pname->pname))) (F_31:((pname->Prop)->pname)), (((finite1282449217_pname F_32) F_31)->((finite_finite_pname A_125)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_125) ((insert_pname X_47) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_31 ((insert_pname X_47) A_125))) X_47))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_125) ((insert_pname X_47) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_31 ((insert_pname X_47) A_125))) ((F_32 X_47) (F_31 ((minus_minus_pname_o A_125) ((insert_pname X_47) bot_bot_pname_o)))))))))).
% Axiom fact_788_folding__one_Oinsert__remove:(forall (X_47:hoare_1708887482_state) (A_125:(hoare_1708887482_state->Prop)) (F_32:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_31:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_32) F_31)->((finite1625599783_state A_125)->((and ((((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_125) ((insert528405184_state X_47) bot_bo19817387tate_o))) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_31 ((insert528405184_state X_47) A_125))) X_47))) ((not (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_125) ((insert528405184_state X_47) bot_bo19817387tate_o))) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_31 ((insert528405184_state X_47) A_125))) ((F_32 X_47) (F_31 ((minus_2056855718tate_o A_125) ((insert528405184_state X_47) bot_bo19817387tate_o)))))))))).
% Axiom fact_789_folding__one_Oinsert__remove:(forall (X_47:(pname->Prop)) (A_125:((pname->Prop)->Prop)) (F_32:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_31:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_32) F_31)->((finite297249702name_o A_125)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_125) ((insert_pname_o X_47) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_31 ((insert_pname_o X_47) A_125))) X_47))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_125) ((insert_pname_o X_47) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_31 ((insert_pname_o X_47) A_125))) ((F_32 X_47) (F_31 ((minus_1480864103me_o_o A_125) ((insert_pname_o X_47) bot_bot_pname_o_o)))))))))).
% Axiom fact_790_folding__one_Oinsert__remove:(forall (X_47:(hoare_1708887482_state->Prop)) (A_125:((hoare_1708887482_state->Prop)->Prop)) (F_32:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_31:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_32) F_31)->((finite1329924456tate_o A_125)->((and ((((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_125) ((insert949073679tate_o X_47) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (F_31 ((insert949073679tate_o X_47) A_125))) X_47))) ((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_125) ((insert949073679tate_o X_47) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_31 ((insert949073679tate_o X_47) A_125))) ((F_32 X_47) (F_31 ((minus_548038231te_o_o A_125) ((insert949073679tate_o X_47) bot_bo1678742418te_o_o)))))))))).
% Axiom fact_791_folding__one_Oremove:(forall (X_46:com) (A_124:(com->Prop)) (F_30:(com->(com->com))) (F_29:((com->Prop)->com)), (((finite860057415ne_com F_30) F_29)->((finite_finite_com A_124)->(((member_com X_46) A_124)->((and ((((eq (com->Prop)) ((minus_minus_com_o A_124) ((insert_com X_46) bot_bot_com_o))) bot_bot_com_o)->(((eq com) (F_29 A_124)) X_46))) ((not (((eq (com->Prop)) ((minus_minus_com_o A_124) ((insert_com X_46) bot_bot_com_o))) bot_bot_com_o))->(((eq com) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_minus_com_o A_124) ((insert_com X_46) bot_bot_com_o))))))))))).
% Axiom fact_792_folding__one_Oremove:(forall (X_46:pname) (A_124:(pname->Prop)) (F_30:(pname->(pname->pname))) (F_29:((pname->Prop)->pname)), (((finite1282449217_pname F_30) F_29)->((finite_finite_pname A_124)->(((member_pname X_46) A_124)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_124) ((insert_pname X_46) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_29 A_124)) X_46))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_124) ((insert_pname X_46) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_minus_pname_o A_124) ((insert_pname X_46) bot_bot_pname_o))))))))))).
% Axiom fact_793_folding__one_Oremove:(forall (X_46:hoare_1708887482_state) (A_124:(hoare_1708887482_state->Prop)) (F_30:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_29:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_30) F_29)->((finite1625599783_state A_124)->(((member451959335_state X_46) A_124)->((and ((((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_124) ((insert528405184_state X_46) bot_bo19817387tate_o))) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_29 A_124)) X_46))) ((not (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_124) ((insert528405184_state X_46) bot_bo19817387tate_o))) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_2056855718tate_o A_124) ((insert528405184_state X_46) bot_bo19817387tate_o))))))))))).
% Axiom fact_794_folding__one_Oremove:(forall (X_46:(pname->Prop)) (A_124:((pname->Prop)->Prop)) (F_30:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_29:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_30) F_29)->((finite297249702name_o A_124)->(((member_pname_o X_46) A_124)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_124) ((insert_pname_o X_46) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_29 A_124)) X_46))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_124) ((insert_pname_o X_46) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_1480864103me_o_o A_124) ((insert_pname_o X_46) bot_bot_pname_o_o))))))))))).
% Axiom fact_795_folding__one_Oremove:(forall (X_46:(hoare_1708887482_state->Prop)) (A_124:((hoare_1708887482_state->Prop)->Prop)) (F_30:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_29:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_30) F_29)->((finite1329924456tate_o A_124)->(((member814030440tate_o X_46) A_124)->((and ((((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_124) ((insert949073679tate_o X_46) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (F_29 A_124)) X_46))) ((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_124) ((insert949073679tate_o X_46) bot_bo1678742418te_o_o))) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (F_29 A_124)) ((F_30 X_46) (F_29 ((minus_548038231te_o_o A_124) ((insert949073679tate_o X_46) bot_bo1678742418te_o_o))))))))))).
% Axiom fact_796_is__none__code_I2_J:(forall (X_45:pname), ((is_none_pname (some_pname X_45))->False)).
% Axiom fact_797_is__none__code_I2_J:(forall (X_45:hoare_1708887482_state), ((is_non163157940_state (some_H1974565227_state X_45))->False)).
% Axiom fact_798_is__none__code_I2_J:(forall (X_45:com), ((is_none_com (some_com X_45))->False)).
% Axiom fact_799_conseq:(forall (Q_2:(state->(state->Prop))) (G_6:(hoare_1708887482_state->Prop)) (C_32:com) (P_7:(state->(state->Prop))), ((forall (Z_11:state) (S_2:state), (((P_7 Z_11) S_2)->((ex (state->(state->Prop))) (fun (P_8:(state->(state->Prop)))=> ((ex (state->(state->Prop))) (fun (Q_3:(state->(state->Prop)))=> ((and ((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state P_8) C_32) Q_3)) bot_bo19817387tate_o))) (forall (S_3:state), ((forall (Z_12:state), (((P_8 Z_12) S_2)->((Q_3 Z_12) S_3)))->((Q_2 Z_11) S_3))))))))))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state P_7) C_32) Q_2)) bot_bo19817387tate_o)))).
% Axiom fact_800_IntE:(forall (C_31:com) (A_123:(com->Prop)) (B_78:(com->Prop)), (((member_com C_31) ((semila513601829_com_o A_123) B_78))->((((member_com C_31) A_123)->(((member_com C_31) B_78)->False))->False))).
% Axiom fact_801_IntE:(forall (C_31:pname) (A_123:(pname->Prop)) (B_78:(pname->Prop)), (((member_pname C_31) ((semila1673364395name_o A_123) B_78))->((((member_pname C_31) A_123)->(((member_pname C_31) B_78)->False))->False))).
% Axiom fact_802_IntE:(forall (C_31:hoare_1708887482_state) (A_123:(hoare_1708887482_state->Prop)) (B_78:(hoare_1708887482_state->Prop)), (((member451959335_state C_31) ((semila129691299tate_o A_123) B_78))->((((member451959335_state C_31) A_123)->(((member451959335_state C_31) B_78)->False))->False))).
% Axiom fact_803_IntI:(forall (B_77:(com->Prop)) (C_30:com) (A_122:(com->Prop)), (((member_com C_30) A_122)->(((member_com C_30) B_77)->((member_com C_30) ((semila513601829_com_o A_122) B_77))))).
% Axiom fact_804_IntI:(forall (B_77:(pname->Prop)) (C_30:pname) (A_122:(pname->Prop)), (((member_pname C_30) A_122)->(((member_pname C_30) B_77)->((member_pname C_30) ((semila1673364395name_o A_122) B_77))))).
% Axiom fact_805_IntI:(forall (B_77:(hoare_1708887482_state->Prop)) (C_30:hoare_1708887482_state) (A_122:(hoare_1708887482_state->Prop)), (((member451959335_state C_30) A_122)->(((member451959335_state C_30) B_77)->((member451959335_state C_30) ((semila129691299tate_o A_122) B_77))))).
% Axiom fact_806_DiffE:(forall (C_29:com) (A_121:(com->Prop)) (B_76:(com->Prop)), (((member_com C_29) ((minus_minus_com_o A_121) B_76))->((((member_com C_29) A_121)->((member_com C_29) B_76))->False))).
% Axiom fact_807_DiffE:(forall (C_29:pname) (A_121:(pname->Prop)) (B_76:(pname->Prop)), (((member_pname C_29) ((minus_minus_pname_o A_121) B_76))->((((member_pname C_29) A_121)->((member_pname C_29) B_76))->False))).
% Axiom fact_808_DiffE:(forall (C_29:hoare_1708887482_state) (A_121:(hoare_1708887482_state->Prop)) (B_76:(hoare_1708887482_state->Prop)), (((member451959335_state C_29) ((minus_2056855718tate_o A_121) B_76))->((((member451959335_state C_29) A_121)->((member451959335_state C_29) B_76))->False))).
% Axiom fact_809_DiffI:(forall (B_75:(com->Prop)) (C_28:com) (A_120:(com->Prop)), (((member_com C_28) A_120)->((((member_com C_28) B_75)->False)->((member_com C_28) ((minus_minus_com_o A_120) B_75))))).
% Axiom fact_810_DiffI:(forall (B_75:(pname->Prop)) (C_28:pname) (A_120:(pname->Prop)), (((member_pname C_28) A_120)->((((member_pname C_28) B_75)->False)->((member_pname C_28) ((minus_minus_pname_o A_120) B_75))))).
% Axiom fact_811_DiffI:(forall (B_75:(hoare_1708887482_state->Prop)) (C_28:hoare_1708887482_state) (A_120:(hoare_1708887482_state->Prop)), (((member451959335_state C_28) A_120)->((((member451959335_state C_28) B_75)->False)->((member451959335_state C_28) ((minus_2056855718tate_o A_120) B_75))))).
% Axiom fact_812_finite__Int:(forall (G_5:((pname->Prop)->Prop)) (F_28:((pname->Prop)->Prop)), (((or (finite297249702name_o F_28)) (finite297249702name_o G_5))->(finite297249702name_o ((semila2013987940me_o_o F_28) G_5)))).
% Axiom fact_813_finite__Int:(forall (G_5:((hoare_1708887482_state->Prop)->Prop)) (F_28:((hoare_1708887482_state->Prop)->Prop)), (((or (finite1329924456tate_o F_28)) (finite1329924456tate_o G_5))->(finite1329924456tate_o ((semila598060698te_o_o F_28) G_5)))).
% Axiom fact_814_finite__Int:(forall (G_5:(pname->Prop)) (F_28:(pname->Prop)), (((or (finite_finite_pname F_28)) (finite_finite_pname G_5))->(finite_finite_pname ((semila1673364395name_o F_28) G_5)))).
% Axiom fact_815_finite__Int:(forall (G_5:(hoare_1708887482_state->Prop)) (F_28:(hoare_1708887482_state->Prop)), (((or (finite1625599783_state F_28)) (finite1625599783_state G_5))->(finite1625599783_state ((semila129691299tate_o F_28) G_5)))).
% Axiom fact_816_finite__Diff:(forall (B_74:((pname->Prop)->Prop)) (A_119:((pname->Prop)->Prop)), ((finite297249702name_o A_119)->(finite297249702name_o ((minus_1480864103me_o_o A_119) B_74)))).
% Axiom fact_817_finite__Diff:(forall (B_74:((hoare_1708887482_state->Prop)->Prop)) (A_119:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_119)->(finite1329924456tate_o ((minus_548038231te_o_o A_119) B_74)))).
% Axiom fact_818_finite__Diff:(forall (B_74:(pname->Prop)) (A_119:(pname->Prop)), ((finite_finite_pname A_119)->(finite_finite_pname ((minus_minus_pname_o A_119) B_74)))).
% Axiom fact_819_finite__Diff:(forall (B_74:(hoare_1708887482_state->Prop)) (A_119:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_119)->(finite1625599783_state ((minus_2056855718tate_o A_119) B_74)))).
% Axiom fact_820_inf__Int__eq:(forall (R:(com->Prop)) (S_1:(com->Prop)) (X_3:com), ((iff (((semila513601829_com_o (fun (Y_4:com)=> ((member_com Y_4) R))) (fun (Y_4:com)=> ((member_com Y_4) S_1))) X_3)) ((member_com X_3) ((semila513601829_com_o R) S_1)))).
% Axiom fact_821_inf__Int__eq:(forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X_3:pname), ((iff (((semila1673364395name_o (fun (Y_4:pname)=> ((member_pname Y_4) R))) (fun (Y_4:pname)=> ((member_pname Y_4) S_1))) X_3)) ((member_pname X_3) ((semila1673364395name_o R) S_1)))).
% Axiom fact_822_inf__Int__eq:(forall (R:(hoare_1708887482_state->Prop)) (S_1:(hoare_1708887482_state->Prop)) (X_3:hoare_1708887482_state), ((iff (((semila129691299tate_o (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) R))) (fun (Y_4:hoare_1708887482_state)=> ((member451959335_state Y_4) S_1))) X_3)) ((member451959335_state X_3) ((semila129691299tate_o R) S_1)))).
% Axiom fact_823_Diff__disjoint:(forall (A_118:(com->Prop)) (B_73:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o A_118) ((minus_minus_com_o B_73) A_118))) bot_bot_com_o)).
% Axiom fact_824_Diff__disjoint:(forall (A_118:(pname->Prop)) (B_73:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_118) ((minus_minus_pname_o B_73) A_118))) bot_bot_pname_o)).
% Axiom fact_825_Diff__disjoint:(forall (A_118:(hoare_1708887482_state->Prop)) (B_73:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_118) ((minus_2056855718tate_o B_73) A_118))) bot_bo19817387tate_o)).
% Axiom fact_826_Diff__triv:(forall (A_117:(com->Prop)) (B_72:(com->Prop)), ((((eq (com->Prop)) ((semila513601829_com_o A_117) B_72)) bot_bot_com_o)->(((eq (com->Prop)) ((minus_minus_com_o A_117) B_72)) A_117))).
% Axiom fact_827_Diff__triv:(forall (A_117:(pname->Prop)) (B_72:(pname->Prop)), ((((eq (pname->Prop)) ((semila1673364395name_o A_117) B_72)) bot_bot_pname_o)->(((eq (pname->Prop)) ((minus_minus_pname_o A_117) B_72)) A_117))).
% Axiom fact_828_Diff__triv:(forall (A_117:(hoare_1708887482_state->Prop)) (B_72:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_117) B_72)) bot_bo19817387tate_o)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_117) B_72)) A_117))).
% Axiom fact_829_DiffD2:(forall (C_27:com) (A_116:(com->Prop)) (B_71:(com->Prop)), (((member_com C_27) ((minus_minus_com_o A_116) B_71))->(((member_com C_27) B_71)->False))).
% Axiom fact_830_DiffD2:(forall (C_27:pname) (A_116:(pname->Prop)) (B_71:(pname->Prop)), (((member_pname C_27) ((minus_minus_pname_o A_116) B_71))->(((member_pname C_27) B_71)->False))).
% Axiom fact_831_DiffD2:(forall (C_27:hoare_1708887482_state) (A_116:(hoare_1708887482_state->Prop)) (B_71:(hoare_1708887482_state->Prop)), (((member451959335_state C_27) ((minus_2056855718tate_o A_116) B_71))->(((member451959335_state C_27) B_71)->False))).
% Axiom fact_832_IntD2:(forall (C_26:com) (A_115:(com->Prop)) (B_70:(com->Prop)), (((member_com C_26) ((semila513601829_com_o A_115) B_70))->((member_com C_26) B_70))).
% Axiom fact_833_IntD2:(forall (C_26:pname) (A_115:(pname->Prop)) (B_70:(pname->Prop)), (((member_pname C_26) ((semila1673364395name_o A_115) B_70))->((member_pname C_26) B_70))).
% Axiom fact_834_IntD2:(forall (C_26:hoare_1708887482_state) (A_115:(hoare_1708887482_state->Prop)) (B_70:(hoare_1708887482_state->Prop)), (((member451959335_state C_26) ((semila129691299tate_o A_115) B_70))->((member451959335_state C_26) B_70))).
% Axiom fact_835_IntD1:(forall (C_25:com) (A_114:(com->Prop)) (B_69:(com->Prop)), (((member_com C_25) ((semila513601829_com_o A_114) B_69))->((member_com C_25) A_114))).
% Axiom fact_836_IntD1:(forall (C_25:pname) (A_114:(pname->Prop)) (B_69:(pname->Prop)), (((member_pname C_25) ((semila1673364395name_o A_114) B_69))->((member_pname C_25) A_114))).
% Axiom fact_837_IntD1:(forall (C_25:hoare_1708887482_state) (A_114:(hoare_1708887482_state->Prop)) (B_69:(hoare_1708887482_state->Prop)), (((member451959335_state C_25) ((semila129691299tate_o A_114) B_69))->((member451959335_state C_25) A_114))).
% Axiom fact_838_DiffD1:(forall (C_24:com) (A_113:(com->Prop)) (B_68:(com->Prop)), (((member_com C_24) ((minus_minus_com_o A_113) B_68))->((member_com C_24) A_113))).
% Axiom fact_839_DiffD1:(forall (C_24:pname) (A_113:(pname->Prop)) (B_68:(pname->Prop)), (((member_pname C_24) ((minus_minus_pname_o A_113) B_68))->((member_pname C_24) A_113))).
% Axiom fact_840_DiffD1:(forall (C_24:hoare_1708887482_state) (A_113:(hoare_1708887482_state->Prop)) (B_68:(hoare_1708887482_state->Prop)), (((member451959335_state C_24) ((minus_2056855718tate_o A_113) B_68))->((member451959335_state C_24) A_113))).
% Axiom fact_841_Int__iff:(forall (C_23:com) (A_112:(com->Prop)) (B_67:(com->Prop)), ((iff ((member_com C_23) ((semila513601829_com_o A_112) B_67))) ((and ((member_com C_23) A_112)) ((member_com C_23) B_67)))).
% Axiom fact_842_Int__iff:(forall (C_23:pname) (A_112:(pname->Prop)) (B_67:(pname->Prop)), ((iff ((member_pname C_23) ((semila1673364395name_o A_112) B_67))) ((and ((member_pname C_23) A_112)) ((member_pname C_23) B_67)))).
% Axiom fact_843_Int__iff:(forall (C_23:hoare_1708887482_state) (A_112:(hoare_1708887482_state->Prop)) (B_67:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_23) ((semila129691299tate_o A_112) B_67))) ((and ((member451959335_state C_23) A_112)) ((member451959335_state C_23) B_67)))).
% Axiom fact_844_Diff__iff:(forall (C_22:com) (A_111:(com->Prop)) (B_66:(com->Prop)), ((iff ((member_com C_22) ((minus_minus_com_o A_111) B_66))) ((and ((member_com C_22) A_111)) (((member_com C_22) B_66)->False)))).
% Axiom fact_845_Diff__iff:(forall (C_22:pname) (A_111:(pname->Prop)) (B_66:(pname->Prop)), ((iff ((member_pname C_22) ((minus_minus_pname_o A_111) B_66))) ((and ((member_pname C_22) A_111)) (((member_pname C_22) B_66)->False)))).
% Axiom fact_846_Diff__iff:(forall (C_22:hoare_1708887482_state) (A_111:(hoare_1708887482_state->Prop)) (B_66:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_22) ((minus_2056855718tate_o A_111) B_66))) ((and ((member451959335_state C_22) A_111)) (((member451959335_state C_22) B_66)->False)))).
% Axiom fact_847_Int__def:(forall (A_110:(com->Prop)) (B_65:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o A_110) B_65)) (collect_com (fun (X_3:com)=> ((and ((member_com X_3) A_110)) ((member_com X_3) B_65)))))).
% Axiom fact_848_Int__def:(forall (A_110:(pname->Prop)) (B_65:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_110) B_65)) (collect_pname (fun (X_3:pname)=> ((and ((member_pname X_3) A_110)) ((member_pname X_3) B_65)))))).
% Axiom fact_849_Int__def:(forall (A_110:(hoare_1708887482_state->Prop)) (B_65:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_110) B_65)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_110)) ((member451959335_state X_3) B_65)))))).
% Axiom fact_850_Int__def:(forall (A_110:((pname->Prop)->Prop)) (B_65:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_110) B_65)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_110)) ((member_pname_o X_3) B_65)))))).
% Axiom fact_851_Int__def:(forall (A_110:((hoare_1708887482_state->Prop)->Prop)) (B_65:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_110) B_65)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_110)) ((member814030440tate_o X_3) B_65)))))).
% Axiom fact_852_set__diff__eq:(forall (A_109:(com->Prop)) (B_64:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_109) B_64)) (collect_com (fun (X_3:com)=> ((and ((member_com X_3) A_109)) (not ((member_com X_3) B_64))))))).
% Axiom fact_853_set__diff__eq:(forall (A_109:(pname->Prop)) (B_64:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_109) B_64)) (collect_pname (fun (X_3:pname)=> ((and ((member_pname X_3) A_109)) (not ((member_pname X_3) B_64))))))).
% Axiom fact_854_set__diff__eq:(forall (A_109:(hoare_1708887482_state->Prop)) (B_64:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_109) B_64)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and ((member451959335_state X_3) A_109)) (not ((member451959335_state X_3) B_64))))))).
% Axiom fact_855_set__diff__eq:(forall (A_109:((pname->Prop)->Prop)) (B_64:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_109) B_64)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and ((member_pname_o X_3) A_109)) (not ((member_pname_o X_3) B_64))))))).
% Axiom fact_856_set__diff__eq:(forall (A_109:((hoare_1708887482_state->Prop)->Prop)) (B_64:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o A_109) B_64)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and ((member814030440tate_o X_3) A_109)) (not ((member814030440tate_o X_3) B_64))))))).
% Axiom fact_857_Int__Collect:(forall (X_44:com) (A_108:(com->Prop)) (P_6:(com->Prop)), ((iff ((member_com X_44) ((semila513601829_com_o A_108) (collect_com P_6)))) ((and ((member_com X_44) A_108)) (P_6 X_44)))).
% Axiom fact_858_Int__Collect:(forall (X_44:pname) (A_108:(pname->Prop)) (P_6:(pname->Prop)), ((iff ((member_pname X_44) ((semila1673364395name_o A_108) (collect_pname P_6)))) ((and ((member_pname X_44) A_108)) (P_6 X_44)))).
% Axiom fact_859_Int__Collect:(forall (X_44:hoare_1708887482_state) (A_108:(hoare_1708887482_state->Prop)) (P_6:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state X_44) ((semila129691299tate_o A_108) (collec1568722789_state P_6)))) ((and ((member451959335_state X_44) A_108)) (P_6 X_44)))).
% Axiom fact_860_Int__Collect:(forall (X_44:(pname->Prop)) (A_108:((pname->Prop)->Prop)) (P_6:((pname->Prop)->Prop)), ((iff ((member_pname_o X_44) ((semila2013987940me_o_o A_108) (collect_pname_o P_6)))) ((and ((member_pname_o X_44) A_108)) (P_6 X_44)))).
% Axiom fact_861_Int__Collect:(forall (X_44:(hoare_1708887482_state->Prop)) (A_108:((hoare_1708887482_state->Prop)->Prop)) (P_6:((hoare_1708887482_state->Prop)->Prop)), ((iff ((member814030440tate_o X_44) ((semila598060698te_o_o A_108) (collec219771562tate_o P_6)))) ((and ((member814030440tate_o X_44) A_108)) (P_6 X_44)))).
% Axiom fact_862_Collect__conj__eq:(forall (P_5:(hoare_1708887482_state->Prop)) (Q_1:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X_3:hoare_1708887482_state)=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila129691299tate_o (collec1568722789_state P_5)) (collec1568722789_state Q_1)))).
% Axiom fact_863_Collect__conj__eq:(forall (P_5:(pname->Prop)) (Q_1:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_3:pname)=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila1673364395name_o (collect_pname P_5)) (collect_pname Q_1)))).
% Axiom fact_864_Collect__conj__eq:(forall (P_5:((pname->Prop)->Prop)) (Q_1:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_3:(pname->Prop))=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila2013987940me_o_o (collect_pname_o P_5)) (collect_pname_o Q_1)))).
% Axiom fact_865_Collect__conj__eq:(forall (P_5:((hoare_1708887482_state->Prop)->Prop)) (Q_1:((hoare_1708887482_state->Prop)->Prop)), (((eq ((hoare_1708887482_state->Prop)->Prop)) (collec219771562tate_o (fun (X_3:(hoare_1708887482_state->Prop))=> ((and (P_5 X_3)) (Q_1 X_3))))) ((semila598060698te_o_o (collec219771562tate_o P_5)) (collec219771562tate_o Q_1)))).
% Axiom fact_866_Diff__Int:(forall (A_107:(pname->Prop)) (B_63:(pname->Prop)) (C_21:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_107) ((semila1673364395name_o B_63) C_21))) ((semila1780557381name_o ((minus_minus_pname_o A_107) B_63)) ((minus_minus_pname_o A_107) C_21)))).
% Axiom fact_867_Diff__Int:(forall (A_107:(hoare_1708887482_state->Prop)) (B_63:(hoare_1708887482_state->Prop)) (C_21:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_107) ((semila129691299tate_o B_63) C_21))) ((semila1122118281tate_o ((minus_2056855718tate_o A_107) B_63)) ((minus_2056855718tate_o A_107) C_21)))).
% Axiom fact_868_Diff__Un:(forall (A_106:(pname->Prop)) (B_62:(pname->Prop)) (C_20:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_106) ((semila1780557381name_o B_62) C_20))) ((semila1673364395name_o ((minus_minus_pname_o A_106) B_62)) ((minus_minus_pname_o A_106) C_20)))).
% Axiom fact_869_Diff__Un:(forall (A_106:(hoare_1708887482_state->Prop)) (B_62:(hoare_1708887482_state->Prop)) (C_20:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_106) ((semila1122118281tate_o B_62) C_20))) ((semila129691299tate_o ((minus_2056855718tate_o A_106) B_62)) ((minus_2056855718tate_o A_106) C_20)))).
% Axiom fact_870_Un__Diff__Int:(forall (A_105:(pname->Prop)) (B_61:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o A_105) B_61)) ((semila1673364395name_o A_105) B_61))) A_105)).
% Axiom fact_871_Un__Diff__Int:(forall (A_105:(hoare_1708887482_state->Prop)) (B_61:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((minus_2056855718tate_o A_105) B_61)) ((semila129691299tate_o A_105) B_61))) A_105)).
% Axiom fact_872_inf__sup__ord_I1_J:(forall (X_43:Prop) (Y_24:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_43) Y_24)) X_43)).
% Axiom fact_873_inf__sup__ord_I1_J:(forall (X_43:(pname->Prop)) (Y_24:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_43) Y_24)) X_43)).
% Axiom fact_874_inf__sup__ord_I1_J:(forall (X_43:(hoare_1708887482_state->Prop)) (Y_24:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_43) Y_24)) X_43)).
% Axiom fact_875_inf__le1:(forall (X_42:Prop) (Y_23:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_42) Y_23)) X_42)).
% Axiom fact_876_inf__le1:(forall (X_42:(pname->Prop)) (Y_23:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_42) Y_23)) X_42)).
% Axiom fact_877_inf__le1:(forall (X_42:(hoare_1708887482_state->Prop)) (Y_23:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_42) Y_23)) X_42)).
% Axiom fact_878_inf__sup__ord_I2_J:(forall (X_41:Prop) (Y_22:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_41) Y_22)) Y_22)).
% Axiom fact_879_inf__sup__ord_I2_J:(forall (X_41:(pname->Prop)) (Y_22:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_41) Y_22)) Y_22)).
% Axiom fact_880_inf__sup__ord_I2_J:(forall (X_41:(hoare_1708887482_state->Prop)) (Y_22:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_41) Y_22)) Y_22)).
% Axiom fact_881_inf__le2:(forall (X_40:Prop) (Y_21:Prop), ((ord_less_eq_o ((semila854092349_inf_o X_40) Y_21)) Y_21)).
% Axiom fact_882_inf__le2:(forall (X_40:(pname->Prop)) (Y_21:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_40) Y_21)) Y_21)).
% Axiom fact_883_inf__le2:(forall (X_40:(hoare_1708887482_state->Prop)) (Y_21:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o X_40) Y_21)) Y_21)).
% Axiom fact_884_le__iff__inf:(forall (X_39:Prop) (Y_20:Prop), ((iff ((ord_less_eq_o X_39) Y_20)) ((iff ((semila854092349_inf_o X_39) Y_20)) X_39))).
% Axiom fact_885_le__iff__inf:(forall (X_39:(pname->Prop)) (Y_20:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_39) Y_20)) (((eq (pname->Prop)) ((semila1673364395name_o X_39) Y_20)) X_39))).
% Axiom fact_886_le__iff__inf:(forall (X_39:(hoare_1708887482_state->Prop)) (Y_20:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o X_39) Y_20)) (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_39) Y_20)) X_39))).
% Axiom fact_887_le__inf__iff:(forall (X_38:Prop) (Y_19:Prop) (Z_10:Prop), ((iff ((ord_less_eq_o X_38) ((semila854092349_inf_o Y_19) Z_10))) ((and ((ord_less_eq_o X_38) Y_19)) ((ord_less_eq_o X_38) Z_10)))).
% Axiom fact_888_le__inf__iff:(forall (X_38:(pname->Prop)) (Y_19:(pname->Prop)) (Z_10:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_38) ((semila1673364395name_o Y_19) Z_10))) ((and ((ord_less_eq_pname_o X_38) Y_19)) ((ord_less_eq_pname_o X_38) Z_10)))).
% Axiom fact_889_le__inf__iff:(forall (X_38:(hoare_1708887482_state->Prop)) (Y_19:(hoare_1708887482_state->Prop)) (Z_10:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o X_38) ((semila129691299tate_o Y_19) Z_10))) ((and ((ord_le777019615tate_o X_38) Y_19)) ((ord_le777019615tate_o X_38) Z_10)))).
% Axiom fact_890_le__infI1:(forall (B_60:Prop) (A_104:Prop) (X_37:Prop), (((ord_less_eq_o A_104) X_37)->((ord_less_eq_o ((semila854092349_inf_o A_104) B_60)) X_37))).
% Axiom fact_891_le__infI1:(forall (B_60:(pname->Prop)) (A_104:(pname->Prop)) (X_37:(pname->Prop)), (((ord_less_eq_pname_o A_104) X_37)->((ord_less_eq_pname_o ((semila1673364395name_o A_104) B_60)) X_37))).
% Axiom fact_892_le__infI1:(forall (B_60:(hoare_1708887482_state->Prop)) (A_104:(hoare_1708887482_state->Prop)) (X_37:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_104) X_37)->((ord_le777019615tate_o ((semila129691299tate_o A_104) B_60)) X_37))).
% Axiom fact_893_le__infI2:(forall (A_103:Prop) (B_59:Prop) (X_36:Prop), (((ord_less_eq_o B_59) X_36)->((ord_less_eq_o ((semila854092349_inf_o A_103) B_59)) X_36))).
% Axiom fact_894_le__infI2:(forall (A_103:(pname->Prop)) (B_59:(pname->Prop)) (X_36:(pname->Prop)), (((ord_less_eq_pname_o B_59) X_36)->((ord_less_eq_pname_o ((semila1673364395name_o A_103) B_59)) X_36))).
% Axiom fact_895_le__infI2:(forall (A_103:(hoare_1708887482_state->Prop)) (B_59:(hoare_1708887482_state->Prop)) (X_36:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_59) X_36)->((ord_le777019615tate_o ((semila129691299tate_o A_103) B_59)) X_36))).
% Axiom fact_896_inf__absorb1:(forall (X_35:Prop) (Y_18:Prop), (((ord_less_eq_o X_35) Y_18)->((iff ((semila854092349_inf_o X_35) Y_18)) X_35))).
% Axiom fact_897_inf__absorb1:(forall (X_35:(pname->Prop)) (Y_18:(pname->Prop)), (((ord_less_eq_pname_o X_35) Y_18)->(((eq (pname->Prop)) ((semila1673364395name_o X_35) Y_18)) X_35))).
% Axiom fact_898_inf__absorb1:(forall (X_35:(hoare_1708887482_state->Prop)) (Y_18:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_35) Y_18)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_35) Y_18)) X_35))).
% Axiom fact_899_inf__absorb2:(forall (Y_17:Prop) (X_34:Prop), (((ord_less_eq_o Y_17) X_34)->((iff ((semila854092349_inf_o X_34) Y_17)) Y_17))).
% Axiom fact_900_inf__absorb2:(forall (Y_17:(pname->Prop)) (X_34:(pname->Prop)), (((ord_less_eq_pname_o Y_17) X_34)->(((eq (pname->Prop)) ((semila1673364395name_o X_34) Y_17)) Y_17))).
% Axiom fact_901_inf__absorb2:(forall (Y_17:(hoare_1708887482_state->Prop)) (X_34:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o Y_17) X_34)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_34) Y_17)) Y_17))).
% Axiom fact_902_le__infI:(forall (B_58:Prop) (X_33:Prop) (A_102:Prop), (((ord_less_eq_o X_33) A_102)->(((ord_less_eq_o X_33) B_58)->((ord_less_eq_o X_33) ((semila854092349_inf_o A_102) B_58))))).
% Axiom fact_903_le__infI:(forall (B_58:(pname->Prop)) (X_33:(pname->Prop)) (A_102:(pname->Prop)), (((ord_less_eq_pname_o X_33) A_102)->(((ord_less_eq_pname_o X_33) B_58)->((ord_less_eq_pname_o X_33) ((semila1673364395name_o A_102) B_58))))).
% Axiom fact_904_le__infI:(forall (B_58:(hoare_1708887482_state->Prop)) (X_33:(hoare_1708887482_state->Prop)) (A_102:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_33) A_102)->(((ord_le777019615tate_o X_33) B_58)->((ord_le777019615tate_o X_33) ((semila129691299tate_o A_102) B_58))))).
% Axiom fact_905_inf__greatest:(forall (Z_9:Prop) (X_32:Prop) (Y_16:Prop), (((ord_less_eq_o X_32) Y_16)->(((ord_less_eq_o X_32) Z_9)->((ord_less_eq_o X_32) ((semila854092349_inf_o Y_16) Z_9))))).
% Axiom fact_906_inf__greatest:(forall (Z_9:(pname->Prop)) (X_32:(pname->Prop)) (Y_16:(pname->Prop)), (((ord_less_eq_pname_o X_32) Y_16)->(((ord_less_eq_pname_o X_32) Z_9)->((ord_less_eq_pname_o X_32) ((semila1673364395name_o Y_16) Z_9))))).
% Axiom fact_907_inf__greatest:(forall (Z_9:(hoare_1708887482_state->Prop)) (X_32:(hoare_1708887482_state->Prop)) (Y_16:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_32) Y_16)->(((ord_le777019615tate_o X_32) Z_9)->((ord_le777019615tate_o X_32) ((semila129691299tate_o Y_16) Z_9))))).
% Axiom fact_908_inf__mono:(forall (B_57:Prop) (D_2:Prop) (A_101:Prop) (C_19:Prop), (((ord_less_eq_o A_101) C_19)->(((ord_less_eq_o B_57) D_2)->((ord_less_eq_o ((semila854092349_inf_o A_101) B_57)) ((semila854092349_inf_o C_19) D_2))))).
% Axiom fact_909_inf__mono:(forall (B_57:(pname->Prop)) (D_2:(pname->Prop)) (A_101:(pname->Prop)) (C_19:(pname->Prop)), (((ord_less_eq_pname_o A_101) C_19)->(((ord_less_eq_pname_o B_57) D_2)->((ord_less_eq_pname_o ((semila1673364395name_o A_101) B_57)) ((semila1673364395name_o C_19) D_2))))).
% Axiom fact_910_inf__mono:(forall (B_57:(hoare_1708887482_state->Prop)) (D_2:(hoare_1708887482_state->Prop)) (A_101:(hoare_1708887482_state->Prop)) (C_19:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_101) C_19)->(((ord_le777019615tate_o B_57) D_2)->((ord_le777019615tate_o ((semila129691299tate_o A_101) B_57)) ((semila129691299tate_o C_19) D_2))))).
% Axiom fact_911_le__infE:(forall (X_31:Prop) (A_100:Prop) (B_56:Prop), (((ord_less_eq_o X_31) ((semila854092349_inf_o A_100) B_56))->((((ord_less_eq_o X_31) A_100)->(((ord_less_eq_o X_31) B_56)->False))->False))).
% Axiom fact_912_le__infE:(forall (X_31:(pname->Prop)) (A_100:(pname->Prop)) (B_56:(pname->Prop)), (((ord_less_eq_pname_o X_31) ((semila1673364395name_o A_100) B_56))->((((ord_less_eq_pname_o X_31) A_100)->(((ord_less_eq_pname_o X_31) B_56)->False))->False))).
% Axiom fact_913_le__infE:(forall (X_31:(hoare_1708887482_state->Prop)) (A_100:(hoare_1708887482_state->Prop)) (B_56:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o X_31) ((semila129691299tate_o A_100) B_56))->((((ord_le777019615tate_o X_31) A_100)->(((ord_le777019615tate_o X_31) B_56)->False))->False))).
% Axiom fact_914_inf__bot__right:(forall (X_30:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o X_30) bot_bot_com_o)) bot_bot_com_o)).
% Axiom fact_915_inf__bot__right:(forall (X_30:Prop), ((iff ((semila854092349_inf_o X_30) bot_bot_o)) bot_bot_o)).
% Axiom fact_916_inf__bot__right:(forall (X_30:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_30) bot_bot_pname_o)) bot_bot_pname_o)).
% Axiom fact_917_inf__bot__right:(forall (X_30:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_30) bot_bo19817387tate_o)) bot_bo19817387tate_o)).
% Axiom fact_918_inf__bot__left:(forall (X_29:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o bot_bot_com_o) X_29)) bot_bot_com_o)).
% Axiom fact_919_inf__bot__left:(forall (X_29:Prop), ((iff ((semila854092349_inf_o bot_bot_o) X_29)) bot_bot_o)).
% Axiom fact_920_inf__bot__left:(forall (X_29:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) X_29)) bot_bot_pname_o)).
% Axiom fact_921_inf__bot__left:(forall (X_29:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o bot_bo19817387tate_o) X_29)) bot_bo19817387tate_o)).
% Axiom fact_922_inf__sup__absorb:(forall (X_28:Prop) (Y_15:Prop), ((iff ((semila854092349_inf_o X_28) ((semila10642723_sup_o X_28) Y_15))) X_28)).
% Axiom fact_923_inf__sup__absorb:(forall (X_28:(pname->Prop)) (Y_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_28) ((semila1780557381name_o X_28) Y_15))) X_28)).
% Axiom fact_924_inf__sup__absorb:(forall (X_28:(hoare_1708887482_state->Prop)) (Y_15:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_28) ((semila1122118281tate_o X_28) Y_15))) X_28)).
% Axiom fact_925_sup__inf__absorb:(forall (X_27:Prop) (Y_14:Prop), ((iff ((semila10642723_sup_o X_27) ((semila854092349_inf_o X_27) Y_14))) X_27)).
% Axiom fact_926_sup__inf__absorb:(forall (X_27:(pname->Prop)) (Y_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_27) ((semila1673364395name_o X_27) Y_14))) X_27)).
% Axiom fact_927_sup__inf__absorb:(forall (X_27:(hoare_1708887482_state->Prop)) (Y_14:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_27) ((semila129691299tate_o X_27) Y_14))) X_27)).
% Axiom fact_928_inf__sup__distrib1:(forall (X_26:Prop) (Y_13:Prop) (Z_8:Prop), ((iff ((semila854092349_inf_o X_26) ((semila10642723_sup_o Y_13) Z_8))) ((semila10642723_sup_o ((semila854092349_inf_o X_26) Y_13)) ((semila854092349_inf_o X_26) Z_8)))).
% Axiom fact_929_inf__sup__distrib1:(forall (X_26:(pname->Prop)) (Y_13:(pname->Prop)) (Z_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_26) ((semila1780557381name_o Y_13) Z_8))) ((semila1780557381name_o ((semila1673364395name_o X_26) Y_13)) ((semila1673364395name_o X_26) Z_8)))).
% Axiom fact_930_inf__sup__distrib1:(forall (X_26:(hoare_1708887482_state->Prop)) (Y_13:(hoare_1708887482_state->Prop)) (Z_8:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_26) ((semila1122118281tate_o Y_13) Z_8))) ((semila1122118281tate_o ((semila129691299tate_o X_26) Y_13)) ((semila129691299tate_o X_26) Z_8)))).
% Axiom fact_931_sup__inf__distrib1:(forall (X_25:Prop) (Y_12:Prop) (Z_7:Prop), ((iff ((semila10642723_sup_o X_25) ((semila854092349_inf_o Y_12) Z_7))) ((semila854092349_inf_o ((semila10642723_sup_o X_25) Y_12)) ((semila10642723_sup_o X_25) Z_7)))).
% Axiom fact_932_sup__inf__distrib1:(forall (X_25:(pname->Prop)) (Y_12:(pname->Prop)) (Z_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_25) ((semila1673364395name_o Y_12) Z_7))) ((semila1673364395name_o ((semila1780557381name_o X_25) Y_12)) ((semila1780557381name_o X_25) Z_7)))).
% Axiom fact_933_sup__inf__distrib1:(forall (X_25:(hoare_1708887482_state->Prop)) (Y_12:(hoare_1708887482_state->Prop)) (Z_7:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_25) ((semila129691299tate_o Y_12) Z_7))) ((semila129691299tate_o ((semila1122118281tate_o X_25) Y_12)) ((semila1122118281tate_o X_25) Z_7)))).
% Axiom fact_934_inf__sup__distrib2:(forall (Y_11:Prop) (Z_6:Prop) (X_24:Prop), ((iff ((semila854092349_inf_o ((semila10642723_sup_o Y_11) Z_6)) X_24)) ((semila10642723_sup_o ((semila854092349_inf_o Y_11) X_24)) ((semila854092349_inf_o Z_6) X_24)))).
% Axiom fact_935_inf__sup__distrib2:(forall (Y_11:(pname->Prop)) (Z_6:(pname->Prop)) (X_24:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o Y_11) Z_6)) X_24)) ((semila1780557381name_o ((semila1673364395name_o Y_11) X_24)) ((semila1673364395name_o Z_6) X_24)))).
% Axiom fact_936_inf__sup__distrib2:(forall (Y_11:(hoare_1708887482_state->Prop)) (Z_6:(hoare_1708887482_state->Prop)) (X_24:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((semila1122118281tate_o Y_11) Z_6)) X_24)) ((semila1122118281tate_o ((semila129691299tate_o Y_11) X_24)) ((semila129691299tate_o Z_6) X_24)))).
% Axiom fact_937_sup__inf__distrib2:(forall (Y_10:Prop) (Z_5:Prop) (X_23:Prop), ((iff ((semila10642723_sup_o ((semila854092349_inf_o Y_10) Z_5)) X_23)) ((semila854092349_inf_o ((semila10642723_sup_o Y_10) X_23)) ((semila10642723_sup_o Z_5) X_23)))).
% Axiom fact_938_sup__inf__distrib2:(forall (Y_10:(pname->Prop)) (Z_5:(pname->Prop)) (X_23:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o Y_10) Z_5)) X_23)) ((semila1673364395name_o ((semila1780557381name_o Y_10) X_23)) ((semila1780557381name_o Z_5) X_23)))).
% Axiom fact_939_sup__inf__distrib2:(forall (Y_10:(hoare_1708887482_state->Prop)) (Z_5:(hoare_1708887482_state->Prop)) (X_23:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila129691299tate_o Y_10) Z_5)) X_23)) ((semila129691299tate_o ((semila1122118281tate_o Y_10) X_23)) ((semila1122118281tate_o Z_5) X_23)))).
% Axiom fact_940_Diff__cancel:(forall (A_99:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_99) A_99)) bot_bot_com_o)).
% Axiom fact_941_Diff__cancel:(forall (A_99:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_99) A_99)) bot_bot_pname_o)).
% Axiom fact_942_Diff__cancel:(forall (A_99:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_99) A_99)) bot_bo19817387tate_o)).
% Axiom fact_943_Diff__empty:(forall (A_98:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_98) bot_bot_com_o)) A_98)).
% Axiom fact_944_Diff__empty:(forall (A_98:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_98) bot_bot_pname_o)) A_98)).
% Axiom fact_945_Diff__empty:(forall (A_98:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_98) bot_bo19817387tate_o)) A_98)).
% Axiom fact_946_empty__Diff:(forall (A_97:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o bot_bot_com_o) A_97)) bot_bot_com_o)).
% Axiom fact_947_empty__Diff:(forall (A_97:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o bot_bot_pname_o) A_97)) bot_bot_pname_o)).
% Axiom fact_948_empty__Diff:(forall (A_97:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o bot_bo19817387tate_o) A_97)) bot_bo19817387tate_o)).
% Axiom fact_949_finite__Diff2:(forall (A_96:((pname->Prop)->Prop)) (B_55:((pname->Prop)->Prop)), ((finite297249702name_o B_55)->((iff (finite297249702name_o ((minus_1480864103me_o_o A_96) B_55))) (finite297249702name_o A_96)))).
% Axiom fact_950_finite__Diff2:(forall (A_96:((hoare_1708887482_state->Prop)->Prop)) (B_55:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o B_55)->((iff (finite1329924456tate_o ((minus_548038231te_o_o A_96) B_55))) (finite1329924456tate_o A_96)))).
% Axiom fact_951_finite__Diff2:(forall (A_96:(pname->Prop)) (B_55:(pname->Prop)), ((finite_finite_pname B_55)->((iff (finite_finite_pname ((minus_minus_pname_o A_96) B_55))) (finite_finite_pname A_96)))).
% Axiom fact_952_finite__Diff2:(forall (A_96:(hoare_1708887482_state->Prop)) (B_55:(hoare_1708887482_state->Prop)), ((finite1625599783_state B_55)->((iff (finite1625599783_state ((minus_2056855718tate_o A_96) B_55))) (finite1625599783_state A_96)))).
% Axiom fact_953_insert__Diff1:(forall (A_95:(com->Prop)) (X_22:com) (B_54:(com->Prop)), (((member_com X_22) B_54)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_22) A_95)) B_54)) ((minus_minus_com_o A_95) B_54)))).
% Axiom fact_954_insert__Diff1:(forall (A_95:(pname->Prop)) (X_22:pname) (B_54:(pname->Prop)), (((member_pname X_22) B_54)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_22) A_95)) B_54)) ((minus_minus_pname_o A_95) B_54)))).
% Axiom fact_955_insert__Diff1:(forall (A_95:(hoare_1708887482_state->Prop)) (X_22:hoare_1708887482_state) (B_54:(hoare_1708887482_state->Prop)), (((member451959335_state X_22) B_54)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_22) A_95)) B_54)) ((minus_2056855718tate_o A_95) B_54)))).
% Axiom fact_956_insert__Diff__if:(forall (A_94:(com->Prop)) (X_21:com) (B_53:(com->Prop)), ((and (((member_com X_21) B_53)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_21) A_94)) B_53)) ((minus_minus_com_o A_94) B_53)))) ((((member_com X_21) B_53)->False)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_21) A_94)) B_53)) ((insert_com X_21) ((minus_minus_com_o A_94) B_53)))))).
% Axiom fact_957_insert__Diff__if:(forall (A_94:(pname->Prop)) (X_21:pname) (B_53:(pname->Prop)), ((and (((member_pname X_21) B_53)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_21) A_94)) B_53)) ((minus_minus_pname_o A_94) B_53)))) ((((member_pname X_21) B_53)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_21) A_94)) B_53)) ((insert_pname X_21) ((minus_minus_pname_o A_94) B_53)))))).
% Axiom fact_958_insert__Diff__if:(forall (A_94:(hoare_1708887482_state->Prop)) (X_21:hoare_1708887482_state) (B_53:(hoare_1708887482_state->Prop)), ((and (((member451959335_state X_21) B_53)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_21) A_94)) B_53)) ((minus_2056855718tate_o A_94) B_53)))) ((((member451959335_state X_21) B_53)->False)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_21) A_94)) B_53)) ((insert528405184_state X_21) ((minus_2056855718tate_o A_94) B_53)))))).
% Axiom fact_959_disjoint__iff__not__equal:(forall (A_93:(com->Prop)) (B_52:(com->Prop)), ((iff (((eq (com->Prop)) ((semila513601829_com_o A_93) B_52)) bot_bot_com_o)) (forall (X_3:com), (((member_com X_3) A_93)->(forall (Xa:com), (((member_com Xa) B_52)->(not (((eq com) X_3) Xa)))))))).
% Axiom fact_960_disjoint__iff__not__equal:(forall (A_93:(pname->Prop)) (B_52:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1673364395name_o A_93) B_52)) bot_bot_pname_o)) (forall (X_3:pname), (((member_pname X_3) A_93)->(forall (Xa:pname), (((member_pname Xa) B_52)->(not (((eq pname) X_3) Xa)))))))).
% Axiom fact_961_disjoint__iff__not__equal:(forall (A_93:(hoare_1708887482_state->Prop)) (B_52:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_93) B_52)) bot_bo19817387tate_o)) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_93)->(forall (Xa:hoare_1708887482_state), (((member451959335_state Xa) B_52)->(not (((eq hoare_1708887482_state) X_3) Xa)))))))).
% Axiom fact_962_Int__empty__right:(forall (A_92:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o A_92) bot_bot_com_o)) bot_bot_com_o)).
% Axiom fact_963_Int__empty__right:(forall (A_92:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_92) bot_bot_pname_o)) bot_bot_pname_o)).
% Axiom fact_964_Int__empty__right:(forall (A_92:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_92) bot_bo19817387tate_o)) bot_bo19817387tate_o)).
% Axiom fact_965_Int__empty__left:(forall (B_51:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o bot_bot_com_o) B_51)) bot_bot_com_o)).
% Axiom fact_966_Int__empty__left:(forall (B_51:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) B_51)) bot_bot_pname_o)).
% Axiom fact_967_Int__empty__left:(forall (B_51:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o bot_bo19817387tate_o) B_51)) bot_bo19817387tate_o)).
% Axiom fact_968_double__diff:(forall (C_18:(pname->Prop)) (A_91:(pname->Prop)) (B_50:(pname->Prop)), (((ord_less_eq_pname_o A_91) B_50)->(((ord_less_eq_pname_o B_50) C_18)->(((eq (pname->Prop)) ((minus_minus_pname_o B_50) ((minus_minus_pname_o C_18) A_91))) A_91)))).
% Axiom fact_969_double__diff:(forall (C_18:(hoare_1708887482_state->Prop)) (A_91:(hoare_1708887482_state->Prop)) (B_50:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_91) B_50)->(((ord_le777019615tate_o B_50) C_18)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o B_50) ((minus_2056855718tate_o C_18) A_91))) A_91)))).
% Axiom fact_970_Diff__mono:(forall (D_1:(pname->Prop)) (B_49:(pname->Prop)) (A_90:(pname->Prop)) (C_17:(pname->Prop)), (((ord_less_eq_pname_o A_90) C_17)->(((ord_less_eq_pname_o D_1) B_49)->((ord_less_eq_pname_o ((minus_minus_pname_o A_90) B_49)) ((minus_minus_pname_o C_17) D_1))))).
% Axiom fact_971_Diff__mono:(forall (D_1:(hoare_1708887482_state->Prop)) (B_49:(hoare_1708887482_state->Prop)) (A_90:(hoare_1708887482_state->Prop)) (C_17:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_90) C_17)->(((ord_le777019615tate_o D_1) B_49)->((ord_le777019615tate_o ((minus_2056855718tate_o A_90) B_49)) ((minus_2056855718tate_o C_17) D_1))))).
% Axiom fact_972_Diff__subset:(forall (A_89:(pname->Prop)) (B_48:(pname->Prop)), ((ord_less_eq_pname_o ((minus_minus_pname_o A_89) B_48)) A_89)).
% Axiom fact_973_Diff__subset:(forall (A_89:(hoare_1708887482_state->Prop)) (B_48:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((minus_2056855718tate_o A_89) B_48)) A_89)).
% Axiom fact_974_Un__Diff:(forall (A_88:(pname->Prop)) (B_47:(pname->Prop)) (C_16:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o ((semila1780557381name_o A_88) B_47)) C_16)) ((semila1780557381name_o ((minus_minus_pname_o A_88) C_16)) ((minus_minus_pname_o B_47) C_16)))).
% Axiom fact_975_Un__Diff:(forall (A_88:(hoare_1708887482_state->Prop)) (B_47:(hoare_1708887482_state->Prop)) (C_16:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((semila1122118281tate_o A_88) B_47)) C_16)) ((semila1122118281tate_o ((minus_2056855718tate_o A_88) C_16)) ((minus_2056855718tate_o B_47) C_16)))).
% Axiom fact_976_Un__Diff__cancel2:(forall (B_46:(pname->Prop)) (A_87:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o B_46) A_87)) A_87)) ((semila1780557381name_o B_46) A_87))).
% Axiom fact_977_Un__Diff__cancel2:(forall (B_46:(hoare_1708887482_state->Prop)) (A_87:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((minus_2056855718tate_o B_46) A_87)) A_87)) ((semila1122118281tate_o B_46) A_87))).
% Axiom fact_978_Un__Diff__cancel:(forall (A_86:(pname->Prop)) (B_45:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_86) ((minus_minus_pname_o B_45) A_86))) ((semila1780557381name_o A_86) B_45))).
% Axiom fact_979_Un__Diff__cancel:(forall (A_86:(hoare_1708887482_state->Prop)) (B_45:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_86) ((minus_2056855718tate_o B_45) A_86))) ((semila1122118281tate_o A_86) B_45))).
% Axiom fact_980_Int__insert__left__if1:(forall (B_44:(com->Prop)) (A_85:com) (C_15:(com->Prop)), (((member_com A_85) C_15)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_85) B_44)) C_15)) ((insert_com A_85) ((semila513601829_com_o B_44) C_15))))).
% Axiom fact_981_Int__insert__left__if1:(forall (B_44:(pname->Prop)) (A_85:pname) (C_15:(pname->Prop)), (((member_pname A_85) C_15)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_85) B_44)) C_15)) ((insert_pname A_85) ((semila1673364395name_o B_44) C_15))))).
% Axiom fact_982_Int__insert__left__if1:(forall (B_44:(hoare_1708887482_state->Prop)) (A_85:hoare_1708887482_state) (C_15:(hoare_1708887482_state->Prop)), (((member451959335_state A_85) C_15)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_85) B_44)) C_15)) ((insert528405184_state A_85) ((semila129691299tate_o B_44) C_15))))).
% Axiom fact_983_Int__insert__right__if1:(forall (B_43:(com->Prop)) (A_84:com) (A_83:(com->Prop)), (((member_com A_84) A_83)->(((eq (com->Prop)) ((semila513601829_com_o A_83) ((insert_com A_84) B_43))) ((insert_com A_84) ((semila513601829_com_o A_83) B_43))))).
% Axiom fact_984_Int__insert__right__if1:(forall (B_43:(pname->Prop)) (A_84:pname) (A_83:(pname->Prop)), (((member_pname A_84) A_83)->(((eq (pname->Prop)) ((semila1673364395name_o A_83) ((insert_pname A_84) B_43))) ((insert_pname A_84) ((semila1673364395name_o A_83) B_43))))).
% Axiom fact_985_Int__insert__right__if1:(forall (B_43:(hoare_1708887482_state->Prop)) (A_84:hoare_1708887482_state) (A_83:(hoare_1708887482_state->Prop)), (((member451959335_state A_84) A_83)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_83) ((insert528405184_state A_84) B_43))) ((insert528405184_state A_84) ((semila129691299tate_o A_83) B_43))))).
% Axiom fact_986_Int__insert__left__if0:(forall (B_42:(com->Prop)) (A_82:com) (C_14:(com->Prop)), ((((member_com A_82) C_14)->False)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_82) B_42)) C_14)) ((semila513601829_com_o B_42) C_14)))).
% Axiom fact_987_Int__insert__left__if0:(forall (B_42:(pname->Prop)) (A_82:pname) (C_14:(pname->Prop)), ((((member_pname A_82) C_14)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_82) B_42)) C_14)) ((semila1673364395name_o B_42) C_14)))).
% Axiom fact_988_Int__insert__left__if0:(forall (B_42:(hoare_1708887482_state->Prop)) (A_82:hoare_1708887482_state) (C_14:(hoare_1708887482_state->Prop)), ((((member451959335_state A_82) C_14)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_82) B_42)) C_14)) ((semila129691299tate_o B_42) C_14)))).
% Axiom fact_989_Int__insert__right__if0:(forall (B_41:(com->Prop)) (A_81:com) (A_80:(com->Prop)), ((((member_com A_81) A_80)->False)->(((eq (com->Prop)) ((semila513601829_com_o A_80) ((insert_com A_81) B_41))) ((semila513601829_com_o A_80) B_41)))).
% Axiom fact_990_Int__insert__right__if0:(forall (B_41:(pname->Prop)) (A_81:pname) (A_80:(pname->Prop)), ((((member_pname A_81) A_80)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_80) ((insert_pname A_81) B_41))) ((semila1673364395name_o A_80) B_41)))).
% Axiom fact_991_Int__insert__right__if0:(forall (B_41:(hoare_1708887482_state->Prop)) (A_81:hoare_1708887482_state) (A_80:(hoare_1708887482_state->Prop)), ((((member451959335_state A_81) A_80)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_80) ((insert528405184_state A_81) B_41))) ((semila129691299tate_o A_80) B_41)))).
% Axiom fact_992_insert__inter__insert:(forall (A_79:com) (A_78:(com->Prop)) (B_40:(com->Prop)), (((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_79) A_78)) ((insert_com A_79) B_40))) ((insert_com A_79) ((semila513601829_com_o A_78) B_40)))).
% Axiom fact_993_insert__inter__insert:(forall (A_79:pname) (A_78:(pname->Prop)) (B_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_79) A_78)) ((insert_pname A_79) B_40))) ((insert_pname A_79) ((semila1673364395name_o A_78) B_40)))).
% Axiom fact_994_insert__inter__insert:(forall (A_79:hoare_1708887482_state) (A_78:(hoare_1708887482_state->Prop)) (B_40:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_79) A_78)) ((insert528405184_state A_79) B_40))) ((insert528405184_state A_79) ((semila129691299tate_o A_78) B_40)))).
% Axiom fact_995_Int__insert__left:(forall (B_39:(com->Prop)) (A_77:com) (C_13:(com->Prop)), ((and (((member_com A_77) C_13)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_77) B_39)) C_13)) ((insert_com A_77) ((semila513601829_com_o B_39) C_13))))) ((((member_com A_77) C_13)->False)->(((eq (com->Prop)) ((semila513601829_com_o ((insert_com A_77) B_39)) C_13)) ((semila513601829_com_o B_39) C_13))))).
% Axiom fact_996_Int__insert__left:(forall (B_39:(pname->Prop)) (A_77:pname) (C_13:(pname->Prop)), ((and (((member_pname A_77) C_13)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_77) B_39)) C_13)) ((insert_pname A_77) ((semila1673364395name_o B_39) C_13))))) ((((member_pname A_77) C_13)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_77) B_39)) C_13)) ((semila1673364395name_o B_39) C_13))))).
% Axiom fact_997_Int__insert__left:(forall (B_39:(hoare_1708887482_state->Prop)) (A_77:hoare_1708887482_state) (C_13:(hoare_1708887482_state->Prop)), ((and (((member451959335_state A_77) C_13)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_77) B_39)) C_13)) ((insert528405184_state A_77) ((semila129691299tate_o B_39) C_13))))) ((((member451959335_state A_77) C_13)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((insert528405184_state A_77) B_39)) C_13)) ((semila129691299tate_o B_39) C_13))))).
% Axiom fact_998_Int__insert__right:(forall (B_38:(com->Prop)) (A_76:com) (A_75:(com->Prop)), ((and (((member_com A_76) A_75)->(((eq (com->Prop)) ((semila513601829_com_o A_75) ((insert_com A_76) B_38))) ((insert_com A_76) ((semila513601829_com_o A_75) B_38))))) ((((member_com A_76) A_75)->False)->(((eq (com->Prop)) ((semila513601829_com_o A_75) ((insert_com A_76) B_38))) ((semila513601829_com_o A_75) B_38))))).
% Axiom fact_999_Int__insert__right:(forall (B_38:(pname->Prop)) (A_76:pname) (A_75:(pname->Prop)), ((and (((member_pname A_76) A_75)->(((eq (pname->Prop)) ((semila1673364395name_o A_75) ((insert_pname A_76) B_38))) ((insert_pname A_76) ((semila1673364395name_o A_75) B_38))))) ((((member_pname A_76) A_75)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_75) ((insert_pname A_76) B_38))) ((semila1673364395name_o A_75) B_38))))).
% Axiom fact_1000_Int__insert__right:(forall (B_38:(hoare_1708887482_state->Prop)) (A_76:hoare_1708887482_state) (A_75:(hoare_1708887482_state->Prop)), ((and (((member451959335_state A_76) A_75)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_75) ((insert528405184_state A_76) B_38))) ((insert528405184_state A_76) ((semila129691299tate_o A_75) B_38))))) ((((member451959335_state A_76) A_75)->False)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_75) ((insert528405184_state A_76) B_38))) ((semila129691299tate_o A_75) B_38))))).
% Axiom fact_1001_Int__mono:(forall (B_37:(pname->Prop)) (D:(pname->Prop)) (A_74:(pname->Prop)) (C_12:(pname->Prop)), (((ord_less_eq_pname_o A_74) C_12)->(((ord_less_eq_pname_o B_37) D)->((ord_less_eq_pname_o ((semila1673364395name_o A_74) B_37)) ((semila1673364395name_o C_12) D))))).
% Axiom fact_1002_Int__mono:(forall (B_37:(hoare_1708887482_state->Prop)) (D:(hoare_1708887482_state->Prop)) (A_74:(hoare_1708887482_state->Prop)) (C_12:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_74) C_12)->(((ord_le777019615tate_o B_37) D)->((ord_le777019615tate_o ((semila129691299tate_o A_74) B_37)) ((semila129691299tate_o C_12) D))))).
% Axiom fact_1003_Int__greatest:(forall (B_36:(pname->Prop)) (C_11:(pname->Prop)) (A_73:(pname->Prop)), (((ord_less_eq_pname_o C_11) A_73)->(((ord_less_eq_pname_o C_11) B_36)->((ord_less_eq_pname_o C_11) ((semila1673364395name_o A_73) B_36))))).
% Axiom fact_1004_Int__greatest:(forall (B_36:(hoare_1708887482_state->Prop)) (C_11:(hoare_1708887482_state->Prop)) (A_73:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o C_11) A_73)->(((ord_le777019615tate_o C_11) B_36)->((ord_le777019615tate_o C_11) ((semila129691299tate_o A_73) B_36))))).
% Axiom fact_1005_Int__absorb1:(forall (B_35:(pname->Prop)) (A_72:(pname->Prop)), (((ord_less_eq_pname_o B_35) A_72)->(((eq (pname->Prop)) ((semila1673364395name_o A_72) B_35)) B_35))).
% Axiom fact_1006_Int__absorb1:(forall (B_35:(hoare_1708887482_state->Prop)) (A_72:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o B_35) A_72)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_72) B_35)) B_35))).
% Axiom fact_1007_Int__absorb2:(forall (A_71:(pname->Prop)) (B_34:(pname->Prop)), (((ord_less_eq_pname_o A_71) B_34)->(((eq (pname->Prop)) ((semila1673364395name_o A_71) B_34)) A_71))).
% Axiom fact_1008_Int__absorb2:(forall (A_71:(hoare_1708887482_state->Prop)) (B_34:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_71) B_34)->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_71) B_34)) A_71))).
% Axiom fact_1009_Int__lower2:(forall (A_70:(pname->Prop)) (B_33:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_70) B_33)) B_33)).
% Axiom fact_1010_Int__lower2:(forall (A_70:(hoare_1708887482_state->Prop)) (B_33:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o A_70) B_33)) B_33)).
% Axiom fact_1011_Int__lower1:(forall (A_69:(pname->Prop)) (B_32:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_69) B_32)) A_69)).
% Axiom fact_1012_Int__lower1:(forall (A_69:(hoare_1708887482_state->Prop)) (B_32:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila129691299tate_o A_69) B_32)) A_69)).
% Axiom fact_1013_Un__Int__crazy:(forall (A_68:(pname->Prop)) (B_31:(pname->Prop)) (C_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o ((semila1673364395name_o A_68) B_31)) ((semila1673364395name_o B_31) C_10))) ((semila1673364395name_o C_10) A_68))) ((semila1673364395name_o ((semila1673364395name_o ((semila1780557381name_o A_68) B_31)) ((semila1780557381name_o B_31) C_10))) ((semila1780557381name_o C_10) A_68)))).
% Axiom fact_1014_Un__Int__crazy:(forall (A_68:(hoare_1708887482_state->Prop)) (B_31:(hoare_1708887482_state->Prop)) (C_10:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o ((semila129691299tate_o A_68) B_31)) ((semila129691299tate_o B_31) C_10))) ((semila129691299tate_o C_10) A_68))) ((semila129691299tate_o ((semila129691299tate_o ((semila1122118281tate_o A_68) B_31)) ((semila1122118281tate_o B_31) C_10))) ((semila1122118281tate_o C_10) A_68)))).
% Axiom fact_1015_Un__Int__distrib2:(forall (B_30:(pname->Prop)) (C_9:(pname->Prop)) (A_67:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o B_30) C_9)) A_67)) ((semila1673364395name_o ((semila1780557381name_o B_30) A_67)) ((semila1780557381name_o C_9) A_67)))).
% Axiom fact_1016_Un__Int__distrib2:(forall (B_30:(hoare_1708887482_state->Prop)) (C_9:(hoare_1708887482_state->Prop)) (A_67:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila129691299tate_o B_30) C_9)) A_67)) ((semila129691299tate_o ((semila1122118281tate_o B_30) A_67)) ((semila1122118281tate_o C_9) A_67)))).
% Axiom fact_1017_Int__Un__distrib2:(forall (B_29:(pname->Prop)) (C_8:(pname->Prop)) (A_66:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o B_29) C_8)) A_66)) ((semila1780557381name_o ((semila1673364395name_o B_29) A_66)) ((semila1673364395name_o C_8) A_66)))).
% Axiom fact_1018_Int__Un__distrib2:(forall (B_29:(hoare_1708887482_state->Prop)) (C_8:(hoare_1708887482_state->Prop)) (A_66:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((semila1122118281tate_o B_29) C_8)) A_66)) ((semila1122118281tate_o ((semila129691299tate_o B_29) A_66)) ((semila129691299tate_o C_8) A_66)))).
% Axiom fact_1019_Un__Int__distrib:(forall (A_65:(pname->Prop)) (B_28:(pname->Prop)) (C_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_65) ((semila1673364395name_o B_28) C_7))) ((semila1673364395name_o ((semila1780557381name_o A_65) B_28)) ((semila1780557381name_o A_65) C_7)))).
% Axiom fact_1020_Un__Int__distrib:(forall (A_65:(hoare_1708887482_state->Prop)) (B_28:(hoare_1708887482_state->Prop)) (C_7:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_65) ((semila129691299tate_o B_28) C_7))) ((semila129691299tate_o ((semila1122118281tate_o A_65) B_28)) ((semila1122118281tate_o A_65) C_7)))).
% Axiom fact_1021_Int__Un__distrib:(forall (A_64:(pname->Prop)) (B_27:(pname->Prop)) (C_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_64) ((semila1780557381name_o B_27) C_6))) ((semila1780557381name_o ((semila1673364395name_o A_64) B_27)) ((semila1673364395name_o A_64) C_6)))).
% Axiom fact_1022_Int__Un__distrib:(forall (A_64:(hoare_1708887482_state->Prop)) (B_27:(hoare_1708887482_state->Prop)) (C_6:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_64) ((semila1122118281tate_o B_27) C_6))) ((semila1122118281tate_o ((semila129691299tate_o A_64) B_27)) ((semila129691299tate_o A_64) C_6)))).
% Axiom fact_1023_distrib__inf__le:(forall (X_20:Prop) (Y_9:Prop) (Z_4:Prop), ((ord_less_eq_o ((semila10642723_sup_o ((semila854092349_inf_o X_20) Y_9)) ((semila854092349_inf_o X_20) Z_4))) ((semila854092349_inf_o X_20) ((semila10642723_sup_o Y_9) Z_4)))).
% Axiom fact_1024_distrib__inf__le:(forall (X_20:(pname->Prop)) (Y_9:(pname->Prop)) (Z_4:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o ((semila1673364395name_o X_20) Y_9)) ((semila1673364395name_o X_20) Z_4))) ((semila1673364395name_o X_20) ((semila1780557381name_o Y_9) Z_4)))).
% Axiom fact_1025_distrib__inf__le:(forall (X_20:(hoare_1708887482_state->Prop)) (Y_9:(hoare_1708887482_state->Prop)) (Z_4:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila1122118281tate_o ((semila129691299tate_o X_20) Y_9)) ((semila129691299tate_o X_20) Z_4))) ((semila129691299tate_o X_20) ((semila1122118281tate_o Y_9) Z_4)))).
% Axiom fact_1026_distrib__sup__le:(forall (X_19:Prop) (Y_8:Prop) (Z_3:Prop), ((ord_less_eq_o ((semila10642723_sup_o X_19) ((semila854092349_inf_o Y_8) Z_3))) ((semila854092349_inf_o ((semila10642723_sup_o X_19) Y_8)) ((semila10642723_sup_o X_19) Z_3)))).
% Axiom fact_1027_distrib__sup__le:(forall (X_19:(pname->Prop)) (Y_8:(pname->Prop)) (Z_3:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o X_19) ((semila1673364395name_o Y_8) Z_3))) ((semila1673364395name_o ((semila1780557381name_o X_19) Y_8)) ((semila1780557381name_o X_19) Z_3)))).
% Axiom fact_1028_distrib__sup__le:(forall (X_19:(hoare_1708887482_state->Prop)) (Y_8:(hoare_1708887482_state->Prop)) (Z_3:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((semila1122118281tate_o X_19) ((semila129691299tate_o Y_8) Z_3))) ((semila129691299tate_o ((semila1122118281tate_o X_19) Y_8)) ((semila1122118281tate_o X_19) Z_3)))).
% Axiom fact_1029_insert__Diff:(forall (A_63:com) (A_62:(com->Prop)), (((member_com A_63) A_62)->(((eq (com->Prop)) ((insert_com A_63) ((minus_minus_com_o A_62) ((insert_com A_63) bot_bot_com_o)))) A_62))).
% Axiom fact_1030_insert__Diff:(forall (A_63:pname) (A_62:(pname->Prop)), (((member_pname A_63) A_62)->(((eq (pname->Prop)) ((insert_pname A_63) ((minus_minus_pname_o A_62) ((insert_pname A_63) bot_bot_pname_o)))) A_62))).
% Axiom fact_1031_insert__Diff:(forall (A_63:hoare_1708887482_state) (A_62:(hoare_1708887482_state->Prop)), (((member451959335_state A_63) A_62)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_63) ((minus_2056855718tate_o A_62) ((insert528405184_state A_63) bot_bo19817387tate_o)))) A_62))).
% Axiom fact_1032_Diff__insert__absorb:(forall (X_18:com) (A_61:(com->Prop)), ((((member_com X_18) A_61)->False)->(((eq (com->Prop)) ((minus_minus_com_o ((insert_com X_18) A_61)) ((insert_com X_18) bot_bot_com_o))) A_61))).
% Axiom fact_1033_Diff__insert__absorb:(forall (X_18:pname) (A_61:(pname->Prop)), ((((member_pname X_18) A_61)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_18) A_61)) ((insert_pname X_18) bot_bot_pname_o))) A_61))).
% Axiom fact_1034_Diff__insert__absorb:(forall (X_18:hoare_1708887482_state) (A_61:(hoare_1708887482_state->Prop)), ((((member451959335_state X_18) A_61)->False)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o ((insert528405184_state X_18) A_61)) ((insert528405184_state X_18) bot_bo19817387tate_o))) A_61))).
% Axiom fact_1035_insert__Diff__single:(forall (A_60:com) (A_59:(com->Prop)), (((eq (com->Prop)) ((insert_com A_60) ((minus_minus_com_o A_59) ((insert_com A_60) bot_bot_com_o)))) ((insert_com A_60) A_59))).
% Axiom fact_1036_insert__Diff__single:(forall (A_60:pname) (A_59:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_60) ((minus_minus_pname_o A_59) ((insert_pname A_60) bot_bot_pname_o)))) ((insert_pname A_60) A_59))).
% Axiom fact_1037_insert__Diff__single:(forall (A_60:hoare_1708887482_state) (A_59:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_60) ((minus_2056855718tate_o A_59) ((insert528405184_state A_60) bot_bo19817387tate_o)))) ((insert528405184_state A_60) A_59))).
% Axiom fact_1038_Diff__insert2:(forall (A_58:(com->Prop)) (A_57:com) (B_26:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_58) ((insert_com A_57) B_26))) ((minus_minus_com_o ((minus_minus_com_o A_58) ((insert_com A_57) bot_bot_com_o))) B_26))).
% Axiom fact_1039_Diff__insert2:(forall (A_58:(pname->Prop)) (A_57:pname) (B_26:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_58) ((insert_pname A_57) B_26))) ((minus_minus_pname_o ((minus_minus_pname_o A_58) ((insert_pname A_57) bot_bot_pname_o))) B_26))).
% Axiom fact_1040_Diff__insert2:(forall (A_58:(hoare_1708887482_state->Prop)) (A_57:hoare_1708887482_state) (B_26:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_58) ((insert528405184_state A_57) B_26))) ((minus_2056855718tate_o ((minus_2056855718tate_o A_58) ((insert528405184_state A_57) bot_bo19817387tate_o))) B_26))).
% Axiom fact_1041_Diff__insert:(forall (A_56:(com->Prop)) (A_55:com) (B_25:(com->Prop)), (((eq (com->Prop)) ((minus_minus_com_o A_56) ((insert_com A_55) B_25))) ((minus_minus_com_o ((minus_minus_com_o A_56) B_25)) ((insert_com A_55) bot_bot_com_o)))).
% Axiom fact_1042_Diff__insert:(forall (A_56:(pname->Prop)) (A_55:pname) (B_25:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_56) ((insert_pname A_55) B_25))) ((minus_minus_pname_o ((minus_minus_pname_o A_56) B_25)) ((insert_pname A_55) bot_bot_pname_o)))).
% Axiom fact_1043_Diff__insert:(forall (A_56:(hoare_1708887482_state->Prop)) (A_55:hoare_1708887482_state) (B_25:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_56) ((insert528405184_state A_55) B_25))) ((minus_2056855718tate_o ((minus_2056855718tate_o A_56) B_25)) ((insert528405184_state A_55) bot_bo19817387tate_o)))).
% Axiom fact_1044_finite__Diff__insert:(forall (A_54:(com->Prop)) (A_53:com) (B_24:(com->Prop)), ((iff (finite_finite_com ((minus_minus_com_o A_54) ((insert_com A_53) B_24)))) (finite_finite_com ((minus_minus_com_o A_54) B_24)))).
% Axiom fact_1045_finite__Diff__insert:(forall (A_54:(pname->Prop)) (A_53:pname) (B_24:(pname->Prop)), ((iff (finite_finite_pname ((minus_minus_pname_o A_54) ((insert_pname A_53) B_24)))) (finite_finite_pname ((minus_minus_pname_o A_54) B_24)))).
% Axiom fact_1046_finite__Diff__insert:(forall (A_54:(hoare_1708887482_state->Prop)) (A_53:hoare_1708887482_state) (B_24:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((minus_2056855718tate_o A_54) ((insert528405184_state A_53) B_24)))) (finite1625599783_state ((minus_2056855718tate_o A_54) B_24)))).
% Axiom fact_1047_finite__Diff__insert:(forall (A_54:((pname->Prop)->Prop)) (A_53:(pname->Prop)) (B_24:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((minus_1480864103me_o_o A_54) ((insert_pname_o A_53) B_24)))) (finite297249702name_o ((minus_1480864103me_o_o A_54) B_24)))).
% Axiom fact_1048_finite__Diff__insert:(forall (A_54:((hoare_1708887482_state->Prop)->Prop)) (A_53:(hoare_1708887482_state->Prop)) (B_24:((hoare_1708887482_state->Prop)->Prop)), ((iff (finite1329924456tate_o ((minus_548038231te_o_o A_54) ((insert949073679tate_o A_53) B_24)))) (finite1329924456tate_o ((minus_548038231te_o_o A_54) B_24)))).
% Axiom fact_1049_image__diff__subset:(forall (F_27:(pname->hoare_1708887482_state)) (A_52:(pname->Prop)) (B_23:(pname->Prop)), ((ord_le777019615tate_o ((minus_2056855718tate_o ((image_1116629049_state F_27) A_52)) ((image_1116629049_state F_27) B_23))) ((image_1116629049_state F_27) ((minus_minus_pname_o A_52) B_23)))).
% Axiom fact_1050_Diff__partition:(forall (A_51:(pname->Prop)) (B_22:(pname->Prop)), (((ord_less_eq_pname_o A_51) B_22)->(((eq (pname->Prop)) ((semila1780557381name_o A_51) ((minus_minus_pname_o B_22) A_51))) B_22))).
% Axiom fact_1051_Diff__partition:(forall (A_51:(hoare_1708887482_state->Prop)) (B_22:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_51) B_22)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_51) ((minus_2056855718tate_o B_22) A_51))) B_22))).
% Axiom fact_1052_Diff__subset__conv:(forall (A_50:(pname->Prop)) (B_21:(pname->Prop)) (C_5:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((minus_minus_pname_o A_50) B_21)) C_5)) ((ord_less_eq_pname_o A_50) ((semila1780557381name_o B_21) C_5)))).
% Axiom fact_1053_Diff__subset__conv:(forall (A_50:(hoare_1708887482_state->Prop)) (B_21:(hoare_1708887482_state->Prop)) (C_5:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o ((minus_2056855718tate_o A_50) B_21)) C_5)) ((ord_le777019615tate_o A_50) ((semila1122118281tate_o B_21) C_5)))).
% Axiom fact_1054_image__Int__subset:(forall (F_26:(pname->hoare_1708887482_state)) (A_49:(pname->Prop)) (B_20:(pname->Prop)), ((ord_le777019615tate_o ((image_1116629049_state F_26) ((semila1673364395name_o A_49) B_20))) ((semila129691299tate_o ((image_1116629049_state F_26) A_49)) ((image_1116629049_state F_26) B_20)))).
% Axiom fact_1055_Un__Int__assoc__eq:(forall (A_48:(pname->Prop)) (B_19:(pname->Prop)) (C_4:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o A_48) B_19)) C_4)) ((semila1673364395name_o A_48) ((semila1780557381name_o B_19) C_4)))) ((ord_less_eq_pname_o C_4) A_48))).
% Axiom fact_1056_Un__Int__assoc__eq:(forall (A_48:(hoare_1708887482_state->Prop)) (B_19:(hoare_1708887482_state->Prop)) (C_4:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila129691299tate_o A_48) B_19)) C_4)) ((semila129691299tate_o A_48) ((semila1122118281tate_o B_19) C_4)))) ((ord_le777019615tate_o C_4) A_48))).
% Axiom fact_1057_if__image__distrib:(forall (P_4:(pname->Prop)) (F_25:(pname->hoare_1708887482_state)) (G_4:(pname->hoare_1708887482_state)) (S:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X_3:pname)=> (((if_Hoa1374726218_state (P_4 X_3)) (F_25 X_3)) (G_4 X_3)))) S)) ((semila1122118281tate_o ((image_1116629049_state F_25) ((semila1673364395name_o S) (collect_pname P_4)))) ((image_1116629049_state G_4) ((semila1673364395name_o S) (collect_pname (fun (X_3:pname)=> (not (P_4 X_3))))))))).
% Axiom fact_1058_dom__if:(forall (P_3:(pname->Prop)) (F_24:(pname->option_com)) (G_3:(pname->option_com)), (((eq (pname->Prop)) (dom_pname_com (fun (X_3:pname)=> (((if_option_com (P_3 X_3)) (F_24 X_3)) (G_3 X_3))))) ((semila1780557381name_o ((semila1673364395name_o (dom_pname_com F_24)) (collect_pname P_3))) ((semila1673364395name_o (dom_pname_com G_3)) (collect_pname (fun (X_3:pname)=> (not (P_3 X_3)))))))).
% Axiom fact_1059_diff__single__insert:(forall (A_47:(com->Prop)) (X_17:com) (B_18:(com->Prop)), (((ord_less_eq_com_o ((minus_minus_com_o A_47) ((insert_com X_17) bot_bot_com_o))) B_18)->(((member_com X_17) A_47)->((ord_less_eq_com_o A_47) ((insert_com X_17) B_18))))).
% Axiom fact_1060_diff__single__insert:(forall (A_47:(pname->Prop)) (X_17:pname) (B_18:(pname->Prop)), (((ord_less_eq_pname_o ((minus_minus_pname_o A_47) ((insert_pname X_17) bot_bot_pname_o))) B_18)->(((member_pname X_17) A_47)->((ord_less_eq_pname_o A_47) ((insert_pname X_17) B_18))))).
% Axiom fact_1061_diff__single__insert:(forall (A_47:(hoare_1708887482_state->Prop)) (X_17:hoare_1708887482_state) (B_18:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o ((minus_2056855718tate_o A_47) ((insert528405184_state X_17) bot_bo19817387tate_o))) B_18)->(((member451959335_state X_17) A_47)->((ord_le777019615tate_o A_47) ((insert528405184_state X_17) B_18))))).
% Axiom fact_1062_subset__insert__iff:(forall (A_46:(com->Prop)) (X_16:com) (B_17:(com->Prop)), ((iff ((ord_less_eq_com_o A_46) ((insert_com X_16) B_17))) ((and (((member_com X_16) A_46)->((ord_less_eq_com_o ((minus_minus_com_o A_46) ((insert_com X_16) bot_bot_com_o))) B_17))) ((((member_com X_16) A_46)->False)->((ord_less_eq_com_o A_46) B_17))))).
% Axiom fact_1063_subset__insert__iff:(forall (A_46:(pname->Prop)) (X_16:pname) (B_17:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_46) ((insert_pname X_16) B_17))) ((and (((member_pname X_16) A_46)->((ord_less_eq_pname_o ((minus_minus_pname_o A_46) ((insert_pname X_16) bot_bot_pname_o))) B_17))) ((((member_pname X_16) A_46)->False)->((ord_less_eq_pname_o A_46) B_17))))).
% Axiom fact_1064_subset__insert__iff:(forall (A_46:(hoare_1708887482_state->Prop)) (X_16:hoare_1708887482_state) (B_17:(hoare_1708887482_state->Prop)), ((iff ((ord_le777019615tate_o A_46) ((insert528405184_state X_16) B_17))) ((and (((member451959335_state X_16) A_46)->((ord_le777019615tate_o ((minus_2056855718tate_o A_46) ((insert528405184_state X_16) bot_bo19817387tate_o))) B_17))) ((((member451959335_state X_16) A_46)->False)->((ord_le777019615tate_o A_46) B_17))))).
% Axiom fact_1065_finite__empty__induct:(forall (P_2:((com->Prop)->Prop)) (A_45:(com->Prop)), ((finite_finite_com A_45)->((P_2 A_45)->((forall (A_6:com) (A_39:(com->Prop)), ((finite_finite_com A_39)->(((member_com A_6) A_39)->((P_2 A_39)->(P_2 ((minus_minus_com_o A_39) ((insert_com A_6) bot_bot_com_o)))))))->(P_2 bot_bot_com_o))))).
% Axiom fact_1066_finite__empty__induct:(forall (P_2:((pname->Prop)->Prop)) (A_45:(pname->Prop)), ((finite_finite_pname A_45)->((P_2 A_45)->((forall (A_6:pname) (A_39:(pname->Prop)), ((finite_finite_pname A_39)->(((member_pname A_6) A_39)->((P_2 A_39)->(P_2 ((minus_minus_pname_o A_39) ((insert_pname A_6) bot_bot_pname_o)))))))->(P_2 bot_bot_pname_o))))).
% Axiom fact_1067_finite__empty__induct:(forall (P_2:((hoare_1708887482_state->Prop)->Prop)) (A_45:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_45)->((P_2 A_45)->((forall (A_6:hoare_1708887482_state) (A_39:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_39)->(((member451959335_state A_6) A_39)->((P_2 A_39)->(P_2 ((minus_2056855718tate_o A_39) ((insert528405184_state A_6) bot_bo19817387tate_o)))))))->(P_2 bot_bo19817387tate_o))))).
% Axiom fact_1068_finite__empty__induct:(forall (P_2:(((pname->Prop)->Prop)->Prop)) (A_45:((pname->Prop)->Prop)), ((finite297249702name_o A_45)->((P_2 A_45)->((forall (A_6:(pname->Prop)) (A_39:((pname->Prop)->Prop)), ((finite297249702name_o A_39)->(((member_pname_o A_6) A_39)->((P_2 A_39)->(P_2 ((minus_1480864103me_o_o A_39) ((insert_pname_o A_6) bot_bot_pname_o_o)))))))->(P_2 bot_bot_pname_o_o))))).
% Axiom fact_1069_finite__empty__induct:(forall (P_2:(((hoare_1708887482_state->Prop)->Prop)->Prop)) (A_45:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_45)->((P_2 A_45)->((forall (A_6:(hoare_1708887482_state->Prop)) (A_39:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_39)->(((member814030440tate_o A_6) A_39)->((P_2 A_39)->(P_2 ((minus_548038231te_o_o A_39) ((insert949073679tate_o A_6) bot_bo1678742418te_o_o)))))))->(P_2 bot_bo1678742418te_o_o))))).
% Axiom fact_1070_dom__override__on:(forall (F_23:(pname->option_com)) (G_2:(pname->option_com)) (A_44:(pname->Prop)), (((eq (pname->Prop)) (dom_pname_com (((overri1496249029on_com F_23) G_2) A_44))) ((semila1780557381name_o ((minus_minus_pname_o (dom_pname_com F_23)) (collect_pname (fun (A_6:pname)=> ((member_pname A_6) ((minus_minus_pname_o A_44) (dom_pname_com G_2))))))) (collect_pname (fun (A_6:pname)=> ((member_pname A_6) ((semila1673364395name_o A_44) (dom_pname_com G_2)))))))).
% Axiom fact_1071_Int__Collect__mono:(forall (Q:(com->Prop)) (P_1:(com->Prop)) (A_43:(com->Prop)) (B_16:(com->Prop)), (((ord_less_eq_com_o A_43) B_16)->((forall (X_3:com), (((member_com X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_less_eq_com_o ((semila513601829_com_o A_43) (collect_com P_1))) ((semila513601829_com_o B_16) (collect_com Q)))))).
% Axiom fact_1072_Int__Collect__mono:(forall (Q:(pname->Prop)) (P_1:(pname->Prop)) (A_43:(pname->Prop)) (B_16:(pname->Prop)), (((ord_less_eq_pname_o A_43) B_16)->((forall (X_3:pname), (((member_pname X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_less_eq_pname_o ((semila1673364395name_o A_43) (collect_pname P_1))) ((semila1673364395name_o B_16) (collect_pname Q)))))).
% Axiom fact_1073_Int__Collect__mono:(forall (Q:(hoare_1708887482_state->Prop)) (P_1:(hoare_1708887482_state->Prop)) (A_43:(hoare_1708887482_state->Prop)) (B_16:(hoare_1708887482_state->Prop)), (((ord_le777019615tate_o A_43) B_16)->((forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_le777019615tate_o ((semila129691299tate_o A_43) (collec1568722789_state P_1))) ((semila129691299tate_o B_16) (collec1568722789_state Q)))))).
% Axiom fact_1074_Int__Collect__mono:(forall (Q:((pname->Prop)->Prop)) (P_1:((pname->Prop)->Prop)) (A_43:((pname->Prop)->Prop)) (B_16:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_43) B_16)->((forall (X_3:(pname->Prop)), (((member_pname_o X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_le1205211808me_o_o ((semila2013987940me_o_o A_43) (collect_pname_o P_1))) ((semila2013987940me_o_o B_16) (collect_pname_o Q)))))).
% Axiom fact_1075_Int__Collect__mono:(forall (Q:((hoare_1708887482_state->Prop)->Prop)) (P_1:((hoare_1708887482_state->Prop)->Prop)) (A_43:((hoare_1708887482_state->Prop)->Prop)) (B_16:((hoare_1708887482_state->Prop)->Prop)), (((ord_le1728773982te_o_o A_43) B_16)->((forall (X_3:(hoare_1708887482_state->Prop)), (((member814030440tate_o X_3) A_43)->((P_1 X_3)->(Q X_3))))->((ord_le1728773982te_o_o ((semila598060698te_o_o A_43) (collec219771562tate_o P_1))) ((semila598060698te_o_o B_16) (collec219771562tate_o Q)))))).
% Axiom fact_1076_distrib__imp2:(forall (X_15:Prop) (Y_7:Prop) (Z_2:Prop), ((forall (X_3:Prop) (Y_4:Prop) (Z_1:Prop), ((iff ((semila10642723_sup_o X_3) ((semila854092349_inf_o Y_4) Z_1))) ((semila854092349_inf_o ((semila10642723_sup_o X_3) Y_4)) ((semila10642723_sup_o X_3) Z_1))))->((iff ((semila854092349_inf_o X_15) ((semila10642723_sup_o Y_7) Z_2))) ((semila10642723_sup_o ((semila854092349_inf_o X_15) Y_7)) ((semila854092349_inf_o X_15) Z_2))))).
% Axiom fact_1077_distrib__imp2:(forall (X_15:(pname->Prop)) (Y_7:(pname->Prop)) (Z_2:(pname->Prop)), ((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_3) ((semila1673364395name_o Y_4) Z_1))) ((semila1673364395name_o ((semila1780557381name_o X_3) Y_4)) ((semila1780557381name_o X_3) Z_1))))->(((eq (pname->Prop)) ((semila1673364395name_o X_15) ((semila1780557381name_o Y_7) Z_2))) ((semila1780557381name_o ((semila1673364395name_o X_15) Y_7)) ((semila1673364395name_o X_15) Z_2))))).
% Axiom fact_1078_distrib__imp2:(forall (X_15:(hoare_1708887482_state->Prop)) (Y_7:(hoare_1708887482_state->Prop)) (Z_2:(hoare_1708887482_state->Prop)), ((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)) (Z_1:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_3) ((semila129691299tate_o Y_4) Z_1))) ((semila129691299tate_o ((semila1122118281tate_o X_3) Y_4)) ((semila1122118281tate_o X_3) Z_1))))->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_15) ((semila1122118281tate_o Y_7) Z_2))) ((semila1122118281tate_o ((semila129691299tate_o X_15) Y_7)) ((semila129691299tate_o X_15) Z_2))))).
% Axiom fact_1079_distrib__imp1:(forall (X_14:Prop) (Y_6:Prop) (Z:Prop), ((forall (X_3:Prop) (Y_4:Prop) (Z_1:Prop), ((iff ((semila854092349_inf_o X_3) ((semila10642723_sup_o Y_4) Z_1))) ((semila10642723_sup_o ((semila854092349_inf_o X_3) Y_4)) ((semila854092349_inf_o X_3) Z_1))))->((iff ((semila10642723_sup_o X_14) ((semila854092349_inf_o Y_6) Z))) ((semila854092349_inf_o ((semila10642723_sup_o X_14) Y_6)) ((semila10642723_sup_o X_14) Z))))).
% Axiom fact_1080_distrib__imp1:(forall (X_14:(pname->Prop)) (Y_6:(pname->Prop)) (Z:(pname->Prop)), ((forall (X_3:(pname->Prop)) (Y_4:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_3) ((semila1780557381name_o Y_4) Z_1))) ((semila1780557381name_o ((semila1673364395name_o X_3) Y_4)) ((semila1673364395name_o X_3) Z_1))))->(((eq (pname->Prop)) ((semila1780557381name_o X_14) ((semila1673364395name_o Y_6) Z))) ((semila1673364395name_o ((semila1780557381name_o X_14) Y_6)) ((semila1780557381name_o X_14) Z))))).
% Axiom fact_1081_distrib__imp1:(forall (X_14:(hoare_1708887482_state->Prop)) (Y_6:(hoare_1708887482_state->Prop)) (Z:(hoare_1708887482_state->Prop)), ((forall (X_3:(hoare_1708887482_state->Prop)) (Y_4:(hoare_1708887482_state->Prop)) (Z_1:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o X_3) ((semila1122118281tate_o Y_4) Z_1))) ((semila1122118281tate_o ((semila129691299tate_o X_3) Y_4)) ((semila129691299tate_o X_3) Z_1))))->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_14) ((semila129691299tate_o Y_6) Z))) ((semila129691299tate_o ((semila1122118281tate_o X_14) Y_6)) ((semila1122118281tate_o X_14) Z))))).
% Axiom fact_1082_flat__lub__def:(forall (A_42:(com->Prop)) (B_15:com), ((and (((ord_less_eq_com_o A_42) ((insert_com B_15) bot_bot_com_o))->(((eq com) ((partial_flat_lub_com B_15) A_42)) B_15))) ((((ord_less_eq_com_o A_42) ((insert_com B_15) bot_bot_com_o))->False)->(((eq com) ((partial_flat_lub_com B_15) A_42)) (the_com_1 (fun (X_3:com)=> ((member_com X_3) ((minus_minus_com_o A_42) ((insert_com B_15) bot_bot_com_o))))))))).
% Axiom fact_1083_flat__lub__def:(forall (A_42:(pname->Prop)) (B_15:pname), ((and (((ord_less_eq_pname_o A_42) ((insert_pname B_15) bot_bot_pname_o))->(((eq pname) ((partia752020666_pname B_15) A_42)) B_15))) ((((ord_less_eq_pname_o A_42) ((insert_pname B_15) bot_bot_pname_o))->False)->(((eq pname) ((partia752020666_pname B_15) A_42)) (the_pname (fun (X_3:pname)=> ((member_pname X_3) ((minus_minus_pname_o A_42) ((insert_pname B_15) bot_bot_pname_o))))))))).
% Axiom fact_1084_flat__lub__def:(forall (A_42:(hoare_1708887482_state->Prop)) (B_15:hoare_1708887482_state), ((and (((ord_le777019615tate_o A_42) ((insert528405184_state B_15) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) ((partia1256728516_state B_15) A_42)) B_15))) ((((ord_le777019615tate_o A_42) ((insert528405184_state B_15) bot_bo19817387tate_o))->False)->(((eq hoare_1708887482_state) ((partia1256728516_state B_15) A_42)) (the_Ho851197897_state (fun (X_3:hoare_1708887482_state)=> ((member451959335_state X_3) ((minus_2056855718tate_o A_42) ((insert528405184_state B_15) bot_bo19817387tate_o))))))))).
% Axiom fact_1085_comp__fun__idem__remove:(finite567462577_com_o (fun (X_3:com) (A_39:(com->Prop))=> ((minus_minus_com_o A_39) ((insert_com X_3) bot_bot_com_o)))).
% Axiom fact_1086_comp__fun__idem__remove:(finite1123817265name_o (fun (X_3:pname) (A_39:(pname->Prop))=> ((minus_minus_pname_o A_39) ((insert_pname X_3) bot_bot_pname_o)))).
% Axiom fact_1087_comp__fun__idem__remove:(finite662762081tate_o (fun (X_3:hoare_1708887482_state) (A_39:(hoare_1708887482_state->Prop))=> ((minus_2056855718tate_o A_39) ((insert528405184_state X_3) bot_bo19817387tate_o)))).
% Axiom fact_1088_fun__upd__image:(forall (F_22:(pname->hoare_1708887482_state)) (Y_5:hoare_1708887482_state) (X_13:pname) (A_41:(pname->Prop)), ((and (((member_pname X_13) A_41)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (((fun_up1986763201_state F_22) X_13) Y_5)) A_41)) ((insert528405184_state Y_5) ((image_1116629049_state F_22) ((minus_minus_pname_o A_41) ((insert_pname X_13) bot_bot_pname_o))))))) ((((member_pname X_13) A_41)->False)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (((fun_up1986763201_state F_22) X_13) Y_5)) A_41)) ((image_1116629049_state F_22) A_41))))).
% Axiom fact_1089_comp__fun__idem__insert:(finite567462577_com_o insert_com).
% Axiom fact_1090_comp__fun__idem__insert:(finite1123817265name_o insert_pname).
% Axiom fact_1091_comp__fun__idem__insert:(finite662762081tate_o insert528405184_state).
% Axiom fact_1092_comp__fun__idem__sup:(finite2048025996em_o_o semila10642723_sup_o).
% Axiom fact_1093_comp__fun__idem__sup:(finite138924780name_o semila1780557381name_o).
% Axiom fact_1094_comp__fun__idem__sup:(finite2034616076tate_o semila1122118281tate_o).
% Axiom fact_1095_inj__on__Un:(forall (F_21:(pname->hoare_1708887482_state)) (A_40:(pname->Prop)) (B_14:(pname->Prop)), ((iff ((inj_on1553129421_state F_21) ((semila1780557381name_o A_40) B_14))) ((and ((and ((inj_on1553129421_state F_21) A_40)) ((inj_on1553129421_state F_21) B_14))) (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o ((image_1116629049_state F_21) ((minus_minus_pname_o A_40) B_14))) ((image_1116629049_state F_21) ((minus_minus_pname_o B_14) A_40)))) bot_bo19817387tate_o)))).
% Axiom fact_1096_dom__eq__singleton__conv:(forall (F_20:(pname->option_com)) (X_12:pname), ((iff (((eq (pname->Prop)) (dom_pname_com F_20)) ((insert_pname X_12) bot_bot_pname_o))) ((ex com) (fun (V:com)=> (((eq (pname->option_com)) F_20) (((fun_up879233478on_com (fun (X_3:pname)=> none_com)) X_12) (some_com V))))))).
% Axiom fact_1097_minus__fold__remove:(forall (B_13:(com->Prop)) (A_38:(com->Prop)), ((finite_finite_com A_38)->(((eq (com->Prop)) ((minus_minus_com_o B_13) A_38)) (((finite504235573_com_o (fun (X_3:com) (A_39:(com->Prop))=> ((minus_minus_com_o A_39) ((insert_com X_3) bot_bot_com_o)))) B_13) A_38)))).
% Axiom fact_1098_minus__fold__remove:(forall (B_13:(pname->Prop)) (A_38:(pname->Prop)), ((finite_finite_pname A_38)->(((eq (pname->Prop)) ((minus_minus_pname_o B_13) A_38)) (((finite603803317name_o (fun (X_3:pname) (A_39:(pname->Prop))=> ((minus_minus_pname_o A_39) ((insert_pname X_3) bot_bot_pname_o)))) B_13) A_38)))).
% Axiom fact_1099_minus__fold__remove:(forall (B_13:(hoare_1708887482_state->Prop)) (A_38:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_38)->(((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o B_13) A_38)) (((finite96880613tate_o (fun (X_3:hoare_1708887482_state) (A_39:(hoare_1708887482_state->Prop))=> ((minus_2056855718tate_o A_39) ((insert528405184_state X_3) bot_bo19817387tate_o)))) B_13) A_38)))).
% Axiom fact_1100_minus__fold__remove:(forall (B_13:((pname->Prop)->Prop)) (A_38:((pname->Prop)->Prop)), ((finite297249702name_o A_38)->(((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o B_13) A_38)) (((finite1849951719me_o_o (fun (X_3:(pname->Prop)) (A_39:((pname->Prop)->Prop))=> ((minus_1480864103me_o_o A_39) ((insert_pname_o X_3) bot_bot_pname_o_o)))) B_13) A_38)))).
% Axiom fact_1101_minus__fold__remove:(forall (B_13:((hoare_1708887482_state->Prop)->Prop)) (A_38:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_38)->(((eq ((hoare_1708887482_state->Prop)->Prop)) ((minus_548038231te_o_o B_13) A_38)) (((finite463603445te_o_o (fun (X_3:(hoare_1708887482_state->Prop)) (A_39:((hoare_1708887482_state->Prop)->Prop))=> ((minus_548038231te_o_o A_39) ((insert949073679tate_o X_3) bot_bo1678742418te_o_o)))) B_13) A_38)))).
% Axiom fact_1102_image__eq__fold__image:(forall (F_19:(pname->hoare_1708887482_state)) (A_37:(pname->Prop)), ((finite_finite_pname A_37)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_19) A_37)) ((((finite2139561282_pname semila1122118281tate_o) (fun (X_3:pname)=> ((insert528405184_state (F_19 X_3)) bot_bo19817387tate_o))) bot_bo19817387tate_o) A_37)))).
% Axiom fact_1103_inj__Some:(forall (A_36:(pname->Prop)), ((inj_on737724108_pname some_pname) A_36)).
% Axiom fact_1104_inj__Some:(forall (A_36:(hoare_1708887482_state->Prop)), ((inj_on945311362_state some_H1974565227_state) A_36)).
% Axiom fact_1105_inj__Some:(forall (A_36:(com->Prop)), ((inj_on11367768on_com some_com) A_36)).
% Axiom fact_1106_option_Osimps_I2_J:(forall (A_35:com), (not (((eq option_com) none_com) (some_com A_35)))).
% Axiom fact_1107_option_Osimps_I2_J:(forall (A_35:pname), (not (((eq option_pname) none_pname) (some_pname A_35)))).
% Axiom fact_1108_option_Osimps_I2_J:(forall (A_35:hoare_1708887482_state), (not (((eq option1624383643_state) none_H1106584047_state) (some_H1974565227_state A_35)))).
% Axiom fact_1109_option_Osimps_I3_J:(forall (A_34:com), (not (((eq option_com) (some_com A_34)) none_com))).
% Axiom fact_1110_option_Osimps_I3_J:(forall (A_34:pname), (not (((eq option_pname) (some_pname A_34)) none_pname))).
% Axiom fact_1111_option_Osimps_I3_J:(forall (A_34:hoare_1708887482_state), (not (((eq option1624383643_state) (some_H1974565227_state A_34)) none_H1106584047_state))).
% Axiom fact_1112_not__Some__eq:(forall (X_11:option_com), ((iff (forall (Y_4:com), (not (((eq option_com) X_11) (some_com Y_4))))) (((eq option_com) X_11) none_com))).
% Axiom fact_1113_not__Some__eq:(forall (X_11:option_pname), ((iff (forall (Y_4:pname), (not (((eq option_pname) X_11) (some_pname Y_4))))) (((eq option_pname) X_11) none_pname))).
% Axiom fact_1114_not__Some__eq:(forall (X_11:option1624383643_state), ((iff (forall (Y_4:hoare_1708887482_state), (not (((eq option1624383643_state) X_11) (some_H1974565227_state Y_4))))) (((eq option1624383643_state) X_11) none_H1106584047_state))).
% Axiom fact_1115_not__None__eq:(forall (X_10:option_com), ((iff (not (((eq option_com) X_10) none_com))) ((ex com) (fun (Y_4:com)=> (((eq option_com) X_10) (some_com Y_4)))))).
% Axiom fact_1116_not__None__eq:(forall (X_10:option_pname), ((iff (not (((eq option_pname) X_10) none_pname))) ((ex pname) (fun (Y_4:pname)=> (((eq option_pname) X_10) (some_pname Y_4)))))).
% Axiom fact_1117_not__None__eq:(forall (X_10:option1624383643_state), ((iff (not (((eq option1624383643_state) X_10) none_H1106584047_state))) ((ex hoare_1708887482_state) (fun (Y_4:hoare_1708887482_state)=> (((eq option1624383643_state) X_10) (some_H1974565227_state Y_4)))))).
% Axiom fact_1118_dom__def:(forall (M_2:(pname->option_com)), (((eq (pname->Prop)) (dom_pname_com M_2)) (collect_pname (fun (A_6:pname)=> (not (((eq option_com) (M_2 A_6)) none_com)))))).
% Axiom fact_1119_domIff:(forall (A_33:pname) (M_1:(pname->option_com)), ((iff ((member_pname A_33) (dom_pname_com M_1))) (not (((eq option_com) (M_1 A_33)) none_com)))).
% Axiom fact_1120_finite__imageD:(forall (F_18:(pname->hoare_1708887482_state)) (A_32:(pname->Prop)), ((finite1625599783_state ((image_1116629049_state F_18) A_32))->(((inj_on1553129421_state F_18) A_32)->(finite_finite_pname A_32)))).
% Axiom fact_1121_inj__on__Un__image__eq__iff:(forall (F_17:(pname->hoare_1708887482_state)) (A_31:(pname->Prop)) (B_12:(pname->Prop)), (((inj_on1553129421_state F_17) ((semila1780557381name_o A_31) B_12))->((iff (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_17) A_31)) ((image_1116629049_state F_17) B_12))) (((eq (pname->Prop)) A_31) B_12)))).
% Axiom fact_1122_is__none__def:(forall (X_9:option_com), ((iff (is_none_com X_9)) (((eq option_com) X_9) none_com))).
% Axiom fact_1123_is__none__code_I1_J:(is_none_com none_com).
% Axiom fact_1124_inj__on__fun__updI:(forall (X_8:pname) (Y_3:hoare_1708887482_state) (F_16:(pname->hoare_1708887482_state)) (A_30:(pname->Prop)), (((inj_on1553129421_state F_16) A_30)->((((member451959335_state Y_3) ((image_1116629049_state F_16) A_30))->False)->((inj_on1553129421_state (((fun_up1986763201_state F_16) X_8) Y_3)) A_30)))).
% Axiom fact_1125_sup__le__fold__sup:(forall (B_11:(pname->Prop)) (A_29:(pname->Prop)) (A_28:((pname->Prop)->Prop)), ((finite297249702name_o A_28)->(((member_pname_o A_29) A_28)->((ord_less_eq_pname_o ((semila1780557381name_o A_29) B_11)) (((finite472615016name_o semila1780557381name_o) B_11) A_28))))).
% Axiom fact_1126_sup__le__fold__sup:(forall (B_11:(hoare_1708887482_state->Prop)) (A_29:(hoare_1708887482_state->Prop)) (A_28:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_28)->(((member814030440tate_o A_29) A_28)->((ord_le777019615tate_o ((semila1122118281tate_o A_29) B_11)) (((finite822533768tate_o semila1122118281tate_o) B_11) A_28))))).
% Axiom fact_1127_sup__le__fold__sup:(forall (B_11:Prop) (A_29:Prop) (A_28:(Prop->Prop)), ((finite_finite_o A_28)->(((member_o A_29) A_28)->((ord_less_eq_o ((semila10642723_sup_o A_29) B_11)) (((finite_fold_o_o semila10642723_sup_o) B_11) A_28))))).
% Axiom fact_1128_fold__inf__le__inf:(forall (B_10:(pname->Prop)) (A_27:(pname->Prop)) (A_26:((pname->Prop)->Prop)), ((finite297249702name_o A_26)->(((member_pname_o A_27) A_26)->((ord_less_eq_pname_o (((finite472615016name_o semila1673364395name_o) B_10) A_26)) ((semila1673364395name_o A_27) B_10))))).
% Axiom fact_1129_fold__inf__le__inf:(forall (B_10:(hoare_1708887482_state->Prop)) (A_27:(hoare_1708887482_state->Prop)) (A_26:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_26)->(((member814030440tate_o A_27) A_26)->((ord_le777019615tate_o (((finite822533768tate_o semila129691299tate_o) B_10) A_26)) ((semila129691299tate_o A_27) B_10))))).
% Axiom fact_1130_fold__inf__le__inf:(forall (B_10:Prop) (A_27:Prop) (A_26:(Prop->Prop)), ((finite_finite_o A_26)->(((member_o A_27) A_26)->((ord_less_eq_o (((finite_fold_o_o semila854092349_inf_o) B_10) A_26)) ((semila854092349_inf_o A_27) B_10))))).
% Axiom fact_1131_fold__sup__insert:(forall (B_9:(pname->Prop)) (A_25:(pname->Prop)) (A_24:((pname->Prop)->Prop)), ((finite297249702name_o A_24)->(((eq (pname->Prop)) (((finite472615016name_o semila1780557381name_o) B_9) ((insert_pname_o A_25) A_24))) ((semila1780557381name_o A_25) (((finite472615016name_o semila1780557381name_o) B_9) A_24))))).
% Axiom fact_1132_fold__sup__insert:(forall (B_9:(hoare_1708887482_state->Prop)) (A_25:(hoare_1708887482_state->Prop)) (A_24:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_24)->(((eq (hoare_1708887482_state->Prop)) (((finite822533768tate_o semila1122118281tate_o) B_9) ((insert949073679tate_o A_25) A_24))) ((semila1122118281tate_o A_25) (((finite822533768tate_o semila1122118281tate_o) B_9) A_24))))).
% Axiom fact_1133_fold__sup__insert:(forall (B_9:Prop) (A_25:Prop) (A_24:(Prop->Prop)), ((finite_finite_o A_24)->((iff (((finite_fold_o_o semila10642723_sup_o) B_9) ((insert_o A_25) A_24))) ((semila10642723_sup_o A_25) (((finite_fold_o_o semila10642723_sup_o) B_9) A_24))))).
% Axiom fact_1134_fold__inf__insert:(forall (B_8:(pname->Prop)) (A_23:(pname->Prop)) (A_22:((pname->Prop)->Prop)), ((finite297249702name_o A_22)->(((eq (pname->Prop)) (((finite472615016name_o semila1673364395name_o) B_8) ((insert_pname_o A_23) A_22))) ((semila1673364395name_o A_23) (((finite472615016name_o semila1673364395name_o) B_8) A_22))))).
% Axiom fact_1135_fold__inf__insert:(forall (B_8:(hoare_1708887482_state->Prop)) (A_23:(hoare_1708887482_state->Prop)) (A_22:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_22)->(((eq (hoare_1708887482_state->Prop)) (((finite822533768tate_o semila129691299tate_o) B_8) ((insert949073679tate_o A_23) A_22))) ((semila129691299tate_o A_23) (((finite822533768tate_o semila129691299tate_o) B_8) A_22))))).
% Axiom fact_1136_dom__eq__empty__conv:(forall (F_15:(pname->option_com)), ((iff (((eq (pname->Prop)) (dom_pname_com F_15)) bot_bot_pname_o)) (forall (X_3:pname), (((eq option_com) (F_15 X_3)) none_com)))).
% Axiom fact_1137_dom__empty:(((eq (pname->Prop)) (dom_pname_com (fun (X_3:pname)=> none_com))) bot_bot_pname_o).
% Axiom fact_1138_Option_Oset_Osimps_I1_J:(((eq (com->Prop)) (set_com none_com)) bot_bot_com_o).
% Axiom fact_1139_Option_Oset_Osimps_I1_J:(((eq (pname->Prop)) (set_pname none_pname)) bot_bot_pname_o).
% Axiom fact_1140_Option_Oset_Osimps_I1_J:(((eq (hoare_1708887482_state->Prop)) (set_Ho525251890_state none_H1106584047_state)) bot_bo19817387tate_o).
% Axiom fact_1141_set__empty__eq:(forall (Xo:option_com), ((iff (((eq (com->Prop)) (set_com Xo)) bot_bot_com_o)) (((eq option_com) Xo) none_com))).
% Axiom fact_1142_set__empty__eq:(forall (Xo:option_pname), ((iff (((eq (pname->Prop)) (set_pname Xo)) bot_bot_pname_o)) (((eq option_pname) Xo) none_pname))).
% Axiom fact_1143_set__empty__eq:(forall (Xo:option1624383643_state), ((iff (((eq (hoare_1708887482_state->Prop)) (set_Ho525251890_state Xo)) bot_bo19817387tate_o)) (((eq option1624383643_state) Xo) none_H1106584047_state))).
% Axiom fact_1144_endo__inj__surj:(forall (F_14:((pname->Prop)->(pname->Prop))) (A_21:((pname->Prop)->Prop)), ((finite297249702name_o A_21)->(((ord_le1205211808me_o_o ((image_1085733413name_o F_14) A_21)) A_21)->(((inj_on691924881name_o F_14) A_21)->(((eq ((pname->Prop)->Prop)) ((image_1085733413name_o F_14) A_21)) A_21))))).
% Axiom fact_1145_endo__inj__surj:(forall (F_14:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (A_21:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_21)->(((ord_le1728773982te_o_o ((image_909543877tate_o F_14) A_21)) A_21)->(((inj_on176908593tate_o F_14) A_21)->(((eq ((hoare_1708887482_state->Prop)->Prop)) ((image_909543877tate_o F_14) A_21)) A_21))))).
% Axiom fact_1146_endo__inj__surj:(forall (F_14:(pname->pname)) (A_21:(pname->Prop)), ((finite_finite_pname A_21)->(((ord_less_eq_pname_o ((image_pname_pname F_14) A_21)) A_21)->(((inj_on_pname_pname F_14) A_21)->(((eq (pname->Prop)) ((image_pname_pname F_14) A_21)) A_21))))).
% Axiom fact_1147_endo__inj__surj:(forall (F_14:(hoare_1708887482_state->hoare_1708887482_state)) (A_21:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_21)->(((ord_le777019615tate_o ((image_757158439_state F_14) A_21)) A_21)->(((inj_on632008595_state F_14) A_21)->(((eq (hoare_1708887482_state->Prop)) ((image_757158439_state F_14) A_21)) A_21))))).
% Axiom fact_1148_finite__surj__inj:(forall (F_13:((pname->Prop)->(pname->Prop))) (A_20:((pname->Prop)->Prop)), ((finite297249702name_o A_20)->(((ord_le1205211808me_o_o A_20) ((image_1085733413name_o F_13) A_20))->((inj_on691924881name_o F_13) A_20)))).
% Axiom fact_1149_finite__surj__inj:(forall (F_13:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))) (A_20:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_20)->(((ord_le1728773982te_o_o A_20) ((image_909543877tate_o F_13) A_20))->((inj_on176908593tate_o F_13) A_20)))).
% Axiom fact_1150_finite__surj__inj:(forall (F_13:(pname->pname)) (A_20:(pname->Prop)), ((finite_finite_pname A_20)->(((ord_less_eq_pname_o A_20) ((image_pname_pname F_13) A_20))->((inj_on_pname_pname F_13) A_20)))).
% Axiom fact_1151_finite__surj__inj:(forall (F_13:(hoare_1708887482_state->hoare_1708887482_state)) (A_20:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_20)->(((ord_le777019615tate_o A_20) ((image_757158439_state F_13) A_20))->((inj_on632008595_state F_13) A_20)))).
% Axiom fact_1152_inj__on__image__Int:(forall (B_7:(pname->Prop)) (A_19:(pname->Prop)) (F_12:(pname->hoare_1708887482_state)) (C_3:(pname->Prop)), (((inj_on1553129421_state F_12) C_3)->(((ord_less_eq_pname_o A_19) C_3)->(((ord_less_eq_pname_o B_7) C_3)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_12) ((semila1673364395name_o A_19) B_7))) ((semila129691299tate_o ((image_1116629049_state F_12) A_19)) ((image_1116629049_state F_12) B_7))))))).
% Axiom fact_1153_inj__on__image__set__diff:(forall (B_6:(pname->Prop)) (A_18:(pname->Prop)) (F_11:(pname->hoare_1708887482_state)) (C_2:(pname->Prop)), (((inj_on1553129421_state F_11) C_2)->(((ord_less_eq_pname_o A_18) C_2)->(((ord_less_eq_pname_o B_6) C_2)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_11) ((minus_minus_pname_o A_18) B_6))) ((minus_2056855718tate_o ((image_1116629049_state F_11) A_18)) ((image_1116629049_state F_11) B_6))))))).
% Axiom fact_1154_union__fold__insert:(forall (B_5:(com->Prop)) (A_17:(com->Prop)), ((finite_finite_com A_17)->(((eq (com->Prop)) ((semila1562558655_com_o A_17) B_5)) (((finite504235573_com_o insert_com) B_5) A_17)))).
% Axiom fact_1155_union__fold__insert:(forall (B_5:(pname->Prop)) (A_17:(pname->Prop)), ((finite_finite_pname A_17)->(((eq (pname->Prop)) ((semila1780557381name_o A_17) B_5)) (((finite603803317name_o insert_pname) B_5) A_17)))).
% Axiom fact_1156_union__fold__insert:(forall (B_5:(hoare_1708887482_state->Prop)) (A_17:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_17)->(((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_17) B_5)) (((finite96880613tate_o insert528405184_state) B_5) A_17)))).
% Axiom fact_1157_union__fold__insert:(forall (B_5:((pname->Prop)->Prop)) (A_17:((pname->Prop)->Prop)), ((finite297249702name_o A_17)->(((eq ((pname->Prop)->Prop)) ((semila181081674me_o_o A_17) B_5)) (((finite1849951719me_o_o insert_pname_o) B_5) A_17)))).
% Axiom fact_1158_union__fold__insert:(forall (B_5:((hoare_1708887482_state->Prop)->Prop)) (A_17:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_17)->(((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila1853742644te_o_o A_17) B_5)) (((finite463603445te_o_o insert949073679tate_o) B_5) A_17)))).
% Axiom fact_1159_dom__minus:(forall (A_16:(pname->Prop)) (F_10:(pname->option_com)) (X_7:pname), ((((eq option_com) (F_10 X_7)) none_com)->(((eq (pname->Prop)) ((minus_minus_pname_o (dom_pname_com F_10)) ((insert_pname X_7) A_16))) ((minus_minus_pname_o (dom_pname_com F_10)) A_16)))).
% Axiom fact_1160_Sup__fin_Oidem:(forall (X_6:Prop), ((iff ((semila10642723_sup_o X_6) X_6)) X_6)).
% Axiom fact_1161_Sup__fin_Oidem:(forall (X_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_6) X_6)) X_6)).
% Axiom fact_1162_Sup__fin_Oidem:(forall (X_6:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_6) X_6)) X_6)).
% Axiom fact_1163_folding__one_Oeq__fold_H:(forall (X_5:com) (A_15:(com->Prop)) (F_9:(com->(com->com))) (F_8:((com->Prop)->com)), (((finite860057415ne_com F_9) F_8)->((finite_finite_com A_15)->((((member_com X_5) A_15)->False)->(((eq com) (F_8 ((insert_com X_5) A_15))) (((finite_fold_com_com F_9) X_5) A_15)))))).
% Axiom fact_1164_folding__one_Oeq__fold_H:(forall (X_5:pname) (A_15:(pname->Prop)) (F_9:(pname->(pname->pname))) (F_8:((pname->Prop)->pname)), (((finite1282449217_pname F_9) F_8)->((finite_finite_pname A_15)->((((member_pname X_5) A_15)->False)->(((eq pname) (F_8 ((insert_pname X_5) A_15))) (((finite1657623752_pname F_9) X_5) A_15)))))).
% Axiom fact_1165_folding__one_Oeq__fold_H:(forall (X_5:hoare_1708887482_state) (A_15:(hoare_1708887482_state->Prop)) (F_9:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_8:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_9) F_8)->((finite1625599783_state A_15)->((((member451959335_state X_5) A_15)->False)->(((eq hoare_1708887482_state) (F_8 ((insert528405184_state X_5) A_15))) (((finite309095018_state F_9) X_5) A_15)))))).
% Axiom fact_1166_folding__one_Oeq__fold_H:(forall (X_5:(pname->Prop)) (A_15:((pname->Prop)->Prop)) (F_9:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_8:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_9) F_8)->((finite297249702name_o A_15)->((((member_pname_o X_5) A_15)->False)->(((eq (pname->Prop)) (F_8 ((insert_pname_o X_5) A_15))) (((finite472615016name_o F_9) X_5) A_15)))))).
% Axiom fact_1167_folding__one_Oeq__fold_H:(forall (X_5:(hoare_1708887482_state->Prop)) (A_15:((hoare_1708887482_state->Prop)->Prop)) (F_9:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_8:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite928843026tate_o F_9) F_8)->((finite1329924456tate_o A_15)->((((member814030440tate_o X_5) A_15)->False)->(((eq (hoare_1708887482_state->Prop)) (F_8 ((insert949073679tate_o X_5) A_15))) (((finite822533768tate_o F_9) X_5) A_15)))))).
% Axiom fact_1168_folding__one__idem_Oeq__fold__idem_H:(forall (A_14:com) (A_13:(com->Prop)) (F_7:(com->(com->com))) (F_6:((com->Prop)->com)), (((finite666746948em_com F_7) F_6)->((finite_finite_com A_13)->(((eq com) (F_6 ((insert_com A_14) A_13))) (((finite_fold_com_com F_7) A_14) A_13))))).
% Axiom fact_1169_folding__one__idem_Oeq__fold__idem_H:(forall (A_14:pname) (A_13:(pname->Prop)) (F_7:(pname->(pname->pname))) (F_6:((pname->Prop)->pname)), (((finite89670078_pname F_7) F_6)->((finite_finite_pname A_13)->(((eq pname) (F_6 ((insert_pname A_14) A_13))) (((finite1657623752_pname F_7) A_14) A_13))))).
% Axiom fact_1170_folding__one__idem_Oeq__fold__idem_H:(forall (A_14:hoare_1708887482_state) (A_13:(hoare_1708887482_state->Prop)) (F_7:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_6:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_7) F_6)->((finite1625599783_state A_13)->(((eq hoare_1708887482_state) (F_6 ((insert528405184_state A_14) A_13))) (((finite309095018_state F_7) A_14) A_13))))).
% Axiom fact_1171_folding__one__idem_Oeq__fold__idem_H:(forall (A_14:(pname->Prop)) (A_13:((pname->Prop)->Prop)) (F_7:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_6:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_7) F_6)->((finite297249702name_o A_13)->(((eq (pname->Prop)) (F_6 ((insert_pname_o A_14) A_13))) (((finite472615016name_o F_7) A_14) A_13))))).
% Axiom fact_1172_folding__one__idem_Oeq__fold__idem_H:(forall (A_14:(hoare_1708887482_state->Prop)) (A_13:((hoare_1708887482_state->Prop)->Prop)) (F_7:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))) (F_6:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))), (((finite621643279tate_o F_7) F_6)->((finite1329924456tate_o A_13)->(((eq (hoare_1708887482_state->Prop)) (F_6 ((insert949073679tate_o A_14) A_13))) (((finite822533768tate_o F_7) A_14) A_13))))).
% Axiom fact_1173_WT_OBody:(forall (Pn_1:pname), ((not (((eq option_com) (body Pn_1)) none_com))->(wt (body_1 Pn_1)))).
% Axiom fact_1174_inj__on__insert:(forall (F_5:(pname->hoare_1708887482_state)) (A_12:pname) (A_11:(pname->Prop)), ((iff ((inj_on1553129421_state F_5) ((insert_pname A_12) A_11))) ((and ((inj_on1553129421_state F_5) A_11)) (((member451959335_state (F_5 A_12)) ((image_1116629049_state F_5) ((minus_minus_pname_o A_11) ((insert_pname A_12) bot_bot_pname_o))))->False)))).
% Axiom fact_1175_dom__fun__upd:(forall (F_4:(pname->option_com)) (X_4:pname) (Y_2:option_com), ((and ((((eq option_com) Y_2) none_com)->(((eq (pname->Prop)) (dom_pname_com (((fun_up879233478on_com F_4) X_4) Y_2))) ((minus_minus_pname_o (dom_pname_com F_4)) ((insert_pname X_4) bot_bot_pname_o))))) ((not (((eq option_com) Y_2) none_com))->(((eq (pname->Prop)) (dom_pname_com (((fun_up879233478on_com F_4) X_4) Y_2))) ((insert_pname X_4) (dom_pname_com F_4)))))).
% Axiom fact_1176_inf__le__fold__inf:(forall (C_1:(pname->Prop)) (B_4:(pname->Prop)) (A_10:((pname->Prop)->Prop)), ((finite297249702name_o A_10)->((forall (X_3:(pname->Prop)), (((member_pname_o X_3) A_10)->((ord_less_eq_pname_o B_4) X_3)))->((ord_less_eq_pname_o ((semila1673364395name_o B_4) C_1)) (((finite472615016name_o semila1673364395name_o) C_1) A_10))))).
% Axiom fact_1177_inf__le__fold__inf:(forall (C_1:(hoare_1708887482_state->Prop)) (B_4:(hoare_1708887482_state->Prop)) (A_10:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_10)->((forall (X_3:(hoare_1708887482_state->Prop)), (((member814030440tate_o X_3) A_10)->((ord_le777019615tate_o B_4) X_3)))->((ord_le777019615tate_o ((semila129691299tate_o B_4) C_1)) (((finite822533768tate_o semila129691299tate_o) C_1) A_10))))).
% Axiom fact_1178_inf__le__fold__inf:(forall (C_1:Prop) (B_4:Prop) (A_10:(Prop->Prop)), ((finite_finite_o A_10)->((forall (X_3:Prop), (((member_o X_3) A_10)->((ord_less_eq_o B_4) X_3)))->((ord_less_eq_o ((semila854092349_inf_o B_4) C_1)) (((finite_fold_o_o semila854092349_inf_o) C_1) A_10))))).
% Axiom fact_1179_fold__sup__le__sup:(forall (C:(pname->Prop)) (B_3:(pname->Prop)) (A_9:((pname->Prop)->Prop)), ((finite297249702name_o A_9)->((forall (X_3:(pname->Prop)), (((member_pname_o X_3) A_9)->((ord_less_eq_pname_o X_3) B_3)))->((ord_less_eq_pname_o (((finite472615016name_o semila1780557381name_o) C) A_9)) ((semila1780557381name_o B_3) C))))).
% Axiom fact_1180_fold__sup__le__sup:(forall (C:(hoare_1708887482_state->Prop)) (B_3:(hoare_1708887482_state->Prop)) (A_9:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_9)->((forall (X_3:(hoare_1708887482_state->Prop)), (((member814030440tate_o X_3) A_9)->((ord_le777019615tate_o X_3) B_3)))->((ord_le777019615tate_o (((finite822533768tate_o semila1122118281tate_o) C) A_9)) ((semila1122118281tate_o B_3) C))))).
% Axiom fact_1181_fold__sup__le__sup:(forall (C:Prop) (B_3:Prop) (A_9:(Prop->Prop)), ((finite_finite_o A_9)->((forall (X_3:Prop), (((member_o X_3) A_9)->((ord_less_eq_o X_3) B_3)))->((ord_less_eq_o (((finite_fold_o_o semila10642723_sup_o) C) A_9)) ((semila10642723_sup_o B_3) C))))).
% Axiom fact_1182_inj__on__iff__surj:(forall (A_8:(pname->Prop)) (A_7:(hoare_1708887482_state->Prop)), ((not (((eq (hoare_1708887482_state->Prop)) A_7) bot_bo19817387tate_o))->((iff ((ex (hoare_1708887482_state->pname)) (fun (F_3:(hoare_1708887482_state->pname))=> ((and ((inj_on1945914667_pname F_3) A_7)) ((ord_less_eq_pname_o ((image_1509414295_pname F_3) A_7)) A_8))))) ((ex (pname->hoare_1708887482_state)) (fun (G_1:(pname->hoare_1708887482_state))=> (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state G_1) A_8)) A_7)))))).
% Axiom fact_1183_inj__on__iff__surj:(forall (A_8:(hoare_1708887482_state->Prop)) (A_7:(pname->Prop)), ((not (((eq (pname->Prop)) A_7) bot_bot_pname_o))->((iff ((ex (pname->hoare_1708887482_state)) (fun (F_3:(pname->hoare_1708887482_state))=> ((and ((inj_on1553129421_state F_3) A_7)) ((ord_le777019615tate_o ((image_1116629049_state F_3) A_7)) A_8))))) ((ex (hoare_1708887482_state->pname)) (fun (G_1:(hoare_1708887482_state->pname))=> (((eq (pname->Prop)) ((image_1509414295_pname G_1) A_8)) A_7)))))).
% Axiom fact_1184_option_Oexhaust:(forall (Y_1:option_com), ((not (((eq option_com) Y_1) none_com))->((forall (A_6:com), (not (((eq option_com) Y_1) (some_com A_6))))->False))).
% Axiom fact_1185_option_Oexhaust:(forall (Y_1:option_pname), ((not (((eq option_pname) Y_1) none_pname))->((forall (A_6:pname), (not (((eq option_pname) Y_1) (some_pname A_6))))->False))).
% Axiom fact_1186_option_Oexhaust:(forall (Y_1:option1624383643_state), ((not (((eq option1624383643_state) Y_1) none_H1106584047_state))->((forall (A_6:hoare_1708887482_state), (not (((eq option1624383643_state) Y_1) (some_H1974565227_state A_6))))->False))).
% Axiom fact_1187_Cantor__Bernstein__aux:(forall (G:(hoare_1708887482_state->pname)) (B_2:(hoare_1708887482_state->Prop)) (F_2:(pname->hoare_1708887482_state)) (A_4:(pname->Prop)), ((ex (pname->Prop)) (fun (A_5:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o A_5) A_4)) (forall (X_3:pname), (((member_pname X_3) A_5)->(((member_pname X_3) ((image_1509414295_pname G) ((minus_2056855718tate_o B_2) ((image_1116629049_state F_2) A_5))))->False))))) ((ex (pname->hoare_1708887482_state)) (fun (H:(pname->hoare_1708887482_state))=> ((and (forall (X_3:pname), (((member_pname X_3) A_5)->(((eq hoare_1708887482_state) (H X_3)) (F_2 X_3))))) (forall (X_3:pname), (((member_pname X_3) ((minus_minus_pname_o A_4) A_5))->((and ((member451959335_state (H X_3)) ((minus_2056855718tate_o B_2) ((image_1116629049_state F_2) A_5)))) (((eq pname) X_3) (G (H X_3))))))))))))).
% Axiom fact_1188_Cantor__Bernstein__aux:(forall (G:(pname->hoare_1708887482_state)) (B_2:(pname->Prop)) (F_2:(hoare_1708887482_state->pname)) (A_4:(hoare_1708887482_state->Prop)), ((ex (hoare_1708887482_state->Prop)) (fun (A_5:(hoare_1708887482_state->Prop))=> ((and ((and ((ord_le777019615tate_o A_5) A_4)) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_5)->(((member451959335_state X_3) ((image_1116629049_state G) ((minus_minus_pname_o B_2) ((image_1509414295_pname F_2) A_5))))->False))))) ((ex (hoare_1708887482_state->pname)) (fun (H:(hoare_1708887482_state->pname))=> ((and (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) A_5)->(((eq pname) (H X_3)) (F_2 X_3))))) (forall (X_3:hoare_1708887482_state), (((member451959335_state X_3) ((minus_2056855718tate_o A_4) A_5))->((and ((member_pname (H X_3)) ((minus_minus_pname_o B_2) ((image_1509414295_pname F_2) A_5)))) (((eq hoare_1708887482_state) X_3) (G (H X_3))))))))))))).
% Axiom fact_1189_image__vimage__subset:(forall (F_1:(pname->hoare_1708887482_state)) (A_3:(hoare_1708887482_state->Prop)), ((ord_le777019615tate_o ((image_1116629049_state F_1) ((vimage1943311875_state F_1) A_3))) A_3)).
% Axiom fact_1190_dom__restrict:(forall (M:(pname->option_com)) (A_2:(pname->Prop)), (((eq (pname->Prop)) (dom_pname_com ((restri1382200118me_com M) A_2))) ((semila1673364395name_o (dom_pname_com M)) A_2))).
% Axiom fact_1191_Inf__fin_Ounion__disjoint:(forall (B_1:((pname->Prop)->Prop)) (A_1:((pname->Prop)->Prop)), ((finite297249702name_o A_1)->((not (((eq ((pname->Prop)->Prop)) A_1) bot_bot_pname_o_o))->((finite297249702name_o B_1)->((not (((eq ((pname->Prop)->Prop)) B_1) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_1) B_1)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (big_la1126801287name_o ((semila181081674me_o_o A_1) B_1))) ((semila1673364395name_o (big_la1126801287name_o A_1)) (big_la1126801287name_o B_1))))))))).
% Axiom fact_1192_Inf__fin_Ounion__disjoint:(forall (B_1:((hoare_1708887482_state->Prop)->Prop)) (A_1:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_1)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_1) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_1)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_1) bot_bo1678742418te_o_o))->((((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A_1) B_1)) bot_bo1678742418te_o_o)->(((eq (hoare_1708887482_state->Prop)) (big_la781588935tate_o ((semila1853742644te_o_o A_1) B_1))) ((semila129691299tate_o (big_la781588935tate_o A_1)) (big_la781588935tate_o B_1))))))))).
% Axiom fact_1193_Inf__fin_Ounion__inter:(forall (B:((pname->Prop)->Prop)) (A:((pname->Prop)->Prop)), ((finite297249702name_o A)->((finite297249702name_o B)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A) B)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((semila1673364395name_o (big_la1126801287name_o ((semila181081674me_o_o A) B))) (big_la1126801287name_o ((semila2013987940me_o_o A) B)))) ((semila1673364395name_o (big_la1126801287name_o A)) (big_la1126801287name_o B))))))).
% Axiom fact_1194_Inf__fin_Ounion__inter:(forall (B:((hoare_1708887482_state->Prop)->Prop)) (A:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A)->((finite1329924456tate_o B)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) ((semila598060698te_o_o A) B)) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o (big_la781588935tate_o ((semila1853742644te_o_o A) B))) (big_la781588935tate_o ((semila598060698te_o_o A) B)))) ((semila129691299tate_o (big_la781588935tate_o A)) (big_la781588935tate_o B))))))).
% Axiom fact_1195_UNIV__I:(forall (X_2:com), ((member_com X_2) top_top_com_o)).
% Axiom fact_1196_UNIV__I:(forall (X_2:pname), ((member_pname X_2) top_top_pname_o)).
% Axiom fact_1197_UNIV__I:(forall (X_2:hoare_1708887482_state), ((member451959335_state X_2) top_to832624271tate_o)).
% Axiom fact_1198_rangeI:(forall (F:(pname->hoare_1708887482_state)) (X_1:pname), ((member451959335_state (F X_1)) ((image_1116629049_state F) top_top_pname_o))).
% Axiom help_fequal_1_1_fequal_000tc__Com__Ocom_T:(forall (X:com) (Y:com), ((or (((fequal_com X) Y)->False)) (((eq com) X) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Com__Ocom_T:(forall (X:com) (Y:com), ((or (not (((eq com) X) Y))) ((fequal_com X) Y))).
% Axiom help_fequal_1_1_fequal_000tc__Com__Opname_T:(forall (X:pname) (Y:pname), ((or (((fequal_pname X) Y)->False)) (((eq pname) X) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Com__Opname_T:(forall (X:pname) (Y:pname), ((or (not (((eq pname) X) Y))) ((fequal_pname X) Y))).
% Axiom help_fequal_1_1_fequal_000tc__Com__Ostate_T:(forall (X:state) (Y:state), ((or (((fequal_state X) Y)->False)) (((eq state) X) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Com__Ostate_T:(forall (X:state) (Y:state), ((or (not (((eq state) X) Y))) ((fequal_state X) Y))).
% Axiom help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T:(forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (((fequal_pname_o X) Y)->False)) (((eq (pname->Prop)) X) Y))).
% Axiom help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T:(forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (not (((eq (pname->Prop)) X) Y))) ((fequal_pname_o X) Y))).
% Axiom help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T:(forall (X:option_com) (Y:option_com), (((eq option_com) (((if_option_com True) X) Y)) X)).
% Axiom help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T:(forall (X:option_com) (Y:option_com), (((eq option_com) (((if_option_com False) X) Y)) Y)).
% Axiom help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T:(forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))).
% Axiom help_If_1_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate:(forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), (((eq hoare_1708887482_state) (((if_Hoa1374726218_state True) X) Y)) X)).
% Axiom help_If_2_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate:(forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), (((eq hoare_1708887482_state) (((if_Hoa1374726218_state False) X) Y)) Y)).
% Axiom help_If_3_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate:(forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))).
% Axiom help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com:(forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), ((or (((fequal224822779_state X) Y)->False)) (((eq hoare_1708887482_state) X) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com:(forall (X:hoare_1708887482_state) (Y:hoare_1708887482_state), ((or (not (((eq hoare_1708887482_state) X) Y))) ((fequal224822779_state X) Y))).
% Axiom help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It:(forall (X:(hoare_1708887482_state->Prop)) (Y:(hoare_1708887482_state->Prop)), ((or (((fequal1436017556tate_o X) Y)->False)) (((eq (hoare_1708887482_state->Prop)) X) Y))).
% Axiom help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It:(forall (X:(hoare_1708887482_state->Prop)) (Y:(hoare_1708887482_state->Prop)), ((or (not (((eq (hoare_1708887482_state->Prop)) X) Y))) ((fequal1436017556tate_o X) Y))).
% Axiom conj_0:hoare_1160767572gleton.
% Axiom conj_1:wT_bodies.
% Axiom conj_2:(finite1625599783_state fa).
% Axiom conj_3:(((member451959335_state (hoare_Mirabelle_MGT y)) fa)->False).
% Axiom conj_4:((ord_le777019615tate_o fa) ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) (dom_pname_com body))).
% Axiom conj_5:(((eq option_com) (body pn)) (some_com y)).
% Axiom conj_6:((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa).
% Trying to prove ((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert528405184_state (hoare_Mirabelle_MGT y)) bot_bo19817387tate_o))
% Found conj_5:(((eq option_com) (body pn)) (some_com y))
% Instantiate: A_140:=(body pn):option_com
% Found conj_5 as proof of (((eq option_com) A_140) (some_com y))
% Found conj_0:hoare_1160767572gleton
% Found conj_0 as proof of hoare_1160767572gleton
% Found conj_6:((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa)
% Instantiate: G_34:=fa:(hoare_1708887482_state->Prop)
% Found conj_6 as proof of ((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_34)
% Found fact_166_subset__refl0:=(fact_166_subset__refl P_16):((ord_less_eq_pname_o P_16) P_16)
% Found (fact_166_subset__refl P_16) as proof of ((ord_less_eq_pname_o P_16) (fun (x1:pname)=> ((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert528405184_state (hoare_Mirabelle_MGT y)) bot_bo19817387tate_o))))
% Found (fact_166_subset__refl P_16) as proof of ((ord_less_eq_pname_o P_16) (fun (x1:pname)=> ((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert528405184_state (hoare_Mirabelle_MGT y)) bot_bo19817387tate_o))))
% Found (fact_166_subset__refl P_16) as proof of ((ord_less_eq_pname_o P_16) (fun (x1:pname)=> ((hoare_90032982_state ((image_1116629049_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert528405184_state (hoare_Mirabelle_MGT y)) bot_bo19817387tate_o))))
% Found conj_5:(((eq option_com) (body pn)) (some_com y))
% Instantiate: A_140:=(body pn):option_com
% Found conj_5 as proof of (((eq option_com) A_140) (some_com y))
% Found conj_5:(((eq option_com) (body pn)) (some_com y))
% Instantiate: A_140:=(body pn):option_com
% Found conj_5 as proof of (((eq option_com) A_140) (some_com y))
% Found conj_5:(((eq option_com) (body pn)) (some_com y))
% Instantiate: A_140:=(body pn):option_com
% Found conj_5 as proof of (((eq option_com) A_140) (some_com y))
% Found conj_5:(((eq option_com) (body pn)) (some_com y))
% Instantiate: A_140:=(body pn):option_com
% Found conj_5 as proof of (((eq option_com) A_140) (some_com y))
% Found conj_0:hoare_1160767572gleton
% Found conj_0 as proof of hoare_1160767572gleton
% Found fact_166_subset__refl:(forall (A_235:(pname->Prop)), ((ord_less_eq_pname_o A_235) A_235))
% Found fact_166_subset__refl as proof of (forall (X_101:(pname->Prop)), ((ord_less_eq_pname_o X_101) X_101))
% Found fact_465_xt1_I6_J:(forall (Z_20:(pname->Prop)) (Y_50:(pname->Prop)) (X_99:(pname->Prop)), (((ord_less_eq_pname_o Y_50) X_99)->(((ord_less_eq_pname_o Z_20) Y_50)->((ord_less_eq_pname_o Z_20) X_99))))
% Found fact_465_xt1_I6_J as proof of (forall (Z_20:(pname->Prop)) (Y_50:(pname->Prop)) (X_99:(pname->Prop)), (((ord_less_eq_pname_o Y_50) X_99)->(((ord_less_eq_pname_o Z_20) Y_50)->((ord_less_eq_pname_o Z_20) X_99))))
% Found fact_546_predicate1D:(forall (X_86:pname) (P_16:(pname->Prop)) (Q_7:(pname->Prop)), (((ord_less_eq_pname_o P_16) Q_7)->((P_16 X_86)->(Q_7 X_86))))
% Found fact_546_predicate1D as proof of (forall (X_86:pname) (P_160:(pname->Prop)) (Q_7:(pname->Prop)), (((ord_less_eq_pname_o P_160) Q_7)->((P_160 X_86)->(Q_7 X_86))))
% Found fact_544_rev__predicate1D:(forall (Q_8:(pname->Prop)) (P_17:(pname->Prop)) (X_87:pname), ((P_17 X_87)->(((ord_less_eq_pname_o P_17) Q_8)->(Q_8 X_87))))
% Found fact_544_rev__predicate1D as proof of (forall (Q_8:(pname->Prop)) (P_170:(pname->Prop)) (X_87:pname), ((P_170 X_87)->(((ord_less_eq_pname_o P_170) Q_8)->(Q_8 X_87))))
% Found fact_746_predicate1I:(forall (Q_4:(pname->Prop)) (P_9:(pname->Prop)), ((forall (X_3:pname), ((P_9 X_3)->(Q_4 X_3)))->((ord_less_eq_pname_o P_9) Q_4)))
% Found fact_746_predicate1I as proof of (forall (Q_4:(pname->Prop)) (P_9:(pname->Prop)), ((forall (X_3:pname), ((P_9 X_3)->(Q_4 X_3)))->((ord_less_eq_pname_o P_9) Q_4)))
% Found fact_149_subset__trans:(forall (C_64:(pname->Prop)) (A_242:(pname->Prop)) (B_157:(pname->Prop)), (((ord_less_eq_pname_o A_242) B_157)->(((ord_less_eq_pname_o B_157) C_64)->((ord_less_eq_pname_o A_242) C_64))))
% Found fact_149_subset__trans as proof of (forall (C_64:(pname->Prop)) (A_242:(pname->Prop)) (B_157:(pname->Prop)), (((ord_less_eq_pname_o A_242) B_157)->(((ord_less_eq_pname_o B_157) C_64)->((ord_less_eq_pname_o A_242) C_64))))
% Found fact_465_xt1_I6_J:(forall (Z_20:(pname->Prop)) (Y_50:(pname->Prop)) (X_99:(pname->Prop)), (((ord_less_eq_pname_o Y_50) X_99)->(((ord_less_eq_pname_o Z_20) Y_50)->((ord_less_eq_pname_o Z_20) X_99))))
% Found fact_465_xt1_I6_J as proof of (forall (Z_20:(pname->Prop)) (Y_50:(pname->Prop)) (X_99:(pname->Prop)), (((ord_less_eq_pname_o Y_50) X_99)->(((ord_less_eq_pname_o Z_20) Y_50)->((ord_less_eq_pname_o Z_20) X_99))))
% Found fact_149_subset__trans:(forall (C_64:(pname->Prop)) (A_242:(pname->
% EOF
%------------------------------------------------------------------------------