%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SWW474^2 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n092.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:37:24 EDT 2014

% Result   : Timeout 300.04s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SWW474^2 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n092.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 09:22:01 CDT 2014
% % CPUTime  : 300.04 
% 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 0x275b710>, <kernel.Type object at 0x275bb48>) of role type named ty_ty_tc__Com__Ocom
% Using role type
% Declaring com:Type
% FOF formula (<kernel.Constant object at 0x2b33128>, <kernel.Type object at 0x275b518>) of role type named ty_ty_tc__Com__Opname
% Using role type
% Declaring pname:Type
% FOF formula (<kernel.Constant object at 0x275b8c0>, <kernel.Type object at 0x275b830>) of role type named ty_ty_tc__Com__Ostate
% Using role type
% Declaring state:Type
% FOF formula (<kernel.Constant object at 0x275bb48>, <kernel.Type object at 0x275b3f8>) of role type named ty_ty_tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J
% Using role type
% Declaring hoare_1167836817_state:Type
% FOF formula (<kernel.Constant object at 0x275b518>, <kernel.Type object at 0x275b488>) 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 0x275b830>, <kernel.Type object at 0x275b6c8>) 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 0x275b3f8>, <kernel.Type object at 0x275bc20>) of role type named ty_ty_tc__Option__Ooption_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Co
% Using role type
% Declaring option1574264306_state:Type
% FOF formula (<kernel.Constant object at 0x275bcb0>, <kernel.DependentProduct object at 0x2b30cb0>) of role type named sy_c_Com_OWT
% Using role type
% Declaring wt:(com->Prop)
% FOF formula (<kernel.Constant object at 0x275b758>, <kernel.Sort object at 0x2640f38>) of role type named sy_c_Com_OWT__bodies
% Using role type
% Declaring wT_bodies:Prop
% FOF formula (<kernel.Constant object at 0x275b3f8>, <kernel.DependentProduct object at 0x2644d88>) of role type named sy_c_Com_Obody
% Using role type
% Declaring body:(pname->option_com)
% FOF formula (<kernel.Constant object at 0x2b30cb0>, <kernel.DependentProduct object at 0x263b7a0>) of role type named sy_c_Com_Ocom_OBODY
% Using role type
% Declaring body_1:(pname->com)
% FOF formula (<kernel.Constant object at 0x2b30cf8>, <kernel.Constant object at 0x275b830>) of role type named sy_c_Com_Ocom_OSKIP
% Using role type
% Declaring skip:com
% FOF formula (<kernel.Constant object at 0x2b30cf8>, <kernel.DependentProduct object at 0x275bcb0>) of role type named sy_c_Com_Ocom_OSemi
% Using role type
% Declaring semi:(com->(com->com))
% FOF formula (<kernel.Constant object at 0x263b7a0>, <kernel.DependentProduct object at 0x275b7a0>) of role type named sy_c_Com_Ocom_OWhile
% Using role type
% Declaring while:((state->Prop)->(com->com))
% FOF formula (<kernel.Constant object at 0x263b7a0>, <kernel.DependentProduct object at 0x2b52bd8>) 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 0x275bcb0>, <kernel.DependentProduct object at 0x2b52488>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____srushsumbx__Ot
% Using role type
% Declaring finite33115244te_o_o:((((hoare_1167836817_state->Prop)->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x275b758>, <kernel.DependentProduct object at 0x2b52bd8>) 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 0x275b4d0>, <kernel.DependentProduct object at 0x2b52488>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_
% Using role type
% Declaring finite1380128977tate_o:(((hoare_1167836817_state->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x275b830>, <kernel.DependentProduct object at 0x2b52368>) 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 0x275b4d0>, <kernel.DependentProduct object at 0x2b52050>) of role type named sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__C
% Using role type
% Declaring finite1084549118_state:((hoare_1167836817_state->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x275b830>, <kernel.DependentProduct object at 0x2b52368>) 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 0x275b830>, <kernel.DependentProduct object at 0x2b52e18>) of role type named sy_c_Finite__Set_Ofolding__one_000_062_Itc__Hoare____Mirabelle____srushsumbx__Ot
% Using role type
% Declaring finite979047547tate_o:(((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))->((((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x2b52050>, <kernel.DependentProduct object at 0x2b52098>) 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 0x2b52fc8>, <kernel.DependentProduct object at 0x2b52c20>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____srushsumbx__Otriple_
% Using role type
% Declaring finite1074406356_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop))
% FOF formula (<kernel.Constant object at 0x2b52f38>, <kernel.DependentProduct object at 0x2b52098>) 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 0x2b52f80>, <kernel.DependentProduct object at 0x2b52ef0>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Hoare____Mirabelle____srushsum
% Using role type
% Declaring finite671847800tate_o:(((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))->((((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x2b52c20>, <kernel.DependentProduct object at 0x2b52f38>) 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 0x2b52950>, <kernel.DependentProduct object at 0x2b52f80>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____srushsumbx__Ot
% Using role type
% Declaring finite806517911_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop))
% FOF formula (<kernel.Constant object at 0x2b52ea8>, <kernel.DependentProduct object at 0x2b52098>) 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 0x2b52758>, <kernel.DependentProduct object at 0x2b52290>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Hoare____Mirabelle____srushs
% Using role type
% Declaring minus_1708687022te_o_o:(((hoare_1167836817_state->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x2b52f38>, <kernel.DependentProduct object at 0x2b52758>) 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 0x2b52320>, <kernel.DependentProduct object at 0x2b52758>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____srushsumbx__
% Using role type
% Declaring minus_2107060239tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x2b52f80>, <kernel.DependentProduct object at 0x2776d88>) 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 0x2b52c20>, <kernel.DependentProduct object at 0x2776cf8>) of role type named sy_c_HOL_OThe_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_
% Using role type
% Declaring the_Ho310147232_state:((hoare_1167836817_state->Prop)->hoare_1167836817_state)
% FOF formula (<kernel.Constant object at 0x2b52320>, <kernel.DependentProduct object at 0x2776f38>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_OMGT
% Using role type
% Declaring hoare_Mirabelle_MGT:(com->hoare_1167836817_state)
% FOF formula (<kernel.Constant object at 0x2b52290>, <kernel.DependentProduct object at 0x2776c68>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__derivs_000tc__Com__Ostate
% Using role type
% Declaring hoare_123228589_state:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x2b52c20>, <kernel.DependentProduct object at 0x2776ab8>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__valids_000tc__Com__Ostate
% Using role type
% Declaring hoare_529639851_state:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x2b52290>, <kernel.Sort object at 0x2640f38>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Ostate__not__singleton
% Using role type
% Declaring hoare_1201148605gleton:Prop
% FOF formula (<kernel.Constant object at 0x2b52320>, <kernel.DependentProduct object at 0x2776cf8>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple_000tc__Com__Ostate
% Using role type
% Declaring hoare_908217195_state:((state->(state->Prop))->(com->((state->(state->Prop))->hoare_1167836817_state)))
% FOF formula (<kernel.Constant object at 0x2b52290>, <kernel.DependentProduct object at 0x2776cf8>) of role type named sy_c_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J
% Using role type
% Declaring if_Hoa833675553_state:(Prop->(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state)))
% FOF formula (<kernel.Constant object at 0x2b52290>, <kernel.DependentProduct object at 0x2776cf8>) 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 0x2776b48>, <kernel.DependentProduct object at 0x2776878>) 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 0x2776998>, <kernel.DependentProduct object at 0x2776d88>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell
% Using role type
% Declaring semila1758709489te_o_o:(((hoare_1167836817_state->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x2776bd8>, <kernel.DependentProduct object at 0x2776758>) 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 0x2776ea8>, <kernel.DependentProduct object at 0x27765a8>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____s
% Using role type
% Declaring semila179895820tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x2776560>, <kernel.DependentProduct object at 0x2776998>) 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 0x2776b48>, <kernel.DependentProduct object at 0x27764d0>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell
% Using role type
% Declaring semila866907787te_o_o:(((hoare_1167836817_state->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x2776758>, <kernel.DependentProduct object at 0x2776bd8>) 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 0x2776320>, <kernel.DependentProduct object at 0x2776e60>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____s
% Using role type
% Declaring semila1172322802tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x2776a28>, <kernel.DependentProduct object at 0x2776bd8>) 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 0x2776758>, <kernel.DependentProduct object at 0x2776320>) 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 0x2776e60>, <kernel.DependentProduct object at 0x2776bd8>) of role type named sy_c_Natural_Oevalc
% Using role type
% Declaring evalc:(com->(state->(state->Prop)))
% FOF formula (<kernel.Constant object at 0x2776830>, <kernel.DependentProduct object at 0x2776368>) 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 0x2776320>, <kernel.DependentProduct object at 0x2776488>) 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 0x2776bd8>, <kernel.DependentProduct object at 0x2b535f0>) of role type named sy_c_Option_Ooption_OSome_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__
% Using role type
% Declaring some_H1433514562_state:(hoare_1167836817_state->option1574264306_state)
% FOF formula (<kernel.Constant object at 0x2776f38>, <kernel.DependentProduct object at 0x2b53b00>) 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 0x2776368>, <kernel.DependentProduct object at 0x2b53170>) 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 0x2776320>, <kernel.DependentProduct object at 0x2b53b00>) of role type named sy_c_Option_Oset_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Osta
% Using role type
% Declaring set_Ho2131684873_state:(option1574264306_state->(hoare_1167836817_state->Prop))
% FOF formula (<kernel.Constant object at 0x2776e60>, <kernel.DependentProduct object at 0x2b532d8>) 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 0x2776320>, <kernel.DependentProduct object at 0x2b53170>) 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 0x2776f38>, <kernel.DependentProduct object at 0x2b53ab8>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____srushsu
% Using role type
% Declaring bot_bo691907561te_o_o:((hoare_1167836817_state->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x2776320>, <kernel.DependentProduct object at 0x2b53368>) 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 0x2776f38>, <kernel.DependentProduct object at 0x2b53290>) 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 0x2776f38>, <kernel.DependentProduct object at 0x2b53200>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____srushsumbx__O
% Using role type
% Declaring bot_bo70021908tate_o:(hoare_1167836817_state->Prop)
% FOF formula (<kernel.Constant object at 0x2b53368>, <kernel.Sort object at 0x2640f38>) 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 0x2b53ab8>, <kernel.DependentProduct object at 0x276c950>) 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 0x2b532d8>, <kernel.DependentProduct object at 0x276c878>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Hoare____Mirabelle____sr
% Using role type
% Declaring ord_le741939125te_o_o:(((hoare_1167836817_state->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x2b53290>, <kernel.DependentProduct object at 0x276c7e8>) 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 0x2b53ab8>, <kernel.DependentProduct object at 0x276c830>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____srushsum
% Using role type
% Declaring ord_le827224136tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x2b532d8>, <kernel.DependentProduct object at 0x276c7e8>) 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 0x2b53248>, <kernel.DependentProduct object at 0x276c758>) 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 0x2b532d8>, <kernel.DependentProduct object at 0x276c7a0>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_I
% Using role type
% Declaring collec1218656682te_o_o:((((hoare_1167836817_state->Prop)->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x2b53290>, <kernel.DependentProduct object at 0x276c710>) 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 0x2b53290>, <kernel.DependentProduct object at 0x276c638>) of role type named sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Co
% Using role type
% Declaring collec269976083tate_o:(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x276c758>, <kernel.DependentProduct object at 0x276c950>) 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 0x276c878>, <kernel.DependentProduct object at 0x276c638>) of role type named sy_c_Set_OCollect_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost
% Using role type
% Declaring collec1027672124_state:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))
% FOF formula (<kernel.Constant object at 0x276c8c0>, <kernel.DependentProduct object at 0x276c5f0>) 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 0x276c7e8>, <kernel.DependentProduct object at 0x276c638>) 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 0x276c950>, <kernel.DependentProduct object at 0x276c878>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Hoare____Mirabelle____sru
% Using role type
% Declaring image_1381916541_state:(((pname->Prop)->hoare_1167836817_state)->(((pname->Prop)->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x276c5a8>, <kernel.DependentProduct object at 0x276c4d0>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com_
% Using role type
% Declaring image_1488525317tate_o:(((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x276c488>, <kernel.DependentProduct object at 0x276c878>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__001
% Using role type
% Declaring image_980295115_pname:(((hoare_1167836817_state->Prop)->pname)->(((hoare_1167836817_state->Prop)->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x276c3f8>, <kernel.DependentProduct object at 0x276c950>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__002
% Using role type
% Declaring image_635813834_state:(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x276c638>, <kernel.DependentProduct object at 0x276c4d0>) 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 0x276c440>, <kernel.DependentProduct object at 0x276c950>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____srushsumbx
% Using role type
% Declaring image_475339327tate_o:((pname->(hoare_1167836817_state->Prop))->((pname->Prop)->((hoare_1167836817_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x276c5a8>, <kernel.DependentProduct object at 0x276c878>) 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 0x276c5f0>, <kernel.DependentProduct object at 0x276c290>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____srushsumbx__Otri
% Using role type
% Declaring image_575578384_state:((pname->hoare_1167836817_state)->((pname->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x276c248>, <kernel.DependentProduct object at 0x276c878>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat
% Using role type
% Declaring image_2066861949name_o:((hoare_1167836817_state->(pname->Prop))->((hoare_1167836817_state->Prop)->((pname->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x276c950>, <kernel.DependentProduct object at 0x276c290>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_003
% Using role type
% Declaring image_1745649338tate_o:((hoare_1167836817_state->(hoare_1167836817_state->Prop))->((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x276c560>, <kernel.DependentProduct object at 0x276c440>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_004
% Using role type
% Declaring image_8178176_pname:((hoare_1167836817_state->pname)->((hoare_1167836817_state->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x276c638>, <kernel.DependentProduct object at 0x276c170>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_005
% Using role type
% Declaring image_31595733_state:((hoare_1167836817_state->hoare_1167836817_state)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x276c878>, <kernel.DependentProduct object at 0x276c440>) 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 0x276c248>, <kernel.DependentProduct object at 0x276c170>) of role type named sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com
% Using role type
% Declaring insert999278200tate_o:((hoare_1167836817_state->Prop)->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x276c7a0>, <kernel.DependentProduct object at 0x276c638>) 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 0x276c950>, <kernel.DependentProduct object at 0x276ca28>) 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 0x276c878>, <kernel.DependentProduct object at 0x276c248>) of role type named sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Osta
% Using role type
% Declaring insert2134838167_state:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x276c7a0>, <kernel.DependentProduct object at 0x276c0e0>) 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 0x276ca28>, <kernel.DependentProduct object at 0x276c9e0>) of role type named sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__O
% Using role type
% Declaring the_el323660082_state:((hoare_1167836817_state->Prop)->hoare_1167836817_state)
% FOF formula (<kernel.Constant object at 0x276c320>, <kernel.DependentProduct object at 0x276cab8>) 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 0x276c170>, <kernel.DependentProduct object at 0x276cb00>) of role type named sy_c_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost
% Using role type
% Declaring fequal1486222077tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x276c200>, <kernel.DependentProduct object at 0x276c170>) 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 0x276c050>, <kernel.DependentProduct object at 0x276c878>) 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 0x276c320>, <kernel.DependentProduct object at 0x276cab8>) of role type named sy_c_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J
% Using role type
% Declaring fequal1831255762_state:(hoare_1167836817_state->(hoare_1167836817_state->Prop))
% FOF formula (<kernel.Constant object at 0x276c200>, <kernel.DependentProduct object at 0x276cbd8>) 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 0x276cb00>, <kernel.DependentProduct object at 0x276cc20>) of role type named sy_c_member_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost
% Using role type
% Declaring member864234961tate_o:((hoare_1167836817_state->Prop)->(((hoare_1167836817_state->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x276ca28>, <kernel.DependentProduct object at 0x276ccf8>) 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 0x276c878>, <kernel.DependentProduct object at 0x276cd40>) 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 0x276c200>, <kernel.DependentProduct object at 0x276cab8>) of role type named sy_c_member_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J
% Using role type
% Declaring member2058392318_state:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x276ca28>, <kernel.DependentProduct object at 0x276cb00>) of role type named sy_v_Fa
% Using role type
% Declaring fa:(hoare_1167836817_state->Prop)
% FOF formula (<kernel.Constant object at 0x276c878>, <kernel.Constant object at 0x276cb00>) of role type named sy_v_pn
% Using role type
% Declaring pn:pname
% FOF formula (<kernel.Constant object at 0x276c200>, <kernel.Constant object at 0x276cb00>) of role type named sy_v_y
% Using role type
% Declaring y:com
% FOF formula (forall (G_3:(hoare_1167836817_state->Prop)), ((hoare_123228589_state G_3) bot_bo70021908tate_o)) of role axiom named fact_0_empty
% A new axiom: (forall (G_3:(hoare_1167836817_state->Prop)), ((hoare_123228589_state G_3) bot_bo70021908tate_o))
% FOF formula (forall (Ts_7:(hoare_1167836817_state->Prop)) (G_35:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Ts_7) G_35)->((hoare_123228589_state G_35) Ts_7))) of role axiom named fact_1_asm
% A new axiom: (forall (Ts_7:(hoare_1167836817_state->Prop)) (G_35:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Ts_7) G_35)->((hoare_123228589_state G_35) Ts_7)))
% FOF formula (forall (Ts_6:(hoare_1167836817_state->Prop)) (G_34:(hoare_1167836817_state->Prop)) (Ts_5:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_34) Ts_5)->(((ord_le827224136tate_o Ts_6) Ts_5)->((hoare_123228589_state G_34) Ts_6)))) of role axiom named fact_2_weaken
% A new axiom: (forall (Ts_6:(hoare_1167836817_state->Prop)) (G_34:(hoare_1167836817_state->Prop)) (Ts_5:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_34) Ts_5)->(((ord_le827224136tate_o Ts_6) Ts_5)->((hoare_123228589_state G_34) Ts_6))))
% FOF formula (forall (G_33:(hoare_1167836817_state->Prop)) (G_32:(hoare_1167836817_state->Prop)) (Ts_4:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_32) Ts_4)->(((ord_le827224136tate_o G_32) G_33)->((hoare_123228589_state G_33) Ts_4)))) of role axiom named fact_3_thin
% A new axiom: (forall (G_33:(hoare_1167836817_state->Prop)) (G_32:(hoare_1167836817_state->Prop)) (Ts_4:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_32) Ts_4)->(((ord_le827224136tate_o G_32) G_33)->((hoare_123228589_state G_33) Ts_4))))
% FOF formula (forall (G_31:(hoare_1167836817_state->Prop)) (G_30:(hoare_1167836817_state->Prop)) (Ts_3:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_30) Ts_3)->(((hoare_123228589_state G_31) G_30)->((hoare_123228589_state G_31) Ts_3)))) of role axiom named fact_4_cut
% A new axiom: (forall (G_31:(hoare_1167836817_state->Prop)) (G_30:(hoare_1167836817_state->Prop)) (Ts_3:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_30) Ts_3)->(((hoare_123228589_state G_31) G_30)->((hoare_123228589_state G_31) Ts_3))))
% FOF formula (forall (Ts_2:(hoare_1167836817_state->Prop)) (G_29:(hoare_1167836817_state->Prop)) (T_3:hoare_1167836817_state), (((hoare_123228589_state G_29) ((insert2134838167_state T_3) bot_bo70021908tate_o))->(((hoare_123228589_state G_29) Ts_2)->((hoare_123228589_state G_29) ((insert2134838167_state T_3) Ts_2))))) of role axiom named fact_5_hoare__derivs_Oinsert
% A new axiom: (forall (Ts_2:(hoare_1167836817_state->Prop)) (G_29:(hoare_1167836817_state->Prop)) (T_3:hoare_1167836817_state), (((hoare_123228589_state G_29) ((insert2134838167_state T_3) bot_bo70021908tate_o))->(((hoare_123228589_state G_29) Ts_2)->((hoare_123228589_state G_29) ((insert2134838167_state T_3) Ts_2)))))
% FOF formula (forall (G_28:(hoare_1167836817_state->Prop)) (T_2:hoare_1167836817_state) (Ts_1:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_28) ((insert2134838167_state T_2) Ts_1))->((and ((hoare_123228589_state G_28) ((insert2134838167_state T_2) bot_bo70021908tate_o))) ((hoare_123228589_state G_28) Ts_1)))) of role axiom named fact_6_derivs__insertD
% A new axiom: (forall (G_28:(hoare_1167836817_state->Prop)) (T_2:hoare_1167836817_state) (Ts_1:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_28) ((insert2134838167_state T_2) Ts_1))->((and ((hoare_123228589_state G_28) ((insert2134838167_state T_2) bot_bo70021908tate_o))) ((hoare_123228589_state G_28) Ts_1))))
% FOF formula (forall (Pn_1:pname) (G_3:(hoare_1167836817_state->Prop)), (((hoare_123228589_state ((insert2134838167_state (hoare_Mirabelle_MGT (body_1 Pn_1))) G_3)) ((insert2134838167_state (hoare_Mirabelle_MGT (the_com (body Pn_1)))) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT (body_1 Pn_1))) bot_bo70021908tate_o)))) of role axiom named fact_7_MGT__BodyN
% A new axiom: (forall (Pn_1:pname) (G_3:(hoare_1167836817_state->Prop)), (((hoare_123228589_state ((insert2134838167_state (hoare_Mirabelle_MGT (body_1 Pn_1))) G_3)) ((insert2134838167_state (hoare_Mirabelle_MGT (the_com (body Pn_1)))) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT (body_1 Pn_1))) bot_bo70021908tate_o))))
% FOF formula (forall (A_201:((pname->Prop)->Prop)), ((finite297249702name_o A_201)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_43:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_43) A_201)))))) of role axiom named fact_8_finite__Collect__subsets
% A new axiom: (forall (A_201:((pname->Prop)->Prop)), ((finite297249702name_o A_201)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_43:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_43) A_201))))))
% FOF formula (forall (A_201:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_201)->(finite33115244te_o_o (collec1218656682te_o_o (fun (B_43:((hoare_1167836817_state->Prop)->Prop))=> ((ord_le741939125te_o_o B_43) A_201)))))) of role axiom named fact_9_finite__Collect__subsets
% A new axiom: (forall (A_201:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_201)->(finite33115244te_o_o (collec1218656682te_o_o (fun (B_43:((hoare_1167836817_state->Prop)->Prop))=> ((ord_le741939125te_o_o B_43) A_201))))))
% FOF formula (forall (A_201:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_201)->(finite1380128977tate_o (collec269976083tate_o (fun (B_43:(hoare_1167836817_state->Prop))=> ((ord_le827224136tate_o B_43) A_201)))))) of role axiom named fact_10_finite__Collect__subsets
% A new axiom: (forall (A_201:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_201)->(finite1380128977tate_o (collec269976083tate_o (fun (B_43:(hoare_1167836817_state->Prop))=> ((ord_le827224136tate_o B_43) A_201))))))
% FOF formula (forall (A_201:(pname->Prop)), ((finite_finite_pname A_201)->(finite297249702name_o (collect_pname_o (fun (B_43:(pname->Prop))=> ((ord_less_eq_pname_o B_43) A_201)))))) of role axiom named fact_11_finite__Collect__subsets
% A new axiom: (forall (A_201:(pname->Prop)), ((finite_finite_pname A_201)->(finite297249702name_o (collect_pname_o (fun (B_43:(pname->Prop))=> ((ord_less_eq_pname_o B_43) A_201))))))
% FOF formula (forall (H_1:(hoare_1167836817_state->(pname->Prop))) (F_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_61)->(finite297249702name_o ((image_2066861949name_o H_1) F_61)))) of role axiom named fact_12_finite__imageI
% A new axiom: (forall (H_1:(hoare_1167836817_state->(pname->Prop))) (F_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_61)->(finite297249702name_o ((image_2066861949name_o H_1) F_61))))
% FOF formula (forall (H_1:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (F_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_61)->(finite1380128977tate_o ((image_1745649338tate_o H_1) F_61)))) of role axiom named fact_13_finite__imageI
% A new axiom: (forall (H_1:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (F_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_61)->(finite1380128977tate_o ((image_1745649338tate_o H_1) F_61))))
% FOF formula (forall (H_1:(pname->(pname->Prop))) (F_61:(pname->Prop)), ((finite_finite_pname F_61)->(finite297249702name_o ((image_pname_pname_o H_1) F_61)))) of role axiom named fact_14_finite__imageI
% A new axiom: (forall (H_1:(pname->(pname->Prop))) (F_61:(pname->Prop)), ((finite_finite_pname F_61)->(finite297249702name_o ((image_pname_pname_o H_1) F_61))))
% FOF formula (forall (H_1:(pname->(hoare_1167836817_state->Prop))) (F_61:(pname->Prop)), ((finite_finite_pname F_61)->(finite1380128977tate_o ((image_475339327tate_o H_1) F_61)))) of role axiom named fact_15_finite__imageI
% A new axiom: (forall (H_1:(pname->(hoare_1167836817_state->Prop))) (F_61:(pname->Prop)), ((finite_finite_pname F_61)->(finite1380128977tate_o ((image_475339327tate_o H_1) F_61))))
% FOF formula (forall (H_1:((pname->Prop)->hoare_1167836817_state)) (F_61:((pname->Prop)->Prop)), ((finite297249702name_o F_61)->(finite1084549118_state ((image_1381916541_state H_1) F_61)))) of role axiom named fact_16_finite__imageI
% A new axiom: (forall (H_1:((pname->Prop)->hoare_1167836817_state)) (F_61:((pname->Prop)->Prop)), ((finite297249702name_o F_61)->(finite1084549118_state ((image_1381916541_state H_1) F_61))))
% FOF formula (forall (H_1:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (F_61:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_61)->(finite1084549118_state ((image_635813834_state H_1) F_61)))) of role axiom named fact_17_finite__imageI
% A new axiom: (forall (H_1:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (F_61:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_61)->(finite1084549118_state ((image_635813834_state H_1) F_61))))
% FOF formula (forall (H_1:((pname->Prop)->pname)) (F_61:((pname->Prop)->Prop)), ((finite297249702name_o F_61)->(finite_finite_pname ((image_pname_o_pname H_1) F_61)))) of role axiom named fact_18_finite__imageI
% A new axiom: (forall (H_1:((pname->Prop)->pname)) (F_61:((pname->Prop)->Prop)), ((finite297249702name_o F_61)->(finite_finite_pname ((image_pname_o_pname H_1) F_61))))
% FOF formula (forall (H_1:((hoare_1167836817_state->Prop)->pname)) (F_61:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_61)->(finite_finite_pname ((image_980295115_pname H_1) F_61)))) of role axiom named fact_19_finite__imageI
% A new axiom: (forall (H_1:((hoare_1167836817_state->Prop)->pname)) (F_61:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_61)->(finite_finite_pname ((image_980295115_pname H_1) F_61))))
% FOF formula (forall (H_1:(pname->hoare_1167836817_state)) (F_61:(pname->Prop)), ((finite_finite_pname F_61)->(finite1084549118_state ((image_575578384_state H_1) F_61)))) of role axiom named fact_20_finite__imageI
% A new axiom: (forall (H_1:(pname->hoare_1167836817_state)) (F_61:(pname->Prop)), ((finite_finite_pname F_61)->(finite1084549118_state ((image_575578384_state H_1) F_61))))
% FOF formula (forall (A_200:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_200)) of role axiom named fact_21_empty__subsetI
% A new axiom: (forall (A_200:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_200))
% FOF formula (forall (A_200:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_200)) of role axiom named fact_22_empty__subsetI
% A new axiom: (forall (A_200:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_200))
% FOF formula (forall (A_199:(pname->Prop)) (A_198:((pname->Prop)->Prop)), ((finite297249702name_o A_198)->(finite297249702name_o ((insert_pname_o A_199) A_198)))) of role axiom named fact_23_finite_OinsertI
% A new axiom: (forall (A_199:(pname->Prop)) (A_198:((pname->Prop)->Prop)), ((finite297249702name_o A_198)->(finite297249702name_o ((insert_pname_o A_199) A_198))))
% FOF formula (forall (A_199:(hoare_1167836817_state->Prop)) (A_198:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_198)->(finite1380128977tate_o ((insert999278200tate_o A_199) A_198)))) of role axiom named fact_24_finite_OinsertI
% A new axiom: (forall (A_199:(hoare_1167836817_state->Prop)) (A_198:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_198)->(finite1380128977tate_o ((insert999278200tate_o A_199) A_198))))
% FOF formula (forall (A_199:pname) (A_198:(pname->Prop)), ((finite_finite_pname A_198)->(finite_finite_pname ((insert_pname A_199) A_198)))) of role axiom named fact_25_finite_OinsertI
% A new axiom: (forall (A_199:pname) (A_198:(pname->Prop)), ((finite_finite_pname A_198)->(finite_finite_pname ((insert_pname A_199) A_198))))
% FOF formula (forall (A_199:hoare_1167836817_state) (A_198:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_198)->(finite1084549118_state ((insert2134838167_state A_199) A_198)))) of role axiom named fact_26_finite_OinsertI
% A new axiom: (forall (A_199:hoare_1167836817_state) (A_198:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_198)->(finite1084549118_state ((insert2134838167_state A_199) A_198))))
% FOF formula (finite297249702name_o bot_bot_pname_o_o) of role axiom named fact_27_finite_OemptyI
% A new axiom: (finite297249702name_o bot_bot_pname_o_o)
% FOF formula (finite1380128977tate_o bot_bo691907561te_o_o) of role axiom named fact_28_finite_OemptyI
% A new axiom: (finite1380128977tate_o bot_bo691907561te_o_o)
% FOF formula (finite1084549118_state bot_bo70021908tate_o) of role axiom named fact_29_finite_OemptyI
% A new axiom: (finite1084549118_state bot_bo70021908tate_o)
% FOF formula (finite_finite_pname bot_bot_pname_o) of role axiom named fact_30_finite_OemptyI
% A new axiom: (finite_finite_pname bot_bot_pname_o)
% FOF formula (forall (Q_24:((pname->Prop)->Prop)) (P_42:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_42))) (finite297249702name_o (collect_pname_o Q_24)))->(finite297249702name_o (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (P_42 X_5)) (Q_24 X_5))))))) of role axiom named fact_31_finite__Collect__conjI
% A new axiom: (forall (Q_24:((pname->Prop)->Prop)) (P_42:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_42))) (finite297249702name_o (collect_pname_o Q_24)))->(finite297249702name_o (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (P_42 X_5)) (Q_24 X_5)))))))
% FOF formula (forall (Q_24:((hoare_1167836817_state->Prop)->Prop)) (P_42:((hoare_1167836817_state->Prop)->Prop)), (((or (finite1380128977tate_o (collec269976083tate_o P_42))) (finite1380128977tate_o (collec269976083tate_o Q_24)))->(finite1380128977tate_o (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (P_42 X_5)) (Q_24 X_5))))))) of role axiom named fact_32_finite__Collect__conjI
% A new axiom: (forall (Q_24:((hoare_1167836817_state->Prop)->Prop)) (P_42:((hoare_1167836817_state->Prop)->Prop)), (((or (finite1380128977tate_o (collec269976083tate_o P_42))) (finite1380128977tate_o (collec269976083tate_o Q_24)))->(finite1380128977tate_o (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (P_42 X_5)) (Q_24 X_5)))))))
% FOF formula (forall (Q_24:(hoare_1167836817_state->Prop)) (P_42:(hoare_1167836817_state->Prop)), (((or (finite1084549118_state (collec1027672124_state P_42))) (finite1084549118_state (collec1027672124_state Q_24)))->(finite1084549118_state (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (P_42 X_5)) (Q_24 X_5))))))) of role axiom named fact_33_finite__Collect__conjI
% A new axiom: (forall (Q_24:(hoare_1167836817_state->Prop)) (P_42:(hoare_1167836817_state->Prop)), (((or (finite1084549118_state (collec1027672124_state P_42))) (finite1084549118_state (collec1027672124_state Q_24)))->(finite1084549118_state (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (P_42 X_5)) (Q_24 X_5)))))))
% FOF formula (forall (Q_24:(pname->Prop)) (P_42:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_42))) (finite_finite_pname (collect_pname Q_24)))->(finite_finite_pname (collect_pname (fun (X_5:pname)=> ((and (P_42 X_5)) (Q_24 X_5))))))) of role axiom named fact_34_finite__Collect__conjI
% A new axiom: (forall (Q_24:(pname->Prop)) (P_42:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_42))) (finite_finite_pname (collect_pname Q_24)))->(finite_finite_pname (collect_pname (fun (X_5:pname)=> ((and (P_42 X_5)) (Q_24 X_5)))))))
% FOF formula (forall (C_54:pname) (A_197:(hoare_1167836817_state->Prop)), ((and ((((eq (hoare_1167836817_state->Prop)) A_197) bot_bo70021908tate_o)->(((eq (pname->Prop)) ((image_8178176_pname (fun (X_5:hoare_1167836817_state)=> C_54)) A_197)) bot_bot_pname_o))) ((not (((eq (hoare_1167836817_state->Prop)) A_197) bot_bo70021908tate_o))->(((eq (pname->Prop)) ((image_8178176_pname (fun (X_5:hoare_1167836817_state)=> C_54)) A_197)) ((insert_pname C_54) bot_bot_pname_o))))) of role axiom named fact_35_image__constant__conv
% A new axiom: (forall (C_54:pname) (A_197:(hoare_1167836817_state->Prop)), ((and ((((eq (hoare_1167836817_state->Prop)) A_197) bot_bo70021908tate_o)->(((eq (pname->Prop)) ((image_8178176_pname (fun (X_5:hoare_1167836817_state)=> C_54)) A_197)) bot_bot_pname_o))) ((not (((eq (hoare_1167836817_state->Prop)) A_197) bot_bo70021908tate_o))->(((eq (pname->Prop)) ((image_8178176_pname (fun (X_5:hoare_1167836817_state)=> C_54)) A_197)) ((insert_pname C_54) bot_bot_pname_o)))))
% FOF formula (forall (C_54:hoare_1167836817_state) (A_197:(pname->Prop)), ((and ((((eq (pname->Prop)) A_197) bot_bot_pname_o)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> C_54)) A_197)) bot_bo70021908tate_o))) ((not (((eq (pname->Prop)) A_197) bot_bot_pname_o))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> C_54)) A_197)) ((insert2134838167_state C_54) bot_bo70021908tate_o))))) of role axiom named fact_36_image__constant__conv
% A new axiom: (forall (C_54:hoare_1167836817_state) (A_197:(pname->Prop)), ((and ((((eq (pname->Prop)) A_197) bot_bot_pname_o)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> C_54)) A_197)) bot_bo70021908tate_o))) ((not (((eq (pname->Prop)) A_197) bot_bot_pname_o))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> C_54)) A_197)) ((insert2134838167_state C_54) bot_bo70021908tate_o)))))
% FOF formula (forall (C_53:pname) (X_101:hoare_1167836817_state) (A_196:(hoare_1167836817_state->Prop)), (((member2058392318_state X_101) A_196)->(((eq (pname->Prop)) ((image_8178176_pname (fun (X_5:hoare_1167836817_state)=> C_53)) A_196)) ((insert_pname C_53) bot_bot_pname_o)))) of role axiom named fact_37_image__constant
% A new axiom: (forall (C_53:pname) (X_101:hoare_1167836817_state) (A_196:(hoare_1167836817_state->Prop)), (((member2058392318_state X_101) A_196)->(((eq (pname->Prop)) ((image_8178176_pname (fun (X_5:hoare_1167836817_state)=> C_53)) A_196)) ((insert_pname C_53) bot_bot_pname_o))))
% FOF formula (forall (C_53:hoare_1167836817_state) (X_101:pname) (A_196:(pname->Prop)), (((member_pname X_101) A_196)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> C_53)) A_196)) ((insert2134838167_state C_53) bot_bo70021908tate_o)))) of role axiom named fact_38_image__constant
% A new axiom: (forall (C_53:hoare_1167836817_state) (X_101:pname) (A_196:(pname->Prop)), (((member_pname X_101) A_196)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> C_53)) A_196)) ((insert2134838167_state C_53) bot_bo70021908tate_o))))
% FOF formula (forall (F_60:(pname->option_com)) (X_100:pname) (Y_49:com), ((((eq option_com) (F_60 X_100)) (some_com Y_49))->(((eq (pname->Prop)) ((insert_pname X_100) (dom_pname_com F_60))) (dom_pname_com F_60)))) of role axiom named fact_39_insert__dom
% A new axiom: (forall (F_60:(pname->option_com)) (X_100:pname) (Y_49:com), ((((eq option_com) (F_60 X_100)) (some_com Y_49))->(((eq (pname->Prop)) ((insert_pname X_100) (dom_pname_com F_60))) (dom_pname_com F_60))))
% FOF formula (forall (B_130:((pname->Prop)->Prop)) (F_59:(hoare_1167836817_state->(pname->Prop))) (A_195:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_195)->(((ord_le1205211808me_o_o B_130) ((image_2066861949name_o F_59) A_195))->(finite297249702name_o B_130)))) of role axiom named fact_40_finite__surj
% A new axiom: (forall (B_130:((pname->Prop)->Prop)) (F_59:(hoare_1167836817_state->(pname->Prop))) (A_195:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_195)->(((ord_le1205211808me_o_o B_130) ((image_2066861949name_o F_59) A_195))->(finite297249702name_o B_130))))
% FOF formula (forall (B_130:((hoare_1167836817_state->Prop)->Prop)) (F_59:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (A_195:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_195)->(((ord_le741939125te_o_o B_130) ((image_1745649338tate_o F_59) A_195))->(finite1380128977tate_o B_130)))) of role axiom named fact_41_finite__surj
% A new axiom: (forall (B_130:((hoare_1167836817_state->Prop)->Prop)) (F_59:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (A_195:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_195)->(((ord_le741939125te_o_o B_130) ((image_1745649338tate_o F_59) A_195))->(finite1380128977tate_o B_130))))
% FOF formula (forall (B_130:(pname->Prop)) (F_59:(hoare_1167836817_state->pname)) (A_195:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_195)->(((ord_less_eq_pname_o B_130) ((image_8178176_pname F_59) A_195))->(finite_finite_pname B_130)))) of role axiom named fact_42_finite__surj
% A new axiom: (forall (B_130:(pname->Prop)) (F_59:(hoare_1167836817_state->pname)) (A_195:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_195)->(((ord_less_eq_pname_o B_130) ((image_8178176_pname F_59) A_195))->(finite_finite_pname B_130))))
% FOF formula (forall (B_130:((pname->Prop)->Prop)) (F_59:(pname->(pname->Prop))) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_le1205211808me_o_o B_130) ((image_pname_pname_o F_59) A_195))->(finite297249702name_o B_130)))) of role axiom named fact_43_finite__surj
% A new axiom: (forall (B_130:((pname->Prop)->Prop)) (F_59:(pname->(pname->Prop))) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_le1205211808me_o_o B_130) ((image_pname_pname_o F_59) A_195))->(finite297249702name_o B_130))))
% FOF formula (forall (B_130:((hoare_1167836817_state->Prop)->Prop)) (F_59:(pname->(hoare_1167836817_state->Prop))) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_le741939125te_o_o B_130) ((image_475339327tate_o F_59) A_195))->(finite1380128977tate_o B_130)))) of role axiom named fact_44_finite__surj
% A new axiom: (forall (B_130:((hoare_1167836817_state->Prop)->Prop)) (F_59:(pname->(hoare_1167836817_state->Prop))) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_le741939125te_o_o B_130) ((image_475339327tate_o F_59) A_195))->(finite1380128977tate_o B_130))))
% FOF formula (forall (B_130:(pname->Prop)) (F_59:(pname->pname)) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_less_eq_pname_o B_130) ((image_pname_pname F_59) A_195))->(finite_finite_pname B_130)))) of role axiom named fact_45_finite__surj
% A new axiom: (forall (B_130:(pname->Prop)) (F_59:(pname->pname)) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_less_eq_pname_o B_130) ((image_pname_pname F_59) A_195))->(finite_finite_pname B_130))))
% FOF formula (forall (B_130:(hoare_1167836817_state->Prop)) (F_59:((pname->Prop)->hoare_1167836817_state)) (A_195:((pname->Prop)->Prop)), ((finite297249702name_o A_195)->(((ord_le827224136tate_o B_130) ((image_1381916541_state F_59) A_195))->(finite1084549118_state B_130)))) of role axiom named fact_46_finite__surj
% A new axiom: (forall (B_130:(hoare_1167836817_state->Prop)) (F_59:((pname->Prop)->hoare_1167836817_state)) (A_195:((pname->Prop)->Prop)), ((finite297249702name_o A_195)->(((ord_le827224136tate_o B_130) ((image_1381916541_state F_59) A_195))->(finite1084549118_state B_130))))
% FOF formula (forall (B_130:(hoare_1167836817_state->Prop)) (F_59:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (A_195:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_195)->(((ord_le827224136tate_o B_130) ((image_635813834_state F_59) A_195))->(finite1084549118_state B_130)))) of role axiom named fact_47_finite__surj
% A new axiom: (forall (B_130:(hoare_1167836817_state->Prop)) (F_59:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (A_195:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_195)->(((ord_le827224136tate_o B_130) ((image_635813834_state F_59) A_195))->(finite1084549118_state B_130))))
% FOF formula (forall (B_130:(pname->Prop)) (F_59:((pname->Prop)->pname)) (A_195:((pname->Prop)->Prop)), ((finite297249702name_o A_195)->(((ord_less_eq_pname_o B_130) ((image_pname_o_pname F_59) A_195))->(finite_finite_pname B_130)))) of role axiom named fact_48_finite__surj
% A new axiom: (forall (B_130:(pname->Prop)) (F_59:((pname->Prop)->pname)) (A_195:((pname->Prop)->Prop)), ((finite297249702name_o A_195)->(((ord_less_eq_pname_o B_130) ((image_pname_o_pname F_59) A_195))->(finite_finite_pname B_130))))
% FOF formula (forall (B_130:(pname->Prop)) (F_59:((hoare_1167836817_state->Prop)->pname)) (A_195:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_195)->(((ord_less_eq_pname_o B_130) ((image_980295115_pname F_59) A_195))->(finite_finite_pname B_130)))) of role axiom named fact_49_finite__surj
% A new axiom: (forall (B_130:(pname->Prop)) (F_59:((hoare_1167836817_state->Prop)->pname)) (A_195:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_195)->(((ord_less_eq_pname_o B_130) ((image_980295115_pname F_59) A_195))->(finite_finite_pname B_130))))
% FOF formula (forall (B_130:(hoare_1167836817_state->Prop)) (F_59:(pname->hoare_1167836817_state)) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_le827224136tate_o B_130) ((image_575578384_state F_59) A_195))->(finite1084549118_state B_130)))) of role axiom named fact_50_finite__surj
% A new axiom: (forall (B_130:(hoare_1167836817_state->Prop)) (F_59:(pname->hoare_1167836817_state)) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_le827224136tate_o B_130) ((image_575578384_state F_59) A_195))->(finite1084549118_state B_130))))
% FOF formula (forall (A_194:(pname->Prop)) (X_99:pname), (((ord_less_eq_pname_o A_194) ((insert_pname X_99) bot_bot_pname_o))->((or (((eq (pname->Prop)) A_194) bot_bot_pname_o)) (((eq (pname->Prop)) A_194) ((insert_pname X_99) bot_bot_pname_o))))) of role axiom named fact_51_subset__singletonD
% A new axiom: (forall (A_194:(pname->Prop)) (X_99:pname), (((ord_less_eq_pname_o A_194) ((insert_pname X_99) bot_bot_pname_o))->((or (((eq (pname->Prop)) A_194) bot_bot_pname_o)) (((eq (pname->Prop)) A_194) ((insert_pname X_99) bot_bot_pname_o)))))
% FOF formula (forall (A_194:(hoare_1167836817_state->Prop)) (X_99:hoare_1167836817_state), (((ord_le827224136tate_o A_194) ((insert2134838167_state X_99) bot_bo70021908tate_o))->((or (((eq (hoare_1167836817_state->Prop)) A_194) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_194) ((insert2134838167_state X_99) bot_bo70021908tate_o))))) of role axiom named fact_52_subset__singletonD
% A new axiom: (forall (A_194:(hoare_1167836817_state->Prop)) (X_99:hoare_1167836817_state), (((ord_le827224136tate_o A_194) ((insert2134838167_state X_99) bot_bo70021908tate_o))->((or (((eq (hoare_1167836817_state->Prop)) A_194) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_194) ((insert2134838167_state X_99) bot_bo70021908tate_o)))))
% FOF formula (forall (C_21:com), (hoare_1201148605gleton->(wT_bodies->((wt C_21)->((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o)))))) of role axiom named fact_53_MGF
% A new axiom: (forall (C_21:com), (hoare_1201148605gleton->(wT_bodies->((wt C_21)->((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o))))))
% FOF formula (forall (A_193:pname), (((member_pname A_193) bot_bot_pname_o)->False)) of role axiom named fact_54_emptyE
% A new axiom: (forall (A_193:pname), (((member_pname A_193) bot_bot_pname_o)->False))
% FOF formula (forall (A_193:hoare_1167836817_state), (((member2058392318_state A_193) bot_bo70021908tate_o)->False)) of role axiom named fact_55_emptyE
% A new axiom: (forall (A_193:hoare_1167836817_state), (((member2058392318_state A_193) bot_bo70021908tate_o)->False))
% FOF formula (forall (B_129:pname) (A_192:pname) (B_128:(pname->Prop)), (((((member_pname A_192) B_128)->False)->(((eq pname) A_192) B_129))->((member_pname A_192) ((insert_pname B_129) B_128)))) of role axiom named fact_56_insertCI
% A new axiom: (forall (B_129:pname) (A_192:pname) (B_128:(pname->Prop)), (((((member_pname A_192) B_128)->False)->(((eq pname) A_192) B_129))->((member_pname A_192) ((insert_pname B_129) B_128))))
% FOF formula (forall (B_129:hoare_1167836817_state) (A_192:hoare_1167836817_state) (B_128:(hoare_1167836817_state->Prop)), (((((member2058392318_state A_192) B_128)->False)->(((eq hoare_1167836817_state) A_192) B_129))->((member2058392318_state A_192) ((insert2134838167_state B_129) B_128)))) of role axiom named fact_57_insertCI
% A new axiom: (forall (B_129:hoare_1167836817_state) (A_192:hoare_1167836817_state) (B_128:(hoare_1167836817_state->Prop)), (((((member2058392318_state A_192) B_128)->False)->(((eq hoare_1167836817_state) A_192) B_129))->((member2058392318_state A_192) ((insert2134838167_state B_129) B_128))))
% FOF formula (forall (A_191:pname) (B_127:pname) (A_190:(pname->Prop)), (((member_pname A_191) ((insert_pname B_127) A_190))->((not (((eq pname) A_191) B_127))->((member_pname A_191) A_190)))) of role axiom named fact_58_insertE
% A new axiom: (forall (A_191:pname) (B_127:pname) (A_190:(pname->Prop)), (((member_pname A_191) ((insert_pname B_127) A_190))->((not (((eq pname) A_191) B_127))->((member_pname A_191) A_190))))
% FOF formula (forall (A_191:hoare_1167836817_state) (B_127:hoare_1167836817_state) (A_190:(hoare_1167836817_state->Prop)), (((member2058392318_state A_191) ((insert2134838167_state B_127) A_190))->((not (((eq hoare_1167836817_state) A_191) B_127))->((member2058392318_state A_191) A_190)))) of role axiom named fact_59_insertE
% A new axiom: (forall (A_191:hoare_1167836817_state) (B_127:hoare_1167836817_state) (A_190:(hoare_1167836817_state->Prop)), (((member2058392318_state A_191) ((insert2134838167_state B_127) A_190))->((not (((eq hoare_1167836817_state) A_191) B_127))->((member2058392318_state A_191) A_190))))
% FOF formula (forall (A_189:(pname->Prop)) (B_126:(pname->Prop)), (((ord_less_eq_pname_o A_189) B_126)->(((ord_less_eq_pname_o B_126) A_189)->(((eq (pname->Prop)) A_189) B_126)))) of role axiom named fact_60_equalityI
% A new axiom: (forall (A_189:(pname->Prop)) (B_126:(pname->Prop)), (((ord_less_eq_pname_o A_189) B_126)->(((ord_less_eq_pname_o B_126) A_189)->(((eq (pname->Prop)) A_189) B_126))))
% FOF formula (forall (A_189:(hoare_1167836817_state->Prop)) (B_126:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_189) B_126)->(((ord_le827224136tate_o B_126) A_189)->(((eq (hoare_1167836817_state->Prop)) A_189) B_126)))) of role axiom named fact_61_equalityI
% A new axiom: (forall (A_189:(hoare_1167836817_state->Prop)) (B_126:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_189) B_126)->(((ord_le827224136tate_o B_126) A_189)->(((eq (hoare_1167836817_state->Prop)) A_189) B_126))))
% FOF formula (forall (C_52:pname) (A_188:(pname->Prop)) (B_125:(pname->Prop)), (((ord_less_eq_pname_o A_188) B_125)->(((member_pname C_52) A_188)->((member_pname C_52) B_125)))) of role axiom named fact_62_subsetD
% A new axiom: (forall (C_52:pname) (A_188:(pname->Prop)) (B_125:(pname->Prop)), (((ord_less_eq_pname_o A_188) B_125)->(((member_pname C_52) A_188)->((member_pname C_52) B_125))))
% FOF formula (forall (C_52:hoare_1167836817_state) (A_188:(hoare_1167836817_state->Prop)) (B_125:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_188) B_125)->(((member2058392318_state C_52) A_188)->((member2058392318_state C_52) B_125)))) of role axiom named fact_63_subsetD
% A new axiom: (forall (C_52:hoare_1167836817_state) (A_188:(hoare_1167836817_state->Prop)) (B_125:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_188) B_125)->(((member2058392318_state C_52) A_188)->((member2058392318_state C_52) B_125))))
% FOF formula (forall (A_187:(hoare_1167836817_state->Prop)) (B_124:pname) (F_58:(hoare_1167836817_state->pname)) (X_98:hoare_1167836817_state), ((((eq pname) B_124) (F_58 X_98))->(((member2058392318_state X_98) A_187)->((member_pname B_124) ((image_8178176_pname F_58) A_187))))) of role axiom named fact_64_image__eqI
% A new axiom: (forall (A_187:(hoare_1167836817_state->Prop)) (B_124:pname) (F_58:(hoare_1167836817_state->pname)) (X_98:hoare_1167836817_state), ((((eq pname) B_124) (F_58 X_98))->(((member2058392318_state X_98) A_187)->((member_pname B_124) ((image_8178176_pname F_58) A_187)))))
% FOF formula (forall (A_187:(pname->Prop)) (B_124:hoare_1167836817_state) (F_58:(pname->hoare_1167836817_state)) (X_98:pname), ((((eq hoare_1167836817_state) B_124) (F_58 X_98))->(((member_pname X_98) A_187)->((member2058392318_state B_124) ((image_575578384_state F_58) A_187))))) of role axiom named fact_65_image__eqI
% A new axiom: (forall (A_187:(pname->Prop)) (B_124:hoare_1167836817_state) (F_58:(pname->hoare_1167836817_state)) (X_98:pname), ((((eq hoare_1167836817_state) B_124) (F_58 X_98))->(((member_pname X_98) A_187)->((member2058392318_state B_124) ((image_575578384_state F_58) A_187)))))
% FOF formula (forall (A_186:pname) (A_185:(pname->Prop)), ((((eq (pname->Prop)) A_185) bot_bot_pname_o)->(((member_pname A_186) A_185)->False))) of role axiom named fact_66_equals0D
% A new axiom: (forall (A_186:pname) (A_185:(pname->Prop)), ((((eq (pname->Prop)) A_185) bot_bot_pname_o)->(((member_pname A_186) A_185)->False)))
% FOF formula (forall (A_186:hoare_1167836817_state) (A_185:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_185) bot_bo70021908tate_o)->(((member2058392318_state A_186) A_185)->False))) of role axiom named fact_67_equals0D
% A new axiom: (forall (A_186:hoare_1167836817_state) (A_185:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_185) bot_bo70021908tate_o)->(((member2058392318_state A_186) A_185)->False)))
% FOF formula (forall (P_41:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_41)) bot_bot_pname_o)) (forall (X_5:pname), ((P_41 X_5)->False)))) of role axiom named fact_68_Collect__empty__eq
% A new axiom: (forall (P_41:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_41)) bot_bot_pname_o)) (forall (X_5:pname), ((P_41 X_5)->False))))
% FOF formula (forall (P_41:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) (collect_pname_o P_41)) bot_bot_pname_o_o)) (forall (X_5:(pname->Prop)), ((P_41 X_5)->False)))) of role axiom named fact_69_Collect__empty__eq
% A new axiom: (forall (P_41:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) (collect_pname_o P_41)) bot_bot_pname_o_o)) (forall (X_5:(pname->Prop)), ((P_41 X_5)->False))))
% FOF formula (forall (P_41:((hoare_1167836817_state->Prop)->Prop)), ((iff (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o P_41)) bot_bo691907561te_o_o)) (forall (X_5:(hoare_1167836817_state->Prop)), ((P_41 X_5)->False)))) of role axiom named fact_70_Collect__empty__eq
% A new axiom: (forall (P_41:((hoare_1167836817_state->Prop)->Prop)), ((iff (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o P_41)) bot_bo691907561te_o_o)) (forall (X_5:(hoare_1167836817_state->Prop)), ((P_41 X_5)->False))))
% FOF formula (forall (P_41:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_41)) bot_bo70021908tate_o)) (forall (X_5:hoare_1167836817_state), ((P_41 X_5)->False)))) of role axiom named fact_71_Collect__empty__eq
% A new axiom: (forall (P_41:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_41)) bot_bo70021908tate_o)) (forall (X_5:hoare_1167836817_state), ((P_41 X_5)->False))))
% FOF formula (forall (C_51:pname), (((member_pname C_51) bot_bot_pname_o)->False)) of role axiom named fact_72_empty__iff
% A new axiom: (forall (C_51:pname), (((member_pname C_51) bot_bot_pname_o)->False))
% FOF formula (forall (C_51:hoare_1167836817_state), (((member2058392318_state C_51) bot_bo70021908tate_o)->False)) of role axiom named fact_73_empty__iff
% A new axiom: (forall (C_51:hoare_1167836817_state), (((member2058392318_state C_51) bot_bo70021908tate_o)->False))
% FOF formula (forall (P_40:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_40))) (forall (X_5:pname), ((P_40 X_5)->False)))) of role axiom named fact_74_empty__Collect__eq
% A new axiom: (forall (P_40:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_40))) (forall (X_5:pname), ((P_40 X_5)->False))))
% FOF formula (forall (P_40:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o P_40))) (forall (X_5:(pname->Prop)), ((P_40 X_5)->False)))) of role axiom named fact_75_empty__Collect__eq
% A new axiom: (forall (P_40:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o P_40))) (forall (X_5:(pname->Prop)), ((P_40 X_5)->False))))
% FOF formula (forall (P_40:((hoare_1167836817_state->Prop)->Prop)), ((iff (((eq ((hoare_1167836817_state->Prop)->Prop)) bot_bo691907561te_o_o) (collec269976083tate_o P_40))) (forall (X_5:(hoare_1167836817_state->Prop)), ((P_40 X_5)->False)))) of role axiom named fact_76_empty__Collect__eq
% A new axiom: (forall (P_40:((hoare_1167836817_state->Prop)->Prop)), ((iff (((eq ((hoare_1167836817_state->Prop)->Prop)) bot_bo691907561te_o_o) (collec269976083tate_o P_40))) (forall (X_5:(hoare_1167836817_state->Prop)), ((P_40 X_5)->False))))
% FOF formula (forall (P_40:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state P_40))) (forall (X_5:hoare_1167836817_state), ((P_40 X_5)->False)))) of role axiom named fact_77_empty__Collect__eq
% A new axiom: (forall (P_40:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state P_40))) (forall (X_5:hoare_1167836817_state), ((P_40 X_5)->False))))
% FOF formula (forall (A_184:(pname->Prop)), ((iff ((ex pname) (fun (X_5:pname)=> ((member_pname X_5) A_184)))) (not (((eq (pname->Prop)) A_184) bot_bot_pname_o)))) of role axiom named fact_78_ex__in__conv
% A new axiom: (forall (A_184:(pname->Prop)), ((iff ((ex pname) (fun (X_5:pname)=> ((member_pname X_5) A_184)))) (not (((eq (pname->Prop)) A_184) bot_bot_pname_o))))
% FOF formula (forall (A_184:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((member2058392318_state X_5) A_184)))) (not (((eq (hoare_1167836817_state->Prop)) A_184) bot_bo70021908tate_o)))) of role axiom named fact_79_ex__in__conv
% A new axiom: (forall (A_184:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((member2058392318_state X_5) A_184)))) (not (((eq (hoare_1167836817_state->Prop)) A_184) bot_bo70021908tate_o))))
% FOF formula (forall (A_183:(pname->Prop)), ((iff (forall (X_5:pname), (((member_pname X_5) A_183)->False))) (((eq (pname->Prop)) A_183) bot_bot_pname_o))) of role axiom named fact_80_all__not__in__conv
% A new axiom: (forall (A_183:(pname->Prop)), ((iff (forall (X_5:pname), (((member_pname X_5) A_183)->False))) (((eq (pname->Prop)) A_183) bot_bot_pname_o)))
% FOF formula (forall (A_183:(hoare_1167836817_state->Prop)), ((iff (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_183)->False))) (((eq (hoare_1167836817_state->Prop)) A_183) bot_bo70021908tate_o))) of role axiom named fact_81_all__not__in__conv
% A new axiom: (forall (A_183:(hoare_1167836817_state->Prop)), ((iff (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_183)->False))) (((eq (hoare_1167836817_state->Prop)) A_183) bot_bo70021908tate_o)))
% FOF formula (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X_5:pname)=> False))) of role axiom named fact_82_empty__def
% A new axiom: (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X_5:pname)=> False)))
% FOF formula (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o (fun (X_5:(pname->Prop))=> False))) of role axiom named fact_83_empty__def
% A new axiom: (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o (fun (X_5:(pname->Prop))=> False)))
% FOF formula (((eq ((hoare_1167836817_state->Prop)->Prop)) bot_bo691907561te_o_o) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> False))) of role axiom named fact_84_empty__def
% A new axiom: (((eq ((hoare_1167836817_state->Prop)->Prop)) bot_bo691907561te_o_o) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> False)))
% FOF formula (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> False))) of role axiom named fact_85_empty__def
% A new axiom: (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> False)))
% FOF formula (forall (A_182:pname) (A_181:(pname->Prop)), (((member_pname A_182) A_181)->(((eq (pname->Prop)) ((insert_pname A_182) A_181)) A_181))) of role axiom named fact_86_insert__absorb
% A new axiom: (forall (A_182:pname) (A_181:(pname->Prop)), (((member_pname A_182) A_181)->(((eq (pname->Prop)) ((insert_pname A_182) A_181)) A_181)))
% FOF formula (forall (A_182:hoare_1167836817_state) (A_181:(hoare_1167836817_state->Prop)), (((member2058392318_state A_182) A_181)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_182) A_181)) A_181))) of role axiom named fact_87_insert__absorb
% A new axiom: (forall (A_182:hoare_1167836817_state) (A_181:(hoare_1167836817_state->Prop)), (((member2058392318_state A_182) A_181)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_182) A_181)) A_181)))
% FOF formula (forall (B_123:pname) (A_180:pname) (B_122:(pname->Prop)), (((member_pname A_180) B_122)->((member_pname A_180) ((insert_pname B_123) B_122)))) of role axiom named fact_88_insertI2
% A new axiom: (forall (B_123:pname) (A_180:pname) (B_122:(pname->Prop)), (((member_pname A_180) B_122)->((member_pname A_180) ((insert_pname B_123) B_122))))
% FOF formula (forall (B_123:hoare_1167836817_state) (A_180:hoare_1167836817_state) (B_122:(hoare_1167836817_state->Prop)), (((member2058392318_state A_180) B_122)->((member2058392318_state A_180) ((insert2134838167_state B_123) B_122)))) of role axiom named fact_89_insertI2
% A new axiom: (forall (B_123:hoare_1167836817_state) (A_180:hoare_1167836817_state) (B_122:(hoare_1167836817_state->Prop)), (((member2058392318_state A_180) B_122)->((member2058392318_state A_180) ((insert2134838167_state B_123) B_122))))
% FOF formula (forall (B_121:(pname->Prop)) (X_97:pname) (A_179:(pname->Prop)), ((((member_pname X_97) A_179)->False)->((((member_pname X_97) B_121)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_97) A_179)) ((insert_pname X_97) B_121))) (((eq (pname->Prop)) A_179) B_121))))) of role axiom named fact_90_insert__ident
% A new axiom: (forall (B_121:(pname->Prop)) (X_97:pname) (A_179:(pname->Prop)), ((((member_pname X_97) A_179)->False)->((((member_pname X_97) B_121)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_97) A_179)) ((insert_pname X_97) B_121))) (((eq (pname->Prop)) A_179) B_121)))))
% FOF formula (forall (B_121:(hoare_1167836817_state->Prop)) (X_97:hoare_1167836817_state) (A_179:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_97) A_179)->False)->((((member2058392318_state X_97) B_121)->False)->((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_97) A_179)) ((insert2134838167_state X_97) B_121))) (((eq (hoare_1167836817_state->Prop)) A_179) B_121))))) of role axiom named fact_91_insert__ident
% A new axiom: (forall (B_121:(hoare_1167836817_state->Prop)) (X_97:hoare_1167836817_state) (A_179:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_97) A_179)->False)->((((member2058392318_state X_97) B_121)->False)->((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_97) A_179)) ((insert2134838167_state X_97) B_121))) (((eq (hoare_1167836817_state->Prop)) A_179) B_121)))))
% FOF formula (forall (Y_48:pname) (A_178:(pname->Prop)) (X_96:pname), ((iff (((insert_pname Y_48) A_178) X_96)) ((or (((eq pname) Y_48) X_96)) (A_178 X_96)))) of role axiom named fact_92_insert__code
% A new axiom: (forall (Y_48:pname) (A_178:(pname->Prop)) (X_96:pname), ((iff (((insert_pname Y_48) A_178) X_96)) ((or (((eq pname) Y_48) X_96)) (A_178 X_96))))
% FOF formula (forall (Y_48:hoare_1167836817_state) (A_178:(hoare_1167836817_state->Prop)) (X_96:hoare_1167836817_state), ((iff (((insert2134838167_state Y_48) A_178) X_96)) ((or (((eq hoare_1167836817_state) Y_48) X_96)) (A_178 X_96)))) of role axiom named fact_93_insert__code
% A new axiom: (forall (Y_48:hoare_1167836817_state) (A_178:(hoare_1167836817_state->Prop)) (X_96:hoare_1167836817_state), ((iff (((insert2134838167_state Y_48) A_178) X_96)) ((or (((eq hoare_1167836817_state) Y_48) X_96)) (A_178 X_96))))
% FOF formula (forall (A_177:pname) (B_120:pname) (A_176:(pname->Prop)), ((iff ((member_pname A_177) ((insert_pname B_120) A_176))) ((or (((eq pname) A_177) B_120)) ((member_pname A_177) A_176)))) of role axiom named fact_94_insert__iff
% A new axiom: (forall (A_177:pname) (B_120:pname) (A_176:(pname->Prop)), ((iff ((member_pname A_177) ((insert_pname B_120) A_176))) ((or (((eq pname) A_177) B_120)) ((member_pname A_177) A_176))))
% FOF formula (forall (A_177:hoare_1167836817_state) (B_120:hoare_1167836817_state) (A_176:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state A_177) ((insert2134838167_state B_120) A_176))) ((or (((eq hoare_1167836817_state) A_177) B_120)) ((member2058392318_state A_177) A_176)))) of role axiom named fact_95_insert__iff
% A new axiom: (forall (A_177:hoare_1167836817_state) (B_120:hoare_1167836817_state) (A_176:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state A_177) ((insert2134838167_state B_120) A_176))) ((or (((eq hoare_1167836817_state) A_177) B_120)) ((member2058392318_state A_177) A_176))))
% FOF formula (forall (X_95:pname) (Y_47:pname) (A_175:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_95) ((insert_pname Y_47) A_175))) ((insert_pname Y_47) ((insert_pname X_95) A_175)))) of role axiom named fact_96_insert__commute
% A new axiom: (forall (X_95:pname) (Y_47:pname) (A_175:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_95) ((insert_pname Y_47) A_175))) ((insert_pname Y_47) ((insert_pname X_95) A_175))))
% FOF formula (forall (X_95:hoare_1167836817_state) (Y_47:hoare_1167836817_state) (A_175:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_95) ((insert2134838167_state Y_47) A_175))) ((insert2134838167_state Y_47) ((insert2134838167_state X_95) A_175)))) of role axiom named fact_97_insert__commute
% A new axiom: (forall (X_95:hoare_1167836817_state) (Y_47:hoare_1167836817_state) (A_175:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_95) ((insert2134838167_state Y_47) A_175))) ((insert2134838167_state Y_47) ((insert2134838167_state X_95) A_175))))
% FOF formula (forall (X_94:pname) (A_174:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_94) ((insert_pname X_94) A_174))) ((insert_pname X_94) A_174))) of role axiom named fact_98_insert__absorb2
% A new axiom: (forall (X_94:pname) (A_174:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_94) ((insert_pname X_94) A_174))) ((insert_pname X_94) A_174)))
% FOF formula (forall (X_94:hoare_1167836817_state) (A_174:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_94) ((insert2134838167_state X_94) A_174))) ((insert2134838167_state X_94) A_174))) of role axiom named fact_99_insert__absorb2
% A new axiom: (forall (X_94:hoare_1167836817_state) (A_174:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_94) ((insert2134838167_state X_94) A_174))) ((insert2134838167_state X_94) A_174)))
% FOF formula (forall (A_173:pname) (P_39:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_173) (collect_pname P_39))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_173))) (P_39 U_2)))))) of role axiom named fact_100_insert__Collect
% A new axiom: (forall (A_173:pname) (P_39:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_173) (collect_pname P_39))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_173))) (P_39 U_2))))))
% FOF formula (forall (A_173:(pname->Prop)) (P_39:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_173) (collect_pname_o P_39))) (collect_pname_o (fun (U_2:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U_2) A_173))) (P_39 U_2)))))) of role axiom named fact_101_insert__Collect
% A new axiom: (forall (A_173:(pname->Prop)) (P_39:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_173) (collect_pname_o P_39))) (collect_pname_o (fun (U_2:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U_2) A_173))) (P_39 U_2))))))
% FOF formula (forall (A_173:(hoare_1167836817_state->Prop)) (P_39:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o A_173) (collec269976083tate_o P_39))) (collec269976083tate_o (fun (U_2:(hoare_1167836817_state->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_1167836817_state->Prop)) U_2) A_173))) (P_39 U_2)))))) of role axiom named fact_102_insert__Collect
% A new axiom: (forall (A_173:(hoare_1167836817_state->Prop)) (P_39:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o A_173) (collec269976083tate_o P_39))) (collec269976083tate_o (fun (U_2:(hoare_1167836817_state->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_1167836817_state->Prop)) U_2) A_173))) (P_39 U_2))))))
% FOF formula (forall (A_173:hoare_1167836817_state) (P_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_173) (collec1027672124_state P_39))) (collec1027672124_state (fun (U_2:hoare_1167836817_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1167836817_state) U_2) A_173))) (P_39 U_2)))))) of role axiom named fact_103_insert__Collect
% A new axiom: (forall (A_173:hoare_1167836817_state) (P_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_173) (collec1027672124_state P_39))) (collec1027672124_state (fun (U_2:hoare_1167836817_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1167836817_state) U_2) A_173))) (P_39 U_2))))))
% FOF formula (forall (A_172:pname) (B_119:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_172) B_119)) (collect_pname (fun (X_5:pname)=> ((or (((eq pname) X_5) A_172)) ((member_pname X_5) B_119)))))) of role axiom named fact_104_insert__compr
% A new axiom: (forall (A_172:pname) (B_119:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_172) B_119)) (collect_pname (fun (X_5:pname)=> ((or (((eq pname) X_5) A_172)) ((member_pname X_5) B_119))))))
% FOF formula (forall (A_172:(pname->Prop)) (B_119:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_172) B_119)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((or (((eq (pname->Prop)) X_5) A_172)) ((member_pname_o X_5) B_119)))))) of role axiom named fact_105_insert__compr
% A new axiom: (forall (A_172:(pname->Prop)) (B_119:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_172) B_119)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((or (((eq (pname->Prop)) X_5) A_172)) ((member_pname_o X_5) B_119))))))
% FOF formula (forall (A_172:(hoare_1167836817_state->Prop)) (B_119:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o A_172) B_119)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or (((eq (hoare_1167836817_state->Prop)) X_5) A_172)) ((member864234961tate_o X_5) B_119)))))) of role axiom named fact_106_insert__compr
% A new axiom: (forall (A_172:(hoare_1167836817_state->Prop)) (B_119:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o A_172) B_119)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or (((eq (hoare_1167836817_state->Prop)) X_5) A_172)) ((member864234961tate_o X_5) B_119))))))
% FOF formula (forall (A_172:hoare_1167836817_state) (B_119:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_172) B_119)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) X_5) A_172)) ((member2058392318_state X_5) B_119)))))) of role axiom named fact_107_insert__compr
% A new axiom: (forall (A_172:hoare_1167836817_state) (B_119:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_172) B_119)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) X_5) A_172)) ((member2058392318_state X_5) B_119))))))
% FOF formula (forall (A_171:pname) (B_118:(pname->Prop)), ((member_pname A_171) ((insert_pname A_171) B_118))) of role axiom named fact_108_insertI1
% A new axiom: (forall (A_171:pname) (B_118:(pname->Prop)), ((member_pname A_171) ((insert_pname A_171) B_118)))
% FOF formula (forall (A_171:hoare_1167836817_state) (B_118:(hoare_1167836817_state->Prop)), ((member2058392318_state A_171) ((insert2134838167_state A_171) B_118))) of role axiom named fact_109_insertI1
% A new axiom: (forall (A_171:hoare_1167836817_state) (B_118:(hoare_1167836817_state->Prop)), ((member2058392318_state A_171) ((insert2134838167_state A_171) B_118)))
% FOF formula (forall (A_170:(pname->Prop)) (B_117:(pname->Prop)), ((((eq (pname->Prop)) A_170) B_117)->((((ord_less_eq_pname_o A_170) B_117)->(((ord_less_eq_pname_o B_117) A_170)->False))->False))) of role axiom named fact_110_equalityE
% A new axiom: (forall (A_170:(pname->Prop)) (B_117:(pname->Prop)), ((((eq (pname->Prop)) A_170) B_117)->((((ord_less_eq_pname_o A_170) B_117)->(((ord_less_eq_pname_o B_117) A_170)->False))->False)))
% FOF formula (forall (A_170:(hoare_1167836817_state->Prop)) (B_117:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_170) B_117)->((((ord_le827224136tate_o A_170) B_117)->(((ord_le827224136tate_o B_117) A_170)->False))->False))) of role axiom named fact_111_equalityE
% A new axiom: (forall (A_170:(hoare_1167836817_state->Prop)) (B_117:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_170) B_117)->((((ord_le827224136tate_o A_170) B_117)->(((ord_le827224136tate_o B_117) A_170)->False))->False)))
% FOF formula (forall (C_50:(pname->Prop)) (A_169:(pname->Prop)) (B_116:(pname->Prop)), (((ord_less_eq_pname_o A_169) B_116)->(((ord_less_eq_pname_o B_116) C_50)->((ord_less_eq_pname_o A_169) C_50)))) of role axiom named fact_112_subset__trans
% A new axiom: (forall (C_50:(pname->Prop)) (A_169:(pname->Prop)) (B_116:(pname->Prop)), (((ord_less_eq_pname_o A_169) B_116)->(((ord_less_eq_pname_o B_116) C_50)->((ord_less_eq_pname_o A_169) C_50))))
% FOF formula (forall (C_50:(hoare_1167836817_state->Prop)) (A_169:(hoare_1167836817_state->Prop)) (B_116:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_169) B_116)->(((ord_le827224136tate_o B_116) C_50)->((ord_le827224136tate_o A_169) C_50)))) of role axiom named fact_113_subset__trans
% A new axiom: (forall (C_50:(hoare_1167836817_state->Prop)) (A_169:(hoare_1167836817_state->Prop)) (B_116:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_169) B_116)->(((ord_le827224136tate_o B_116) C_50)->((ord_le827224136tate_o A_169) C_50))))
% FOF formula (forall (X_93:pname) (A_168:(pname->Prop)) (B_115:(pname->Prop)), (((ord_less_eq_pname_o A_168) B_115)->(((member_pname X_93) A_168)->((member_pname X_93) B_115)))) of role axiom named fact_114_set__mp
% A new axiom: (forall (X_93:pname) (A_168:(pname->Prop)) (B_115:(pname->Prop)), (((ord_less_eq_pname_o A_168) B_115)->(((member_pname X_93) A_168)->((member_pname X_93) B_115))))
% FOF formula (forall (X_93:hoare_1167836817_state) (A_168:(hoare_1167836817_state->Prop)) (B_115:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_168) B_115)->(((member2058392318_state X_93) A_168)->((member2058392318_state X_93) B_115)))) of role axiom named fact_115_set__mp
% A new axiom: (forall (X_93:hoare_1167836817_state) (A_168:(hoare_1167836817_state->Prop)) (B_115:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_168) B_115)->(((member2058392318_state X_93) A_168)->((member2058392318_state X_93) B_115))))
% FOF formula (forall (B_114:(pname->Prop)) (X_92:pname) (A_167:(pname->Prop)), (((member_pname X_92) A_167)->(((ord_less_eq_pname_o A_167) B_114)->((member_pname X_92) B_114)))) of role axiom named fact_116_set__rev__mp
% A new axiom: (forall (B_114:(pname->Prop)) (X_92:pname) (A_167:(pname->Prop)), (((member_pname X_92) A_167)->(((ord_less_eq_pname_o A_167) B_114)->((member_pname X_92) B_114))))
% FOF formula (forall (B_114:(hoare_1167836817_state->Prop)) (X_92:hoare_1167836817_state) (A_167:(hoare_1167836817_state->Prop)), (((member2058392318_state X_92) A_167)->(((ord_le827224136tate_o A_167) B_114)->((member2058392318_state X_92) B_114)))) of role axiom named fact_117_set__rev__mp
% A new axiom: (forall (B_114:(hoare_1167836817_state->Prop)) (X_92:hoare_1167836817_state) (A_167:(hoare_1167836817_state->Prop)), (((member2058392318_state X_92) A_167)->(((ord_le827224136tate_o A_167) B_114)->((member2058392318_state X_92) B_114))))
% FOF formula (forall (X_91:pname) (A_166:(pname->Prop)) (B_113:(pname->Prop)), (((ord_less_eq_pname_o A_166) B_113)->(((member_pname X_91) A_166)->((member_pname X_91) B_113)))) of role axiom named fact_118_in__mono
% A new axiom: (forall (X_91:pname) (A_166:(pname->Prop)) (B_113:(pname->Prop)), (((ord_less_eq_pname_o A_166) B_113)->(((member_pname X_91) A_166)->((member_pname X_91) B_113))))
% FOF formula (forall (X_91:hoare_1167836817_state) (A_166:(hoare_1167836817_state->Prop)) (B_113:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_166) B_113)->(((member2058392318_state X_91) A_166)->((member2058392318_state X_91) B_113)))) of role axiom named fact_119_in__mono
% A new axiom: (forall (X_91:hoare_1167836817_state) (A_166:(hoare_1167836817_state->Prop)) (B_113:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_166) B_113)->(((member2058392318_state X_91) A_166)->((member2058392318_state X_91) B_113))))
% FOF formula (forall (A_165:(pname->Prop)) (B_112:(pname->Prop)), ((((eq (pname->Prop)) A_165) B_112)->((ord_less_eq_pname_o B_112) A_165))) of role axiom named fact_120_equalityD2
% A new axiom: (forall (A_165:(pname->Prop)) (B_112:(pname->Prop)), ((((eq (pname->Prop)) A_165) B_112)->((ord_less_eq_pname_o B_112) A_165)))
% FOF formula (forall (A_165:(hoare_1167836817_state->Prop)) (B_112:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_165) B_112)->((ord_le827224136tate_o B_112) A_165))) of role axiom named fact_121_equalityD2
% A new axiom: (forall (A_165:(hoare_1167836817_state->Prop)) (B_112:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_165) B_112)->((ord_le827224136tate_o B_112) A_165)))
% FOF formula (forall (A_164:(pname->Prop)) (B_111:(pname->Prop)), ((((eq (pname->Prop)) A_164) B_111)->((ord_less_eq_pname_o A_164) B_111))) of role axiom named fact_122_equalityD1
% A new axiom: (forall (A_164:(pname->Prop)) (B_111:(pname->Prop)), ((((eq (pname->Prop)) A_164) B_111)->((ord_less_eq_pname_o A_164) B_111)))
% FOF formula (forall (A_164:(hoare_1167836817_state->Prop)) (B_111:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_164) B_111)->((ord_le827224136tate_o A_164) B_111))) of role axiom named fact_123_equalityD1
% A new axiom: (forall (A_164:(hoare_1167836817_state->Prop)) (B_111:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_164) B_111)->((ord_le827224136tate_o A_164) B_111)))
% FOF formula (forall (A_163:(pname->Prop)) (B_110:(pname->Prop)), ((iff (((eq (pname->Prop)) A_163) B_110)) ((and ((ord_less_eq_pname_o A_163) B_110)) ((ord_less_eq_pname_o B_110) A_163)))) of role axiom named fact_124_set__eq__subset
% A new axiom: (forall (A_163:(pname->Prop)) (B_110:(pname->Prop)), ((iff (((eq (pname->Prop)) A_163) B_110)) ((and ((ord_less_eq_pname_o A_163) B_110)) ((ord_less_eq_pname_o B_110) A_163))))
% FOF formula (forall (A_163:(hoare_1167836817_state->Prop)) (B_110:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) A_163) B_110)) ((and ((ord_le827224136tate_o A_163) B_110)) ((ord_le827224136tate_o B_110) A_163)))) of role axiom named fact_125_set__eq__subset
% A new axiom: (forall (A_163:(hoare_1167836817_state->Prop)) (B_110:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) A_163) B_110)) ((and ((ord_le827224136tate_o A_163) B_110)) ((ord_le827224136tate_o B_110) A_163))))
% FOF formula (forall (A_162:(pname->Prop)), ((ord_less_eq_pname_o A_162) A_162)) of role axiom named fact_126_subset__refl
% A new axiom: (forall (A_162:(pname->Prop)), ((ord_less_eq_pname_o A_162) A_162))
% FOF formula (forall (A_162:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o A_162) A_162)) of role axiom named fact_127_subset__refl
% A new axiom: (forall (A_162:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o A_162) A_162))
% FOF formula (forall (B_109:pname) (F_57:(hoare_1167836817_state->pname)) (X_90:hoare_1167836817_state) (A_161:(hoare_1167836817_state->Prop)), (((member2058392318_state X_90) A_161)->((((eq pname) B_109) (F_57 X_90))->((member_pname B_109) ((image_8178176_pname F_57) A_161))))) of role axiom named fact_128_rev__image__eqI
% A new axiom: (forall (B_109:pname) (F_57:(hoare_1167836817_state->pname)) (X_90:hoare_1167836817_state) (A_161:(hoare_1167836817_state->Prop)), (((member2058392318_state X_90) A_161)->((((eq pname) B_109) (F_57 X_90))->((member_pname B_109) ((image_8178176_pname F_57) A_161)))))
% FOF formula (forall (B_109:hoare_1167836817_state) (F_57:(pname->hoare_1167836817_state)) (X_90:pname) (A_161:(pname->Prop)), (((member_pname X_90) A_161)->((((eq hoare_1167836817_state) B_109) (F_57 X_90))->((member2058392318_state B_109) ((image_575578384_state F_57) A_161))))) of role axiom named fact_129_rev__image__eqI
% A new axiom: (forall (B_109:hoare_1167836817_state) (F_57:(pname->hoare_1167836817_state)) (X_90:pname) (A_161:(pname->Prop)), (((member_pname X_90) A_161)->((((eq hoare_1167836817_state) B_109) (F_57 X_90))->((member2058392318_state B_109) ((image_575578384_state F_57) A_161)))))
% FOF formula (forall (F_56:(hoare_1167836817_state->pname)) (X_89:hoare_1167836817_state) (A_160:(hoare_1167836817_state->Prop)), (((member2058392318_state X_89) A_160)->((member_pname (F_56 X_89)) ((image_8178176_pname F_56) A_160)))) of role axiom named fact_130_imageI
% A new axiom: (forall (F_56:(hoare_1167836817_state->pname)) (X_89:hoare_1167836817_state) (A_160:(hoare_1167836817_state->Prop)), (((member2058392318_state X_89) A_160)->((member_pname (F_56 X_89)) ((image_8178176_pname F_56) A_160))))
% FOF formula (forall (F_56:(pname->hoare_1167836817_state)) (X_89:pname) (A_160:(pname->Prop)), (((member_pname X_89) A_160)->((member2058392318_state (F_56 X_89)) ((image_575578384_state F_56) A_160)))) of role axiom named fact_131_imageI
% A new axiom: (forall (F_56:(pname->hoare_1167836817_state)) (X_89:pname) (A_160:(pname->Prop)), (((member_pname X_89) A_160)->((member2058392318_state (F_56 X_89)) ((image_575578384_state F_56) A_160))))
% FOF formula (forall (Z_21:hoare_1167836817_state) (F_55:(pname->hoare_1167836817_state)) (A_159:(pname->Prop)), ((iff ((member2058392318_state Z_21) ((image_575578384_state F_55) A_159))) ((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_159)) (((eq hoare_1167836817_state) Z_21) (F_55 X_5))))))) of role axiom named fact_132_image__iff
% A new axiom: (forall (Z_21:hoare_1167836817_state) (F_55:(pname->hoare_1167836817_state)) (A_159:(pname->Prop)), ((iff ((member2058392318_state Z_21) ((image_575578384_state F_55) A_159))) ((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_159)) (((eq hoare_1167836817_state) Z_21) (F_55 X_5)))))))
% FOF formula (forall (P_38:((pname->Prop)->Prop)) (Q_23:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_5:(pname->Prop))=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite297249702name_o (collect_pname_o P_38))) (finite297249702name_o (collect_pname_o Q_23))))) of role axiom named fact_133_finite__Collect__disjI
% A new axiom: (forall (P_38:((pname->Prop)->Prop)) (Q_23:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_5:(pname->Prop))=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite297249702name_o (collect_pname_o P_38))) (finite297249702name_o (collect_pname_o Q_23)))))
% FOF formula (forall (P_38:((hoare_1167836817_state->Prop)->Prop)) (Q_23:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite1380128977tate_o (collec269976083tate_o P_38))) (finite1380128977tate_o (collec269976083tate_o Q_23))))) of role axiom named fact_134_finite__Collect__disjI
% A new axiom: (forall (P_38:((hoare_1167836817_state->Prop)->Prop)) (Q_23:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite1380128977tate_o (collec269976083tate_o P_38))) (finite1380128977tate_o (collec269976083tate_o Q_23)))))
% FOF formula (forall (P_38:(hoare_1167836817_state->Prop)) (Q_23:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite1084549118_state (collec1027672124_state P_38))) (finite1084549118_state (collec1027672124_state Q_23))))) of role axiom named fact_135_finite__Collect__disjI
% A new axiom: (forall (P_38:(hoare_1167836817_state->Prop)) (Q_23:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite1084549118_state (collec1027672124_state P_38))) (finite1084549118_state (collec1027672124_state Q_23)))))
% FOF formula (forall (P_38:(pname->Prop)) (Q_23:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_5:pname)=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite_finite_pname (collect_pname P_38))) (finite_finite_pname (collect_pname Q_23))))) of role axiom named fact_136_finite__Collect__disjI
% A new axiom: (forall (P_38:(pname->Prop)) (Q_23:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_5:pname)=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite_finite_pname (collect_pname P_38))) (finite_finite_pname (collect_pname Q_23)))))
% FOF formula (forall (X_5:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_5) Xa)) (collect_pname (fun (Y_2:pname)=> ((or (((eq pname) Y_2) X_5)) ((member_pname Y_2) Xa)))))) of role axiom named fact_137_insert__compr__raw
% A new axiom: (forall (X_5:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_5) Xa)) (collect_pname (fun (Y_2:pname)=> ((or (((eq pname) Y_2) X_5)) ((member_pname Y_2) Xa))))))
% FOF formula (forall (X_5:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X_5) Xa)) (collect_pname_o (fun (Y_2:(pname->Prop))=> ((or (((eq (pname->Prop)) Y_2) X_5)) ((member_pname_o Y_2) Xa)))))) of role axiom named fact_138_insert__compr__raw
% A new axiom: (forall (X_5:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X_5) Xa)) (collect_pname_o (fun (Y_2:(pname->Prop))=> ((or (((eq (pname->Prop)) Y_2) X_5)) ((member_pname_o Y_2) Xa))))))
% FOF formula (forall (X_5:(hoare_1167836817_state->Prop)) (Xa:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o X_5) Xa)) (collec269976083tate_o (fun (Y_2:(hoare_1167836817_state->Prop))=> ((or (((eq (hoare_1167836817_state->Prop)) Y_2) X_5)) ((member864234961tate_o Y_2) Xa)))))) of role axiom named fact_139_insert__compr__raw
% A new axiom: (forall (X_5:(hoare_1167836817_state->Prop)) (Xa:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o X_5) Xa)) (collec269976083tate_o (fun (Y_2:(hoare_1167836817_state->Prop))=> ((or (((eq (hoare_1167836817_state->Prop)) Y_2) X_5)) ((member864234961tate_o Y_2) Xa))))))
% FOF formula (forall (X_5:hoare_1167836817_state) (Xa:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_5) Xa)) (collec1027672124_state (fun (Y_2:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) Y_2) X_5)) ((member2058392318_state Y_2) Xa)))))) of role axiom named fact_140_insert__compr__raw
% A new axiom: (forall (X_5:hoare_1167836817_state) (Xa:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_5) Xa)) (collec1027672124_state (fun (Y_2:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) Y_2) X_5)) ((member2058392318_state Y_2) Xa))))))
% FOF formula (forall (A_158:pname) (B_108:pname), ((((eq (pname->Prop)) ((insert_pname A_158) bot_bot_pname_o)) ((insert_pname B_108) bot_bot_pname_o))->(((eq pname) A_158) B_108))) of role axiom named fact_141_singleton__inject
% A new axiom: (forall (A_158:pname) (B_108:pname), ((((eq (pname->Prop)) ((insert_pname A_158) bot_bot_pname_o)) ((insert_pname B_108) bot_bot_pname_o))->(((eq pname) A_158) B_108)))
% FOF formula (forall (A_158:hoare_1167836817_state) (B_108:hoare_1167836817_state), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_158) bot_bo70021908tate_o)) ((insert2134838167_state B_108) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) A_158) B_108))) of role axiom named fact_142_singleton__inject
% A new axiom: (forall (A_158:hoare_1167836817_state) (B_108:hoare_1167836817_state), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_158) bot_bo70021908tate_o)) ((insert2134838167_state B_108) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) A_158) B_108)))
% FOF formula (forall (B_107:pname) (A_157:pname), (((member_pname B_107) ((insert_pname A_157) bot_bot_pname_o))->(((eq pname) B_107) A_157))) of role axiom named fact_143_singletonE
% A new axiom: (forall (B_107:pname) (A_157:pname), (((member_pname B_107) ((insert_pname A_157) bot_bot_pname_o))->(((eq pname) B_107) A_157)))
% FOF formula (forall (B_107:hoare_1167836817_state) (A_157:hoare_1167836817_state), (((member2058392318_state B_107) ((insert2134838167_state A_157) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) B_107) A_157))) of role axiom named fact_144_singletonE
% A new axiom: (forall (B_107:hoare_1167836817_state) (A_157:hoare_1167836817_state), (((member2058392318_state B_107) ((insert2134838167_state A_157) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) B_107) A_157)))
% FOF formula (forall (A_156:pname) (B_106:pname) (C_49:pname) (D_6:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_156) ((insert_pname B_106) bot_bot_pname_o))) ((insert_pname C_49) ((insert_pname D_6) bot_bot_pname_o)))) ((or ((and (((eq pname) A_156) C_49)) (((eq pname) B_106) D_6))) ((and (((eq pname) A_156) D_6)) (((eq pname) B_106) C_49))))) of role axiom named fact_145_doubleton__eq__iff
% A new axiom: (forall (A_156:pname) (B_106:pname) (C_49:pname) (D_6:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_156) ((insert_pname B_106) bot_bot_pname_o))) ((insert_pname C_49) ((insert_pname D_6) bot_bot_pname_o)))) ((or ((and (((eq pname) A_156) C_49)) (((eq pname) B_106) D_6))) ((and (((eq pname) A_156) D_6)) (((eq pname) B_106) C_49)))))
% FOF formula (forall (A_156:hoare_1167836817_state) (B_106:hoare_1167836817_state) (C_49:hoare_1167836817_state) (D_6:hoare_1167836817_state), ((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_156) ((insert2134838167_state B_106) bot_bo70021908tate_o))) ((insert2134838167_state C_49) ((insert2134838167_state D_6) bot_bo70021908tate_o)))) ((or ((and (((eq hoare_1167836817_state) A_156) C_49)) (((eq hoare_1167836817_state) B_106) D_6))) ((and (((eq hoare_1167836817_state) A_156) D_6)) (((eq hoare_1167836817_state) B_106) C_49))))) of role axiom named fact_146_doubleton__eq__iff
% A new axiom: (forall (A_156:hoare_1167836817_state) (B_106:hoare_1167836817_state) (C_49:hoare_1167836817_state) (D_6:hoare_1167836817_state), ((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_156) ((insert2134838167_state B_106) bot_bo70021908tate_o))) ((insert2134838167_state C_49) ((insert2134838167_state D_6) bot_bo70021908tate_o)))) ((or ((and (((eq hoare_1167836817_state) A_156) C_49)) (((eq hoare_1167836817_state) B_106) D_6))) ((and (((eq hoare_1167836817_state) A_156) D_6)) (((eq hoare_1167836817_state) B_106) C_49)))))
% FOF formula (forall (B_105:pname) (A_155:pname), ((iff ((member_pname B_105) ((insert_pname A_155) bot_bot_pname_o))) (((eq pname) B_105) A_155))) of role axiom named fact_147_singleton__iff
% A new axiom: (forall (B_105:pname) (A_155:pname), ((iff ((member_pname B_105) ((insert_pname A_155) bot_bot_pname_o))) (((eq pname) B_105) A_155)))
% FOF formula (forall (B_105:hoare_1167836817_state) (A_155:hoare_1167836817_state), ((iff ((member2058392318_state B_105) ((insert2134838167_state A_155) bot_bo70021908tate_o))) (((eq hoare_1167836817_state) B_105) A_155))) of role axiom named fact_148_singleton__iff
% A new axiom: (forall (B_105:hoare_1167836817_state) (A_155:hoare_1167836817_state), ((iff ((member2058392318_state B_105) ((insert2134838167_state A_155) bot_bo70021908tate_o))) (((eq hoare_1167836817_state) B_105) A_155)))
% FOF formula (forall (A_154:pname) (A_153:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_154) A_153)) bot_bot_pname_o))) of role axiom named fact_149_insert__not__empty
% A new axiom: (forall (A_154:pname) (A_153:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_154) A_153)) bot_bot_pname_o)))
% FOF formula (forall (A_154:hoare_1167836817_state) (A_153:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_154) A_153)) bot_bo70021908tate_o))) of role axiom named fact_150_insert__not__empty
% A new axiom: (forall (A_154:hoare_1167836817_state) (A_153:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_154) A_153)) bot_bo70021908tate_o)))
% FOF formula (forall (A_152:pname) (A_151:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_152) A_151)))) of role axiom named fact_151_empty__not__insert
% A new axiom: (forall (A_152:pname) (A_151:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_152) A_151))))
% FOF formula (forall (A_152:hoare_1167836817_state) (A_151:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((insert2134838167_state A_152) A_151)))) of role axiom named fact_152_empty__not__insert
% A new axiom: (forall (A_152:hoare_1167836817_state) (A_151:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((insert2134838167_state A_152) A_151))))
% FOF formula (forall (A_150:(pname->Prop)) (A_149:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_150) A_149))) (finite297249702name_o A_149))) of role axiom named fact_153_finite__insert
% A new axiom: (forall (A_150:(pname->Prop)) (A_149:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_150) A_149))) (finite297249702name_o A_149)))
% FOF formula (forall (A_150:(hoare_1167836817_state->Prop)) (A_149:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o ((insert999278200tate_o A_150) A_149))) (finite1380128977tate_o A_149))) of role axiom named fact_154_finite__insert
% A new axiom: (forall (A_150:(hoare_1167836817_state->Prop)) (A_149:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o ((insert999278200tate_o A_150) A_149))) (finite1380128977tate_o A_149)))
% FOF formula (forall (A_150:pname) (A_149:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_150) A_149))) (finite_finite_pname A_149))) of role axiom named fact_155_finite__insert
% A new axiom: (forall (A_150:pname) (A_149:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_150) A_149))) (finite_finite_pname A_149)))
% FOF formula (forall (A_150:hoare_1167836817_state) (A_149:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((insert2134838167_state A_150) A_149))) (finite1084549118_state A_149))) of role axiom named fact_156_finite__insert
% A new axiom: (forall (A_150:hoare_1167836817_state) (A_149:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((insert2134838167_state A_150) A_149))) (finite1084549118_state A_149)))
% FOF formula (forall (A_148:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_148) bot_bot_pname_o)) (((eq (pname->Prop)) A_148) bot_bot_pname_o))) of role axiom named fact_157_subset__empty
% A new axiom: (forall (A_148:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_148) bot_bot_pname_o)) (((eq (pname->Prop)) A_148) bot_bot_pname_o)))
% FOF formula (forall (A_148:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_148) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_148) bot_bo70021908tate_o))) of role axiom named fact_158_subset__empty
% A new axiom: (forall (A_148:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_148) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_148) bot_bo70021908tate_o)))
% FOF formula (forall (F_54:(hoare_1167836817_state->pname)) (A_147:(hoare_1167836817_state->Prop)), ((iff (((eq (pname->Prop)) ((image_8178176_pname F_54) A_147)) bot_bot_pname_o)) (((eq (hoare_1167836817_state->Prop)) A_147) bot_bo70021908tate_o))) of role axiom named fact_159_image__is__empty
% A new axiom: (forall (F_54:(hoare_1167836817_state->pname)) (A_147:(hoare_1167836817_state->Prop)), ((iff (((eq (pname->Prop)) ((image_8178176_pname F_54) A_147)) bot_bot_pname_o)) (((eq (hoare_1167836817_state->Prop)) A_147) bot_bo70021908tate_o)))
% FOF formula (forall (F_54:(pname->hoare_1167836817_state)) (A_147:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_54) A_147)) bot_bo70021908tate_o)) (((eq (pname->Prop)) A_147) bot_bot_pname_o))) of role axiom named fact_160_image__is__empty
% A new axiom: (forall (F_54:(pname->hoare_1167836817_state)) (A_147:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_54) A_147)) bot_bo70021908tate_o)) (((eq (pname->Prop)) A_147) bot_bot_pname_o)))
% FOF formula (forall (F_53:(hoare_1167836817_state->pname)), (((eq (pname->Prop)) ((image_8178176_pname F_53) bot_bo70021908tate_o)) bot_bot_pname_o)) of role axiom named fact_161_image__empty
% A new axiom: (forall (F_53:(hoare_1167836817_state->pname)), (((eq (pname->Prop)) ((image_8178176_pname F_53) bot_bo70021908tate_o)) bot_bot_pname_o))
% FOF formula (forall (F_53:(pname->hoare_1167836817_state)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_53) bot_bot_pname_o)) bot_bo70021908tate_o)) of role axiom named fact_162_image__empty
% A new axiom: (forall (F_53:(pname->hoare_1167836817_state)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_53) bot_bot_pname_o)) bot_bo70021908tate_o))
% FOF formula (forall (F_52:(hoare_1167836817_state->pname)) (A_146:(hoare_1167836817_state->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) ((image_8178176_pname F_52) A_146))) (((eq (hoare_1167836817_state->Prop)) A_146) bot_bo70021908tate_o))) of role axiom named fact_163_empty__is__image
% A new axiom: (forall (F_52:(hoare_1167836817_state->pname)) (A_146:(hoare_1167836817_state->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) ((image_8178176_pname F_52) A_146))) (((eq (hoare_1167836817_state->Prop)) A_146) bot_bo70021908tate_o)))
% FOF formula (forall (F_52:(pname->hoare_1167836817_state)) (A_146:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((image_575578384_state F_52) A_146))) (((eq (pname->Prop)) A_146) bot_bot_pname_o))) of role axiom named fact_164_empty__is__image
% A new axiom: (forall (F_52:(pname->hoare_1167836817_state)) (A_146:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((image_575578384_state F_52) A_146))) (((eq (pname->Prop)) A_146) bot_bot_pname_o)))
% FOF formula (forall (A_145:((pname->Prop)->Prop)) (B_104:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_145) B_104)->((finite297249702name_o B_104)->(finite297249702name_o A_145)))) of role axiom named fact_165_finite__subset
% A new axiom: (forall (A_145:((pname->Prop)->Prop)) (B_104:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_145) B_104)->((finite297249702name_o B_104)->(finite297249702name_o A_145))))
% FOF formula (forall (A_145:((hoare_1167836817_state->Prop)->Prop)) (B_104:((hoare_1167836817_state->Prop)->Prop)), (((ord_le741939125te_o_o A_145) B_104)->((finite1380128977tate_o B_104)->(finite1380128977tate_o A_145)))) of role axiom named fact_166_finite__subset
% A new axiom: (forall (A_145:((hoare_1167836817_state->Prop)->Prop)) (B_104:((hoare_1167836817_state->Prop)->Prop)), (((ord_le741939125te_o_o A_145) B_104)->((finite1380128977tate_o B_104)->(finite1380128977tate_o A_145))))
% FOF formula (forall (A_145:(hoare_1167836817_state->Prop)) (B_104:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_145) B_104)->((finite1084549118_state B_104)->(finite1084549118_state A_145)))) of role axiom named fact_167_finite__subset
% A new axiom: (forall (A_145:(hoare_1167836817_state->Prop)) (B_104:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_145) B_104)->((finite1084549118_state B_104)->(finite1084549118_state A_145))))
% FOF formula (forall (A_145:(pname->Prop)) (B_104:(pname->Prop)), (((ord_less_eq_pname_o A_145) B_104)->((finite_finite_pname B_104)->(finite_finite_pname A_145)))) of role axiom named fact_168_finite__subset
% A new axiom: (forall (A_145:(pname->Prop)) (B_104:(pname->Prop)), (((ord_less_eq_pname_o A_145) B_104)->((finite_finite_pname B_104)->(finite_finite_pname A_145))))
% FOF formula (forall (A_144:((pname->Prop)->Prop)) (B_103:((pname->Prop)->Prop)), ((finite297249702name_o B_103)->(((ord_le1205211808me_o_o A_144) B_103)->(finite297249702name_o A_144)))) of role axiom named fact_169_rev__finite__subset
% A new axiom: (forall (A_144:((pname->Prop)->Prop)) (B_103:((pname->Prop)->Prop)), ((finite297249702name_o B_103)->(((ord_le1205211808me_o_o A_144) B_103)->(finite297249702name_o A_144))))
% FOF formula (forall (A_144:((hoare_1167836817_state->Prop)->Prop)) (B_103:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o B_103)->(((ord_le741939125te_o_o A_144) B_103)->(finite1380128977tate_o A_144)))) of role axiom named fact_170_rev__finite__subset
% A new axiom: (forall (A_144:((hoare_1167836817_state->Prop)->Prop)) (B_103:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o B_103)->(((ord_le741939125te_o_o A_144) B_103)->(finite1380128977tate_o A_144))))
% FOF formula (forall (A_144:(hoare_1167836817_state->Prop)) (B_103:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_103)->(((ord_le827224136tate_o A_144) B_103)->(finite1084549118_state A_144)))) of role axiom named fact_171_rev__finite__subset
% A new axiom: (forall (A_144:(hoare_1167836817_state->Prop)) (B_103:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_103)->(((ord_le827224136tate_o A_144) B_103)->(finite1084549118_state A_144))))
% FOF formula (forall (A_144:(pname->Prop)) (B_103:(pname->Prop)), ((finite_finite_pname B_103)->(((ord_less_eq_pname_o A_144) B_103)->(finite_finite_pname A_144)))) of role axiom named fact_172_rev__finite__subset
% A new axiom: (forall (A_144:(pname->Prop)) (B_103:(pname->Prop)), ((finite_finite_pname B_103)->(((ord_less_eq_pname_o A_144) B_103)->(finite_finite_pname A_144))))
% FOF formula (forall (A_143:pname) (C_48:(pname->Prop)) (D_5:(pname->Prop)), (((ord_less_eq_pname_o C_48) D_5)->((ord_less_eq_pname_o ((insert_pname A_143) C_48)) ((insert_pname A_143) D_5)))) of role axiom named fact_173_insert__mono
% A new axiom: (forall (A_143:pname) (C_48:(pname->Prop)) (D_5:(pname->Prop)), (((ord_less_eq_pname_o C_48) D_5)->((ord_less_eq_pname_o ((insert_pname A_143) C_48)) ((insert_pname A_143) D_5))))
% FOF formula (forall (A_143:hoare_1167836817_state) (C_48:(hoare_1167836817_state->Prop)) (D_5:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o C_48) D_5)->((ord_le827224136tate_o ((insert2134838167_state A_143) C_48)) ((insert2134838167_state A_143) D_5)))) of role axiom named fact_174_insert__mono
% A new axiom: (forall (A_143:hoare_1167836817_state) (C_48:(hoare_1167836817_state->Prop)) (D_5:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o C_48) D_5)->((ord_le827224136tate_o ((insert2134838167_state A_143) C_48)) ((insert2134838167_state A_143) D_5))))
% FOF formula (forall (X_88:pname) (A_142:(pname->Prop)), ((iff ((member_pname X_88) A_142)) (A_142 X_88))) of role axiom named fact_175_mem__def
% A new axiom: (forall (X_88:pname) (A_142:(pname->Prop)), ((iff ((member_pname X_88) A_142)) (A_142 X_88)))
% FOF formula (forall (X_88:hoare_1167836817_state) (A_142:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state X_88) A_142)) (A_142 X_88))) of role axiom named fact_176_mem__def
% A new axiom: (forall (X_88:hoare_1167836817_state) (A_142:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state X_88) A_142)) (A_142 X_88)))
% FOF formula (forall (P_37:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_37)) P_37)) of role axiom named fact_177_Collect__def
% A new axiom: (forall (P_37:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_37)) P_37))
% FOF formula (forall (P_37:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_37)) P_37)) of role axiom named fact_178_Collect__def
% A new axiom: (forall (P_37:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_37)) P_37))
% FOF formula (forall (P_37:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_37)) P_37)) of role axiom named fact_179_Collect__def
% A new axiom: (forall (P_37:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_37)) P_37))
% FOF formula (forall (P_37:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o P_37)) P_37)) of role axiom named fact_180_Collect__def
% A new axiom: (forall (P_37:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o P_37)) P_37))
% FOF formula (forall (B_102:pname) (A_141:(pname->Prop)) (B_101:(pname->Prop)), (((ord_less_eq_pname_o A_141) B_101)->((ord_less_eq_pname_o A_141) ((insert_pname B_102) B_101)))) of role axiom named fact_181_subset__insertI2
% A new axiom: (forall (B_102:pname) (A_141:(pname->Prop)) (B_101:(pname->Prop)), (((ord_less_eq_pname_o A_141) B_101)->((ord_less_eq_pname_o A_141) ((insert_pname B_102) B_101))))
% FOF formula (forall (B_102:hoare_1167836817_state) (A_141:(hoare_1167836817_state->Prop)) (B_101:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_141) B_101)->((ord_le827224136tate_o A_141) ((insert2134838167_state B_102) B_101)))) of role axiom named fact_182_subset__insertI2
% A new axiom: (forall (B_102:hoare_1167836817_state) (A_141:(hoare_1167836817_state->Prop)) (B_101:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_141) B_101)->((ord_le827224136tate_o A_141) ((insert2134838167_state B_102) B_101))))
% FOF formula (forall (B_100:(pname->Prop)) (X_87:pname) (A_140:(pname->Prop)), ((((member_pname X_87) A_140)->False)->((iff ((ord_less_eq_pname_o A_140) ((insert_pname X_87) B_100))) ((ord_less_eq_pname_o A_140) B_100)))) of role axiom named fact_183_subset__insert
% A new axiom: (forall (B_100:(pname->Prop)) (X_87:pname) (A_140:(pname->Prop)), ((((member_pname X_87) A_140)->False)->((iff ((ord_less_eq_pname_o A_140) ((insert_pname X_87) B_100))) ((ord_less_eq_pname_o A_140) B_100))))
% FOF formula (forall (B_100:(hoare_1167836817_state->Prop)) (X_87:hoare_1167836817_state) (A_140:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_87) A_140)->False)->((iff ((ord_le827224136tate_o A_140) ((insert2134838167_state X_87) B_100))) ((ord_le827224136tate_o A_140) B_100)))) of role axiom named fact_184_subset__insert
% A new axiom: (forall (B_100:(hoare_1167836817_state->Prop)) (X_87:hoare_1167836817_state) (A_140:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_87) A_140)->False)->((iff ((ord_le827224136tate_o A_140) ((insert2134838167_state X_87) B_100))) ((ord_le827224136tate_o A_140) B_100))))
% FOF formula (forall (X_86:pname) (A_139:(pname->Prop)) (B_99:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_86) A_139)) B_99)) ((and ((member_pname X_86) B_99)) ((ord_less_eq_pname_o A_139) B_99)))) of role axiom named fact_185_insert__subset
% A new axiom: (forall (X_86:pname) (A_139:(pname->Prop)) (B_99:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_86) A_139)) B_99)) ((and ((member_pname X_86) B_99)) ((ord_less_eq_pname_o A_139) B_99))))
% FOF formula (forall (X_86:hoare_1167836817_state) (A_139:(hoare_1167836817_state->Prop)) (B_99:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o ((insert2134838167_state X_86) A_139)) B_99)) ((and ((member2058392318_state X_86) B_99)) ((ord_le827224136tate_o A_139) B_99)))) of role axiom named fact_186_insert__subset
% A new axiom: (forall (X_86:hoare_1167836817_state) (A_139:(hoare_1167836817_state->Prop)) (B_99:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o ((insert2134838167_state X_86) A_139)) B_99)) ((and ((member2058392318_state X_86) B_99)) ((ord_le827224136tate_o A_139) B_99))))
% FOF formula (forall (B_98:(pname->Prop)) (A_138:pname), ((ord_less_eq_pname_o B_98) ((insert_pname A_138) B_98))) of role axiom named fact_187_subset__insertI
% A new axiom: (forall (B_98:(pname->Prop)) (A_138:pname), ((ord_less_eq_pname_o B_98) ((insert_pname A_138) B_98)))
% FOF formula (forall (B_98:(hoare_1167836817_state->Prop)) (A_138:hoare_1167836817_state), ((ord_le827224136tate_o B_98) ((insert2134838167_state A_138) B_98))) of role axiom named fact_188_subset__insertI
% A new axiom: (forall (B_98:(hoare_1167836817_state->Prop)) (A_138:hoare_1167836817_state), ((ord_le827224136tate_o B_98) ((insert2134838167_state A_138) B_98)))
% FOF formula (forall (F_51:(hoare_1167836817_state->pname)) (X_85:hoare_1167836817_state) (A_137:(hoare_1167836817_state->Prop)), (((member2058392318_state X_85) A_137)->(((eq (pname->Prop)) ((insert_pname (F_51 X_85)) ((image_8178176_pname F_51) A_137))) ((image_8178176_pname F_51) A_137)))) of role axiom named fact_189_insert__image
% A new axiom: (forall (F_51:(hoare_1167836817_state->pname)) (X_85:hoare_1167836817_state) (A_137:(hoare_1167836817_state->Prop)), (((member2058392318_state X_85) A_137)->(((eq (pname->Prop)) ((insert_pname (F_51 X_85)) ((image_8178176_pname F_51) A_137))) ((image_8178176_pname F_51) A_137))))
% FOF formula (forall (F_51:(pname->hoare_1167836817_state)) (X_85:pname) (A_137:(pname->Prop)), (((member_pname X_85) A_137)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state (F_51 X_85)) ((image_575578384_state F_51) A_137))) ((image_575578384_state F_51) A_137)))) of role axiom named fact_190_insert__image
% A new axiom: (forall (F_51:(pname->hoare_1167836817_state)) (X_85:pname) (A_137:(pname->Prop)), (((member_pname X_85) A_137)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state (F_51 X_85)) ((image_575578384_state F_51) A_137))) ((image_575578384_state F_51) A_137))))
% FOF formula (forall (F_50:(hoare_1167836817_state->pname)) (A_136:hoare_1167836817_state) (B_97:(hoare_1167836817_state->Prop)), (((eq (pname->Prop)) ((image_8178176_pname F_50) ((insert2134838167_state A_136) B_97))) ((insert_pname (F_50 A_136)) ((image_8178176_pname F_50) B_97)))) of role axiom named fact_191_image__insert
% A new axiom: (forall (F_50:(hoare_1167836817_state->pname)) (A_136:hoare_1167836817_state) (B_97:(hoare_1167836817_state->Prop)), (((eq (pname->Prop)) ((image_8178176_pname F_50) ((insert2134838167_state A_136) B_97))) ((insert_pname (F_50 A_136)) ((image_8178176_pname F_50) B_97))))
% FOF formula (forall (F_50:(pname->hoare_1167836817_state)) (A_136:pname) (B_97:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_50) ((insert_pname A_136) B_97))) ((insert2134838167_state (F_50 A_136)) ((image_575578384_state F_50) B_97)))) of role axiom named fact_192_image__insert
% A new axiom: (forall (F_50:(pname->hoare_1167836817_state)) (A_136:pname) (B_97:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_50) ((insert_pname A_136) B_97))) ((insert2134838167_state (F_50 A_136)) ((image_575578384_state F_50) B_97))))
% FOF formula (forall (F_49:(hoare_1167836817_state->pname)) (A_135:(hoare_1167836817_state->Prop)) (B_96:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_135) B_96)->((ord_less_eq_pname_o ((image_8178176_pname F_49) A_135)) ((image_8178176_pname F_49) B_96)))) of role axiom named fact_193_image__mono
% A new axiom: (forall (F_49:(hoare_1167836817_state->pname)) (A_135:(hoare_1167836817_state->Prop)) (B_96:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_135) B_96)->((ord_less_eq_pname_o ((image_8178176_pname F_49) A_135)) ((image_8178176_pname F_49) B_96))))
% FOF formula (forall (F_49:(pname->hoare_1167836817_state)) (A_135:(pname->Prop)) (B_96:(pname->Prop)), (((ord_less_eq_pname_o A_135) B_96)->((ord_le827224136tate_o ((image_575578384_state F_49) A_135)) ((image_575578384_state F_49) B_96)))) of role axiom named fact_194_image__mono
% A new axiom: (forall (F_49:(pname->hoare_1167836817_state)) (A_135:(pname->Prop)) (B_96:(pname->Prop)), (((ord_less_eq_pname_o A_135) B_96)->((ord_le827224136tate_o ((image_575578384_state F_49) A_135)) ((image_575578384_state F_49) B_96))))
% FOF formula (forall (B_95:(pname->Prop)) (F_48:(hoare_1167836817_state->pname)) (A_134:(hoare_1167836817_state->Prop)), ((iff ((ord_less_eq_pname_o B_95) ((image_8178176_pname F_48) A_134))) ((ex (hoare_1167836817_state->Prop)) (fun (AA:(hoare_1167836817_state->Prop))=> ((and ((ord_le827224136tate_o AA) A_134)) (((eq (pname->Prop)) B_95) ((image_8178176_pname F_48) AA))))))) of role axiom named fact_195_subset__image__iff
% A new axiom: (forall (B_95:(pname->Prop)) (F_48:(hoare_1167836817_state->pname)) (A_134:(hoare_1167836817_state->Prop)), ((iff ((ord_less_eq_pname_o B_95) ((image_8178176_pname F_48) A_134))) ((ex (hoare_1167836817_state->Prop)) (fun (AA:(hoare_1167836817_state->Prop))=> ((and ((ord_le827224136tate_o AA) A_134)) (((eq (pname->Prop)) B_95) ((image_8178176_pname F_48) AA)))))))
% FOF formula (forall (B_95:(hoare_1167836817_state->Prop)) (F_48:(pname->hoare_1167836817_state)) (A_134:(pname->Prop)), ((iff ((ord_le827224136tate_o B_95) ((image_575578384_state F_48) A_134))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_134)) (((eq (hoare_1167836817_state->Prop)) B_95) ((image_575578384_state F_48) AA))))))) of role axiom named fact_196_subset__image__iff
% A new axiom: (forall (B_95:(hoare_1167836817_state->Prop)) (F_48:(pname->hoare_1167836817_state)) (A_134:(pname->Prop)), ((iff ((ord_le827224136tate_o B_95) ((image_575578384_state F_48) A_134))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_134)) (((eq (hoare_1167836817_state->Prop)) B_95) ((image_575578384_state F_48) AA)))))))
% FOF formula (forall (M_2:(pname->option_com)) (A_133:pname) (B_94:com), ((((eq option_com) (M_2 A_133)) (some_com B_94))->((member_pname A_133) (dom_pname_com M_2)))) of role axiom named fact_197_domI
% A new axiom: (forall (M_2:(pname->option_com)) (A_133:pname) (B_94:com), ((((eq option_com) (M_2 A_133)) (some_com B_94))->((member_pname A_133) (dom_pname_com M_2))))
% FOF formula (forall (P_36:(pname->Prop)) (A_132:pname), ((and ((P_36 A_132)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) X_5) A_132)) (P_36 X_5))))) ((insert_pname A_132) bot_bot_pname_o)))) (((P_36 A_132)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) X_5) A_132)) (P_36 X_5))))) bot_bot_pname_o)))) of role axiom named fact_198_Collect__conv__if
% A new axiom: (forall (P_36:(pname->Prop)) (A_132:pname), ((and ((P_36 A_132)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) X_5) A_132)) (P_36 X_5))))) ((insert_pname A_132) bot_bot_pname_o)))) (((P_36 A_132)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) X_5) A_132)) (P_36 X_5))))) bot_bot_pname_o))))
% FOF formula (forall (P_36:((pname->Prop)->Prop)) (A_132:(pname->Prop)), ((and ((P_36 A_132)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) X_5) A_132)) (P_36 X_5))))) ((insert_pname_o A_132) bot_bot_pname_o_o)))) (((P_36 A_132)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) X_5) A_132)) (P_36 X_5))))) bot_bot_pname_o_o)))) of role axiom named fact_199_Collect__conv__if
% A new axiom: (forall (P_36:((pname->Prop)->Prop)) (A_132:(pname->Prop)), ((and ((P_36 A_132)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) X_5) A_132)) (P_36 X_5))))) ((insert_pname_o A_132) bot_bot_pname_o_o)))) (((P_36 A_132)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) X_5) A_132)) (P_36 X_5))))) bot_bot_pname_o_o))))
% FOF formula (forall (P_36:((hoare_1167836817_state->Prop)->Prop)) (A_132:(hoare_1167836817_state->Prop)), ((and ((P_36 A_132)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) X_5) A_132)) (P_36 X_5))))) ((insert999278200tate_o A_132) bot_bo691907561te_o_o)))) (((P_36 A_132)->False)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) X_5) A_132)) (P_36 X_5))))) bot_bo691907561te_o_o)))) of role axiom named fact_200_Collect__conv__if
% A new axiom: (forall (P_36:((hoare_1167836817_state->Prop)->Prop)) (A_132:(hoare_1167836817_state->Prop)), ((and ((P_36 A_132)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) X_5) A_132)) (P_36 X_5))))) ((insert999278200tate_o A_132) bot_bo691907561te_o_o)))) (((P_36 A_132)->False)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) X_5) A_132)) (P_36 X_5))))) bot_bo691907561te_o_o))))
% FOF formula (forall (P_36:(hoare_1167836817_state->Prop)) (A_132:hoare_1167836817_state), ((and ((P_36 A_132)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X_5) A_132)) (P_36 X_5))))) ((insert2134838167_state A_132) bot_bo70021908tate_o)))) (((P_36 A_132)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X_5) A_132)) (P_36 X_5))))) bot_bo70021908tate_o)))) of role axiom named fact_201_Collect__conv__if
% A new axiom: (forall (P_36:(hoare_1167836817_state->Prop)) (A_132:hoare_1167836817_state), ((and ((P_36 A_132)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X_5) A_132)) (P_36 X_5))))) ((insert2134838167_state A_132) bot_bo70021908tate_o)))) (((P_36 A_132)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X_5) A_132)) (P_36 X_5))))) bot_bo70021908tate_o))))
% FOF formula (forall (P_35:(pname->Prop)) (A_131:pname), ((and ((P_35 A_131)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) A_131) X_5)) (P_35 X_5))))) ((insert_pname A_131) bot_bot_pname_o)))) (((P_35 A_131)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) A_131) X_5)) (P_35 X_5))))) bot_bot_pname_o)))) of role axiom named fact_202_Collect__conv__if2
% A new axiom: (forall (P_35:(pname->Prop)) (A_131:pname), ((and ((P_35 A_131)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) A_131) X_5)) (P_35 X_5))))) ((insert_pname A_131) bot_bot_pname_o)))) (((P_35 A_131)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) A_131) X_5)) (P_35 X_5))))) bot_bot_pname_o))))
% FOF formula (forall (P_35:((pname->Prop)->Prop)) (A_131:(pname->Prop)), ((and ((P_35 A_131)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) A_131) X_5)) (P_35 X_5))))) ((insert_pname_o A_131) bot_bot_pname_o_o)))) (((P_35 A_131)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) A_131) X_5)) (P_35 X_5))))) bot_bot_pname_o_o)))) of role axiom named fact_203_Collect__conv__if2
% A new axiom: (forall (P_35:((pname->Prop)->Prop)) (A_131:(pname->Prop)), ((and ((P_35 A_131)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) A_131) X_5)) (P_35 X_5))))) ((insert_pname_o A_131) bot_bot_pname_o_o)))) (((P_35 A_131)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) A_131) X_5)) (P_35 X_5))))) bot_bot_pname_o_o))))
% FOF formula (forall (P_35:((hoare_1167836817_state->Prop)->Prop)) (A_131:(hoare_1167836817_state->Prop)), ((and ((P_35 A_131)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_131) X_5)) (P_35 X_5))))) ((insert999278200tate_o A_131) bot_bo691907561te_o_o)))) (((P_35 A_131)->False)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_131) X_5)) (P_35 X_5))))) bot_bo691907561te_o_o)))) of role axiom named fact_204_Collect__conv__if2
% A new axiom: (forall (P_35:((hoare_1167836817_state->Prop)->Prop)) (A_131:(hoare_1167836817_state->Prop)), ((and ((P_35 A_131)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_131) X_5)) (P_35 X_5))))) ((insert999278200tate_o A_131) bot_bo691907561te_o_o)))) (((P_35 A_131)->False)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_131) X_5)) (P_35 X_5))))) bot_bo691907561te_o_o))))
% FOF formula (forall (P_35:(hoare_1167836817_state->Prop)) (A_131:hoare_1167836817_state), ((and ((P_35 A_131)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_131) X_5)) (P_35 X_5))))) ((insert2134838167_state A_131) bot_bo70021908tate_o)))) (((P_35 A_131)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_131) X_5)) (P_35 X_5))))) bot_bo70021908tate_o)))) of role axiom named fact_205_Collect__conv__if2
% A new axiom: (forall (P_35:(hoare_1167836817_state->Prop)) (A_131:hoare_1167836817_state), ((and ((P_35 A_131)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_131) X_5)) (P_35 X_5))))) ((insert2134838167_state A_131) bot_bo70021908tate_o)))) (((P_35 A_131)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_131) X_5)) (P_35 X_5))))) bot_bo70021908tate_o))))
% FOF formula (forall (A_130:pname), (((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> (((eq pname) X_5) A_130)))) ((insert_pname A_130) bot_bot_pname_o))) of role axiom named fact_206_singleton__conv
% A new axiom: (forall (A_130:pname), (((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> (((eq pname) X_5) A_130)))) ((insert_pname A_130) bot_bot_pname_o)))
% FOF formula (forall (A_130:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> (((eq (pname->Prop)) X_5) A_130)))) ((insert_pname_o A_130) bot_bot_pname_o_o))) of role axiom named fact_207_singleton__conv
% A new axiom: (forall (A_130:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> (((eq (pname->Prop)) X_5) A_130)))) ((insert_pname_o A_130) bot_bot_pname_o_o)))
% FOF formula (forall (A_130:(hoare_1167836817_state->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> (((eq (hoare_1167836817_state->Prop)) X_5) A_130)))) ((insert999278200tate_o A_130) bot_bo691907561te_o_o))) of role axiom named fact_208_singleton__conv
% A new axiom: (forall (A_130:(hoare_1167836817_state->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> (((eq (hoare_1167836817_state->Prop)) X_5) A_130)))) ((insert999278200tate_o A_130) bot_bo691907561te_o_o)))
% FOF formula (forall (A_130:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X_5) A_130)))) ((insert2134838167_state A_130) bot_bo70021908tate_o))) of role axiom named fact_209_singleton__conv
% A new axiom: (forall (A_130:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X_5) A_130)))) ((insert2134838167_state A_130) bot_bo70021908tate_o)))
% FOF formula (forall (A_129:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_129))) ((insert_pname A_129) bot_bot_pname_o))) of role axiom named fact_210_singleton__conv2
% A new axiom: (forall (A_129:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_129))) ((insert_pname A_129) bot_bot_pname_o)))
% FOF formula (forall (A_129:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fequal_pname_o A_129))) ((insert_pname_o A_129) bot_bot_pname_o_o))) of role axiom named fact_211_singleton__conv2
% A new axiom: (forall (A_129:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fequal_pname_o A_129))) ((insert_pname_o A_129) bot_bot_pname_o_o)))
% FOF formula (forall (A_129:(hoare_1167836817_state->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fequal1486222077tate_o A_129))) ((insert999278200tate_o A_129) bot_bo691907561te_o_o))) of role axiom named fact_212_singleton__conv2
% A new axiom: (forall (A_129:(hoare_1167836817_state->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fequal1486222077tate_o A_129))) ((insert999278200tate_o A_129) bot_bo691907561te_o_o)))
% FOF formula (forall (A_129:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fequal1831255762_state A_129))) ((insert2134838167_state A_129) bot_bo70021908tate_o))) of role axiom named fact_213_singleton__conv2
% A new axiom: (forall (A_129:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fequal1831255762_state A_129))) ((insert2134838167_state A_129) bot_bo70021908tate_o)))
% FOF formula (forall (C_21:com) (G_3:(hoare_1167836817_state->Prop)), (hoare_1201148605gleton->((forall (X_5:pname), (((member_pname X_5) (dom_pname_com body))->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT (body_1 X_5))) bot_bo70021908tate_o))))->((wt C_21)->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o)))))) of role axiom named fact_214_MGF__lemma1
% A new axiom: (forall (C_21:com) (G_3:(hoare_1167836817_state->Prop)), (hoare_1201148605gleton->((forall (X_5:pname), (((member_pname X_5) (dom_pname_com body))->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT (body_1 X_5))) bot_bo70021908tate_o))))->((wt C_21)->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o))))))
% FOF formula (forall (Pn_1:pname) (B_42:com), (wT_bodies->((((eq option_com) (body Pn_1)) (some_com B_42))->(wt B_42)))) of role axiom named fact_215_WT__bodiesD
% A new axiom: (forall (Pn_1:pname) (B_42:com), (wT_bodies->((((eq option_com) (body Pn_1)) (some_com B_42))->(wt B_42))))
% FOF formula (forall (B_93:pname) (F_47:(hoare_1167836817_state->pname)) (A_128:(hoare_1167836817_state->Prop)), (((member_pname B_93) ((image_8178176_pname F_47) A_128))->((forall (X_5:hoare_1167836817_state), ((((eq pname) B_93) (F_47 X_5))->(((member2058392318_state X_5) A_128)->False)))->False))) of role axiom named fact_216_imageE
% A new axiom: (forall (B_93:pname) (F_47:(hoare_1167836817_state->pname)) (A_128:(hoare_1167836817_state->Prop)), (((member_pname B_93) ((image_8178176_pname F_47) A_128))->((forall (X_5:hoare_1167836817_state), ((((eq pname) B_93) (F_47 X_5))->(((member2058392318_state X_5) A_128)->False)))->False)))
% FOF formula (forall (B_93:hoare_1167836817_state) (F_47:(pname->hoare_1167836817_state)) (A_128:(pname->Prop)), (((member2058392318_state B_93) ((image_575578384_state F_47) A_128))->((forall (X_5:pname), ((((eq hoare_1167836817_state) B_93) (F_47 X_5))->(((member_pname X_5) A_128)->False)))->False))) of role axiom named fact_217_imageE
% A new axiom: (forall (B_93:hoare_1167836817_state) (F_47:(pname->hoare_1167836817_state)) (A_128:(pname->Prop)), (((member2058392318_state B_93) ((image_575578384_state F_47) A_128))->((forall (X_5:pname), ((((eq hoare_1167836817_state) B_93) (F_47 X_5))->(((member_pname X_5) A_128)->False)))->False)))
% FOF formula (forall (P_34:(((pname->Prop)->Prop)->Prop)) (A_127:((pname->Prop)->Prop)) (F_46:((pname->Prop)->Prop)), ((finite297249702name_o F_46)->(((ord_le1205211808me_o_o F_46) A_127)->((P_34 bot_bot_pname_o_o)->((forall (A_122:(pname->Prop)) (F_26:((pname->Prop)->Prop)), ((finite297249702name_o F_26)->(((member_pname_o A_122) A_127)->((((member_pname_o A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert_pname_o A_122) F_26)))))))->(P_34 F_46)))))) of role axiom named fact_218_finite__subset__induct
% A new axiom: (forall (P_34:(((pname->Prop)->Prop)->Prop)) (A_127:((pname->Prop)->Prop)) (F_46:((pname->Prop)->Prop)), ((finite297249702name_o F_46)->(((ord_le1205211808me_o_o F_46) A_127)->((P_34 bot_bot_pname_o_o)->((forall (A_122:(pname->Prop)) (F_26:((pname->Prop)->Prop)), ((finite297249702name_o F_26)->(((member_pname_o A_122) A_127)->((((member_pname_o A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert_pname_o A_122) F_26)))))))->(P_34 F_46))))))
% FOF formula (forall (P_34:(((hoare_1167836817_state->Prop)->Prop)->Prop)) (A_127:((hoare_1167836817_state->Prop)->Prop)) (F_46:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_46)->(((ord_le741939125te_o_o F_46) A_127)->((P_34 bot_bo691907561te_o_o)->((forall (A_122:(hoare_1167836817_state->Prop)) (F_26:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_26)->(((member864234961tate_o A_122) A_127)->((((member864234961tate_o A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert999278200tate_o A_122) F_26)))))))->(P_34 F_46)))))) of role axiom named fact_219_finite__subset__induct
% A new axiom: (forall (P_34:(((hoare_1167836817_state->Prop)->Prop)->Prop)) (A_127:((hoare_1167836817_state->Prop)->Prop)) (F_46:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_46)->(((ord_le741939125te_o_o F_46) A_127)->((P_34 bot_bo691907561te_o_o)->((forall (A_122:(hoare_1167836817_state->Prop)) (F_26:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_26)->(((member864234961tate_o A_122) A_127)->((((member864234961tate_o A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert999278200tate_o A_122) F_26)))))))->(P_34 F_46))))))
% FOF formula (forall (P_34:((pname->Prop)->Prop)) (A_127:(pname->Prop)) (F_46:(pname->Prop)), ((finite_finite_pname F_46)->(((ord_less_eq_pname_o F_46) A_127)->((P_34 bot_bot_pname_o)->((forall (A_122:pname) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->(((member_pname A_122) A_127)->((((member_pname A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert_pname A_122) F_26)))))))->(P_34 F_46)))))) of role axiom named fact_220_finite__subset__induct
% A new axiom: (forall (P_34:((pname->Prop)->Prop)) (A_127:(pname->Prop)) (F_46:(pname->Prop)), ((finite_finite_pname F_46)->(((ord_less_eq_pname_o F_46) A_127)->((P_34 bot_bot_pname_o)->((forall (A_122:pname) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->(((member_pname A_122) A_127)->((((member_pname A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert_pname A_122) F_26)))))))->(P_34 F_46))))))
% FOF formula (forall (P_34:((hoare_1167836817_state->Prop)->Prop)) (A_127:(hoare_1167836817_state->Prop)) (F_46:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_46)->(((ord_le827224136tate_o F_46) A_127)->((P_34 bot_bo70021908tate_o)->((forall (A_122:hoare_1167836817_state) (F_26:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_26)->(((member2058392318_state A_122) A_127)->((((member2058392318_state A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert2134838167_state A_122) F_26)))))))->(P_34 F_46)))))) of role axiom named fact_221_finite__subset__induct
% A new axiom: (forall (P_34:((hoare_1167836817_state->Prop)->Prop)) (A_127:(hoare_1167836817_state->Prop)) (F_46:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_46)->(((ord_le827224136tate_o F_46) A_127)->((P_34 bot_bo70021908tate_o)->((forall (A_122:hoare_1167836817_state) (F_26:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_26)->(((member2058392318_state A_122) A_127)->((((member2058392318_state A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert2134838167_state A_122) F_26)))))))->(P_34 F_46))))))
% FOF formula (forall (P:pname), ((wt (body_1 P))->((forall (Y_2:com), (not (((eq option_com) (body P)) (some_com Y_2))))->False))) of role axiom named fact_222_WTs__elim__cases_I7_J
% A new axiom: (forall (P:pname), ((wt (body_1 P))->((forall (Y_2:com), (not (((eq option_com) (body P)) (some_com Y_2))))->False)))
% FOF formula (forall (B_92:(pname->Prop)) (A_126:(pname->Prop)), ((forall (X_5:pname), (((member_pname X_5) A_126)->((member_pname X_5) B_92)))->((ord_less_eq_pname_o A_126) B_92))) of role axiom named fact_223_subsetI
% A new axiom: (forall (B_92:(pname->Prop)) (A_126:(pname->Prop)), ((forall (X_5:pname), (((member_pname X_5) A_126)->((member_pname X_5) B_92)))->((ord_less_eq_pname_o A_126) B_92)))
% FOF formula (forall (B_92:(hoare_1167836817_state->Prop)) (A_126:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_126)->((member2058392318_state X_5) B_92)))->((ord_le827224136tate_o A_126) B_92))) of role axiom named fact_224_subsetI
% A new axiom: (forall (B_92:(hoare_1167836817_state->Prop)) (A_126:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_126)->((member2058392318_state X_5) B_92)))->((ord_le827224136tate_o A_126) B_92)))
% FOF formula (forall (F_45:((pname->Prop)->hoare_1167836817_state)) (A_125:((pname->Prop)->Prop)) (B_91:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_91)->(((ord_le827224136tate_o B_91) ((image_1381916541_state F_45) A_125))->((ex ((pname->Prop)->Prop)) (fun (C_47:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_47) A_125)) (finite297249702name_o C_47))) (((eq (hoare_1167836817_state->Prop)) B_91) ((image_1381916541_state F_45) C_47)))))))) of role axiom named fact_225_finite__subset__image
% A new axiom: (forall (F_45:((pname->Prop)->hoare_1167836817_state)) (A_125:((pname->Prop)->Prop)) (B_91:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_91)->(((ord_le827224136tate_o B_91) ((image_1381916541_state F_45) A_125))->((ex ((pname->Prop)->Prop)) (fun (C_47:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_47) A_125)) (finite297249702name_o C_47))) (((eq (hoare_1167836817_state->Prop)) B_91) ((image_1381916541_state F_45) C_47))))))))
% FOF formula (forall (F_45:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (A_125:((hoare_1167836817_state->Prop)->Prop)) (B_91:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_91)->(((ord_le827224136tate_o B_91) ((image_635813834_state F_45) A_125))->((ex ((hoare_1167836817_state->Prop)->Prop)) (fun (C_47:((hoare_1167836817_state->Prop)->Prop))=> ((and ((and ((ord_le741939125te_o_o C_47) A_125)) (finite1380128977tate_o C_47))) (((eq (hoare_1167836817_state->Prop)) B_91) ((image_635813834_state F_45) C_47)))))))) of role axiom named fact_226_finite__subset__image
% A new axiom: (forall (F_45:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (A_125:((hoare_1167836817_state->Prop)->Prop)) (B_91:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_91)->(((ord_le827224136tate_o B_91) ((image_635813834_state F_45) A_125))->((ex ((hoare_1167836817_state->Prop)->Prop)) (fun (C_47:((hoare_1167836817_state->Prop)->Prop))=> ((and ((and ((ord_le741939125te_o_o C_47) A_125)) (finite1380128977tate_o C_47))) (((eq (hoare_1167836817_state->Prop)) B_91) ((image_635813834_state F_45) C_47))))))))
% FOF formula (forall (F_45:((pname->Prop)->pname)) (A_125:((pname->Prop)->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_pname_o_pname F_45) A_125))->((ex ((pname->Prop)->Prop)) (fun (C_47:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_47) A_125)) (finite297249702name_o C_47))) (((eq (pname->Prop)) B_91) ((image_pname_o_pname F_45) C_47)))))))) of role axiom named fact_227_finite__subset__image
% A new axiom: (forall (F_45:((pname->Prop)->pname)) (A_125:((pname->Prop)->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_pname_o_pname F_45) A_125))->((ex ((pname->Prop)->Prop)) (fun (C_47:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_47) A_125)) (finite297249702name_o C_47))) (((eq (pname->Prop)) B_91) ((image_pname_o_pname F_45) C_47))))))))
% FOF formula (forall (F_45:((hoare_1167836817_state->Prop)->pname)) (A_125:((hoare_1167836817_state->Prop)->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_980295115_pname F_45) A_125))->((ex ((hoare_1167836817_state->Prop)->Prop)) (fun (C_47:((hoare_1167836817_state->Prop)->Prop))=> ((and ((and ((ord_le741939125te_o_o C_47) A_125)) (finite1380128977tate_o C_47))) (((eq (pname->Prop)) B_91) ((image_980295115_pname F_45) C_47)))))))) of role axiom named fact_228_finite__subset__image
% A new axiom: (forall (F_45:((hoare_1167836817_state->Prop)->pname)) (A_125:((hoare_1167836817_state->Prop)->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_980295115_pname F_45) A_125))->((ex ((hoare_1167836817_state->Prop)->Prop)) (fun (C_47:((hoare_1167836817_state->Prop)->Prop))=> ((and ((and ((ord_le741939125te_o_o C_47) A_125)) (finite1380128977tate_o C_47))) (((eq (pname->Prop)) B_91) ((image_980295115_pname F_45) C_47))))))))
% FOF formula (forall (F_45:(hoare_1167836817_state->(pname->Prop))) (A_125:(hoare_1167836817_state->Prop)) (B_91:((pname->Prop)->Prop)), ((finite297249702name_o B_91)->(((ord_le1205211808me_o_o B_91) ((image_2066861949name_o F_45) A_125))->((ex (hoare_1167836817_state->Prop)) (fun (C_47:(hoare_1167836817_state->Prop))=> ((and ((and ((ord_le827224136tate_o C_47) A_125)) (finite1084549118_state C_47))) (((eq ((pname->Prop)->Prop)) B_91) ((image_2066861949name_o F_45) C_47)))))))) of role axiom named fact_229_finite__subset__image
% A new axiom: (forall (F_45:(hoare_1167836817_state->(pname->Prop))) (A_125:(hoare_1167836817_state->Prop)) (B_91:((pname->Prop)->Prop)), ((finite297249702name_o B_91)->(((ord_le1205211808me_o_o B_91) ((image_2066861949name_o F_45) A_125))->((ex (hoare_1167836817_state->Prop)) (fun (C_47:(hoare_1167836817_state->Prop))=> ((and ((and ((ord_le827224136tate_o C_47) A_125)) (finite1084549118_state C_47))) (((eq ((pname->Prop)->Prop)) B_91) ((image_2066861949name_o F_45) C_47))))))))
% FOF formula (forall (F_45:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (A_125:(hoare_1167836817_state->Prop)) (B_91:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o B_91)->(((ord_le741939125te_o_o B_91) ((image_1745649338tate_o F_45) A_125))->((ex (hoare_1167836817_state->Prop)) (fun (C_47:(hoare_1167836817_state->Prop))=> ((and ((and ((ord_le827224136tate_o C_47) A_125)) (finite1084549118_state C_47))) (((eq ((hoare_1167836817_state->Prop)->Prop)) B_91) ((image_1745649338tate_o F_45) C_47)))))))) of role axiom named fact_230_finite__subset__image
% A new axiom: (forall (F_45:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (A_125:(hoare_1167836817_state->Prop)) (B_91:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o B_91)->(((ord_le741939125te_o_o B_91) ((image_1745649338tate_o F_45) A_125))->((ex (hoare_1167836817_state->Prop)) (fun (C_47:(hoare_1167836817_state->Prop))=> ((and ((and ((ord_le827224136tate_o C_47) A_125)) (finite1084549118_state C_47))) (((eq ((hoare_1167836817_state->Prop)->Prop)) B_91) ((image_1745649338tate_o F_45) C_47))))))))
% FOF formula (forall (F_45:(hoare_1167836817_state->pname)) (A_125:(hoare_1167836817_state->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_8178176_pname F_45) A_125))->((ex (hoare_1167836817_state->Prop)) (fun (C_47:(hoare_1167836817_state->Prop))=> ((and ((and ((ord_le827224136tate_o C_47) A_125)) (finite1084549118_state C_47))) (((eq (pname->Prop)) B_91) ((image_8178176_pname F_45) C_47)))))))) of role axiom named fact_231_finite__subset__image
% A new axiom: (forall (F_45:(hoare_1167836817_state->pname)) (A_125:(hoare_1167836817_state->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_8178176_pname F_45) A_125))->((ex (hoare_1167836817_state->Prop)) (fun (C_47:(hoare_1167836817_state->Prop))=> ((and ((and ((ord_le827224136tate_o C_47) A_125)) (finite1084549118_state C_47))) (((eq (pname->Prop)) B_91) ((image_8178176_pname F_45) C_47))))))))
% FOF formula (forall (F_45:(pname->(pname->Prop))) (A_125:(pname->Prop)) (B_91:((pname->Prop)->Prop)), ((finite297249702name_o B_91)->(((ord_le1205211808me_o_o B_91) ((image_pname_pname_o F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq ((pname->Prop)->Prop)) B_91) ((image_pname_pname_o F_45) C_47)))))))) of role axiom named fact_232_finite__subset__image
% A new axiom: (forall (F_45:(pname->(pname->Prop))) (A_125:(pname->Prop)) (B_91:((pname->Prop)->Prop)), ((finite297249702name_o B_91)->(((ord_le1205211808me_o_o B_91) ((image_pname_pname_o F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq ((pname->Prop)->Prop)) B_91) ((image_pname_pname_o F_45) C_47))))))))
% FOF formula (forall (F_45:(pname->(hoare_1167836817_state->Prop))) (A_125:(pname->Prop)) (B_91:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o B_91)->(((ord_le741939125te_o_o B_91) ((image_475339327tate_o F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq ((hoare_1167836817_state->Prop)->Prop)) B_91) ((image_475339327tate_o F_45) C_47)))))))) of role axiom named fact_233_finite__subset__image
% A new axiom: (forall (F_45:(pname->(hoare_1167836817_state->Prop))) (A_125:(pname->Prop)) (B_91:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o B_91)->(((ord_le741939125te_o_o B_91) ((image_475339327tate_o F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq ((hoare_1167836817_state->Prop)->Prop)) B_91) ((image_475339327tate_o F_45) C_47))))))))
% FOF formula (forall (F_45:(pname->pname)) (A_125:(pname->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_pname_pname F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq (pname->Prop)) B_91) ((image_pname_pname F_45) C_47)))))))) of role axiom named fact_234_finite__subset__image
% A new axiom: (forall (F_45:(pname->pname)) (A_125:(pname->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_pname_pname F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq (pname->Prop)) B_91) ((image_pname_pname F_45) C_47))))))))
% FOF formula (forall (F_45:(pname->hoare_1167836817_state)) (A_125:(pname->Prop)) (B_91:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_91)->(((ord_le827224136tate_o B_91) ((image_575578384_state F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq (hoare_1167836817_state->Prop)) B_91) ((image_575578384_state F_45) C_47)))))))) of role axiom named fact_235_finite__subset__image
% A new axiom: (forall (F_45:(pname->hoare_1167836817_state)) (A_125:(pname->Prop)) (B_91:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_91)->(((ord_le827224136tate_o B_91) ((image_575578384_state F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq (hoare_1167836817_state->Prop)) B_91) ((image_575578384_state F_45) C_47))))))))
% FOF formula (finite_finite_pname (dom_pname_com body)) of role axiom named fact_236_finite__dom__body
% A new axiom: (finite_finite_pname (dom_pname_com body))
% FOF formula (forall (P_33:(((pname->Prop)->Prop)->Prop)) (F_44:((pname->Prop)->Prop)), ((finite297249702name_o F_44)->((P_33 bot_bot_pname_o_o)->((forall (X_5:(pname->Prop)) (F_26:((pname->Prop)->Prop)), ((finite297249702name_o F_26)->((((member_pname_o X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert_pname_o X_5) F_26))))))->(P_33 F_44))))) of role axiom named fact_237_finite__induct
% A new axiom: (forall (P_33:(((pname->Prop)->Prop)->Prop)) (F_44:((pname->Prop)->Prop)), ((finite297249702name_o F_44)->((P_33 bot_bot_pname_o_o)->((forall (X_5:(pname->Prop)) (F_26:((pname->Prop)->Prop)), ((finite297249702name_o F_26)->((((member_pname_o X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert_pname_o X_5) F_26))))))->(P_33 F_44)))))
% FOF formula (forall (P_33:(((hoare_1167836817_state->Prop)->Prop)->Prop)) (F_44:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_44)->((P_33 bot_bo691907561te_o_o)->((forall (X_5:(hoare_1167836817_state->Prop)) (F_26:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_26)->((((member864234961tate_o X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert999278200tate_o X_5) F_26))))))->(P_33 F_44))))) of role axiom named fact_238_finite__induct
% A new axiom: (forall (P_33:(((hoare_1167836817_state->Prop)->Prop)->Prop)) (F_44:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_44)->((P_33 bot_bo691907561te_o_o)->((forall (X_5:(hoare_1167836817_state->Prop)) (F_26:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_26)->((((member864234961tate_o X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert999278200tate_o X_5) F_26))))))->(P_33 F_44)))))
% FOF formula (forall (P_33:((pname->Prop)->Prop)) (F_44:(pname->Prop)), ((finite_finite_pname F_44)->((P_33 bot_bot_pname_o)->((forall (X_5:pname) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->((((member_pname X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert_pname X_5) F_26))))))->(P_33 F_44))))) of role axiom named fact_239_finite__induct
% A new axiom: (forall (P_33:((pname->Prop)->Prop)) (F_44:(pname->Prop)), ((finite_finite_pname F_44)->((P_33 bot_bot_pname_o)->((forall (X_5:pname) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->((((member_pname X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert_pname X_5) F_26))))))->(P_33 F_44)))))
% FOF formula (forall (P_33:((hoare_1167836817_state->Prop)->Prop)) (F_44:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_44)->((P_33 bot_bo70021908tate_o)->((forall (X_5:hoare_1167836817_state) (F_26:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_26)->((((member2058392318_state X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert2134838167_state X_5) F_26))))))->(P_33 F_44))))) of role axiom named fact_240_finite__induct
% A new axiom: (forall (P_33:((hoare_1167836817_state->Prop)->Prop)) (F_44:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_44)->((P_33 bot_bo70021908tate_o)->((forall (X_5:hoare_1167836817_state) (F_26:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_26)->((((member2058392318_state X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert2134838167_state X_5) F_26))))))->(P_33 F_44)))))
% FOF formula (forall (A_123:((pname->Prop)->Prop)), ((iff (finite297249702name_o A_123)) ((or (((eq ((pname->Prop)->Prop)) A_123) bot_bot_pname_o_o)) ((ex ((pname->Prop)->Prop)) (fun (A_124:((pname->Prop)->Prop))=> ((ex (pname->Prop)) (fun (A_122:(pname->Prop))=> ((and (((eq ((pname->Prop)->Prop)) A_123) ((insert_pname_o A_122) A_124))) (finite297249702name_o A_124))))))))) of role axiom named fact_241_finite_Osimps
% A new axiom: (forall (A_123:((pname->Prop)->Prop)), ((iff (finite297249702name_o A_123)) ((or (((eq ((pname->Prop)->Prop)) A_123) bot_bot_pname_o_o)) ((ex ((pname->Prop)->Prop)) (fun (A_124:((pname->Prop)->Prop))=> ((ex (pname->Prop)) (fun (A_122:(pname->Prop))=> ((and (((eq ((pname->Prop)->Prop)) A_123) ((insert_pname_o A_122) A_124))) (finite297249702name_o A_124)))))))))
% FOF formula (forall (A_123:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o A_123)) ((or (((eq ((hoare_1167836817_state->Prop)->Prop)) A_123) bot_bo691907561te_o_o)) ((ex ((hoare_1167836817_state->Prop)->Prop)) (fun (A_124:((hoare_1167836817_state->Prop)->Prop))=> ((ex (hoare_1167836817_state->Prop)) (fun (A_122:(hoare_1167836817_state->Prop))=> ((and (((eq ((hoare_1167836817_state->Prop)->Prop)) A_123) ((insert999278200tate_o A_122) A_124))) (finite1380128977tate_o A_124))))))))) of role axiom named fact_242_finite_Osimps
% A new axiom: (forall (A_123:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o A_123)) ((or (((eq ((hoare_1167836817_state->Prop)->Prop)) A_123) bot_bo691907561te_o_o)) ((ex ((hoare_1167836817_state->Prop)->Prop)) (fun (A_124:((hoare_1167836817_state->Prop)->Prop))=> ((ex (hoare_1167836817_state->Prop)) (fun (A_122:(hoare_1167836817_state->Prop))=> ((and (((eq ((hoare_1167836817_state->Prop)->Prop)) A_123) ((insert999278200tate_o A_122) A_124))) (finite1380128977tate_o A_124)))))))))
% FOF formula (forall (A_123:(pname->Prop)), ((iff (finite_finite_pname A_123)) ((or (((eq (pname->Prop)) A_123) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_124:(pname->Prop))=> ((ex pname) (fun (A_122:pname)=> ((and (((eq (pname->Prop)) A_123) ((insert_pname A_122) A_124))) (finite_finite_pname A_124))))))))) of role axiom named fact_243_finite_Osimps
% A new axiom: (forall (A_123:(pname->Prop)), ((iff (finite_finite_pname A_123)) ((or (((eq (pname->Prop)) A_123) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_124:(pname->Prop))=> ((ex pname) (fun (A_122:pname)=> ((and (((eq (pname->Prop)) A_123) ((insert_pname A_122) A_124))) (finite_finite_pname A_124)))))))))
% FOF formula (forall (A_123:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state A_123)) ((or (((eq (hoare_1167836817_state->Prop)) A_123) bot_bo70021908tate_o)) ((ex (hoare_1167836817_state->Prop)) (fun (A_124:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (A_122:hoare_1167836817_state)=> ((and (((eq (hoare_1167836817_state->Prop)) A_123) ((insert2134838167_state A_122) A_124))) (finite1084549118_state A_124))))))))) of role axiom named fact_244_finite_Osimps
% A new axiom: (forall (A_123:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state A_123)) ((or (((eq (hoare_1167836817_state->Prop)) A_123) bot_bo70021908tate_o)) ((ex (hoare_1167836817_state->Prop)) (fun (A_124:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (A_122:hoare_1167836817_state)=> ((and (((eq (hoare_1167836817_state->Prop)) A_123) ((insert2134838167_state A_122) A_124))) (finite1084549118_state A_124)))))))))
% FOF formula (forall (F_43:(pname->(pname->Prop))) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite297249702name_o ((image_pname_pname_o F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq (pname->Prop)) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_245_pigeonhole__infinite
% A new axiom: (forall (F_43:(pname->(pname->Prop))) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite297249702name_o ((image_pname_pname_o F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq (pname->Prop)) (F_43 A_122)) (F_43 X_5))))))->False)))))))
% FOF formula (forall (F_43:(pname->(hoare_1167836817_state->Prop))) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite1380128977tate_o ((image_475339327tate_o F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq (hoare_1167836817_state->Prop)) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_246_pigeonhole__infinite
% A new axiom: (forall (F_43:(pname->(hoare_1167836817_state->Prop))) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite1380128977tate_o ((image_475339327tate_o F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq (hoare_1167836817_state->Prop)) (F_43 A_122)) (F_43 X_5))))))->False)))))))
% FOF formula (forall (F_43:(hoare_1167836817_state->hoare_1167836817_state)) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite1084549118_state ((image_31595733_state F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_247_pigeonhole__infinite
% A new axiom: (forall (F_43:(hoare_1167836817_state->hoare_1167836817_state)) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite1084549118_state ((image_31595733_state F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->False)))))))
% FOF formula (forall (F_43:((pname->Prop)->hoare_1167836817_state)) (A_121:((pname->Prop)->Prop)), (((finite297249702name_o A_121)->False)->((finite1084549118_state ((image_1381916541_state F_43) A_121))->((ex (pname->Prop)) (fun (X_5:(pname->Prop))=> ((and ((member_pname_o X_5) A_121)) ((finite297249702name_o (collect_pname_o (fun (A_122:(pname->Prop))=> ((and ((member_pname_o A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_248_pigeonhole__infinite
% A new axiom: (forall (F_43:((pname->Prop)->hoare_1167836817_state)) (A_121:((pname->Prop)->Prop)), (((finite297249702name_o A_121)->False)->((finite1084549118_state ((image_1381916541_state F_43) A_121))->((ex (pname->Prop)) (fun (X_5:(pname->Prop))=> ((and ((member_pname_o X_5) A_121)) ((finite297249702name_o (collect_pname_o (fun (A_122:(pname->Prop))=> ((and ((member_pname_o A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->False)))))))
% FOF formula (forall (F_43:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (A_121:((hoare_1167836817_state->Prop)->Prop)), (((finite1380128977tate_o A_121)->False)->((finite1084549118_state ((image_635813834_state F_43) A_121))->((ex (hoare_1167836817_state->Prop)) (fun (X_5:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o X_5) A_121)) ((finite1380128977tate_o (collec269976083tate_o (fun (A_122:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_249_pigeonhole__infinite
% A new axiom: (forall (F_43:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (A_121:((hoare_1167836817_state->Prop)->Prop)), (((finite1380128977tate_o A_121)->False)->((finite1084549118_state ((image_635813834_state F_43) A_121))->((ex (hoare_1167836817_state->Prop)) (fun (X_5:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o X_5) A_121)) ((finite1380128977tate_o (collec269976083tate_o (fun (A_122:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->False)))))))
% FOF formula (forall (F_43:(pname->pname)) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite_finite_pname ((image_pname_pname F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_250_pigeonhole__infinite
% A new axiom: (forall (F_43:(pname->pname)) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite_finite_pname ((image_pname_pname F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False)))))))
% FOF formula (forall (F_43:(hoare_1167836817_state->pname)) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite_finite_pname ((image_8178176_pname F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_251_pigeonhole__infinite
% A new axiom: (forall (F_43:(hoare_1167836817_state->pname)) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite_finite_pname ((image_8178176_pname F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False)))))))
% FOF formula (forall (F_43:((pname->Prop)->pname)) (A_121:((pname->Prop)->Prop)), (((finite297249702name_o A_121)->False)->((finite_finite_pname ((image_pname_o_pname F_43) A_121))->((ex (pname->Prop)) (fun (X_5:(pname->Prop))=> ((and ((member_pname_o X_5) A_121)) ((finite297249702name_o (collect_pname_o (fun (A_122:(pname->Prop))=> ((and ((member_pname_o A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_252_pigeonhole__infinite
% A new axiom: (forall (F_43:((pname->Prop)->pname)) (A_121:((pname->Prop)->Prop)), (((finite297249702name_o A_121)->False)->((finite_finite_pname ((image_pname_o_pname F_43) A_121))->((ex (pname->Prop)) (fun (X_5:(pname->Prop))=> ((and ((member_pname_o X_5) A_121)) ((finite297249702name_o (collect_pname_o (fun (A_122:(pname->Prop))=> ((and ((member_pname_o A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False)))))))
% FOF formula (forall (F_43:((hoare_1167836817_state->Prop)->pname)) (A_121:((hoare_1167836817_state->Prop)->Prop)), (((finite1380128977tate_o A_121)->False)->((finite_finite_pname ((image_980295115_pname F_43) A_121))->((ex (hoare_1167836817_state->Prop)) (fun (X_5:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o X_5) A_121)) ((finite1380128977tate_o (collec269976083tate_o (fun (A_122:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_253_pigeonhole__infinite
% A new axiom: (forall (F_43:((hoare_1167836817_state->Prop)->pname)) (A_121:((hoare_1167836817_state->Prop)->Prop)), (((finite1380128977tate_o A_121)->False)->((finite_finite_pname ((image_980295115_pname F_43) A_121))->((ex (hoare_1167836817_state->Prop)) (fun (X_5:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o X_5) A_121)) ((finite1380128977tate_o (collec269976083tate_o (fun (A_122:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False)))))))
% FOF formula (forall (F_43:(hoare_1167836817_state->(pname->Prop))) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite297249702name_o ((image_2066861949name_o F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq (pname->Prop)) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_254_pigeonhole__infinite
% A new axiom: (forall (F_43:(hoare_1167836817_state->(pname->Prop))) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite297249702name_o ((image_2066861949name_o F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq (pname->Prop)) (F_43 A_122)) (F_43 X_5))))))->False)))))))
% FOF formula (forall (F_43:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite1380128977tate_o ((image_1745649338tate_o F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq (hoare_1167836817_state->Prop)) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_255_pigeonhole__infinite
% A new axiom: (forall (F_43:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite1380128977tate_o ((image_1745649338tate_o F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq (hoare_1167836817_state->Prop)) (F_43 A_122)) (F_43 X_5))))))->False)))))))
% FOF formula (forall (F_43:(pname->hoare_1167836817_state)) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite1084549118_state ((image_575578384_state F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->False))))))) of role axiom named fact_256_pigeonhole__infinite
% A new axiom: (forall (F_43:(pname->hoare_1167836817_state)) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite1084549118_state ((image_575578384_state F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->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_257_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_3:(hoare_1167836817_state->Prop)) (Procs_3:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_3) ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3))) ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) Procs_3))->((finite_finite_pname Procs_3)->((hoare_123228589_state G_3) ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3))))) of role axiom named fact_258_MGT__Body
% A new axiom: (forall (G_3:(hoare_1167836817_state->Prop)) (Procs_3:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_3) ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3))) ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) Procs_3))->((finite_finite_pname Procs_3)->((hoare_123228589_state G_3) ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3)))))
% FOF formula (forall (A_120:pname) (M_1:(pname->option_com)), (((member_pname A_120) (dom_pname_com M_1))->((ex com) (fun (B_90:com)=> (((eq option_com) (M_1 A_120)) (some_com B_90)))))) of role axiom named fact_259_domD
% A new axiom: (forall (A_120:pname) (M_1:(pname->option_com)), (((member_pname A_120) (dom_pname_com M_1))->((ex com) (fun (B_90:com)=> (((eq option_com) (M_1 A_120)) (some_com B_90))))))
% FOF formula (forall (X_84:pname), (((eq pname) (the_elem_pname ((insert_pname X_84) bot_bot_pname_o))) X_84)) of role axiom named fact_260_the__elem__eq
% A new axiom: (forall (X_84:pname), (((eq pname) (the_elem_pname ((insert_pname X_84) bot_bot_pname_o))) X_84))
% FOF formula (forall (X_84:hoare_1167836817_state), (((eq hoare_1167836817_state) (the_el323660082_state ((insert2134838167_state X_84) bot_bo70021908tate_o))) X_84)) of role axiom named fact_261_the__elem__eq
% A new axiom: (forall (X_84:hoare_1167836817_state), (((eq hoare_1167836817_state) (the_el323660082_state ((insert2134838167_state X_84) bot_bo70021908tate_o))) X_84))
% FOF formula (forall (F_42:(hoare_1167836817_state->pname)) (B_89:(pname->Prop)) (A_119:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_119)->((member_pname (F_42 X_5)) B_89)))->((ord_less_eq_pname_o ((image_8178176_pname F_42) A_119)) B_89))) of role axiom named fact_262_image__subsetI
% A new axiom: (forall (F_42:(hoare_1167836817_state->pname)) (B_89:(pname->Prop)) (A_119:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_119)->((member_pname (F_42 X_5)) B_89)))->((ord_less_eq_pname_o ((image_8178176_pname F_42) A_119)) B_89)))
% FOF formula (forall (F_42:(pname->hoare_1167836817_state)) (B_89:(hoare_1167836817_state->Prop)) (A_119:(pname->Prop)), ((forall (X_5:pname), (((member_pname X_5) A_119)->((member2058392318_state (F_42 X_5)) B_89)))->((ord_le827224136tate_o ((image_575578384_state F_42) A_119)) B_89))) of role axiom named fact_263_image__subsetI
% A new axiom: (forall (F_42:(pname->hoare_1167836817_state)) (B_89:(hoare_1167836817_state->Prop)) (A_119:(pname->Prop)), ((forall (X_5:pname), (((member_pname X_5) A_119)->((member2058392318_state (F_42 X_5)) B_89)))->((ord_le827224136tate_o ((image_575578384_state F_42) A_119)) B_89)))
% FOF formula (forall (X_83:(pname->Prop)), ((ord_less_eq_pname_o X_83) X_83)) of role axiom named fact_264_order__refl
% A new axiom: (forall (X_83:(pname->Prop)), ((ord_less_eq_pname_o X_83) X_83))
% FOF formula (forall (X_83:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_83) X_83)) of role axiom named fact_265_order__refl
% A new axiom: (forall (X_83:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_83) X_83))
% FOF formula (forall (A_118:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_118) bot_bot_pname_o))) ((ex pname) (fun (X_5:pname)=> ((ex (pname->Prop)) (fun (B_43:(pname->Prop))=> ((and (((eq (pname->Prop)) A_118) ((insert_pname X_5) B_43))) (((member_pname X_5) B_43)->False)))))))) of role axiom named fact_266_nonempty__iff
% A new axiom: (forall (A_118:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_118) bot_bot_pname_o))) ((ex pname) (fun (X_5:pname)=> ((ex (pname->Prop)) (fun (B_43:(pname->Prop))=> ((and (((eq (pname->Prop)) A_118) ((insert_pname X_5) B_43))) (((member_pname X_5) B_43)->False))))))))
% FOF formula (forall (A_118:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_118) bot_bo70021908tate_o))) ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (B_43:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_118) ((insert2134838167_state X_5) B_43))) (((member2058392318_state X_5) B_43)->False)))))))) of role axiom named fact_267_nonempty__iff
% A new axiom: (forall (A_118:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_118) bot_bo70021908tate_o))) ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (B_43:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_118) ((insert2134838167_state X_5) B_43))) (((member2058392318_state X_5) B_43)->False))))))))
% FOF formula (forall (X_82:com), (((eq com) (the_com (some_com X_82))) X_82)) of role axiom named fact_268_the_Osimps
% A new axiom: (forall (X_82:com), (((eq com) (the_com (some_com X_82))) X_82))
% FOF formula (forall (G_27:(hoare_1167836817_state->Prop)) (P_32:(state->(state->Prop))) (Pn_4:pname) (Q_22:(state->(state->Prop))), (((hoare_123228589_state G_27) ((insert2134838167_state (((hoare_908217195_state P_32) (the_com (body Pn_4))) Q_22)) bot_bo70021908tate_o))->((hoare_123228589_state G_27) ((insert2134838167_state (((hoare_908217195_state P_32) (body_1 Pn_4)) Q_22)) bot_bo70021908tate_o)))) of role axiom named fact_269_weak__Body
% A new axiom: (forall (G_27:(hoare_1167836817_state->Prop)) (P_32:(state->(state->Prop))) (Pn_4:pname) (Q_22:(state->(state->Prop))), (((hoare_123228589_state G_27) ((insert2134838167_state (((hoare_908217195_state P_32) (the_com (body Pn_4))) Q_22)) bot_bo70021908tate_o))->((hoare_123228589_state G_27) ((insert2134838167_state (((hoare_908217195_state P_32) (body_1 Pn_4)) Q_22)) bot_bo70021908tate_o))))
% FOF formula (forall (A_117:(pname->Prop)) (C_46:pname) (B_88:(pname->Prop)), (((((member_pname C_46) B_88)->False)->((member_pname C_46) A_117))->((member_pname C_46) ((semila1780557381name_o A_117) B_88)))) of role axiom named fact_270_UnCI
% A new axiom: (forall (A_117:(pname->Prop)) (C_46:pname) (B_88:(pname->Prop)), (((((member_pname C_46) B_88)->False)->((member_pname C_46) A_117))->((member_pname C_46) ((semila1780557381name_o A_117) B_88))))
% FOF formula (forall (A_117:(hoare_1167836817_state->Prop)) (C_46:hoare_1167836817_state) (B_88:(hoare_1167836817_state->Prop)), (((((member2058392318_state C_46) B_88)->False)->((member2058392318_state C_46) A_117))->((member2058392318_state C_46) ((semila1172322802tate_o A_117) B_88)))) of role axiom named fact_271_UnCI
% A new axiom: (forall (A_117:(hoare_1167836817_state->Prop)) (C_46:hoare_1167836817_state) (B_88:(hoare_1167836817_state->Prop)), (((((member2058392318_state C_46) B_88)->False)->((member2058392318_state C_46) A_117))->((member2058392318_state C_46) ((semila1172322802tate_o A_117) B_88))))
% FOF formula (forall (C_45:pname) (A_116:(pname->Prop)) (B_87:(pname->Prop)), (((member_pname C_45) ((semila1780557381name_o A_116) B_87))->((((member_pname C_45) A_116)->False)->((member_pname C_45) B_87)))) of role axiom named fact_272_UnE
% A new axiom: (forall (C_45:pname) (A_116:(pname->Prop)) (B_87:(pname->Prop)), (((member_pname C_45) ((semila1780557381name_o A_116) B_87))->((((member_pname C_45) A_116)->False)->((member_pname C_45) B_87))))
% FOF formula (forall (C_45:hoare_1167836817_state) (A_116:(hoare_1167836817_state->Prop)) (B_87:(hoare_1167836817_state->Prop)), (((member2058392318_state C_45) ((semila1172322802tate_o A_116) B_87))->((((member2058392318_state C_45) A_116)->False)->((member2058392318_state C_45) B_87)))) of role axiom named fact_273_UnE
% A new axiom: (forall (C_45:hoare_1167836817_state) (A_116:(hoare_1167836817_state->Prop)) (B_87:(hoare_1167836817_state->Prop)), (((member2058392318_state C_45) ((semila1172322802tate_o A_116) B_87))->((((member2058392318_state C_45) A_116)->False)->((member2058392318_state C_45) B_87))))
% FOF formula (forall (P_31:(pname->Prop)) (Q_21:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila1780557381name_o (collect_pname P_31)) (collect_pname Q_21)))) of role axiom named fact_274_Collect__disj__eq
% A new axiom: (forall (P_31:(pname->Prop)) (Q_21:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila1780557381name_o (collect_pname P_31)) (collect_pname Q_21))))
% FOF formula (forall (P_31:((pname->Prop)->Prop)) (Q_21:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila181081674me_o_o (collect_pname_o P_31)) (collect_pname_o Q_21)))) of role axiom named fact_275_Collect__disj__eq
% A new axiom: (forall (P_31:((pname->Prop)->Prop)) (Q_21:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila181081674me_o_o (collect_pname_o P_31)) (collect_pname_o Q_21))))
% FOF formula (forall (P_31:((hoare_1167836817_state->Prop)->Prop)) (Q_21:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila866907787te_o_o (collec269976083tate_o P_31)) (collec269976083tate_o Q_21)))) of role axiom named fact_276_Collect__disj__eq
% A new axiom: (forall (P_31:((hoare_1167836817_state->Prop)->Prop)) (Q_21:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila866907787te_o_o (collec269976083tate_o P_31)) (collec269976083tate_o Q_21))))
% FOF formula (forall (P_31:(hoare_1167836817_state->Prop)) (Q_21:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila1172322802tate_o (collec1027672124_state P_31)) (collec1027672124_state Q_21)))) of role axiom named fact_277_Collect__disj__eq
% A new axiom: (forall (P_31:(hoare_1167836817_state->Prop)) (Q_21:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila1172322802tate_o (collec1027672124_state P_31)) (collec1027672124_state Q_21))))
% 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_1167836817_state) (((hoare_908217195_state Fun1_2) Com_4) Fun2_2)) (((hoare_908217195_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_278_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_1167836817_state) (((hoare_908217195_state Fun1_2) Com_4) Fun2_2)) (((hoare_908217195_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_115:(pname->Prop)) (C_44:pname) (B_86:(pname->Prop)), (((member_pname C_44) B_86)->((member_pname C_44) ((semila1780557381name_o A_115) B_86)))) of role axiom named fact_279_UnI2
% A new axiom: (forall (A_115:(pname->Prop)) (C_44:pname) (B_86:(pname->Prop)), (((member_pname C_44) B_86)->((member_pname C_44) ((semila1780557381name_o A_115) B_86))))
% FOF formula (forall (A_115:(hoare_1167836817_state->Prop)) (C_44:hoare_1167836817_state) (B_86:(hoare_1167836817_state->Prop)), (((member2058392318_state C_44) B_86)->((member2058392318_state C_44) ((semila1172322802tate_o A_115) B_86)))) of role axiom named fact_280_UnI2
% A new axiom: (forall (A_115:(hoare_1167836817_state->Prop)) (C_44:hoare_1167836817_state) (B_86:(hoare_1167836817_state->Prop)), (((member2058392318_state C_44) B_86)->((member2058392318_state C_44) ((semila1172322802tate_o A_115) B_86))))
% FOF formula (forall (B_85:(pname->Prop)) (C_43:pname) (A_114:(pname->Prop)), (((member_pname C_43) A_114)->((member_pname C_43) ((semila1780557381name_o A_114) B_85)))) of role axiom named fact_281_UnI1
% A new axiom: (forall (B_85:(pname->Prop)) (C_43:pname) (A_114:(pname->Prop)), (((member_pname C_43) A_114)->((member_pname C_43) ((semila1780557381name_o A_114) B_85))))
% FOF formula (forall (B_85:(hoare_1167836817_state->Prop)) (C_43:hoare_1167836817_state) (A_114:(hoare_1167836817_state->Prop)), (((member2058392318_state C_43) A_114)->((member2058392318_state C_43) ((semila1172322802tate_o A_114) B_85)))) of role axiom named fact_282_UnI1
% A new axiom: (forall (B_85:(hoare_1167836817_state->Prop)) (C_43:hoare_1167836817_state) (A_114:(hoare_1167836817_state->Prop)), (((member2058392318_state C_43) A_114)->((member2058392318_state C_43) ((semila1172322802tate_o A_114) B_85))))
% FOF formula (forall (P_30:(hoare_1167836817_state->Prop)) (A_113:(hoare_1167836817_state->Prop)) (B_84:(hoare_1167836817_state->Prop)), ((iff (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) ((semila1172322802tate_o A_113) B_84))->(P_30 X_5)))) ((and (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_113)->(P_30 X_5)))) (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) B_84)->(P_30 X_5)))))) of role axiom named fact_283_ball__Un
% A new axiom: (forall (P_30:(hoare_1167836817_state->Prop)) (A_113:(hoare_1167836817_state->Prop)) (B_84:(hoare_1167836817_state->Prop)), ((iff (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) ((semila1172322802tate_o A_113) B_84))->(P_30 X_5)))) ((and (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_113)->(P_30 X_5)))) (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) B_84)->(P_30 X_5))))))
% FOF formula (forall (P_29:(hoare_1167836817_state->Prop)) (A_112:(hoare_1167836817_state->Prop)) (B_83:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) ((semila1172322802tate_o A_112) B_83))) (P_29 X_5))))) ((or ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_112)) (P_29 X_5))))) ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) B_83)) (P_29 X_5))))))) of role axiom named fact_284_bex__Un
% A new axiom: (forall (P_29:(hoare_1167836817_state->Prop)) (A_112:(hoare_1167836817_state->Prop)) (B_83:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) ((semila1172322802tate_o A_112) B_83))) (P_29 X_5))))) ((or ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_112)) (P_29 X_5))))) ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) B_83)) (P_29 X_5)))))))
% FOF formula (forall (A_111:(hoare_1167836817_state->Prop)) (B_82:(hoare_1167836817_state->Prop)) (C_42:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_111) B_82)) C_42)) ((semila1172322802tate_o A_111) ((semila1172322802tate_o B_82) C_42)))) of role axiom named fact_285_Un__assoc
% A new axiom: (forall (A_111:(hoare_1167836817_state->Prop)) (B_82:(hoare_1167836817_state->Prop)) (C_42:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_111) B_82)) C_42)) ((semila1172322802tate_o A_111) ((semila1172322802tate_o B_82) C_42))))
% FOF formula (forall (C_41:pname) (A_110:(pname->Prop)) (B_81:(pname->Prop)), ((iff ((member_pname C_41) ((semila1780557381name_o A_110) B_81))) ((or ((member_pname C_41) A_110)) ((member_pname C_41) B_81)))) of role axiom named fact_286_Un__iff
% A new axiom: (forall (C_41:pname) (A_110:(pname->Prop)) (B_81:(pname->Prop)), ((iff ((member_pname C_41) ((semila1780557381name_o A_110) B_81))) ((or ((member_pname C_41) A_110)) ((member_pname C_41) B_81))))
% FOF formula (forall (C_41:hoare_1167836817_state) (A_110:(hoare_1167836817_state->Prop)) (B_81:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_41) ((semila1172322802tate_o A_110) B_81))) ((or ((member2058392318_state C_41) A_110)) ((member2058392318_state C_41) B_81)))) of role axiom named fact_287_Un__iff
% A new axiom: (forall (C_41:hoare_1167836817_state) (A_110:(hoare_1167836817_state->Prop)) (B_81:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_41) ((semila1172322802tate_o A_110) B_81))) ((or ((member2058392318_state C_41) A_110)) ((member2058392318_state C_41) B_81))))
% FOF formula (forall (A_109:(hoare_1167836817_state->Prop)) (B_80:(hoare_1167836817_state->Prop)) (C_40:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_109) ((semila1172322802tate_o B_80) C_40))) ((semila1172322802tate_o B_80) ((semila1172322802tate_o A_109) C_40)))) of role axiom named fact_288_Un__left__commute
% A new axiom: (forall (A_109:(hoare_1167836817_state->Prop)) (B_80:(hoare_1167836817_state->Prop)) (C_40:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_109) ((semila1172322802tate_o B_80) C_40))) ((semila1172322802tate_o B_80) ((semila1172322802tate_o A_109) C_40))))
% FOF formula (forall (A_108:(hoare_1167836817_state->Prop)) (B_79:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_108) ((semila1172322802tate_o A_108) B_79))) ((semila1172322802tate_o A_108) B_79))) of role axiom named fact_289_Un__left__absorb
% A new axiom: (forall (A_108:(hoare_1167836817_state->Prop)) (B_79:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_108) ((semila1172322802tate_o A_108) B_79))) ((semila1172322802tate_o A_108) B_79)))
% FOF formula (forall (A_107:(hoare_1167836817_state->Prop)) (B_78:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_107) B_78)) ((semila1172322802tate_o B_78) A_107))) of role axiom named fact_290_Un__commute
% A new axiom: (forall (A_107:(hoare_1167836817_state->Prop)) (B_78:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_107) B_78)) ((semila1172322802tate_o B_78) A_107)))
% FOF formula (forall (A_106:(pname->Prop)) (B_77:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_106) B_77)) (collect_pname (fun (X_5:pname)=> ((or ((member_pname X_5) A_106)) ((member_pname X_5) B_77)))))) of role axiom named fact_291_Un__def
% A new axiom: (forall (A_106:(pname->Prop)) (B_77:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_106) B_77)) (collect_pname (fun (X_5:pname)=> ((or ((member_pname X_5) A_106)) ((member_pname X_5) B_77))))))
% FOF formula (forall (A_106:((pname->Prop)->Prop)) (B_77:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila181081674me_o_o A_106) B_77)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((or ((member_pname_o X_5) A_106)) ((member_pname_o X_5) B_77)))))) of role axiom named fact_292_Un__def
% A new axiom: (forall (A_106:((pname->Prop)->Prop)) (B_77:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila181081674me_o_o A_106) B_77)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((or ((member_pname_o X_5) A_106)) ((member_pname_o X_5) B_77))))))
% FOF formula (forall (A_106:((hoare_1167836817_state->Prop)->Prop)) (B_77:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila866907787te_o_o A_106) B_77)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or ((member864234961tate_o X_5) A_106)) ((member864234961tate_o X_5) B_77)))))) of role axiom named fact_293_Un__def
% A new axiom: (forall (A_106:((hoare_1167836817_state->Prop)->Prop)) (B_77:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila866907787te_o_o A_106) B_77)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or ((member864234961tate_o X_5) A_106)) ((member864234961tate_o X_5) B_77))))))
% FOF formula (forall (A_106:(hoare_1167836817_state->Prop)) (B_77:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_106) B_77)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or ((member2058392318_state X_5) A_106)) ((member2058392318_state X_5) B_77)))))) of role axiom named fact_294_Un__def
% A new axiom: (forall (A_106:(hoare_1167836817_state->Prop)) (B_77:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_106) B_77)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or ((member2058392318_state X_5) A_106)) ((member2058392318_state X_5) B_77))))))
% FOF formula (forall (A_105:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_105) A_105)) A_105)) of role axiom named fact_295_Un__absorb
% A new axiom: (forall (A_105:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_105) A_105)) A_105))
% FOF formula (forall (A_104:(pname->Prop)) (B_76:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_104) B_76)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_104) bot_bot_pname_o)) (((eq (pname->Prop)) B_76) bot_bot_pname_o)))) of role axiom named fact_296_Un__empty
% A new axiom: (forall (A_104:(pname->Prop)) (B_76:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_104) B_76)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_104) bot_bot_pname_o)) (((eq (pname->Prop)) B_76) bot_bot_pname_o))))
% FOF formula (forall (A_104:(hoare_1167836817_state->Prop)) (B_76:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_104) B_76)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) A_104) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) B_76) bot_bo70021908tate_o)))) of role axiom named fact_297_Un__empty
% A new axiom: (forall (A_104:(hoare_1167836817_state->Prop)) (B_76:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_104) B_76)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) A_104) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) B_76) bot_bo70021908tate_o))))
% FOF formula (forall (A_103:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_103) bot_bot_pname_o)) A_103)) of role axiom named fact_298_Un__empty__right
% A new axiom: (forall (A_103:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_103) bot_bot_pname_o)) A_103))
% FOF formula (forall (A_103:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_103) bot_bo70021908tate_o)) A_103)) of role axiom named fact_299_Un__empty__right
% A new axiom: (forall (A_103:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_103) bot_bo70021908tate_o)) A_103))
% FOF formula (forall (B_75:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_75)) B_75)) of role axiom named fact_300_Un__empty__left
% A new axiom: (forall (B_75:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_75)) B_75))
% FOF formula (forall (B_75:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) B_75)) B_75)) of role axiom named fact_301_Un__empty__left
% A new axiom: (forall (B_75:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) B_75)) B_75))
% FOF formula (forall (G_26:((pname->Prop)->Prop)) (F_41:((pname->Prop)->Prop)), ((finite297249702name_o F_41)->((finite297249702name_o G_26)->(finite297249702name_o ((semila181081674me_o_o F_41) G_26))))) of role axiom named fact_302_finite__UnI
% A new axiom: (forall (G_26:((pname->Prop)->Prop)) (F_41:((pname->Prop)->Prop)), ((finite297249702name_o F_41)->((finite297249702name_o G_26)->(finite297249702name_o ((semila181081674me_o_o F_41) G_26)))))
% FOF formula (forall (G_26:((hoare_1167836817_state->Prop)->Prop)) (F_41:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_41)->((finite1380128977tate_o G_26)->(finite1380128977tate_o ((semila866907787te_o_o F_41) G_26))))) of role axiom named fact_303_finite__UnI
% A new axiom: (forall (G_26:((hoare_1167836817_state->Prop)->Prop)) (F_41:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_41)->((finite1380128977tate_o G_26)->(finite1380128977tate_o ((semila866907787te_o_o F_41) G_26)))))
% FOF formula (forall (G_26:(pname->Prop)) (F_41:(pname->Prop)), ((finite_finite_pname F_41)->((finite_finite_pname G_26)->(finite_finite_pname ((semila1780557381name_o F_41) G_26))))) of role axiom named fact_304_finite__UnI
% A new axiom: (forall (G_26:(pname->Prop)) (F_41:(pname->Prop)), ((finite_finite_pname F_41)->((finite_finite_pname G_26)->(finite_finite_pname ((semila1780557381name_o F_41) G_26)))))
% FOF formula (forall (G_26:(hoare_1167836817_state->Prop)) (F_41:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_41)->((finite1084549118_state G_26)->(finite1084549118_state ((semila1172322802tate_o F_41) G_26))))) of role axiom named fact_305_finite__UnI
% A new axiom: (forall (G_26:(hoare_1167836817_state->Prop)) (F_41:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_41)->((finite1084549118_state G_26)->(finite1084549118_state ((semila1172322802tate_o F_41) G_26)))))
% FOF formula (forall (F_40:((pname->Prop)->Prop)) (G_25:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((semila181081674me_o_o F_40) G_25))) ((and (finite297249702name_o F_40)) (finite297249702name_o G_25)))) of role axiom named fact_306_finite__Un
% A new axiom: (forall (F_40:((pname->Prop)->Prop)) (G_25:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((semila181081674me_o_o F_40) G_25))) ((and (finite297249702name_o F_40)) (finite297249702name_o G_25))))
% FOF formula (forall (F_40:((hoare_1167836817_state->Prop)->Prop)) (G_25:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o ((semila866907787te_o_o F_40) G_25))) ((and (finite1380128977tate_o F_40)) (finite1380128977tate_o G_25)))) of role axiom named fact_307_finite__Un
% A new axiom: (forall (F_40:((hoare_1167836817_state->Prop)->Prop)) (G_25:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o ((semila866907787te_o_o F_40) G_25))) ((and (finite1380128977tate_o F_40)) (finite1380128977tate_o G_25))))
% FOF formula (forall (F_40:(pname->Prop)) (G_25:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_40) G_25))) ((and (finite_finite_pname F_40)) (finite_finite_pname G_25)))) of role axiom named fact_308_finite__Un
% A new axiom: (forall (F_40:(pname->Prop)) (G_25:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_40) G_25))) ((and (finite_finite_pname F_40)) (finite_finite_pname G_25))))
% FOF formula (forall (F_40:(hoare_1167836817_state->Prop)) (G_25:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((semila1172322802tate_o F_40) G_25))) ((and (finite1084549118_state F_40)) (finite1084549118_state G_25)))) of role axiom named fact_309_finite__Un
% A new axiom: (forall (F_40:(hoare_1167836817_state->Prop)) (G_25:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((semila1172322802tate_o F_40) G_25))) ((and (finite1084549118_state F_40)) (finite1084549118_state G_25))))
% FOF formula (forall (A_102:pname) (B_74:(pname->Prop)) (C_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_102) B_74)) C_39)) ((insert_pname A_102) ((semila1780557381name_o B_74) C_39)))) of role axiom named fact_310_Un__insert__left
% A new axiom: (forall (A_102:pname) (B_74:(pname->Prop)) (C_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_102) B_74)) C_39)) ((insert_pname A_102) ((semila1780557381name_o B_74) C_39))))
% FOF formula (forall (A_102:hoare_1167836817_state) (B_74:(hoare_1167836817_state->Prop)) (C_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((insert2134838167_state A_102) B_74)) C_39)) ((insert2134838167_state A_102) ((semila1172322802tate_o B_74) C_39)))) of role axiom named fact_311_Un__insert__left
% A new axiom: (forall (A_102:hoare_1167836817_state) (B_74:(hoare_1167836817_state->Prop)) (C_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((insert2134838167_state A_102) B_74)) C_39)) ((insert2134838167_state A_102) ((semila1172322802tate_o B_74) C_39))))
% FOF formula (forall (A_101:(pname->Prop)) (A_100:pname) (B_73:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_101) ((insert_pname A_100) B_73))) ((insert_pname A_100) ((semila1780557381name_o A_101) B_73)))) of role axiom named fact_312_Un__insert__right
% A new axiom: (forall (A_101:(pname->Prop)) (A_100:pname) (B_73:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_101) ((insert_pname A_100) B_73))) ((insert_pname A_100) ((semila1780557381name_o A_101) B_73))))
% FOF formula (forall (A_101:(hoare_1167836817_state->Prop)) (A_100:hoare_1167836817_state) (B_73:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_101) ((insert2134838167_state A_100) B_73))) ((insert2134838167_state A_100) ((semila1172322802tate_o A_101) B_73)))) of role axiom named fact_313_Un__insert__right
% A new axiom: (forall (A_101:(hoare_1167836817_state->Prop)) (A_100:hoare_1167836817_state) (B_73:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_101) ((insert2134838167_state A_100) B_73))) ((insert2134838167_state A_100) ((semila1172322802tate_o A_101) B_73))))
% FOF formula (forall (B_72:(pname->Prop)) (D_4:(pname->Prop)) (A_99:(pname->Prop)) (C_38:(pname->Prop)), (((ord_less_eq_pname_o A_99) C_38)->(((ord_less_eq_pname_o B_72) D_4)->((ord_less_eq_pname_o ((semila1780557381name_o A_99) B_72)) ((semila1780557381name_o C_38) D_4))))) of role axiom named fact_314_Un__mono
% A new axiom: (forall (B_72:(pname->Prop)) (D_4:(pname->Prop)) (A_99:(pname->Prop)) (C_38:(pname->Prop)), (((ord_less_eq_pname_o A_99) C_38)->(((ord_less_eq_pname_o B_72) D_4)->((ord_less_eq_pname_o ((semila1780557381name_o A_99) B_72)) ((semila1780557381name_o C_38) D_4)))))
% FOF formula (forall (B_72:(hoare_1167836817_state->Prop)) (D_4:(hoare_1167836817_state->Prop)) (A_99:(hoare_1167836817_state->Prop)) (C_38:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_99) C_38)->(((ord_le827224136tate_o B_72) D_4)->((ord_le827224136tate_o ((semila1172322802tate_o A_99) B_72)) ((semila1172322802tate_o C_38) D_4))))) of role axiom named fact_315_Un__mono
% A new axiom: (forall (B_72:(hoare_1167836817_state->Prop)) (D_4:(hoare_1167836817_state->Prop)) (A_99:(hoare_1167836817_state->Prop)) (C_38:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_99) C_38)->(((ord_le827224136tate_o B_72) D_4)->((ord_le827224136tate_o ((semila1172322802tate_o A_99) B_72)) ((semila1172322802tate_o C_38) D_4)))))
% FOF formula (forall (B_71:(pname->Prop)) (A_98:(pname->Prop)) (C_37:(pname->Prop)), (((ord_less_eq_pname_o A_98) C_37)->(((ord_less_eq_pname_o B_71) C_37)->((ord_less_eq_pname_o ((semila1780557381name_o A_98) B_71)) C_37)))) of role axiom named fact_316_Un__least
% A new axiom: (forall (B_71:(pname->Prop)) (A_98:(pname->Prop)) (C_37:(pname->Prop)), (((ord_less_eq_pname_o A_98) C_37)->(((ord_less_eq_pname_o B_71) C_37)->((ord_less_eq_pname_o ((semila1780557381name_o A_98) B_71)) C_37))))
% FOF formula (forall (B_71:(hoare_1167836817_state->Prop)) (A_98:(hoare_1167836817_state->Prop)) (C_37:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_98) C_37)->(((ord_le827224136tate_o B_71) C_37)->((ord_le827224136tate_o ((semila1172322802tate_o A_98) B_71)) C_37)))) of role axiom named fact_317_Un__least
% A new axiom: (forall (B_71:(hoare_1167836817_state->Prop)) (A_98:(hoare_1167836817_state->Prop)) (C_37:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_98) C_37)->(((ord_le827224136tate_o B_71) C_37)->((ord_le827224136tate_o ((semila1172322802tate_o A_98) B_71)) C_37))))
% FOF formula (forall (B_70:(pname->Prop)) (A_97:(pname->Prop)), (((ord_less_eq_pname_o B_70) A_97)->(((eq (pname->Prop)) ((semila1780557381name_o A_97) B_70)) A_97))) of role axiom named fact_318_Un__absorb2
% A new axiom: (forall (B_70:(pname->Prop)) (A_97:(pname->Prop)), (((ord_less_eq_pname_o B_70) A_97)->(((eq (pname->Prop)) ((semila1780557381name_o A_97) B_70)) A_97)))
% FOF formula (forall (B_70:(hoare_1167836817_state->Prop)) (A_97:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_70) A_97)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_97) B_70)) A_97))) of role axiom named fact_319_Un__absorb2
% A new axiom: (forall (B_70:(hoare_1167836817_state->Prop)) (A_97:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_70) A_97)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_97) B_70)) A_97)))
% FOF formula (forall (A_96:(pname->Prop)) (B_69:(pname->Prop)), (((ord_less_eq_pname_o A_96) B_69)->(((eq (pname->Prop)) ((semila1780557381name_o A_96) B_69)) B_69))) of role axiom named fact_320_Un__absorb1
% A new axiom: (forall (A_96:(pname->Prop)) (B_69:(pname->Prop)), (((ord_less_eq_pname_o A_96) B_69)->(((eq (pname->Prop)) ((semila1780557381name_o A_96) B_69)) B_69)))
% FOF formula (forall (A_96:(hoare_1167836817_state->Prop)) (B_69:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_96) B_69)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_96) B_69)) B_69))) of role axiom named fact_321_Un__absorb1
% A new axiom: (forall (A_96:(hoare_1167836817_state->Prop)) (B_69:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_96) B_69)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_96) B_69)) B_69)))
% FOF formula (forall (A_95:(pname->Prop)) (B_68:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_95) B_68)) (((eq (pname->Prop)) ((semila1780557381name_o A_95) B_68)) B_68))) of role axiom named fact_322_subset__Un__eq
% A new axiom: (forall (A_95:(pname->Prop)) (B_68:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_95) B_68)) (((eq (pname->Prop)) ((semila1780557381name_o A_95) B_68)) B_68)))
% FOF formula (forall (A_95:(hoare_1167836817_state->Prop)) (B_68:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_95) B_68)) (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_95) B_68)) B_68))) of role axiom named fact_323_subset__Un__eq
% A new axiom: (forall (A_95:(hoare_1167836817_state->Prop)) (B_68:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_95) B_68)) (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_95) B_68)) B_68)))
% FOF formula (forall (B_67:(pname->Prop)) (A_94:(pname->Prop)), ((ord_less_eq_pname_o B_67) ((semila1780557381name_o A_94) B_67))) of role axiom named fact_324_Un__upper2
% A new axiom: (forall (B_67:(pname->Prop)) (A_94:(pname->Prop)), ((ord_less_eq_pname_o B_67) ((semila1780557381name_o A_94) B_67)))
% FOF formula (forall (B_67:(hoare_1167836817_state->Prop)) (A_94:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o B_67) ((semila1172322802tate_o A_94) B_67))) of role axiom named fact_325_Un__upper2
% A new axiom: (forall (B_67:(hoare_1167836817_state->Prop)) (A_94:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o B_67) ((semila1172322802tate_o A_94) B_67)))
% FOF formula (forall (A_93:(pname->Prop)) (B_66:(pname->Prop)), ((ord_less_eq_pname_o A_93) ((semila1780557381name_o A_93) B_66))) of role axiom named fact_326_Un__upper1
% A new axiom: (forall (A_93:(pname->Prop)) (B_66:(pname->Prop)), ((ord_less_eq_pname_o A_93) ((semila1780557381name_o A_93) B_66)))
% FOF formula (forall (A_93:(hoare_1167836817_state->Prop)) (B_66:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o A_93) ((semila1172322802tate_o A_93) B_66))) of role axiom named fact_327_Un__upper1
% A new axiom: (forall (A_93:(hoare_1167836817_state->Prop)) (B_66:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o A_93) ((semila1172322802tate_o A_93) B_66)))
% FOF formula (forall (F_39:(pname->hoare_1167836817_state)) (A_92:(pname->Prop)) (B_65:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_39) ((semila1780557381name_o A_92) B_65))) ((semila1172322802tate_o ((image_575578384_state F_39) A_92)) ((image_575578384_state F_39) B_65)))) of role axiom named fact_328_image__Un
% A new axiom: (forall (F_39:(pname->hoare_1167836817_state)) (A_92:(pname->Prop)) (B_65:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_39) ((semila1780557381name_o A_92) B_65))) ((semila1172322802tate_o ((image_575578384_state F_39) A_92)) ((image_575578384_state F_39) B_65))))
% FOF formula (forall (A_91:pname) (B_64:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_91) B_64)) ((semila1780557381name_o (collect_pname (fun (X_5:pname)=> (((eq pname) X_5) A_91)))) B_64))) of role axiom named fact_329_insert__def
% A new axiom: (forall (A_91:pname) (B_64:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_91) B_64)) ((semila1780557381name_o (collect_pname (fun (X_5:pname)=> (((eq pname) X_5) A_91)))) B_64)))
% FOF formula (forall (A_91:hoare_1167836817_state) (B_64:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_91) B_64)) ((semila1172322802tate_o (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X_5) A_91)))) B_64))) of role axiom named fact_330_insert__def
% A new axiom: (forall (A_91:hoare_1167836817_state) (B_64:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_91) B_64)) ((semila1172322802tate_o (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X_5) A_91)))) B_64)))
% FOF formula (forall (A_91:(pname->Prop)) (B_64:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_91) B_64)) ((semila181081674me_o_o (collect_pname_o (fun (X_5:(pname->Prop))=> (((eq (pname->Prop)) X_5) A_91)))) B_64))) of role axiom named fact_331_insert__def
% A new axiom: (forall (A_91:(pname->Prop)) (B_64:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_91) B_64)) ((semila181081674me_o_o (collect_pname_o (fun (X_5:(pname->Prop))=> (((eq (pname->Prop)) X_5) A_91)))) B_64)))
% FOF formula (forall (A_91:(hoare_1167836817_state->Prop)) (B_64:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o A_91) B_64)) ((semila866907787te_o_o (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> (((eq (hoare_1167836817_state->Prop)) X_5) A_91)))) B_64))) of role axiom named fact_332_insert__def
% A new axiom: (forall (A_91:(hoare_1167836817_state->Prop)) (B_64:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o A_91) B_64)) ((semila866907787te_o_o (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> (((eq (hoare_1167836817_state->Prop)) X_5) A_91)))) B_64)))
% FOF formula (forall (A_90:pname) (A_89:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_90) A_89)) ((semila1780557381name_o ((insert_pname A_90) bot_bot_pname_o)) A_89))) of role axiom named fact_333_insert__is__Un
% A new axiom: (forall (A_90:pname) (A_89:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_90) A_89)) ((semila1780557381name_o ((insert_pname A_90) bot_bot_pname_o)) A_89)))
% FOF formula (forall (A_90:hoare_1167836817_state) (A_89:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_90) A_89)) ((semila1172322802tate_o ((insert2134838167_state A_90) bot_bo70021908tate_o)) A_89))) of role axiom named fact_334_insert__is__Un
% A new axiom: (forall (A_90:hoare_1167836817_state) (A_89:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_90) A_89)) ((semila1172322802tate_o ((insert2134838167_state A_90) bot_bo70021908tate_o)) A_89)))
% FOF formula (forall (G_24:(hoare_1167836817_state->Prop)) (P_28:(pname->(state->(state->Prop)))) (Q_20:(pname->(state->(state->Prop)))) (Procs_2:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_24) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_28 P_24)) (body_1 P_24)) (Q_20 P_24)))) Procs_2))) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_28 P_24)) (the_com (body P_24))) (Q_20 P_24)))) Procs_2))->((hoare_123228589_state G_24) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_28 P_24)) (body_1 P_24)) (Q_20 P_24)))) Procs_2)))) of role axiom named fact_335_hoare__derivs_OBody
% A new axiom: (forall (G_24:(hoare_1167836817_state->Prop)) (P_28:(pname->(state->(state->Prop)))) (Q_20:(pname->(state->(state->Prop)))) (Procs_2:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_24) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_28 P_24)) (body_1 P_24)) (Q_20 P_24)))) Procs_2))) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_28 P_24)) (the_com (body P_24))) (Q_20 P_24)))) Procs_2))->((hoare_123228589_state G_24) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_28 P_24)) (body_1 P_24)) (Q_20 P_24)))) Procs_2))))
% FOF formula (forall (Z_20:(pname->Prop)) (Y_46:(pname->Prop)) (X_81:(pname->Prop)), (((ord_less_eq_pname_o Y_46) X_81)->(((ord_less_eq_pname_o Z_20) Y_46)->((ord_less_eq_pname_o Z_20) X_81)))) of role axiom named fact_336_xt1_I6_J
% A new axiom: (forall (Z_20:(pname->Prop)) (Y_46:(pname->Prop)) (X_81:(pname->Prop)), (((ord_less_eq_pname_o Y_46) X_81)->(((ord_less_eq_pname_o Z_20) Y_46)->((ord_less_eq_pname_o Z_20) X_81))))
% FOF formula (forall (Z_20:(hoare_1167836817_state->Prop)) (Y_46:(hoare_1167836817_state->Prop)) (X_81:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_46) X_81)->(((ord_le827224136tate_o Z_20) Y_46)->((ord_le827224136tate_o Z_20) X_81)))) of role axiom named fact_337_xt1_I6_J
% A new axiom: (forall (Z_20:(hoare_1167836817_state->Prop)) (Y_46:(hoare_1167836817_state->Prop)) (X_81:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_46) X_81)->(((ord_le827224136tate_o Z_20) Y_46)->((ord_le827224136tate_o Z_20) X_81))))
% FOF formula (forall (Y_45:(pname->Prop)) (X_80:(pname->Prop)), (((ord_less_eq_pname_o Y_45) X_80)->(((ord_less_eq_pname_o X_80) Y_45)->(((eq (pname->Prop)) X_80) Y_45)))) of role axiom named fact_338_xt1_I5_J
% A new axiom: (forall (Y_45:(pname->Prop)) (X_80:(pname->Prop)), (((ord_less_eq_pname_o Y_45) X_80)->(((ord_less_eq_pname_o X_80) Y_45)->(((eq (pname->Prop)) X_80) Y_45))))
% FOF formula (forall (Y_45:(hoare_1167836817_state->Prop)) (X_80:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_45) X_80)->(((ord_le827224136tate_o X_80) Y_45)->(((eq (hoare_1167836817_state->Prop)) X_80) Y_45)))) of role axiom named fact_339_xt1_I5_J
% A new axiom: (forall (Y_45:(hoare_1167836817_state->Prop)) (X_80:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_45) X_80)->(((ord_le827224136tate_o X_80) Y_45)->(((eq (hoare_1167836817_state->Prop)) X_80) Y_45))))
% FOF formula (forall (Z_19:(pname->Prop)) (X_79:(pname->Prop)) (Y_44:(pname->Prop)), (((ord_less_eq_pname_o X_79) Y_44)->(((ord_less_eq_pname_o Y_44) Z_19)->((ord_less_eq_pname_o X_79) Z_19)))) of role axiom named fact_340_order__trans
% A new axiom: (forall (Z_19:(pname->Prop)) (X_79:(pname->Prop)) (Y_44:(pname->Prop)), (((ord_less_eq_pname_o X_79) Y_44)->(((ord_less_eq_pname_o Y_44) Z_19)->((ord_less_eq_pname_o X_79) Z_19))))
% FOF formula (forall (Z_19:(hoare_1167836817_state->Prop)) (X_79:(hoare_1167836817_state->Prop)) (Y_44:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_79) Y_44)->(((ord_le827224136tate_o Y_44) Z_19)->((ord_le827224136tate_o X_79) Z_19)))) of role axiom named fact_341_order__trans
% A new axiom: (forall (Z_19:(hoare_1167836817_state->Prop)) (X_79:(hoare_1167836817_state->Prop)) (Y_44:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_79) Y_44)->(((ord_le827224136tate_o Y_44) Z_19)->((ord_le827224136tate_o X_79) Z_19))))
% FOF formula (forall (X_78:(pname->Prop)) (Y_43:(pname->Prop)), (((ord_less_eq_pname_o X_78) Y_43)->(((ord_less_eq_pname_o Y_43) X_78)->(((eq (pname->Prop)) X_78) Y_43)))) of role axiom named fact_342_order__antisym
% A new axiom: (forall (X_78:(pname->Prop)) (Y_43:(pname->Prop)), (((ord_less_eq_pname_o X_78) Y_43)->(((ord_less_eq_pname_o Y_43) X_78)->(((eq (pname->Prop)) X_78) Y_43))))
% FOF formula (forall (X_78:(hoare_1167836817_state->Prop)) (Y_43:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_78) Y_43)->(((ord_le827224136tate_o Y_43) X_78)->(((eq (hoare_1167836817_state->Prop)) X_78) Y_43)))) of role axiom named fact_343_order__antisym
% A new axiom: (forall (X_78:(hoare_1167836817_state->Prop)) (Y_43:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_78) Y_43)->(((ord_le827224136tate_o Y_43) X_78)->(((eq (hoare_1167836817_state->Prop)) X_78) Y_43))))
% FOF formula (forall (C_36:(pname->Prop)) (B_63:(pname->Prop)) (A_88:(pname->Prop)), (((ord_less_eq_pname_o B_63) A_88)->((((eq (pname->Prop)) B_63) C_36)->((ord_less_eq_pname_o C_36) A_88)))) of role axiom named fact_344_xt1_I4_J
% A new axiom: (forall (C_36:(pname->Prop)) (B_63:(pname->Prop)) (A_88:(pname->Prop)), (((ord_less_eq_pname_o B_63) A_88)->((((eq (pname->Prop)) B_63) C_36)->((ord_less_eq_pname_o C_36) A_88))))
% FOF formula (forall (C_36:(hoare_1167836817_state->Prop)) (B_63:(hoare_1167836817_state->Prop)) (A_88:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_63) A_88)->((((eq (hoare_1167836817_state->Prop)) B_63) C_36)->((ord_le827224136tate_o C_36) A_88)))) of role axiom named fact_345_xt1_I4_J
% A new axiom: (forall (C_36:(hoare_1167836817_state->Prop)) (B_63:(hoare_1167836817_state->Prop)) (A_88:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_63) A_88)->((((eq (hoare_1167836817_state->Prop)) B_63) C_36)->((ord_le827224136tate_o C_36) A_88))))
% FOF formula (forall (C_35:(pname->Prop)) (A_87:(pname->Prop)) (B_62:(pname->Prop)), (((ord_less_eq_pname_o A_87) B_62)->((((eq (pname->Prop)) B_62) C_35)->((ord_less_eq_pname_o A_87) C_35)))) of role axiom named fact_346_ord__le__eq__trans
% A new axiom: (forall (C_35:(pname->Prop)) (A_87:(pname->Prop)) (B_62:(pname->Prop)), (((ord_less_eq_pname_o A_87) B_62)->((((eq (pname->Prop)) B_62) C_35)->((ord_less_eq_pname_o A_87) C_35))))
% FOF formula (forall (C_35:(hoare_1167836817_state->Prop)) (A_87:(hoare_1167836817_state->Prop)) (B_62:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_87) B_62)->((((eq (hoare_1167836817_state->Prop)) B_62) C_35)->((ord_le827224136tate_o A_87) C_35)))) of role axiom named fact_347_ord__le__eq__trans
% A new axiom: (forall (C_35:(hoare_1167836817_state->Prop)) (A_87:(hoare_1167836817_state->Prop)) (B_62:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_87) B_62)->((((eq (hoare_1167836817_state->Prop)) B_62) C_35)->((ord_le827224136tate_o A_87) C_35))))
% FOF formula (forall (C_34:(pname->Prop)) (A_86:(pname->Prop)) (B_61:(pname->Prop)), ((((eq (pname->Prop)) A_86) B_61)->(((ord_less_eq_pname_o C_34) B_61)->((ord_less_eq_pname_o C_34) A_86)))) of role axiom named fact_348_xt1_I3_J
% A new axiom: (forall (C_34:(pname->Prop)) (A_86:(pname->Prop)) (B_61:(pname->Prop)), ((((eq (pname->Prop)) A_86) B_61)->(((ord_less_eq_pname_o C_34) B_61)->((ord_less_eq_pname_o C_34) A_86))))
% FOF formula (forall (C_34:(hoare_1167836817_state->Prop)) (A_86:(hoare_1167836817_state->Prop)) (B_61:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_86) B_61)->(((ord_le827224136tate_o C_34) B_61)->((ord_le827224136tate_o C_34) A_86)))) of role axiom named fact_349_xt1_I3_J
% A new axiom: (forall (C_34:(hoare_1167836817_state->Prop)) (A_86:(hoare_1167836817_state->Prop)) (B_61:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_86) B_61)->(((ord_le827224136tate_o C_34) B_61)->((ord_le827224136tate_o C_34) A_86))))
% FOF formula (forall (C_33:(pname->Prop)) (A_85:(pname->Prop)) (B_60:(pname->Prop)), ((((eq (pname->Prop)) A_85) B_60)->(((ord_less_eq_pname_o B_60) C_33)->((ord_less_eq_pname_o A_85) C_33)))) of role axiom named fact_350_ord__eq__le__trans
% A new axiom: (forall (C_33:(pname->Prop)) (A_85:(pname->Prop)) (B_60:(pname->Prop)), ((((eq (pname->Prop)) A_85) B_60)->(((ord_less_eq_pname_o B_60) C_33)->((ord_less_eq_pname_o A_85) C_33))))
% FOF formula (forall (C_33:(hoare_1167836817_state->Prop)) (A_85:(hoare_1167836817_state->Prop)) (B_60:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_85) B_60)->(((ord_le827224136tate_o B_60) C_33)->((ord_le827224136tate_o A_85) C_33)))) of role axiom named fact_351_ord__eq__le__trans
% A new axiom: (forall (C_33:(hoare_1167836817_state->Prop)) (A_85:(hoare_1167836817_state->Prop)) (B_60:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_85) B_60)->(((ord_le827224136tate_o B_60) C_33)->((ord_le827224136tate_o A_85) C_33))))
% FOF formula (forall (Y_42:(pname->Prop)) (X_77:(pname->Prop)), (((ord_less_eq_pname_o Y_42) X_77)->((iff ((ord_less_eq_pname_o X_77) Y_42)) (((eq (pname->Prop)) X_77) Y_42)))) of role axiom named fact_352_order__antisym__conv
% A new axiom: (forall (Y_42:(pname->Prop)) (X_77:(pname->Prop)), (((ord_less_eq_pname_o Y_42) X_77)->((iff ((ord_less_eq_pname_o X_77) Y_42)) (((eq (pname->Prop)) X_77) Y_42))))
% FOF formula (forall (Y_42:(hoare_1167836817_state->Prop)) (X_77:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_42) X_77)->((iff ((ord_le827224136tate_o X_77) Y_42)) (((eq (hoare_1167836817_state->Prop)) X_77) Y_42)))) of role axiom named fact_353_order__antisym__conv
% A new axiom: (forall (Y_42:(hoare_1167836817_state->Prop)) (X_77:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_42) X_77)->((iff ((ord_le827224136tate_o X_77) Y_42)) (((eq (hoare_1167836817_state->Prop)) X_77) Y_42))))
% FOF formula (forall (X_76:(pname->Prop)) (Y_41:(pname->Prop)), ((((eq (pname->Prop)) X_76) Y_41)->((ord_less_eq_pname_o X_76) Y_41))) of role axiom named fact_354_order__eq__refl
% A new axiom: (forall (X_76:(pname->Prop)) (Y_41:(pname->Prop)), ((((eq (pname->Prop)) X_76) Y_41)->((ord_less_eq_pname_o X_76) Y_41)))
% FOF formula (forall (X_76:(hoare_1167836817_state->Prop)) (Y_41:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) X_76) Y_41)->((ord_le827224136tate_o X_76) Y_41))) of role axiom named fact_355_order__eq__refl
% A new axiom: (forall (X_76:(hoare_1167836817_state->Prop)) (Y_41:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) X_76) Y_41)->((ord_le827224136tate_o X_76) Y_41)))
% FOF formula (forall (X_75:(pname->Prop)) (Y_40:(pname->Prop)), ((iff (((eq (pname->Prop)) X_75) Y_40)) ((and ((ord_less_eq_pname_o X_75) Y_40)) ((ord_less_eq_pname_o Y_40) X_75)))) of role axiom named fact_356_order__eq__iff
% A new axiom: (forall (X_75:(pname->Prop)) (Y_40:(pname->Prop)), ((iff (((eq (pname->Prop)) X_75) Y_40)) ((and ((ord_less_eq_pname_o X_75) Y_40)) ((ord_less_eq_pname_o Y_40) X_75))))
% FOF formula (forall (X_75:(hoare_1167836817_state->Prop)) (Y_40:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) X_75) Y_40)) ((and ((ord_le827224136tate_o X_75) Y_40)) ((ord_le827224136tate_o Y_40) X_75)))) of role axiom named fact_357_order__eq__iff
% A new axiom: (forall (X_75:(hoare_1167836817_state->Prop)) (Y_40:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) X_75) Y_40)) ((and ((ord_le827224136tate_o X_75) Y_40)) ((ord_le827224136tate_o Y_40) X_75))))
% FOF formula (forall (A_84:com) (A_83:com), ((iff (((eq option_com) (some_com A_84)) (some_com A_83))) (((eq com) A_84) A_83))) of role axiom named fact_358_option_Oinject
% A new axiom: (forall (A_84:com) (A_83:com), ((iff (((eq option_com) (some_com A_84)) (some_com A_83))) (((eq com) A_84) A_83)))
% FOF formula (forall (G_23:(hoare_1167836817_state->Prop)) (P_27:(state->(state->Prop))) (C_32:com) (Q_19:(state->(state->Prop))) (C_31:Prop), ((C_31->((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state P_27) C_32) Q_19)) bot_bo70021908tate_o)))->((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S_3:state)=> ((and ((P_27 Z_11) S_3)) C_31))) C_32) Q_19)) bot_bo70021908tate_o)))) of role axiom named fact_359_constant
% A new axiom: (forall (G_23:(hoare_1167836817_state->Prop)) (P_27:(state->(state->Prop))) (C_32:com) (Q_19:(state->(state->Prop))) (C_31:Prop), ((C_31->((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state P_27) C_32) Q_19)) bot_bo70021908tate_o)))->((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S_3:state)=> ((and ((P_27 Z_11) S_3)) C_31))) C_32) Q_19)) bot_bo70021908tate_o))))
% FOF formula (forall (Pn_3:pname) (G_22:(hoare_1167836817_state->Prop)) (P_26:(pname->(state->(state->Prop)))) (Q_18:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_22) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_26 P_24)) (body_1 P_24)) (Q_18 P_24)))) Procs_1))) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_26 P_24)) (the_com (body P_24))) (Q_18 P_24)))) Procs_1))->(((member_pname Pn_3) Procs_1)->((hoare_123228589_state G_22) ((insert2134838167_state (((hoare_908217195_state (P_26 Pn_3)) (body_1 Pn_3)) (Q_18 Pn_3))) bot_bo70021908tate_o))))) of role axiom named fact_360_Body1
% A new axiom: (forall (Pn_3:pname) (G_22:(hoare_1167836817_state->Prop)) (P_26:(pname->(state->(state->Prop)))) (Q_18:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_22) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_26 P_24)) (body_1 P_24)) (Q_18 P_24)))) Procs_1))) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_26 P_24)) (the_com (body P_24))) (Q_18 P_24)))) Procs_1))->(((member_pname Pn_3) Procs_1)->((hoare_123228589_state G_22) ((insert2134838167_state (((hoare_908217195_state (P_26 Pn_3)) (body_1 Pn_3)) (Q_18 Pn_3))) bot_bo70021908tate_o)))))
% FOF formula (forall (A_82:(pname->Prop)), (((ord_less_eq_pname_o A_82) bot_bot_pname_o)->(((eq (pname->Prop)) A_82) bot_bot_pname_o))) of role axiom named fact_361_le__bot
% A new axiom: (forall (A_82:(pname->Prop)), (((ord_less_eq_pname_o A_82) bot_bot_pname_o)->(((eq (pname->Prop)) A_82) bot_bot_pname_o)))
% FOF formula (forall (A_82:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_82) bot_bo70021908tate_o)->(((eq (hoare_1167836817_state->Prop)) A_82) bot_bo70021908tate_o))) of role axiom named fact_362_le__bot
% A new axiom: (forall (A_82:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_82) bot_bo70021908tate_o)->(((eq (hoare_1167836817_state->Prop)) A_82) bot_bo70021908tate_o)))
% FOF formula (forall (A_81:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_81) bot_bot_pname_o)) (((eq (pname->Prop)) A_81) bot_bot_pname_o))) of role axiom named fact_363_bot__unique
% A new axiom: (forall (A_81:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_81) bot_bot_pname_o)) (((eq (pname->Prop)) A_81) bot_bot_pname_o)))
% FOF formula (forall (A_81:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_81) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_81) bot_bo70021908tate_o))) of role axiom named fact_364_bot__unique
% A new axiom: (forall (A_81:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_81) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_81) bot_bo70021908tate_o)))
% FOF formula (forall (A_80:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_80)) of role axiom named fact_365_bot__least
% A new axiom: (forall (A_80:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_80))
% FOF formula (forall (A_80:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_80)) of role axiom named fact_366_bot__least
% A new axiom: (forall (A_80:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_80))
% FOF formula (forall (X_74:pname) (F_38:(pname->Prop)) (G_21:(pname->Prop)), (((ord_less_eq_pname_o F_38) G_21)->((ord_less_eq_o (F_38 X_74)) (G_21 X_74)))) of role axiom named fact_367_le__funE
% A new axiom: (forall (X_74:pname) (F_38:(pname->Prop)) (G_21:(pname->Prop)), (((ord_less_eq_pname_o F_38) G_21)->((ord_less_eq_o (F_38 X_74)) (G_21 X_74))))
% FOF formula (forall (X_74:hoare_1167836817_state) (F_38:(hoare_1167836817_state->Prop)) (G_21:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_38) G_21)->((ord_less_eq_o (F_38 X_74)) (G_21 X_74)))) of role axiom named fact_368_le__funE
% A new axiom: (forall (X_74:hoare_1167836817_state) (F_38:(hoare_1167836817_state->Prop)) (G_21:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_38) G_21)->((ord_less_eq_o (F_38 X_74)) (G_21 X_74))))
% FOF formula (forall (X_73:pname) (F_37:(pname->Prop)) (G_20:(pname->Prop)), (((ord_less_eq_pname_o F_37) G_20)->((ord_less_eq_o (F_37 X_73)) (G_20 X_73)))) of role axiom named fact_369_le__funD
% A new axiom: (forall (X_73:pname) (F_37:(pname->Prop)) (G_20:(pname->Prop)), (((ord_less_eq_pname_o F_37) G_20)->((ord_less_eq_o (F_37 X_73)) (G_20 X_73))))
% FOF formula (forall (X_73:hoare_1167836817_state) (F_37:(hoare_1167836817_state->Prop)) (G_20:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_37) G_20)->((ord_less_eq_o (F_37 X_73)) (G_20 X_73)))) of role axiom named fact_370_le__funD
% A new axiom: (forall (X_73:hoare_1167836817_state) (F_37:(hoare_1167836817_state->Prop)) (G_20:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_37) G_20)->((ord_less_eq_o (F_37 X_73)) (G_20 X_73))))
% FOF formula (forall (F_36:(pname->Prop)) (G_19:(pname->Prop)), ((iff ((ord_less_eq_pname_o F_36) G_19)) (forall (X_5:pname), ((ord_less_eq_o (F_36 X_5)) (G_19 X_5))))) of role axiom named fact_371_le__fun__def
% A new axiom: (forall (F_36:(pname->Prop)) (G_19:(pname->Prop)), ((iff ((ord_less_eq_pname_o F_36) G_19)) (forall (X_5:pname), ((ord_less_eq_o (F_36 X_5)) (G_19 X_5)))))
% FOF formula (forall (F_36:(hoare_1167836817_state->Prop)) (G_19:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o F_36) G_19)) (forall (X_5:hoare_1167836817_state), ((ord_less_eq_o (F_36 X_5)) (G_19 X_5))))) of role axiom named fact_372_le__fun__def
% A new axiom: (forall (F_36:(hoare_1167836817_state->Prop)) (G_19:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o F_36) G_19)) (forall (X_5:hoare_1167836817_state), ((ord_less_eq_o (F_36 X_5)) (G_19 X_5)))))
% FOF formula (forall (X_72:pname), ((iff (bot_bot_pname_o X_72)) bot_bot_o)) of role axiom named fact_373_bot__apply
% A new axiom: (forall (X_72:pname), ((iff (bot_bot_pname_o X_72)) bot_bot_o))
% FOF formula (forall (X_72:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_72)) bot_bot_o)) of role axiom named fact_374_bot__apply
% A new axiom: (forall (X_72:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_72)) bot_bot_o))
% FOF formula (forall (X_5:pname), ((iff (bot_bot_pname_o X_5)) bot_bot_o)) of role axiom named fact_375_bot__fun__def
% A new axiom: (forall (X_5:pname), ((iff (bot_bot_pname_o X_5)) bot_bot_o))
% FOF formula (forall (X_5:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_5)) bot_bot_o)) of role axiom named fact_376_bot__fun__def
% A new axiom: (forall (X_5:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_5)) bot_bot_o))
% FOF formula (forall (P_25:(state->(state->Prop))) (Pn_2:pname) (Q_17:(state->(state->Prop))) (G_18:(hoare_1167836817_state->Prop)), (((hoare_123228589_state ((insert2134838167_state (((hoare_908217195_state P_25) (body_1 Pn_2)) Q_17)) G_18)) ((insert2134838167_state (((hoare_908217195_state P_25) (the_com (body Pn_2))) Q_17)) bot_bo70021908tate_o))->((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state P_25) (body_1 Pn_2)) Q_17)) bot_bo70021908tate_o)))) of role axiom named fact_377_BodyN
% A new axiom: (forall (P_25:(state->(state->Prop))) (Pn_2:pname) (Q_17:(state->(state->Prop))) (G_18:(hoare_1167836817_state->Prop)), (((hoare_123228589_state ((insert2134838167_state (((hoare_908217195_state P_25) (body_1 Pn_2)) Q_17)) G_18)) ((insert2134838167_state (((hoare_908217195_state P_25) (the_com (body Pn_2))) Q_17)) bot_bo70021908tate_o))->((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state P_25) (body_1 Pn_2)) Q_17)) bot_bo70021908tate_o))))
% FOF formula (forall (P_23:(pname->(state->(state->Prop)))) (Q_16:(pname->(state->(state->Prop)))) (G_17:(hoare_1167836817_state->Prop)) (P_22:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_15:(pname->(state->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_24:pname), (((hoare_123228589_state G_17) ((insert2134838167_state (((hoare_908217195_state (P_22 P_24)) (C0_1 P_24)) (Q_15 P_24))) bot_bo70021908tate_o))->((hoare_123228589_state G_17) ((insert2134838167_state (((hoare_908217195_state (P_23 P_24)) (C0_1 P_24)) (Q_16 P_24))) bot_bo70021908tate_o))))->(((hoare_123228589_state G_17) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_22 P_24)) (C0_1 P_24)) (Q_15 P_24)))) U_1))->((hoare_123228589_state G_17) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_23 P_24)) (C0_1 P_24)) (Q_16 P_24)))) U_1)))))) of role axiom named fact_378_finite__pointwise
% A new axiom: (forall (P_23:(pname->(state->(state->Prop)))) (Q_16:(pname->(state->(state->Prop)))) (G_17:(hoare_1167836817_state->Prop)) (P_22:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_15:(pname->(state->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_24:pname), (((hoare_123228589_state G_17) ((insert2134838167_state (((hoare_908217195_state (P_22 P_24)) (C0_1 P_24)) (Q_15 P_24))) bot_bo70021908tate_o))->((hoare_123228589_state G_17) ((insert2134838167_state (((hoare_908217195_state (P_23 P_24)) (C0_1 P_24)) (Q_16 P_24))) bot_bo70021908tate_o))))->(((hoare_123228589_state G_17) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_22 P_24)) (C0_1 P_24)) (Q_15 P_24)))) U_1))->((hoare_123228589_state G_17) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_23 P_24)) (C0_1 P_24)) (Q_16 P_24)))) U_1))))))
% FOF formula (forall (G_16:(hoare_1167836817_state->Prop)) (C_30:com) (Q_14:(state->(state->Prop))) (P_21:(state->(state->Prop))), ((forall (Z_11:state) (S_3:state), (((P_21 Z_11) S_3)->((hoare_123228589_state G_16) ((insert2134838167_state (((hoare_908217195_state (fun (Za:state) (S_4:state)=> (((eq state) S_4) S_3))) C_30) (fun (Z_18:state)=> (Q_14 Z_11)))) bot_bo70021908tate_o))))->((hoare_123228589_state G_16) ((insert2134838167_state (((hoare_908217195_state P_21) C_30) Q_14)) bot_bo70021908tate_o)))) of role axiom named fact_379_escape
% A new axiom: (forall (G_16:(hoare_1167836817_state->Prop)) (C_30:com) (Q_14:(state->(state->Prop))) (P_21:(state->(state->Prop))), ((forall (Z_11:state) (S_3:state), (((P_21 Z_11) S_3)->((hoare_123228589_state G_16) ((insert2134838167_state (((hoare_908217195_state (fun (Za:state) (S_4:state)=> (((eq state) S_4) S_3))) C_30) (fun (Z_18:state)=> (Q_14 Z_11)))) bot_bo70021908tate_o))))->((hoare_123228589_state G_16) ((insert2134838167_state (((hoare_908217195_state P_21) C_30) Q_14)) bot_bo70021908tate_o))))
% FOF formula (forall (G_15:(hoare_1167836817_state->Prop)) (P_20:(pname->(state->(state->Prop)))) (Q_13:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_529639851_state ((semila1172322802tate_o G_15) ((image_575578384_state (fun (Pn:pname)=> (((hoare_908217195_state (P_20 Pn)) (body_1 Pn)) (Q_13 Pn)))) Procs))) ((image_575578384_state (fun (Pn:pname)=> (((hoare_908217195_state (P_20 Pn)) (the_com (body Pn))) (Q_13 Pn)))) Procs))->((hoare_529639851_state G_15) ((image_575578384_state (fun (Pn:pname)=> (((hoare_908217195_state (P_20 Pn)) (body_1 Pn)) (Q_13 Pn)))) Procs)))) of role axiom named fact_380_Body__sound__lemma
% A new axiom: (forall (G_15:(hoare_1167836817_state->Prop)) (P_20:(pname->(state->(state->Prop)))) (Q_13:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_529639851_state ((semila1172322802tate_o G_15) ((image_575578384_state (fun (Pn:pname)=> (((hoare_908217195_state (P_20 Pn)) (body_1 Pn)) (Q_13 Pn)))) Procs))) ((image_575578384_state (fun (Pn:pname)=> (((hoare_908217195_state (P_20 Pn)) (the_com (body Pn))) (Q_13 Pn)))) Procs))->((hoare_529639851_state G_15) ((image_575578384_state (fun (Pn:pname)=> (((hoare_908217195_state (P_20 Pn)) (body_1 Pn)) (Q_13 Pn)))) Procs))))
% FOF formula (forall (P_19:(state->(state->Prop))) (G_14:(hoare_1167836817_state->Prop)) (P_18:(state->(state->Prop))) (C_29:com) (Q_12:(state->(state->Prop))), (((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state P_18) C_29) Q_12)) bot_bo70021908tate_o))->((forall (Z_11:state) (S_3:state), (((P_19 Z_11) S_3)->((P_18 Z_11) S_3)))->((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state P_19) C_29) Q_12)) bot_bo70021908tate_o))))) of role axiom named fact_381_conseq1
% A new axiom: (forall (P_19:(state->(state->Prop))) (G_14:(hoare_1167836817_state->Prop)) (P_18:(state->(state->Prop))) (C_29:com) (Q_12:(state->(state->Prop))), (((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state P_18) C_29) Q_12)) bot_bo70021908tate_o))->((forall (Z_11:state) (S_3:state), (((P_19 Z_11) S_3)->((P_18 Z_11) S_3)))->((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state P_19) C_29) Q_12)) bot_bo70021908tate_o)))))
% FOF formula (forall (Q_11:(state->(state->Prop))) (G_13:(hoare_1167836817_state->Prop)) (P_17:(state->(state->Prop))) (C_28:com) (Q_10:(state->(state->Prop))), (((hoare_123228589_state G_13) ((insert2134838167_state (((hoare_908217195_state P_17) C_28) Q_10)) bot_bo70021908tate_o))->((forall (Z_11:state) (S_3:state), (((Q_10 Z_11) S_3)->((Q_11 Z_11) S_3)))->((hoare_123228589_state G_13) ((insert2134838167_state (((hoare_908217195_state P_17) C_28) Q_11)) bot_bo70021908tate_o))))) of role axiom named fact_382_conseq2
% A new axiom: (forall (Q_11:(state->(state->Prop))) (G_13:(hoare_1167836817_state->Prop)) (P_17:(state->(state->Prop))) (C_28:com) (Q_10:(state->(state->Prop))), (((hoare_123228589_state G_13) ((insert2134838167_state (((hoare_908217195_state P_17) C_28) Q_10)) bot_bo70021908tate_o))->((forall (Z_11:state) (S_3:state), (((Q_10 Z_11) S_3)->((Q_11 Z_11) S_3)))->((hoare_123228589_state G_13) ((insert2134838167_state (((hoare_908217195_state P_17) C_28) Q_11)) bot_bo70021908tate_o)))))
% FOF formula (forall (P:(state->(state->Prop))) (Q_9:(state->(state->Prop))) (C_21:com), (((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o))->(((hoare_529639851_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P) C_21) Q_9)) bot_bo70021908tate_o))->((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P) C_21) Q_9)) bot_bo70021908tate_o))))) of role axiom named fact_383_MGF__complete
% A new axiom: (forall (P:(state->(state->Prop))) (Q_9:(state->(state->Prop))) (C_21:com), (((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o))->(((hoare_529639851_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P) C_21) Q_9)) bot_bo70021908tate_o))->((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P) C_21) Q_9)) bot_bo70021908tate_o)))))
% FOF formula (forall (A_79:(hoare_1167836817_state->Prop)) (B_59:(hoare_1167836817_state->Prop)) (X_71:hoare_1167836817_state), ((((semila1172322802tate_o A_79) B_59) X_71)->(((A_79 X_71)->False)->(B_59 X_71)))) of role axiom named fact_384_sup1E
% A new axiom: (forall (A_79:(hoare_1167836817_state->Prop)) (B_59:(hoare_1167836817_state->Prop)) (X_71:hoare_1167836817_state), ((((semila1172322802tate_o A_79) B_59) X_71)->(((A_79 X_71)->False)->(B_59 X_71))))
% FOF formula (forall (A_78:(hoare_1167836817_state->Prop)) (B_58:(hoare_1167836817_state->Prop)) (X_70:hoare_1167836817_state), ((((B_58 X_70)->False)->(A_78 X_70))->(((semila1172322802tate_o A_78) B_58) X_70))) of role axiom named fact_385_sup1CI
% A new axiom: (forall (A_78:(hoare_1167836817_state->Prop)) (B_58:(hoare_1167836817_state->Prop)) (X_70:hoare_1167836817_state), ((((B_58 X_70)->False)->(A_78 X_70))->(((semila1172322802tate_o A_78) B_58) X_70)))
% FOF formula (forall (G_12:(hoare_1167836817_state->Prop)) (Ts:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_12) Ts)->((hoare_529639851_state G_12) Ts))) of role axiom named fact_386_hoare__sound
% A new axiom: (forall (G_12:(hoare_1167836817_state->Prop)) (Ts:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_12) Ts)->((hoare_529639851_state G_12) Ts)))
% FOF formula (forall (X_5:pname), ((iff (bot_bot_pname_o X_5)) ((member_pname X_5) bot_bot_pname_o))) of role axiom named fact_387_bot__empty__eq
% A new axiom: (forall (X_5:pname), ((iff (bot_bot_pname_o X_5)) ((member_pname X_5) bot_bot_pname_o)))
% FOF formula (forall (X_5:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_5)) ((member2058392318_state X_5) bot_bo70021908tate_o))) of role axiom named fact_388_bot__empty__eq
% A new axiom: (forall (X_5:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_5)) ((member2058392318_state X_5) bot_bo70021908tate_o)))
% FOF formula (forall (Q_8:(pname->Prop)) (P_16:(pname->Prop)) (X_69:pname), ((P_16 X_69)->(((ord_less_eq_pname_o P_16) Q_8)->(Q_8 X_69)))) of role axiom named fact_389_rev__predicate1D
% A new axiom: (forall (Q_8:(pname->Prop)) (P_16:(pname->Prop)) (X_69:pname), ((P_16 X_69)->(((ord_less_eq_pname_o P_16) Q_8)->(Q_8 X_69))))
% FOF formula (forall (Q_8:(hoare_1167836817_state->Prop)) (P_16:(hoare_1167836817_state->Prop)) (X_69:hoare_1167836817_state), ((P_16 X_69)->(((ord_le827224136tate_o P_16) Q_8)->(Q_8 X_69)))) of role axiom named fact_390_rev__predicate1D
% A new axiom: (forall (Q_8:(hoare_1167836817_state->Prop)) (P_16:(hoare_1167836817_state->Prop)) (X_69:hoare_1167836817_state), ((P_16 X_69)->(((ord_le827224136tate_o P_16) Q_8)->(Q_8 X_69))))
% FOF formula (forall (X_68:pname) (P_15:(pname->Prop)) (Q_7:(pname->Prop)), (((ord_less_eq_pname_o P_15) Q_7)->((P_15 X_68)->(Q_7 X_68)))) of role axiom named fact_391_predicate1D
% A new axiom: (forall (X_68:pname) (P_15:(pname->Prop)) (Q_7:(pname->Prop)), (((ord_less_eq_pname_o P_15) Q_7)->((P_15 X_68)->(Q_7 X_68))))
% FOF formula (forall (X_68:hoare_1167836817_state) (P_15:(hoare_1167836817_state->Prop)) (Q_7:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o P_15) Q_7)->((P_15 X_68)->(Q_7 X_68)))) of role axiom named fact_392_predicate1D
% A new axiom: (forall (X_68:hoare_1167836817_state) (P_15:(hoare_1167836817_state->Prop)) (Q_7:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o P_15) Q_7)->((P_15 X_68)->(Q_7 X_68))))
% FOF formula (forall (A_77:(hoare_1167836817_state->Prop)) (B_57:(hoare_1167836817_state->Prop)) (X_67:hoare_1167836817_state), ((B_57 X_67)->(((semila1172322802tate_o A_77) B_57) X_67))) of role axiom named fact_393_sup1I2
% A new axiom: (forall (A_77:(hoare_1167836817_state->Prop)) (B_57:(hoare_1167836817_state->Prop)) (X_67:hoare_1167836817_state), ((B_57 X_67)->(((semila1172322802tate_o A_77) B_57) X_67)))
% FOF formula (forall (B_56:(hoare_1167836817_state->Prop)) (A_76:(hoare_1167836817_state->Prop)) (X_66:hoare_1167836817_state), ((A_76 X_66)->(((semila1172322802tate_o A_76) B_56) X_66))) of role axiom named fact_394_sup1I1
% A new axiom: (forall (B_56:(hoare_1167836817_state->Prop)) (A_76:(hoare_1167836817_state->Prop)) (X_66:hoare_1167836817_state), ((A_76 X_66)->(((semila1172322802tate_o A_76) B_56) X_66)))
% FOF formula (forall (R_3:(pname->Prop)) (S_6:(pname->Prop)), ((iff ((ord_less_eq_pname_o (fun (X_5:pname)=> ((member_pname X_5) R_3))) (fun (X_5:pname)=> ((member_pname X_5) S_6)))) ((ord_less_eq_pname_o R_3) S_6))) of role axiom named fact_395_pred__subset__eq
% A new axiom: (forall (R_3:(pname->Prop)) (S_6:(pname->Prop)), ((iff ((ord_less_eq_pname_o (fun (X_5:pname)=> ((member_pname X_5) R_3))) (fun (X_5:pname)=> ((member_pname X_5) S_6)))) ((ord_less_eq_pname_o R_3) S_6)))
% FOF formula (forall (R_3:(hoare_1167836817_state->Prop)) (S_6:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o (fun (X_5:hoare_1167836817_state)=> ((member2058392318_state X_5) R_3))) (fun (X_5:hoare_1167836817_state)=> ((member2058392318_state X_5) S_6)))) ((ord_le827224136tate_o R_3) S_6))) of role axiom named fact_396_pred__subset__eq
% A new axiom: (forall (R_3:(hoare_1167836817_state->Prop)) (S_6:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o (fun (X_5:hoare_1167836817_state)=> ((member2058392318_state X_5) R_3))) (fun (X_5:hoare_1167836817_state)=> ((member2058392318_state X_5) S_6)))) ((ord_le827224136tate_o R_3) S_6)))
% FOF formula (forall (R_2:(pname->Prop)) (S_5:(pname->Prop)) (X_5:pname), ((iff (((semila1780557381name_o (fun (Y_2:pname)=> ((member_pname Y_2) R_2))) (fun (Y_2:pname)=> ((member_pname Y_2) S_5))) X_5)) ((member_pname X_5) ((semila1780557381name_o R_2) S_5)))) of role axiom named fact_397_sup__Un__eq
% A new axiom: (forall (R_2:(pname->Prop)) (S_5:(pname->Prop)) (X_5:pname), ((iff (((semila1780557381name_o (fun (Y_2:pname)=> ((member_pname Y_2) R_2))) (fun (Y_2:pname)=> ((member_pname Y_2) S_5))) X_5)) ((member_pname X_5) ((semila1780557381name_o R_2) S_5))))
% FOF formula (forall (R_2:(hoare_1167836817_state->Prop)) (S_5:(hoare_1167836817_state->Prop)) (X_5:hoare_1167836817_state), ((iff (((semila1172322802tate_o (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) R_2))) (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) S_5))) X_5)) ((member2058392318_state X_5) ((semila1172322802tate_o R_2) S_5)))) of role axiom named fact_398_sup__Un__eq
% A new axiom: (forall (R_2:(hoare_1167836817_state->Prop)) (S_5:(hoare_1167836817_state->Prop)) (X_5:hoare_1167836817_state), ((iff (((semila1172322802tate_o (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) R_2))) (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) S_5))) X_5)) ((member2058392318_state X_5) ((semila1172322802tate_o R_2) S_5))))
% FOF formula (forall (Q_6:(state->(state->Prop))) (P_14:(state->(state->Prop))) (G_11:(hoare_1167836817_state->Prop)) (P_13:(state->(state->Prop))) (C_27:com) (Q_5:(state->(state->Prop))), (((hoare_123228589_state G_11) ((insert2134838167_state (((hoare_908217195_state P_13) C_27) Q_5)) bot_bo70021908tate_o))->((forall (Z_11:state) (S_3:state), (((P_14 Z_11) S_3)->(forall (S_4:state), ((forall (Z_18:state), (((P_13 Z_18) S_3)->((Q_5 Z_18) S_4)))->((Q_6 Z_11) S_4)))))->((hoare_123228589_state G_11) ((insert2134838167_state (((hoare_908217195_state P_14) C_27) Q_6)) bot_bo70021908tate_o))))) of role axiom named fact_399_conseq12
% A new axiom: (forall (Q_6:(state->(state->Prop))) (P_14:(state->(state->Prop))) (G_11:(hoare_1167836817_state->Prop)) (P_13:(state->(state->Prop))) (C_27:com) (Q_5:(state->(state->Prop))), (((hoare_123228589_state G_11) ((insert2134838167_state (((hoare_908217195_state P_13) C_27) Q_5)) bot_bo70021908tate_o))->((forall (Z_11:state) (S_3:state), (((P_14 Z_11) S_3)->(forall (S_4:state), ((forall (Z_18:state), (((P_13 Z_18) S_3)->((Q_5 Z_18) S_4)))->((Q_6 Z_11) S_4)))))->((hoare_123228589_state G_11) ((insert2134838167_state (((hoare_908217195_state P_14) C_27) Q_6)) bot_bo70021908tate_o)))))
% FOF formula (forall (F_35:(pname->Prop)) (G_10:(pname->Prop)), ((forall (X_5:pname), ((ord_less_eq_o (F_35 X_5)) (G_10 X_5)))->((ord_less_eq_pname_o F_35) G_10))) of role axiom named fact_400_le__funI
% A new axiom: (forall (F_35:(pname->Prop)) (G_10:(pname->Prop)), ((forall (X_5:pname), ((ord_less_eq_o (F_35 X_5)) (G_10 X_5)))->((ord_less_eq_pname_o F_35) G_10)))
% FOF formula (forall (F_35:(hoare_1167836817_state->Prop)) (G_10:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), ((ord_less_eq_o (F_35 X_5)) (G_10 X_5)))->((ord_le827224136tate_o F_35) G_10))) of role axiom named fact_401_le__funI
% A new axiom: (forall (F_35:(hoare_1167836817_state->Prop)) (G_10:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), ((ord_less_eq_o (F_35 X_5)) (G_10 X_5)))->((ord_le827224136tate_o F_35) G_10)))
% FOF formula (forall (X_65:pname), (((eq (pname->Prop)) (set_pname (some_pname X_65))) ((insert_pname X_65) bot_bot_pname_o))) of role axiom named fact_402_Option_Oset_Osimps_I2_J
% A new axiom: (forall (X_65:pname), (((eq (pname->Prop)) (set_pname (some_pname X_65))) ((insert_pname X_65) bot_bot_pname_o)))
% FOF formula (forall (X_65:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (set_Ho2131684873_state (some_H1433514562_state X_65))) ((insert2134838167_state X_65) bot_bo70021908tate_o))) of role axiom named fact_403_Option_Oset_Osimps_I2_J
% A new axiom: (forall (X_65:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (set_Ho2131684873_state (some_H1433514562_state X_65))) ((insert2134838167_state X_65) bot_bo70021908tate_o)))
% FOF formula (forall (X_65:com), (((eq (com->Prop)) (set_com (some_com X_65))) ((insert_com X_65) bot_bot_com_o))) of role axiom named fact_404_Option_Oset_Osimps_I2_J
% A new axiom: (forall (X_65:com), (((eq (com->Prop)) (set_com (some_com X_65))) ((insert_com X_65) bot_bot_com_o)))
% FOF formula (forall (X_64:pname) (Xo:option_pname), ((iff ((member_pname X_64) (set_pname Xo))) (((eq option_pname) Xo) (some_pname X_64)))) of role axiom named fact_405_elem__set
% A new axiom: (forall (X_64:pname) (Xo:option_pname), ((iff ((member_pname X_64) (set_pname Xo))) (((eq option_pname) Xo) (some_pname X_64))))
% FOF formula (forall (X_64:hoare_1167836817_state) (Xo:option1574264306_state), ((iff ((member2058392318_state X_64) (set_Ho2131684873_state Xo))) (((eq option1574264306_state) Xo) (some_H1433514562_state X_64)))) of role axiom named fact_406_elem__set
% A new axiom: (forall (X_64:hoare_1167836817_state) (Xo:option1574264306_state), ((iff ((member2058392318_state X_64) (set_Ho2131684873_state Xo))) (((eq option1574264306_state) Xo) (some_H1433514562_state X_64))))
% FOF formula (forall (X_64:com) (Xo:option_com), ((iff ((member_com X_64) (set_com Xo))) (((eq option_com) Xo) (some_com X_64)))) of role axiom named fact_407_elem__set
% A new axiom: (forall (X_64:com) (Xo:option_com), ((iff ((member_com X_64) (set_com Xo))) (((eq option_com) Xo) (some_com X_64))))
% FOF formula (forall (X_63:com) (P_12:(com->Prop)) (A_75:option_com), ((forall (X_5:com), (((member_com X_5) (set_com A_75))->(P_12 X_5)))->((((eq option_com) A_75) (some_com X_63))->(P_12 X_63)))) of role axiom named fact_408_ospec
% A new axiom: (forall (X_63:com) (P_12:(com->Prop)) (A_75:option_com), ((forall (X_5:com), (((member_com X_5) (set_com A_75))->(P_12 X_5)))->((((eq option_com) A_75) (some_com X_63))->(P_12 X_63))))
% FOF formula (forall (F_34:(hoare_1167836817_state->Prop)) (G_9:(hoare_1167836817_state->Prop)) (X_5:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_34) G_9) X_5)) ((semila10642723_sup_o (F_34 X_5)) (G_9 X_5)))) of role axiom named fact_409_sup__fun__def
% A new axiom: (forall (F_34:(hoare_1167836817_state->Prop)) (G_9:(hoare_1167836817_state->Prop)) (X_5:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_34) G_9) X_5)) ((semila10642723_sup_o (F_34 X_5)) (G_9 X_5))))
% FOF formula (forall (F_33:(hoare_1167836817_state->Prop)) (G_8:(hoare_1167836817_state->Prop)) (X_62:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_33) G_8) X_62)) ((semila10642723_sup_o (F_33 X_62)) (G_8 X_62)))) of role axiom named fact_410_sup__apply
% A new axiom: (forall (F_33:(hoare_1167836817_state->Prop)) (G_8:(hoare_1167836817_state->Prop)) (X_62:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_33) G_8) X_62)) ((semila10642723_sup_o (F_33 X_62)) (G_8 X_62))))
% FOF formula (hoare_1201148605gleton->(forall (T_1:state), ((forall (S_3:state), (((eq state) S_3) T_1))->False))) of role axiom named fact_411_single__stateE
% A new axiom: (hoare_1201148605gleton->(forall (T_1:state), ((forall (S_3:state), (((eq state) S_3) T_1))->False)))
% FOF formula ((iff hoare_1201148605gleton) ((ex state) (fun (S_3:state)=> ((ex state) (fun (T_1:state)=> (not (((eq state) S_3) T_1))))))) of role axiom named fact_412_state__not__singleton__def
% A new axiom: ((iff hoare_1201148605gleton) ((ex state) (fun (S_3:state)=> ((ex state) (fun (T_1:state)=> (not (((eq state) S_3) T_1)))))))
% FOF formula (forall (X_61:(hoare_1167836817_state->Prop)) (Y_39:(hoare_1167836817_state->Prop)) (Z_17:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_61) Y_39)) Z_17)) ((semila1172322802tate_o X_61) ((semila1172322802tate_o Y_39) Z_17)))) of role axiom named fact_413_sup__assoc
% A new axiom: (forall (X_61:(hoare_1167836817_state->Prop)) (Y_39:(hoare_1167836817_state->Prop)) (Z_17:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_61) Y_39)) Z_17)) ((semila1172322802tate_o X_61) ((semila1172322802tate_o Y_39) Z_17))))
% FOF formula (forall (X_60:(hoare_1167836817_state->Prop)) (Y_38:(hoare_1167836817_state->Prop)) (Z_16:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_60) Y_38)) Z_16)) ((semila1172322802tate_o X_60) ((semila1172322802tate_o Y_38) Z_16)))) of role axiom named fact_414_inf__sup__aci_I6_J
% A new axiom: (forall (X_60:(hoare_1167836817_state->Prop)) (Y_38:(hoare_1167836817_state->Prop)) (Z_16:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_60) Y_38)) Z_16)) ((semila1172322802tate_o X_60) ((semila1172322802tate_o Y_38) Z_16))))
% FOF formula (forall (A_74:(hoare_1167836817_state->Prop)) (B_55:(hoare_1167836817_state->Prop)) (C_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_74) B_55)) C_26)) ((semila1172322802tate_o A_74) ((semila1172322802tate_o B_55) C_26)))) of role axiom named fact_415_sup_Oassoc
% A new axiom: (forall (A_74:(hoare_1167836817_state->Prop)) (B_55:(hoare_1167836817_state->Prop)) (C_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_74) B_55)) C_26)) ((semila1172322802tate_o A_74) ((semila1172322802tate_o B_55) C_26))))
% FOF formula (forall (X_59:(hoare_1167836817_state->Prop)) (Y_37:(hoare_1167836817_state->Prop)) (Z_15:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_59) ((semila1172322802tate_o Y_37) Z_15))) ((semila1172322802tate_o Y_37) ((semila1172322802tate_o X_59) Z_15)))) of role axiom named fact_416_sup__left__commute
% A new axiom: (forall (X_59:(hoare_1167836817_state->Prop)) (Y_37:(hoare_1167836817_state->Prop)) (Z_15:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_59) ((semila1172322802tate_o Y_37) Z_15))) ((semila1172322802tate_o Y_37) ((semila1172322802tate_o X_59) Z_15))))
% FOF formula (forall (X_58:(hoare_1167836817_state->Prop)) (Y_36:(hoare_1167836817_state->Prop)) (Z_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_58) ((semila1172322802tate_o Y_36) Z_14))) ((semila1172322802tate_o Y_36) ((semila1172322802tate_o X_58) Z_14)))) of role axiom named fact_417_inf__sup__aci_I7_J
% A new axiom: (forall (X_58:(hoare_1167836817_state->Prop)) (Y_36:(hoare_1167836817_state->Prop)) (Z_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_58) ((semila1172322802tate_o Y_36) Z_14))) ((semila1172322802tate_o Y_36) ((semila1172322802tate_o X_58) Z_14))))
% FOF formula (forall (B_54:(hoare_1167836817_state->Prop)) (A_73:(hoare_1167836817_state->Prop)) (C_25:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o B_54) ((semila1172322802tate_o A_73) C_25))) ((semila1172322802tate_o A_73) ((semila1172322802tate_o B_54) C_25)))) of role axiom named fact_418_sup_Oleft__commute
% A new axiom: (forall (B_54:(hoare_1167836817_state->Prop)) (A_73:(hoare_1167836817_state->Prop)) (C_25:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o B_54) ((semila1172322802tate_o A_73) C_25))) ((semila1172322802tate_o A_73) ((semila1172322802tate_o B_54) C_25))))
% FOF formula (forall (X_57:(hoare_1167836817_state->Prop)) (Y_35:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_57) ((semila1172322802tate_o X_57) Y_35))) ((semila1172322802tate_o X_57) Y_35))) of role axiom named fact_419_sup__left__idem
% A new axiom: (forall (X_57:(hoare_1167836817_state->Prop)) (Y_35:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_57) ((semila1172322802tate_o X_57) Y_35))) ((semila1172322802tate_o X_57) Y_35)))
% FOF formula (forall (X_56:(hoare_1167836817_state->Prop)) (Y_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_56) ((semila1172322802tate_o X_56) Y_34))) ((semila1172322802tate_o X_56) Y_34))) of role axiom named fact_420_inf__sup__aci_I8_J
% A new axiom: (forall (X_56:(hoare_1167836817_state->Prop)) (Y_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_56) ((semila1172322802tate_o X_56) Y_34))) ((semila1172322802tate_o X_56) Y_34)))
% FOF formula (forall (A_72:(hoare_1167836817_state->Prop)) (B_53:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_72) ((semila1172322802tate_o A_72) B_53))) ((semila1172322802tate_o A_72) B_53))) of role axiom named fact_421_sup_Oleft__idem
% A new axiom: (forall (A_72:(hoare_1167836817_state->Prop)) (B_53:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_72) ((semila1172322802tate_o A_72) B_53))) ((semila1172322802tate_o A_72) B_53)))
% FOF formula (forall (X_55:(hoare_1167836817_state->Prop)) (Y_33:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_55) Y_33)) ((semila1172322802tate_o Y_33) X_55))) of role axiom named fact_422_sup__commute
% A new axiom: (forall (X_55:(hoare_1167836817_state->Prop)) (Y_33:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_55) Y_33)) ((semila1172322802tate_o Y_33) X_55)))
% FOF formula (forall (X_54:(hoare_1167836817_state->Prop)) (Y_32:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_54) Y_32)) ((semila1172322802tate_o Y_32) X_54))) of role axiom named fact_423_inf__sup__aci_I5_J
% A new axiom: (forall (X_54:(hoare_1167836817_state->Prop)) (Y_32:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_54) Y_32)) ((semila1172322802tate_o Y_32) X_54)))
% FOF formula (forall (A_71:(hoare_1167836817_state->Prop)) (B_52:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_71) B_52)) ((semila1172322802tate_o B_52) A_71))) of role axiom named fact_424_sup_Ocommute
% A new axiom: (forall (A_71:(hoare_1167836817_state->Prop)) (B_52:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_71) B_52)) ((semila1172322802tate_o B_52) A_71)))
% FOF formula (forall (X_53:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_53) X_53)) X_53)) of role axiom named fact_425_sup__idem
% A new axiom: (forall (X_53:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_53) X_53)) X_53))
% FOF formula (forall (A_70:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_70) A_70)) A_70)) of role axiom named fact_426_sup_Oidem
% A new axiom: (forall (A_70:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_70) A_70)) A_70))
% FOF formula (forall (A_69:(pname->Prop)) (B_51:(pname->Prop)) (X_52:(pname->Prop)), (((ord_less_eq_pname_o ((semila1780557381name_o A_69) B_51)) X_52)->((((ord_less_eq_pname_o A_69) X_52)->(((ord_less_eq_pname_o B_51) X_52)->False))->False))) of role axiom named fact_427_le__supE
% A new axiom: (forall (A_69:(pname->Prop)) (B_51:(pname->Prop)) (X_52:(pname->Prop)), (((ord_less_eq_pname_o ((semila1780557381name_o A_69) B_51)) X_52)->((((ord_less_eq_pname_o A_69) X_52)->(((ord_less_eq_pname_o B_51) X_52)->False))->False)))
% FOF formula (forall (A_69:(hoare_1167836817_state->Prop)) (B_51:(hoare_1167836817_state->Prop)) (X_52:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o ((semila1172322802tate_o A_69) B_51)) X_52)->((((ord_le827224136tate_o A_69) X_52)->(((ord_le827224136tate_o B_51) X_52)->False))->False))) of role axiom named fact_428_le__supE
% A new axiom: (forall (A_69:(hoare_1167836817_state->Prop)) (B_51:(hoare_1167836817_state->Prop)) (X_52:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o ((semila1172322802tate_o A_69) B_51)) X_52)->((((ord_le827224136tate_o A_69) X_52)->(((ord_le827224136tate_o B_51) X_52)->False))->False)))
% FOF formula (forall (B_50:(pname->Prop)) (D_3:(pname->Prop)) (A_68:(pname->Prop)) (C_24:(pname->Prop)), (((ord_less_eq_pname_o A_68) C_24)->(((ord_less_eq_pname_o B_50) D_3)->((ord_less_eq_pname_o ((semila1780557381name_o A_68) B_50)) ((semila1780557381name_o C_24) D_3))))) of role axiom named fact_429_sup__mono
% A new axiom: (forall (B_50:(pname->Prop)) (D_3:(pname->Prop)) (A_68:(pname->Prop)) (C_24:(pname->Prop)), (((ord_less_eq_pname_o A_68) C_24)->(((ord_less_eq_pname_o B_50) D_3)->((ord_less_eq_pname_o ((semila1780557381name_o A_68) B_50)) ((semila1780557381name_o C_24) D_3)))))
% FOF formula (forall (B_50:(hoare_1167836817_state->Prop)) (D_3:(hoare_1167836817_state->Prop)) (A_68:(hoare_1167836817_state->Prop)) (C_24:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_68) C_24)->(((ord_le827224136tate_o B_50) D_3)->((ord_le827224136tate_o ((semila1172322802tate_o A_68) B_50)) ((semila1172322802tate_o C_24) D_3))))) of role axiom named fact_430_sup__mono
% A new axiom: (forall (B_50:(hoare_1167836817_state->Prop)) (D_3:(hoare_1167836817_state->Prop)) (A_68:(hoare_1167836817_state->Prop)) (C_24:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_68) C_24)->(((ord_le827224136tate_o B_50) D_3)->((ord_le827224136tate_o ((semila1172322802tate_o A_68) B_50)) ((semila1172322802tate_o C_24) D_3)))))
% FOF formula (forall (Z_13:(pname->Prop)) (Y_31:(pname->Prop)) (X_51:(pname->Prop)), (((ord_less_eq_pname_o Y_31) X_51)->(((ord_less_eq_pname_o Z_13) X_51)->((ord_less_eq_pname_o ((semila1780557381name_o Y_31) Z_13)) X_51)))) of role axiom named fact_431_sup__least
% A new axiom: (forall (Z_13:(pname->Prop)) (Y_31:(pname->Prop)) (X_51:(pname->Prop)), (((ord_less_eq_pname_o Y_31) X_51)->(((ord_less_eq_pname_o Z_13) X_51)->((ord_less_eq_pname_o ((semila1780557381name_o Y_31) Z_13)) X_51))))
% FOF formula (forall (Z_13:(hoare_1167836817_state->Prop)) (Y_31:(hoare_1167836817_state->Prop)) (X_51:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_31) X_51)->(((ord_le827224136tate_o Z_13) X_51)->((ord_le827224136tate_o ((semila1172322802tate_o Y_31) Z_13)) X_51)))) of role axiom named fact_432_sup__least
% A new axiom: (forall (Z_13:(hoare_1167836817_state->Prop)) (Y_31:(hoare_1167836817_state->Prop)) (X_51:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_31) X_51)->(((ord_le827224136tate_o Z_13) X_51)->((ord_le827224136tate_o ((semila1172322802tate_o Y_31) Z_13)) X_51))))
% FOF formula (forall (B_49:(pname->Prop)) (A_67:(pname->Prop)) (X_50:(pname->Prop)), (((ord_less_eq_pname_o A_67) X_50)->(((ord_less_eq_pname_o B_49) X_50)->((ord_less_eq_pname_o ((semila1780557381name_o A_67) B_49)) X_50)))) of role axiom named fact_433_le__supI
% A new axiom: (forall (B_49:(pname->Prop)) (A_67:(pname->Prop)) (X_50:(pname->Prop)), (((ord_less_eq_pname_o A_67) X_50)->(((ord_less_eq_pname_o B_49) X_50)->((ord_less_eq_pname_o ((semila1780557381name_o A_67) B_49)) X_50))))
% FOF formula (forall (B_49:(hoare_1167836817_state->Prop)) (A_67:(hoare_1167836817_state->Prop)) (X_50:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_67) X_50)->(((ord_le827224136tate_o B_49) X_50)->((ord_le827224136tate_o ((semila1172322802tate_o A_67) B_49)) X_50)))) of role axiom named fact_434_le__supI
% A new axiom: (forall (B_49:(hoare_1167836817_state->Prop)) (A_67:(hoare_1167836817_state->Prop)) (X_50:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_67) X_50)->(((ord_le827224136tate_o B_49) X_50)->((ord_le827224136tate_o ((semila1172322802tate_o A_67) B_49)) X_50))))
% FOF formula (forall (Y_30:(pname->Prop)) (X_49:(pname->Prop)), (((ord_less_eq_pname_o Y_30) X_49)->(((eq (pname->Prop)) ((semila1780557381name_o X_49) Y_30)) X_49))) of role axiom named fact_435_sup__absorb1
% A new axiom: (forall (Y_30:(pname->Prop)) (X_49:(pname->Prop)), (((ord_less_eq_pname_o Y_30) X_49)->(((eq (pname->Prop)) ((semila1780557381name_o X_49) Y_30)) X_49)))
% FOF formula (forall (Y_30:(hoare_1167836817_state->Prop)) (X_49:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_30) X_49)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_49) Y_30)) X_49))) of role axiom named fact_436_sup__absorb1
% A new axiom: (forall (Y_30:(hoare_1167836817_state->Prop)) (X_49:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_30) X_49)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_49) Y_30)) X_49)))
% FOF formula (forall (X_48:(pname->Prop)) (Y_29:(pname->Prop)), (((ord_less_eq_pname_o X_48) Y_29)->(((eq (pname->Prop)) ((semila1780557381name_o X_48) Y_29)) Y_29))) of role axiom named fact_437_sup__absorb2
% A new axiom: (forall (X_48:(pname->Prop)) (Y_29:(pname->Prop)), (((ord_less_eq_pname_o X_48) Y_29)->(((eq (pname->Prop)) ((semila1780557381name_o X_48) Y_29)) Y_29)))
% FOF formula (forall (X_48:(hoare_1167836817_state->Prop)) (Y_29:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_48) Y_29)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_48) Y_29)) Y_29))) of role axiom named fact_438_sup__absorb2
% A new axiom: (forall (X_48:(hoare_1167836817_state->Prop)) (Y_29:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_48) Y_29)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_48) Y_29)) Y_29)))
% FOF formula (forall (A_66:(pname->Prop)) (X_47:(pname->Prop)) (B_48:(pname->Prop)), (((ord_less_eq_pname_o X_47) B_48)->((ord_less_eq_pname_o X_47) ((semila1780557381name_o A_66) B_48)))) of role axiom named fact_439_le__supI2
% A new axiom: (forall (A_66:(pname->Prop)) (X_47:(pname->Prop)) (B_48:(pname->Prop)), (((ord_less_eq_pname_o X_47) B_48)->((ord_less_eq_pname_o X_47) ((semila1780557381name_o A_66) B_48))))
% FOF formula (forall (A_66:(hoare_1167836817_state->Prop)) (X_47:(hoare_1167836817_state->Prop)) (B_48:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_47) B_48)->((ord_le827224136tate_o X_47) ((semila1172322802tate_o A_66) B_48)))) of role axiom named fact_440_le__supI2
% A new axiom: (forall (A_66:(hoare_1167836817_state->Prop)) (X_47:(hoare_1167836817_state->Prop)) (B_48:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_47) B_48)->((ord_le827224136tate_o X_47) ((semila1172322802tate_o A_66) B_48))))
% FOF formula (forall (B_47:(pname->Prop)) (X_46:(pname->Prop)) (A_65:(pname->Prop)), (((ord_less_eq_pname_o X_46) A_65)->((ord_less_eq_pname_o X_46) ((semila1780557381name_o A_65) B_47)))) of role axiom named fact_441_le__supI1
% A new axiom: (forall (B_47:(pname->Prop)) (X_46:(pname->Prop)) (A_65:(pname->Prop)), (((ord_less_eq_pname_o X_46) A_65)->((ord_less_eq_pname_o X_46) ((semila1780557381name_o A_65) B_47))))
% FOF formula (forall (B_47:(hoare_1167836817_state->Prop)) (X_46:(hoare_1167836817_state->Prop)) (A_65:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_46) A_65)->((ord_le827224136tate_o X_46) ((semila1172322802tate_o A_65) B_47)))) of role axiom named fact_442_le__supI1
% A new axiom: (forall (B_47:(hoare_1167836817_state->Prop)) (X_46:(hoare_1167836817_state->Prop)) (A_65:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_46) A_65)->((ord_le827224136tate_o X_46) ((semila1172322802tate_o A_65) B_47))))
% FOF formula (forall (X_45:(pname->Prop)) (Y_28:(pname->Prop)) (Z_12:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((semila1780557381name_o X_45) Y_28)) Z_12)) ((and ((ord_less_eq_pname_o X_45) Z_12)) ((ord_less_eq_pname_o Y_28) Z_12)))) of role axiom named fact_443_le__sup__iff
% A new axiom: (forall (X_45:(pname->Prop)) (Y_28:(pname->Prop)) (Z_12:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((semila1780557381name_o X_45) Y_28)) Z_12)) ((and ((ord_less_eq_pname_o X_45) Z_12)) ((ord_less_eq_pname_o Y_28) Z_12))))
% FOF formula (forall (X_45:(hoare_1167836817_state->Prop)) (Y_28:(hoare_1167836817_state->Prop)) (Z_12:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o ((semila1172322802tate_o X_45) Y_28)) Z_12)) ((and ((ord_le827224136tate_o X_45) Z_12)) ((ord_le827224136tate_o Y_28) Z_12)))) of role axiom named fact_444_le__sup__iff
% A new axiom: (forall (X_45:(hoare_1167836817_state->Prop)) (Y_28:(hoare_1167836817_state->Prop)) (Z_12:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o ((semila1172322802tate_o X_45) Y_28)) Z_12)) ((and ((ord_le827224136tate_o X_45) Z_12)) ((ord_le827224136tate_o Y_28) Z_12))))
% FOF formula (forall (X_44:(pname->Prop)) (Y_27:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_44) Y_27)) (((eq (pname->Prop)) ((semila1780557381name_o X_44) Y_27)) Y_27))) of role axiom named fact_445_le__iff__sup
% A new axiom: (forall (X_44:(pname->Prop)) (Y_27:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_44) Y_27)) (((eq (pname->Prop)) ((semila1780557381name_o X_44) Y_27)) Y_27)))
% FOF formula (forall (X_44:(hoare_1167836817_state->Prop)) (Y_27:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_44) Y_27)) (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_44) Y_27)) Y_27))) of role axiom named fact_446_le__iff__sup
% A new axiom: (forall (X_44:(hoare_1167836817_state->Prop)) (Y_27:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_44) Y_27)) (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_44) Y_27)) Y_27)))
% FOF formula (forall (Y_26:(pname->Prop)) (X_43:(pname->Prop)), ((ord_less_eq_pname_o Y_26) ((semila1780557381name_o X_43) Y_26))) of role axiom named fact_447_sup__ge2
% A new axiom: (forall (Y_26:(pname->Prop)) (X_43:(pname->Prop)), ((ord_less_eq_pname_o Y_26) ((semila1780557381name_o X_43) Y_26)))
% FOF formula (forall (Y_26:(hoare_1167836817_state->Prop)) (X_43:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o Y_26) ((semila1172322802tate_o X_43) Y_26))) of role axiom named fact_448_sup__ge2
% A new axiom: (forall (Y_26:(hoare_1167836817_state->Prop)) (X_43:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o Y_26) ((semila1172322802tate_o X_43) Y_26)))
% FOF formula (forall (Y_25:(pname->Prop)) (X_42:(pname->Prop)), ((ord_less_eq_pname_o Y_25) ((semila1780557381name_o X_42) Y_25))) of role axiom named fact_449_inf__sup__ord_I4_J
% A new axiom: (forall (Y_25:(pname->Prop)) (X_42:(pname->Prop)), ((ord_less_eq_pname_o Y_25) ((semila1780557381name_o X_42) Y_25)))
% FOF formula (forall (Y_25:(hoare_1167836817_state->Prop)) (X_42:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o Y_25) ((semila1172322802tate_o X_42) Y_25))) of role axiom named fact_450_inf__sup__ord_I4_J
% A new axiom: (forall (Y_25:(hoare_1167836817_state->Prop)) (X_42:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o Y_25) ((semila1172322802tate_o X_42) Y_25)))
% FOF formula (forall (X_41:(pname->Prop)) (Y_24:(pname->Prop)), ((ord_less_eq_pname_o X_41) ((semila1780557381name_o X_41) Y_24))) of role axiom named fact_451_sup__ge1
% A new axiom: (forall (X_41:(pname->Prop)) (Y_24:(pname->Prop)), ((ord_less_eq_pname_o X_41) ((semila1780557381name_o X_41) Y_24)))
% FOF formula (forall (X_41:(hoare_1167836817_state->Prop)) (Y_24:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_41) ((semila1172322802tate_o X_41) Y_24))) of role axiom named fact_452_sup__ge1
% A new axiom: (forall (X_41:(hoare_1167836817_state->Prop)) (Y_24:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_41) ((semila1172322802tate_o X_41) Y_24)))
% FOF formula (forall (X_40:(pname->Prop)) (Y_23:(pname->Prop)), ((ord_less_eq_pname_o X_40) ((semila1780557381name_o X_40) Y_23))) of role axiom named fact_453_inf__sup__ord_I3_J
% A new axiom: (forall (X_40:(pname->Prop)) (Y_23:(pname->Prop)), ((ord_less_eq_pname_o X_40) ((semila1780557381name_o X_40) Y_23)))
% FOF formula (forall (X_40:(hoare_1167836817_state->Prop)) (Y_23:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_40) ((semila1172322802tate_o X_40) Y_23))) of role axiom named fact_454_inf__sup__ord_I3_J
% A new axiom: (forall (X_40:(hoare_1167836817_state->Prop)) (Y_23:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_40) ((semila1172322802tate_o X_40) Y_23)))
% FOF formula (forall (X_39:(pname->Prop)) (Y_22:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_39) Y_22)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_39) bot_bot_pname_o)) (((eq (pname->Prop)) Y_22) bot_bot_pname_o)))) of role axiom named fact_455_sup__eq__bot__iff
% A new axiom: (forall (X_39:(pname->Prop)) (Y_22:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_39) Y_22)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_39) bot_bot_pname_o)) (((eq (pname->Prop)) Y_22) bot_bot_pname_o))))
% FOF formula (forall (X_39:(hoare_1167836817_state->Prop)) (Y_22:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_39) Y_22)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) X_39) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) Y_22) bot_bo70021908tate_o)))) of role axiom named fact_456_sup__eq__bot__iff
% A new axiom: (forall (X_39:(hoare_1167836817_state->Prop)) (Y_22:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_39) Y_22)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) X_39) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) Y_22) bot_bo70021908tate_o))))
% FOF formula (forall (X_38:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_38) bot_bot_pname_o)) X_38)) of role axiom named fact_457_sup__bot__right
% A new axiom: (forall (X_38:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_38) bot_bot_pname_o)) X_38))
% FOF formula (forall (X_38:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_38) bot_bo70021908tate_o)) X_38)) of role axiom named fact_458_sup__bot__right
% A new axiom: (forall (X_38:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_38) bot_bo70021908tate_o)) X_38))
% FOF formula (forall (X_37:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) X_37)) X_37)) of role axiom named fact_459_sup__bot__left
% A new axiom: (forall (X_37:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) X_37)) X_37))
% FOF formula (forall (X_37:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) X_37)) X_37)) of role axiom named fact_460_sup__bot__left
% A new axiom: (forall (X_37:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) X_37)) X_37))
% FOF formula (forall (B_46:((pname->Prop)->Prop)) (A_64:((pname->Prop)->Prop)) (F_32:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_31:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_32) F_31)->((finite297249702name_o A_64)->((not (((eq ((pname->Prop)->Prop)) A_64) bot_bot_pname_o_o))->((finite297249702name_o B_46)->((not (((eq ((pname->Prop)->Prop)) B_46) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_31 ((semila181081674me_o_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46))))))))) of role axiom named fact_461_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_46:((pname->Prop)->Prop)) (A_64:((pname->Prop)->Prop)) (F_32:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_31:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_32) F_31)->((finite297249702name_o A_64)->((not (((eq ((pname->Prop)->Prop)) A_64) bot_bot_pname_o_o))->((finite297249702name_o B_46)->((not (((eq ((pname->Prop)->Prop)) B_46) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_31 ((semila181081674me_o_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46)))))))))
% FOF formula (forall (B_46:((hoare_1167836817_state->Prop)->Prop)) (A_64:((hoare_1167836817_state->Prop)->Prop)) (F_32:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_31:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_32) F_31)->((finite1380128977tate_o A_64)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_64) bot_bo691907561te_o_o))->((finite1380128977tate_o B_46)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_46) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_31 ((semila866907787te_o_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46))))))))) of role axiom named fact_462_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_46:((hoare_1167836817_state->Prop)->Prop)) (A_64:((hoare_1167836817_state->Prop)->Prop)) (F_32:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_31:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_32) F_31)->((finite1380128977tate_o A_64)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_64) bot_bo691907561te_o_o))->((finite1380128977tate_o B_46)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_46) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_31 ((semila866907787te_o_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46)))))))))
% FOF formula (forall (B_46:(pname->Prop)) (A_64:(pname->Prop)) (F_32:(pname->(pname->pname))) (F_31:((pname->Prop)->pname)), (((finite89670078_pname F_32) F_31)->((finite_finite_pname A_64)->((not (((eq (pname->Prop)) A_64) bot_bot_pname_o))->((finite_finite_pname B_46)->((not (((eq (pname->Prop)) B_46) bot_bot_pname_o))->(((eq pname) (F_31 ((semila1780557381name_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46))))))))) of role axiom named fact_463_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_46:(pname->Prop)) (A_64:(pname->Prop)) (F_32:(pname->(pname->pname))) (F_31:((pname->Prop)->pname)), (((finite89670078_pname F_32) F_31)->((finite_finite_pname A_64)->((not (((eq (pname->Prop)) A_64) bot_bot_pname_o))->((finite_finite_pname B_46)->((not (((eq (pname->Prop)) B_46) bot_bot_pname_o))->(((eq pname) (F_31 ((semila1780557381name_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46)))))))))
% FOF formula (forall (B_46:(hoare_1167836817_state->Prop)) (A_64:(hoare_1167836817_state->Prop)) (F_32:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_31:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_32) F_31)->((finite1084549118_state A_64)->((not (((eq (hoare_1167836817_state->Prop)) A_64) bot_bo70021908tate_o))->((finite1084549118_state B_46)->((not (((eq (hoare_1167836817_state->Prop)) B_46) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_31 ((semila1172322802tate_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46))))))))) of role axiom named fact_464_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_46:(hoare_1167836817_state->Prop)) (A_64:(hoare_1167836817_state->Prop)) (F_32:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_31:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_32) F_31)->((finite1084549118_state A_64)->((not (((eq (hoare_1167836817_state->Prop)) A_64) bot_bo70021908tate_o))->((finite1084549118_state B_46)->((not (((eq (hoare_1167836817_state->Prop)) B_46) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_31 ((semila1172322802tate_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46)))))))))
% FOF formula (forall (B_45:((pname->Prop)->Prop)) (A_63:((pname->Prop)->Prop)) (F_30:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_29:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_30) F_29)->((finite297249702name_o A_63)->((not (((eq ((pname->Prop)->Prop)) B_45) bot_bot_pname_o_o))->(((ord_le1205211808me_o_o B_45) A_63)->(((eq (pname->Prop)) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63))))))) of role axiom named fact_465_folding__one__idem_Osubset__idem
% A new axiom: (forall (B_45:((pname->Prop)->Prop)) (A_63:((pname->Prop)->Prop)) (F_30:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_29:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_30) F_29)->((finite297249702name_o A_63)->((not (((eq ((pname->Prop)->Prop)) B_45) bot_bot_pname_o_o))->(((ord_le1205211808me_o_o B_45) A_63)->(((eq (pname->Prop)) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63)))))))
% FOF formula (forall (B_45:((hoare_1167836817_state->Prop)->Prop)) (A_63:((hoare_1167836817_state->Prop)->Prop)) (F_30:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_29:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_30) F_29)->((finite1380128977tate_o A_63)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_45) bot_bo691907561te_o_o))->(((ord_le741939125te_o_o B_45) A_63)->(((eq (hoare_1167836817_state->Prop)) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63))))))) of role axiom named fact_466_folding__one__idem_Osubset__idem
% A new axiom: (forall (B_45:((hoare_1167836817_state->Prop)->Prop)) (A_63:((hoare_1167836817_state->Prop)->Prop)) (F_30:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_29:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_30) F_29)->((finite1380128977tate_o A_63)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_45) bot_bo691907561te_o_o))->(((ord_le741939125te_o_o B_45) A_63)->(((eq (hoare_1167836817_state->Prop)) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63)))))))
% FOF formula (forall (B_45:(pname->Prop)) (A_63:(pname->Prop)) (F_30:(pname->(pname->pname))) (F_29:((pname->Prop)->pname)), (((finite89670078_pname F_30) F_29)->((finite_finite_pname A_63)->((not (((eq (pname->Prop)) B_45) bot_bot_pname_o))->(((ord_less_eq_pname_o B_45) A_63)->(((eq pname) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63))))))) of role axiom named fact_467_folding__one__idem_Osubset__idem
% A new axiom: (forall (B_45:(pname->Prop)) (A_63:(pname->Prop)) (F_30:(pname->(pname->pname))) (F_29:((pname->Prop)->pname)), (((finite89670078_pname F_30) F_29)->((finite_finite_pname A_63)->((not (((eq (pname->Prop)) B_45) bot_bot_pname_o))->(((ord_less_eq_pname_o B_45) A_63)->(((eq pname) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63)))))))
% FOF formula (forall (B_45:(hoare_1167836817_state->Prop)) (A_63:(hoare_1167836817_state->Prop)) (F_30:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_29:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_30) F_29)->((finite1084549118_state A_63)->((not (((eq (hoare_1167836817_state->Prop)) B_45) bot_bo70021908tate_o))->(((ord_le827224136tate_o B_45) A_63)->(((eq hoare_1167836817_state) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63))))))) of role axiom named fact_468_folding__one__idem_Osubset__idem
% A new axiom: (forall (B_45:(hoare_1167836817_state->Prop)) (A_63:(hoare_1167836817_state->Prop)) (F_30:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_29:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_30) F_29)->((finite1084549118_state A_63)->((not (((eq (hoare_1167836817_state->Prop)) B_45) bot_bo70021908tate_o))->(((ord_le827224136tate_o B_45) A_63)->(((eq hoare_1167836817_state) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63)))))))
% FOF formula (forall (G_7:(hoare_1167836817_state->Prop)) (P_11:(state->(state->Prop))), ((hoare_123228589_state G_7) ((insert2134838167_state (((hoare_908217195_state P_11) skip) P_11)) bot_bo70021908tate_o))) of role axiom named fact_469_hoare__derivs_OSkip
% A new axiom: (forall (G_7:(hoare_1167836817_state->Prop)) (P_11:(state->(state->Prop))), ((hoare_123228589_state G_7) ((insert2134838167_state (((hoare_908217195_state P_11) skip) P_11)) bot_bo70021908tate_o)))
% FOF formula (forall (X_36:pname) (A_62:(pname->Prop)) (F_28:(pname->(pname->pname))) (F_27:((pname->Prop)->pname)), (((finite89670078_pname F_28) F_27)->((finite_finite_pname A_62)->((not (((eq (pname->Prop)) A_62) bot_bot_pname_o))->(((eq pname) (F_27 ((insert_pname X_36) A_62))) ((F_28 X_36) (F_27 A_62))))))) of role axiom named fact_470_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_36:pname) (A_62:(pname->Prop)) (F_28:(pname->(pname->pname))) (F_27:((pname->Prop)->pname)), (((finite89670078_pname F_28) F_27)->((finite_finite_pname A_62)->((not (((eq (pname->Prop)) A_62) bot_bot_pname_o))->(((eq pname) (F_27 ((insert_pname X_36) A_62))) ((F_28 X_36) (F_27 A_62)))))))
% FOF formula (forall (X_36:hoare_1167836817_state) (A_62:(hoare_1167836817_state->Prop)) (F_28:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_27:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_28) F_27)->((finite1084549118_state A_62)->((not (((eq (hoare_1167836817_state->Prop)) A_62) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_27 ((insert2134838167_state X_36) A_62))) ((F_28 X_36) (F_27 A_62))))))) of role axiom named fact_471_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_36:hoare_1167836817_state) (A_62:(hoare_1167836817_state->Prop)) (F_28:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_27:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_28) F_27)->((finite1084549118_state A_62)->((not (((eq (hoare_1167836817_state->Prop)) A_62) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_27 ((insert2134838167_state X_36) A_62))) ((F_28 X_36) (F_27 A_62)))))))
% FOF formula (forall (X_36:(pname->Prop)) (A_62:((pname->Prop)->Prop)) (F_28:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_27:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_28) F_27)->((finite297249702name_o A_62)->((not (((eq ((pname->Prop)->Prop)) A_62) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_27 ((insert_pname_o X_36) A_62))) ((F_28 X_36) (F_27 A_62))))))) of role axiom named fact_472_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_36:(pname->Prop)) (A_62:((pname->Prop)->Prop)) (F_28:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_27:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_28) F_27)->((finite297249702name_o A_62)->((not (((eq ((pname->Prop)->Prop)) A_62) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_27 ((insert_pname_o X_36) A_62))) ((F_28 X_36) (F_27 A_62)))))))
% FOF formula (forall (X_36:(hoare_1167836817_state->Prop)) (A_62:((hoare_1167836817_state->Prop)->Prop)) (F_28:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_27:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_28) F_27)->((finite1380128977tate_o A_62)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_62) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_27 ((insert999278200tate_o X_36) A_62))) ((F_28 X_36) (F_27 A_62))))))) of role axiom named fact_473_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_36:(hoare_1167836817_state->Prop)) (A_62:((hoare_1167836817_state->Prop)->Prop)) (F_28:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_27:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_28) F_27)->((finite1380128977tate_o A_62)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_62) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_27 ((insert999278200tate_o X_36) A_62))) ((F_28 X_36) (F_27 A_62)))))))
% FOF formula (forall (P_10:((pname->Prop)->Prop)) (F_25:(pname->Prop)), ((finite_finite_pname F_25)->((not (((eq (pname->Prop)) F_25) bot_bot_pname_o))->((forall (X_5:pname), (P_10 ((insert_pname X_5) bot_bot_pname_o)))->((forall (X_5:pname) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->((not (((eq (pname->Prop)) F_26) bot_bot_pname_o))->((((member_pname X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert_pname X_5) F_26)))))))->(P_10 F_25)))))) of role axiom named fact_474_finite__ne__induct
% A new axiom: (forall (P_10:((pname->Prop)->Prop)) (F_25:(pname->Prop)), ((finite_finite_pname F_25)->((not (((eq (pname->Prop)) F_25) bot_bot_pname_o))->((forall (X_5:pname), (P_10 ((insert_pname X_5) bot_bot_pname_o)))->((forall (X_5:pname) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->((not (((eq (pname->Prop)) F_26) bot_bot_pname_o))->((((member_pname X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert_pname X_5) F_26)))))))->(P_10 F_25))))))
% FOF formula (forall (P_10:((hoare_1167836817_state->Prop)->Prop)) (F_25:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_25)->((not (((eq (hoare_1167836817_state->Prop)) F_25) bot_bo70021908tate_o))->((forall (X_5:hoare_1167836817_state), (P_10 ((insert2134838167_state X_5) bot_bo70021908tate_o)))->((forall (X_5:hoare_1167836817_state) (F_26:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_26)->((not (((eq (hoare_1167836817_state->Prop)) F_26) bot_bo70021908tate_o))->((((member2058392318_state X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert2134838167_state X_5) F_26)))))))->(P_10 F_25)))))) of role axiom named fact_475_finite__ne__induct
% A new axiom: (forall (P_10:((hoare_1167836817_state->Prop)->Prop)) (F_25:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_25)->((not (((eq (hoare_1167836817_state->Prop)) F_25) bot_bo70021908tate_o))->((forall (X_5:hoare_1167836817_state), (P_10 ((insert2134838167_state X_5) bot_bo70021908tate_o)))->((forall (X_5:hoare_1167836817_state) (F_26:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_26)->((not (((eq (hoare_1167836817_state->Prop)) F_26) bot_bo70021908tate_o))->((((member2058392318_state X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert2134838167_state X_5) F_26)))))))->(P_10 F_25))))))
% FOF formula (forall (P_10:(((pname->Prop)->Prop)->Prop)) (F_25:((pname->Prop)->Prop)), ((finite297249702name_o F_25)->((not (((eq ((pname->Prop)->Prop)) F_25) bot_bot_pname_o_o))->((forall (X_5:(pname->Prop)), (P_10 ((insert_pname_o X_5) bot_bot_pname_o_o)))->((forall (X_5:(pname->Prop)) (F_26:((pname->Prop)->Prop)), ((finite297249702name_o F_26)->((not (((eq ((pname->Prop)->Prop)) F_26) bot_bot_pname_o_o))->((((member_pname_o X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert_pname_o X_5) F_26)))))))->(P_10 F_25)))))) of role axiom named fact_476_finite__ne__induct
% A new axiom: (forall (P_10:(((pname->Prop)->Prop)->Prop)) (F_25:((pname->Prop)->Prop)), ((finite297249702name_o F_25)->((not (((eq ((pname->Prop)->Prop)) F_25) bot_bot_pname_o_o))->((forall (X_5:(pname->Prop)), (P_10 ((insert_pname_o X_5) bot_bot_pname_o_o)))->((forall (X_5:(pname->Prop)) (F_26:((pname->Prop)->Prop)), ((finite297249702name_o F_26)->((not (((eq ((pname->Prop)->Prop)) F_26) bot_bot_pname_o_o))->((((member_pname_o X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert_pname_o X_5) F_26)))))))->(P_10 F_25))))))
% FOF formula (forall (P_10:(((hoare_1167836817_state->Prop)->Prop)->Prop)) (F_25:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_25)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) F_25) bot_bo691907561te_o_o))->((forall (X_5:(hoare_1167836817_state->Prop)), (P_10 ((insert999278200tate_o X_5) bot_bo691907561te_o_o)))->((forall (X_5:(hoare_1167836817_state->Prop)) (F_26:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_26)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) F_26) bot_bo691907561te_o_o))->((((member864234961tate_o X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert999278200tate_o X_5) F_26)))))))->(P_10 F_25)))))) of role axiom named fact_477_finite__ne__induct
% A new axiom: (forall (P_10:(((hoare_1167836817_state->Prop)->Prop)->Prop)) (F_25:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_25)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) F_25) bot_bo691907561te_o_o))->((forall (X_5:(hoare_1167836817_state->Prop)), (P_10 ((insert999278200tate_o X_5) bot_bo691907561te_o_o)))->((forall (X_5:(hoare_1167836817_state->Prop)) (F_26:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_26)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) F_26) bot_bo691907561te_o_o))->((((member864234961tate_o X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert999278200tate_o X_5) F_26)))))))->(P_10 F_25))))))
% FOF formula (forall (Pname:pname), (not (((eq com) (body_1 Pname)) skip))) of role axiom named fact_478_com_Osimps_I19_J
% A new axiom: (forall (Pname:pname), (not (((eq com) (body_1 Pname)) skip)))
% FOF formula (forall (Pname:pname), (not (((eq com) skip) (body_1 Pname)))) of role axiom named fact_479_com_Osimps_I18_J
% A new axiom: (forall (Pname:pname), (not (((eq com) skip) (body_1 Pname))))
% FOF formula (wt skip) of role axiom named fact_480_WT_OSkip
% A new axiom: (wt skip)
% FOF formula (forall (X_35:pname) (A_61:(pname->Prop)) (F_24:(pname->(pname->pname))) (F_23:((pname->Prop)->pname)), (((finite89670078_pname F_24) F_23)->((finite_finite_pname A_61)->(((member_pname X_35) A_61)->(((eq pname) ((F_24 X_35) (F_23 A_61))) (F_23 A_61)))))) of role axiom named fact_481_folding__one__idem_Oin__idem
% A new axiom: (forall (X_35:pname) (A_61:(pname->Prop)) (F_24:(pname->(pname->pname))) (F_23:((pname->Prop)->pname)), (((finite89670078_pname F_24) F_23)->((finite_finite_pname A_61)->(((member_pname X_35) A_61)->(((eq pname) ((F_24 X_35) (F_23 A_61))) (F_23 A_61))))))
% FOF formula (forall (X_35:hoare_1167836817_state) (A_61:(hoare_1167836817_state->Prop)) (F_24:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_23:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_24) F_23)->((finite1084549118_state A_61)->(((member2058392318_state X_35) A_61)->(((eq hoare_1167836817_state) ((F_24 X_35) (F_23 A_61))) (F_23 A_61)))))) of role axiom named fact_482_folding__one__idem_Oin__idem
% A new axiom: (forall (X_35:hoare_1167836817_state) (A_61:(hoare_1167836817_state->Prop)) (F_24:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_23:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_24) F_23)->((finite1084549118_state A_61)->(((member2058392318_state X_35) A_61)->(((eq hoare_1167836817_state) ((F_24 X_35) (F_23 A_61))) (F_23 A_61))))))
% FOF formula (forall (X_35:(pname->Prop)) (A_61:((pname->Prop)->Prop)) (F_24:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_23:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_24) F_23)->((finite297249702name_o A_61)->(((member_pname_o X_35) A_61)->(((eq (pname->Prop)) ((F_24 X_35) (F_23 A_61))) (F_23 A_61)))))) of role axiom named fact_483_folding__one__idem_Oin__idem
% A new axiom: (forall (X_35:(pname->Prop)) (A_61:((pname->Prop)->Prop)) (F_24:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_23:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_24) F_23)->((finite297249702name_o A_61)->(((member_pname_o X_35) A_61)->(((eq (pname->Prop)) ((F_24 X_35) (F_23 A_61))) (F_23 A_61))))))
% FOF formula (forall (X_35:(hoare_1167836817_state->Prop)) (A_61:((hoare_1167836817_state->Prop)->Prop)) (F_24:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_23:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_24) F_23)->((finite1380128977tate_o A_61)->(((member864234961tate_o X_35) A_61)->(((eq (hoare_1167836817_state->Prop)) ((F_24 X_35) (F_23 A_61))) (F_23 A_61)))))) of role axiom named fact_484_folding__one__idem_Oin__idem
% A new axiom: (forall (X_35:(hoare_1167836817_state->Prop)) (A_61:((hoare_1167836817_state->Prop)->Prop)) (F_24:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_23:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_24) F_23)->((finite1380128977tate_o A_61)->(((member864234961tate_o X_35) A_61)->(((eq (hoare_1167836817_state->Prop)) ((F_24 X_35) (F_23 A_61))) (F_23 A_61))))))
% FOF formula (forall (N_1:((pname->Prop)->Prop)) (H:((pname->Prop)->(pname->Prop))) (F_22:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_21:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_22) F_21)->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), (((eq (pname->Prop)) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite297249702name_o N_1)->((not (((eq ((pname->Prop)->Prop)) N_1) bot_bot_pname_o_o))->(((eq (pname->Prop)) (H (F_21 N_1))) (F_21 ((image_1085733413name_o H) N_1)))))))) of role axiom named fact_485_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_1:((pname->Prop)->Prop)) (H:((pname->Prop)->(pname->Prop))) (F_22:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_21:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_22) F_21)->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), (((eq (pname->Prop)) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite297249702name_o N_1)->((not (((eq ((pname->Prop)->Prop)) N_1) bot_bot_pname_o_o))->(((eq (pname->Prop)) (H (F_21 N_1))) (F_21 ((image_1085733413name_o H) N_1))))))))
% FOF formula (forall (N_1:((hoare_1167836817_state->Prop)->Prop)) (H:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (F_22:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_21:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_22) F_21)->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite1380128977tate_o N_1)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) N_1) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (H (F_21 N_1))) (F_21 ((image_1488525317tate_o H) N_1)))))))) of role axiom named fact_486_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_1:((hoare_1167836817_state->Prop)->Prop)) (H:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (F_22:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_21:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_22) F_21)->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite1380128977tate_o N_1)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) N_1) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (H (F_21 N_1))) (F_21 ((image_1488525317tate_o H) N_1))))))))
% FOF formula (forall (N_1:(pname->Prop)) (H:(pname->pname)) (F_22:(pname->(pname->pname))) (F_21:((pname->Prop)->pname)), (((finite89670078_pname F_22) F_21)->((forall (X_5:pname) (Y_2:pname), (((eq pname) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite_finite_pname N_1)->((not (((eq (pname->Prop)) N_1) bot_bot_pname_o))->(((eq pname) (H (F_21 N_1))) (F_21 ((image_pname_pname H) N_1)))))))) of role axiom named fact_487_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_1:(pname->Prop)) (H:(pname->pname)) (F_22:(pname->(pname->pname))) (F_21:((pname->Prop)->pname)), (((finite89670078_pname F_22) F_21)->((forall (X_5:pname) (Y_2:pname), (((eq pname) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite_finite_pname N_1)->((not (((eq (pname->Prop)) N_1) bot_bot_pname_o))->(((eq pname) (H (F_21 N_1))) (F_21 ((image_pname_pname H) N_1))))))))
% FOF formula (forall (N_1:(hoare_1167836817_state->Prop)) (H:(hoare_1167836817_state->hoare_1167836817_state)) (F_22:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_21:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_22) F_21)->((forall (X_5:hoare_1167836817_state) (Y_2:hoare_1167836817_state), (((eq hoare_1167836817_state) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite1084549118_state N_1)->((not (((eq (hoare_1167836817_state->Prop)) N_1) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (H (F_21 N_1))) (F_21 ((image_31595733_state H) N_1)))))))) of role axiom named fact_488_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_1:(hoare_1167836817_state->Prop)) (H:(hoare_1167836817_state->hoare_1167836817_state)) (F_22:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_21:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_22) F_21)->((forall (X_5:hoare_1167836817_state) (Y_2:hoare_1167836817_state), (((eq hoare_1167836817_state) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite1084549118_state N_1)->((not (((eq (hoare_1167836817_state->Prop)) N_1) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (H (F_21 N_1))) (F_21 ((image_31595733_state H) N_1))))))))
% FOF formula (forall (G_6:(hoare_1167836817_state->Prop)) (P_9:(state->(state->Prop))) (B_44:(state->Prop)) (C_23:com), ((hoare_123228589_state G_6) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S_3:state)=> ((and ((P_9 Z_11) S_3)) (not (B_44 S_3))))) ((while B_44) C_23)) P_9)) bot_bo70021908tate_o))) of role axiom named fact_489_LoopF
% A new axiom: (forall (G_6:(hoare_1167836817_state->Prop)) (P_9:(state->(state->Prop))) (B_44:(state->Prop)) (C_23:com), ((hoare_123228589_state G_6) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S_3:state)=> ((and ((P_9 Z_11) S_3)) (not (B_44 S_3))))) ((while B_44) C_23)) P_9)) bot_bo70021908tate_o)))
% FOF formula (forall (D_2:com) (R_1:(state->(state->Prop))) (G_5:(hoare_1167836817_state->Prop)) (P_8:(state->(state->Prop))) (C_22:com) (Q_4:(state->(state->Prop))), (((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state P_8) C_22) Q_4)) bot_bo70021908tate_o))->(((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state Q_4) D_2) R_1)) bot_bo70021908tate_o))->((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state P_8) ((semi C_22) D_2)) R_1)) bot_bo70021908tate_o))))) of role axiom named fact_490_Comp
% A new axiom: (forall (D_2:com) (R_1:(state->(state->Prop))) (G_5:(hoare_1167836817_state->Prop)) (P_8:(state->(state->Prop))) (C_22:com) (Q_4:(state->(state->Prop))), (((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state P_8) C_22) Q_4)) bot_bo70021908tate_o))->(((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state Q_4) D_2) R_1)) bot_bo70021908tate_o))->((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state P_8) ((semi C_22) D_2)) R_1)) bot_bo70021908tate_o)))))
% FOF formula (forall (X_34:(pname->Prop)), (((eq pname) (the_elem_pname X_34)) (the_pname (fun (X_5:pname)=> (((eq (pname->Prop)) X_34) ((insert_pname X_5) bot_bot_pname_o)))))) of role axiom named fact_491_the__elem__def
% A new axiom: (forall (X_34:(pname->Prop)), (((eq pname) (the_elem_pname X_34)) (the_pname (fun (X_5:pname)=> (((eq (pname->Prop)) X_34) ((insert_pname X_5) bot_bot_pname_o))))))
% FOF formula (forall (X_34:(hoare_1167836817_state->Prop)), (((eq hoare_1167836817_state) (the_el323660082_state X_34)) (the_Ho310147232_state (fun (X_5:hoare_1167836817_state)=> (((eq (hoare_1167836817_state->Prop)) X_34) ((insert2134838167_state X_5) bot_bo70021908tate_o)))))) of role axiom named fact_492_the__elem__def
% A new axiom: (forall (X_34:(hoare_1167836817_state->Prop)), (((eq hoare_1167836817_state) (the_el323660082_state X_34)) (the_Ho310147232_state (fun (X_5:hoare_1167836817_state)=> (((eq (hoare_1167836817_state->Prop)) X_34) ((insert2134838167_state X_5) bot_bo70021908tate_o))))))
% FOF formula (forall (B_42:(state->Prop)) (C_21:com), ((wt ((while B_42) C_21))->(wt C_21))) of role axiom named fact_493_WTs__elim__cases_I6_J
% A new axiom: (forall (B_42:(state->Prop)) (C_21:com), ((wt ((while B_42) C_21))->(wt C_21)))
% FOF formula (forall (C1:com) (C2:com), ((wt ((semi C1) C2))->(((wt C1)->((wt C2)->False))->False))) of role axiom named fact_494_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 (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com_1:com), (not (((eq com) ((semi Com1_1) Com2_1)) ((while Fun) Com_1)))) of role axiom named fact_495_com_Osimps_I46_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com_1:com), (not (((eq com) ((semi Com1_1) Com2_1)) ((while Fun) Com_1))))
% FOF formula (forall (Fun:(state->Prop)) (Com_1:com) (Com1_1:com) (Com2_1:com), (not (((eq com) ((while Fun) Com_1)) ((semi Com1_1) Com2_1)))) of role axiom named fact_496_com_Osimps_I47_J
% A new axiom: (forall (Fun:(state->Prop)) (Com_1:com) (Com1_1:com) (Com2_1:com), (not (((eq com) ((while Fun) Com_1)) ((semi Com1_1) Com2_1))))
% FOF formula (forall (Com1_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2)))) of role axiom named fact_497_com_Osimps_I3_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_2:com) (Fun:(state->Prop)) (Com_1:com), ((iff (((eq com) ((while Fun_1) Com_2)) ((while Fun) Com_1))) ((and (((eq (state->Prop)) Fun_1) Fun)) (((eq com) Com_2) Com_1)))) of role axiom named fact_498_com_Osimps_I5_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_2:com) (Fun:(state->Prop)) (Com_1:com), ((iff (((eq com) ((while Fun_1) Com_2)) ((while Fun) Com_1))) ((and (((eq (state->Prop)) Fun_1) Fun)) (((eq com) Com_2) Com_1))))
% FOF formula (forall (Pname:pname) (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) (body_1 Pname)) ((while Fun_1) Com_2)))) of role axiom named fact_499_com_Osimps_I59_J
% A new axiom: (forall (Pname:pname) (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) (body_1 Pname)) ((while Fun_1) Com_2))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_2:com) (Pname:pname), (not (((eq com) ((while Fun_1) Com_2)) (body_1 Pname)))) of role axiom named fact_500_com_Osimps_I58_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_2:com) (Pname:pname), (not (((eq com) ((while Fun_1) Com_2)) (body_1 Pname))))
% FOF formula (forall (B_42:(state->Prop)) (C_21:com), ((wt C_21)->(wt ((while B_42) C_21)))) of role axiom named fact_501_While
% A new axiom: (forall (B_42:(state->Prop)) (C_21:com), ((wt C_21)->(wt ((while B_42) C_21))))
% FOF formula (forall (Fun:(state->Prop)) (Com_1:com), (not (((eq com) skip) ((while Fun) Com_1)))) of role axiom named fact_502_com_Osimps_I16_J
% A new axiom: (forall (Fun:(state->Prop)) (Com_1:com), (not (((eq com) skip) ((while Fun) Com_1))))
% FOF formula (forall (Fun:(state->Prop)) (Com_1:com), (not (((eq com) ((while Fun) Com_1)) skip))) of role axiom named fact_503_com_Osimps_I17_J
% A new axiom: (forall (Fun:(state->Prop)) (Com_1:com), (not (((eq com) ((while Fun) Com_1)) skip)))
% FOF formula (forall (Pname:pname) (Com1_1:com) (Com2_1:com), (not (((eq com) (body_1 Pname)) ((semi Com1_1) Com2_1)))) of role axiom named fact_504_com_Osimps_I49_J
% A new axiom: (forall (Pname:pname) (Com1_1:com) (Com2_1:com), (not (((eq com) (body_1 Pname)) ((semi Com1_1) Com2_1))))
% FOF formula (forall (Com1_1:com) (Com2_1:com) (Pname:pname), (not (((eq com) ((semi Com1_1) Com2_1)) (body_1 Pname)))) of role axiom named fact_505_com_Osimps_I48_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com) (Pname:pname), (not (((eq com) ((semi Com1_1) Com2_1)) (body_1 Pname))))
% FOF formula (forall (C1:com) (C0:com), ((wt C0)->((wt C1)->(wt ((semi C0) C1))))) of role axiom named fact_506_WT_OSemi
% A new axiom: (forall (C1:com) (C0:com), ((wt C0)->((wt C1)->(wt ((semi C0) C1)))))
% FOF formula (forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2)))) of role axiom named fact_507_com_Osimps_I12_J
% A new axiom: (forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2))))
% FOF formula (forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip))) of role axiom named fact_508_com_Osimps_I13_J
% A new axiom: (forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip)))
% FOF formula (forall (X_33:pname) (A_60:(pname->Prop)) (F_20:(pname->(pname->pname))) (F_19:((pname->Prop)->pname)), (((finite1282449217_pname F_20) F_19)->((finite_finite_pname A_60)->((((member_pname X_33) A_60)->False)->((not (((eq (pname->Prop)) A_60) bot_bot_pname_o))->(((eq pname) (F_19 ((insert_pname X_33) A_60))) ((F_20 X_33) (F_19 A_60)))))))) of role axiom named fact_509_folding__one_Oinsert
% A new axiom: (forall (X_33:pname) (A_60:(pname->Prop)) (F_20:(pname->(pname->pname))) (F_19:((pname->Prop)->pname)), (((finite1282449217_pname F_20) F_19)->((finite_finite_pname A_60)->((((member_pname X_33) A_60)->False)->((not (((eq (pname->Prop)) A_60) bot_bot_pname_o))->(((eq pname) (F_19 ((insert_pname X_33) A_60))) ((F_20 X_33) (F_19 A_60))))))))
% FOF formula (forall (X_33:hoare_1167836817_state) (A_60:(hoare_1167836817_state->Prop)) (F_20:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_19:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_20) F_19)->((finite1084549118_state A_60)->((((member2058392318_state X_33) A_60)->False)->((not (((eq (hoare_1167836817_state->Prop)) A_60) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_19 ((insert2134838167_state X_33) A_60))) ((F_20 X_33) (F_19 A_60)))))))) of role axiom named fact_510_folding__one_Oinsert
% A new axiom: (forall (X_33:hoare_1167836817_state) (A_60:(hoare_1167836817_state->Prop)) (F_20:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_19:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_20) F_19)->((finite1084549118_state A_60)->((((member2058392318_state X_33) A_60)->False)->((not (((eq (hoare_1167836817_state->Prop)) A_60) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_19 ((insert2134838167_state X_33) A_60))) ((F_20 X_33) (F_19 A_60))))))))
% FOF formula (forall (X_33:(pname->Prop)) (A_60:((pname->Prop)->Prop)) (F_20:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_19:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_20) F_19)->((finite297249702name_o A_60)->((((member_pname_o X_33) A_60)->False)->((not (((eq ((pname->Prop)->Prop)) A_60) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_19 ((insert_pname_o X_33) A_60))) ((F_20 X_33) (F_19 A_60)))))))) of role axiom named fact_511_folding__one_Oinsert
% A new axiom: (forall (X_33:(pname->Prop)) (A_60:((pname->Prop)->Prop)) (F_20:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_19:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_20) F_19)->((finite297249702name_o A_60)->((((member_pname_o X_33) A_60)->False)->((not (((eq ((pname->Prop)->Prop)) A_60) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_19 ((insert_pname_o X_33) A_60))) ((F_20 X_33) (F_19 A_60))))))))
% FOF formula (forall (X_33:(hoare_1167836817_state->Prop)) (A_60:((hoare_1167836817_state->Prop)->Prop)) (F_20:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_19:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_20) F_19)->((finite1380128977tate_o A_60)->((((member864234961tate_o X_33) A_60)->False)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_60) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_19 ((insert999278200tate_o X_33) A_60))) ((F_20 X_33) (F_19 A_60)))))))) of role axiom named fact_512_folding__one_Oinsert
% A new axiom: (forall (X_33:(hoare_1167836817_state->Prop)) (A_60:((hoare_1167836817_state->Prop)->Prop)) (F_20:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_19:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_20) F_19)->((finite1380128977tate_o A_60)->((((member864234961tate_o X_33) A_60)->False)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_60) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_19 ((insert999278200tate_o X_33) A_60))) ((F_20 X_33) (F_19 A_60))))))))
% FOF formula (forall (X_32:pname) (F_18:(pname->(pname->pname))) (F_17:((pname->Prop)->pname)), (((finite1282449217_pname F_18) F_17)->(((eq pname) (F_17 ((insert_pname X_32) bot_bot_pname_o))) X_32))) of role axiom named fact_513_folding__one_Osingleton
% A new axiom: (forall (X_32:pname) (F_18:(pname->(pname->pname))) (F_17:((pname->Prop)->pname)), (((finite1282449217_pname F_18) F_17)->(((eq pname) (F_17 ((insert_pname X_32) bot_bot_pname_o))) X_32)))
% FOF formula (forall (X_32:hoare_1167836817_state) (F_18:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_17:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_18) F_17)->(((eq hoare_1167836817_state) (F_17 ((insert2134838167_state X_32) bot_bo70021908tate_o))) X_32))) of role axiom named fact_514_folding__one_Osingleton
% A new axiom: (forall (X_32:hoare_1167836817_state) (F_18:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_17:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_18) F_17)->(((eq hoare_1167836817_state) (F_17 ((insert2134838167_state X_32) bot_bo70021908tate_o))) X_32)))
% FOF formula (forall (A_59:(pname->Prop)) (F_16:(pname->(pname->pname))) (F_15:((pname->Prop)->pname)), (((finite1282449217_pname F_16) F_15)->((finite_finite_pname A_59)->((not (((eq (pname->Prop)) A_59) bot_bot_pname_o))->((forall (X_5:pname) (Y_2:pname), ((member_pname ((F_16 X_5) Y_2)) ((insert_pname X_5) ((insert_pname Y_2) bot_bot_pname_o))))->((member_pname (F_15 A_59)) A_59)))))) of role axiom named fact_515_folding__one_Oclosed
% A new axiom: (forall (A_59:(pname->Prop)) (F_16:(pname->(pname->pname))) (F_15:((pname->Prop)->pname)), (((finite1282449217_pname F_16) F_15)->((finite_finite_pname A_59)->((not (((eq (pname->Prop)) A_59) bot_bot_pname_o))->((forall (X_5:pname) (Y_2:pname), ((member_pname ((F_16 X_5) Y_2)) ((insert_pname X_5) ((insert_pname Y_2) bot_bot_pname_o))))->((member_pname (F_15 A_59)) A_59))))))
% FOF formula (forall (A_59:(hoare_1167836817_state->Prop)) (F_16:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_15:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_16) F_15)->((finite1084549118_state A_59)->((not (((eq (hoare_1167836817_state->Prop)) A_59) bot_bo70021908tate_o))->((forall (X_5:hoare_1167836817_state) (Y_2:hoare_1167836817_state), ((member2058392318_state ((F_16 X_5) Y_2)) ((insert2134838167_state X_5) ((insert2134838167_state Y_2) bot_bo70021908tate_o))))->((member2058392318_state (F_15 A_59)) A_59)))))) of role axiom named fact_516_folding__one_Oclosed
% A new axiom: (forall (A_59:(hoare_1167836817_state->Prop)) (F_16:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_15:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_16) F_15)->((finite1084549118_state A_59)->((not (((eq (hoare_1167836817_state->Prop)) A_59) bot_bo70021908tate_o))->((forall (X_5:hoare_1167836817_state) (Y_2:hoare_1167836817_state), ((member2058392318_state ((F_16 X_5) Y_2)) ((insert2134838167_state X_5) ((insert2134838167_state Y_2) bot_bo70021908tate_o))))->((member2058392318_state (F_15 A_59)) A_59))))))
% FOF formula (forall (A_59:((pname->Prop)->Prop)) (F_16:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_15:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_16) F_15)->((finite297249702name_o A_59)->((not (((eq ((pname->Prop)->Prop)) A_59) bot_bot_pname_o_o))->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), ((member_pname_o ((F_16 X_5) Y_2)) ((insert_pname_o X_5) ((insert_pname_o Y_2) bot_bot_pname_o_o))))->((member_pname_o (F_15 A_59)) A_59)))))) of role axiom named fact_517_folding__one_Oclosed
% A new axiom: (forall (A_59:((pname->Prop)->Prop)) (F_16:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_15:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_16) F_15)->((finite297249702name_o A_59)->((not (((eq ((pname->Prop)->Prop)) A_59) bot_bot_pname_o_o))->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), ((member_pname_o ((F_16 X_5) Y_2)) ((insert_pname_o X_5) ((insert_pname_o Y_2) bot_bot_pname_o_o))))->((member_pname_o (F_15 A_59)) A_59))))))
% FOF formula (forall (A_59:((hoare_1167836817_state->Prop)->Prop)) (F_16:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_15:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_16) F_15)->((finite1380128977tate_o A_59)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_59) bot_bo691907561te_o_o))->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), ((member864234961tate_o ((F_16 X_5) Y_2)) ((insert999278200tate_o X_5) ((insert999278200tate_o Y_2) bot_bo691907561te_o_o))))->((member864234961tate_o (F_15 A_59)) A_59)))))) of role axiom named fact_518_folding__one_Oclosed
% A new axiom: (forall (A_59:((hoare_1167836817_state->Prop)->Prop)) (F_16:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_15:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_16) F_15)->((finite1380128977tate_o A_59)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_59) bot_bo691907561te_o_o))->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), ((member864234961tate_o ((F_16 X_5) Y_2)) ((insert999278200tate_o X_5) ((insert999278200tate_o Y_2) bot_bo691907561te_o_o))))->((member864234961tate_o (F_15 A_59)) A_59))))))
% FOF formula (forall (Y_21:hoare_1167836817_state), ((forall (Fun1:(state->(state->Prop))) (Com:com) (Fun2:(state->(state->Prop))), (not (((eq hoare_1167836817_state) Y_21) (((hoare_908217195_state Fun1) Com) Fun2))))->False)) of role axiom named fact_519_triple_Oexhaust
% A new axiom: (forall (Y_21:hoare_1167836817_state), ((forall (Fun1:(state->(state->Prop))) (Com:com) (Fun2:(state->(state->Prop))), (not (((eq hoare_1167836817_state) Y_21) (((hoare_908217195_state Fun1) Com) Fun2))))->False))
% FOF formula (forall (F_14:(pname->hoare_1167836817_state)) (G_4:(pname->hoare_1167836817_state)) (M:(pname->Prop)) (N:(pname->Prop)), ((((eq (pname->Prop)) M) N)->((forall (X_5:pname), (((member_pname X_5) N)->(((eq hoare_1167836817_state) (F_14 X_5)) (G_4 X_5))))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_14) M)) ((image_575578384_state G_4) N))))) of role axiom named fact_520_image__cong
% A new axiom: (forall (F_14:(pname->hoare_1167836817_state)) (G_4:(pname->hoare_1167836817_state)) (M:(pname->Prop)) (N:(pname->Prop)), ((((eq (pname->Prop)) M) N)->((forall (X_5:pname), (((member_pname X_5) N)->(((eq hoare_1167836817_state) (F_14 X_5)) (G_4 X_5))))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_14) M)) ((image_575578384_state G_4) N)))))
% FOF formula (forall (Q_3:(hoare_1167836817_state->Prop)) (P_7:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), ((P_7 X_5)->(Q_3 X_5)))->((ord_le827224136tate_o (collec1027672124_state P_7)) (collec1027672124_state Q_3)))) of role axiom named fact_521_Collect__mono
% A new axiom: (forall (Q_3:(hoare_1167836817_state->Prop)) (P_7:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), ((P_7 X_5)->(Q_3 X_5)))->((ord_le827224136tate_o (collec1027672124_state P_7)) (collec1027672124_state Q_3))))
% FOF formula (forall (Q_3:(pname->Prop)) (P_7:(pname->Prop)), ((forall (X_5:pname), ((P_7 X_5)->(Q_3 X_5)))->((ord_less_eq_pname_o (collect_pname P_7)) (collect_pname Q_3)))) of role axiom named fact_522_Collect__mono
% A new axiom: (forall (Q_3:(pname->Prop)) (P_7:(pname->Prop)), ((forall (X_5:pname), ((P_7 X_5)->(Q_3 X_5)))->((ord_less_eq_pname_o (collect_pname P_7)) (collect_pname Q_3))))
% FOF formula (forall (Q_3:((pname->Prop)->Prop)) (P_7:((pname->Prop)->Prop)), ((forall (X_5:(pname->Prop)), ((P_7 X_5)->(Q_3 X_5)))->((ord_le1205211808me_o_o (collect_pname_o P_7)) (collect_pname_o Q_3)))) of role axiom named fact_523_Collect__mono
% A new axiom: (forall (Q_3:((pname->Prop)->Prop)) (P_7:((pname->Prop)->Prop)), ((forall (X_5:(pname->Prop)), ((P_7 X_5)->(Q_3 X_5)))->((ord_le1205211808me_o_o (collect_pname_o P_7)) (collect_pname_o Q_3))))
% FOF formula (forall (Q_3:((hoare_1167836817_state->Prop)->Prop)) (P_7:((hoare_1167836817_state->Prop)->Prop)), ((forall (X_5:(hoare_1167836817_state->Prop)), ((P_7 X_5)->(Q_3 X_5)))->((ord_le741939125te_o_o (collec269976083tate_o P_7)) (collec269976083tate_o Q_3)))) of role axiom named fact_524_Collect__mono
% A new axiom: (forall (Q_3:((hoare_1167836817_state->Prop)->Prop)) (P_7:((hoare_1167836817_state->Prop)->Prop)), ((forall (X_5:(hoare_1167836817_state->Prop)), ((P_7 X_5)->(Q_3 X_5)))->((ord_le741939125te_o_o (collec269976083tate_o P_7)) (collec269976083tate_o Q_3))))
% FOF formula (forall (Q_2:(pname->Prop)) (P_6:(pname->Prop)), ((forall (X_5:pname), ((P_6 X_5)->(Q_2 X_5)))->((ord_less_eq_pname_o P_6) Q_2))) of role axiom named fact_525_predicate1I
% A new axiom: (forall (Q_2:(pname->Prop)) (P_6:(pname->Prop)), ((forall (X_5:pname), ((P_6 X_5)->(Q_2 X_5)))->((ord_less_eq_pname_o P_6) Q_2)))
% FOF formula (forall (Q_2:(hoare_1167836817_state->Prop)) (P_6:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), ((P_6 X_5)->(Q_2 X_5)))->((ord_le827224136tate_o P_6) Q_2))) of role axiom named fact_526_predicate1I
% A new axiom: (forall (Q_2:(hoare_1167836817_state->Prop)) (P_6:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), ((P_6 X_5)->(Q_2 X_5)))->((ord_le827224136tate_o P_6) Q_2)))
% FOF formula (forall (A_58:pname) (A_57:(pname->Prop)), (((member_pname A_58) A_57)->((ex (pname->Prop)) (fun (B_43:(pname->Prop))=> ((and (((eq (pname->Prop)) A_57) ((insert_pname A_58) B_43))) (((member_pname A_58) B_43)->False)))))) of role axiom named fact_527_mk__disjoint__insert
% A new axiom: (forall (A_58:pname) (A_57:(pname->Prop)), (((member_pname A_58) A_57)->((ex (pname->Prop)) (fun (B_43:(pname->Prop))=> ((and (((eq (pname->Prop)) A_57) ((insert_pname A_58) B_43))) (((member_pname A_58) B_43)->False))))))
% FOF formula (forall (A_58:hoare_1167836817_state) (A_57:(hoare_1167836817_state->Prop)), (((member2058392318_state A_58) A_57)->((ex (hoare_1167836817_state->Prop)) (fun (B_43:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_57) ((insert2134838167_state A_58) B_43))) (((member2058392318_state A_58) B_43)->False)))))) of role axiom named fact_528_mk__disjoint__insert
% A new axiom: (forall (A_58:hoare_1167836817_state) (A_57:(hoare_1167836817_state->Prop)), (((member2058392318_state A_58) A_57)->((ex (hoare_1167836817_state->Prop)) (fun (B_43:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_57) ((insert2134838167_state A_58) B_43))) (((member2058392318_state A_58) B_43)->False))))))
% FOF formula (forall (X_31:pname) (A_56:(pname->Prop)), (((member_pname X_31) A_56)->((forall (B_43:(pname->Prop)), ((((eq (pname->Prop)) A_56) ((insert_pname X_31) B_43))->((member_pname X_31) B_43)))->False))) of role axiom named fact_529_Set_Oset__insert
% A new axiom: (forall (X_31:pname) (A_56:(pname->Prop)), (((member_pname X_31) A_56)->((forall (B_43:(pname->Prop)), ((((eq (pname->Prop)) A_56) ((insert_pname X_31) B_43))->((member_pname X_31) B_43)))->False)))
% FOF formula (forall (X_31:hoare_1167836817_state) (A_56:(hoare_1167836817_state->Prop)), (((member2058392318_state X_31) A_56)->((forall (B_43:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_56) ((insert2134838167_state X_31) B_43))->((member2058392318_state X_31) B_43)))->False))) of role axiom named fact_530_Set_Oset__insert
% A new axiom: (forall (X_31:hoare_1167836817_state) (A_56:(hoare_1167836817_state->Prop)), (((member2058392318_state X_31) A_56)->((forall (B_43:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_56) ((insert2134838167_state X_31) B_43))->((member2058392318_state X_31) B_43)))->False)))
% FOF formula (forall (A_55:(pname->Prop)), ((forall (Y_2:pname), (((member_pname Y_2) A_55)->False))->(((eq (pname->Prop)) A_55) bot_bot_pname_o))) of role axiom named fact_531_equals0I
% A new axiom: (forall (A_55:(pname->Prop)), ((forall (Y_2:pname), (((member_pname Y_2) A_55)->False))->(((eq (pname->Prop)) A_55) bot_bot_pname_o)))
% FOF formula (forall (A_55:(hoare_1167836817_state->Prop)), ((forall (Y_2:hoare_1167836817_state), (((member2058392318_state Y_2) A_55)->False))->(((eq (hoare_1167836817_state->Prop)) A_55) bot_bo70021908tate_o))) of role axiom named fact_532_equals0I
% A new axiom: (forall (A_55:(hoare_1167836817_state->Prop)), ((forall (Y_2:hoare_1167836817_state), (((member2058392318_state Y_2) A_55)->False))->(((eq (hoare_1167836817_state->Prop)) A_55) bot_bo70021908tate_o)))
% FOF formula (forall (G_3:(hoare_1167836817_state->Prop)) (C_21:com), (hoare_1201148605gleton->(((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_21) S0_1) S1)) (((eq state) Z_11) S1))))) C_21) fequal_state)) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o))))) of role axiom named fact_533_MGT__alternD
% A new axiom: (forall (G_3:(hoare_1167836817_state->Prop)) (C_21:com), (hoare_1201148605gleton->(((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_21) S0_1) S1)) (((eq state) Z_11) S1))))) C_21) fequal_state)) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o)))))
% FOF formula (forall (G_3:(hoare_1167836817_state->Prop)) (C_21:com), (((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_21) S0_1) S1)) (((eq state) Z_11) S1))))) C_21) fequal_state)) bot_bo70021908tate_o)))) of role axiom named fact_534_MGT__alternI
% A new axiom: (forall (G_3:(hoare_1167836817_state->Prop)) (C_21:com), (((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_21) S0_1) S1)) (((eq state) Z_11) S1))))) C_21) fequal_state)) bot_bo70021908tate_o))))
% FOF formula (forall (C_21:com), (((eq hoare_1167836817_state) (hoare_Mirabelle_MGT C_21)) (((hoare_908217195_state fequal_state) C_21) (evalc C_21)))) of role axiom named fact_535_MGT__def
% A new axiom: (forall (C_21:com), (((eq hoare_1167836817_state) (hoare_Mirabelle_MGT C_21)) (((hoare_908217195_state fequal_state) C_21) (evalc C_21))))
% 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_536_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 (P:pname) (S_2:state) (S1_1:state), ((((evalc (body_1 P)) S_2) S1_1)->(((evalc (the_com (body P))) S_2) S1_1))) of role axiom named fact_537_evalc__elim__cases_I6_J
% A new axiom: (forall (P:pname) (S_2:state) (S1_1:state), ((((evalc (body_1 P)) S_2) S1_1)->(((evalc (the_com (body P))) S_2) S1_1)))
% FOF formula (forall (S_2:state) (T:state), ((((evalc skip) S_2) T)->(((eq state) T) S_2))) of role axiom named fact_538_evalc__elim__cases_I1_J
% A new axiom: (forall (S_2:state) (T:state), ((((evalc skip) S_2) T)->(((eq state) T) S_2)))
% FOF formula (forall (C_21:com) (B_42:(state->Prop)) (S_2:state), (((B_42 S_2)->False)->(((evalc ((while B_42) C_21)) S_2) S_2))) of role axiom named fact_539_evalc_OWhileFalse
% A new axiom: (forall (C_21:com) (B_42:(state->Prop)) (S_2:state), (((B_42 S_2)->False)->(((evalc ((while B_42) C_21)) S_2) S_2)))
% FOF formula (forall (S2:state) (C_21:com) (S1_1:state) (B_42:(state->Prop)) (S0:state), ((B_42 S0)->((((evalc C_21) S0) S1_1)->((((evalc ((while B_42) C_21)) S1_1) S2)->(((evalc ((while B_42) C_21)) S0) S2))))) of role axiom named fact_540_evalc_OWhileTrue
% A new axiom: (forall (S2:state) (C_21:com) (S1_1:state) (B_42:(state->Prop)) (S0:state), ((B_42 S0)->((((evalc C_21) S0) S1_1)->((((evalc ((while B_42) C_21)) S1_1) S2)->(((evalc ((while B_42) C_21)) S0) S2)))))
% 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_541_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 (S_2:state), (((evalc skip) S_2) S_2)) of role axiom named fact_542_evalc_OSkip
% A new axiom: (forall (S_2:state), (((evalc skip) S_2) S_2))
% FOF formula (forall (U:state) (C_21:com) (S_2:state) (T:state), ((((evalc C_21) S_2) T)->((((evalc C_21) S_2) U)->(((eq state) U) T)))) of role axiom named fact_543_com__det
% A new axiom: (forall (U:state) (C_21:com) (S_2:state) (T:state), ((((evalc C_21) S_2) T)->((((evalc C_21) S_2) U)->(((eq state) U) T))))
% FOF formula (forall (C1:com) (C2:com) (S_2:state) (T:state), ((((evalc ((semi C1) C2)) S_2) T)->((forall (S1:state), ((((evalc C1) S_2) S1)->((((evalc C2) S1) T)->False)))->False))) of role axiom named fact_544_evalc__elim__cases_I4_J
% A new axiom: (forall (C1:com) (C2:com) (S_2:state) (T:state), ((((evalc ((semi C1) C2)) S_2) T)->((forall (S1:state), ((((evalc C1) S_2) S1)->((((evalc C2) S1) T)->False)))->False)))
% FOF formula (forall (B_42:(state->Prop)) (C_21:com) (S_2:state) (T:state), ((((evalc ((while B_42) C_21)) S_2) T)->(((((eq state) T) S_2)->(B_42 S_2))->(((B_42 S_2)->(forall (S1:state), ((((evalc C_21) S_2) S1)->((((evalc ((while B_42) C_21)) S1) T)->False))))->False)))) of role axiom named fact_545_evalc__WHILE__case
% A new axiom: (forall (B_42:(state->Prop)) (C_21:com) (S_2:state) (T:state), ((((evalc ((while B_42) C_21)) S_2) T)->(((((eq state) T) S_2)->(B_42 S_2))->(((B_42 S_2)->(forall (S1:state), ((((evalc C_21) S_2) S1)->((((evalc ((while B_42) C_21)) S1) T)->False))))->False))))
% FOF formula (forall (C_20:(pname->Prop)) (A_54:(pname->Prop)) (F_13:((pname->Prop)->(pname->Prop))) (B_41:(pname->Prop)), ((((eq (pname->Prop)) A_54) (F_13 B_41))->(((ord_less_eq_pname_o C_20) B_41)->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), (((ord_less_eq_pname_o Y_2) X_5)->((ord_less_eq_pname_o (F_13 Y_2)) (F_13 X_5))))->((ord_less_eq_pname_o (F_13 C_20)) A_54))))) of role axiom named fact_546_xt1_I15_J
% A new axiom: (forall (C_20:(pname->Prop)) (A_54:(pname->Prop)) (F_13:((pname->Prop)->(pname->Prop))) (B_41:(pname->Prop)), ((((eq (pname->Prop)) A_54) (F_13 B_41))->(((ord_less_eq_pname_o C_20) B_41)->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), (((ord_less_eq_pname_o Y_2) X_5)->((ord_less_eq_pname_o (F_13 Y_2)) (F_13 X_5))))->((ord_less_eq_pname_o (F_13 C_20)) A_54)))))
% FOF formula (forall (C_20:(hoare_1167836817_state->Prop)) (A_54:(hoare_1167836817_state->Prop)) (F_13:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_41:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_54) (F_13 B_41))->(((ord_le827224136tate_o C_20) B_41)->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_2) X_5)->((ord_le827224136tate_o (F_13 Y_2)) (F_13 X_5))))->((ord_le827224136tate_o (F_13 C_20)) A_54))))) of role axiom named fact_547_xt1_I15_J
% A new axiom: (forall (C_20:(hoare_1167836817_state->Prop)) (A_54:(hoare_1167836817_state->Prop)) (F_13:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_41:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_54) (F_13 B_41))->(((ord_le827224136tate_o C_20) B_41)->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_2) X_5)->((ord_le827224136tate_o (F_13 Y_2)) (F_13 X_5))))->((ord_le827224136tate_o (F_13 C_20)) A_54)))))
% FOF formula (forall (F_12:((pname->Prop)->(pname->Prop))) (C_19:(pname->Prop)) (B_40:(pname->Prop)) (A_53:(pname->Prop)), (((ord_less_eq_pname_o B_40) A_53)->((((eq (pname->Prop)) (F_12 B_40)) C_19)->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), (((ord_less_eq_pname_o Y_2) X_5)->((ord_less_eq_pname_o (F_12 Y_2)) (F_12 X_5))))->((ord_less_eq_pname_o C_19) (F_12 A_53)))))) of role axiom named fact_548_xt1_I16_J
% A new axiom: (forall (F_12:((pname->Prop)->(pname->Prop))) (C_19:(pname->Prop)) (B_40:(pname->Prop)) (A_53:(pname->Prop)), (((ord_less_eq_pname_o B_40) A_53)->((((eq (pname->Prop)) (F_12 B_40)) C_19)->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), (((ord_less_eq_pname_o Y_2) X_5)->((ord_less_eq_pname_o (F_12 Y_2)) (F_12 X_5))))->((ord_less_eq_pname_o C_19) (F_12 A_53))))))
% FOF formula (forall (F_12:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (C_19:(hoare_1167836817_state->Prop)) (B_40:(hoare_1167836817_state->Prop)) (A_53:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_40) A_53)->((((eq (hoare_1167836817_state->Prop)) (F_12 B_40)) C_19)->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_2) X_5)->((ord_le827224136tate_o (F_12 Y_2)) (F_12 X_5))))->((ord_le827224136tate_o C_19) (F_12 A_53)))))) of role axiom named fact_549_xt1_I16_J
% A new axiom: (forall (F_12:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (C_19:(hoare_1167836817_state->Prop)) (B_40:(hoare_1167836817_state->Prop)) (A_53:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_40) A_53)->((((eq (hoare_1167836817_state->Prop)) (F_12 B_40)) C_19)->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_2) X_5)->((ord_le827224136tate_o (F_12 Y_2)) (F_12 X_5))))->((ord_le827224136tate_o C_19) (F_12 A_53))))))
% FOF formula (forall (B_39:((pname->Prop)->Prop)) (A_52:((pname->Prop)->Prop)) (F_11:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_10:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_11) F_10)->((finite297249702name_o A_52)->((finite297249702name_o B_39)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_52) B_39)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((F_11 (F_10 ((semila181081674me_o_o A_52) B_39))) (F_10 ((semila2013987940me_o_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39)))))))) of role axiom named fact_550_folding__one_Ounion__inter
% A new axiom: (forall (B_39:((pname->Prop)->Prop)) (A_52:((pname->Prop)->Prop)) (F_11:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_10:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_11) F_10)->((finite297249702name_o A_52)->((finite297249702name_o B_39)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_52) B_39)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((F_11 (F_10 ((semila181081674me_o_o A_52) B_39))) (F_10 ((semila2013987940me_o_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39))))))))
% FOF formula (forall (B_39:((hoare_1167836817_state->Prop)->Prop)) (A_52:((hoare_1167836817_state->Prop)->Prop)) (F_11:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_10:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_11) F_10)->((finite1380128977tate_o A_52)->((finite1380128977tate_o B_39)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_52) B_39)) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) ((F_11 (F_10 ((semila866907787te_o_o A_52) B_39))) (F_10 ((semila1758709489te_o_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39)))))))) of role axiom named fact_551_folding__one_Ounion__inter
% A new axiom: (forall (B_39:((hoare_1167836817_state->Prop)->Prop)) (A_52:((hoare_1167836817_state->Prop)->Prop)) (F_11:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_10:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_11) F_10)->((finite1380128977tate_o A_52)->((finite1380128977tate_o B_39)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_52) B_39)) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) ((F_11 (F_10 ((semila866907787te_o_o A_52) B_39))) (F_10 ((semila1758709489te_o_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39))))))))
% FOF formula (forall (B_39:(pname->Prop)) (A_52:(pname->Prop)) (F_11:(pname->(pname->pname))) (F_10:((pname->Prop)->pname)), (((finite1282449217_pname F_11) F_10)->((finite_finite_pname A_52)->((finite_finite_pname B_39)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_52) B_39)) bot_bot_pname_o))->(((eq pname) ((F_11 (F_10 ((semila1780557381name_o A_52) B_39))) (F_10 ((semila1673364395name_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39)))))))) of role axiom named fact_552_folding__one_Ounion__inter
% A new axiom: (forall (B_39:(pname->Prop)) (A_52:(pname->Prop)) (F_11:(pname->(pname->pname))) (F_10:((pname->Prop)->pname)), (((finite1282449217_pname F_11) F_10)->((finite_finite_pname A_52)->((finite_finite_pname B_39)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_52) B_39)) bot_bot_pname_o))->(((eq pname) ((F_11 (F_10 ((semila1780557381name_o A_52) B_39))) (F_10 ((semila1673364395name_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39))))))))
% FOF formula (forall (B_39:(hoare_1167836817_state->Prop)) (A_52:(hoare_1167836817_state->Prop)) (F_11:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_10:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_11) F_10)->((finite1084549118_state A_52)->((finite1084549118_state B_39)->((not (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_52) B_39)) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) ((F_11 (F_10 ((semila1172322802tate_o A_52) B_39))) (F_10 ((semila179895820tate_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39)))))))) of role axiom named fact_553_folding__one_Ounion__inter
% A new axiom: (forall (B_39:(hoare_1167836817_state->Prop)) (A_52:(hoare_1167836817_state->Prop)) (F_11:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_10:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_11) F_10)->((finite1084549118_state A_52)->((finite1084549118_state B_39)->((not (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_52) B_39)) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) ((F_11 (F_10 ((semila1172322802tate_o A_52) B_39))) (F_10 ((semila179895820tate_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39))))))))
% FOF formula (forall (B_38:((pname->Prop)->Prop)) (A_51:((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_51)->((not (((eq ((pname->Prop)->Prop)) A_51) bot_bot_pname_o_o))->((finite297249702name_o B_38)->((not (((eq ((pname->Prop)->Prop)) B_38) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_51) B_38)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_8 ((semila181081674me_o_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38)))))))))) of role axiom named fact_554_folding__one_Ounion__disjoint
% A new axiom: (forall (B_38:((pname->Prop)->Prop)) (A_51:((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_51)->((not (((eq ((pname->Prop)->Prop)) A_51) bot_bot_pname_o_o))->((finite297249702name_o B_38)->((not (((eq ((pname->Prop)->Prop)) B_38) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_51) B_38)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_8 ((semila181081674me_o_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38))))))))))
% FOF formula (forall (B_38:((hoare_1167836817_state->Prop)->Prop)) (A_51:((hoare_1167836817_state->Prop)->Prop)) (F_9:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_8:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_9) F_8)->((finite1380128977tate_o A_51)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_51) bot_bo691907561te_o_o))->((finite1380128977tate_o B_38)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_38) bot_bo691907561te_o_o))->((((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_51) B_38)) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (F_8 ((semila866907787te_o_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38)))))))))) of role axiom named fact_555_folding__one_Ounion__disjoint
% A new axiom: (forall (B_38:((hoare_1167836817_state->Prop)->Prop)) (A_51:((hoare_1167836817_state->Prop)->Prop)) (F_9:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_8:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_9) F_8)->((finite1380128977tate_o A_51)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_51) bot_bo691907561te_o_o))->((finite1380128977tate_o B_38)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_38) bot_bo691907561te_o_o))->((((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_51) B_38)) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (F_8 ((semila866907787te_o_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38))))))))))
% FOF formula (forall (B_38:(pname->Prop)) (A_51:(pname->Prop)) (F_9:(pname->(pname->pname))) (F_8:((pname->Prop)->pname)), (((finite1282449217_pname F_9) F_8)->((finite_finite_pname A_51)->((not (((eq (pname->Prop)) A_51) bot_bot_pname_o))->((finite_finite_pname B_38)->((not (((eq (pname->Prop)) B_38) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_51) B_38)) bot_bot_pname_o)->(((eq pname) (F_8 ((semila1780557381name_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38)))))))))) of role axiom named fact_556_folding__one_Ounion__disjoint
% A new axiom: (forall (B_38:(pname->Prop)) (A_51:(pname->Prop)) (F_9:(pname->(pname->pname))) (F_8:((pname->Prop)->pname)), (((finite1282449217_pname F_9) F_8)->((finite_finite_pname A_51)->((not (((eq (pname->Prop)) A_51) bot_bot_pname_o))->((finite_finite_pname B_38)->((not (((eq (pname->Prop)) B_38) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_51) B_38)) bot_bot_pname_o)->(((eq pname) (F_8 ((semila1780557381name_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38))))))))))
% FOF formula (forall (B_38:(hoare_1167836817_state->Prop)) (A_51:(hoare_1167836817_state->Prop)) (F_9:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_8:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_9) F_8)->((finite1084549118_state A_51)->((not (((eq (hoare_1167836817_state->Prop)) A_51) bot_bo70021908tate_o))->((finite1084549118_state B_38)->((not (((eq (hoare_1167836817_state->Prop)) B_38) bot_bo70021908tate_o))->((((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_51) B_38)) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_8 ((semila1172322802tate_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38)))))))))) of role axiom named fact_557_folding__one_Ounion__disjoint
% A new axiom: (forall (B_38:(hoare_1167836817_state->Prop)) (A_51:(hoare_1167836817_state->Prop)) (F_9:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_8:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_9) F_8)->((finite1084549118_state A_51)->((not (((eq (hoare_1167836817_state->Prop)) A_51) bot_bo70021908tate_o))->((finite1084549118_state B_38)->((not (((eq (hoare_1167836817_state->Prop)) B_38) bot_bo70021908tate_o))->((((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_51) B_38)) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_8 ((semila1172322802tate_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38))))))))))
% FOF formula (forall (B_37:(pname->Prop)) (C_18:pname) (A_50:(pname->Prop)), (((member_pname C_18) A_50)->(((member_pname C_18) B_37)->((member_pname C_18) ((semila1673364395name_o A_50) B_37))))) of role axiom named fact_558_IntI
% A new axiom: (forall (B_37:(pname->Prop)) (C_18:pname) (A_50:(pname->Prop)), (((member_pname C_18) A_50)->(((member_pname C_18) B_37)->((member_pname C_18) ((semila1673364395name_o A_50) B_37)))))
% FOF formula (forall (B_37:(hoare_1167836817_state->Prop)) (C_18:hoare_1167836817_state) (A_50:(hoare_1167836817_state->Prop)), (((member2058392318_state C_18) A_50)->(((member2058392318_state C_18) B_37)->((member2058392318_state C_18) ((semila179895820tate_o A_50) B_37))))) of role axiom named fact_559_IntI
% A new axiom: (forall (B_37:(hoare_1167836817_state->Prop)) (C_18:hoare_1167836817_state) (A_50:(hoare_1167836817_state->Prop)), (((member2058392318_state C_18) A_50)->(((member2058392318_state C_18) B_37)->((member2058392318_state C_18) ((semila179895820tate_o A_50) B_37)))))
% FOF formula (forall (C_17:pname) (A_49:(pname->Prop)) (B_36:(pname->Prop)), (((member_pname C_17) ((semila1673364395name_o A_49) B_36))->((((member_pname C_17) A_49)->(((member_pname C_17) B_36)->False))->False))) of role axiom named fact_560_IntE
% A new axiom: (forall (C_17:pname) (A_49:(pname->Prop)) (B_36:(pname->Prop)), (((member_pname C_17) ((semila1673364395name_o A_49) B_36))->((((member_pname C_17) A_49)->(((member_pname C_17) B_36)->False))->False)))
% FOF formula (forall (C_17:hoare_1167836817_state) (A_49:(hoare_1167836817_state->Prop)) (B_36:(hoare_1167836817_state->Prop)), (((member2058392318_state C_17) ((semila179895820tate_o A_49) B_36))->((((member2058392318_state C_17) A_49)->(((member2058392318_state C_17) B_36)->False))->False))) of role axiom named fact_561_IntE
% A new axiom: (forall (C_17:hoare_1167836817_state) (A_49:(hoare_1167836817_state->Prop)) (B_36:(hoare_1167836817_state->Prop)), (((member2058392318_state C_17) ((semila179895820tate_o A_49) B_36))->((((member2058392318_state C_17) A_49)->(((member2058392318_state C_17) B_36)->False))->False)))
% FOF formula (forall (G_2:((pname->Prop)->Prop)) (F_7:((pname->Prop)->Prop)), (((or (finite297249702name_o F_7)) (finite297249702name_o G_2))->(finite297249702name_o ((semila2013987940me_o_o F_7) G_2)))) of role axiom named fact_562_finite__Int
% A new axiom: (forall (G_2:((pname->Prop)->Prop)) (F_7:((pname->Prop)->Prop)), (((or (finite297249702name_o F_7)) (finite297249702name_o G_2))->(finite297249702name_o ((semila2013987940me_o_o F_7) G_2))))
% FOF formula (forall (G_2:((hoare_1167836817_state->Prop)->Prop)) (F_7:((hoare_1167836817_state->Prop)->Prop)), (((or (finite1380128977tate_o F_7)) (finite1380128977tate_o G_2))->(finite1380128977tate_o ((semila1758709489te_o_o F_7) G_2)))) of role axiom named fact_563_finite__Int
% A new axiom: (forall (G_2:((hoare_1167836817_state->Prop)->Prop)) (F_7:((hoare_1167836817_state->Prop)->Prop)), (((or (finite1380128977tate_o F_7)) (finite1380128977tate_o G_2))->(finite1380128977tate_o ((semila1758709489te_o_o F_7) G_2))))
% FOF formula (forall (G_2:(pname->Prop)) (F_7:(pname->Prop)), (((or (finite_finite_pname F_7)) (finite_finite_pname G_2))->(finite_finite_pname ((semila1673364395name_o F_7) G_2)))) of role axiom named fact_564_finite__Int
% A new axiom: (forall (G_2:(pname->Prop)) (F_7:(pname->Prop)), (((or (finite_finite_pname F_7)) (finite_finite_pname G_2))->(finite_finite_pname ((semila1673364395name_o F_7) G_2))))
% FOF formula (forall (G_2:(hoare_1167836817_state->Prop)) (F_7:(hoare_1167836817_state->Prop)), (((or (finite1084549118_state F_7)) (finite1084549118_state G_2))->(finite1084549118_state ((semila179895820tate_o F_7) G_2)))) of role axiom named fact_565_finite__Int
% A new axiom: (forall (G_2:(hoare_1167836817_state->Prop)) (F_7:(hoare_1167836817_state->Prop)), (((or (finite1084549118_state F_7)) (finite1084549118_state G_2))->(finite1084549118_state ((semila179895820tate_o F_7) G_2))))
% FOF formula (forall (A_48:(pname->Prop)) (B_35:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1673364395name_o A_48) B_35)) bot_bot_pname_o)) (forall (X_5:pname), (((member_pname X_5) A_48)->(forall (Xa:pname), (((member_pname Xa) B_35)->(not (((eq pname) X_5) Xa)))))))) of role axiom named fact_566_disjoint__iff__not__equal
% A new axiom: (forall (A_48:(pname->Prop)) (B_35:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1673364395name_o A_48) B_35)) bot_bot_pname_o)) (forall (X_5:pname), (((member_pname X_5) A_48)->(forall (Xa:pname), (((member_pname Xa) B_35)->(not (((eq pname) X_5) Xa))))))))
% FOF formula (forall (A_48:(hoare_1167836817_state->Prop)) (B_35:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_48) B_35)) bot_bo70021908tate_o)) (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_48)->(forall (Xa:hoare_1167836817_state), (((member2058392318_state Xa) B_35)->(not (((eq hoare_1167836817_state) X_5) Xa)))))))) of role axiom named fact_567_disjoint__iff__not__equal
% A new axiom: (forall (A_48:(hoare_1167836817_state->Prop)) (B_35:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_48) B_35)) bot_bo70021908tate_o)) (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_48)->(forall (Xa:hoare_1167836817_state), (((member2058392318_state Xa) B_35)->(not (((eq hoare_1167836817_state) X_5) Xa))))))))
% FOF formula (forall (A_47:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_47) bot_bot_pname_o)) bot_bot_pname_o)) of role axiom named fact_568_Int__empty__right
% A new axiom: (forall (A_47:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_47) bot_bot_pname_o)) bot_bot_pname_o))
% FOF formula (forall (A_47:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_47) bot_bo70021908tate_o)) bot_bo70021908tate_o)) of role axiom named fact_569_Int__empty__right
% A new axiom: (forall (A_47:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_47) bot_bo70021908tate_o)) bot_bo70021908tate_o))
% FOF formula (forall (B_34:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) B_34)) bot_bot_pname_o)) of role axiom named fact_570_Int__empty__left
% A new axiom: (forall (B_34:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) B_34)) bot_bot_pname_o))
% FOF formula (forall (B_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) B_34)) bot_bo70021908tate_o)) of role axiom named fact_571_Int__empty__left
% A new axiom: (forall (B_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) B_34)) bot_bo70021908tate_o))
% FOF formula (forall (A_46:(pname->Prop)) (B_33:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_46) B_33)) (collect_pname (fun (X_5:pname)=> ((and ((member_pname X_5) A_46)) ((member_pname X_5) B_33)))))) of role axiom named fact_572_Int__def
% A new axiom: (forall (A_46:(pname->Prop)) (B_33:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_46) B_33)) (collect_pname (fun (X_5:pname)=> ((and ((member_pname X_5) A_46)) ((member_pname X_5) B_33))))))
% FOF formula (forall (A_46:(hoare_1167836817_state->Prop)) (B_33:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_46) B_33)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_46)) ((member2058392318_state X_5) B_33)))))) of role axiom named fact_573_Int__def
% A new axiom: (forall (A_46:(hoare_1167836817_state->Prop)) (B_33:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_46) B_33)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_46)) ((member2058392318_state X_5) B_33))))))
% FOF formula (forall (A_46:((pname->Prop)->Prop)) (B_33:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_46) B_33)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and ((member_pname_o X_5) A_46)) ((member_pname_o X_5) B_33)))))) of role axiom named fact_574_Int__def
% A new axiom: (forall (A_46:((pname->Prop)->Prop)) (B_33:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_46) B_33)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and ((member_pname_o X_5) A_46)) ((member_pname_o X_5) B_33))))))
% FOF formula (forall (A_46:((hoare_1167836817_state->Prop)->Prop)) (B_33:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_46) B_33)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o X_5) A_46)) ((member864234961tate_o X_5) B_33)))))) of role axiom named fact_575_Int__def
% A new axiom: (forall (A_46:((hoare_1167836817_state->Prop)->Prop)) (B_33:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_46) B_33)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o X_5) A_46)) ((member864234961tate_o X_5) B_33))))))
% FOF formula (forall (C_16:pname) (A_45:(pname->Prop)) (B_32:(pname->Prop)), ((iff ((member_pname C_16) ((semila1673364395name_o A_45) B_32))) ((and ((member_pname C_16) A_45)) ((member_pname C_16) B_32)))) of role axiom named fact_576_Int__iff
% A new axiom: (forall (C_16:pname) (A_45:(pname->Prop)) (B_32:(pname->Prop)), ((iff ((member_pname C_16) ((semila1673364395name_o A_45) B_32))) ((and ((member_pname C_16) A_45)) ((member_pname C_16) B_32))))
% FOF formula (forall (C_16:hoare_1167836817_state) (A_45:(hoare_1167836817_state->Prop)) (B_32:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_16) ((semila179895820tate_o A_45) B_32))) ((and ((member2058392318_state C_16) A_45)) ((member2058392318_state C_16) B_32)))) of role axiom named fact_577_Int__iff
% A new axiom: (forall (C_16:hoare_1167836817_state) (A_45:(hoare_1167836817_state->Prop)) (B_32:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_16) ((semila179895820tate_o A_45) B_32))) ((and ((member2058392318_state C_16) A_45)) ((member2058392318_state C_16) B_32))))
% FOF formula (forall (C_15:pname) (A_44:(pname->Prop)) (B_31:(pname->Prop)), (((member_pname C_15) ((semila1673364395name_o A_44) B_31))->((member_pname C_15) A_44))) of role axiom named fact_578_IntD1
% A new axiom: (forall (C_15:pname) (A_44:(pname->Prop)) (B_31:(pname->Prop)), (((member_pname C_15) ((semila1673364395name_o A_44) B_31))->((member_pname C_15) A_44)))
% FOF formula (forall (C_15:hoare_1167836817_state) (A_44:(hoare_1167836817_state->Prop)) (B_31:(hoare_1167836817_state->Prop)), (((member2058392318_state C_15) ((semila179895820tate_o A_44) B_31))->((member2058392318_state C_15) A_44))) of role axiom named fact_579_IntD1
% A new axiom: (forall (C_15:hoare_1167836817_state) (A_44:(hoare_1167836817_state->Prop)) (B_31:(hoare_1167836817_state->Prop)), (((member2058392318_state C_15) ((semila179895820tate_o A_44) B_31))->((member2058392318_state C_15) A_44)))
% FOF formula (forall (C_14:pname) (A_43:(pname->Prop)) (B_30:(pname->Prop)), (((member_pname C_14) ((semila1673364395name_o A_43) B_30))->((member_pname C_14) B_30))) of role axiom named fact_580_IntD2
% A new axiom: (forall (C_14:pname) (A_43:(pname->Prop)) (B_30:(pname->Prop)), (((member_pname C_14) ((semila1673364395name_o A_43) B_30))->((member_pname C_14) B_30)))
% FOF formula (forall (C_14:hoare_1167836817_state) (A_43:(hoare_1167836817_state->Prop)) (B_30:(hoare_1167836817_state->Prop)), (((member2058392318_state C_14) ((semila179895820tate_o A_43) B_30))->((member2058392318_state C_14) B_30))) of role axiom named fact_581_IntD2
% A new axiom: (forall (C_14:hoare_1167836817_state) (A_43:(hoare_1167836817_state->Prop)) (B_30:(hoare_1167836817_state->Prop)), (((member2058392318_state C_14) ((semila179895820tate_o A_43) B_30))->((member2058392318_state C_14) B_30)))
% FOF formula (forall (P_5:(hoare_1167836817_state->Prop)) (Q_1:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (P_5 X_5)) (Q_1 X_5))))) ((semila179895820tate_o (collec1027672124_state P_5)) (collec1027672124_state Q_1)))) of role axiom named fact_582_Collect__conj__eq
% A new axiom: (forall (P_5:(hoare_1167836817_state->Prop)) (Q_1:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (P_5 X_5)) (Q_1 X_5))))) ((semila179895820tate_o (collec1027672124_state P_5)) (collec1027672124_state Q_1))))
% FOF formula (forall (P_5:(pname->Prop)) (Q_1:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (P_5 X_5)) (Q_1 X_5))))) ((semila1673364395name_o (collect_pname P_5)) (collect_pname Q_1)))) of role axiom named fact_583_Collect__conj__eq
% A new axiom: (forall (P_5:(pname->Prop)) (Q_1:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (P_5 X_5)) (Q_1 X_5))))) ((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_5:(pname->Prop))=> ((and (P_5 X_5)) (Q_1 X_5))))) ((semila2013987940me_o_o (collect_pname_o P_5)) (collect_pname_o Q_1)))) of role axiom named fact_584_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_5:(pname->Prop))=> ((and (P_5 X_5)) (Q_1 X_5))))) ((semila2013987940me_o_o (collect_pname_o P_5)) (collect_pname_o Q_1))))
% FOF formula (forall (P_5:((hoare_1167836817_state->Prop)->Prop)) (Q_1:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (P_5 X_5)) (Q_1 X_5))))) ((semila1758709489te_o_o (collec269976083tate_o P_5)) (collec269976083tate_o Q_1)))) of role axiom named fact_585_Collect__conj__eq
% A new axiom: (forall (P_5:((hoare_1167836817_state->Prop)->Prop)) (Q_1:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (P_5 X_5)) (Q_1 X_5))))) ((semila1758709489te_o_o (collec269976083tate_o P_5)) (collec269976083tate_o Q_1))))
% FOF formula (forall (X_30:pname) (A_42:(pname->Prop)) (P_4:(pname->Prop)), ((iff ((member_pname X_30) ((semila1673364395name_o A_42) (collect_pname P_4)))) ((and ((member_pname X_30) A_42)) (P_4 X_30)))) of role axiom named fact_586_Int__Collect
% A new axiom: (forall (X_30:pname) (A_42:(pname->Prop)) (P_4:(pname->Prop)), ((iff ((member_pname X_30) ((semila1673364395name_o A_42) (collect_pname P_4)))) ((and ((member_pname X_30) A_42)) (P_4 X_30))))
% FOF formula (forall (X_30:hoare_1167836817_state) (A_42:(hoare_1167836817_state->Prop)) (P_4:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state X_30) ((semila179895820tate_o A_42) (collec1027672124_state P_4)))) ((and ((member2058392318_state X_30) A_42)) (P_4 X_30)))) of role axiom named fact_587_Int__Collect
% A new axiom: (forall (X_30:hoare_1167836817_state) (A_42:(hoare_1167836817_state->Prop)) (P_4:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state X_30) ((semila179895820tate_o A_42) (collec1027672124_state P_4)))) ((and ((member2058392318_state X_30) A_42)) (P_4 X_30))))
% FOF formula (forall (X_30:(pname->Prop)) (A_42:((pname->Prop)->Prop)) (P_4:((pname->Prop)->Prop)), ((iff ((member_pname_o X_30) ((semila2013987940me_o_o A_42) (collect_pname_o P_4)))) ((and ((member_pname_o X_30) A_42)) (P_4 X_30)))) of role axiom named fact_588_Int__Collect
% A new axiom: (forall (X_30:(pname->Prop)) (A_42:((pname->Prop)->Prop)) (P_4:((pname->Prop)->Prop)), ((iff ((member_pname_o X_30) ((semila2013987940me_o_o A_42) (collect_pname_o P_4)))) ((and ((member_pname_o X_30) A_42)) (P_4 X_30))))
% FOF formula (forall (X_30:(hoare_1167836817_state->Prop)) (A_42:((hoare_1167836817_state->Prop)->Prop)) (P_4:((hoare_1167836817_state->Prop)->Prop)), ((iff ((member864234961tate_o X_30) ((semila1758709489te_o_o A_42) (collec269976083tate_o P_4)))) ((and ((member864234961tate_o X_30) A_42)) (P_4 X_30)))) of role axiom named fact_589_Int__Collect
% A new axiom: (forall (X_30:(hoare_1167836817_state->Prop)) (A_42:((hoare_1167836817_state->Prop)->Prop)) (P_4:((hoare_1167836817_state->Prop)->Prop)), ((iff ((member864234961tate_o X_30) ((semila1758709489te_o_o A_42) (collec269976083tate_o P_4)))) ((and ((member864234961tate_o X_30) A_42)) (P_4 X_30))))
% FOF formula (forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X_5:pname), ((iff (((semila1673364395name_o (fun (Y_2:pname)=> ((member_pname Y_2) R))) (fun (Y_2:pname)=> ((member_pname Y_2) S_1))) X_5)) ((member_pname X_5) ((semila1673364395name_o R) S_1)))) of role axiom named fact_590_inf__Int__eq
% A new axiom: (forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X_5:pname), ((iff (((semila1673364395name_o (fun (Y_2:pname)=> ((member_pname Y_2) R))) (fun (Y_2:pname)=> ((member_pname Y_2) S_1))) X_5)) ((member_pname X_5) ((semila1673364395name_o R) S_1))))
% FOF formula (forall (R:(hoare_1167836817_state->Prop)) (S_1:(hoare_1167836817_state->Prop)) (X_5:hoare_1167836817_state), ((iff (((semila179895820tate_o (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) R))) (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) S_1))) X_5)) ((member2058392318_state X_5) ((semila179895820tate_o R) S_1)))) of role axiom named fact_591_inf__Int__eq
% A new axiom: (forall (R:(hoare_1167836817_state->Prop)) (S_1:(hoare_1167836817_state->Prop)) (X_5:hoare_1167836817_state), ((iff (((semila179895820tate_o (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) R))) (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) S_1))) X_5)) ((member2058392318_state X_5) ((semila179895820tate_o R) S_1))))
% FOF formula (forall (A_41:(hoare_1167836817_state->Prop)) (B_29:(hoare_1167836817_state->Prop)) (C_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o ((semila179895820tate_o A_41) B_29)) ((semila179895820tate_o B_29) C_13))) ((semila179895820tate_o C_13) A_41))) ((semila179895820tate_o ((semila179895820tate_o ((semila1172322802tate_o A_41) B_29)) ((semila1172322802tate_o B_29) C_13))) ((semila1172322802tate_o C_13) A_41)))) of role axiom named fact_592_Un__Int__crazy
% A new axiom: (forall (A_41:(hoare_1167836817_state->Prop)) (B_29:(hoare_1167836817_state->Prop)) (C_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o ((semila179895820tate_o A_41) B_29)) ((semila179895820tate_o B_29) C_13))) ((semila179895820tate_o C_13) A_41))) ((semila179895820tate_o ((semila179895820tate_o ((semila1172322802tate_o A_41) B_29)) ((semila1172322802tate_o B_29) C_13))) ((semila1172322802tate_o C_13) A_41))))
% FOF formula (forall (B_28:(hoare_1167836817_state->Prop)) (C_12:(hoare_1167836817_state->Prop)) (A_40:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o B_28) C_12)) A_40)) ((semila179895820tate_o ((semila1172322802tate_o B_28) A_40)) ((semila1172322802tate_o C_12) A_40)))) of role axiom named fact_593_Un__Int__distrib2
% A new axiom: (forall (B_28:(hoare_1167836817_state->Prop)) (C_12:(hoare_1167836817_state->Prop)) (A_40:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o B_28) C_12)) A_40)) ((semila179895820tate_o ((semila1172322802tate_o B_28) A_40)) ((semila1172322802tate_o C_12) A_40))))
% FOF formula (forall (B_27:(hoare_1167836817_state->Prop)) (C_11:(hoare_1167836817_state->Prop)) (A_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o B_27) C_11)) A_39)) ((semila1172322802tate_o ((semila179895820tate_o B_27) A_39)) ((semila179895820tate_o C_11) A_39)))) of role axiom named fact_594_Int__Un__distrib2
% A new axiom: (forall (B_27:(hoare_1167836817_state->Prop)) (C_11:(hoare_1167836817_state->Prop)) (A_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o B_27) C_11)) A_39)) ((semila1172322802tate_o ((semila179895820tate_o B_27) A_39)) ((semila179895820tate_o C_11) A_39))))
% FOF formula (forall (A_38:(hoare_1167836817_state->Prop)) (B_26:(hoare_1167836817_state->Prop)) (C_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_38) ((semila179895820tate_o B_26) C_10))) ((semila179895820tate_o ((semila1172322802tate_o A_38) B_26)) ((semila1172322802tate_o A_38) C_10)))) of role axiom named fact_595_Un__Int__distrib
% A new axiom: (forall (A_38:(hoare_1167836817_state->Prop)) (B_26:(hoare_1167836817_state->Prop)) (C_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_38) ((semila179895820tate_o B_26) C_10))) ((semila179895820tate_o ((semila1172322802tate_o A_38) B_26)) ((semila1172322802tate_o A_38) C_10))))
% FOF formula (forall (A_37:(hoare_1167836817_state->Prop)) (B_25:(hoare_1167836817_state->Prop)) (C_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_37) ((semila1172322802tate_o B_25) C_9))) ((semila1172322802tate_o ((semila179895820tate_o A_37) B_25)) ((semila179895820tate_o A_37) C_9)))) of role axiom named fact_596_Int__Un__distrib
% A new axiom: (forall (A_37:(hoare_1167836817_state->Prop)) (B_25:(hoare_1167836817_state->Prop)) (C_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_37) ((semila1172322802tate_o B_25) C_9))) ((semila1172322802tate_o ((semila179895820tate_o A_37) B_25)) ((semila179895820tate_o A_37) C_9))))
% FOF formula (forall (B_24:(pname->Prop)) (D_1:(pname->Prop)) (A_36:(pname->Prop)) (C_8:(pname->Prop)), (((ord_less_eq_pname_o A_36) C_8)->(((ord_less_eq_pname_o B_24) D_1)->((ord_less_eq_pname_o ((semila1673364395name_o A_36) B_24)) ((semila1673364395name_o C_8) D_1))))) of role axiom named fact_597_Int__mono
% A new axiom: (forall (B_24:(pname->Prop)) (D_1:(pname->Prop)) (A_36:(pname->Prop)) (C_8:(pname->Prop)), (((ord_less_eq_pname_o A_36) C_8)->(((ord_less_eq_pname_o B_24) D_1)->((ord_less_eq_pname_o ((semila1673364395name_o A_36) B_24)) ((semila1673364395name_o C_8) D_1)))))
% FOF formula (forall (B_24:(hoare_1167836817_state->Prop)) (D_1:(hoare_1167836817_state->Prop)) (A_36:(hoare_1167836817_state->Prop)) (C_8:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_36) C_8)->(((ord_le827224136tate_o B_24) D_1)->((ord_le827224136tate_o ((semila179895820tate_o A_36) B_24)) ((semila179895820tate_o C_8) D_1))))) of role axiom named fact_598_Int__mono
% A new axiom: (forall (B_24:(hoare_1167836817_state->Prop)) (D_1:(hoare_1167836817_state->Prop)) (A_36:(hoare_1167836817_state->Prop)) (C_8:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_36) C_8)->(((ord_le827224136tate_o B_24) D_1)->((ord_le827224136tate_o ((semila179895820tate_o A_36) B_24)) ((semila179895820tate_o C_8) D_1)))))
% FOF formula (forall (B_23:(pname->Prop)) (C_7:(pname->Prop)) (A_35:(pname->Prop)), (((ord_less_eq_pname_o C_7) A_35)->(((ord_less_eq_pname_o C_7) B_23)->((ord_less_eq_pname_o C_7) ((semila1673364395name_o A_35) B_23))))) of role axiom named fact_599_Int__greatest
% A new axiom: (forall (B_23:(pname->Prop)) (C_7:(pname->Prop)) (A_35:(pname->Prop)), (((ord_less_eq_pname_o C_7) A_35)->(((ord_less_eq_pname_o C_7) B_23)->((ord_less_eq_pname_o C_7) ((semila1673364395name_o A_35) B_23)))))
% FOF formula (forall (B_23:(hoare_1167836817_state->Prop)) (C_7:(hoare_1167836817_state->Prop)) (A_35:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o C_7) A_35)->(((ord_le827224136tate_o C_7) B_23)->((ord_le827224136tate_o C_7) ((semila179895820tate_o A_35) B_23))))) of role axiom named fact_600_Int__greatest
% A new axiom: (forall (B_23:(hoare_1167836817_state->Prop)) (C_7:(hoare_1167836817_state->Prop)) (A_35:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o C_7) A_35)->(((ord_le827224136tate_o C_7) B_23)->((ord_le827224136tate_o C_7) ((semila179895820tate_o A_35) B_23)))))
% FOF formula (forall (B_22:(pname->Prop)) (A_34:(pname->Prop)), (((ord_less_eq_pname_o B_22) A_34)->(((eq (pname->Prop)) ((semila1673364395name_o A_34) B_22)) B_22))) of role axiom named fact_601_Int__absorb1
% A new axiom: (forall (B_22:(pname->Prop)) (A_34:(pname->Prop)), (((ord_less_eq_pname_o B_22) A_34)->(((eq (pname->Prop)) ((semila1673364395name_o A_34) B_22)) B_22)))
% FOF formula (forall (B_22:(hoare_1167836817_state->Prop)) (A_34:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_22) A_34)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_34) B_22)) B_22))) of role axiom named fact_602_Int__absorb1
% A new axiom: (forall (B_22:(hoare_1167836817_state->Prop)) (A_34:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_22) A_34)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_34) B_22)) B_22)))
% FOF formula (forall (A_33:(pname->Prop)) (B_21:(pname->Prop)), (((ord_less_eq_pname_o A_33) B_21)->(((eq (pname->Prop)) ((semila1673364395name_o A_33) B_21)) A_33))) of role axiom named fact_603_Int__absorb2
% A new axiom: (forall (A_33:(pname->Prop)) (B_21:(pname->Prop)), (((ord_less_eq_pname_o A_33) B_21)->(((eq (pname->Prop)) ((semila1673364395name_o A_33) B_21)) A_33)))
% FOF formula (forall (A_33:(hoare_1167836817_state->Prop)) (B_21:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_33) B_21)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_33) B_21)) A_33))) of role axiom named fact_604_Int__absorb2
% A new axiom: (forall (A_33:(hoare_1167836817_state->Prop)) (B_21:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_33) B_21)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_33) B_21)) A_33)))
% FOF formula (forall (A_32:(pname->Prop)) (B_20:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_32) B_20)) B_20)) of role axiom named fact_605_Int__lower2
% A new axiom: (forall (A_32:(pname->Prop)) (B_20:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_32) B_20)) B_20))
% FOF formula (forall (A_32:(hoare_1167836817_state->Prop)) (B_20:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o A_32) B_20)) B_20)) of role axiom named fact_606_Int__lower2
% A new axiom: (forall (A_32:(hoare_1167836817_state->Prop)) (B_20:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o A_32) B_20)) B_20))
% FOF formula (forall (A_31:(pname->Prop)) (B_19:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_31) B_19)) A_31)) of role axiom named fact_607_Int__lower1
% A new axiom: (forall (A_31:(pname->Prop)) (B_19:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_31) B_19)) A_31))
% FOF formula (forall (A_31:(hoare_1167836817_state->Prop)) (B_19:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o A_31) B_19)) A_31)) of role axiom named fact_608_Int__lower1
% A new axiom: (forall (A_31:(hoare_1167836817_state->Prop)) (B_19:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o A_31) B_19)) A_31))
% FOF formula (forall (B_18:(pname->Prop)) (A_30:pname) (C_6:(pname->Prop)), (((member_pname A_30) C_6)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_30) B_18)) C_6)) ((insert_pname A_30) ((semila1673364395name_o B_18) C_6))))) of role axiom named fact_609_Int__insert__left__if1
% A new axiom: (forall (B_18:(pname->Prop)) (A_30:pname) (C_6:(pname->Prop)), (((member_pname A_30) C_6)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_30) B_18)) C_6)) ((insert_pname A_30) ((semila1673364395name_o B_18) C_6)))))
% FOF formula (forall (B_18:(hoare_1167836817_state->Prop)) (A_30:hoare_1167836817_state) (C_6:(hoare_1167836817_state->Prop)), (((member2058392318_state A_30) C_6)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_30) B_18)) C_6)) ((insert2134838167_state A_30) ((semila179895820tate_o B_18) C_6))))) of role axiom named fact_610_Int__insert__left__if1
% A new axiom: (forall (B_18:(hoare_1167836817_state->Prop)) (A_30:hoare_1167836817_state) (C_6:(hoare_1167836817_state->Prop)), (((member2058392318_state A_30) C_6)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_30) B_18)) C_6)) ((insert2134838167_state A_30) ((semila179895820tate_o B_18) C_6)))))
% FOF formula (forall (B_17:(pname->Prop)) (A_29:pname) (A_28:(pname->Prop)), (((member_pname A_29) A_28)->(((eq (pname->Prop)) ((semila1673364395name_o A_28) ((insert_pname A_29) B_17))) ((insert_pname A_29) ((semila1673364395name_o A_28) B_17))))) of role axiom named fact_611_Int__insert__right__if1
% A new axiom: (forall (B_17:(pname->Prop)) (A_29:pname) (A_28:(pname->Prop)), (((member_pname A_29) A_28)->(((eq (pname->Prop)) ((semila1673364395name_o A_28) ((insert_pname A_29) B_17))) ((insert_pname A_29) ((semila1673364395name_o A_28) B_17)))))
% FOF formula (forall (B_17:(hoare_1167836817_state->Prop)) (A_29:hoare_1167836817_state) (A_28:(hoare_1167836817_state->Prop)), (((member2058392318_state A_29) A_28)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_28) ((insert2134838167_state A_29) B_17))) ((insert2134838167_state A_29) ((semila179895820tate_o A_28) B_17))))) of role axiom named fact_612_Int__insert__right__if1
% A new axiom: (forall (B_17:(hoare_1167836817_state->Prop)) (A_29:hoare_1167836817_state) (A_28:(hoare_1167836817_state->Prop)), (((member2058392318_state A_29) A_28)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_28) ((insert2134838167_state A_29) B_17))) ((insert2134838167_state A_29) ((semila179895820tate_o A_28) B_17)))))
% FOF formula (forall (B_16:(pname->Prop)) (A_27:pname) (C_5:(pname->Prop)), ((((member_pname A_27) C_5)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_27) B_16)) C_5)) ((semila1673364395name_o B_16) C_5)))) of role axiom named fact_613_Int__insert__left__if0
% A new axiom: (forall (B_16:(pname->Prop)) (A_27:pname) (C_5:(pname->Prop)), ((((member_pname A_27) C_5)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_27) B_16)) C_5)) ((semila1673364395name_o B_16) C_5))))
% FOF formula (forall (B_16:(hoare_1167836817_state->Prop)) (A_27:hoare_1167836817_state) (C_5:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_27) C_5)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_27) B_16)) C_5)) ((semila179895820tate_o B_16) C_5)))) of role axiom named fact_614_Int__insert__left__if0
% A new axiom: (forall (B_16:(hoare_1167836817_state->Prop)) (A_27:hoare_1167836817_state) (C_5:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_27) C_5)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_27) B_16)) C_5)) ((semila179895820tate_o B_16) C_5))))
% FOF formula (forall (B_15:(pname->Prop)) (A_26:pname) (A_25:(pname->Prop)), ((((member_pname A_26) A_25)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_25) ((insert_pname A_26) B_15))) ((semila1673364395name_o A_25) B_15)))) of role axiom named fact_615_Int__insert__right__if0
% A new axiom: (forall (B_15:(pname->Prop)) (A_26:pname) (A_25:(pname->Prop)), ((((member_pname A_26) A_25)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_25) ((insert_pname A_26) B_15))) ((semila1673364395name_o A_25) B_15))))
% FOF formula (forall (B_15:(hoare_1167836817_state->Prop)) (A_26:hoare_1167836817_state) (A_25:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_26) A_25)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_25) ((insert2134838167_state A_26) B_15))) ((semila179895820tate_o A_25) B_15)))) of role axiom named fact_616_Int__insert__right__if0
% A new axiom: (forall (B_15:(hoare_1167836817_state->Prop)) (A_26:hoare_1167836817_state) (A_25:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_26) A_25)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_25) ((insert2134838167_state A_26) B_15))) ((semila179895820tate_o A_25) B_15))))
% FOF formula (forall (A_24:pname) (A_23:(pname->Prop)) (B_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_24) A_23)) ((insert_pname A_24) B_14))) ((insert_pname A_24) ((semila1673364395name_o A_23) B_14)))) of role axiom named fact_617_insert__inter__insert
% A new axiom: (forall (A_24:pname) (A_23:(pname->Prop)) (B_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_24) A_23)) ((insert_pname A_24) B_14))) ((insert_pname A_24) ((semila1673364395name_o A_23) B_14))))
% FOF formula (forall (A_24:hoare_1167836817_state) (A_23:(hoare_1167836817_state->Prop)) (B_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_24) A_23)) ((insert2134838167_state A_24) B_14))) ((insert2134838167_state A_24) ((semila179895820tate_o A_23) B_14)))) of role axiom named fact_618_insert__inter__insert
% A new axiom: (forall (A_24:hoare_1167836817_state) (A_23:(hoare_1167836817_state->Prop)) (B_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_24) A_23)) ((insert2134838167_state A_24) B_14))) ((insert2134838167_state A_24) ((semila179895820tate_o A_23) B_14))))
% FOF formula (forall (B_13:(pname->Prop)) (A_22:pname) (C_4:(pname->Prop)), ((and (((member_pname A_22) C_4)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_22) B_13)) C_4)) ((insert_pname A_22) ((semila1673364395name_o B_13) C_4))))) ((((member_pname A_22) C_4)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_22) B_13)) C_4)) ((semila1673364395name_o B_13) C_4))))) of role axiom named fact_619_Int__insert__left
% A new axiom: (forall (B_13:(pname->Prop)) (A_22:pname) (C_4:(pname->Prop)), ((and (((member_pname A_22) C_4)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_22) B_13)) C_4)) ((insert_pname A_22) ((semila1673364395name_o B_13) C_4))))) ((((member_pname A_22) C_4)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_22) B_13)) C_4)) ((semila1673364395name_o B_13) C_4)))))
% FOF formula (forall (B_13:(hoare_1167836817_state->Prop)) (A_22:hoare_1167836817_state) (C_4:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_22) C_4)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_22) B_13)) C_4)) ((insert2134838167_state A_22) ((semila179895820tate_o B_13) C_4))))) ((((member2058392318_state A_22) C_4)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_22) B_13)) C_4)) ((semila179895820tate_o B_13) C_4))))) of role axiom named fact_620_Int__insert__left
% A new axiom: (forall (B_13:(hoare_1167836817_state->Prop)) (A_22:hoare_1167836817_state) (C_4:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_22) C_4)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_22) B_13)) C_4)) ((insert2134838167_state A_22) ((semila179895820tate_o B_13) C_4))))) ((((member2058392318_state A_22) C_4)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_22) B_13)) C_4)) ((semila179895820tate_o B_13) C_4)))))
% FOF formula (forall (B_12:(pname->Prop)) (A_21:pname) (A_20:(pname->Prop)), ((and (((member_pname A_21) A_20)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) ((insert_pname A_21) B_12))) ((insert_pname A_21) ((semila1673364395name_o A_20) B_12))))) ((((member_pname A_21) A_20)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) ((insert_pname A_21) B_12))) ((semila1673364395name_o A_20) B_12))))) of role axiom named fact_621_Int__insert__right
% A new axiom: (forall (B_12:(pname->Prop)) (A_21:pname) (A_20:(pname->Prop)), ((and (((member_pname A_21) A_20)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) ((insert_pname A_21) B_12))) ((insert_pname A_21) ((semila1673364395name_o A_20) B_12))))) ((((member_pname A_21) A_20)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) ((insert_pname A_21) B_12))) ((semila1673364395name_o A_20) B_12)))))
% FOF formula (forall (B_12:(hoare_1167836817_state->Prop)) (A_21:hoare_1167836817_state) (A_20:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_21) A_20)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_20) ((insert2134838167_state A_21) B_12))) ((insert2134838167_state A_21) ((semila179895820tate_o A_20) B_12))))) ((((member2058392318_state A_21) A_20)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_20) ((insert2134838167_state A_21) B_12))) ((semila179895820tate_o A_20) B_12))))) of role axiom named fact_622_Int__insert__right
% A new axiom: (forall (B_12:(hoare_1167836817_state->Prop)) (A_21:hoare_1167836817_state) (A_20:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_21) A_20)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_20) ((insert2134838167_state A_21) B_12))) ((insert2134838167_state A_21) ((semila179895820tate_o A_20) B_12))))) ((((member2058392318_state A_21) A_20)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_20) ((insert2134838167_state A_21) B_12))) ((semila179895820tate_o A_20) B_12)))))
% FOF formula (forall (X_29:(pname->Prop)) (Y_20:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_29) Y_20)) X_29)) of role axiom named fact_623_inf__sup__ord_I1_J
% A new axiom: (forall (X_29:(pname->Prop)) (Y_20:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_29) Y_20)) X_29))
% FOF formula (forall (X_29:(hoare_1167836817_state->Prop)) (Y_20:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_29) Y_20)) X_29)) of role axiom named fact_624_inf__sup__ord_I1_J
% A new axiom: (forall (X_29:(hoare_1167836817_state->Prop)) (Y_20:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_29) Y_20)) X_29))
% FOF formula (forall (X_28:(pname->Prop)) (Y_19:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_28) Y_19)) X_28)) of role axiom named fact_625_inf__le1
% A new axiom: (forall (X_28:(pname->Prop)) (Y_19:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_28) Y_19)) X_28))
% FOF formula (forall (X_28:(hoare_1167836817_state->Prop)) (Y_19:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_28) Y_19)) X_28)) of role axiom named fact_626_inf__le1
% A new axiom: (forall (X_28:(hoare_1167836817_state->Prop)) (Y_19:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_28) Y_19)) X_28))
% FOF formula (forall (X_27:(pname->Prop)) (Y_18:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_27) Y_18)) Y_18)) of role axiom named fact_627_inf__sup__ord_I2_J
% A new axiom: (forall (X_27:(pname->Prop)) (Y_18:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_27) Y_18)) Y_18))
% FOF formula (forall (X_27:(hoare_1167836817_state->Prop)) (Y_18:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_27) Y_18)) Y_18)) of role axiom named fact_628_inf__sup__ord_I2_J
% A new axiom: (forall (X_27:(hoare_1167836817_state->Prop)) (Y_18:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_27) Y_18)) Y_18))
% FOF formula (forall (X_26:(pname->Prop)) (Y_17:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_26) Y_17)) Y_17)) of role axiom named fact_629_inf__le2
% A new axiom: (forall (X_26:(pname->Prop)) (Y_17:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_26) Y_17)) Y_17))
% FOF formula (forall (X_26:(hoare_1167836817_state->Prop)) (Y_17:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_26) Y_17)) Y_17)) of role axiom named fact_630_inf__le2
% A new axiom: (forall (X_26:(hoare_1167836817_state->Prop)) (Y_17:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_26) Y_17)) Y_17))
% FOF formula (forall (X_25:(pname->Prop)) (Y_16:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_25) Y_16)) (((eq (pname->Prop)) ((semila1673364395name_o X_25) Y_16)) X_25))) of role axiom named fact_631_le__iff__inf
% A new axiom: (forall (X_25:(pname->Prop)) (Y_16:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_25) Y_16)) (((eq (pname->Prop)) ((semila1673364395name_o X_25) Y_16)) X_25)))
% FOF formula (forall (X_25:(hoare_1167836817_state->Prop)) (Y_16:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_25) Y_16)) (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_25) Y_16)) X_25))) of role axiom named fact_632_le__iff__inf
% A new axiom: (forall (X_25:(hoare_1167836817_state->Prop)) (Y_16:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_25) Y_16)) (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_25) Y_16)) X_25)))
% FOF formula (forall (X_24:(pname->Prop)) (Y_15:(pname->Prop)) (Z_10:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_24) ((semila1673364395name_o Y_15) Z_10))) ((and ((ord_less_eq_pname_o X_24) Y_15)) ((ord_less_eq_pname_o X_24) Z_10)))) of role axiom named fact_633_le__inf__iff
% A new axiom: (forall (X_24:(pname->Prop)) (Y_15:(pname->Prop)) (Z_10:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_24) ((semila1673364395name_o Y_15) Z_10))) ((and ((ord_less_eq_pname_o X_24) Y_15)) ((ord_less_eq_pname_o X_24) Z_10))))
% FOF formula (forall (X_24:(hoare_1167836817_state->Prop)) (Y_15:(hoare_1167836817_state->Prop)) (Z_10:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_24) ((semila179895820tate_o Y_15) Z_10))) ((and ((ord_le827224136tate_o X_24) Y_15)) ((ord_le827224136tate_o X_24) Z_10)))) of role axiom named fact_634_le__inf__iff
% A new axiom: (forall (X_24:(hoare_1167836817_state->Prop)) (Y_15:(hoare_1167836817_state->Prop)) (Z_10:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_24) ((semila179895820tate_o Y_15) Z_10))) ((and ((ord_le827224136tate_o X_24) Y_15)) ((ord_le827224136tate_o X_24) Z_10))))
% FOF formula (forall (B_11:(pname->Prop)) (A_19:(pname->Prop)) (X_23:(pname->Prop)), (((ord_less_eq_pname_o A_19) X_23)->((ord_less_eq_pname_o ((semila1673364395name_o A_19) B_11)) X_23))) of role axiom named fact_635_le__infI1
% A new axiom: (forall (B_11:(pname->Prop)) (A_19:(pname->Prop)) (X_23:(pname->Prop)), (((ord_less_eq_pname_o A_19) X_23)->((ord_less_eq_pname_o ((semila1673364395name_o A_19) B_11)) X_23)))
% FOF formula (forall (B_11:(hoare_1167836817_state->Prop)) (A_19:(hoare_1167836817_state->Prop)) (X_23:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_19) X_23)->((ord_le827224136tate_o ((semila179895820tate_o A_19) B_11)) X_23))) of role axiom named fact_636_le__infI1
% A new axiom: (forall (B_11:(hoare_1167836817_state->Prop)) (A_19:(hoare_1167836817_state->Prop)) (X_23:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_19) X_23)->((ord_le827224136tate_o ((semila179895820tate_o A_19) B_11)) X_23)))
% FOF formula (forall (A_18:(pname->Prop)) (B_10:(pname->Prop)) (X_22:(pname->Prop)), (((ord_less_eq_pname_o B_10) X_22)->((ord_less_eq_pname_o ((semila1673364395name_o A_18) B_10)) X_22))) of role axiom named fact_637_le__infI2
% A new axiom: (forall (A_18:(pname->Prop)) (B_10:(pname->Prop)) (X_22:(pname->Prop)), (((ord_less_eq_pname_o B_10) X_22)->((ord_less_eq_pname_o ((semila1673364395name_o A_18) B_10)) X_22)))
% FOF formula (forall (A_18:(hoare_1167836817_state->Prop)) (B_10:(hoare_1167836817_state->Prop)) (X_22:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_10) X_22)->((ord_le827224136tate_o ((semila179895820tate_o A_18) B_10)) X_22))) of role axiom named fact_638_le__infI2
% A new axiom: (forall (A_18:(hoare_1167836817_state->Prop)) (B_10:(hoare_1167836817_state->Prop)) (X_22:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_10) X_22)->((ord_le827224136tate_o ((semila179895820tate_o A_18) B_10)) X_22)))
% FOF formula (forall (X_21:(pname->Prop)) (Y_14:(pname->Prop)), (((ord_less_eq_pname_o X_21) Y_14)->(((eq (pname->Prop)) ((semila1673364395name_o X_21) Y_14)) X_21))) of role axiom named fact_639_inf__absorb1
% A new axiom: (forall (X_21:(pname->Prop)) (Y_14:(pname->Prop)), (((ord_less_eq_pname_o X_21) Y_14)->(((eq (pname->Prop)) ((semila1673364395name_o X_21) Y_14)) X_21)))
% FOF formula (forall (X_21:(hoare_1167836817_state->Prop)) (Y_14:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_21) Y_14)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_21) Y_14)) X_21))) of role axiom named fact_640_inf__absorb1
% A new axiom: (forall (X_21:(hoare_1167836817_state->Prop)) (Y_14:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_21) Y_14)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_21) Y_14)) X_21)))
% FOF formula (forall (Y_13:(pname->Prop)) (X_20:(pname->Prop)), (((ord_less_eq_pname_o Y_13) X_20)->(((eq (pname->Prop)) ((semila1673364395name_o X_20) Y_13)) Y_13))) of role axiom named fact_641_inf__absorb2
% A new axiom: (forall (Y_13:(pname->Prop)) (X_20:(pname->Prop)), (((ord_less_eq_pname_o Y_13) X_20)->(((eq (pname->Prop)) ((semila1673364395name_o X_20) Y_13)) Y_13)))
% FOF formula (forall (Y_13:(hoare_1167836817_state->Prop)) (X_20:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_13) X_20)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_20) Y_13)) Y_13))) of role axiom named fact_642_inf__absorb2
% A new axiom: (forall (Y_13:(hoare_1167836817_state->Prop)) (X_20:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_13) X_20)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_20) Y_13)) Y_13)))
% FOF formula (forall (B_9:(pname->Prop)) (X_19:(pname->Prop)) (A_17:(pname->Prop)), (((ord_less_eq_pname_o X_19) A_17)->(((ord_less_eq_pname_o X_19) B_9)->((ord_less_eq_pname_o X_19) ((semila1673364395name_o A_17) B_9))))) of role axiom named fact_643_le__infI
% A new axiom: (forall (B_9:(pname->Prop)) (X_19:(pname->Prop)) (A_17:(pname->Prop)), (((ord_less_eq_pname_o X_19) A_17)->(((ord_less_eq_pname_o X_19) B_9)->((ord_less_eq_pname_o X_19) ((semila1673364395name_o A_17) B_9)))))
% FOF formula (forall (B_9:(hoare_1167836817_state->Prop)) (X_19:(hoare_1167836817_state->Prop)) (A_17:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_19) A_17)->(((ord_le827224136tate_o X_19) B_9)->((ord_le827224136tate_o X_19) ((semila179895820tate_o A_17) B_9))))) of role axiom named fact_644_le__infI
% A new axiom: (forall (B_9:(hoare_1167836817_state->Prop)) (X_19:(hoare_1167836817_state->Prop)) (A_17:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_19) A_17)->(((ord_le827224136tate_o X_19) B_9)->((ord_le827224136tate_o X_19) ((semila179895820tate_o A_17) B_9)))))
% FOF formula (forall (Z_9:(pname->Prop)) (X_18:(pname->Prop)) (Y_12:(pname->Prop)), (((ord_less_eq_pname_o X_18) Y_12)->(((ord_less_eq_pname_o X_18) Z_9)->((ord_less_eq_pname_o X_18) ((semila1673364395name_o Y_12) Z_9))))) of role axiom named fact_645_inf__greatest
% A new axiom: (forall (Z_9:(pname->Prop)) (X_18:(pname->Prop)) (Y_12:(pname->Prop)), (((ord_less_eq_pname_o X_18) Y_12)->(((ord_less_eq_pname_o X_18) Z_9)->((ord_less_eq_pname_o X_18) ((semila1673364395name_o Y_12) Z_9)))))
% FOF formula (forall (Z_9:(hoare_1167836817_state->Prop)) (X_18:(hoare_1167836817_state->Prop)) (Y_12:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_18) Y_12)->(((ord_le827224136tate_o X_18) Z_9)->((ord_le827224136tate_o X_18) ((semila179895820tate_o Y_12) Z_9))))) of role axiom named fact_646_inf__greatest
% A new axiom: (forall (Z_9:(hoare_1167836817_state->Prop)) (X_18:(hoare_1167836817_state->Prop)) (Y_12:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_18) Y_12)->(((ord_le827224136tate_o X_18) Z_9)->((ord_le827224136tate_o X_18) ((semila179895820tate_o Y_12) Z_9)))))
% FOF formula (forall (B_8:(pname->Prop)) (D:(pname->Prop)) (A_16:(pname->Prop)) (C_3:(pname->Prop)), (((ord_less_eq_pname_o A_16) C_3)->(((ord_less_eq_pname_o B_8) D)->((ord_less_eq_pname_o ((semila1673364395name_o A_16) B_8)) ((semila1673364395name_o C_3) D))))) of role axiom named fact_647_inf__mono
% A new axiom: (forall (B_8:(pname->Prop)) (D:(pname->Prop)) (A_16:(pname->Prop)) (C_3:(pname->Prop)), (((ord_less_eq_pname_o A_16) C_3)->(((ord_less_eq_pname_o B_8) D)->((ord_less_eq_pname_o ((semila1673364395name_o A_16) B_8)) ((semila1673364395name_o C_3) D)))))
% FOF formula (forall (B_8:(hoare_1167836817_state->Prop)) (D:(hoare_1167836817_state->Prop)) (A_16:(hoare_1167836817_state->Prop)) (C_3:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_16) C_3)->(((ord_le827224136tate_o B_8) D)->((ord_le827224136tate_o ((semila179895820tate_o A_16) B_8)) ((semila179895820tate_o C_3) D))))) of role axiom named fact_648_inf__mono
% A new axiom: (forall (B_8:(hoare_1167836817_state->Prop)) (D:(hoare_1167836817_state->Prop)) (A_16:(hoare_1167836817_state->Prop)) (C_3:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_16) C_3)->(((ord_le827224136tate_o B_8) D)->((ord_le827224136tate_o ((semila179895820tate_o A_16) B_8)) ((semila179895820tate_o C_3) D)))))
% FOF formula (forall (X_17:(pname->Prop)) (A_15:(pname->Prop)) (B_7:(pname->Prop)), (((ord_less_eq_pname_o X_17) ((semila1673364395name_o A_15) B_7))->((((ord_less_eq_pname_o X_17) A_15)->(((ord_less_eq_pname_o X_17) B_7)->False))->False))) of role axiom named fact_649_le__infE
% A new axiom: (forall (X_17:(pname->Prop)) (A_15:(pname->Prop)) (B_7:(pname->Prop)), (((ord_less_eq_pname_o X_17) ((semila1673364395name_o A_15) B_7))->((((ord_less_eq_pname_o X_17) A_15)->(((ord_less_eq_pname_o X_17) B_7)->False))->False)))
% FOF formula (forall (X_17:(hoare_1167836817_state->Prop)) (A_15:(hoare_1167836817_state->Prop)) (B_7:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_17) ((semila179895820tate_o A_15) B_7))->((((ord_le827224136tate_o X_17) A_15)->(((ord_le827224136tate_o X_17) B_7)->False))->False))) of role axiom named fact_650_le__infE
% A new axiom: (forall (X_17:(hoare_1167836817_state->Prop)) (A_15:(hoare_1167836817_state->Prop)) (B_7:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_17) ((semila179895820tate_o A_15) B_7))->((((ord_le827224136tate_o X_17) A_15)->(((ord_le827224136tate_o X_17) B_7)->False))->False)))
% FOF formula (forall (X_16:(hoare_1167836817_state->Prop)) (Y_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_16) ((semila1172322802tate_o X_16) Y_11))) X_16)) of role axiom named fact_651_inf__sup__absorb
% A new axiom: (forall (X_16:(hoare_1167836817_state->Prop)) (Y_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_16) ((semila1172322802tate_o X_16) Y_11))) X_16))
% FOF formula (forall (X_15:(hoare_1167836817_state->Prop)) (Y_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_15) ((semila179895820tate_o X_15) Y_10))) X_15)) of role axiom named fact_652_sup__inf__absorb
% A new axiom: (forall (X_15:(hoare_1167836817_state->Prop)) (Y_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_15) ((semila179895820tate_o X_15) Y_10))) X_15))
% FOF formula (forall (X_14:(hoare_1167836817_state->Prop)) (Y_9:(hoare_1167836817_state->Prop)) (Z_8:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_14) ((semila1172322802tate_o Y_9) Z_8))) ((semila1172322802tate_o ((semila179895820tate_o X_14) Y_9)) ((semila179895820tate_o X_14) Z_8)))) of role axiom named fact_653_inf__sup__distrib1
% A new axiom: (forall (X_14:(hoare_1167836817_state->Prop)) (Y_9:(hoare_1167836817_state->Prop)) (Z_8:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_14) ((semila1172322802tate_o Y_9) Z_8))) ((semila1172322802tate_o ((semila179895820tate_o X_14) Y_9)) ((semila179895820tate_o X_14) Z_8))))
% FOF formula (forall (X_13:(hoare_1167836817_state->Prop)) (Y_8:(hoare_1167836817_state->Prop)) (Z_7:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_13) ((semila179895820tate_o Y_8) Z_7))) ((semila179895820tate_o ((semila1172322802tate_o X_13) Y_8)) ((semila1172322802tate_o X_13) Z_7)))) of role axiom named fact_654_sup__inf__distrib1
% A new axiom: (forall (X_13:(hoare_1167836817_state->Prop)) (Y_8:(hoare_1167836817_state->Prop)) (Z_7:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_13) ((semila179895820tate_o Y_8) Z_7))) ((semila179895820tate_o ((semila1172322802tate_o X_13) Y_8)) ((semila1172322802tate_o X_13) Z_7))))
% FOF formula (forall (Y_7:(hoare_1167836817_state->Prop)) (Z_6:(hoare_1167836817_state->Prop)) (X_12:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o Y_7) Z_6)) X_12)) ((semila1172322802tate_o ((semila179895820tate_o Y_7) X_12)) ((semila179895820tate_o Z_6) X_12)))) of role axiom named fact_655_inf__sup__distrib2
% A new axiom: (forall (Y_7:(hoare_1167836817_state->Prop)) (Z_6:(hoare_1167836817_state->Prop)) (X_12:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o Y_7) Z_6)) X_12)) ((semila1172322802tate_o ((semila179895820tate_o Y_7) X_12)) ((semila179895820tate_o Z_6) X_12))))
% FOF formula (forall (Y_6:(hoare_1167836817_state->Prop)) (Z_5:(hoare_1167836817_state->Prop)) (X_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o Y_6) Z_5)) X_11)) ((semila179895820tate_o ((semila1172322802tate_o Y_6) X_11)) ((semila1172322802tate_o Z_5) X_11)))) of role axiom named fact_656_sup__inf__distrib2
% A new axiom: (forall (Y_6:(hoare_1167836817_state->Prop)) (Z_5:(hoare_1167836817_state->Prop)) (X_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o Y_6) Z_5)) X_11)) ((semila179895820tate_o ((semila1172322802tate_o Y_6) X_11)) ((semila1172322802tate_o Z_5) X_11))))
% FOF formula (forall (X_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_10) bot_bot_pname_o)) bot_bot_pname_o)) of role axiom named fact_657_inf__bot__right
% A new axiom: (forall (X_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_10) bot_bot_pname_o)) bot_bot_pname_o))
% FOF formula (forall (X_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_10) bot_bo70021908tate_o)) bot_bo70021908tate_o)) of role axiom named fact_658_inf__bot__right
% A new axiom: (forall (X_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_10) bot_bo70021908tate_o)) bot_bo70021908tate_o))
% FOF formula (forall (X_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) X_9)) bot_bot_pname_o)) of role axiom named fact_659_inf__bot__left
% A new axiom: (forall (X_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) X_9)) bot_bot_pname_o))
% FOF formula (forall (X_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) X_9)) bot_bo70021908tate_o)) of role axiom named fact_660_inf__bot__left
% A new axiom: (forall (X_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) X_9)) bot_bo70021908tate_o))
% FOF formula (forall (X_8:(pname->Prop)) (Y_5:(pname->Prop)) (Z_4:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o X_8) ((semila1673364395name_o Y_5) Z_4))) ((semila1673364395name_o ((semila1780557381name_o X_8) Y_5)) ((semila1780557381name_o X_8) Z_4)))) of role axiom named fact_661_distrib__sup__le
% A new axiom: (forall (X_8:(pname->Prop)) (Y_5:(pname->Prop)) (Z_4:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o X_8) ((semila1673364395name_o Y_5) Z_4))) ((semila1673364395name_o ((semila1780557381name_o X_8) Y_5)) ((semila1780557381name_o X_8) Z_4))))
% FOF formula (forall (X_8:(hoare_1167836817_state->Prop)) (Y_5:(hoare_1167836817_state->Prop)) (Z_4:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila1172322802tate_o X_8) ((semila179895820tate_o Y_5) Z_4))) ((semila179895820tate_o ((semila1172322802tate_o X_8) Y_5)) ((semila1172322802tate_o X_8) Z_4)))) of role axiom named fact_662_distrib__sup__le
% A new axiom: (forall (X_8:(hoare_1167836817_state->Prop)) (Y_5:(hoare_1167836817_state->Prop)) (Z_4:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila1172322802tate_o X_8) ((semila179895820tate_o Y_5) Z_4))) ((semila179895820tate_o ((semila1172322802tate_o X_8) Y_5)) ((semila1172322802tate_o X_8) Z_4))))
% FOF formula (forall (X_7:(pname->Prop)) (Y_4:(pname->Prop)) (Z_3:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o ((semila1673364395name_o X_7) Y_4)) ((semila1673364395name_o X_7) Z_3))) ((semila1673364395name_o X_7) ((semila1780557381name_o Y_4) Z_3)))) of role axiom named fact_663_distrib__inf__le
% A new axiom: (forall (X_7:(pname->Prop)) (Y_4:(pname->Prop)) (Z_3:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o ((semila1673364395name_o X_7) Y_4)) ((semila1673364395name_o X_7) Z_3))) ((semila1673364395name_o X_7) ((semila1780557381name_o Y_4) Z_3))))
% FOF formula (forall (X_7:(hoare_1167836817_state->Prop)) (Y_4:(hoare_1167836817_state->Prop)) (Z_3:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila1172322802tate_o ((semila179895820tate_o X_7) Y_4)) ((semila179895820tate_o X_7) Z_3))) ((semila179895820tate_o X_7) ((semila1172322802tate_o Y_4) Z_3)))) of role axiom named fact_664_distrib__inf__le
% A new axiom: (forall (X_7:(hoare_1167836817_state->Prop)) (Y_4:(hoare_1167836817_state->Prop)) (Z_3:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila1172322802tate_o ((semila179895820tate_o X_7) Y_4)) ((semila179895820tate_o X_7) Z_3))) ((semila179895820tate_o X_7) ((semila1172322802tate_o Y_4) Z_3))))
% FOF formula (forall (F_6:(pname->hoare_1167836817_state)) (A_14:(pname->Prop)) (B_6:(pname->Prop)), ((ord_le827224136tate_o ((image_575578384_state F_6) ((semila1673364395name_o A_14) B_6))) ((semila179895820tate_o ((image_575578384_state F_6) A_14)) ((image_575578384_state F_6) B_6)))) of role axiom named fact_665_image__Int__subset
% A new axiom: (forall (F_6:(pname->hoare_1167836817_state)) (A_14:(pname->Prop)) (B_6:(pname->Prop)), ((ord_le827224136tate_o ((image_575578384_state F_6) ((semila1673364395name_o A_14) B_6))) ((semila179895820tate_o ((image_575578384_state F_6) A_14)) ((image_575578384_state F_6) B_6))))
% FOF formula (forall (A_13:(pname->Prop)) (B_5:(pname->Prop)) (C_2:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o A_13) B_5)) C_2)) ((semila1673364395name_o A_13) ((semila1780557381name_o B_5) C_2)))) ((ord_less_eq_pname_o C_2) A_13))) of role axiom named fact_666_Un__Int__assoc__eq
% A new axiom: (forall (A_13:(pname->Prop)) (B_5:(pname->Prop)) (C_2:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o A_13) B_5)) C_2)) ((semila1673364395name_o A_13) ((semila1780557381name_o B_5) C_2)))) ((ord_less_eq_pname_o C_2) A_13)))
% FOF formula (forall (A_13:(hoare_1167836817_state->Prop)) (B_5:(hoare_1167836817_state->Prop)) (C_2:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o A_13) B_5)) C_2)) ((semila179895820tate_o A_13) ((semila1172322802tate_o B_5) C_2)))) ((ord_le827224136tate_o C_2) A_13))) of role axiom named fact_667_Un__Int__assoc__eq
% A new axiom: (forall (A_13:(hoare_1167836817_state->Prop)) (B_5:(hoare_1167836817_state->Prop)) (C_2:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o A_13) B_5)) C_2)) ((semila179895820tate_o A_13) ((semila1172322802tate_o B_5) C_2)))) ((ord_le827224136tate_o C_2) A_13)))
% FOF formula (forall (P_3:(pname->Prop)) (F_5:(pname->hoare_1167836817_state)) (G_1:(pname->hoare_1167836817_state)) (S:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> (((if_Hoa833675553_state (P_3 X_5)) (F_5 X_5)) (G_1 X_5)))) S)) ((semila1172322802tate_o ((image_575578384_state F_5) ((semila1673364395name_o S) (collect_pname P_3)))) ((image_575578384_state G_1) ((semila1673364395name_o S) (collect_pname (fun (X_5:pname)=> (not (P_3 X_5))))))))) of role axiom named fact_668_if__image__distrib
% A new axiom: (forall (P_3:(pname->Prop)) (F_5:(pname->hoare_1167836817_state)) (G_1:(pname->hoare_1167836817_state)) (S:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> (((if_Hoa833675553_state (P_3 X_5)) (F_5 X_5)) (G_1 X_5)))) S)) ((semila1172322802tate_o ((image_575578384_state F_5) ((semila1673364395name_o S) (collect_pname P_3)))) ((image_575578384_state G_1) ((semila1673364395name_o S) (collect_pname (fun (X_5:pname)=> (not (P_3 X_5)))))))))
% FOF formula (forall (P_2:(pname->Prop)) (F_4:(pname->option_com)) (G:(pname->option_com)), (((eq (pname->Prop)) (dom_pname_com (fun (X_5:pname)=> (((if_option_com (P_2 X_5)) (F_4 X_5)) (G X_5))))) ((semila1780557381name_o ((semila1673364395name_o (dom_pname_com F_4)) (collect_pname P_2))) ((semila1673364395name_o (dom_pname_com G)) (collect_pname (fun (X_5:pname)=> (not (P_2 X_5)))))))) of role axiom named fact_669_dom__if
% A new axiom: (forall (P_2:(pname->Prop)) (F_4:(pname->option_com)) (G:(pname->option_com)), (((eq (pname->Prop)) (dom_pname_com (fun (X_5:pname)=> (((if_option_com (P_2 X_5)) (F_4 X_5)) (G X_5))))) ((semila1780557381name_o ((semila1673364395name_o (dom_pname_com F_4)) (collect_pname P_2))) ((semila1673364395name_o (dom_pname_com G)) (collect_pname (fun (X_5:pname)=> (not (P_2 X_5))))))))
% FOF formula (forall (Q:(pname->Prop)) (P_1:(pname->Prop)) (A_12:(pname->Prop)) (B_4:(pname->Prop)), (((ord_less_eq_pname_o A_12) B_4)->((forall (X_5:pname), (((member_pname X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_less_eq_pname_o ((semila1673364395name_o A_12) (collect_pname P_1))) ((semila1673364395name_o B_4) (collect_pname Q)))))) of role axiom named fact_670_Int__Collect__mono
% A new axiom: (forall (Q:(pname->Prop)) (P_1:(pname->Prop)) (A_12:(pname->Prop)) (B_4:(pname->Prop)), (((ord_less_eq_pname_o A_12) B_4)->((forall (X_5:pname), (((member_pname X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_less_eq_pname_o ((semila1673364395name_o A_12) (collect_pname P_1))) ((semila1673364395name_o B_4) (collect_pname Q))))))
% FOF formula (forall (Q:(hoare_1167836817_state->Prop)) (P_1:(hoare_1167836817_state->Prop)) (A_12:(hoare_1167836817_state->Prop)) (B_4:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_12) B_4)->((forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_le827224136tate_o ((semila179895820tate_o A_12) (collec1027672124_state P_1))) ((semila179895820tate_o B_4) (collec1027672124_state Q)))))) of role axiom named fact_671_Int__Collect__mono
% A new axiom: (forall (Q:(hoare_1167836817_state->Prop)) (P_1:(hoare_1167836817_state->Prop)) (A_12:(hoare_1167836817_state->Prop)) (B_4:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_12) B_4)->((forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_le827224136tate_o ((semila179895820tate_o A_12) (collec1027672124_state P_1))) ((semila179895820tate_o B_4) (collec1027672124_state Q))))))
% FOF formula (forall (Q:((pname->Prop)->Prop)) (P_1:((pname->Prop)->Prop)) (A_12:((pname->Prop)->Prop)) (B_4:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_12) B_4)->((forall (X_5:(pname->Prop)), (((member_pname_o X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_le1205211808me_o_o ((semila2013987940me_o_o A_12) (collect_pname_o P_1))) ((semila2013987940me_o_o B_4) (collect_pname_o Q)))))) of role axiom named fact_672_Int__Collect__mono
% A new axiom: (forall (Q:((pname->Prop)->Prop)) (P_1:((pname->Prop)->Prop)) (A_12:((pname->Prop)->Prop)) (B_4:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_12) B_4)->((forall (X_5:(pname->Prop)), (((member_pname_o X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_le1205211808me_o_o ((semila2013987940me_o_o A_12) (collect_pname_o P_1))) ((semila2013987940me_o_o B_4) (collect_pname_o Q))))))
% FOF formula (forall (Q:((hoare_1167836817_state->Prop)->Prop)) (P_1:((hoare_1167836817_state->Prop)->Prop)) (A_12:((hoare_1167836817_state->Prop)->Prop)) (B_4:((hoare_1167836817_state->Prop)->Prop)), (((ord_le741939125te_o_o A_12) B_4)->((forall (X_5:(hoare_1167836817_state->Prop)), (((member864234961tate_o X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_le741939125te_o_o ((semila1758709489te_o_o A_12) (collec269976083tate_o P_1))) ((semila1758709489te_o_o B_4) (collec269976083tate_o Q)))))) of role axiom named fact_673_Int__Collect__mono
% A new axiom: (forall (Q:((hoare_1167836817_state->Prop)->Prop)) (P_1:((hoare_1167836817_state->Prop)->Prop)) (A_12:((hoare_1167836817_state->Prop)->Prop)) (B_4:((hoare_1167836817_state->Prop)->Prop)), (((ord_le741939125te_o_o A_12) B_4)->((forall (X_5:(hoare_1167836817_state->Prop)), (((member864234961tate_o X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_le741939125te_o_o ((semila1758709489te_o_o A_12) (collec269976083tate_o P_1))) ((semila1758709489te_o_o B_4) (collec269976083tate_o Q))))))
% FOF formula (forall (X_6:(hoare_1167836817_state->Prop)) (Y_3:(hoare_1167836817_state->Prop)) (Z_2:(hoare_1167836817_state->Prop)), ((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_1:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_5) ((semila1172322802tate_o Y_2) Z_1))) ((semila1172322802tate_o ((semila179895820tate_o X_5) Y_2)) ((semila179895820tate_o X_5) Z_1))))->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_6) ((semila179895820tate_o Y_3) Z_2))) ((semila179895820tate_o ((semila1172322802tate_o X_6) Y_3)) ((semila1172322802tate_o X_6) Z_2))))) of role axiom named fact_674_distrib__imp1
% A new axiom: (forall (X_6:(hoare_1167836817_state->Prop)) (Y_3:(hoare_1167836817_state->Prop)) (Z_2:(hoare_1167836817_state->Prop)), ((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_1:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_5) ((semila1172322802tate_o Y_2) Z_1))) ((semila1172322802tate_o ((semila179895820tate_o X_5) Y_2)) ((semila179895820tate_o X_5) Z_1))))->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_6) ((semila179895820tate_o Y_3) Z_2))) ((semila179895820tate_o ((semila1172322802tate_o X_6) Y_3)) ((semila1172322802tate_o X_6) Z_2)))))
% FOF formula (forall (X_4:(hoare_1167836817_state->Prop)) (Y_1:(hoare_1167836817_state->Prop)) (Z:(hoare_1167836817_state->Prop)), ((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_1:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_5) ((semila179895820tate_o Y_2) Z_1))) ((semila179895820tate_o ((semila1172322802tate_o X_5) Y_2)) ((semila1172322802tate_o X_5) Z_1))))->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_4) ((semila1172322802tate_o Y_1) Z))) ((semila1172322802tate_o ((semila179895820tate_o X_4) Y_1)) ((semila179895820tate_o X_4) Z))))) of role axiom named fact_675_distrib__imp2
% A new axiom: (forall (X_4:(hoare_1167836817_state->Prop)) (Y_1:(hoare_1167836817_state->Prop)) (Z:(hoare_1167836817_state->Prop)), ((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_1:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_5) ((semila179895820tate_o Y_2) Z_1))) ((semila179895820tate_o ((semila1172322802tate_o X_5) Y_2)) ((semila1172322802tate_o X_5) Z_1))))->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_4) ((semila1172322802tate_o Y_1) Z))) ((semila1172322802tate_o ((semila179895820tate_o X_4) Y_1)) ((semila179895820tate_o X_4) Z)))))
% FOF formula (forall (X_3:pname) (A_11:(pname->Prop)) (F_3:(pname->(pname->pname))) (F_2:((pname->Prop)->pname)), (((finite1282449217_pname F_3) F_2)->((finite_finite_pname A_11)->(((member_pname X_3) A_11)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_11) ((insert_pname X_3) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_2 A_11)) X_3))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_11) ((insert_pname X_3) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_minus_pname_o A_11) ((insert_pname X_3) bot_bot_pname_o))))))))))) of role axiom named fact_676_folding__one_Oremove
% A new axiom: (forall (X_3:pname) (A_11:(pname->Prop)) (F_3:(pname->(pname->pname))) (F_2:((pname->Prop)->pname)), (((finite1282449217_pname F_3) F_2)->((finite_finite_pname A_11)->(((member_pname X_3) A_11)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_11) ((insert_pname X_3) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_2 A_11)) X_3))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_11) ((insert_pname X_3) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_minus_pname_o A_11) ((insert_pname X_3) bot_bot_pname_o)))))))))))
% FOF formula (forall (X_3:hoare_1167836817_state) (A_11:(hoare_1167836817_state->Prop)) (F_3:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_2:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_3) F_2)->((finite1084549118_state A_11)->(((member2058392318_state X_3) A_11)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_11) ((insert2134838167_state X_3) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_2 A_11)) X_3))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_11) ((insert2134838167_state X_3) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_2107060239tate_o A_11) ((insert2134838167_state X_3) bot_bo70021908tate_o))))))))))) of role axiom named fact_677_folding__one_Oremove
% A new axiom: (forall (X_3:hoare_1167836817_state) (A_11:(hoare_1167836817_state->Prop)) (F_3:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_2:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_3) F_2)->((finite1084549118_state A_11)->(((member2058392318_state X_3) A_11)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_11) ((insert2134838167_state X_3) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_2 A_11)) X_3))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_11) ((insert2134838167_state X_3) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_2107060239tate_o A_11) ((insert2134838167_state X_3) bot_bo70021908tate_o)))))))))))
% FOF formula (forall (X_3:(pname->Prop)) (A_11:((pname->Prop)->Prop)) (F_3:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_2:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_3) F_2)->((finite297249702name_o A_11)->(((member_pname_o X_3) A_11)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_11) ((insert_pname_o X_3) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_2 A_11)) X_3))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_11) ((insert_pname_o X_3) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_1480864103me_o_o A_11) ((insert_pname_o X_3) bot_bot_pname_o_o))))))))))) of role axiom named fact_678_folding__one_Oremove
% A new axiom: (forall (X_3:(pname->Prop)) (A_11:((pname->Prop)->Prop)) (F_3:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_2:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_3) F_2)->((finite297249702name_o A_11)->(((member_pname_o X_3) A_11)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_11) ((insert_pname_o X_3) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_2 A_11)) X_3))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_11) ((insert_pname_o X_3) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_1480864103me_o_o A_11) ((insert_pname_o X_3) bot_bot_pname_o_o)))))))))))
% FOF formula (forall (X_3:(hoare_1167836817_state->Prop)) (A_11:((hoare_1167836817_state->Prop)->Prop)) (F_3:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_2:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_3) F_2)->((finite1380128977tate_o A_11)->(((member864234961tate_o X_3) A_11)->((and ((((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_11) ((insert999278200tate_o X_3) bot_bo691907561te_o_o))) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (F_2 A_11)) X_3))) ((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_11) ((insert999278200tate_o X_3) bot_bo691907561te_o_o))) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_1708687022te_o_o A_11) ((insert999278200tate_o X_3) bot_bo691907561te_o_o))))))))))) of role axiom named fact_679_folding__one_Oremove
% A new axiom: (forall (X_3:(hoare_1167836817_state->Prop)) (A_11:((hoare_1167836817_state->Prop)->Prop)) (F_3:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_2:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_3) F_2)->((finite1380128977tate_o A_11)->(((member864234961tate_o X_3) A_11)->((and ((((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_11) ((insert999278200tate_o X_3) bot_bo691907561te_o_o))) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (F_2 A_11)) X_3))) ((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_11) ((insert999278200tate_o X_3) bot_bo691907561te_o_o))) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_1708687022te_o_o A_11) ((insert999278200tate_o X_3) bot_bo691907561te_o_o)))))))))))
% FOF formula (forall (X_2:pname) (A_10:(pname->Prop)) (F_1:(pname->(pname->pname))) (F:((pname->Prop)->pname)), (((finite1282449217_pname F_1) F)->((finite_finite_pname A_10)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_10) ((insert_pname X_2) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F ((insert_pname X_2) A_10))) X_2))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_10) ((insert_pname X_2) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F ((insert_pname X_2) A_10))) ((F_1 X_2) (F ((minus_minus_pname_o A_10) ((insert_pname X_2) bot_bot_pname_o)))))))))) of role axiom named fact_680_folding__one_Oinsert__remove
% A new axiom: (forall (X_2:pname) (A_10:(pname->Prop)) (F_1:(pname->(pname->pname))) (F:((pname->Prop)->pname)), (((finite1282449217_pname F_1) F)->((finite_finite_pname A_10)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_10) ((insert_pname X_2) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F ((insert_pname X_2) A_10))) X_2))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_10) ((insert_pname X_2) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F ((insert_pname X_2) A_10))) ((F_1 X_2) (F ((minus_minus_pname_o A_10) ((insert_pname X_2) bot_bot_pname_o))))))))))
% FOF formula (forall (X_2:hoare_1167836817_state) (A_10:(hoare_1167836817_state->Prop)) (F_1:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_1) F)->((finite1084549118_state A_10)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_10) ((insert2134838167_state X_2) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F ((insert2134838167_state X_2) A_10))) X_2))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_10) ((insert2134838167_state X_2) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F ((insert2134838167_state X_2) A_10))) ((F_1 X_2) (F ((minus_2107060239tate_o A_10) ((insert2134838167_state X_2) bot_bo70021908tate_o)))))))))) of role axiom named fact_681_folding__one_Oinsert__remove
% A new axiom: (forall (X_2:hoare_1167836817_state) (A_10:(hoare_1167836817_state->Prop)) (F_1:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_1) F)->((finite1084549118_state A_10)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_10) ((insert2134838167_state X_2) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F ((insert2134838167_state X_2) A_10))) X_2))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_10) ((insert2134838167_state X_2) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F ((insert2134838167_state X_2) A_10))) ((F_1 X_2) (F ((minus_2107060239tate_o A_10) ((insert2134838167_state X_2) bot_bo70021908tate_o))))))))))
% FOF formula (forall (X_2:(pname->Prop)) (A_10:((pname->Prop)->Prop)) (F_1:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_1) F)->((finite297249702name_o A_10)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_10) ((insert_pname_o X_2) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F ((insert_pname_o X_2) A_10))) X_2))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_10) ((insert_pname_o X_2) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F ((insert_pname_o X_2) A_10))) ((F_1 X_2) (F ((minus_1480864103me_o_o A_10) ((insert_pname_o X_2) bot_bot_pname_o_o)))))))))) of role axiom named fact_682_folding__one_Oinsert__remove
% A new axiom: (forall (X_2:(pname->Prop)) (A_10:((pname->Prop)->Prop)) (F_1:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_1) F)->((finite297249702name_o A_10)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_10) ((insert_pname_o X_2) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F ((insert_pname_o X_2) A_10))) X_2))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_10) ((insert_pname_o X_2) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F ((insert_pname_o X_2) A_10))) ((F_1 X_2) (F ((minus_1480864103me_o_o A_10) ((insert_pname_o X_2) bot_bot_pname_o_o))))))))))
% FOF formula (forall (X_2:(hoare_1167836817_state->Prop)) (A_10:((hoare_1167836817_state->Prop)->Prop)) (F_1:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_1) F)->((finite1380128977tate_o A_10)->((and ((((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_10) ((insert999278200tate_o X_2) bot_bo691907561te_o_o))) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (F ((insert999278200tate_o X_2) A_10))) X_2))) ((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_10) ((insert999278200tate_o X_2) bot_bo691907561te_o_o))) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F ((insert999278200tate_o X_2) A_10))) ((F_1 X_2) (F ((minus_1708687022te_o_o A_10) ((insert999278200tate_o X_2) bot_bo691907561te_o_o)))))))))) of role axiom named fact_683_folding__one_Oinsert__remove
% A new axiom: (forall (X_2:(hoare_1167836817_state->Prop)) (A_10:((hoare_1167836817_state->Prop)->Prop)) (F_1:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_1) F)->((finite1380128977tate_o A_10)->((and ((((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_10) ((insert999278200tate_o X_2) bot_bo691907561te_o_o))) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (F ((insert999278200tate_o X_2) A_10))) X_2))) ((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_10) ((insert999278200tate_o X_2) bot_bo691907561te_o_o))) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F ((insert999278200tate_o X_2) A_10))) ((F_1 X_2) (F ((minus_1708687022te_o_o A_10) ((insert999278200tate_o X_2) bot_bo691907561te_o_o))))))))))
% FOF formula (forall (B_3:(pname->Prop)) (C_1:pname) (A_9:(pname->Prop)), (((member_pname C_1) A_9)->((((member_pname C_1) B_3)->False)->((member_pname C_1) ((minus_minus_pname_o A_9) B_3))))) of role axiom named fact_684_DiffI
% A new axiom: (forall (B_3:(pname->Prop)) (C_1:pname) (A_9:(pname->Prop)), (((member_pname C_1) A_9)->((((member_pname C_1) B_3)->False)->((member_pname C_1) ((minus_minus_pname_o A_9) B_3)))))
% FOF formula (forall (B_3:(hoare_1167836817_state->Prop)) (C_1:hoare_1167836817_state) (A_9:(hoare_1167836817_state->Prop)), (((member2058392318_state C_1) A_9)->((((member2058392318_state C_1) B_3)->False)->((member2058392318_state C_1) ((minus_2107060239tate_o A_9) B_3))))) of role axiom named fact_685_DiffI
% A new axiom: (forall (B_3:(hoare_1167836817_state->Prop)) (C_1:hoare_1167836817_state) (A_9:(hoare_1167836817_state->Prop)), (((member2058392318_state C_1) A_9)->((((member2058392318_state C_1) B_3)->False)->((member2058392318_state C_1) ((minus_2107060239tate_o A_9) B_3)))))
% FOF formula (forall (C:pname) (A_8:(pname->Prop)) (B_2:(pname->Prop)), (((member_pname C) ((minus_minus_pname_o A_8) B_2))->((((member_pname C) A_8)->((member_pname C) B_2))->False))) of role axiom named fact_686_DiffE
% A new axiom: (forall (C:pname) (A_8:(pname->Prop)) (B_2:(pname->Prop)), (((member_pname C) ((minus_minus_pname_o A_8) B_2))->((((member_pname C) A_8)->((member_pname C) B_2))->False)))
% FOF formula (forall (C:hoare_1167836817_state) (A_8:(hoare_1167836817_state->Prop)) (B_2:(hoare_1167836817_state->Prop)), (((member2058392318_state C) ((minus_2107060239tate_o A_8) B_2))->((((member2058392318_state C) A_8)->((member2058392318_state C) B_2))->False))) of role axiom named fact_687_DiffE
% A new axiom: (forall (C:hoare_1167836817_state) (A_8:(hoare_1167836817_state->Prop)) (B_2:(hoare_1167836817_state->Prop)), (((member2058392318_state C) ((minus_2107060239tate_o A_8) B_2))->((((member2058392318_state C) A_8)->((member2058392318_state C) B_2))->False)))
% FOF formula (forall (B_1:((pname->Prop)->Prop)) (A_7:((pname->Prop)->Prop)), ((finite297249702name_o A_7)->(finite297249702name_o ((minus_1480864103me_o_o A_7) B_1)))) of role axiom named fact_688_finite__Diff
% A new axiom: (forall (B_1:((pname->Prop)->Prop)) (A_7:((pname->Prop)->Prop)), ((finite297249702name_o A_7)->(finite297249702name_o ((minus_1480864103me_o_o A_7) B_1))))
% FOF formula (forall (B_1:((hoare_1167836817_state->Prop)->Prop)) (A_7:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_7)->(finite1380128977tate_o ((minus_1708687022te_o_o A_7) B_1)))) of role axiom named fact_689_finite__Diff
% A new axiom: (forall (B_1:((hoare_1167836817_state->Prop)->Prop)) (A_7:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_7)->(finite1380128977tate_o ((minus_1708687022te_o_o A_7) B_1))))
% FOF formula (forall (B_1:(pname->Prop)) (A_7:(pname->Prop)), ((finite_finite_pname A_7)->(finite_finite_pname ((minus_minus_pname_o A_7) B_1)))) of role axiom named fact_690_finite__Diff
% A new axiom: (forall (B_1:(pname->Prop)) (A_7:(pname->Prop)), ((finite_finite_pname A_7)->(finite_finite_pname ((minus_minus_pname_o A_7) B_1))))
% FOF formula (forall (B_1:(hoare_1167836817_state->Prop)) (A_7:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_7)->(finite1084549118_state ((minus_2107060239tate_o A_7) B_1)))) of role axiom named fact_691_finite__Diff
% A new axiom: (forall (B_1:(hoare_1167836817_state->Prop)) (A_7:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_7)->(finite1084549118_state ((minus_2107060239tate_o A_7) B_1))))
% FOF formula (forall (A_6:pname) (A_5:(pname->Prop)), (((member_pname A_6) A_5)->(((eq (pname->Prop)) ((insert_pname A_6) ((minus_minus_pname_o A_5) ((insert_pname A_6) bot_bot_pname_o)))) A_5))) of role axiom named fact_692_insert__Diff
% A new axiom: (forall (A_6:pname) (A_5:(pname->Prop)), (((member_pname A_6) A_5)->(((eq (pname->Prop)) ((insert_pname A_6) ((minus_minus_pname_o A_5) ((insert_pname A_6) bot_bot_pname_o)))) A_5)))
% FOF formula (forall (A_6:hoare_1167836817_state) (A_5:(hoare_1167836817_state->Prop)), (((member2058392318_state A_6) A_5)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_6) ((minus_2107060239tate_o A_5) ((insert2134838167_state A_6) bot_bo70021908tate_o)))) A_5))) of role axiom named fact_693_insert__Diff
% A new axiom: (forall (A_6:hoare_1167836817_state) (A_5:(hoare_1167836817_state->Prop)), (((member2058392318_state A_6) A_5)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_6) ((minus_2107060239tate_o A_5) ((insert2134838167_state A_6) bot_bo70021908tate_o)))) A_5)))
% FOF formula (forall (X_1:pname) (A_4:(pname->Prop)), ((((member_pname X_1) A_4)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_1) A_4)) ((insert_pname X_1) bot_bot_pname_o))) A_4))) of role axiom named fact_694_Diff__insert__absorb
% A new axiom: (forall (X_1:pname) (A_4:(pname->Prop)), ((((member_pname X_1) A_4)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_1) A_4)) ((insert_pname X_1) bot_bot_pname_o))) A_4)))
% FOF formula (forall (X_1:hoare_1167836817_state) (A_4:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_1) A_4)->False)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_1) A_4)) ((insert2134838167_state X_1) bot_bo70021908tate_o))) A_4))) of role axiom named fact_695_Diff__insert__absorb
% A new axiom: (forall (X_1:hoare_1167836817_state) (A_4:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_1) A_4)->False)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_1) A_4)) ((insert2134838167_state X_1) bot_bo70021908tate_o))) A_4)))
% FOF formula (forall (A_3:pname) (A_2:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_3) ((minus_minus_pname_o A_2) ((insert_pname A_3) bot_bot_pname_o)))) ((insert_pname A_3) A_2))) of role axiom named fact_696_insert__Diff__single
% A new axiom: (forall (A_3:pname) (A_2:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_3) ((minus_minus_pname_o A_2) ((insert_pname A_3) bot_bot_pname_o)))) ((insert_pname A_3) A_2)))
% FOF formula (forall (A_3:hoare_1167836817_state) (A_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_3) ((minus_2107060239tate_o A_2) ((insert2134838167_state A_3) bot_bo70021908tate_o)))) ((insert2134838167_state A_3) A_2))) of role axiom named fact_697_insert__Diff__single
% A new axiom: (forall (A_3:hoare_1167836817_state) (A_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_3) ((minus_2107060239tate_o A_2) ((insert2134838167_state A_3) bot_bo70021908tate_o)))) ((insert2134838167_state A_3) A_2)))
% FOF formula (forall (A_1:(hoare_1167836817_state->Prop)) (A:hoare_1167836817_state) (B:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_1) ((insert2134838167_state A) B))) ((minus_2107060239tate_o ((minus_2107060239tate_o A_1) ((insert2134838167_state A) bot_bo70021908tate_o))) B))) of role axiom named fact_698_Diff__insert2
% A new axiom: (forall (A_1:(hoare_1167836817_state->Prop)) (A:hoare_1167836817_state) (B:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_1) ((insert2134838167_state A) B))) ((minus_2107060239tate_o ((minus_2107060239tate_o A_1) ((insert2134838167_state A) bot_bo70021908tate_o))) B)))
% 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_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_state True) X) Y)) X)) of role axiom named help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate
% A new axiom: (forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_state True) X) Y)) X))
% FOF formula (forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_state False) X) Y)) Y)) of role axiom named help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate
% A new axiom: (forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_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____srushsumbx__Otriple_Itc__Com__Ostate
% A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False)))
% FOF formula (forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), ((or (((fequal1831255762_state X) Y)->False)) (((eq hoare_1167836817_state) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com
% A new axiom: (forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), ((or (((fequal1831255762_state X) Y)->False)) (((eq hoare_1167836817_state) X) Y)))
% FOF formula (forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), ((or (not (((eq hoare_1167836817_state) X) Y))) ((fequal1831255762_state X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com
% A new axiom: (forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), ((or (not (((eq hoare_1167836817_state) X) Y))) ((fequal1831255762_state X) Y)))
% FOF formula (forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), ((or (((fequal1486222077tate_o X) Y)->False)) (((eq (hoare_1167836817_state->Prop)) X) Y))) of role axiom named help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It
% A new axiom: (forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), ((or (((fequal1486222077tate_o X) Y)->False)) (((eq (hoare_1167836817_state->Prop)) X) Y)))
% FOF formula (forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), ((or (not (((eq (hoare_1167836817_state->Prop)) X) Y))) ((fequal1486222077tate_o X) Y))) of role axiom named help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It
% A new axiom: (forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), ((or (not (((eq (hoare_1167836817_state->Prop)) X) Y))) ((fequal1486222077tate_o X) Y)))
% FOF formula hoare_1201148605gleton of role hypothesis named conj_0
% A new axiom: hoare_1201148605gleton
% FOF formula wT_bodies of role hypothesis named conj_1
% A new axiom: wT_bodies
% FOF formula (finite1084549118_state fa) of role hypothesis named conj_2
% A new axiom: (finite1084549118_state fa)
% FOF formula (((member2058392318_state (hoare_Mirabelle_MGT y)) fa)->False) of role hypothesis named conj_3
% A new axiom: (((member2058392318_state (hoare_Mirabelle_MGT y)) fa)->False)
% FOF formula ((ord_le827224136tate_o fa) ((image_575578384_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_le827224136tate_o fa) ((image_575578384_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_123228589_state ((image_575578384_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_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa)
% FOF formula ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)) of role conjecture named conj_7
% Conjecture to prove = ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)):Prop
% Parameter state_DUMMY:state.
% Parameter hoare_1167836817_state_DUMMY:hoare_1167836817_state.
% Parameter option_com_DUMMY:option_com.
% Parameter option_pname_DUMMY:option_pname.
% Parameter option1574264306_state_DUMMY:option1574264306_state.
% We need to prove ['((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o))']
% Parameter com:Type.
% Parameter pname:Type.
% Parameter state:Type.
% Parameter hoare_1167836817_state:Type.
% Parameter option_com:Type.
% Parameter option_pname:Type.
% Parameter option1574264306_state:Type.
% 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 finite1066544169me_o_o:((((pname->Prop)->Prop)->Prop)->Prop).
% Parameter finite33115244te_o_o:((((hoare_1167836817_state->Prop)->Prop)->Prop)->Prop).
% Parameter finite297249702name_o:(((pname->Prop)->Prop)->Prop).
% Parameter finite1380128977tate_o:(((hoare_1167836817_state->Prop)->Prop)->Prop).
% Parameter finite_finite_pname:((pname->Prop)->Prop).
% Parameter finite1084549118_state:((hoare_1167836817_state->Prop)->Prop).
% Parameter finite349908348name_o:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->((((pname->Prop)->Prop)->(pname->Prop))->Prop)).
% Parameter finite979047547tate_o:(((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))->((((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))->Prop)).
% Parameter finite1282449217_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)).
% Parameter finite1074406356_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop)).
% Parameter finite697516351name_o:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->((((pname->Prop)->Prop)->(pname->Prop))->Prop)).
% Parameter finite671847800tate_o:(((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))->((((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))->Prop)).
% Parameter finite89670078_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)).
% Parameter finite806517911_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop)).
% Parameter minus_1480864103me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter minus_1708687022te_o_o:(((hoare_1167836817_state->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop))).
% Parameter minus_minus_pname_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter minus_2107060239tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))).
% Parameter the_pname:((pname->Prop)->pname).
% Parameter the_Ho310147232_state:((hoare_1167836817_state->Prop)->hoare_1167836817_state).
% Parameter hoare_Mirabelle_MGT:(com->hoare_1167836817_state).
% Parameter hoare_123228589_state:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)).
% Parameter hoare_529639851_state:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)).
% Parameter hoare_1201148605gleton:Prop.
% Parameter hoare_908217195_state:((state->(state->Prop))->(com->((state->(state->Prop))->hoare_1167836817_state))).
% Parameter if_Hoa833675553_state:(Prop->(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_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 semila1758709489te_o_o:(((hoare_1167836817_state->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop))).
% Parameter semila1673364395name_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter semila179895820tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))).
% Parameter semila181081674me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter semila866907787te_o_o:(((hoare_1167836817_state->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop))).
% Parameter semila1780557381name_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter semila1172322802tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))).
% Parameter semila10642723_sup_o:(Prop->(Prop->Prop)).
% Parameter dom_pname_com:((pname->option_com)->(pname->Prop)).
% Parameter evalc:(com->(state->(state->Prop))).
% Parameter some_com:(com->option_com).
% Parameter some_pname:(pname->option_pname).
% Parameter some_H1433514562_state:(hoare_1167836817_state->option1574264306_state).
% Parameter set_com:(option_com->(com->Prop)).
% Parameter set_pname:(option_pname->(pname->Prop)).
% Parameter set_Ho2131684873_state:(option1574264306_state->(hoare_1167836817_state->Prop)).
% Parameter the_com:(option_com->com).
% Parameter bot_bot_pname_o_o:((pname->Prop)->Prop).
% Parameter bot_bo691907561te_o_o:((hoare_1167836817_state->Prop)->Prop).
% Parameter bot_bot_com_o:(com->Prop).
% Parameter bot_bot_pname_o:(pname->Prop).
% Parameter bot_bo70021908tate_o:(hoare_1167836817_state->Prop).
% Parameter bot_bot_o:Prop.
% Parameter ord_le1205211808me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)).
% Parameter ord_le741939125te_o_o:(((hoare_1167836817_state->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->Prop)).
% Parameter ord_less_eq_pname_o:((pname->Prop)->((pname->Prop)->Prop)).
% Parameter ord_le827224136tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)).
% Parameter ord_less_eq_o:(Prop->(Prop->Prop)).
% Parameter collect_pname_o_o:((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)).
% Parameter collec1218656682te_o_o:((((hoare_1167836817_state->Prop)->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->Prop)).
% Parameter collect_pname_o:(((pname->Prop)->Prop)->((pname->Prop)->Prop)).
% Parameter collec269976083tate_o:(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop)).
% Parameter collect_pname:((pname->Prop)->(pname->Prop)).
% Parameter collec1027672124_state:((hoare_1167836817_state->Prop)->(hoare_1167836817_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_1381916541_state:(((pname->Prop)->hoare_1167836817_state)->(((pname->Prop)->Prop)->(hoare_1167836817_state->Prop))).
% Parameter image_1488525317tate_o:(((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop))).
% Parameter image_980295115_pname:(((hoare_1167836817_state->Prop)->pname)->(((hoare_1167836817_state->Prop)->Prop)->(pname->Prop))).
% Parameter image_635813834_state:(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))).
% Parameter image_pname_pname_o:((pname->(pname->Prop))->((pname->Prop)->((pname->Prop)->Prop))).
% Parameter image_475339327tate_o:((pname->(hoare_1167836817_state->Prop))->((pname->Prop)->((hoare_1167836817_state->Prop)->Prop))).
% Parameter image_pname_pname:((pname->pname)->((pname->Prop)->(pname->Prop))).
% Parameter image_575578384_state:((pname->hoare_1167836817_state)->((pname->Prop)->(hoare_1167836817_state->Prop))).
% Parameter image_2066861949name_o:((hoare_1167836817_state->(pname->Prop))->((hoare_1167836817_state->Prop)->((pname->Prop)->Prop))).
% Parameter image_1745649338tate_o:((hoare_1167836817_state->(hoare_1167836817_state->Prop))->((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop))).
% Parameter image_8178176_pname:((hoare_1167836817_state->pname)->((hoare_1167836817_state->Prop)->(pname->Prop))).
% Parameter image_31595733_state:((hoare_1167836817_state->hoare_1167836817_state)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))).
% Parameter insert_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter insert999278200tate_o:((hoare_1167836817_state->Prop)->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop))).
% Parameter insert_com:(com->((com->Prop)->(com->Prop))).
% Parameter insert_pname:(pname->((pname->Prop)->(pname->Prop))).
% Parameter insert2134838167_state:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))).
% Parameter the_elem_pname:((pname->Prop)->pname).
% Parameter the_el323660082_state:((hoare_1167836817_state->Prop)->hoare_1167836817_state).
% Parameter fequal_pname_o:((pname->Prop)->((pname->Prop)->Prop)).
% Parameter fequal1486222077tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)).
% Parameter fequal_pname:(pname->(pname->Prop)).
% Parameter fequal_state:(state->(state->Prop)).
% Parameter fequal1831255762_state:(hoare_1167836817_state->(hoare_1167836817_state->Prop)).
% Parameter member_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->Prop)).
% Parameter member864234961tate_o:((hoare_1167836817_state->Prop)->(((hoare_1167836817_state->Prop)->Prop)->Prop)).
% Parameter member_com:(com->((com->Prop)->Prop)).
% Parameter member_pname:(pname->((pname->Prop)->Prop)).
% Parameter member2058392318_state:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->Prop)).
% Parameter fa:(hoare_1167836817_state->Prop).
% Parameter pn:pname.
% Parameter y:com.
% Axiom fact_0_empty:(forall (G_3:(hoare_1167836817_state->Prop)), ((hoare_123228589_state G_3) bot_bo70021908tate_o)).
% Axiom fact_1_asm:(forall (Ts_7:(hoare_1167836817_state->Prop)) (G_35:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Ts_7) G_35)->((hoare_123228589_state G_35) Ts_7))).
% Axiom fact_2_weaken:(forall (Ts_6:(hoare_1167836817_state->Prop)) (G_34:(hoare_1167836817_state->Prop)) (Ts_5:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_34) Ts_5)->(((ord_le827224136tate_o Ts_6) Ts_5)->((hoare_123228589_state G_34) Ts_6)))).
% Axiom fact_3_thin:(forall (G_33:(hoare_1167836817_state->Prop)) (G_32:(hoare_1167836817_state->Prop)) (Ts_4:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_32) Ts_4)->(((ord_le827224136tate_o G_32) G_33)->((hoare_123228589_state G_33) Ts_4)))).
% Axiom fact_4_cut:(forall (G_31:(hoare_1167836817_state->Prop)) (G_30:(hoare_1167836817_state->Prop)) (Ts_3:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_30) Ts_3)->(((hoare_123228589_state G_31) G_30)->((hoare_123228589_state G_31) Ts_3)))).
% Axiom fact_5_hoare__derivs_Oinsert:(forall (Ts_2:(hoare_1167836817_state->Prop)) (G_29:(hoare_1167836817_state->Prop)) (T_3:hoare_1167836817_state), (((hoare_123228589_state G_29) ((insert2134838167_state T_3) bot_bo70021908tate_o))->(((hoare_123228589_state G_29) Ts_2)->((hoare_123228589_state G_29) ((insert2134838167_state T_3) Ts_2))))).
% Axiom fact_6_derivs__insertD:(forall (G_28:(hoare_1167836817_state->Prop)) (T_2:hoare_1167836817_state) (Ts_1:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_28) ((insert2134838167_state T_2) Ts_1))->((and ((hoare_123228589_state G_28) ((insert2134838167_state T_2) bot_bo70021908tate_o))) ((hoare_123228589_state G_28) Ts_1)))).
% Axiom fact_7_MGT__BodyN:(forall (Pn_1:pname) (G_3:(hoare_1167836817_state->Prop)), (((hoare_123228589_state ((insert2134838167_state (hoare_Mirabelle_MGT (body_1 Pn_1))) G_3)) ((insert2134838167_state (hoare_Mirabelle_MGT (the_com (body Pn_1)))) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT (body_1 Pn_1))) bot_bo70021908tate_o)))).
% Axiom fact_8_finite__Collect__subsets:(forall (A_201:((pname->Prop)->Prop)), ((finite297249702name_o A_201)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_43:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_43) A_201)))))).
% Axiom fact_9_finite__Collect__subsets:(forall (A_201:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_201)->(finite33115244te_o_o (collec1218656682te_o_o (fun (B_43:((hoare_1167836817_state->Prop)->Prop))=> ((ord_le741939125te_o_o B_43) A_201)))))).
% Axiom fact_10_finite__Collect__subsets:(forall (A_201:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_201)->(finite1380128977tate_o (collec269976083tate_o (fun (B_43:(hoare_1167836817_state->Prop))=> ((ord_le827224136tate_o B_43) A_201)))))).
% Axiom fact_11_finite__Collect__subsets:(forall (A_201:(pname->Prop)), ((finite_finite_pname A_201)->(finite297249702name_o (collect_pname_o (fun (B_43:(pname->Prop))=> ((ord_less_eq_pname_o B_43) A_201)))))).
% Axiom fact_12_finite__imageI:(forall (H_1:(hoare_1167836817_state->(pname->Prop))) (F_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_61)->(finite297249702name_o ((image_2066861949name_o H_1) F_61)))).
% Axiom fact_13_finite__imageI:(forall (H_1:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (F_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_61)->(finite1380128977tate_o ((image_1745649338tate_o H_1) F_61)))).
% Axiom fact_14_finite__imageI:(forall (H_1:(pname->(pname->Prop))) (F_61:(pname->Prop)), ((finite_finite_pname F_61)->(finite297249702name_o ((image_pname_pname_o H_1) F_61)))).
% Axiom fact_15_finite__imageI:(forall (H_1:(pname->(hoare_1167836817_state->Prop))) (F_61:(pname->Prop)), ((finite_finite_pname F_61)->(finite1380128977tate_o ((image_475339327tate_o H_1) F_61)))).
% Axiom fact_16_finite__imageI:(forall (H_1:((pname->Prop)->hoare_1167836817_state)) (F_61:((pname->Prop)->Prop)), ((finite297249702name_o F_61)->(finite1084549118_state ((image_1381916541_state H_1) F_61)))).
% Axiom fact_17_finite__imageI:(forall (H_1:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (F_61:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_61)->(finite1084549118_state ((image_635813834_state H_1) F_61)))).
% Axiom fact_18_finite__imageI:(forall (H_1:((pname->Prop)->pname)) (F_61:((pname->Prop)->Prop)), ((finite297249702name_o F_61)->(finite_finite_pname ((image_pname_o_pname H_1) F_61)))).
% Axiom fact_19_finite__imageI:(forall (H_1:((hoare_1167836817_state->Prop)->pname)) (F_61:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_61)->(finite_finite_pname ((image_980295115_pname H_1) F_61)))).
% Axiom fact_20_finite__imageI:(forall (H_1:(pname->hoare_1167836817_state)) (F_61:(pname->Prop)), ((finite_finite_pname F_61)->(finite1084549118_state ((image_575578384_state H_1) F_61)))).
% Axiom fact_21_empty__subsetI:(forall (A_200:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_200)).
% Axiom fact_22_empty__subsetI:(forall (A_200:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_200)).
% Axiom fact_23_finite_OinsertI:(forall (A_199:(pname->Prop)) (A_198:((pname->Prop)->Prop)), ((finite297249702name_o A_198)->(finite297249702name_o ((insert_pname_o A_199) A_198)))).
% Axiom fact_24_finite_OinsertI:(forall (A_199:(hoare_1167836817_state->Prop)) (A_198:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_198)->(finite1380128977tate_o ((insert999278200tate_o A_199) A_198)))).
% Axiom fact_25_finite_OinsertI:(forall (A_199:pname) (A_198:(pname->Prop)), ((finite_finite_pname A_198)->(finite_finite_pname ((insert_pname A_199) A_198)))).
% Axiom fact_26_finite_OinsertI:(forall (A_199:hoare_1167836817_state) (A_198:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_198)->(finite1084549118_state ((insert2134838167_state A_199) A_198)))).
% Axiom fact_27_finite_OemptyI:(finite297249702name_o bot_bot_pname_o_o).
% Axiom fact_28_finite_OemptyI:(finite1380128977tate_o bot_bo691907561te_o_o).
% Axiom fact_29_finite_OemptyI:(finite1084549118_state bot_bo70021908tate_o).
% Axiom fact_30_finite_OemptyI:(finite_finite_pname bot_bot_pname_o).
% Axiom fact_31_finite__Collect__conjI:(forall (Q_24:((pname->Prop)->Prop)) (P_42:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_42))) (finite297249702name_o (collect_pname_o Q_24)))->(finite297249702name_o (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (P_42 X_5)) (Q_24 X_5))))))).
% Axiom fact_32_finite__Collect__conjI:(forall (Q_24:((hoare_1167836817_state->Prop)->Prop)) (P_42:((hoare_1167836817_state->Prop)->Prop)), (((or (finite1380128977tate_o (collec269976083tate_o P_42))) (finite1380128977tate_o (collec269976083tate_o Q_24)))->(finite1380128977tate_o (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (P_42 X_5)) (Q_24 X_5))))))).
% Axiom fact_33_finite__Collect__conjI:(forall (Q_24:(hoare_1167836817_state->Prop)) (P_42:(hoare_1167836817_state->Prop)), (((or (finite1084549118_state (collec1027672124_state P_42))) (finite1084549118_state (collec1027672124_state Q_24)))->(finite1084549118_state (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (P_42 X_5)) (Q_24 X_5))))))).
% Axiom fact_34_finite__Collect__conjI:(forall (Q_24:(pname->Prop)) (P_42:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_42))) (finite_finite_pname (collect_pname Q_24)))->(finite_finite_pname (collect_pname (fun (X_5:pname)=> ((and (P_42 X_5)) (Q_24 X_5))))))).
% Axiom fact_35_image__constant__conv:(forall (C_54:pname) (A_197:(hoare_1167836817_state->Prop)), ((and ((((eq (hoare_1167836817_state->Prop)) A_197) bot_bo70021908tate_o)->(((eq (pname->Prop)) ((image_8178176_pname (fun (X_5:hoare_1167836817_state)=> C_54)) A_197)) bot_bot_pname_o))) ((not (((eq (hoare_1167836817_state->Prop)) A_197) bot_bo70021908tate_o))->(((eq (pname->Prop)) ((image_8178176_pname (fun (X_5:hoare_1167836817_state)=> C_54)) A_197)) ((insert_pname C_54) bot_bot_pname_o))))).
% Axiom fact_36_image__constant__conv:(forall (C_54:hoare_1167836817_state) (A_197:(pname->Prop)), ((and ((((eq (pname->Prop)) A_197) bot_bot_pname_o)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> C_54)) A_197)) bot_bo70021908tate_o))) ((not (((eq (pname->Prop)) A_197) bot_bot_pname_o))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> C_54)) A_197)) ((insert2134838167_state C_54) bot_bo70021908tate_o))))).
% Axiom fact_37_image__constant:(forall (C_53:pname) (X_101:hoare_1167836817_state) (A_196:(hoare_1167836817_state->Prop)), (((member2058392318_state X_101) A_196)->(((eq (pname->Prop)) ((image_8178176_pname (fun (X_5:hoare_1167836817_state)=> C_53)) A_196)) ((insert_pname C_53) bot_bot_pname_o)))).
% Axiom fact_38_image__constant:(forall (C_53:hoare_1167836817_state) (X_101:pname) (A_196:(pname->Prop)), (((member_pname X_101) A_196)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> C_53)) A_196)) ((insert2134838167_state C_53) bot_bo70021908tate_o)))).
% Axiom fact_39_insert__dom:(forall (F_60:(pname->option_com)) (X_100:pname) (Y_49:com), ((((eq option_com) (F_60 X_100)) (some_com Y_49))->(((eq (pname->Prop)) ((insert_pname X_100) (dom_pname_com F_60))) (dom_pname_com F_60)))).
% Axiom fact_40_finite__surj:(forall (B_130:((pname->Prop)->Prop)) (F_59:(hoare_1167836817_state->(pname->Prop))) (A_195:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_195)->(((ord_le1205211808me_o_o B_130) ((image_2066861949name_o F_59) A_195))->(finite297249702name_o B_130)))).
% Axiom fact_41_finite__surj:(forall (B_130:((hoare_1167836817_state->Prop)->Prop)) (F_59:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (A_195:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_195)->(((ord_le741939125te_o_o B_130) ((image_1745649338tate_o F_59) A_195))->(finite1380128977tate_o B_130)))).
% Axiom fact_42_finite__surj:(forall (B_130:(pname->Prop)) (F_59:(hoare_1167836817_state->pname)) (A_195:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_195)->(((ord_less_eq_pname_o B_130) ((image_8178176_pname F_59) A_195))->(finite_finite_pname B_130)))).
% Axiom fact_43_finite__surj:(forall (B_130:((pname->Prop)->Prop)) (F_59:(pname->(pname->Prop))) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_le1205211808me_o_o B_130) ((image_pname_pname_o F_59) A_195))->(finite297249702name_o B_130)))).
% Axiom fact_44_finite__surj:(forall (B_130:((hoare_1167836817_state->Prop)->Prop)) (F_59:(pname->(hoare_1167836817_state->Prop))) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_le741939125te_o_o B_130) ((image_475339327tate_o F_59) A_195))->(finite1380128977tate_o B_130)))).
% Axiom fact_45_finite__surj:(forall (B_130:(pname->Prop)) (F_59:(pname->pname)) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_less_eq_pname_o B_130) ((image_pname_pname F_59) A_195))->(finite_finite_pname B_130)))).
% Axiom fact_46_finite__surj:(forall (B_130:(hoare_1167836817_state->Prop)) (F_59:((pname->Prop)->hoare_1167836817_state)) (A_195:((pname->Prop)->Prop)), ((finite297249702name_o A_195)->(((ord_le827224136tate_o B_130) ((image_1381916541_state F_59) A_195))->(finite1084549118_state B_130)))).
% Axiom fact_47_finite__surj:(forall (B_130:(hoare_1167836817_state->Prop)) (F_59:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (A_195:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_195)->(((ord_le827224136tate_o B_130) ((image_635813834_state F_59) A_195))->(finite1084549118_state B_130)))).
% Axiom fact_48_finite__surj:(forall (B_130:(pname->Prop)) (F_59:((pname->Prop)->pname)) (A_195:((pname->Prop)->Prop)), ((finite297249702name_o A_195)->(((ord_less_eq_pname_o B_130) ((image_pname_o_pname F_59) A_195))->(finite_finite_pname B_130)))).
% Axiom fact_49_finite__surj:(forall (B_130:(pname->Prop)) (F_59:((hoare_1167836817_state->Prop)->pname)) (A_195:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_195)->(((ord_less_eq_pname_o B_130) ((image_980295115_pname F_59) A_195))->(finite_finite_pname B_130)))).
% Axiom fact_50_finite__surj:(forall (B_130:(hoare_1167836817_state->Prop)) (F_59:(pname->hoare_1167836817_state)) (A_195:(pname->Prop)), ((finite_finite_pname A_195)->(((ord_le827224136tate_o B_130) ((image_575578384_state F_59) A_195))->(finite1084549118_state B_130)))).
% Axiom fact_51_subset__singletonD:(forall (A_194:(pname->Prop)) (X_99:pname), (((ord_less_eq_pname_o A_194) ((insert_pname X_99) bot_bot_pname_o))->((or (((eq (pname->Prop)) A_194) bot_bot_pname_o)) (((eq (pname->Prop)) A_194) ((insert_pname X_99) bot_bot_pname_o))))).
% Axiom fact_52_subset__singletonD:(forall (A_194:(hoare_1167836817_state->Prop)) (X_99:hoare_1167836817_state), (((ord_le827224136tate_o A_194) ((insert2134838167_state X_99) bot_bo70021908tate_o))->((or (((eq (hoare_1167836817_state->Prop)) A_194) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_194) ((insert2134838167_state X_99) bot_bo70021908tate_o))))).
% Axiom fact_53_MGF:(forall (C_21:com), (hoare_1201148605gleton->(wT_bodies->((wt C_21)->((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o)))))).
% Axiom fact_54_emptyE:(forall (A_193:pname), (((member_pname A_193) bot_bot_pname_o)->False)).
% Axiom fact_55_emptyE:(forall (A_193:hoare_1167836817_state), (((member2058392318_state A_193) bot_bo70021908tate_o)->False)).
% Axiom fact_56_insertCI:(forall (B_129:pname) (A_192:pname) (B_128:(pname->Prop)), (((((member_pname A_192) B_128)->False)->(((eq pname) A_192) B_129))->((member_pname A_192) ((insert_pname B_129) B_128)))).
% Axiom fact_57_insertCI:(forall (B_129:hoare_1167836817_state) (A_192:hoare_1167836817_state) (B_128:(hoare_1167836817_state->Prop)), (((((member2058392318_state A_192) B_128)->False)->(((eq hoare_1167836817_state) A_192) B_129))->((member2058392318_state A_192) ((insert2134838167_state B_129) B_128)))).
% Axiom fact_58_insertE:(forall (A_191:pname) (B_127:pname) (A_190:(pname->Prop)), (((member_pname A_191) ((insert_pname B_127) A_190))->((not (((eq pname) A_191) B_127))->((member_pname A_191) A_190)))).
% Axiom fact_59_insertE:(forall (A_191:hoare_1167836817_state) (B_127:hoare_1167836817_state) (A_190:(hoare_1167836817_state->Prop)), (((member2058392318_state A_191) ((insert2134838167_state B_127) A_190))->((not (((eq hoare_1167836817_state) A_191) B_127))->((member2058392318_state A_191) A_190)))).
% Axiom fact_60_equalityI:(forall (A_189:(pname->Prop)) (B_126:(pname->Prop)), (((ord_less_eq_pname_o A_189) B_126)->(((ord_less_eq_pname_o B_126) A_189)->(((eq (pname->Prop)) A_189) B_126)))).
% Axiom fact_61_equalityI:(forall (A_189:(hoare_1167836817_state->Prop)) (B_126:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_189) B_126)->(((ord_le827224136tate_o B_126) A_189)->(((eq (hoare_1167836817_state->Prop)) A_189) B_126)))).
% Axiom fact_62_subsetD:(forall (C_52:pname) (A_188:(pname->Prop)) (B_125:(pname->Prop)), (((ord_less_eq_pname_o A_188) B_125)->(((member_pname C_52) A_188)->((member_pname C_52) B_125)))).
% Axiom fact_63_subsetD:(forall (C_52:hoare_1167836817_state) (A_188:(hoare_1167836817_state->Prop)) (B_125:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_188) B_125)->(((member2058392318_state C_52) A_188)->((member2058392318_state C_52) B_125)))).
% Axiom fact_64_image__eqI:(forall (A_187:(hoare_1167836817_state->Prop)) (B_124:pname) (F_58:(hoare_1167836817_state->pname)) (X_98:hoare_1167836817_state), ((((eq pname) B_124) (F_58 X_98))->(((member2058392318_state X_98) A_187)->((member_pname B_124) ((image_8178176_pname F_58) A_187))))).
% Axiom fact_65_image__eqI:(forall (A_187:(pname->Prop)) (B_124:hoare_1167836817_state) (F_58:(pname->hoare_1167836817_state)) (X_98:pname), ((((eq hoare_1167836817_state) B_124) (F_58 X_98))->(((member_pname X_98) A_187)->((member2058392318_state B_124) ((image_575578384_state F_58) A_187))))).
% Axiom fact_66_equals0D:(forall (A_186:pname) (A_185:(pname->Prop)), ((((eq (pname->Prop)) A_185) bot_bot_pname_o)->(((member_pname A_186) A_185)->False))).
% Axiom fact_67_equals0D:(forall (A_186:hoare_1167836817_state) (A_185:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_185) bot_bo70021908tate_o)->(((member2058392318_state A_186) A_185)->False))).
% Axiom fact_68_Collect__empty__eq:(forall (P_41:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_41)) bot_bot_pname_o)) (forall (X_5:pname), ((P_41 X_5)->False)))).
% Axiom fact_69_Collect__empty__eq:(forall (P_41:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) (collect_pname_o P_41)) bot_bot_pname_o_o)) (forall (X_5:(pname->Prop)), ((P_41 X_5)->False)))).
% Axiom fact_70_Collect__empty__eq:(forall (P_41:((hoare_1167836817_state->Prop)->Prop)), ((iff (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o P_41)) bot_bo691907561te_o_o)) (forall (X_5:(hoare_1167836817_state->Prop)), ((P_41 X_5)->False)))).
% Axiom fact_71_Collect__empty__eq:(forall (P_41:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_41)) bot_bo70021908tate_o)) (forall (X_5:hoare_1167836817_state), ((P_41 X_5)->False)))).
% Axiom fact_72_empty__iff:(forall (C_51:pname), (((member_pname C_51) bot_bot_pname_o)->False)).
% Axiom fact_73_empty__iff:(forall (C_51:hoare_1167836817_state), (((member2058392318_state C_51) bot_bo70021908tate_o)->False)).
% Axiom fact_74_empty__Collect__eq:(forall (P_40:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_40))) (forall (X_5:pname), ((P_40 X_5)->False)))).
% Axiom fact_75_empty__Collect__eq:(forall (P_40:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o P_40))) (forall (X_5:(pname->Prop)), ((P_40 X_5)->False)))).
% Axiom fact_76_empty__Collect__eq:(forall (P_40:((hoare_1167836817_state->Prop)->Prop)), ((iff (((eq ((hoare_1167836817_state->Prop)->Prop)) bot_bo691907561te_o_o) (collec269976083tate_o P_40))) (forall (X_5:(hoare_1167836817_state->Prop)), ((P_40 X_5)->False)))).
% Axiom fact_77_empty__Collect__eq:(forall (P_40:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state P_40))) (forall (X_5:hoare_1167836817_state), ((P_40 X_5)->False)))).
% Axiom fact_78_ex__in__conv:(forall (A_184:(pname->Prop)), ((iff ((ex pname) (fun (X_5:pname)=> ((member_pname X_5) A_184)))) (not (((eq (pname->Prop)) A_184) bot_bot_pname_o)))).
% Axiom fact_79_ex__in__conv:(forall (A_184:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((member2058392318_state X_5) A_184)))) (not (((eq (hoare_1167836817_state->Prop)) A_184) bot_bo70021908tate_o)))).
% Axiom fact_80_all__not__in__conv:(forall (A_183:(pname->Prop)), ((iff (forall (X_5:pname), (((member_pname X_5) A_183)->False))) (((eq (pname->Prop)) A_183) bot_bot_pname_o))).
% Axiom fact_81_all__not__in__conv:(forall (A_183:(hoare_1167836817_state->Prop)), ((iff (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_183)->False))) (((eq (hoare_1167836817_state->Prop)) A_183) bot_bo70021908tate_o))).
% Axiom fact_82_empty__def:(((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X_5:pname)=> False))).
% Axiom fact_83_empty__def:(((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o (fun (X_5:(pname->Prop))=> False))).
% Axiom fact_84_empty__def:(((eq ((hoare_1167836817_state->Prop)->Prop)) bot_bo691907561te_o_o) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> False))).
% Axiom fact_85_empty__def:(((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> False))).
% Axiom fact_86_insert__absorb:(forall (A_182:pname) (A_181:(pname->Prop)), (((member_pname A_182) A_181)->(((eq (pname->Prop)) ((insert_pname A_182) A_181)) A_181))).
% Axiom fact_87_insert__absorb:(forall (A_182:hoare_1167836817_state) (A_181:(hoare_1167836817_state->Prop)), (((member2058392318_state A_182) A_181)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_182) A_181)) A_181))).
% Axiom fact_88_insertI2:(forall (B_123:pname) (A_180:pname) (B_122:(pname->Prop)), (((member_pname A_180) B_122)->((member_pname A_180) ((insert_pname B_123) B_122)))).
% Axiom fact_89_insertI2:(forall (B_123:hoare_1167836817_state) (A_180:hoare_1167836817_state) (B_122:(hoare_1167836817_state->Prop)), (((member2058392318_state A_180) B_122)->((member2058392318_state A_180) ((insert2134838167_state B_123) B_122)))).
% Axiom fact_90_insert__ident:(forall (B_121:(pname->Prop)) (X_97:pname) (A_179:(pname->Prop)), ((((member_pname X_97) A_179)->False)->((((member_pname X_97) B_121)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_97) A_179)) ((insert_pname X_97) B_121))) (((eq (pname->Prop)) A_179) B_121))))).
% Axiom fact_91_insert__ident:(forall (B_121:(hoare_1167836817_state->Prop)) (X_97:hoare_1167836817_state) (A_179:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_97) A_179)->False)->((((member2058392318_state X_97) B_121)->False)->((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_97) A_179)) ((insert2134838167_state X_97) B_121))) (((eq (hoare_1167836817_state->Prop)) A_179) B_121))))).
% Axiom fact_92_insert__code:(forall (Y_48:pname) (A_178:(pname->Prop)) (X_96:pname), ((iff (((insert_pname Y_48) A_178) X_96)) ((or (((eq pname) Y_48) X_96)) (A_178 X_96)))).
% Axiom fact_93_insert__code:(forall (Y_48:hoare_1167836817_state) (A_178:(hoare_1167836817_state->Prop)) (X_96:hoare_1167836817_state), ((iff (((insert2134838167_state Y_48) A_178) X_96)) ((or (((eq hoare_1167836817_state) Y_48) X_96)) (A_178 X_96)))).
% Axiom fact_94_insert__iff:(forall (A_177:pname) (B_120:pname) (A_176:(pname->Prop)), ((iff ((member_pname A_177) ((insert_pname B_120) A_176))) ((or (((eq pname) A_177) B_120)) ((member_pname A_177) A_176)))).
% Axiom fact_95_insert__iff:(forall (A_177:hoare_1167836817_state) (B_120:hoare_1167836817_state) (A_176:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state A_177) ((insert2134838167_state B_120) A_176))) ((or (((eq hoare_1167836817_state) A_177) B_120)) ((member2058392318_state A_177) A_176)))).
% Axiom fact_96_insert__commute:(forall (X_95:pname) (Y_47:pname) (A_175:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_95) ((insert_pname Y_47) A_175))) ((insert_pname Y_47) ((insert_pname X_95) A_175)))).
% Axiom fact_97_insert__commute:(forall (X_95:hoare_1167836817_state) (Y_47:hoare_1167836817_state) (A_175:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_95) ((insert2134838167_state Y_47) A_175))) ((insert2134838167_state Y_47) ((insert2134838167_state X_95) A_175)))).
% Axiom fact_98_insert__absorb2:(forall (X_94:pname) (A_174:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_94) ((insert_pname X_94) A_174))) ((insert_pname X_94) A_174))).
% Axiom fact_99_insert__absorb2:(forall (X_94:hoare_1167836817_state) (A_174:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_94) ((insert2134838167_state X_94) A_174))) ((insert2134838167_state X_94) A_174))).
% Axiom fact_100_insert__Collect:(forall (A_173:pname) (P_39:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_173) (collect_pname P_39))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_173))) (P_39 U_2)))))).
% Axiom fact_101_insert__Collect:(forall (A_173:(pname->Prop)) (P_39:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_173) (collect_pname_o P_39))) (collect_pname_o (fun (U_2:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U_2) A_173))) (P_39 U_2)))))).
% Axiom fact_102_insert__Collect:(forall (A_173:(hoare_1167836817_state->Prop)) (P_39:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o A_173) (collec269976083tate_o P_39))) (collec269976083tate_o (fun (U_2:(hoare_1167836817_state->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_1167836817_state->Prop)) U_2) A_173))) (P_39 U_2)))))).
% Axiom fact_103_insert__Collect:(forall (A_173:hoare_1167836817_state) (P_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_173) (collec1027672124_state P_39))) (collec1027672124_state (fun (U_2:hoare_1167836817_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1167836817_state) U_2) A_173))) (P_39 U_2)))))).
% Axiom fact_104_insert__compr:(forall (A_172:pname) (B_119:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_172) B_119)) (collect_pname (fun (X_5:pname)=> ((or (((eq pname) X_5) A_172)) ((member_pname X_5) B_119)))))).
% Axiom fact_105_insert__compr:(forall (A_172:(pname->Prop)) (B_119:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_172) B_119)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((or (((eq (pname->Prop)) X_5) A_172)) ((member_pname_o X_5) B_119)))))).
% Axiom fact_106_insert__compr:(forall (A_172:(hoare_1167836817_state->Prop)) (B_119:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o A_172) B_119)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or (((eq (hoare_1167836817_state->Prop)) X_5) A_172)) ((member864234961tate_o X_5) B_119)))))).
% Axiom fact_107_insert__compr:(forall (A_172:hoare_1167836817_state) (B_119:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_172) B_119)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) X_5) A_172)) ((member2058392318_state X_5) B_119)))))).
% Axiom fact_108_insertI1:(forall (A_171:pname) (B_118:(pname->Prop)), ((member_pname A_171) ((insert_pname A_171) B_118))).
% Axiom fact_109_insertI1:(forall (A_171:hoare_1167836817_state) (B_118:(hoare_1167836817_state->Prop)), ((member2058392318_state A_171) ((insert2134838167_state A_171) B_118))).
% Axiom fact_110_equalityE:(forall (A_170:(pname->Prop)) (B_117:(pname->Prop)), ((((eq (pname->Prop)) A_170) B_117)->((((ord_less_eq_pname_o A_170) B_117)->(((ord_less_eq_pname_o B_117) A_170)->False))->False))).
% Axiom fact_111_equalityE:(forall (A_170:(hoare_1167836817_state->Prop)) (B_117:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_170) B_117)->((((ord_le827224136tate_o A_170) B_117)->(((ord_le827224136tate_o B_117) A_170)->False))->False))).
% Axiom fact_112_subset__trans:(forall (C_50:(pname->Prop)) (A_169:(pname->Prop)) (B_116:(pname->Prop)), (((ord_less_eq_pname_o A_169) B_116)->(((ord_less_eq_pname_o B_116) C_50)->((ord_less_eq_pname_o A_169) C_50)))).
% Axiom fact_113_subset__trans:(forall (C_50:(hoare_1167836817_state->Prop)) (A_169:(hoare_1167836817_state->Prop)) (B_116:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_169) B_116)->(((ord_le827224136tate_o B_116) C_50)->((ord_le827224136tate_o A_169) C_50)))).
% Axiom fact_114_set__mp:(forall (X_93:pname) (A_168:(pname->Prop)) (B_115:(pname->Prop)), (((ord_less_eq_pname_o A_168) B_115)->(((member_pname X_93) A_168)->((member_pname X_93) B_115)))).
% Axiom fact_115_set__mp:(forall (X_93:hoare_1167836817_state) (A_168:(hoare_1167836817_state->Prop)) (B_115:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_168) B_115)->(((member2058392318_state X_93) A_168)->((member2058392318_state X_93) B_115)))).
% Axiom fact_116_set__rev__mp:(forall (B_114:(pname->Prop)) (X_92:pname) (A_167:(pname->Prop)), (((member_pname X_92) A_167)->(((ord_less_eq_pname_o A_167) B_114)->((member_pname X_92) B_114)))).
% Axiom fact_117_set__rev__mp:(forall (B_114:(hoare_1167836817_state->Prop)) (X_92:hoare_1167836817_state) (A_167:(hoare_1167836817_state->Prop)), (((member2058392318_state X_92) A_167)->(((ord_le827224136tate_o A_167) B_114)->((member2058392318_state X_92) B_114)))).
% Axiom fact_118_in__mono:(forall (X_91:pname) (A_166:(pname->Prop)) (B_113:(pname->Prop)), (((ord_less_eq_pname_o A_166) B_113)->(((member_pname X_91) A_166)->((member_pname X_91) B_113)))).
% Axiom fact_119_in__mono:(forall (X_91:hoare_1167836817_state) (A_166:(hoare_1167836817_state->Prop)) (B_113:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_166) B_113)->(((member2058392318_state X_91) A_166)->((member2058392318_state X_91) B_113)))).
% Axiom fact_120_equalityD2:(forall (A_165:(pname->Prop)) (B_112:(pname->Prop)), ((((eq (pname->Prop)) A_165) B_112)->((ord_less_eq_pname_o B_112) A_165))).
% Axiom fact_121_equalityD2:(forall (A_165:(hoare_1167836817_state->Prop)) (B_112:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_165) B_112)->((ord_le827224136tate_o B_112) A_165))).
% Axiom fact_122_equalityD1:(forall (A_164:(pname->Prop)) (B_111:(pname->Prop)), ((((eq (pname->Prop)) A_164) B_111)->((ord_less_eq_pname_o A_164) B_111))).
% Axiom fact_123_equalityD1:(forall (A_164:(hoare_1167836817_state->Prop)) (B_111:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_164) B_111)->((ord_le827224136tate_o A_164) B_111))).
% Axiom fact_124_set__eq__subset:(forall (A_163:(pname->Prop)) (B_110:(pname->Prop)), ((iff (((eq (pname->Prop)) A_163) B_110)) ((and ((ord_less_eq_pname_o A_163) B_110)) ((ord_less_eq_pname_o B_110) A_163)))).
% Axiom fact_125_set__eq__subset:(forall (A_163:(hoare_1167836817_state->Prop)) (B_110:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) A_163) B_110)) ((and ((ord_le827224136tate_o A_163) B_110)) ((ord_le827224136tate_o B_110) A_163)))).
% Axiom fact_126_subset__refl:(forall (A_162:(pname->Prop)), ((ord_less_eq_pname_o A_162) A_162)).
% Axiom fact_127_subset__refl:(forall (A_162:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o A_162) A_162)).
% Axiom fact_128_rev__image__eqI:(forall (B_109:pname) (F_57:(hoare_1167836817_state->pname)) (X_90:hoare_1167836817_state) (A_161:(hoare_1167836817_state->Prop)), (((member2058392318_state X_90) A_161)->((((eq pname) B_109) (F_57 X_90))->((member_pname B_109) ((image_8178176_pname F_57) A_161))))).
% Axiom fact_129_rev__image__eqI:(forall (B_109:hoare_1167836817_state) (F_57:(pname->hoare_1167836817_state)) (X_90:pname) (A_161:(pname->Prop)), (((member_pname X_90) A_161)->((((eq hoare_1167836817_state) B_109) (F_57 X_90))->((member2058392318_state B_109) ((image_575578384_state F_57) A_161))))).
% Axiom fact_130_imageI:(forall (F_56:(hoare_1167836817_state->pname)) (X_89:hoare_1167836817_state) (A_160:(hoare_1167836817_state->Prop)), (((member2058392318_state X_89) A_160)->((member_pname (F_56 X_89)) ((image_8178176_pname F_56) A_160)))).
% Axiom fact_131_imageI:(forall (F_56:(pname->hoare_1167836817_state)) (X_89:pname) (A_160:(pname->Prop)), (((member_pname X_89) A_160)->((member2058392318_state (F_56 X_89)) ((image_575578384_state F_56) A_160)))).
% Axiom fact_132_image__iff:(forall (Z_21:hoare_1167836817_state) (F_55:(pname->hoare_1167836817_state)) (A_159:(pname->Prop)), ((iff ((member2058392318_state Z_21) ((image_575578384_state F_55) A_159))) ((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_159)) (((eq hoare_1167836817_state) Z_21) (F_55 X_5))))))).
% Axiom fact_133_finite__Collect__disjI:(forall (P_38:((pname->Prop)->Prop)) (Q_23:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_5:(pname->Prop))=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite297249702name_o (collect_pname_o P_38))) (finite297249702name_o (collect_pname_o Q_23))))).
% Axiom fact_134_finite__Collect__disjI:(forall (P_38:((hoare_1167836817_state->Prop)->Prop)) (Q_23:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite1380128977tate_o (collec269976083tate_o P_38))) (finite1380128977tate_o (collec269976083tate_o Q_23))))).
% Axiom fact_135_finite__Collect__disjI:(forall (P_38:(hoare_1167836817_state->Prop)) (Q_23:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite1084549118_state (collec1027672124_state P_38))) (finite1084549118_state (collec1027672124_state Q_23))))).
% Axiom fact_136_finite__Collect__disjI:(forall (P_38:(pname->Prop)) (Q_23:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_5:pname)=> ((or (P_38 X_5)) (Q_23 X_5)))))) ((and (finite_finite_pname (collect_pname P_38))) (finite_finite_pname (collect_pname Q_23))))).
% Axiom fact_137_insert__compr__raw:(forall (X_5:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_5) Xa)) (collect_pname (fun (Y_2:pname)=> ((or (((eq pname) Y_2) X_5)) ((member_pname Y_2) Xa)))))).
% Axiom fact_138_insert__compr__raw:(forall (X_5:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X_5) Xa)) (collect_pname_o (fun (Y_2:(pname->Prop))=> ((or (((eq (pname->Prop)) Y_2) X_5)) ((member_pname_o Y_2) Xa)))))).
% Axiom fact_139_insert__compr__raw:(forall (X_5:(hoare_1167836817_state->Prop)) (Xa:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o X_5) Xa)) (collec269976083tate_o (fun (Y_2:(hoare_1167836817_state->Prop))=> ((or (((eq (hoare_1167836817_state->Prop)) Y_2) X_5)) ((member864234961tate_o Y_2) Xa)))))).
% Axiom fact_140_insert__compr__raw:(forall (X_5:hoare_1167836817_state) (Xa:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_5) Xa)) (collec1027672124_state (fun (Y_2:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) Y_2) X_5)) ((member2058392318_state Y_2) Xa)))))).
% Axiom fact_141_singleton__inject:(forall (A_158:pname) (B_108:pname), ((((eq (pname->Prop)) ((insert_pname A_158) bot_bot_pname_o)) ((insert_pname B_108) bot_bot_pname_o))->(((eq pname) A_158) B_108))).
% Axiom fact_142_singleton__inject:(forall (A_158:hoare_1167836817_state) (B_108:hoare_1167836817_state), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_158) bot_bo70021908tate_o)) ((insert2134838167_state B_108) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) A_158) B_108))).
% Axiom fact_143_singletonE:(forall (B_107:pname) (A_157:pname), (((member_pname B_107) ((insert_pname A_157) bot_bot_pname_o))->(((eq pname) B_107) A_157))).
% Axiom fact_144_singletonE:(forall (B_107:hoare_1167836817_state) (A_157:hoare_1167836817_state), (((member2058392318_state B_107) ((insert2134838167_state A_157) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) B_107) A_157))).
% Axiom fact_145_doubleton__eq__iff:(forall (A_156:pname) (B_106:pname) (C_49:pname) (D_6:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_156) ((insert_pname B_106) bot_bot_pname_o))) ((insert_pname C_49) ((insert_pname D_6) bot_bot_pname_o)))) ((or ((and (((eq pname) A_156) C_49)) (((eq pname) B_106) D_6))) ((and (((eq pname) A_156) D_6)) (((eq pname) B_106) C_49))))).
% Axiom fact_146_doubleton__eq__iff:(forall (A_156:hoare_1167836817_state) (B_106:hoare_1167836817_state) (C_49:hoare_1167836817_state) (D_6:hoare_1167836817_state), ((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_156) ((insert2134838167_state B_106) bot_bo70021908tate_o))) ((insert2134838167_state C_49) ((insert2134838167_state D_6) bot_bo70021908tate_o)))) ((or ((and (((eq hoare_1167836817_state) A_156) C_49)) (((eq hoare_1167836817_state) B_106) D_6))) ((and (((eq hoare_1167836817_state) A_156) D_6)) (((eq hoare_1167836817_state) B_106) C_49))))).
% Axiom fact_147_singleton__iff:(forall (B_105:pname) (A_155:pname), ((iff ((member_pname B_105) ((insert_pname A_155) bot_bot_pname_o))) (((eq pname) B_105) A_155))).
% Axiom fact_148_singleton__iff:(forall (B_105:hoare_1167836817_state) (A_155:hoare_1167836817_state), ((iff ((member2058392318_state B_105) ((insert2134838167_state A_155) bot_bo70021908tate_o))) (((eq hoare_1167836817_state) B_105) A_155))).
% Axiom fact_149_insert__not__empty:(forall (A_154:pname) (A_153:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_154) A_153)) bot_bot_pname_o))).
% Axiom fact_150_insert__not__empty:(forall (A_154:hoare_1167836817_state) (A_153:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_154) A_153)) bot_bo70021908tate_o))).
% Axiom fact_151_empty__not__insert:(forall (A_152:pname) (A_151:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_152) A_151)))).
% Axiom fact_152_empty__not__insert:(forall (A_152:hoare_1167836817_state) (A_151:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((insert2134838167_state A_152) A_151)))).
% Axiom fact_153_finite__insert:(forall (A_150:(pname->Prop)) (A_149:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_150) A_149))) (finite297249702name_o A_149))).
% Axiom fact_154_finite__insert:(forall (A_150:(hoare_1167836817_state->Prop)) (A_149:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o ((insert999278200tate_o A_150) A_149))) (finite1380128977tate_o A_149))).
% Axiom fact_155_finite__insert:(forall (A_150:pname) (A_149:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_150) A_149))) (finite_finite_pname A_149))).
% Axiom fact_156_finite__insert:(forall (A_150:hoare_1167836817_state) (A_149:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((insert2134838167_state A_150) A_149))) (finite1084549118_state A_149))).
% Axiom fact_157_subset__empty:(forall (A_148:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_148) bot_bot_pname_o)) (((eq (pname->Prop)) A_148) bot_bot_pname_o))).
% Axiom fact_158_subset__empty:(forall (A_148:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_148) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_148) bot_bo70021908tate_o))).
% Axiom fact_159_image__is__empty:(forall (F_54:(hoare_1167836817_state->pname)) (A_147:(hoare_1167836817_state->Prop)), ((iff (((eq (pname->Prop)) ((image_8178176_pname F_54) A_147)) bot_bot_pname_o)) (((eq (hoare_1167836817_state->Prop)) A_147) bot_bo70021908tate_o))).
% Axiom fact_160_image__is__empty:(forall (F_54:(pname->hoare_1167836817_state)) (A_147:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_54) A_147)) bot_bo70021908tate_o)) (((eq (pname->Prop)) A_147) bot_bot_pname_o))).
% Axiom fact_161_image__empty:(forall (F_53:(hoare_1167836817_state->pname)), (((eq (pname->Prop)) ((image_8178176_pname F_53) bot_bo70021908tate_o)) bot_bot_pname_o)).
% Axiom fact_162_image__empty:(forall (F_53:(pname->hoare_1167836817_state)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_53) bot_bot_pname_o)) bot_bo70021908tate_o)).
% Axiom fact_163_empty__is__image:(forall (F_52:(hoare_1167836817_state->pname)) (A_146:(hoare_1167836817_state->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) ((image_8178176_pname F_52) A_146))) (((eq (hoare_1167836817_state->Prop)) A_146) bot_bo70021908tate_o))).
% Axiom fact_164_empty__is__image:(forall (F_52:(pname->hoare_1167836817_state)) (A_146:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((image_575578384_state F_52) A_146))) (((eq (pname->Prop)) A_146) bot_bot_pname_o))).
% Axiom fact_165_finite__subset:(forall (A_145:((pname->Prop)->Prop)) (B_104:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_145) B_104)->((finite297249702name_o B_104)->(finite297249702name_o A_145)))).
% Axiom fact_166_finite__subset:(forall (A_145:((hoare_1167836817_state->Prop)->Prop)) (B_104:((hoare_1167836817_state->Prop)->Prop)), (((ord_le741939125te_o_o A_145) B_104)->((finite1380128977tate_o B_104)->(finite1380128977tate_o A_145)))).
% Axiom fact_167_finite__subset:(forall (A_145:(hoare_1167836817_state->Prop)) (B_104:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_145) B_104)->((finite1084549118_state B_104)->(finite1084549118_state A_145)))).
% Axiom fact_168_finite__subset:(forall (A_145:(pname->Prop)) (B_104:(pname->Prop)), (((ord_less_eq_pname_o A_145) B_104)->((finite_finite_pname B_104)->(finite_finite_pname A_145)))).
% Axiom fact_169_rev__finite__subset:(forall (A_144:((pname->Prop)->Prop)) (B_103:((pname->Prop)->Prop)), ((finite297249702name_o B_103)->(((ord_le1205211808me_o_o A_144) B_103)->(finite297249702name_o A_144)))).
% Axiom fact_170_rev__finite__subset:(forall (A_144:((hoare_1167836817_state->Prop)->Prop)) (B_103:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o B_103)->(((ord_le741939125te_o_o A_144) B_103)->(finite1380128977tate_o A_144)))).
% Axiom fact_171_rev__finite__subset:(forall (A_144:(hoare_1167836817_state->Prop)) (B_103:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_103)->(((ord_le827224136tate_o A_144) B_103)->(finite1084549118_state A_144)))).
% Axiom fact_172_rev__finite__subset:(forall (A_144:(pname->Prop)) (B_103:(pname->Prop)), ((finite_finite_pname B_103)->(((ord_less_eq_pname_o A_144) B_103)->(finite_finite_pname A_144)))).
% Axiom fact_173_insert__mono:(forall (A_143:pname) (C_48:(pname->Prop)) (D_5:(pname->Prop)), (((ord_less_eq_pname_o C_48) D_5)->((ord_less_eq_pname_o ((insert_pname A_143) C_48)) ((insert_pname A_143) D_5)))).
% Axiom fact_174_insert__mono:(forall (A_143:hoare_1167836817_state) (C_48:(hoare_1167836817_state->Prop)) (D_5:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o C_48) D_5)->((ord_le827224136tate_o ((insert2134838167_state A_143) C_48)) ((insert2134838167_state A_143) D_5)))).
% Axiom fact_175_mem__def:(forall (X_88:pname) (A_142:(pname->Prop)), ((iff ((member_pname X_88) A_142)) (A_142 X_88))).
% Axiom fact_176_mem__def:(forall (X_88:hoare_1167836817_state) (A_142:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state X_88) A_142)) (A_142 X_88))).
% Axiom fact_177_Collect__def:(forall (P_37:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_37)) P_37)).
% Axiom fact_178_Collect__def:(forall (P_37:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_37)) P_37)).
% Axiom fact_179_Collect__def:(forall (P_37:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_37)) P_37)).
% Axiom fact_180_Collect__def:(forall (P_37:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o P_37)) P_37)).
% Axiom fact_181_subset__insertI2:(forall (B_102:pname) (A_141:(pname->Prop)) (B_101:(pname->Prop)), (((ord_less_eq_pname_o A_141) B_101)->((ord_less_eq_pname_o A_141) ((insert_pname B_102) B_101)))).
% Axiom fact_182_subset__insertI2:(forall (B_102:hoare_1167836817_state) (A_141:(hoare_1167836817_state->Prop)) (B_101:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_141) B_101)->((ord_le827224136tate_o A_141) ((insert2134838167_state B_102) B_101)))).
% Axiom fact_183_subset__insert:(forall (B_100:(pname->Prop)) (X_87:pname) (A_140:(pname->Prop)), ((((member_pname X_87) A_140)->False)->((iff ((ord_less_eq_pname_o A_140) ((insert_pname X_87) B_100))) ((ord_less_eq_pname_o A_140) B_100)))).
% Axiom fact_184_subset__insert:(forall (B_100:(hoare_1167836817_state->Prop)) (X_87:hoare_1167836817_state) (A_140:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_87) A_140)->False)->((iff ((ord_le827224136tate_o A_140) ((insert2134838167_state X_87) B_100))) ((ord_le827224136tate_o A_140) B_100)))).
% Axiom fact_185_insert__subset:(forall (X_86:pname) (A_139:(pname->Prop)) (B_99:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_86) A_139)) B_99)) ((and ((member_pname X_86) B_99)) ((ord_less_eq_pname_o A_139) B_99)))).
% Axiom fact_186_insert__subset:(forall (X_86:hoare_1167836817_state) (A_139:(hoare_1167836817_state->Prop)) (B_99:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o ((insert2134838167_state X_86) A_139)) B_99)) ((and ((member2058392318_state X_86) B_99)) ((ord_le827224136tate_o A_139) B_99)))).
% Axiom fact_187_subset__insertI:(forall (B_98:(pname->Prop)) (A_138:pname), ((ord_less_eq_pname_o B_98) ((insert_pname A_138) B_98))).
% Axiom fact_188_subset__insertI:(forall (B_98:(hoare_1167836817_state->Prop)) (A_138:hoare_1167836817_state), ((ord_le827224136tate_o B_98) ((insert2134838167_state A_138) B_98))).
% Axiom fact_189_insert__image:(forall (F_51:(hoare_1167836817_state->pname)) (X_85:hoare_1167836817_state) (A_137:(hoare_1167836817_state->Prop)), (((member2058392318_state X_85) A_137)->(((eq (pname->Prop)) ((insert_pname (F_51 X_85)) ((image_8178176_pname F_51) A_137))) ((image_8178176_pname F_51) A_137)))).
% Axiom fact_190_insert__image:(forall (F_51:(pname->hoare_1167836817_state)) (X_85:pname) (A_137:(pname->Prop)), (((member_pname X_85) A_137)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state (F_51 X_85)) ((image_575578384_state F_51) A_137))) ((image_575578384_state F_51) A_137)))).
% Axiom fact_191_image__insert:(forall (F_50:(hoare_1167836817_state->pname)) (A_136:hoare_1167836817_state) (B_97:(hoare_1167836817_state->Prop)), (((eq (pname->Prop)) ((image_8178176_pname F_50) ((insert2134838167_state A_136) B_97))) ((insert_pname (F_50 A_136)) ((image_8178176_pname F_50) B_97)))).
% Axiom fact_192_image__insert:(forall (F_50:(pname->hoare_1167836817_state)) (A_136:pname) (B_97:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_50) ((insert_pname A_136) B_97))) ((insert2134838167_state (F_50 A_136)) ((image_575578384_state F_50) B_97)))).
% Axiom fact_193_image__mono:(forall (F_49:(hoare_1167836817_state->pname)) (A_135:(hoare_1167836817_state->Prop)) (B_96:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_135) B_96)->((ord_less_eq_pname_o ((image_8178176_pname F_49) A_135)) ((image_8178176_pname F_49) B_96)))).
% Axiom fact_194_image__mono:(forall (F_49:(pname->hoare_1167836817_state)) (A_135:(pname->Prop)) (B_96:(pname->Prop)), (((ord_less_eq_pname_o A_135) B_96)->((ord_le827224136tate_o ((image_575578384_state F_49) A_135)) ((image_575578384_state F_49) B_96)))).
% Axiom fact_195_subset__image__iff:(forall (B_95:(pname->Prop)) (F_48:(hoare_1167836817_state->pname)) (A_134:(hoare_1167836817_state->Prop)), ((iff ((ord_less_eq_pname_o B_95) ((image_8178176_pname F_48) A_134))) ((ex (hoare_1167836817_state->Prop)) (fun (AA:(hoare_1167836817_state->Prop))=> ((and ((ord_le827224136tate_o AA) A_134)) (((eq (pname->Prop)) B_95) ((image_8178176_pname F_48) AA))))))).
% Axiom fact_196_subset__image__iff:(forall (B_95:(hoare_1167836817_state->Prop)) (F_48:(pname->hoare_1167836817_state)) (A_134:(pname->Prop)), ((iff ((ord_le827224136tate_o B_95) ((image_575578384_state F_48) A_134))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_134)) (((eq (hoare_1167836817_state->Prop)) B_95) ((image_575578384_state F_48) AA))))))).
% Axiom fact_197_domI:(forall (M_2:(pname->option_com)) (A_133:pname) (B_94:com), ((((eq option_com) (M_2 A_133)) (some_com B_94))->((member_pname A_133) (dom_pname_com M_2)))).
% Axiom fact_198_Collect__conv__if:(forall (P_36:(pname->Prop)) (A_132:pname), ((and ((P_36 A_132)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) X_5) A_132)) (P_36 X_5))))) ((insert_pname A_132) bot_bot_pname_o)))) (((P_36 A_132)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) X_5) A_132)) (P_36 X_5))))) bot_bot_pname_o)))).
% Axiom fact_199_Collect__conv__if:(forall (P_36:((pname->Prop)->Prop)) (A_132:(pname->Prop)), ((and ((P_36 A_132)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) X_5) A_132)) (P_36 X_5))))) ((insert_pname_o A_132) bot_bot_pname_o_o)))) (((P_36 A_132)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) X_5) A_132)) (P_36 X_5))))) bot_bot_pname_o_o)))).
% Axiom fact_200_Collect__conv__if:(forall (P_36:((hoare_1167836817_state->Prop)->Prop)) (A_132:(hoare_1167836817_state->Prop)), ((and ((P_36 A_132)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) X_5) A_132)) (P_36 X_5))))) ((insert999278200tate_o A_132) bot_bo691907561te_o_o)))) (((P_36 A_132)->False)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) X_5) A_132)) (P_36 X_5))))) bot_bo691907561te_o_o)))).
% Axiom fact_201_Collect__conv__if:(forall (P_36:(hoare_1167836817_state->Prop)) (A_132:hoare_1167836817_state), ((and ((P_36 A_132)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X_5) A_132)) (P_36 X_5))))) ((insert2134838167_state A_132) bot_bo70021908tate_o)))) (((P_36 A_132)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X_5) A_132)) (P_36 X_5))))) bot_bo70021908tate_o)))).
% Axiom fact_202_Collect__conv__if2:(forall (P_35:(pname->Prop)) (A_131:pname), ((and ((P_35 A_131)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) A_131) X_5)) (P_35 X_5))))) ((insert_pname A_131) bot_bot_pname_o)))) (((P_35 A_131)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (((eq pname) A_131) X_5)) (P_35 X_5))))) bot_bot_pname_o)))).
% Axiom fact_203_Collect__conv__if2:(forall (P_35:((pname->Prop)->Prop)) (A_131:(pname->Prop)), ((and ((P_35 A_131)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) A_131) X_5)) (P_35 X_5))))) ((insert_pname_o A_131) bot_bot_pname_o_o)))) (((P_35 A_131)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (((eq (pname->Prop)) A_131) X_5)) (P_35 X_5))))) bot_bot_pname_o_o)))).
% Axiom fact_204_Collect__conv__if2:(forall (P_35:((hoare_1167836817_state->Prop)->Prop)) (A_131:(hoare_1167836817_state->Prop)), ((and ((P_35 A_131)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_131) X_5)) (P_35 X_5))))) ((insert999278200tate_o A_131) bot_bo691907561te_o_o)))) (((P_35 A_131)->False)->(((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_131) X_5)) (P_35 X_5))))) bot_bo691907561te_o_o)))).
% Axiom fact_205_Collect__conv__if2:(forall (P_35:(hoare_1167836817_state->Prop)) (A_131:hoare_1167836817_state), ((and ((P_35 A_131)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_131) X_5)) (P_35 X_5))))) ((insert2134838167_state A_131) bot_bo70021908tate_o)))) (((P_35 A_131)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_131) X_5)) (P_35 X_5))))) bot_bo70021908tate_o)))).
% Axiom fact_206_singleton__conv:(forall (A_130:pname), (((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> (((eq pname) X_5) A_130)))) ((insert_pname A_130) bot_bot_pname_o))).
% Axiom fact_207_singleton__conv:(forall (A_130:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> (((eq (pname->Prop)) X_5) A_130)))) ((insert_pname_o A_130) bot_bot_pname_o_o))).
% Axiom fact_208_singleton__conv:(forall (A_130:(hoare_1167836817_state->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> (((eq (hoare_1167836817_state->Prop)) X_5) A_130)))) ((insert999278200tate_o A_130) bot_bo691907561te_o_o))).
% Axiom fact_209_singleton__conv:(forall (A_130:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X_5) A_130)))) ((insert2134838167_state A_130) bot_bo70021908tate_o))).
% Axiom fact_210_singleton__conv2:(forall (A_129:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_129))) ((insert_pname A_129) bot_bot_pname_o))).
% Axiom fact_211_singleton__conv2:(forall (A_129:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fequal_pname_o A_129))) ((insert_pname_o A_129) bot_bot_pname_o_o))).
% Axiom fact_212_singleton__conv2:(forall (A_129:(hoare_1167836817_state->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fequal1486222077tate_o A_129))) ((insert999278200tate_o A_129) bot_bo691907561te_o_o))).
% Axiom fact_213_singleton__conv2:(forall (A_129:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fequal1831255762_state A_129))) ((insert2134838167_state A_129) bot_bo70021908tate_o))).
% Axiom fact_214_MGF__lemma1:(forall (C_21:com) (G_3:(hoare_1167836817_state->Prop)), (hoare_1201148605gleton->((forall (X_5:pname), (((member_pname X_5) (dom_pname_com body))->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT (body_1 X_5))) bot_bo70021908tate_o))))->((wt C_21)->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o)))))).
% Axiom fact_215_WT__bodiesD:(forall (Pn_1:pname) (B_42:com), (wT_bodies->((((eq option_com) (body Pn_1)) (some_com B_42))->(wt B_42)))).
% Axiom fact_216_imageE:(forall (B_93:pname) (F_47:(hoare_1167836817_state->pname)) (A_128:(hoare_1167836817_state->Prop)), (((member_pname B_93) ((image_8178176_pname F_47) A_128))->((forall (X_5:hoare_1167836817_state), ((((eq pname) B_93) (F_47 X_5))->(((member2058392318_state X_5) A_128)->False)))->False))).
% Axiom fact_217_imageE:(forall (B_93:hoare_1167836817_state) (F_47:(pname->hoare_1167836817_state)) (A_128:(pname->Prop)), (((member2058392318_state B_93) ((image_575578384_state F_47) A_128))->((forall (X_5:pname), ((((eq hoare_1167836817_state) B_93) (F_47 X_5))->(((member_pname X_5) A_128)->False)))->False))).
% Axiom fact_218_finite__subset__induct:(forall (P_34:(((pname->Prop)->Prop)->Prop)) (A_127:((pname->Prop)->Prop)) (F_46:((pname->Prop)->Prop)), ((finite297249702name_o F_46)->(((ord_le1205211808me_o_o F_46) A_127)->((P_34 bot_bot_pname_o_o)->((forall (A_122:(pname->Prop)) (F_26:((pname->Prop)->Prop)), ((finite297249702name_o F_26)->(((member_pname_o A_122) A_127)->((((member_pname_o A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert_pname_o A_122) F_26)))))))->(P_34 F_46)))))).
% Axiom fact_219_finite__subset__induct:(forall (P_34:(((hoare_1167836817_state->Prop)->Prop)->Prop)) (A_127:((hoare_1167836817_state->Prop)->Prop)) (F_46:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_46)->(((ord_le741939125te_o_o F_46) A_127)->((P_34 bot_bo691907561te_o_o)->((forall (A_122:(hoare_1167836817_state->Prop)) (F_26:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_26)->(((member864234961tate_o A_122) A_127)->((((member864234961tate_o A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert999278200tate_o A_122) F_26)))))))->(P_34 F_46)))))).
% Axiom fact_220_finite__subset__induct:(forall (P_34:((pname->Prop)->Prop)) (A_127:(pname->Prop)) (F_46:(pname->Prop)), ((finite_finite_pname F_46)->(((ord_less_eq_pname_o F_46) A_127)->((P_34 bot_bot_pname_o)->((forall (A_122:pname) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->(((member_pname A_122) A_127)->((((member_pname A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert_pname A_122) F_26)))))))->(P_34 F_46)))))).
% Axiom fact_221_finite__subset__induct:(forall (P_34:((hoare_1167836817_state->Prop)->Prop)) (A_127:(hoare_1167836817_state->Prop)) (F_46:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_46)->(((ord_le827224136tate_o F_46) A_127)->((P_34 bot_bo70021908tate_o)->((forall (A_122:hoare_1167836817_state) (F_26:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_26)->(((member2058392318_state A_122) A_127)->((((member2058392318_state A_122) F_26)->False)->((P_34 F_26)->(P_34 ((insert2134838167_state A_122) F_26)))))))->(P_34 F_46)))))).
% Axiom fact_222_WTs__elim__cases_I7_J:(forall (P:pname), ((wt (body_1 P))->((forall (Y_2:com), (not (((eq option_com) (body P)) (some_com Y_2))))->False))).
% Axiom fact_223_subsetI:(forall (B_92:(pname->Prop)) (A_126:(pname->Prop)), ((forall (X_5:pname), (((member_pname X_5) A_126)->((member_pname X_5) B_92)))->((ord_less_eq_pname_o A_126) B_92))).
% Axiom fact_224_subsetI:(forall (B_92:(hoare_1167836817_state->Prop)) (A_126:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_126)->((member2058392318_state X_5) B_92)))->((ord_le827224136tate_o A_126) B_92))).
% Axiom fact_225_finite__subset__image:(forall (F_45:((pname->Prop)->hoare_1167836817_state)) (A_125:((pname->Prop)->Prop)) (B_91:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_91)->(((ord_le827224136tate_o B_91) ((image_1381916541_state F_45) A_125))->((ex ((pname->Prop)->Prop)) (fun (C_47:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_47) A_125)) (finite297249702name_o C_47))) (((eq (hoare_1167836817_state->Prop)) B_91) ((image_1381916541_state F_45) C_47)))))))).
% Axiom fact_226_finite__subset__image:(forall (F_45:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (A_125:((hoare_1167836817_state->Prop)->Prop)) (B_91:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_91)->(((ord_le827224136tate_o B_91) ((image_635813834_state F_45) A_125))->((ex ((hoare_1167836817_state->Prop)->Prop)) (fun (C_47:((hoare_1167836817_state->Prop)->Prop))=> ((and ((and ((ord_le741939125te_o_o C_47) A_125)) (finite1380128977tate_o C_47))) (((eq (hoare_1167836817_state->Prop)) B_91) ((image_635813834_state F_45) C_47)))))))).
% Axiom fact_227_finite__subset__image:(forall (F_45:((pname->Prop)->pname)) (A_125:((pname->Prop)->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_pname_o_pname F_45) A_125))->((ex ((pname->Prop)->Prop)) (fun (C_47:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_47) A_125)) (finite297249702name_o C_47))) (((eq (pname->Prop)) B_91) ((image_pname_o_pname F_45) C_47)))))))).
% Axiom fact_228_finite__subset__image:(forall (F_45:((hoare_1167836817_state->Prop)->pname)) (A_125:((hoare_1167836817_state->Prop)->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_980295115_pname F_45) A_125))->((ex ((hoare_1167836817_state->Prop)->Prop)) (fun (C_47:((hoare_1167836817_state->Prop)->Prop))=> ((and ((and ((ord_le741939125te_o_o C_47) A_125)) (finite1380128977tate_o C_47))) (((eq (pname->Prop)) B_91) ((image_980295115_pname F_45) C_47)))))))).
% Axiom fact_229_finite__subset__image:(forall (F_45:(hoare_1167836817_state->(pname->Prop))) (A_125:(hoare_1167836817_state->Prop)) (B_91:((pname->Prop)->Prop)), ((finite297249702name_o B_91)->(((ord_le1205211808me_o_o B_91) ((image_2066861949name_o F_45) A_125))->((ex (hoare_1167836817_state->Prop)) (fun (C_47:(hoare_1167836817_state->Prop))=> ((and ((and ((ord_le827224136tate_o C_47) A_125)) (finite1084549118_state C_47))) (((eq ((pname->Prop)->Prop)) B_91) ((image_2066861949name_o F_45) C_47)))))))).
% Axiom fact_230_finite__subset__image:(forall (F_45:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (A_125:(hoare_1167836817_state->Prop)) (B_91:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o B_91)->(((ord_le741939125te_o_o B_91) ((image_1745649338tate_o F_45) A_125))->((ex (hoare_1167836817_state->Prop)) (fun (C_47:(hoare_1167836817_state->Prop))=> ((and ((and ((ord_le827224136tate_o C_47) A_125)) (finite1084549118_state C_47))) (((eq ((hoare_1167836817_state->Prop)->Prop)) B_91) ((image_1745649338tate_o F_45) C_47)))))))).
% Axiom fact_231_finite__subset__image:(forall (F_45:(hoare_1167836817_state->pname)) (A_125:(hoare_1167836817_state->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_8178176_pname F_45) A_125))->((ex (hoare_1167836817_state->Prop)) (fun (C_47:(hoare_1167836817_state->Prop))=> ((and ((and ((ord_le827224136tate_o C_47) A_125)) (finite1084549118_state C_47))) (((eq (pname->Prop)) B_91) ((image_8178176_pname F_45) C_47)))))))).
% Axiom fact_232_finite__subset__image:(forall (F_45:(pname->(pname->Prop))) (A_125:(pname->Prop)) (B_91:((pname->Prop)->Prop)), ((finite297249702name_o B_91)->(((ord_le1205211808me_o_o B_91) ((image_pname_pname_o F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq ((pname->Prop)->Prop)) B_91) ((image_pname_pname_o F_45) C_47)))))))).
% Axiom fact_233_finite__subset__image:(forall (F_45:(pname->(hoare_1167836817_state->Prop))) (A_125:(pname->Prop)) (B_91:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o B_91)->(((ord_le741939125te_o_o B_91) ((image_475339327tate_o F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq ((hoare_1167836817_state->Prop)->Prop)) B_91) ((image_475339327tate_o F_45) C_47)))))))).
% Axiom fact_234_finite__subset__image:(forall (F_45:(pname->pname)) (A_125:(pname->Prop)) (B_91:(pname->Prop)), ((finite_finite_pname B_91)->(((ord_less_eq_pname_o B_91) ((image_pname_pname F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq (pname->Prop)) B_91) ((image_pname_pname F_45) C_47)))))))).
% Axiom fact_235_finite__subset__image:(forall (F_45:(pname->hoare_1167836817_state)) (A_125:(pname->Prop)) (B_91:(hoare_1167836817_state->Prop)), ((finite1084549118_state B_91)->(((ord_le827224136tate_o B_91) ((image_575578384_state F_45) A_125))->((ex (pname->Prop)) (fun (C_47:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_47) A_125)) (finite_finite_pname C_47))) (((eq (hoare_1167836817_state->Prop)) B_91) ((image_575578384_state F_45) C_47)))))))).
% Axiom fact_236_finite__dom__body:(finite_finite_pname (dom_pname_com body)).
% Axiom fact_237_finite__induct:(forall (P_33:(((pname->Prop)->Prop)->Prop)) (F_44:((pname->Prop)->Prop)), ((finite297249702name_o F_44)->((P_33 bot_bot_pname_o_o)->((forall (X_5:(pname->Prop)) (F_26:((pname->Prop)->Prop)), ((finite297249702name_o F_26)->((((member_pname_o X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert_pname_o X_5) F_26))))))->(P_33 F_44))))).
% Axiom fact_238_finite__induct:(forall (P_33:(((hoare_1167836817_state->Prop)->Prop)->Prop)) (F_44:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_44)->((P_33 bot_bo691907561te_o_o)->((forall (X_5:(hoare_1167836817_state->Prop)) (F_26:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_26)->((((member864234961tate_o X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert999278200tate_o X_5) F_26))))))->(P_33 F_44))))).
% Axiom fact_239_finite__induct:(forall (P_33:((pname->Prop)->Prop)) (F_44:(pname->Prop)), ((finite_finite_pname F_44)->((P_33 bot_bot_pname_o)->((forall (X_5:pname) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->((((member_pname X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert_pname X_5) F_26))))))->(P_33 F_44))))).
% Axiom fact_240_finite__induct:(forall (P_33:((hoare_1167836817_state->Prop)->Prop)) (F_44:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_44)->((P_33 bot_bo70021908tate_o)->((forall (X_5:hoare_1167836817_state) (F_26:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_26)->((((member2058392318_state X_5) F_26)->False)->((P_33 F_26)->(P_33 ((insert2134838167_state X_5) F_26))))))->(P_33 F_44))))).
% Axiom fact_241_finite_Osimps:(forall (A_123:((pname->Prop)->Prop)), ((iff (finite297249702name_o A_123)) ((or (((eq ((pname->Prop)->Prop)) A_123) bot_bot_pname_o_o)) ((ex ((pname->Prop)->Prop)) (fun (A_124:((pname->Prop)->Prop))=> ((ex (pname->Prop)) (fun (A_122:(pname->Prop))=> ((and (((eq ((pname->Prop)->Prop)) A_123) ((insert_pname_o A_122) A_124))) (finite297249702name_o A_124))))))))).
% Axiom fact_242_finite_Osimps:(forall (A_123:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o A_123)) ((or (((eq ((hoare_1167836817_state->Prop)->Prop)) A_123) bot_bo691907561te_o_o)) ((ex ((hoare_1167836817_state->Prop)->Prop)) (fun (A_124:((hoare_1167836817_state->Prop)->Prop))=> ((ex (hoare_1167836817_state->Prop)) (fun (A_122:(hoare_1167836817_state->Prop))=> ((and (((eq ((hoare_1167836817_state->Prop)->Prop)) A_123) ((insert999278200tate_o A_122) A_124))) (finite1380128977tate_o A_124))))))))).
% Axiom fact_243_finite_Osimps:(forall (A_123:(pname->Prop)), ((iff (finite_finite_pname A_123)) ((or (((eq (pname->Prop)) A_123) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_124:(pname->Prop))=> ((ex pname) (fun (A_122:pname)=> ((and (((eq (pname->Prop)) A_123) ((insert_pname A_122) A_124))) (finite_finite_pname A_124))))))))).
% Axiom fact_244_finite_Osimps:(forall (A_123:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state A_123)) ((or (((eq (hoare_1167836817_state->Prop)) A_123) bot_bo70021908tate_o)) ((ex (hoare_1167836817_state->Prop)) (fun (A_124:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (A_122:hoare_1167836817_state)=> ((and (((eq (hoare_1167836817_state->Prop)) A_123) ((insert2134838167_state A_122) A_124))) (finite1084549118_state A_124))))))))).
% Axiom fact_245_pigeonhole__infinite:(forall (F_43:(pname->(pname->Prop))) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite297249702name_o ((image_pname_pname_o F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq (pname->Prop)) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_246_pigeonhole__infinite:(forall (F_43:(pname->(hoare_1167836817_state->Prop))) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite1380128977tate_o ((image_475339327tate_o F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq (hoare_1167836817_state->Prop)) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_247_pigeonhole__infinite:(forall (F_43:(hoare_1167836817_state->hoare_1167836817_state)) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite1084549118_state ((image_31595733_state F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_248_pigeonhole__infinite:(forall (F_43:((pname->Prop)->hoare_1167836817_state)) (A_121:((pname->Prop)->Prop)), (((finite297249702name_o A_121)->False)->((finite1084549118_state ((image_1381916541_state F_43) A_121))->((ex (pname->Prop)) (fun (X_5:(pname->Prop))=> ((and ((member_pname_o X_5) A_121)) ((finite297249702name_o (collect_pname_o (fun (A_122:(pname->Prop))=> ((and ((member_pname_o A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_249_pigeonhole__infinite:(forall (F_43:((hoare_1167836817_state->Prop)->hoare_1167836817_state)) (A_121:((hoare_1167836817_state->Prop)->Prop)), (((finite1380128977tate_o A_121)->False)->((finite1084549118_state ((image_635813834_state F_43) A_121))->((ex (hoare_1167836817_state->Prop)) (fun (X_5:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o X_5) A_121)) ((finite1380128977tate_o (collec269976083tate_o (fun (A_122:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_250_pigeonhole__infinite:(forall (F_43:(pname->pname)) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite_finite_pname ((image_pname_pname F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_251_pigeonhole__infinite:(forall (F_43:(hoare_1167836817_state->pname)) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite_finite_pname ((image_8178176_pname F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_252_pigeonhole__infinite:(forall (F_43:((pname->Prop)->pname)) (A_121:((pname->Prop)->Prop)), (((finite297249702name_o A_121)->False)->((finite_finite_pname ((image_pname_o_pname F_43) A_121))->((ex (pname->Prop)) (fun (X_5:(pname->Prop))=> ((and ((member_pname_o X_5) A_121)) ((finite297249702name_o (collect_pname_o (fun (A_122:(pname->Prop))=> ((and ((member_pname_o A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_253_pigeonhole__infinite:(forall (F_43:((hoare_1167836817_state->Prop)->pname)) (A_121:((hoare_1167836817_state->Prop)->Prop)), (((finite1380128977tate_o A_121)->False)->((finite_finite_pname ((image_980295115_pname F_43) A_121))->((ex (hoare_1167836817_state->Prop)) (fun (X_5:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o X_5) A_121)) ((finite1380128977tate_o (collec269976083tate_o (fun (A_122:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o A_122) A_121)) (((eq pname) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_254_pigeonhole__infinite:(forall (F_43:(hoare_1167836817_state->(pname->Prop))) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite297249702name_o ((image_2066861949name_o F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq (pname->Prop)) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_255_pigeonhole__infinite:(forall (F_43:(hoare_1167836817_state->(hoare_1167836817_state->Prop))) (A_121:(hoare_1167836817_state->Prop)), (((finite1084549118_state A_121)->False)->((finite1380128977tate_o ((image_1745649338tate_o F_43) A_121))->((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_121)) ((finite1084549118_state (collec1027672124_state (fun (A_122:hoare_1167836817_state)=> ((and ((member2058392318_state A_122) A_121)) (((eq (hoare_1167836817_state->Prop)) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_256_pigeonhole__infinite:(forall (F_43:(pname->hoare_1167836817_state)) (A_121:(pname->Prop)), (((finite_finite_pname A_121)->False)->((finite1084549118_state ((image_575578384_state F_43) A_121))->((ex pname) (fun (X_5:pname)=> ((and ((member_pname X_5) A_121)) ((finite_finite_pname (collect_pname (fun (A_122:pname)=> ((and ((member_pname A_122) A_121)) (((eq hoare_1167836817_state) (F_43 A_122)) (F_43 X_5))))))->False))))))).
% Axiom fact_257_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_258_MGT__Body:(forall (G_3:(hoare_1167836817_state->Prop)) (Procs_3:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_3) ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3))) ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) Procs_3))->((finite_finite_pname Procs_3)->((hoare_123228589_state G_3) ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) Procs_3))))).
% Axiom fact_259_domD:(forall (A_120:pname) (M_1:(pname->option_com)), (((member_pname A_120) (dom_pname_com M_1))->((ex com) (fun (B_90:com)=> (((eq option_com) (M_1 A_120)) (some_com B_90)))))).
% Axiom fact_260_the__elem__eq:(forall (X_84:pname), (((eq pname) (the_elem_pname ((insert_pname X_84) bot_bot_pname_o))) X_84)).
% Axiom fact_261_the__elem__eq:(forall (X_84:hoare_1167836817_state), (((eq hoare_1167836817_state) (the_el323660082_state ((insert2134838167_state X_84) bot_bo70021908tate_o))) X_84)).
% Axiom fact_262_image__subsetI:(forall (F_42:(hoare_1167836817_state->pname)) (B_89:(pname->Prop)) (A_119:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_119)->((member_pname (F_42 X_5)) B_89)))->((ord_less_eq_pname_o ((image_8178176_pname F_42) A_119)) B_89))).
% Axiom fact_263_image__subsetI:(forall (F_42:(pname->hoare_1167836817_state)) (B_89:(hoare_1167836817_state->Prop)) (A_119:(pname->Prop)), ((forall (X_5:pname), (((member_pname X_5) A_119)->((member2058392318_state (F_42 X_5)) B_89)))->((ord_le827224136tate_o ((image_575578384_state F_42) A_119)) B_89))).
% Axiom fact_264_order__refl:(forall (X_83:(pname->Prop)), ((ord_less_eq_pname_o X_83) X_83)).
% Axiom fact_265_order__refl:(forall (X_83:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_83) X_83)).
% Axiom fact_266_nonempty__iff:(forall (A_118:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_118) bot_bot_pname_o))) ((ex pname) (fun (X_5:pname)=> ((ex (pname->Prop)) (fun (B_43:(pname->Prop))=> ((and (((eq (pname->Prop)) A_118) ((insert_pname X_5) B_43))) (((member_pname X_5) B_43)->False)))))))).
% Axiom fact_267_nonempty__iff:(forall (A_118:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_118) bot_bo70021908tate_o))) ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (B_43:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_118) ((insert2134838167_state X_5) B_43))) (((member2058392318_state X_5) B_43)->False)))))))).
% Axiom fact_268_the_Osimps:(forall (X_82:com), (((eq com) (the_com (some_com X_82))) X_82)).
% Axiom fact_269_weak__Body:(forall (G_27:(hoare_1167836817_state->Prop)) (P_32:(state->(state->Prop))) (Pn_4:pname) (Q_22:(state->(state->Prop))), (((hoare_123228589_state G_27) ((insert2134838167_state (((hoare_908217195_state P_32) (the_com (body Pn_4))) Q_22)) bot_bo70021908tate_o))->((hoare_123228589_state G_27) ((insert2134838167_state (((hoare_908217195_state P_32) (body_1 Pn_4)) Q_22)) bot_bo70021908tate_o)))).
% Axiom fact_270_UnCI:(forall (A_117:(pname->Prop)) (C_46:pname) (B_88:(pname->Prop)), (((((member_pname C_46) B_88)->False)->((member_pname C_46) A_117))->((member_pname C_46) ((semila1780557381name_o A_117) B_88)))).
% Axiom fact_271_UnCI:(forall (A_117:(hoare_1167836817_state->Prop)) (C_46:hoare_1167836817_state) (B_88:(hoare_1167836817_state->Prop)), (((((member2058392318_state C_46) B_88)->False)->((member2058392318_state C_46) A_117))->((member2058392318_state C_46) ((semila1172322802tate_o A_117) B_88)))).
% Axiom fact_272_UnE:(forall (C_45:pname) (A_116:(pname->Prop)) (B_87:(pname->Prop)), (((member_pname C_45) ((semila1780557381name_o A_116) B_87))->((((member_pname C_45) A_116)->False)->((member_pname C_45) B_87)))).
% Axiom fact_273_UnE:(forall (C_45:hoare_1167836817_state) (A_116:(hoare_1167836817_state->Prop)) (B_87:(hoare_1167836817_state->Prop)), (((member2058392318_state C_45) ((semila1172322802tate_o A_116) B_87))->((((member2058392318_state C_45) A_116)->False)->((member2058392318_state C_45) B_87)))).
% Axiom fact_274_Collect__disj__eq:(forall (P_31:(pname->Prop)) (Q_21:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila1780557381name_o (collect_pname P_31)) (collect_pname Q_21)))).
% Axiom fact_275_Collect__disj__eq:(forall (P_31:((pname->Prop)->Prop)) (Q_21:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila181081674me_o_o (collect_pname_o P_31)) (collect_pname_o Q_21)))).
% Axiom fact_276_Collect__disj__eq:(forall (P_31:((hoare_1167836817_state->Prop)->Prop)) (Q_21:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila866907787te_o_o (collec269976083tate_o P_31)) (collec269976083tate_o Q_21)))).
% Axiom fact_277_Collect__disj__eq:(forall (P_31:(hoare_1167836817_state->Prop)) (Q_21:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or (P_31 X_5)) (Q_21 X_5))))) ((semila1172322802tate_o (collec1027672124_state P_31)) (collec1027672124_state Q_21)))).
% Axiom fact_278_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_1167836817_state) (((hoare_908217195_state Fun1_2) Com_4) Fun2_2)) (((hoare_908217195_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_279_UnI2:(forall (A_115:(pname->Prop)) (C_44:pname) (B_86:(pname->Prop)), (((member_pname C_44) B_86)->((member_pname C_44) ((semila1780557381name_o A_115) B_86)))).
% Axiom fact_280_UnI2:(forall (A_115:(hoare_1167836817_state->Prop)) (C_44:hoare_1167836817_state) (B_86:(hoare_1167836817_state->Prop)), (((member2058392318_state C_44) B_86)->((member2058392318_state C_44) ((semila1172322802tate_o A_115) B_86)))).
% Axiom fact_281_UnI1:(forall (B_85:(pname->Prop)) (C_43:pname) (A_114:(pname->Prop)), (((member_pname C_43) A_114)->((member_pname C_43) ((semila1780557381name_o A_114) B_85)))).
% Axiom fact_282_UnI1:(forall (B_85:(hoare_1167836817_state->Prop)) (C_43:hoare_1167836817_state) (A_114:(hoare_1167836817_state->Prop)), (((member2058392318_state C_43) A_114)->((member2058392318_state C_43) ((semila1172322802tate_o A_114) B_85)))).
% Axiom fact_283_ball__Un:(forall (P_30:(hoare_1167836817_state->Prop)) (A_113:(hoare_1167836817_state->Prop)) (B_84:(hoare_1167836817_state->Prop)), ((iff (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) ((semila1172322802tate_o A_113) B_84))->(P_30 X_5)))) ((and (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_113)->(P_30 X_5)))) (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) B_84)->(P_30 X_5)))))).
% Axiom fact_284_bex__Un:(forall (P_29:(hoare_1167836817_state->Prop)) (A_112:(hoare_1167836817_state->Prop)) (B_83:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) ((semila1172322802tate_o A_112) B_83))) (P_29 X_5))))) ((or ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_112)) (P_29 X_5))))) ((ex hoare_1167836817_state) (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) B_83)) (P_29 X_5))))))).
% Axiom fact_285_Un__assoc:(forall (A_111:(hoare_1167836817_state->Prop)) (B_82:(hoare_1167836817_state->Prop)) (C_42:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_111) B_82)) C_42)) ((semila1172322802tate_o A_111) ((semila1172322802tate_o B_82) C_42)))).
% Axiom fact_286_Un__iff:(forall (C_41:pname) (A_110:(pname->Prop)) (B_81:(pname->Prop)), ((iff ((member_pname C_41) ((semila1780557381name_o A_110) B_81))) ((or ((member_pname C_41) A_110)) ((member_pname C_41) B_81)))).
% Axiom fact_287_Un__iff:(forall (C_41:hoare_1167836817_state) (A_110:(hoare_1167836817_state->Prop)) (B_81:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_41) ((semila1172322802tate_o A_110) B_81))) ((or ((member2058392318_state C_41) A_110)) ((member2058392318_state C_41) B_81)))).
% Axiom fact_288_Un__left__commute:(forall (A_109:(hoare_1167836817_state->Prop)) (B_80:(hoare_1167836817_state->Prop)) (C_40:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_109) ((semila1172322802tate_o B_80) C_40))) ((semila1172322802tate_o B_80) ((semila1172322802tate_o A_109) C_40)))).
% Axiom fact_289_Un__left__absorb:(forall (A_108:(hoare_1167836817_state->Prop)) (B_79:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_108) ((semila1172322802tate_o A_108) B_79))) ((semila1172322802tate_o A_108) B_79))).
% Axiom fact_290_Un__commute:(forall (A_107:(hoare_1167836817_state->Prop)) (B_78:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_107) B_78)) ((semila1172322802tate_o B_78) A_107))).
% Axiom fact_291_Un__def:(forall (A_106:(pname->Prop)) (B_77:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_106) B_77)) (collect_pname (fun (X_5:pname)=> ((or ((member_pname X_5) A_106)) ((member_pname X_5) B_77)))))).
% Axiom fact_292_Un__def:(forall (A_106:((pname->Prop)->Prop)) (B_77:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila181081674me_o_o A_106) B_77)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((or ((member_pname_o X_5) A_106)) ((member_pname_o X_5) B_77)))))).
% Axiom fact_293_Un__def:(forall (A_106:((hoare_1167836817_state->Prop)->Prop)) (B_77:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila866907787te_o_o A_106) B_77)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((or ((member864234961tate_o X_5) A_106)) ((member864234961tate_o X_5) B_77)))))).
% Axiom fact_294_Un__def:(forall (A_106:(hoare_1167836817_state->Prop)) (B_77:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_106) B_77)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((or ((member2058392318_state X_5) A_106)) ((member2058392318_state X_5) B_77)))))).
% Axiom fact_295_Un__absorb:(forall (A_105:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_105) A_105)) A_105)).
% Axiom fact_296_Un__empty:(forall (A_104:(pname->Prop)) (B_76:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_104) B_76)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_104) bot_bot_pname_o)) (((eq (pname->Prop)) B_76) bot_bot_pname_o)))).
% Axiom fact_297_Un__empty:(forall (A_104:(hoare_1167836817_state->Prop)) (B_76:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_104) B_76)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) A_104) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) B_76) bot_bo70021908tate_o)))).
% Axiom fact_298_Un__empty__right:(forall (A_103:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_103) bot_bot_pname_o)) A_103)).
% Axiom fact_299_Un__empty__right:(forall (A_103:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_103) bot_bo70021908tate_o)) A_103)).
% Axiom fact_300_Un__empty__left:(forall (B_75:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_75)) B_75)).
% Axiom fact_301_Un__empty__left:(forall (B_75:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) B_75)) B_75)).
% Axiom fact_302_finite__UnI:(forall (G_26:((pname->Prop)->Prop)) (F_41:((pname->Prop)->Prop)), ((finite297249702name_o F_41)->((finite297249702name_o G_26)->(finite297249702name_o ((semila181081674me_o_o F_41) G_26))))).
% Axiom fact_303_finite__UnI:(forall (G_26:((hoare_1167836817_state->Prop)->Prop)) (F_41:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_41)->((finite1380128977tate_o G_26)->(finite1380128977tate_o ((semila866907787te_o_o F_41) G_26))))).
% Axiom fact_304_finite__UnI:(forall (G_26:(pname->Prop)) (F_41:(pname->Prop)), ((finite_finite_pname F_41)->((finite_finite_pname G_26)->(finite_finite_pname ((semila1780557381name_o F_41) G_26))))).
% Axiom fact_305_finite__UnI:(forall (G_26:(hoare_1167836817_state->Prop)) (F_41:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_41)->((finite1084549118_state G_26)->(finite1084549118_state ((semila1172322802tate_o F_41) G_26))))).
% Axiom fact_306_finite__Un:(forall (F_40:((pname->Prop)->Prop)) (G_25:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((semila181081674me_o_o F_40) G_25))) ((and (finite297249702name_o F_40)) (finite297249702name_o G_25)))).
% Axiom fact_307_finite__Un:(forall (F_40:((hoare_1167836817_state->Prop)->Prop)) (G_25:((hoare_1167836817_state->Prop)->Prop)), ((iff (finite1380128977tate_o ((semila866907787te_o_o F_40) G_25))) ((and (finite1380128977tate_o F_40)) (finite1380128977tate_o G_25)))).
% Axiom fact_308_finite__Un:(forall (F_40:(pname->Prop)) (G_25:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_40) G_25))) ((and (finite_finite_pname F_40)) (finite_finite_pname G_25)))).
% Axiom fact_309_finite__Un:(forall (F_40:(hoare_1167836817_state->Prop)) (G_25:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((semila1172322802tate_o F_40) G_25))) ((and (finite1084549118_state F_40)) (finite1084549118_state G_25)))).
% Axiom fact_310_Un__insert__left:(forall (A_102:pname) (B_74:(pname->Prop)) (C_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_102) B_74)) C_39)) ((insert_pname A_102) ((semila1780557381name_o B_74) C_39)))).
% Axiom fact_311_Un__insert__left:(forall (A_102:hoare_1167836817_state) (B_74:(hoare_1167836817_state->Prop)) (C_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((insert2134838167_state A_102) B_74)) C_39)) ((insert2134838167_state A_102) ((semila1172322802tate_o B_74) C_39)))).
% Axiom fact_312_Un__insert__right:(forall (A_101:(pname->Prop)) (A_100:pname) (B_73:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_101) ((insert_pname A_100) B_73))) ((insert_pname A_100) ((semila1780557381name_o A_101) B_73)))).
% Axiom fact_313_Un__insert__right:(forall (A_101:(hoare_1167836817_state->Prop)) (A_100:hoare_1167836817_state) (B_73:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_101) ((insert2134838167_state A_100) B_73))) ((insert2134838167_state A_100) ((semila1172322802tate_o A_101) B_73)))).
% Axiom fact_314_Un__mono:(forall (B_72:(pname->Prop)) (D_4:(pname->Prop)) (A_99:(pname->Prop)) (C_38:(pname->Prop)), (((ord_less_eq_pname_o A_99) C_38)->(((ord_less_eq_pname_o B_72) D_4)->((ord_less_eq_pname_o ((semila1780557381name_o A_99) B_72)) ((semila1780557381name_o C_38) D_4))))).
% Axiom fact_315_Un__mono:(forall (B_72:(hoare_1167836817_state->Prop)) (D_4:(hoare_1167836817_state->Prop)) (A_99:(hoare_1167836817_state->Prop)) (C_38:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_99) C_38)->(((ord_le827224136tate_o B_72) D_4)->((ord_le827224136tate_o ((semila1172322802tate_o A_99) B_72)) ((semila1172322802tate_o C_38) D_4))))).
% Axiom fact_316_Un__least:(forall (B_71:(pname->Prop)) (A_98:(pname->Prop)) (C_37:(pname->Prop)), (((ord_less_eq_pname_o A_98) C_37)->(((ord_less_eq_pname_o B_71) C_37)->((ord_less_eq_pname_o ((semila1780557381name_o A_98) B_71)) C_37)))).
% Axiom fact_317_Un__least:(forall (B_71:(hoare_1167836817_state->Prop)) (A_98:(hoare_1167836817_state->Prop)) (C_37:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_98) C_37)->(((ord_le827224136tate_o B_71) C_37)->((ord_le827224136tate_o ((semila1172322802tate_o A_98) B_71)) C_37)))).
% Axiom fact_318_Un__absorb2:(forall (B_70:(pname->Prop)) (A_97:(pname->Prop)), (((ord_less_eq_pname_o B_70) A_97)->(((eq (pname->Prop)) ((semila1780557381name_o A_97) B_70)) A_97))).
% Axiom fact_319_Un__absorb2:(forall (B_70:(hoare_1167836817_state->Prop)) (A_97:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_70) A_97)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_97) B_70)) A_97))).
% Axiom fact_320_Un__absorb1:(forall (A_96:(pname->Prop)) (B_69:(pname->Prop)), (((ord_less_eq_pname_o A_96) B_69)->(((eq (pname->Prop)) ((semila1780557381name_o A_96) B_69)) B_69))).
% Axiom fact_321_Un__absorb1:(forall (A_96:(hoare_1167836817_state->Prop)) (B_69:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_96) B_69)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_96) B_69)) B_69))).
% Axiom fact_322_subset__Un__eq:(forall (A_95:(pname->Prop)) (B_68:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_95) B_68)) (((eq (pname->Prop)) ((semila1780557381name_o A_95) B_68)) B_68))).
% Axiom fact_323_subset__Un__eq:(forall (A_95:(hoare_1167836817_state->Prop)) (B_68:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_95) B_68)) (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_95) B_68)) B_68))).
% Axiom fact_324_Un__upper2:(forall (B_67:(pname->Prop)) (A_94:(pname->Prop)), ((ord_less_eq_pname_o B_67) ((semila1780557381name_o A_94) B_67))).
% Axiom fact_325_Un__upper2:(forall (B_67:(hoare_1167836817_state->Prop)) (A_94:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o B_67) ((semila1172322802tate_o A_94) B_67))).
% Axiom fact_326_Un__upper1:(forall (A_93:(pname->Prop)) (B_66:(pname->Prop)), ((ord_less_eq_pname_o A_93) ((semila1780557381name_o A_93) B_66))).
% Axiom fact_327_Un__upper1:(forall (A_93:(hoare_1167836817_state->Prop)) (B_66:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o A_93) ((semila1172322802tate_o A_93) B_66))).
% Axiom fact_328_image__Un:(forall (F_39:(pname->hoare_1167836817_state)) (A_92:(pname->Prop)) (B_65:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_39) ((semila1780557381name_o A_92) B_65))) ((semila1172322802tate_o ((image_575578384_state F_39) A_92)) ((image_575578384_state F_39) B_65)))).
% Axiom fact_329_insert__def:(forall (A_91:pname) (B_64:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_91) B_64)) ((semila1780557381name_o (collect_pname (fun (X_5:pname)=> (((eq pname) X_5) A_91)))) B_64))).
% Axiom fact_330_insert__def:(forall (A_91:hoare_1167836817_state) (B_64:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_91) B_64)) ((semila1172322802tate_o (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X_5) A_91)))) B_64))).
% Axiom fact_331_insert__def:(forall (A_91:(pname->Prop)) (B_64:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_91) B_64)) ((semila181081674me_o_o (collect_pname_o (fun (X_5:(pname->Prop))=> (((eq (pname->Prop)) X_5) A_91)))) B_64))).
% Axiom fact_332_insert__def:(forall (A_91:(hoare_1167836817_state->Prop)) (B_64:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((insert999278200tate_o A_91) B_64)) ((semila866907787te_o_o (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> (((eq (hoare_1167836817_state->Prop)) X_5) A_91)))) B_64))).
% Axiom fact_333_insert__is__Un:(forall (A_90:pname) (A_89:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_90) A_89)) ((semila1780557381name_o ((insert_pname A_90) bot_bot_pname_o)) A_89))).
% Axiom fact_334_insert__is__Un:(forall (A_90:hoare_1167836817_state) (A_89:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_90) A_89)) ((semila1172322802tate_o ((insert2134838167_state A_90) bot_bo70021908tate_o)) A_89))).
% Axiom fact_335_hoare__derivs_OBody:(forall (G_24:(hoare_1167836817_state->Prop)) (P_28:(pname->(state->(state->Prop)))) (Q_20:(pname->(state->(state->Prop)))) (Procs_2:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_24) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_28 P_24)) (body_1 P_24)) (Q_20 P_24)))) Procs_2))) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_28 P_24)) (the_com (body P_24))) (Q_20 P_24)))) Procs_2))->((hoare_123228589_state G_24) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_28 P_24)) (body_1 P_24)) (Q_20 P_24)))) Procs_2)))).
% Axiom fact_336_xt1_I6_J:(forall (Z_20:(pname->Prop)) (Y_46:(pname->Prop)) (X_81:(pname->Prop)), (((ord_less_eq_pname_o Y_46) X_81)->(((ord_less_eq_pname_o Z_20) Y_46)->((ord_less_eq_pname_o Z_20) X_81)))).
% Axiom fact_337_xt1_I6_J:(forall (Z_20:(hoare_1167836817_state->Prop)) (Y_46:(hoare_1167836817_state->Prop)) (X_81:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_46) X_81)->(((ord_le827224136tate_o Z_20) Y_46)->((ord_le827224136tate_o Z_20) X_81)))).
% Axiom fact_338_xt1_I5_J:(forall (Y_45:(pname->Prop)) (X_80:(pname->Prop)), (((ord_less_eq_pname_o Y_45) X_80)->(((ord_less_eq_pname_o X_80) Y_45)->(((eq (pname->Prop)) X_80) Y_45)))).
% Axiom fact_339_xt1_I5_J:(forall (Y_45:(hoare_1167836817_state->Prop)) (X_80:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_45) X_80)->(((ord_le827224136tate_o X_80) Y_45)->(((eq (hoare_1167836817_state->Prop)) X_80) Y_45)))).
% Axiom fact_340_order__trans:(forall (Z_19:(pname->Prop)) (X_79:(pname->Prop)) (Y_44:(pname->Prop)), (((ord_less_eq_pname_o X_79) Y_44)->(((ord_less_eq_pname_o Y_44) Z_19)->((ord_less_eq_pname_o X_79) Z_19)))).
% Axiom fact_341_order__trans:(forall (Z_19:(hoare_1167836817_state->Prop)) (X_79:(hoare_1167836817_state->Prop)) (Y_44:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_79) Y_44)->(((ord_le827224136tate_o Y_44) Z_19)->((ord_le827224136tate_o X_79) Z_19)))).
% Axiom fact_342_order__antisym:(forall (X_78:(pname->Prop)) (Y_43:(pname->Prop)), (((ord_less_eq_pname_o X_78) Y_43)->(((ord_less_eq_pname_o Y_43) X_78)->(((eq (pname->Prop)) X_78) Y_43)))).
% Axiom fact_343_order__antisym:(forall (X_78:(hoare_1167836817_state->Prop)) (Y_43:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_78) Y_43)->(((ord_le827224136tate_o Y_43) X_78)->(((eq (hoare_1167836817_state->Prop)) X_78) Y_43)))).
% Axiom fact_344_xt1_I4_J:(forall (C_36:(pname->Prop)) (B_63:(pname->Prop)) (A_88:(pname->Prop)), (((ord_less_eq_pname_o B_63) A_88)->((((eq (pname->Prop)) B_63) C_36)->((ord_less_eq_pname_o C_36) A_88)))).
% Axiom fact_345_xt1_I4_J:(forall (C_36:(hoare_1167836817_state->Prop)) (B_63:(hoare_1167836817_state->Prop)) (A_88:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_63) A_88)->((((eq (hoare_1167836817_state->Prop)) B_63) C_36)->((ord_le827224136tate_o C_36) A_88)))).
% Axiom fact_346_ord__le__eq__trans:(forall (C_35:(pname->Prop)) (A_87:(pname->Prop)) (B_62:(pname->Prop)), (((ord_less_eq_pname_o A_87) B_62)->((((eq (pname->Prop)) B_62) C_35)->((ord_less_eq_pname_o A_87) C_35)))).
% Axiom fact_347_ord__le__eq__trans:(forall (C_35:(hoare_1167836817_state->Prop)) (A_87:(hoare_1167836817_state->Prop)) (B_62:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_87) B_62)->((((eq (hoare_1167836817_state->Prop)) B_62) C_35)->((ord_le827224136tate_o A_87) C_35)))).
% Axiom fact_348_xt1_I3_J:(forall (C_34:(pname->Prop)) (A_86:(pname->Prop)) (B_61:(pname->Prop)), ((((eq (pname->Prop)) A_86) B_61)->(((ord_less_eq_pname_o C_34) B_61)->((ord_less_eq_pname_o C_34) A_86)))).
% Axiom fact_349_xt1_I3_J:(forall (C_34:(hoare_1167836817_state->Prop)) (A_86:(hoare_1167836817_state->Prop)) (B_61:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_86) B_61)->(((ord_le827224136tate_o C_34) B_61)->((ord_le827224136tate_o C_34) A_86)))).
% Axiom fact_350_ord__eq__le__trans:(forall (C_33:(pname->Prop)) (A_85:(pname->Prop)) (B_60:(pname->Prop)), ((((eq (pname->Prop)) A_85) B_60)->(((ord_less_eq_pname_o B_60) C_33)->((ord_less_eq_pname_o A_85) C_33)))).
% Axiom fact_351_ord__eq__le__trans:(forall (C_33:(hoare_1167836817_state->Prop)) (A_85:(hoare_1167836817_state->Prop)) (B_60:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_85) B_60)->(((ord_le827224136tate_o B_60) C_33)->((ord_le827224136tate_o A_85) C_33)))).
% Axiom fact_352_order__antisym__conv:(forall (Y_42:(pname->Prop)) (X_77:(pname->Prop)), (((ord_less_eq_pname_o Y_42) X_77)->((iff ((ord_less_eq_pname_o X_77) Y_42)) (((eq (pname->Prop)) X_77) Y_42)))).
% Axiom fact_353_order__antisym__conv:(forall (Y_42:(hoare_1167836817_state->Prop)) (X_77:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_42) X_77)->((iff ((ord_le827224136tate_o X_77) Y_42)) (((eq (hoare_1167836817_state->Prop)) X_77) Y_42)))).
% Axiom fact_354_order__eq__refl:(forall (X_76:(pname->Prop)) (Y_41:(pname->Prop)), ((((eq (pname->Prop)) X_76) Y_41)->((ord_less_eq_pname_o X_76) Y_41))).
% Axiom fact_355_order__eq__refl:(forall (X_76:(hoare_1167836817_state->Prop)) (Y_41:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) X_76) Y_41)->((ord_le827224136tate_o X_76) Y_41))).
% Axiom fact_356_order__eq__iff:(forall (X_75:(pname->Prop)) (Y_40:(pname->Prop)), ((iff (((eq (pname->Prop)) X_75) Y_40)) ((and ((ord_less_eq_pname_o X_75) Y_40)) ((ord_less_eq_pname_o Y_40) X_75)))).
% Axiom fact_357_order__eq__iff:(forall (X_75:(hoare_1167836817_state->Prop)) (Y_40:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) X_75) Y_40)) ((and ((ord_le827224136tate_o X_75) Y_40)) ((ord_le827224136tate_o Y_40) X_75)))).
% Axiom fact_358_option_Oinject:(forall (A_84:com) (A_83:com), ((iff (((eq option_com) (some_com A_84)) (some_com A_83))) (((eq com) A_84) A_83))).
% Axiom fact_359_constant:(forall (G_23:(hoare_1167836817_state->Prop)) (P_27:(state->(state->Prop))) (C_32:com) (Q_19:(state->(state->Prop))) (C_31:Prop), ((C_31->((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state P_27) C_32) Q_19)) bot_bo70021908tate_o)))->((hoare_123228589_state G_23) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S_3:state)=> ((and ((P_27 Z_11) S_3)) C_31))) C_32) Q_19)) bot_bo70021908tate_o)))).
% Axiom fact_360_Body1:(forall (Pn_3:pname) (G_22:(hoare_1167836817_state->Prop)) (P_26:(pname->(state->(state->Prop)))) (Q_18:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_22) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_26 P_24)) (body_1 P_24)) (Q_18 P_24)))) Procs_1))) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_26 P_24)) (the_com (body P_24))) (Q_18 P_24)))) Procs_1))->(((member_pname Pn_3) Procs_1)->((hoare_123228589_state G_22) ((insert2134838167_state (((hoare_908217195_state (P_26 Pn_3)) (body_1 Pn_3)) (Q_18 Pn_3))) bot_bo70021908tate_o))))).
% Axiom fact_361_le__bot:(forall (A_82:(pname->Prop)), (((ord_less_eq_pname_o A_82) bot_bot_pname_o)->(((eq (pname->Prop)) A_82) bot_bot_pname_o))).
% Axiom fact_362_le__bot:(forall (A_82:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_82) bot_bo70021908tate_o)->(((eq (hoare_1167836817_state->Prop)) A_82) bot_bo70021908tate_o))).
% Axiom fact_363_bot__unique:(forall (A_81:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_81) bot_bot_pname_o)) (((eq (pname->Prop)) A_81) bot_bot_pname_o))).
% Axiom fact_364_bot__unique:(forall (A_81:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o A_81) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) A_81) bot_bo70021908tate_o))).
% Axiom fact_365_bot__least:(forall (A_80:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_80)).
% Axiom fact_366_bot__least:(forall (A_80:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o bot_bo70021908tate_o) A_80)).
% Axiom fact_367_le__funE:(forall (X_74:pname) (F_38:(pname->Prop)) (G_21:(pname->Prop)), (((ord_less_eq_pname_o F_38) G_21)->((ord_less_eq_o (F_38 X_74)) (G_21 X_74)))).
% Axiom fact_368_le__funE:(forall (X_74:hoare_1167836817_state) (F_38:(hoare_1167836817_state->Prop)) (G_21:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_38) G_21)->((ord_less_eq_o (F_38 X_74)) (G_21 X_74)))).
% Axiom fact_369_le__funD:(forall (X_73:pname) (F_37:(pname->Prop)) (G_20:(pname->Prop)), (((ord_less_eq_pname_o F_37) G_20)->((ord_less_eq_o (F_37 X_73)) (G_20 X_73)))).
% Axiom fact_370_le__funD:(forall (X_73:hoare_1167836817_state) (F_37:(hoare_1167836817_state->Prop)) (G_20:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o F_37) G_20)->((ord_less_eq_o (F_37 X_73)) (G_20 X_73)))).
% Axiom fact_371_le__fun__def:(forall (F_36:(pname->Prop)) (G_19:(pname->Prop)), ((iff ((ord_less_eq_pname_o F_36) G_19)) (forall (X_5:pname), ((ord_less_eq_o (F_36 X_5)) (G_19 X_5))))).
% Axiom fact_372_le__fun__def:(forall (F_36:(hoare_1167836817_state->Prop)) (G_19:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o F_36) G_19)) (forall (X_5:hoare_1167836817_state), ((ord_less_eq_o (F_36 X_5)) (G_19 X_5))))).
% Axiom fact_373_bot__apply:(forall (X_72:pname), ((iff (bot_bot_pname_o X_72)) bot_bot_o)).
% Axiom fact_374_bot__apply:(forall (X_72:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_72)) bot_bot_o)).
% Axiom fact_375_bot__fun__def:(forall (X_5:pname), ((iff (bot_bot_pname_o X_5)) bot_bot_o)).
% Axiom fact_376_bot__fun__def:(forall (X_5:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_5)) bot_bot_o)).
% Axiom fact_377_BodyN:(forall (P_25:(state->(state->Prop))) (Pn_2:pname) (Q_17:(state->(state->Prop))) (G_18:(hoare_1167836817_state->Prop)), (((hoare_123228589_state ((insert2134838167_state (((hoare_908217195_state P_25) (body_1 Pn_2)) Q_17)) G_18)) ((insert2134838167_state (((hoare_908217195_state P_25) (the_com (body Pn_2))) Q_17)) bot_bo70021908tate_o))->((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state P_25) (body_1 Pn_2)) Q_17)) bot_bo70021908tate_o)))).
% Axiom fact_378_finite__pointwise:(forall (P_23:(pname->(state->(state->Prop)))) (Q_16:(pname->(state->(state->Prop)))) (G_17:(hoare_1167836817_state->Prop)) (P_22:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_15:(pname->(state->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_24:pname), (((hoare_123228589_state G_17) ((insert2134838167_state (((hoare_908217195_state (P_22 P_24)) (C0_1 P_24)) (Q_15 P_24))) bot_bo70021908tate_o))->((hoare_123228589_state G_17) ((insert2134838167_state (((hoare_908217195_state (P_23 P_24)) (C0_1 P_24)) (Q_16 P_24))) bot_bo70021908tate_o))))->(((hoare_123228589_state G_17) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_22 P_24)) (C0_1 P_24)) (Q_15 P_24)))) U_1))->((hoare_123228589_state G_17) ((image_575578384_state (fun (P_24:pname)=> (((hoare_908217195_state (P_23 P_24)) (C0_1 P_24)) (Q_16 P_24)))) U_1)))))).
% Axiom fact_379_escape:(forall (G_16:(hoare_1167836817_state->Prop)) (C_30:com) (Q_14:(state->(state->Prop))) (P_21:(state->(state->Prop))), ((forall (Z_11:state) (S_3:state), (((P_21 Z_11) S_3)->((hoare_123228589_state G_16) ((insert2134838167_state (((hoare_908217195_state (fun (Za:state) (S_4:state)=> (((eq state) S_4) S_3))) C_30) (fun (Z_18:state)=> (Q_14 Z_11)))) bot_bo70021908tate_o))))->((hoare_123228589_state G_16) ((insert2134838167_state (((hoare_908217195_state P_21) C_30) Q_14)) bot_bo70021908tate_o)))).
% Axiom fact_380_Body__sound__lemma:(forall (G_15:(hoare_1167836817_state->Prop)) (P_20:(pname->(state->(state->Prop)))) (Q_13:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_529639851_state ((semila1172322802tate_o G_15) ((image_575578384_state (fun (Pn:pname)=> (((hoare_908217195_state (P_20 Pn)) (body_1 Pn)) (Q_13 Pn)))) Procs))) ((image_575578384_state (fun (Pn:pname)=> (((hoare_908217195_state (P_20 Pn)) (the_com (body Pn))) (Q_13 Pn)))) Procs))->((hoare_529639851_state G_15) ((image_575578384_state (fun (Pn:pname)=> (((hoare_908217195_state (P_20 Pn)) (body_1 Pn)) (Q_13 Pn)))) Procs)))).
% Axiom fact_381_conseq1:(forall (P_19:(state->(state->Prop))) (G_14:(hoare_1167836817_state->Prop)) (P_18:(state->(state->Prop))) (C_29:com) (Q_12:(state->(state->Prop))), (((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state P_18) C_29) Q_12)) bot_bo70021908tate_o))->((forall (Z_11:state) (S_3:state), (((P_19 Z_11) S_3)->((P_18 Z_11) S_3)))->((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state P_19) C_29) Q_12)) bot_bo70021908tate_o))))).
% Axiom fact_382_conseq2:(forall (Q_11:(state->(state->Prop))) (G_13:(hoare_1167836817_state->Prop)) (P_17:(state->(state->Prop))) (C_28:com) (Q_10:(state->(state->Prop))), (((hoare_123228589_state G_13) ((insert2134838167_state (((hoare_908217195_state P_17) C_28) Q_10)) bot_bo70021908tate_o))->((forall (Z_11:state) (S_3:state), (((Q_10 Z_11) S_3)->((Q_11 Z_11) S_3)))->((hoare_123228589_state G_13) ((insert2134838167_state (((hoare_908217195_state P_17) C_28) Q_11)) bot_bo70021908tate_o))))).
% Axiom fact_383_MGF__complete:(forall (P:(state->(state->Prop))) (Q_9:(state->(state->Prop))) (C_21:com), (((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o))->(((hoare_529639851_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P) C_21) Q_9)) bot_bo70021908tate_o))->((hoare_123228589_state bot_bo70021908tate_o) ((insert2134838167_state (((hoare_908217195_state P) C_21) Q_9)) bot_bo70021908tate_o))))).
% Axiom fact_384_sup1E:(forall (A_79:(hoare_1167836817_state->Prop)) (B_59:(hoare_1167836817_state->Prop)) (X_71:hoare_1167836817_state), ((((semila1172322802tate_o A_79) B_59) X_71)->(((A_79 X_71)->False)->(B_59 X_71)))).
% Axiom fact_385_sup1CI:(forall (A_78:(hoare_1167836817_state->Prop)) (B_58:(hoare_1167836817_state->Prop)) (X_70:hoare_1167836817_state), ((((B_58 X_70)->False)->(A_78 X_70))->(((semila1172322802tate_o A_78) B_58) X_70))).
% Axiom fact_386_hoare__sound:(forall (G_12:(hoare_1167836817_state->Prop)) (Ts:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_12) Ts)->((hoare_529639851_state G_12) Ts))).
% Axiom fact_387_bot__empty__eq:(forall (X_5:pname), ((iff (bot_bot_pname_o X_5)) ((member_pname X_5) bot_bot_pname_o))).
% Axiom fact_388_bot__empty__eq:(forall (X_5:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_5)) ((member2058392318_state X_5) bot_bo70021908tate_o))).
% Axiom fact_389_rev__predicate1D:(forall (Q_8:(pname->Prop)) (P_16:(pname->Prop)) (X_69:pname), ((P_16 X_69)->(((ord_less_eq_pname_o P_16) Q_8)->(Q_8 X_69)))).
% Axiom fact_390_rev__predicate1D:(forall (Q_8:(hoare_1167836817_state->Prop)) (P_16:(hoare_1167836817_state->Prop)) (X_69:hoare_1167836817_state), ((P_16 X_69)->(((ord_le827224136tate_o P_16) Q_8)->(Q_8 X_69)))).
% Axiom fact_391_predicate1D:(forall (X_68:pname) (P_15:(pname->Prop)) (Q_7:(pname->Prop)), (((ord_less_eq_pname_o P_15) Q_7)->((P_15 X_68)->(Q_7 X_68)))).
% Axiom fact_392_predicate1D:(forall (X_68:hoare_1167836817_state) (P_15:(hoare_1167836817_state->Prop)) (Q_7:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o P_15) Q_7)->((P_15 X_68)->(Q_7 X_68)))).
% Axiom fact_393_sup1I2:(forall (A_77:(hoare_1167836817_state->Prop)) (B_57:(hoare_1167836817_state->Prop)) (X_67:hoare_1167836817_state), ((B_57 X_67)->(((semila1172322802tate_o A_77) B_57) X_67))).
% Axiom fact_394_sup1I1:(forall (B_56:(hoare_1167836817_state->Prop)) (A_76:(hoare_1167836817_state->Prop)) (X_66:hoare_1167836817_state), ((A_76 X_66)->(((semila1172322802tate_o A_76) B_56) X_66))).
% Axiom fact_395_pred__subset__eq:(forall (R_3:(pname->Prop)) (S_6:(pname->Prop)), ((iff ((ord_less_eq_pname_o (fun (X_5:pname)=> ((member_pname X_5) R_3))) (fun (X_5:pname)=> ((member_pname X_5) S_6)))) ((ord_less_eq_pname_o R_3) S_6))).
% Axiom fact_396_pred__subset__eq:(forall (R_3:(hoare_1167836817_state->Prop)) (S_6:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o (fun (X_5:hoare_1167836817_state)=> ((member2058392318_state X_5) R_3))) (fun (X_5:hoare_1167836817_state)=> ((member2058392318_state X_5) S_6)))) ((ord_le827224136tate_o R_3) S_6))).
% Axiom fact_397_sup__Un__eq:(forall (R_2:(pname->Prop)) (S_5:(pname->Prop)) (X_5:pname), ((iff (((semila1780557381name_o (fun (Y_2:pname)=> ((member_pname Y_2) R_2))) (fun (Y_2:pname)=> ((member_pname Y_2) S_5))) X_5)) ((member_pname X_5) ((semila1780557381name_o R_2) S_5)))).
% Axiom fact_398_sup__Un__eq:(forall (R_2:(hoare_1167836817_state->Prop)) (S_5:(hoare_1167836817_state->Prop)) (X_5:hoare_1167836817_state), ((iff (((semila1172322802tate_o (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) R_2))) (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) S_5))) X_5)) ((member2058392318_state X_5) ((semila1172322802tate_o R_2) S_5)))).
% Axiom fact_399_conseq12:(forall (Q_6:(state->(state->Prop))) (P_14:(state->(state->Prop))) (G_11:(hoare_1167836817_state->Prop)) (P_13:(state->(state->Prop))) (C_27:com) (Q_5:(state->(state->Prop))), (((hoare_123228589_state G_11) ((insert2134838167_state (((hoare_908217195_state P_13) C_27) Q_5)) bot_bo70021908tate_o))->((forall (Z_11:state) (S_3:state), (((P_14 Z_11) S_3)->(forall (S_4:state), ((forall (Z_18:state), (((P_13 Z_18) S_3)->((Q_5 Z_18) S_4)))->((Q_6 Z_11) S_4)))))->((hoare_123228589_state G_11) ((insert2134838167_state (((hoare_908217195_state P_14) C_27) Q_6)) bot_bo70021908tate_o))))).
% Axiom fact_400_le__funI:(forall (F_35:(pname->Prop)) (G_10:(pname->Prop)), ((forall (X_5:pname), ((ord_less_eq_o (F_35 X_5)) (G_10 X_5)))->((ord_less_eq_pname_o F_35) G_10))).
% Axiom fact_401_le__funI:(forall (F_35:(hoare_1167836817_state->Prop)) (G_10:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), ((ord_less_eq_o (F_35 X_5)) (G_10 X_5)))->((ord_le827224136tate_o F_35) G_10))).
% Axiom fact_402_Option_Oset_Osimps_I2_J:(forall (X_65:pname), (((eq (pname->Prop)) (set_pname (some_pname X_65))) ((insert_pname X_65) bot_bot_pname_o))).
% Axiom fact_403_Option_Oset_Osimps_I2_J:(forall (X_65:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (set_Ho2131684873_state (some_H1433514562_state X_65))) ((insert2134838167_state X_65) bot_bo70021908tate_o))).
% Axiom fact_404_Option_Oset_Osimps_I2_J:(forall (X_65:com), (((eq (com->Prop)) (set_com (some_com X_65))) ((insert_com X_65) bot_bot_com_o))).
% Axiom fact_405_elem__set:(forall (X_64:pname) (Xo:option_pname), ((iff ((member_pname X_64) (set_pname Xo))) (((eq option_pname) Xo) (some_pname X_64)))).
% Axiom fact_406_elem__set:(forall (X_64:hoare_1167836817_state) (Xo:option1574264306_state), ((iff ((member2058392318_state X_64) (set_Ho2131684873_state Xo))) (((eq option1574264306_state) Xo) (some_H1433514562_state X_64)))).
% Axiom fact_407_elem__set:(forall (X_64:com) (Xo:option_com), ((iff ((member_com X_64) (set_com Xo))) (((eq option_com) Xo) (some_com X_64)))).
% Axiom fact_408_ospec:(forall (X_63:com) (P_12:(com->Prop)) (A_75:option_com), ((forall (X_5:com), (((member_com X_5) (set_com A_75))->(P_12 X_5)))->((((eq option_com) A_75) (some_com X_63))->(P_12 X_63)))).
% Axiom fact_409_sup__fun__def:(forall (F_34:(hoare_1167836817_state->Prop)) (G_9:(hoare_1167836817_state->Prop)) (X_5:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_34) G_9) X_5)) ((semila10642723_sup_o (F_34 X_5)) (G_9 X_5)))).
% Axiom fact_410_sup__apply:(forall (F_33:(hoare_1167836817_state->Prop)) (G_8:(hoare_1167836817_state->Prop)) (X_62:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_33) G_8) X_62)) ((semila10642723_sup_o (F_33 X_62)) (G_8 X_62)))).
% Axiom fact_411_single__stateE:(hoare_1201148605gleton->(forall (T_1:state), ((forall (S_3:state), (((eq state) S_3) T_1))->False))).
% Axiom fact_412_state__not__singleton__def:((iff hoare_1201148605gleton) ((ex state) (fun (S_3:state)=> ((ex state) (fun (T_1:state)=> (not (((eq state) S_3) T_1))))))).
% Axiom fact_413_sup__assoc:(forall (X_61:(hoare_1167836817_state->Prop)) (Y_39:(hoare_1167836817_state->Prop)) (Z_17:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_61) Y_39)) Z_17)) ((semila1172322802tate_o X_61) ((semila1172322802tate_o Y_39) Z_17)))).
% Axiom fact_414_inf__sup__aci_I6_J:(forall (X_60:(hoare_1167836817_state->Prop)) (Y_38:(hoare_1167836817_state->Prop)) (Z_16:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_60) Y_38)) Z_16)) ((semila1172322802tate_o X_60) ((semila1172322802tate_o Y_38) Z_16)))).
% Axiom fact_415_sup_Oassoc:(forall (A_74:(hoare_1167836817_state->Prop)) (B_55:(hoare_1167836817_state->Prop)) (C_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_74) B_55)) C_26)) ((semila1172322802tate_o A_74) ((semila1172322802tate_o B_55) C_26)))).
% Axiom fact_416_sup__left__commute:(forall (X_59:(hoare_1167836817_state->Prop)) (Y_37:(hoare_1167836817_state->Prop)) (Z_15:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_59) ((semila1172322802tate_o Y_37) Z_15))) ((semila1172322802tate_o Y_37) ((semila1172322802tate_o X_59) Z_15)))).
% Axiom fact_417_inf__sup__aci_I7_J:(forall (X_58:(hoare_1167836817_state->Prop)) (Y_36:(hoare_1167836817_state->Prop)) (Z_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_58) ((semila1172322802tate_o Y_36) Z_14))) ((semila1172322802tate_o Y_36) ((semila1172322802tate_o X_58) Z_14)))).
% Axiom fact_418_sup_Oleft__commute:(forall (B_54:(hoare_1167836817_state->Prop)) (A_73:(hoare_1167836817_state->Prop)) (C_25:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o B_54) ((semila1172322802tate_o A_73) C_25))) ((semila1172322802tate_o A_73) ((semila1172322802tate_o B_54) C_25)))).
% Axiom fact_419_sup__left__idem:(forall (X_57:(hoare_1167836817_state->Prop)) (Y_35:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_57) ((semila1172322802tate_o X_57) Y_35))) ((semila1172322802tate_o X_57) Y_35))).
% Axiom fact_420_inf__sup__aci_I8_J:(forall (X_56:(hoare_1167836817_state->Prop)) (Y_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_56) ((semila1172322802tate_o X_56) Y_34))) ((semila1172322802tate_o X_56) Y_34))).
% Axiom fact_421_sup_Oleft__idem:(forall (A_72:(hoare_1167836817_state->Prop)) (B_53:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_72) ((semila1172322802tate_o A_72) B_53))) ((semila1172322802tate_o A_72) B_53))).
% Axiom fact_422_sup__commute:(forall (X_55:(hoare_1167836817_state->Prop)) (Y_33:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_55) Y_33)) ((semila1172322802tate_o Y_33) X_55))).
% Axiom fact_423_inf__sup__aci_I5_J:(forall (X_54:(hoare_1167836817_state->Prop)) (Y_32:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_54) Y_32)) ((semila1172322802tate_o Y_32) X_54))).
% Axiom fact_424_sup_Ocommute:(forall (A_71:(hoare_1167836817_state->Prop)) (B_52:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_71) B_52)) ((semila1172322802tate_o B_52) A_71))).
% Axiom fact_425_sup__idem:(forall (X_53:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_53) X_53)) X_53)).
% Axiom fact_426_sup_Oidem:(forall (A_70:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_70) A_70)) A_70)).
% Axiom fact_427_le__supE:(forall (A_69:(pname->Prop)) (B_51:(pname->Prop)) (X_52:(pname->Prop)), (((ord_less_eq_pname_o ((semila1780557381name_o A_69) B_51)) X_52)->((((ord_less_eq_pname_o A_69) X_52)->(((ord_less_eq_pname_o B_51) X_52)->False))->False))).
% Axiom fact_428_le__supE:(forall (A_69:(hoare_1167836817_state->Prop)) (B_51:(hoare_1167836817_state->Prop)) (X_52:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o ((semila1172322802tate_o A_69) B_51)) X_52)->((((ord_le827224136tate_o A_69) X_52)->(((ord_le827224136tate_o B_51) X_52)->False))->False))).
% Axiom fact_429_sup__mono:(forall (B_50:(pname->Prop)) (D_3:(pname->Prop)) (A_68:(pname->Prop)) (C_24:(pname->Prop)), (((ord_less_eq_pname_o A_68) C_24)->(((ord_less_eq_pname_o B_50) D_3)->((ord_less_eq_pname_o ((semila1780557381name_o A_68) B_50)) ((semila1780557381name_o C_24) D_3))))).
% Axiom fact_430_sup__mono:(forall (B_50:(hoare_1167836817_state->Prop)) (D_3:(hoare_1167836817_state->Prop)) (A_68:(hoare_1167836817_state->Prop)) (C_24:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_68) C_24)->(((ord_le827224136tate_o B_50) D_3)->((ord_le827224136tate_o ((semila1172322802tate_o A_68) B_50)) ((semila1172322802tate_o C_24) D_3))))).
% Axiom fact_431_sup__least:(forall (Z_13:(pname->Prop)) (Y_31:(pname->Prop)) (X_51:(pname->Prop)), (((ord_less_eq_pname_o Y_31) X_51)->(((ord_less_eq_pname_o Z_13) X_51)->((ord_less_eq_pname_o ((semila1780557381name_o Y_31) Z_13)) X_51)))).
% Axiom fact_432_sup__least:(forall (Z_13:(hoare_1167836817_state->Prop)) (Y_31:(hoare_1167836817_state->Prop)) (X_51:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_31) X_51)->(((ord_le827224136tate_o Z_13) X_51)->((ord_le827224136tate_o ((semila1172322802tate_o Y_31) Z_13)) X_51)))).
% Axiom fact_433_le__supI:(forall (B_49:(pname->Prop)) (A_67:(pname->Prop)) (X_50:(pname->Prop)), (((ord_less_eq_pname_o A_67) X_50)->(((ord_less_eq_pname_o B_49) X_50)->((ord_less_eq_pname_o ((semila1780557381name_o A_67) B_49)) X_50)))).
% Axiom fact_434_le__supI:(forall (B_49:(hoare_1167836817_state->Prop)) (A_67:(hoare_1167836817_state->Prop)) (X_50:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_67) X_50)->(((ord_le827224136tate_o B_49) X_50)->((ord_le827224136tate_o ((semila1172322802tate_o A_67) B_49)) X_50)))).
% Axiom fact_435_sup__absorb1:(forall (Y_30:(pname->Prop)) (X_49:(pname->Prop)), (((ord_less_eq_pname_o Y_30) X_49)->(((eq (pname->Prop)) ((semila1780557381name_o X_49) Y_30)) X_49))).
% Axiom fact_436_sup__absorb1:(forall (Y_30:(hoare_1167836817_state->Prop)) (X_49:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_30) X_49)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_49) Y_30)) X_49))).
% Axiom fact_437_sup__absorb2:(forall (X_48:(pname->Prop)) (Y_29:(pname->Prop)), (((ord_less_eq_pname_o X_48) Y_29)->(((eq (pname->Prop)) ((semila1780557381name_o X_48) Y_29)) Y_29))).
% Axiom fact_438_sup__absorb2:(forall (X_48:(hoare_1167836817_state->Prop)) (Y_29:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_48) Y_29)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_48) Y_29)) Y_29))).
% Axiom fact_439_le__supI2:(forall (A_66:(pname->Prop)) (X_47:(pname->Prop)) (B_48:(pname->Prop)), (((ord_less_eq_pname_o X_47) B_48)->((ord_less_eq_pname_o X_47) ((semila1780557381name_o A_66) B_48)))).
% Axiom fact_440_le__supI2:(forall (A_66:(hoare_1167836817_state->Prop)) (X_47:(hoare_1167836817_state->Prop)) (B_48:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_47) B_48)->((ord_le827224136tate_o X_47) ((semila1172322802tate_o A_66) B_48)))).
% Axiom fact_441_le__supI1:(forall (B_47:(pname->Prop)) (X_46:(pname->Prop)) (A_65:(pname->Prop)), (((ord_less_eq_pname_o X_46) A_65)->((ord_less_eq_pname_o X_46) ((semila1780557381name_o A_65) B_47)))).
% Axiom fact_442_le__supI1:(forall (B_47:(hoare_1167836817_state->Prop)) (X_46:(hoare_1167836817_state->Prop)) (A_65:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_46) A_65)->((ord_le827224136tate_o X_46) ((semila1172322802tate_o A_65) B_47)))).
% Axiom fact_443_le__sup__iff:(forall (X_45:(pname->Prop)) (Y_28:(pname->Prop)) (Z_12:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((semila1780557381name_o X_45) Y_28)) Z_12)) ((and ((ord_less_eq_pname_o X_45) Z_12)) ((ord_less_eq_pname_o Y_28) Z_12)))).
% Axiom fact_444_le__sup__iff:(forall (X_45:(hoare_1167836817_state->Prop)) (Y_28:(hoare_1167836817_state->Prop)) (Z_12:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o ((semila1172322802tate_o X_45) Y_28)) Z_12)) ((and ((ord_le827224136tate_o X_45) Z_12)) ((ord_le827224136tate_o Y_28) Z_12)))).
% Axiom fact_445_le__iff__sup:(forall (X_44:(pname->Prop)) (Y_27:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_44) Y_27)) (((eq (pname->Prop)) ((semila1780557381name_o X_44) Y_27)) Y_27))).
% Axiom fact_446_le__iff__sup:(forall (X_44:(hoare_1167836817_state->Prop)) (Y_27:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_44) Y_27)) (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_44) Y_27)) Y_27))).
% Axiom fact_447_sup__ge2:(forall (Y_26:(pname->Prop)) (X_43:(pname->Prop)), ((ord_less_eq_pname_o Y_26) ((semila1780557381name_o X_43) Y_26))).
% Axiom fact_448_sup__ge2:(forall (Y_26:(hoare_1167836817_state->Prop)) (X_43:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o Y_26) ((semila1172322802tate_o X_43) Y_26))).
% Axiom fact_449_inf__sup__ord_I4_J:(forall (Y_25:(pname->Prop)) (X_42:(pname->Prop)), ((ord_less_eq_pname_o Y_25) ((semila1780557381name_o X_42) Y_25))).
% Axiom fact_450_inf__sup__ord_I4_J:(forall (Y_25:(hoare_1167836817_state->Prop)) (X_42:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o Y_25) ((semila1172322802tate_o X_42) Y_25))).
% Axiom fact_451_sup__ge1:(forall (X_41:(pname->Prop)) (Y_24:(pname->Prop)), ((ord_less_eq_pname_o X_41) ((semila1780557381name_o X_41) Y_24))).
% Axiom fact_452_sup__ge1:(forall (X_41:(hoare_1167836817_state->Prop)) (Y_24:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_41) ((semila1172322802tate_o X_41) Y_24))).
% Axiom fact_453_inf__sup__ord_I3_J:(forall (X_40:(pname->Prop)) (Y_23:(pname->Prop)), ((ord_less_eq_pname_o X_40) ((semila1780557381name_o X_40) Y_23))).
% Axiom fact_454_inf__sup__ord_I3_J:(forall (X_40:(hoare_1167836817_state->Prop)) (Y_23:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o X_40) ((semila1172322802tate_o X_40) Y_23))).
% Axiom fact_455_sup__eq__bot__iff:(forall (X_39:(pname->Prop)) (Y_22:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_39) Y_22)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_39) bot_bot_pname_o)) (((eq (pname->Prop)) Y_22) bot_bot_pname_o)))).
% Axiom fact_456_sup__eq__bot__iff:(forall (X_39:(hoare_1167836817_state->Prop)) (Y_22:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_39) Y_22)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) X_39) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) Y_22) bot_bo70021908tate_o)))).
% Axiom fact_457_sup__bot__right:(forall (X_38:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_38) bot_bot_pname_o)) X_38)).
% Axiom fact_458_sup__bot__right:(forall (X_38:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_38) bot_bo70021908tate_o)) X_38)).
% Axiom fact_459_sup__bot__left:(forall (X_37:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) X_37)) X_37)).
% Axiom fact_460_sup__bot__left:(forall (X_37:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) X_37)) X_37)).
% Axiom fact_461_folding__one__idem_Ounion__idem:(forall (B_46:((pname->Prop)->Prop)) (A_64:((pname->Prop)->Prop)) (F_32:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_31:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_32) F_31)->((finite297249702name_o A_64)->((not (((eq ((pname->Prop)->Prop)) A_64) bot_bot_pname_o_o))->((finite297249702name_o B_46)->((not (((eq ((pname->Prop)->Prop)) B_46) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_31 ((semila181081674me_o_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46))))))))).
% Axiom fact_462_folding__one__idem_Ounion__idem:(forall (B_46:((hoare_1167836817_state->Prop)->Prop)) (A_64:((hoare_1167836817_state->Prop)->Prop)) (F_32:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_31:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_32) F_31)->((finite1380128977tate_o A_64)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_64) bot_bo691907561te_o_o))->((finite1380128977tate_o B_46)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_46) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_31 ((semila866907787te_o_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46))))))))).
% Axiom fact_463_folding__one__idem_Ounion__idem:(forall (B_46:(pname->Prop)) (A_64:(pname->Prop)) (F_32:(pname->(pname->pname))) (F_31:((pname->Prop)->pname)), (((finite89670078_pname F_32) F_31)->((finite_finite_pname A_64)->((not (((eq (pname->Prop)) A_64) bot_bot_pname_o))->((finite_finite_pname B_46)->((not (((eq (pname->Prop)) B_46) bot_bot_pname_o))->(((eq pname) (F_31 ((semila1780557381name_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46))))))))).
% Axiom fact_464_folding__one__idem_Ounion__idem:(forall (B_46:(hoare_1167836817_state->Prop)) (A_64:(hoare_1167836817_state->Prop)) (F_32:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_31:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_32) F_31)->((finite1084549118_state A_64)->((not (((eq (hoare_1167836817_state->Prop)) A_64) bot_bo70021908tate_o))->((finite1084549118_state B_46)->((not (((eq (hoare_1167836817_state->Prop)) B_46) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_31 ((semila1172322802tate_o A_64) B_46))) ((F_32 (F_31 A_64)) (F_31 B_46))))))))).
% Axiom fact_465_folding__one__idem_Osubset__idem:(forall (B_45:((pname->Prop)->Prop)) (A_63:((pname->Prop)->Prop)) (F_30:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_29:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_30) F_29)->((finite297249702name_o A_63)->((not (((eq ((pname->Prop)->Prop)) B_45) bot_bot_pname_o_o))->(((ord_le1205211808me_o_o B_45) A_63)->(((eq (pname->Prop)) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63))))))).
% Axiom fact_466_folding__one__idem_Osubset__idem:(forall (B_45:((hoare_1167836817_state->Prop)->Prop)) (A_63:((hoare_1167836817_state->Prop)->Prop)) (F_30:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_29:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_30) F_29)->((finite1380128977tate_o A_63)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_45) bot_bo691907561te_o_o))->(((ord_le741939125te_o_o B_45) A_63)->(((eq (hoare_1167836817_state->Prop)) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63))))))).
% Axiom fact_467_folding__one__idem_Osubset__idem:(forall (B_45:(pname->Prop)) (A_63:(pname->Prop)) (F_30:(pname->(pname->pname))) (F_29:((pname->Prop)->pname)), (((finite89670078_pname F_30) F_29)->((finite_finite_pname A_63)->((not (((eq (pname->Prop)) B_45) bot_bot_pname_o))->(((ord_less_eq_pname_o B_45) A_63)->(((eq pname) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63))))))).
% Axiom fact_468_folding__one__idem_Osubset__idem:(forall (B_45:(hoare_1167836817_state->Prop)) (A_63:(hoare_1167836817_state->Prop)) (F_30:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_29:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_30) F_29)->((finite1084549118_state A_63)->((not (((eq (hoare_1167836817_state->Prop)) B_45) bot_bo70021908tate_o))->(((ord_le827224136tate_o B_45) A_63)->(((eq hoare_1167836817_state) ((F_30 (F_29 B_45)) (F_29 A_63))) (F_29 A_63))))))).
% Axiom fact_469_hoare__derivs_OSkip:(forall (G_7:(hoare_1167836817_state->Prop)) (P_11:(state->(state->Prop))), ((hoare_123228589_state G_7) ((insert2134838167_state (((hoare_908217195_state P_11) skip) P_11)) bot_bo70021908tate_o))).
% Axiom fact_470_folding__one__idem_Oinsert__idem:(forall (X_36:pname) (A_62:(pname->Prop)) (F_28:(pname->(pname->pname))) (F_27:((pname->Prop)->pname)), (((finite89670078_pname F_28) F_27)->((finite_finite_pname A_62)->((not (((eq (pname->Prop)) A_62) bot_bot_pname_o))->(((eq pname) (F_27 ((insert_pname X_36) A_62))) ((F_28 X_36) (F_27 A_62))))))).
% Axiom fact_471_folding__one__idem_Oinsert__idem:(forall (X_36:hoare_1167836817_state) (A_62:(hoare_1167836817_state->Prop)) (F_28:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_27:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_28) F_27)->((finite1084549118_state A_62)->((not (((eq (hoare_1167836817_state->Prop)) A_62) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_27 ((insert2134838167_state X_36) A_62))) ((F_28 X_36) (F_27 A_62))))))).
% Axiom fact_472_folding__one__idem_Oinsert__idem:(forall (X_36:(pname->Prop)) (A_62:((pname->Prop)->Prop)) (F_28:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_27:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_28) F_27)->((finite297249702name_o A_62)->((not (((eq ((pname->Prop)->Prop)) A_62) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_27 ((insert_pname_o X_36) A_62))) ((F_28 X_36) (F_27 A_62))))))).
% Axiom fact_473_folding__one__idem_Oinsert__idem:(forall (X_36:(hoare_1167836817_state->Prop)) (A_62:((hoare_1167836817_state->Prop)->Prop)) (F_28:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_27:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_28) F_27)->((finite1380128977tate_o A_62)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_62) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_27 ((insert999278200tate_o X_36) A_62))) ((F_28 X_36) (F_27 A_62))))))).
% Axiom fact_474_finite__ne__induct:(forall (P_10:((pname->Prop)->Prop)) (F_25:(pname->Prop)), ((finite_finite_pname F_25)->((not (((eq (pname->Prop)) F_25) bot_bot_pname_o))->((forall (X_5:pname), (P_10 ((insert_pname X_5) bot_bot_pname_o)))->((forall (X_5:pname) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->((not (((eq (pname->Prop)) F_26) bot_bot_pname_o))->((((member_pname X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert_pname X_5) F_26)))))))->(P_10 F_25)))))).
% Axiom fact_475_finite__ne__induct:(forall (P_10:((hoare_1167836817_state->Prop)->Prop)) (F_25:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_25)->((not (((eq (hoare_1167836817_state->Prop)) F_25) bot_bo70021908tate_o))->((forall (X_5:hoare_1167836817_state), (P_10 ((insert2134838167_state X_5) bot_bo70021908tate_o)))->((forall (X_5:hoare_1167836817_state) (F_26:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_26)->((not (((eq (hoare_1167836817_state->Prop)) F_26) bot_bo70021908tate_o))->((((member2058392318_state X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert2134838167_state X_5) F_26)))))))->(P_10 F_25)))))).
% Axiom fact_476_finite__ne__induct:(forall (P_10:(((pname->Prop)->Prop)->Prop)) (F_25:((pname->Prop)->Prop)), ((finite297249702name_o F_25)->((not (((eq ((pname->Prop)->Prop)) F_25) bot_bot_pname_o_o))->((forall (X_5:(pname->Prop)), (P_10 ((insert_pname_o X_5) bot_bot_pname_o_o)))->((forall (X_5:(pname->Prop)) (F_26:((pname->Prop)->Prop)), ((finite297249702name_o F_26)->((not (((eq ((pname->Prop)->Prop)) F_26) bot_bot_pname_o_o))->((((member_pname_o X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert_pname_o X_5) F_26)))))))->(P_10 F_25)))))).
% Axiom fact_477_finite__ne__induct:(forall (P_10:(((hoare_1167836817_state->Prop)->Prop)->Prop)) (F_25:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_25)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) F_25) bot_bo691907561te_o_o))->((forall (X_5:(hoare_1167836817_state->Prop)), (P_10 ((insert999278200tate_o X_5) bot_bo691907561te_o_o)))->((forall (X_5:(hoare_1167836817_state->Prop)) (F_26:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o F_26)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) F_26) bot_bo691907561te_o_o))->((((member864234961tate_o X_5) F_26)->False)->((P_10 F_26)->(P_10 ((insert999278200tate_o X_5) F_26)))))))->(P_10 F_25)))))).
% Axiom fact_478_com_Osimps_I19_J:(forall (Pname:pname), (not (((eq com) (body_1 Pname)) skip))).
% Axiom fact_479_com_Osimps_I18_J:(forall (Pname:pname), (not (((eq com) skip) (body_1 Pname)))).
% Axiom fact_480_WT_OSkip:(wt skip).
% Axiom fact_481_folding__one__idem_Oin__idem:(forall (X_35:pname) (A_61:(pname->Prop)) (F_24:(pname->(pname->pname))) (F_23:((pname->Prop)->pname)), (((finite89670078_pname F_24) F_23)->((finite_finite_pname A_61)->(((member_pname X_35) A_61)->(((eq pname) ((F_24 X_35) (F_23 A_61))) (F_23 A_61)))))).
% Axiom fact_482_folding__one__idem_Oin__idem:(forall (X_35:hoare_1167836817_state) (A_61:(hoare_1167836817_state->Prop)) (F_24:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_23:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_24) F_23)->((finite1084549118_state A_61)->(((member2058392318_state X_35) A_61)->(((eq hoare_1167836817_state) ((F_24 X_35) (F_23 A_61))) (F_23 A_61)))))).
% Axiom fact_483_folding__one__idem_Oin__idem:(forall (X_35:(pname->Prop)) (A_61:((pname->Prop)->Prop)) (F_24:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_23:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_24) F_23)->((finite297249702name_o A_61)->(((member_pname_o X_35) A_61)->(((eq (pname->Prop)) ((F_24 X_35) (F_23 A_61))) (F_23 A_61)))))).
% Axiom fact_484_folding__one__idem_Oin__idem:(forall (X_35:(hoare_1167836817_state->Prop)) (A_61:((hoare_1167836817_state->Prop)->Prop)) (F_24:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_23:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_24) F_23)->((finite1380128977tate_o A_61)->(((member864234961tate_o X_35) A_61)->(((eq (hoare_1167836817_state->Prop)) ((F_24 X_35) (F_23 A_61))) (F_23 A_61)))))).
% Axiom fact_485_folding__one__idem_Ohom__commute:(forall (N_1:((pname->Prop)->Prop)) (H:((pname->Prop)->(pname->Prop))) (F_22:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_21:(((pname->Prop)->Prop)->(pname->Prop))), (((finite697516351name_o F_22) F_21)->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), (((eq (pname->Prop)) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite297249702name_o N_1)->((not (((eq ((pname->Prop)->Prop)) N_1) bot_bot_pname_o_o))->(((eq (pname->Prop)) (H (F_21 N_1))) (F_21 ((image_1085733413name_o H) N_1)))))))).
% Axiom fact_486_folding__one__idem_Ohom__commute:(forall (N_1:((hoare_1167836817_state->Prop)->Prop)) (H:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (F_22:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_21:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite671847800tate_o F_22) F_21)->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite1380128977tate_o N_1)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) N_1) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (H (F_21 N_1))) (F_21 ((image_1488525317tate_o H) N_1)))))))).
% Axiom fact_487_folding__one__idem_Ohom__commute:(forall (N_1:(pname->Prop)) (H:(pname->pname)) (F_22:(pname->(pname->pname))) (F_21:((pname->Prop)->pname)), (((finite89670078_pname F_22) F_21)->((forall (X_5:pname) (Y_2:pname), (((eq pname) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite_finite_pname N_1)->((not (((eq (pname->Prop)) N_1) bot_bot_pname_o))->(((eq pname) (H (F_21 N_1))) (F_21 ((image_pname_pname H) N_1)))))))).
% Axiom fact_488_folding__one__idem_Ohom__commute:(forall (N_1:(hoare_1167836817_state->Prop)) (H:(hoare_1167836817_state->hoare_1167836817_state)) (F_22:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_21:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_22) F_21)->((forall (X_5:hoare_1167836817_state) (Y_2:hoare_1167836817_state), (((eq hoare_1167836817_state) (H ((F_22 X_5) Y_2))) ((F_22 (H X_5)) (H Y_2))))->((finite1084549118_state N_1)->((not (((eq (hoare_1167836817_state->Prop)) N_1) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (H (F_21 N_1))) (F_21 ((image_31595733_state H) N_1)))))))).
% Axiom fact_489_LoopF:(forall (G_6:(hoare_1167836817_state->Prop)) (P_9:(state->(state->Prop))) (B_44:(state->Prop)) (C_23:com), ((hoare_123228589_state G_6) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S_3:state)=> ((and ((P_9 Z_11) S_3)) (not (B_44 S_3))))) ((while B_44) C_23)) P_9)) bot_bo70021908tate_o))).
% Axiom fact_490_Comp:(forall (D_2:com) (R_1:(state->(state->Prop))) (G_5:(hoare_1167836817_state->Prop)) (P_8:(state->(state->Prop))) (C_22:com) (Q_4:(state->(state->Prop))), (((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state P_8) C_22) Q_4)) bot_bo70021908tate_o))->(((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state Q_4) D_2) R_1)) bot_bo70021908tate_o))->((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state P_8) ((semi C_22) D_2)) R_1)) bot_bo70021908tate_o))))).
% Axiom fact_491_the__elem__def:(forall (X_34:(pname->Prop)), (((eq pname) (the_elem_pname X_34)) (the_pname (fun (X_5:pname)=> (((eq (pname->Prop)) X_34) ((insert_pname X_5) bot_bot_pname_o)))))).
% Axiom fact_492_the__elem__def:(forall (X_34:(hoare_1167836817_state->Prop)), (((eq hoare_1167836817_state) (the_el323660082_state X_34)) (the_Ho310147232_state (fun (X_5:hoare_1167836817_state)=> (((eq (hoare_1167836817_state->Prop)) X_34) ((insert2134838167_state X_5) bot_bo70021908tate_o)))))).
% Axiom fact_493_WTs__elim__cases_I6_J:(forall (B_42:(state->Prop)) (C_21:com), ((wt ((while B_42) C_21))->(wt C_21))).
% Axiom fact_494_WTs__elim__cases_I4_J:(forall (C1:com) (C2:com), ((wt ((semi C1) C2))->(((wt C1)->((wt C2)->False))->False))).
% Axiom fact_495_com_Osimps_I46_J:(forall (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com_1:com), (not (((eq com) ((semi Com1_1) Com2_1)) ((while Fun) Com_1)))).
% Axiom fact_496_com_Osimps_I47_J:(forall (Fun:(state->Prop)) (Com_1:com) (Com1_1:com) (Com2_1:com), (not (((eq com) ((while Fun) Com_1)) ((semi Com1_1) Com2_1)))).
% Axiom fact_497_com_Osimps_I3_J:(forall (Com1_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2)))).
% Axiom fact_498_com_Osimps_I5_J:(forall (Fun_1:(state->Prop)) (Com_2:com) (Fun:(state->Prop)) (Com_1:com), ((iff (((eq com) ((while Fun_1) Com_2)) ((while Fun) Com_1))) ((and (((eq (state->Prop)) Fun_1) Fun)) (((eq com) Com_2) Com_1)))).
% Axiom fact_499_com_Osimps_I59_J:(forall (Pname:pname) (Fun_1:(state->Prop)) (Com_2:com), (not (((eq com) (body_1 Pname)) ((while Fun_1) Com_2)))).
% Axiom fact_500_com_Osimps_I58_J:(forall (Fun_1:(state->Prop)) (Com_2:com) (Pname:pname), (not (((eq com) ((while Fun_1) Com_2)) (body_1 Pname)))).
% Axiom fact_501_While:(forall (B_42:(state->Prop)) (C_21:com), ((wt C_21)->(wt ((while B_42) C_21)))).
% Axiom fact_502_com_Osimps_I16_J:(forall (Fun:(state->Prop)) (Com_1:com), (not (((eq com) skip) ((while Fun) Com_1)))).
% Axiom fact_503_com_Osimps_I17_J:(forall (Fun:(state->Prop)) (Com_1:com), (not (((eq com) ((while Fun) Com_1)) skip))).
% Axiom fact_504_com_Osimps_I49_J:(forall (Pname:pname) (Com1_1:com) (Com2_1:com), (not (((eq com) (body_1 Pname)) ((semi Com1_1) Com2_1)))).
% Axiom fact_505_com_Osimps_I48_J:(forall (Com1_1:com) (Com2_1:com) (Pname:pname), (not (((eq com) ((semi Com1_1) Com2_1)) (body_1 Pname)))).
% Axiom fact_506_WT_OSemi:(forall (C1:com) (C0:com), ((wt C0)->((wt C1)->(wt ((semi C0) C1))))).
% Axiom fact_507_com_Osimps_I12_J:(forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2)))).
% Axiom fact_508_com_Osimps_I13_J:(forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip))).
% Axiom fact_509_folding__one_Oinsert:(forall (X_33:pname) (A_60:(pname->Prop)) (F_20:(pname->(pname->pname))) (F_19:((pname->Prop)->pname)), (((finite1282449217_pname F_20) F_19)->((finite_finite_pname A_60)->((((member_pname X_33) A_60)->False)->((not (((eq (pname->Prop)) A_60) bot_bot_pname_o))->(((eq pname) (F_19 ((insert_pname X_33) A_60))) ((F_20 X_33) (F_19 A_60)))))))).
% Axiom fact_510_folding__one_Oinsert:(forall (X_33:hoare_1167836817_state) (A_60:(hoare_1167836817_state->Prop)) (F_20:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_19:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_20) F_19)->((finite1084549118_state A_60)->((((member2058392318_state X_33) A_60)->False)->((not (((eq (hoare_1167836817_state->Prop)) A_60) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_19 ((insert2134838167_state X_33) A_60))) ((F_20 X_33) (F_19 A_60)))))))).
% Axiom fact_511_folding__one_Oinsert:(forall (X_33:(pname->Prop)) (A_60:((pname->Prop)->Prop)) (F_20:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_19:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_20) F_19)->((finite297249702name_o A_60)->((((member_pname_o X_33) A_60)->False)->((not (((eq ((pname->Prop)->Prop)) A_60) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_19 ((insert_pname_o X_33) A_60))) ((F_20 X_33) (F_19 A_60)))))))).
% Axiom fact_512_folding__one_Oinsert:(forall (X_33:(hoare_1167836817_state->Prop)) (A_60:((hoare_1167836817_state->Prop)->Prop)) (F_20:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_19:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_20) F_19)->((finite1380128977tate_o A_60)->((((member864234961tate_o X_33) A_60)->False)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_60) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_19 ((insert999278200tate_o X_33) A_60))) ((F_20 X_33) (F_19 A_60)))))))).
% Axiom fact_513_folding__one_Osingleton:(forall (X_32:pname) (F_18:(pname->(pname->pname))) (F_17:((pname->Prop)->pname)), (((finite1282449217_pname F_18) F_17)->(((eq pname) (F_17 ((insert_pname X_32) bot_bot_pname_o))) X_32))).
% Axiom fact_514_folding__one_Osingleton:(forall (X_32:hoare_1167836817_state) (F_18:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_17:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_18) F_17)->(((eq hoare_1167836817_state) (F_17 ((insert2134838167_state X_32) bot_bo70021908tate_o))) X_32))).
% Axiom fact_515_folding__one_Oclosed:(forall (A_59:(pname->Prop)) (F_16:(pname->(pname->pname))) (F_15:((pname->Prop)->pname)), (((finite1282449217_pname F_16) F_15)->((finite_finite_pname A_59)->((not (((eq (pname->Prop)) A_59) bot_bot_pname_o))->((forall (X_5:pname) (Y_2:pname), ((member_pname ((F_16 X_5) Y_2)) ((insert_pname X_5) ((insert_pname Y_2) bot_bot_pname_o))))->((member_pname (F_15 A_59)) A_59)))))).
% Axiom fact_516_folding__one_Oclosed:(forall (A_59:(hoare_1167836817_state->Prop)) (F_16:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_15:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_16) F_15)->((finite1084549118_state A_59)->((not (((eq (hoare_1167836817_state->Prop)) A_59) bot_bo70021908tate_o))->((forall (X_5:hoare_1167836817_state) (Y_2:hoare_1167836817_state), ((member2058392318_state ((F_16 X_5) Y_2)) ((insert2134838167_state X_5) ((insert2134838167_state Y_2) bot_bo70021908tate_o))))->((member2058392318_state (F_15 A_59)) A_59)))))).
% Axiom fact_517_folding__one_Oclosed:(forall (A_59:((pname->Prop)->Prop)) (F_16:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_15:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_16) F_15)->((finite297249702name_o A_59)->((not (((eq ((pname->Prop)->Prop)) A_59) bot_bot_pname_o_o))->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), ((member_pname_o ((F_16 X_5) Y_2)) ((insert_pname_o X_5) ((insert_pname_o Y_2) bot_bot_pname_o_o))))->((member_pname_o (F_15 A_59)) A_59)))))).
% Axiom fact_518_folding__one_Oclosed:(forall (A_59:((hoare_1167836817_state->Prop)->Prop)) (F_16:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_15:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_16) F_15)->((finite1380128977tate_o A_59)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_59) bot_bo691907561te_o_o))->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), ((member864234961tate_o ((F_16 X_5) Y_2)) ((insert999278200tate_o X_5) ((insert999278200tate_o Y_2) bot_bo691907561te_o_o))))->((member864234961tate_o (F_15 A_59)) A_59)))))).
% Axiom fact_519_triple_Oexhaust:(forall (Y_21:hoare_1167836817_state), ((forall (Fun1:(state->(state->Prop))) (Com:com) (Fun2:(state->(state->Prop))), (not (((eq hoare_1167836817_state) Y_21) (((hoare_908217195_state Fun1) Com) Fun2))))->False)).
% Axiom fact_520_image__cong:(forall (F_14:(pname->hoare_1167836817_state)) (G_4:(pname->hoare_1167836817_state)) (M:(pname->Prop)) (N:(pname->Prop)), ((((eq (pname->Prop)) M) N)->((forall (X_5:pname), (((member_pname X_5) N)->(((eq hoare_1167836817_state) (F_14 X_5)) (G_4 X_5))))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_14) M)) ((image_575578384_state G_4) N))))).
% Axiom fact_521_Collect__mono:(forall (Q_3:(hoare_1167836817_state->Prop)) (P_7:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), ((P_7 X_5)->(Q_3 X_5)))->((ord_le827224136tate_o (collec1027672124_state P_7)) (collec1027672124_state Q_3)))).
% Axiom fact_522_Collect__mono:(forall (Q_3:(pname->Prop)) (P_7:(pname->Prop)), ((forall (X_5:pname), ((P_7 X_5)->(Q_3 X_5)))->((ord_less_eq_pname_o (collect_pname P_7)) (collect_pname Q_3)))).
% Axiom fact_523_Collect__mono:(forall (Q_3:((pname->Prop)->Prop)) (P_7:((pname->Prop)->Prop)), ((forall (X_5:(pname->Prop)), ((P_7 X_5)->(Q_3 X_5)))->((ord_le1205211808me_o_o (collect_pname_o P_7)) (collect_pname_o Q_3)))).
% Axiom fact_524_Collect__mono:(forall (Q_3:((hoare_1167836817_state->Prop)->Prop)) (P_7:((hoare_1167836817_state->Prop)->Prop)), ((forall (X_5:(hoare_1167836817_state->Prop)), ((P_7 X_5)->(Q_3 X_5)))->((ord_le741939125te_o_o (collec269976083tate_o P_7)) (collec269976083tate_o Q_3)))).
% Axiom fact_525_predicate1I:(forall (Q_2:(pname->Prop)) (P_6:(pname->Prop)), ((forall (X_5:pname), ((P_6 X_5)->(Q_2 X_5)))->((ord_less_eq_pname_o P_6) Q_2))).
% Axiom fact_526_predicate1I:(forall (Q_2:(hoare_1167836817_state->Prop)) (P_6:(hoare_1167836817_state->Prop)), ((forall (X_5:hoare_1167836817_state), ((P_6 X_5)->(Q_2 X_5)))->((ord_le827224136tate_o P_6) Q_2))).
% Axiom fact_527_mk__disjoint__insert:(forall (A_58:pname) (A_57:(pname->Prop)), (((member_pname A_58) A_57)->((ex (pname->Prop)) (fun (B_43:(pname->Prop))=> ((and (((eq (pname->Prop)) A_57) ((insert_pname A_58) B_43))) (((member_pname A_58) B_43)->False)))))).
% Axiom fact_528_mk__disjoint__insert:(forall (A_58:hoare_1167836817_state) (A_57:(hoare_1167836817_state->Prop)), (((member2058392318_state A_58) A_57)->((ex (hoare_1167836817_state->Prop)) (fun (B_43:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_57) ((insert2134838167_state A_58) B_43))) (((member2058392318_state A_58) B_43)->False)))))).
% Axiom fact_529_Set_Oset__insert:(forall (X_31:pname) (A_56:(pname->Prop)), (((member_pname X_31) A_56)->((forall (B_43:(pname->Prop)), ((((eq (pname->Prop)) A_56) ((insert_pname X_31) B_43))->((member_pname X_31) B_43)))->False))).
% Axiom fact_530_Set_Oset__insert:(forall (X_31:hoare_1167836817_state) (A_56:(hoare_1167836817_state->Prop)), (((member2058392318_state X_31) A_56)->((forall (B_43:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_56) ((insert2134838167_state X_31) B_43))->((member2058392318_state X_31) B_43)))->False))).
% Axiom fact_531_equals0I:(forall (A_55:(pname->Prop)), ((forall (Y_2:pname), (((member_pname Y_2) A_55)->False))->(((eq (pname->Prop)) A_55) bot_bot_pname_o))).
% Axiom fact_532_equals0I:(forall (A_55:(hoare_1167836817_state->Prop)), ((forall (Y_2:hoare_1167836817_state), (((member2058392318_state Y_2) A_55)->False))->(((eq (hoare_1167836817_state->Prop)) A_55) bot_bo70021908tate_o))).
% Axiom fact_533_MGT__alternD:(forall (G_3:(hoare_1167836817_state->Prop)) (C_21:com), (hoare_1201148605gleton->(((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_21) S0_1) S1)) (((eq state) Z_11) S1))))) C_21) fequal_state)) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o))))).
% Axiom fact_534_MGT__alternI:(forall (G_3:(hoare_1167836817_state->Prop)) (C_21:com), (((hoare_123228589_state G_3) ((insert2134838167_state (hoare_Mirabelle_MGT C_21)) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (fun (Z_11:state) (S0_1:state)=> (forall (S1:state), (((fun (X:Prop) (Y:Prop)=> (X->Y)) (((evalc C_21) S0_1) S1)) (((eq state) Z_11) S1))))) C_21) fequal_state)) bot_bo70021908tate_o)))).
% Axiom fact_535_MGT__def:(forall (C_21:com), (((eq hoare_1167836817_state) (hoare_Mirabelle_MGT C_21)) (((hoare_908217195_state fequal_state) C_21) (evalc C_21)))).
% Axiom fact_536_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_537_evalc__elim__cases_I6_J:(forall (P:pname) (S_2:state) (S1_1:state), ((((evalc (body_1 P)) S_2) S1_1)->(((evalc (the_com (body P))) S_2) S1_1))).
% Axiom fact_538_evalc__elim__cases_I1_J:(forall (S_2:state) (T:state), ((((evalc skip) S_2) T)->(((eq state) T) S_2))).
% Axiom fact_539_evalc_OWhileFalse:(forall (C_21:com) (B_42:(state->Prop)) (S_2:state), (((B_42 S_2)->False)->(((evalc ((while B_42) C_21)) S_2) S_2))).
% Axiom fact_540_evalc_OWhileTrue:(forall (S2:state) (C_21:com) (S1_1:state) (B_42:(state->Prop)) (S0:state), ((B_42 S0)->((((evalc C_21) S0) S1_1)->((((evalc ((while B_42) C_21)) S1_1) S2)->(((evalc ((while B_42) C_21)) S0) S2))))).
% Axiom fact_541_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_542_evalc_OSkip:(forall (S_2:state), (((evalc skip) S_2) S_2)).
% Axiom fact_543_com__det:(forall (U:state) (C_21:com) (S_2:state) (T:state), ((((evalc C_21) S_2) T)->((((evalc C_21) S_2) U)->(((eq state) U) T)))).
% Axiom fact_544_evalc__elim__cases_I4_J:(forall (C1:com) (C2:com) (S_2:state) (T:state), ((((evalc ((semi C1) C2)) S_2) T)->((forall (S1:state), ((((evalc C1) S_2) S1)->((((evalc C2) S1) T)->False)))->False))).
% Axiom fact_545_evalc__WHILE__case:(forall (B_42:(state->Prop)) (C_21:com) (S_2:state) (T:state), ((((evalc ((while B_42) C_21)) S_2) T)->(((((eq state) T) S_2)->(B_42 S_2))->(((B_42 S_2)->(forall (S1:state), ((((evalc C_21) S_2) S1)->((((evalc ((while B_42) C_21)) S1) T)->False))))->False)))).
% Axiom fact_546_xt1_I15_J:(forall (C_20:(pname->Prop)) (A_54:(pname->Prop)) (F_13:((pname->Prop)->(pname->Prop))) (B_41:(pname->Prop)), ((((eq (pname->Prop)) A_54) (F_13 B_41))->(((ord_less_eq_pname_o C_20) B_41)->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), (((ord_less_eq_pname_o Y_2) X_5)->((ord_less_eq_pname_o (F_13 Y_2)) (F_13 X_5))))->((ord_less_eq_pname_o (F_13 C_20)) A_54))))).
% Axiom fact_547_xt1_I15_J:(forall (C_20:(hoare_1167836817_state->Prop)) (A_54:(hoare_1167836817_state->Prop)) (F_13:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (B_41:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_54) (F_13 B_41))->(((ord_le827224136tate_o C_20) B_41)->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_2) X_5)->((ord_le827224136tate_o (F_13 Y_2)) (F_13 X_5))))->((ord_le827224136tate_o (F_13 C_20)) A_54))))).
% Axiom fact_548_xt1_I16_J:(forall (F_12:((pname->Prop)->(pname->Prop))) (C_19:(pname->Prop)) (B_40:(pname->Prop)) (A_53:(pname->Prop)), (((ord_less_eq_pname_o B_40) A_53)->((((eq (pname->Prop)) (F_12 B_40)) C_19)->((forall (X_5:(pname->Prop)) (Y_2:(pname->Prop)), (((ord_less_eq_pname_o Y_2) X_5)->((ord_less_eq_pname_o (F_12 Y_2)) (F_12 X_5))))->((ord_less_eq_pname_o C_19) (F_12 A_53)))))).
% Axiom fact_549_xt1_I16_J:(forall (F_12:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))) (C_19:(hoare_1167836817_state->Prop)) (B_40:(hoare_1167836817_state->Prop)) (A_53:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_40) A_53)->((((eq (hoare_1167836817_state->Prop)) (F_12 B_40)) C_19)->((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_2) X_5)->((ord_le827224136tate_o (F_12 Y_2)) (F_12 X_5))))->((ord_le827224136tate_o C_19) (F_12 A_53)))))).
% Axiom fact_550_folding__one_Ounion__inter:(forall (B_39:((pname->Prop)->Prop)) (A_52:((pname->Prop)->Prop)) (F_11:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_10:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_11) F_10)->((finite297249702name_o A_52)->((finite297249702name_o B_39)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_52) B_39)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((F_11 (F_10 ((semila181081674me_o_o A_52) B_39))) (F_10 ((semila2013987940me_o_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39)))))))).
% Axiom fact_551_folding__one_Ounion__inter:(forall (B_39:((hoare_1167836817_state->Prop)->Prop)) (A_52:((hoare_1167836817_state->Prop)->Prop)) (F_11:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_10:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_11) F_10)->((finite1380128977tate_o A_52)->((finite1380128977tate_o B_39)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_52) B_39)) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) ((F_11 (F_10 ((semila866907787te_o_o A_52) B_39))) (F_10 ((semila1758709489te_o_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39)))))))).
% Axiom fact_552_folding__one_Ounion__inter:(forall (B_39:(pname->Prop)) (A_52:(pname->Prop)) (F_11:(pname->(pname->pname))) (F_10:((pname->Prop)->pname)), (((finite1282449217_pname F_11) F_10)->((finite_finite_pname A_52)->((finite_finite_pname B_39)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_52) B_39)) bot_bot_pname_o))->(((eq pname) ((F_11 (F_10 ((semila1780557381name_o A_52) B_39))) (F_10 ((semila1673364395name_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39)))))))).
% Axiom fact_553_folding__one_Ounion__inter:(forall (B_39:(hoare_1167836817_state->Prop)) (A_52:(hoare_1167836817_state->Prop)) (F_11:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_10:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_11) F_10)->((finite1084549118_state A_52)->((finite1084549118_state B_39)->((not (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_52) B_39)) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) ((F_11 (F_10 ((semila1172322802tate_o A_52) B_39))) (F_10 ((semila179895820tate_o A_52) B_39)))) ((F_11 (F_10 A_52)) (F_10 B_39)))))))).
% Axiom fact_554_folding__one_Ounion__disjoint:(forall (B_38:((pname->Prop)->Prop)) (A_51:((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_51)->((not (((eq ((pname->Prop)->Prop)) A_51) bot_bot_pname_o_o))->((finite297249702name_o B_38)->((not (((eq ((pname->Prop)->Prop)) B_38) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_51) B_38)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_8 ((semila181081674me_o_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38)))))))))).
% Axiom fact_555_folding__one_Ounion__disjoint:(forall (B_38:((hoare_1167836817_state->Prop)->Prop)) (A_51:((hoare_1167836817_state->Prop)->Prop)) (F_9:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_8:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_9) F_8)->((finite1380128977tate_o A_51)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_51) bot_bo691907561te_o_o))->((finite1380128977tate_o B_38)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_38) bot_bo691907561te_o_o))->((((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_51) B_38)) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (F_8 ((semila866907787te_o_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38)))))))))).
% Axiom fact_556_folding__one_Ounion__disjoint:(forall (B_38:(pname->Prop)) (A_51:(pname->Prop)) (F_9:(pname->(pname->pname))) (F_8:((pname->Prop)->pname)), (((finite1282449217_pname F_9) F_8)->((finite_finite_pname A_51)->((not (((eq (pname->Prop)) A_51) bot_bot_pname_o))->((finite_finite_pname B_38)->((not (((eq (pname->Prop)) B_38) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_51) B_38)) bot_bot_pname_o)->(((eq pname) (F_8 ((semila1780557381name_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38)))))))))).
% Axiom fact_557_folding__one_Ounion__disjoint:(forall (B_38:(hoare_1167836817_state->Prop)) (A_51:(hoare_1167836817_state->Prop)) (F_9:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_8:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_9) F_8)->((finite1084549118_state A_51)->((not (((eq (hoare_1167836817_state->Prop)) A_51) bot_bo70021908tate_o))->((finite1084549118_state B_38)->((not (((eq (hoare_1167836817_state->Prop)) B_38) bot_bo70021908tate_o))->((((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_51) B_38)) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_8 ((semila1172322802tate_o A_51) B_38))) ((F_9 (F_8 A_51)) (F_8 B_38)))))))))).
% Axiom fact_558_IntI:(forall (B_37:(pname->Prop)) (C_18:pname) (A_50:(pname->Prop)), (((member_pname C_18) A_50)->(((member_pname C_18) B_37)->((member_pname C_18) ((semila1673364395name_o A_50) B_37))))).
% Axiom fact_559_IntI:(forall (B_37:(hoare_1167836817_state->Prop)) (C_18:hoare_1167836817_state) (A_50:(hoare_1167836817_state->Prop)), (((member2058392318_state C_18) A_50)->(((member2058392318_state C_18) B_37)->((member2058392318_state C_18) ((semila179895820tate_o A_50) B_37))))).
% Axiom fact_560_IntE:(forall (C_17:pname) (A_49:(pname->Prop)) (B_36:(pname->Prop)), (((member_pname C_17) ((semila1673364395name_o A_49) B_36))->((((member_pname C_17) A_49)->(((member_pname C_17) B_36)->False))->False))).
% Axiom fact_561_IntE:(forall (C_17:hoare_1167836817_state) (A_49:(hoare_1167836817_state->Prop)) (B_36:(hoare_1167836817_state->Prop)), (((member2058392318_state C_17) ((semila179895820tate_o A_49) B_36))->((((member2058392318_state C_17) A_49)->(((member2058392318_state C_17) B_36)->False))->False))).
% Axiom fact_562_finite__Int:(forall (G_2:((pname->Prop)->Prop)) (F_7:((pname->Prop)->Prop)), (((or (finite297249702name_o F_7)) (finite297249702name_o G_2))->(finite297249702name_o ((semila2013987940me_o_o F_7) G_2)))).
% Axiom fact_563_finite__Int:(forall (G_2:((hoare_1167836817_state->Prop)->Prop)) (F_7:((hoare_1167836817_state->Prop)->Prop)), (((or (finite1380128977tate_o F_7)) (finite1380128977tate_o G_2))->(finite1380128977tate_o ((semila1758709489te_o_o F_7) G_2)))).
% Axiom fact_564_finite__Int:(forall (G_2:(pname->Prop)) (F_7:(pname->Prop)), (((or (finite_finite_pname F_7)) (finite_finite_pname G_2))->(finite_finite_pname ((semila1673364395name_o F_7) G_2)))).
% Axiom fact_565_finite__Int:(forall (G_2:(hoare_1167836817_state->Prop)) (F_7:(hoare_1167836817_state->Prop)), (((or (finite1084549118_state F_7)) (finite1084549118_state G_2))->(finite1084549118_state ((semila179895820tate_o F_7) G_2)))).
% Axiom fact_566_disjoint__iff__not__equal:(forall (A_48:(pname->Prop)) (B_35:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1673364395name_o A_48) B_35)) bot_bot_pname_o)) (forall (X_5:pname), (((member_pname X_5) A_48)->(forall (Xa:pname), (((member_pname Xa) B_35)->(not (((eq pname) X_5) Xa)))))))).
% Axiom fact_567_disjoint__iff__not__equal:(forall (A_48:(hoare_1167836817_state->Prop)) (B_35:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_48) B_35)) bot_bo70021908tate_o)) (forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_48)->(forall (Xa:hoare_1167836817_state), (((member2058392318_state Xa) B_35)->(not (((eq hoare_1167836817_state) X_5) Xa)))))))).
% Axiom fact_568_Int__empty__right:(forall (A_47:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_47) bot_bot_pname_o)) bot_bot_pname_o)).
% Axiom fact_569_Int__empty__right:(forall (A_47:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_47) bot_bo70021908tate_o)) bot_bo70021908tate_o)).
% Axiom fact_570_Int__empty__left:(forall (B_34:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) B_34)) bot_bot_pname_o)).
% Axiom fact_571_Int__empty__left:(forall (B_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) B_34)) bot_bo70021908tate_o)).
% Axiom fact_572_Int__def:(forall (A_46:(pname->Prop)) (B_33:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_46) B_33)) (collect_pname (fun (X_5:pname)=> ((and ((member_pname X_5) A_46)) ((member_pname X_5) B_33)))))).
% Axiom fact_573_Int__def:(forall (A_46:(hoare_1167836817_state->Prop)) (B_33:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_46) B_33)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and ((member2058392318_state X_5) A_46)) ((member2058392318_state X_5) B_33)))))).
% Axiom fact_574_Int__def:(forall (A_46:((pname->Prop)->Prop)) (B_33:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_46) B_33)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and ((member_pname_o X_5) A_46)) ((member_pname_o X_5) B_33)))))).
% Axiom fact_575_Int__def:(forall (A_46:((hoare_1167836817_state->Prop)->Prop)) (B_33:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_46) B_33)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and ((member864234961tate_o X_5) A_46)) ((member864234961tate_o X_5) B_33)))))).
% Axiom fact_576_Int__iff:(forall (C_16:pname) (A_45:(pname->Prop)) (B_32:(pname->Prop)), ((iff ((member_pname C_16) ((semila1673364395name_o A_45) B_32))) ((and ((member_pname C_16) A_45)) ((member_pname C_16) B_32)))).
% Axiom fact_577_Int__iff:(forall (C_16:hoare_1167836817_state) (A_45:(hoare_1167836817_state->Prop)) (B_32:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_16) ((semila179895820tate_o A_45) B_32))) ((and ((member2058392318_state C_16) A_45)) ((member2058392318_state C_16) B_32)))).
% Axiom fact_578_IntD1:(forall (C_15:pname) (A_44:(pname->Prop)) (B_31:(pname->Prop)), (((member_pname C_15) ((semila1673364395name_o A_44) B_31))->((member_pname C_15) A_44))).
% Axiom fact_579_IntD1:(forall (C_15:hoare_1167836817_state) (A_44:(hoare_1167836817_state->Prop)) (B_31:(hoare_1167836817_state->Prop)), (((member2058392318_state C_15) ((semila179895820tate_o A_44) B_31))->((member2058392318_state C_15) A_44))).
% Axiom fact_580_IntD2:(forall (C_14:pname) (A_43:(pname->Prop)) (B_30:(pname->Prop)), (((member_pname C_14) ((semila1673364395name_o A_43) B_30))->((member_pname C_14) B_30))).
% Axiom fact_581_IntD2:(forall (C_14:hoare_1167836817_state) (A_43:(hoare_1167836817_state->Prop)) (B_30:(hoare_1167836817_state->Prop)), (((member2058392318_state C_14) ((semila179895820tate_o A_43) B_30))->((member2058392318_state C_14) B_30))).
% Axiom fact_582_Collect__conj__eq:(forall (P_5:(hoare_1167836817_state->Prop)) (Q_1:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X_5:hoare_1167836817_state)=> ((and (P_5 X_5)) (Q_1 X_5))))) ((semila179895820tate_o (collec1027672124_state P_5)) (collec1027672124_state Q_1)))).
% Axiom fact_583_Collect__conj__eq:(forall (P_5:(pname->Prop)) (Q_1:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X_5:pname)=> ((and (P_5 X_5)) (Q_1 X_5))))) ((semila1673364395name_o (collect_pname P_5)) (collect_pname Q_1)))).
% Axiom fact_584_Collect__conj__eq:(forall (P_5:((pname->Prop)->Prop)) (Q_1:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_5:(pname->Prop))=> ((and (P_5 X_5)) (Q_1 X_5))))) ((semila2013987940me_o_o (collect_pname_o P_5)) (collect_pname_o Q_1)))).
% Axiom fact_585_Collect__conj__eq:(forall (P_5:((hoare_1167836817_state->Prop)->Prop)) (Q_1:((hoare_1167836817_state->Prop)->Prop)), (((eq ((hoare_1167836817_state->Prop)->Prop)) (collec269976083tate_o (fun (X_5:(hoare_1167836817_state->Prop))=> ((and (P_5 X_5)) (Q_1 X_5))))) ((semila1758709489te_o_o (collec269976083tate_o P_5)) (collec269976083tate_o Q_1)))).
% Axiom fact_586_Int__Collect:(forall (X_30:pname) (A_42:(pname->Prop)) (P_4:(pname->Prop)), ((iff ((member_pname X_30) ((semila1673364395name_o A_42) (collect_pname P_4)))) ((and ((member_pname X_30) A_42)) (P_4 X_30)))).
% Axiom fact_587_Int__Collect:(forall (X_30:hoare_1167836817_state) (A_42:(hoare_1167836817_state->Prop)) (P_4:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state X_30) ((semila179895820tate_o A_42) (collec1027672124_state P_4)))) ((and ((member2058392318_state X_30) A_42)) (P_4 X_30)))).
% Axiom fact_588_Int__Collect:(forall (X_30:(pname->Prop)) (A_42:((pname->Prop)->Prop)) (P_4:((pname->Prop)->Prop)), ((iff ((member_pname_o X_30) ((semila2013987940me_o_o A_42) (collect_pname_o P_4)))) ((and ((member_pname_o X_30) A_42)) (P_4 X_30)))).
% Axiom fact_589_Int__Collect:(forall (X_30:(hoare_1167836817_state->Prop)) (A_42:((hoare_1167836817_state->Prop)->Prop)) (P_4:((hoare_1167836817_state->Prop)->Prop)), ((iff ((member864234961tate_o X_30) ((semila1758709489te_o_o A_42) (collec269976083tate_o P_4)))) ((and ((member864234961tate_o X_30) A_42)) (P_4 X_30)))).
% Axiom fact_590_inf__Int__eq:(forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X_5:pname), ((iff (((semila1673364395name_o (fun (Y_2:pname)=> ((member_pname Y_2) R))) (fun (Y_2:pname)=> ((member_pname Y_2) S_1))) X_5)) ((member_pname X_5) ((semila1673364395name_o R) S_1)))).
% Axiom fact_591_inf__Int__eq:(forall (R:(hoare_1167836817_state->Prop)) (S_1:(hoare_1167836817_state->Prop)) (X_5:hoare_1167836817_state), ((iff (((semila179895820tate_o (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) R))) (fun (Y_2:hoare_1167836817_state)=> ((member2058392318_state Y_2) S_1))) X_5)) ((member2058392318_state X_5) ((semila179895820tate_o R) S_1)))).
% Axiom fact_592_Un__Int__crazy:(forall (A_41:(hoare_1167836817_state->Prop)) (B_29:(hoare_1167836817_state->Prop)) (C_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o ((semila179895820tate_o A_41) B_29)) ((semila179895820tate_o B_29) C_13))) ((semila179895820tate_o C_13) A_41))) ((semila179895820tate_o ((semila179895820tate_o ((semila1172322802tate_o A_41) B_29)) ((semila1172322802tate_o B_29) C_13))) ((semila1172322802tate_o C_13) A_41)))).
% Axiom fact_593_Un__Int__distrib2:(forall (B_28:(hoare_1167836817_state->Prop)) (C_12:(hoare_1167836817_state->Prop)) (A_40:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o B_28) C_12)) A_40)) ((semila179895820tate_o ((semila1172322802tate_o B_28) A_40)) ((semila1172322802tate_o C_12) A_40)))).
% Axiom fact_594_Int__Un__distrib2:(forall (B_27:(hoare_1167836817_state->Prop)) (C_11:(hoare_1167836817_state->Prop)) (A_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o B_27) C_11)) A_39)) ((semila1172322802tate_o ((semila179895820tate_o B_27) A_39)) ((semila179895820tate_o C_11) A_39)))).
% Axiom fact_595_Un__Int__distrib:(forall (A_38:(hoare_1167836817_state->Prop)) (B_26:(hoare_1167836817_state->Prop)) (C_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_38) ((semila179895820tate_o B_26) C_10))) ((semila179895820tate_o ((semila1172322802tate_o A_38) B_26)) ((semila1172322802tate_o A_38) C_10)))).
% Axiom fact_596_Int__Un__distrib:(forall (A_37:(hoare_1167836817_state->Prop)) (B_25:(hoare_1167836817_state->Prop)) (C_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_37) ((semila1172322802tate_o B_25) C_9))) ((semila1172322802tate_o ((semila179895820tate_o A_37) B_25)) ((semila179895820tate_o A_37) C_9)))).
% Axiom fact_597_Int__mono:(forall (B_24:(pname->Prop)) (D_1:(pname->Prop)) (A_36:(pname->Prop)) (C_8:(pname->Prop)), (((ord_less_eq_pname_o A_36) C_8)->(((ord_less_eq_pname_o B_24) D_1)->((ord_less_eq_pname_o ((semila1673364395name_o A_36) B_24)) ((semila1673364395name_o C_8) D_1))))).
% Axiom fact_598_Int__mono:(forall (B_24:(hoare_1167836817_state->Prop)) (D_1:(hoare_1167836817_state->Prop)) (A_36:(hoare_1167836817_state->Prop)) (C_8:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_36) C_8)->(((ord_le827224136tate_o B_24) D_1)->((ord_le827224136tate_o ((semila179895820tate_o A_36) B_24)) ((semila179895820tate_o C_8) D_1))))).
% Axiom fact_599_Int__greatest:(forall (B_23:(pname->Prop)) (C_7:(pname->Prop)) (A_35:(pname->Prop)), (((ord_less_eq_pname_o C_7) A_35)->(((ord_less_eq_pname_o C_7) B_23)->((ord_less_eq_pname_o C_7) ((semila1673364395name_o A_35) B_23))))).
% Axiom fact_600_Int__greatest:(forall (B_23:(hoare_1167836817_state->Prop)) (C_7:(hoare_1167836817_state->Prop)) (A_35:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o C_7) A_35)->(((ord_le827224136tate_o C_7) B_23)->((ord_le827224136tate_o C_7) ((semila179895820tate_o A_35) B_23))))).
% Axiom fact_601_Int__absorb1:(forall (B_22:(pname->Prop)) (A_34:(pname->Prop)), (((ord_less_eq_pname_o B_22) A_34)->(((eq (pname->Prop)) ((semila1673364395name_o A_34) B_22)) B_22))).
% Axiom fact_602_Int__absorb1:(forall (B_22:(hoare_1167836817_state->Prop)) (A_34:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_22) A_34)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_34) B_22)) B_22))).
% Axiom fact_603_Int__absorb2:(forall (A_33:(pname->Prop)) (B_21:(pname->Prop)), (((ord_less_eq_pname_o A_33) B_21)->(((eq (pname->Prop)) ((semila1673364395name_o A_33) B_21)) A_33))).
% Axiom fact_604_Int__absorb2:(forall (A_33:(hoare_1167836817_state->Prop)) (B_21:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_33) B_21)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_33) B_21)) A_33))).
% Axiom fact_605_Int__lower2:(forall (A_32:(pname->Prop)) (B_20:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_32) B_20)) B_20)).
% Axiom fact_606_Int__lower2:(forall (A_32:(hoare_1167836817_state->Prop)) (B_20:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o A_32) B_20)) B_20)).
% Axiom fact_607_Int__lower1:(forall (A_31:(pname->Prop)) (B_19:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o A_31) B_19)) A_31)).
% Axiom fact_608_Int__lower1:(forall (A_31:(hoare_1167836817_state->Prop)) (B_19:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o A_31) B_19)) A_31)).
% Axiom fact_609_Int__insert__left__if1:(forall (B_18:(pname->Prop)) (A_30:pname) (C_6:(pname->Prop)), (((member_pname A_30) C_6)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_30) B_18)) C_6)) ((insert_pname A_30) ((semila1673364395name_o B_18) C_6))))).
% Axiom fact_610_Int__insert__left__if1:(forall (B_18:(hoare_1167836817_state->Prop)) (A_30:hoare_1167836817_state) (C_6:(hoare_1167836817_state->Prop)), (((member2058392318_state A_30) C_6)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_30) B_18)) C_6)) ((insert2134838167_state A_30) ((semila179895820tate_o B_18) C_6))))).
% Axiom fact_611_Int__insert__right__if1:(forall (B_17:(pname->Prop)) (A_29:pname) (A_28:(pname->Prop)), (((member_pname A_29) A_28)->(((eq (pname->Prop)) ((semila1673364395name_o A_28) ((insert_pname A_29) B_17))) ((insert_pname A_29) ((semila1673364395name_o A_28) B_17))))).
% Axiom fact_612_Int__insert__right__if1:(forall (B_17:(hoare_1167836817_state->Prop)) (A_29:hoare_1167836817_state) (A_28:(hoare_1167836817_state->Prop)), (((member2058392318_state A_29) A_28)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_28) ((insert2134838167_state A_29) B_17))) ((insert2134838167_state A_29) ((semila179895820tate_o A_28) B_17))))).
% Axiom fact_613_Int__insert__left__if0:(forall (B_16:(pname->Prop)) (A_27:pname) (C_5:(pname->Prop)), ((((member_pname A_27) C_5)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_27) B_16)) C_5)) ((semila1673364395name_o B_16) C_5)))).
% Axiom fact_614_Int__insert__left__if0:(forall (B_16:(hoare_1167836817_state->Prop)) (A_27:hoare_1167836817_state) (C_5:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_27) C_5)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_27) B_16)) C_5)) ((semila179895820tate_o B_16) C_5)))).
% Axiom fact_615_Int__insert__right__if0:(forall (B_15:(pname->Prop)) (A_26:pname) (A_25:(pname->Prop)), ((((member_pname A_26) A_25)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_25) ((insert_pname A_26) B_15))) ((semila1673364395name_o A_25) B_15)))).
% Axiom fact_616_Int__insert__right__if0:(forall (B_15:(hoare_1167836817_state->Prop)) (A_26:hoare_1167836817_state) (A_25:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_26) A_25)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_25) ((insert2134838167_state A_26) B_15))) ((semila179895820tate_o A_25) B_15)))).
% Axiom fact_617_insert__inter__insert:(forall (A_24:pname) (A_23:(pname->Prop)) (B_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_24) A_23)) ((insert_pname A_24) B_14))) ((insert_pname A_24) ((semila1673364395name_o A_23) B_14)))).
% Axiom fact_618_insert__inter__insert:(forall (A_24:hoare_1167836817_state) (A_23:(hoare_1167836817_state->Prop)) (B_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_24) A_23)) ((insert2134838167_state A_24) B_14))) ((insert2134838167_state A_24) ((semila179895820tate_o A_23) B_14)))).
% Axiom fact_619_Int__insert__left:(forall (B_13:(pname->Prop)) (A_22:pname) (C_4:(pname->Prop)), ((and (((member_pname A_22) C_4)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_22) B_13)) C_4)) ((insert_pname A_22) ((semila1673364395name_o B_13) C_4))))) ((((member_pname A_22) C_4)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_22) B_13)) C_4)) ((semila1673364395name_o B_13) C_4))))).
% Axiom fact_620_Int__insert__left:(forall (B_13:(hoare_1167836817_state->Prop)) (A_22:hoare_1167836817_state) (C_4:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_22) C_4)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_22) B_13)) C_4)) ((insert2134838167_state A_22) ((semila179895820tate_o B_13) C_4))))) ((((member2058392318_state A_22) C_4)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_22) B_13)) C_4)) ((semila179895820tate_o B_13) C_4))))).
% Axiom fact_621_Int__insert__right:(forall (B_12:(pname->Prop)) (A_21:pname) (A_20:(pname->Prop)), ((and (((member_pname A_21) A_20)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) ((insert_pname A_21) B_12))) ((insert_pname A_21) ((semila1673364395name_o A_20) B_12))))) ((((member_pname A_21) A_20)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) ((insert_pname A_21) B_12))) ((semila1673364395name_o A_20) B_12))))).
% Axiom fact_622_Int__insert__right:(forall (B_12:(hoare_1167836817_state->Prop)) (A_21:hoare_1167836817_state) (A_20:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_21) A_20)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_20) ((insert2134838167_state A_21) B_12))) ((insert2134838167_state A_21) ((semila179895820tate_o A_20) B_12))))) ((((member2058392318_state A_21) A_20)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_20) ((insert2134838167_state A_21) B_12))) ((semila179895820tate_o A_20) B_12))))).
% Axiom fact_623_inf__sup__ord_I1_J:(forall (X_29:(pname->Prop)) (Y_20:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_29) Y_20)) X_29)).
% Axiom fact_624_inf__sup__ord_I1_J:(forall (X_29:(hoare_1167836817_state->Prop)) (Y_20:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_29) Y_20)) X_29)).
% Axiom fact_625_inf__le1:(forall (X_28:(pname->Prop)) (Y_19:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_28) Y_19)) X_28)).
% Axiom fact_626_inf__le1:(forall (X_28:(hoare_1167836817_state->Prop)) (Y_19:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_28) Y_19)) X_28)).
% Axiom fact_627_inf__sup__ord_I2_J:(forall (X_27:(pname->Prop)) (Y_18:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_27) Y_18)) Y_18)).
% Axiom fact_628_inf__sup__ord_I2_J:(forall (X_27:(hoare_1167836817_state->Prop)) (Y_18:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_27) Y_18)) Y_18)).
% Axiom fact_629_inf__le2:(forall (X_26:(pname->Prop)) (Y_17:(pname->Prop)), ((ord_less_eq_pname_o ((semila1673364395name_o X_26) Y_17)) Y_17)).
% Axiom fact_630_inf__le2:(forall (X_26:(hoare_1167836817_state->Prop)) (Y_17:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila179895820tate_o X_26) Y_17)) Y_17)).
% Axiom fact_631_le__iff__inf:(forall (X_25:(pname->Prop)) (Y_16:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_25) Y_16)) (((eq (pname->Prop)) ((semila1673364395name_o X_25) Y_16)) X_25))).
% Axiom fact_632_le__iff__inf:(forall (X_25:(hoare_1167836817_state->Prop)) (Y_16:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_25) Y_16)) (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_25) Y_16)) X_25))).
% Axiom fact_633_le__inf__iff:(forall (X_24:(pname->Prop)) (Y_15:(pname->Prop)) (Z_10:(pname->Prop)), ((iff ((ord_less_eq_pname_o X_24) ((semila1673364395name_o Y_15) Z_10))) ((and ((ord_less_eq_pname_o X_24) Y_15)) ((ord_less_eq_pname_o X_24) Z_10)))).
% Axiom fact_634_le__inf__iff:(forall (X_24:(hoare_1167836817_state->Prop)) (Y_15:(hoare_1167836817_state->Prop)) (Z_10:(hoare_1167836817_state->Prop)), ((iff ((ord_le827224136tate_o X_24) ((semila179895820tate_o Y_15) Z_10))) ((and ((ord_le827224136tate_o X_24) Y_15)) ((ord_le827224136tate_o X_24) Z_10)))).
% Axiom fact_635_le__infI1:(forall (B_11:(pname->Prop)) (A_19:(pname->Prop)) (X_23:(pname->Prop)), (((ord_less_eq_pname_o A_19) X_23)->((ord_less_eq_pname_o ((semila1673364395name_o A_19) B_11)) X_23))).
% Axiom fact_636_le__infI1:(forall (B_11:(hoare_1167836817_state->Prop)) (A_19:(hoare_1167836817_state->Prop)) (X_23:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_19) X_23)->((ord_le827224136tate_o ((semila179895820tate_o A_19) B_11)) X_23))).
% Axiom fact_637_le__infI2:(forall (A_18:(pname->Prop)) (B_10:(pname->Prop)) (X_22:(pname->Prop)), (((ord_less_eq_pname_o B_10) X_22)->((ord_less_eq_pname_o ((semila1673364395name_o A_18) B_10)) X_22))).
% Axiom fact_638_le__infI2:(forall (A_18:(hoare_1167836817_state->Prop)) (B_10:(hoare_1167836817_state->Prop)) (X_22:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o B_10) X_22)->((ord_le827224136tate_o ((semila179895820tate_o A_18) B_10)) X_22))).
% Axiom fact_639_inf__absorb1:(forall (X_21:(pname->Prop)) (Y_14:(pname->Prop)), (((ord_less_eq_pname_o X_21) Y_14)->(((eq (pname->Prop)) ((semila1673364395name_o X_21) Y_14)) X_21))).
% Axiom fact_640_inf__absorb1:(forall (X_21:(hoare_1167836817_state->Prop)) (Y_14:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_21) Y_14)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_21) Y_14)) X_21))).
% Axiom fact_641_inf__absorb2:(forall (Y_13:(pname->Prop)) (X_20:(pname->Prop)), (((ord_less_eq_pname_o Y_13) X_20)->(((eq (pname->Prop)) ((semila1673364395name_o X_20) Y_13)) Y_13))).
% Axiom fact_642_inf__absorb2:(forall (Y_13:(hoare_1167836817_state->Prop)) (X_20:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o Y_13) X_20)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_20) Y_13)) Y_13))).
% Axiom fact_643_le__infI:(forall (B_9:(pname->Prop)) (X_19:(pname->Prop)) (A_17:(pname->Prop)), (((ord_less_eq_pname_o X_19) A_17)->(((ord_less_eq_pname_o X_19) B_9)->((ord_less_eq_pname_o X_19) ((semila1673364395name_o A_17) B_9))))).
% Axiom fact_644_le__infI:(forall (B_9:(hoare_1167836817_state->Prop)) (X_19:(hoare_1167836817_state->Prop)) (A_17:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_19) A_17)->(((ord_le827224136tate_o X_19) B_9)->((ord_le827224136tate_o X_19) ((semila179895820tate_o A_17) B_9))))).
% Axiom fact_645_inf__greatest:(forall (Z_9:(pname->Prop)) (X_18:(pname->Prop)) (Y_12:(pname->Prop)), (((ord_less_eq_pname_o X_18) Y_12)->(((ord_less_eq_pname_o X_18) Z_9)->((ord_less_eq_pname_o X_18) ((semila1673364395name_o Y_12) Z_9))))).
% Axiom fact_646_inf__greatest:(forall (Z_9:(hoare_1167836817_state->Prop)) (X_18:(hoare_1167836817_state->Prop)) (Y_12:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_18) Y_12)->(((ord_le827224136tate_o X_18) Z_9)->((ord_le827224136tate_o X_18) ((semila179895820tate_o Y_12) Z_9))))).
% Axiom fact_647_inf__mono:(forall (B_8:(pname->Prop)) (D:(pname->Prop)) (A_16:(pname->Prop)) (C_3:(pname->Prop)), (((ord_less_eq_pname_o A_16) C_3)->(((ord_less_eq_pname_o B_8) D)->((ord_less_eq_pname_o ((semila1673364395name_o A_16) B_8)) ((semila1673364395name_o C_3) D))))).
% Axiom fact_648_inf__mono:(forall (B_8:(hoare_1167836817_state->Prop)) (D:(hoare_1167836817_state->Prop)) (A_16:(hoare_1167836817_state->Prop)) (C_3:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_16) C_3)->(((ord_le827224136tate_o B_8) D)->((ord_le827224136tate_o ((semila179895820tate_o A_16) B_8)) ((semila179895820tate_o C_3) D))))).
% Axiom fact_649_le__infE:(forall (X_17:(pname->Prop)) (A_15:(pname->Prop)) (B_7:(pname->Prop)), (((ord_less_eq_pname_o X_17) ((semila1673364395name_o A_15) B_7))->((((ord_less_eq_pname_o X_17) A_15)->(((ord_less_eq_pname_o X_17) B_7)->False))->False))).
% Axiom fact_650_le__infE:(forall (X_17:(hoare_1167836817_state->Prop)) (A_15:(hoare_1167836817_state->Prop)) (B_7:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o X_17) ((semila179895820tate_o A_15) B_7))->((((ord_le827224136tate_o X_17) A_15)->(((ord_le827224136tate_o X_17) B_7)->False))->False))).
% Axiom fact_651_inf__sup__absorb:(forall (X_16:(hoare_1167836817_state->Prop)) (Y_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_16) ((semila1172322802tate_o X_16) Y_11))) X_16)).
% Axiom fact_652_sup__inf__absorb:(forall (X_15:(hoare_1167836817_state->Prop)) (Y_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_15) ((semila179895820tate_o X_15) Y_10))) X_15)).
% Axiom fact_653_inf__sup__distrib1:(forall (X_14:(hoare_1167836817_state->Prop)) (Y_9:(hoare_1167836817_state->Prop)) (Z_8:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_14) ((semila1172322802tate_o Y_9) Z_8))) ((semila1172322802tate_o ((semila179895820tate_o X_14) Y_9)) ((semila179895820tate_o X_14) Z_8)))).
% Axiom fact_654_sup__inf__distrib1:(forall (X_13:(hoare_1167836817_state->Prop)) (Y_8:(hoare_1167836817_state->Prop)) (Z_7:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_13) ((semila179895820tate_o Y_8) Z_7))) ((semila179895820tate_o ((semila1172322802tate_o X_13) Y_8)) ((semila1172322802tate_o X_13) Z_7)))).
% Axiom fact_655_inf__sup__distrib2:(forall (Y_7:(hoare_1167836817_state->Prop)) (Z_6:(hoare_1167836817_state->Prop)) (X_12:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o Y_7) Z_6)) X_12)) ((semila1172322802tate_o ((semila179895820tate_o Y_7) X_12)) ((semila179895820tate_o Z_6) X_12)))).
% Axiom fact_656_sup__inf__distrib2:(forall (Y_6:(hoare_1167836817_state->Prop)) (Z_5:(hoare_1167836817_state->Prop)) (X_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o Y_6) Z_5)) X_11)) ((semila179895820tate_o ((semila1172322802tate_o Y_6) X_11)) ((semila1172322802tate_o Z_5) X_11)))).
% Axiom fact_657_inf__bot__right:(forall (X_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_10) bot_bot_pname_o)) bot_bot_pname_o)).
% Axiom fact_658_inf__bot__right:(forall (X_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_10) bot_bo70021908tate_o)) bot_bo70021908tate_o)).
% Axiom fact_659_inf__bot__left:(forall (X_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) X_9)) bot_bot_pname_o)).
% Axiom fact_660_inf__bot__left:(forall (X_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) X_9)) bot_bo70021908tate_o)).
% Axiom fact_661_distrib__sup__le:(forall (X_8:(pname->Prop)) (Y_5:(pname->Prop)) (Z_4:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o X_8) ((semila1673364395name_o Y_5) Z_4))) ((semila1673364395name_o ((semila1780557381name_o X_8) Y_5)) ((semila1780557381name_o X_8) Z_4)))).
% Axiom fact_662_distrib__sup__le:(forall (X_8:(hoare_1167836817_state->Prop)) (Y_5:(hoare_1167836817_state->Prop)) (Z_4:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila1172322802tate_o X_8) ((semila179895820tate_o Y_5) Z_4))) ((semila179895820tate_o ((semila1172322802tate_o X_8) Y_5)) ((semila1172322802tate_o X_8) Z_4)))).
% Axiom fact_663_distrib__inf__le:(forall (X_7:(pname->Prop)) (Y_4:(pname->Prop)) (Z_3:(pname->Prop)), ((ord_less_eq_pname_o ((semila1780557381name_o ((semila1673364395name_o X_7) Y_4)) ((semila1673364395name_o X_7) Z_3))) ((semila1673364395name_o X_7) ((semila1780557381name_o Y_4) Z_3)))).
% Axiom fact_664_distrib__inf__le:(forall (X_7:(hoare_1167836817_state->Prop)) (Y_4:(hoare_1167836817_state->Prop)) (Z_3:(hoare_1167836817_state->Prop)), ((ord_le827224136tate_o ((semila1172322802tate_o ((semila179895820tate_o X_7) Y_4)) ((semila179895820tate_o X_7) Z_3))) ((semila179895820tate_o X_7) ((semila1172322802tate_o Y_4) Z_3)))).
% Axiom fact_665_image__Int__subset:(forall (F_6:(pname->hoare_1167836817_state)) (A_14:(pname->Prop)) (B_6:(pname->Prop)), ((ord_le827224136tate_o ((image_575578384_state F_6) ((semila1673364395name_o A_14) B_6))) ((semila179895820tate_o ((image_575578384_state F_6) A_14)) ((image_575578384_state F_6) B_6)))).
% Axiom fact_666_Un__Int__assoc__eq:(forall (A_13:(pname->Prop)) (B_5:(pname->Prop)) (C_2:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o A_13) B_5)) C_2)) ((semila1673364395name_o A_13) ((semila1780557381name_o B_5) C_2)))) ((ord_less_eq_pname_o C_2) A_13))).
% Axiom fact_667_Un__Int__assoc__eq:(forall (A_13:(hoare_1167836817_state->Prop)) (B_5:(hoare_1167836817_state->Prop)) (C_2:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o A_13) B_5)) C_2)) ((semila179895820tate_o A_13) ((semila1172322802tate_o B_5) C_2)))) ((ord_le827224136tate_o C_2) A_13))).
% Axiom fact_668_if__image__distrib:(forall (P_3:(pname->Prop)) (F_5:(pname->hoare_1167836817_state)) (G_1:(pname->hoare_1167836817_state)) (S:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X_5:pname)=> (((if_Hoa833675553_state (P_3 X_5)) (F_5 X_5)) (G_1 X_5)))) S)) ((semila1172322802tate_o ((image_575578384_state F_5) ((semila1673364395name_o S) (collect_pname P_3)))) ((image_575578384_state G_1) ((semila1673364395name_o S) (collect_pname (fun (X_5:pname)=> (not (P_3 X_5))))))))).
% Axiom fact_669_dom__if:(forall (P_2:(pname->Prop)) (F_4:(pname->option_com)) (G:(pname->option_com)), (((eq (pname->Prop)) (dom_pname_com (fun (X_5:pname)=> (((if_option_com (P_2 X_5)) (F_4 X_5)) (G X_5))))) ((semila1780557381name_o ((semila1673364395name_o (dom_pname_com F_4)) (collect_pname P_2))) ((semila1673364395name_o (dom_pname_com G)) (collect_pname (fun (X_5:pname)=> (not (P_2 X_5)))))))).
% Axiom fact_670_Int__Collect__mono:(forall (Q:(pname->Prop)) (P_1:(pname->Prop)) (A_12:(pname->Prop)) (B_4:(pname->Prop)), (((ord_less_eq_pname_o A_12) B_4)->((forall (X_5:pname), (((member_pname X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_less_eq_pname_o ((semila1673364395name_o A_12) (collect_pname P_1))) ((semila1673364395name_o B_4) (collect_pname Q)))))).
% Axiom fact_671_Int__Collect__mono:(forall (Q:(hoare_1167836817_state->Prop)) (P_1:(hoare_1167836817_state->Prop)) (A_12:(hoare_1167836817_state->Prop)) (B_4:(hoare_1167836817_state->Prop)), (((ord_le827224136tate_o A_12) B_4)->((forall (X_5:hoare_1167836817_state), (((member2058392318_state X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_le827224136tate_o ((semila179895820tate_o A_12) (collec1027672124_state P_1))) ((semila179895820tate_o B_4) (collec1027672124_state Q)))))).
% Axiom fact_672_Int__Collect__mono:(forall (Q:((pname->Prop)->Prop)) (P_1:((pname->Prop)->Prop)) (A_12:((pname->Prop)->Prop)) (B_4:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_12) B_4)->((forall (X_5:(pname->Prop)), (((member_pname_o X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_le1205211808me_o_o ((semila2013987940me_o_o A_12) (collect_pname_o P_1))) ((semila2013987940me_o_o B_4) (collect_pname_o Q)))))).
% Axiom fact_673_Int__Collect__mono:(forall (Q:((hoare_1167836817_state->Prop)->Prop)) (P_1:((hoare_1167836817_state->Prop)->Prop)) (A_12:((hoare_1167836817_state->Prop)->Prop)) (B_4:((hoare_1167836817_state->Prop)->Prop)), (((ord_le741939125te_o_o A_12) B_4)->((forall (X_5:(hoare_1167836817_state->Prop)), (((member864234961tate_o X_5) A_12)->((P_1 X_5)->(Q X_5))))->((ord_le741939125te_o_o ((semila1758709489te_o_o A_12) (collec269976083tate_o P_1))) ((semila1758709489te_o_o B_4) (collec269976083tate_o Q)))))).
% Axiom fact_674_distrib__imp1:(forall (X_6:(hoare_1167836817_state->Prop)) (Y_3:(hoare_1167836817_state->Prop)) (Z_2:(hoare_1167836817_state->Prop)), ((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_1:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_5) ((semila1172322802tate_o Y_2) Z_1))) ((semila1172322802tate_o ((semila179895820tate_o X_5) Y_2)) ((semila179895820tate_o X_5) Z_1))))->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_6) ((semila179895820tate_o Y_3) Z_2))) ((semila179895820tate_o ((semila1172322802tate_o X_6) Y_3)) ((semila1172322802tate_o X_6) Z_2))))).
% Axiom fact_675_distrib__imp2:(forall (X_4:(hoare_1167836817_state->Prop)) (Y_1:(hoare_1167836817_state->Prop)) (Z:(hoare_1167836817_state->Prop)), ((forall (X_5:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_1:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_5) ((semila179895820tate_o Y_2) Z_1))) ((semila179895820tate_o ((semila1172322802tate_o X_5) Y_2)) ((semila1172322802tate_o X_5) Z_1))))->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_4) ((semila1172322802tate_o Y_1) Z))) ((semila1172322802tate_o ((semila179895820tate_o X_4) Y_1)) ((semila179895820tate_o X_4) Z))))).
% Axiom fact_676_folding__one_Oremove:(forall (X_3:pname) (A_11:(pname->Prop)) (F_3:(pname->(pname->pname))) (F_2:((pname->Prop)->pname)), (((finite1282449217_pname F_3) F_2)->((finite_finite_pname A_11)->(((member_pname X_3) A_11)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_11) ((insert_pname X_3) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_2 A_11)) X_3))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_11) ((insert_pname X_3) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_minus_pname_o A_11) ((insert_pname X_3) bot_bot_pname_o))))))))))).
% Axiom fact_677_folding__one_Oremove:(forall (X_3:hoare_1167836817_state) (A_11:(hoare_1167836817_state->Prop)) (F_3:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_2:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_3) F_2)->((finite1084549118_state A_11)->(((member2058392318_state X_3) A_11)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_11) ((insert2134838167_state X_3) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F_2 A_11)) X_3))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_11) ((insert2134838167_state X_3) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_2107060239tate_o A_11) ((insert2134838167_state X_3) bot_bo70021908tate_o))))))))))).
% Axiom fact_678_folding__one_Oremove:(forall (X_3:(pname->Prop)) (A_11:((pname->Prop)->Prop)) (F_3:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F_2:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_3) F_2)->((finite297249702name_o A_11)->(((member_pname_o X_3) A_11)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_11) ((insert_pname_o X_3) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F_2 A_11)) X_3))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_11) ((insert_pname_o X_3) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_1480864103me_o_o A_11) ((insert_pname_o X_3) bot_bot_pname_o_o))))))))))).
% Axiom fact_679_folding__one_Oremove:(forall (X_3:(hoare_1167836817_state->Prop)) (A_11:((hoare_1167836817_state->Prop)->Prop)) (F_3:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F_2:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_3) F_2)->((finite1380128977tate_o A_11)->(((member864234961tate_o X_3) A_11)->((and ((((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_11) ((insert999278200tate_o X_3) bot_bo691907561te_o_o))) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (F_2 A_11)) X_3))) ((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_11) ((insert999278200tate_o X_3) bot_bo691907561te_o_o))) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F_2 A_11)) ((F_3 X_3) (F_2 ((minus_1708687022te_o_o A_11) ((insert999278200tate_o X_3) bot_bo691907561te_o_o))))))))))).
% Axiom fact_680_folding__one_Oinsert__remove:(forall (X_2:pname) (A_10:(pname->Prop)) (F_1:(pname->(pname->pname))) (F:((pname->Prop)->pname)), (((finite1282449217_pname F_1) F)->((finite_finite_pname A_10)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_10) ((insert_pname X_2) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F ((insert_pname X_2) A_10))) X_2))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_10) ((insert_pname X_2) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F ((insert_pname X_2) A_10))) ((F_1 X_2) (F ((minus_minus_pname_o A_10) ((insert_pname X_2) bot_bot_pname_o)))))))))).
% Axiom fact_681_folding__one_Oinsert__remove:(forall (X_2:hoare_1167836817_state) (A_10:(hoare_1167836817_state->Prop)) (F_1:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_1) F)->((finite1084549118_state A_10)->((and ((((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_10) ((insert2134838167_state X_2) bot_bo70021908tate_o))) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F ((insert2134838167_state X_2) A_10))) X_2))) ((not (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_10) ((insert2134838167_state X_2) bot_bo70021908tate_o))) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F ((insert2134838167_state X_2) A_10))) ((F_1 X_2) (F ((minus_2107060239tate_o A_10) ((insert2134838167_state X_2) bot_bo70021908tate_o)))))))))).
% Axiom fact_682_folding__one_Oinsert__remove:(forall (X_2:(pname->Prop)) (A_10:((pname->Prop)->Prop)) (F_1:((pname->Prop)->((pname->Prop)->(pname->Prop)))) (F:(((pname->Prop)->Prop)->(pname->Prop))), (((finite349908348name_o F_1) F)->((finite297249702name_o A_10)->((and ((((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_10) ((insert_pname_o X_2) bot_bot_pname_o_o))) bot_bot_pname_o_o)->(((eq (pname->Prop)) (F ((insert_pname_o X_2) A_10))) X_2))) ((not (((eq ((pname->Prop)->Prop)) ((minus_1480864103me_o_o A_10) ((insert_pname_o X_2) bot_bot_pname_o_o))) bot_bot_pname_o_o))->(((eq (pname->Prop)) (F ((insert_pname_o X_2) A_10))) ((F_1 X_2) (F ((minus_1480864103me_o_o A_10) ((insert_pname_o X_2) bot_bot_pname_o_o)))))))))).
% Axiom fact_683_folding__one_Oinsert__remove:(forall (X_2:(hoare_1167836817_state->Prop)) (A_10:((hoare_1167836817_state->Prop)->Prop)) (F_1:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))) (F:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))), (((finite979047547tate_o F_1) F)->((finite1380128977tate_o A_10)->((and ((((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_10) ((insert999278200tate_o X_2) bot_bo691907561te_o_o))) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (F ((insert999278200tate_o X_2) A_10))) X_2))) ((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((minus_1708687022te_o_o A_10) ((insert999278200tate_o X_2) bot_bo691907561te_o_o))) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (F ((insert999278200tate_o X_2) A_10))) ((F_1 X_2) (F ((minus_1708687022te_o_o A_10) ((insert999278200tate_o X_2) bot_bo691907561te_o_o)))))))))).
% Axiom fact_684_DiffI:(forall (B_3:(pname->Prop)) (C_1:pname) (A_9:(pname->Prop)), (((member_pname C_1) A_9)->((((member_pname C_1) B_3)->False)->((member_pname C_1) ((minus_minus_pname_o A_9) B_3))))).
% Axiom fact_685_DiffI:(forall (B_3:(hoare_1167836817_state->Prop)) (C_1:hoare_1167836817_state) (A_9:(hoare_1167836817_state->Prop)), (((member2058392318_state C_1) A_9)->((((member2058392318_state C_1) B_3)->False)->((member2058392318_state C_1) ((minus_2107060239tate_o A_9) B_3))))).
% Axiom fact_686_DiffE:(forall (C:pname) (A_8:(pname->Prop)) (B_2:(pname->Prop)), (((member_pname C) ((minus_minus_pname_o A_8) B_2))->((((member_pname C) A_8)->((member_pname C) B_2))->False))).
% Axiom fact_687_DiffE:(forall (C:hoare_1167836817_state) (A_8:(hoare_1167836817_state->Prop)) (B_2:(hoare_1167836817_state->Prop)), (((member2058392318_state C) ((minus_2107060239tate_o A_8) B_2))->((((member2058392318_state C) A_8)->((member2058392318_state C) B_2))->False))).
% Axiom fact_688_finite__Diff:(forall (B_1:((pname->Prop)->Prop)) (A_7:((pname->Prop)->Prop)), ((finite297249702name_o A_7)->(finite297249702name_o ((minus_1480864103me_o_o A_7) B_1)))).
% Axiom fact_689_finite__Diff:(forall (B_1:((hoare_1167836817_state->Prop)->Prop)) (A_7:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_7)->(finite1380128977tate_o ((minus_1708687022te_o_o A_7) B_1)))).
% Axiom fact_690_finite__Diff:(forall (B_1:(pname->Prop)) (A_7:(pname->Prop)), ((finite_finite_pname A_7)->(finite_finite_pname ((minus_minus_pname_o A_7) B_1)))).
% Axiom fact_691_finite__Diff:(forall (B_1:(hoare_1167836817_state->Prop)) (A_7:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_7)->(finite1084549118_state ((minus_2107060239tate_o A_7) B_1)))).
% Axiom fact_692_insert__Diff:(forall (A_6:pname) (A_5:(pname->Prop)), (((member_pname A_6) A_5)->(((eq (pname->Prop)) ((insert_pname A_6) ((minus_minus_pname_o A_5) ((insert_pname A_6) bot_bot_pname_o)))) A_5))).
% Axiom fact_693_insert__Diff:(forall (A_6:hoare_1167836817_state) (A_5:(hoare_1167836817_state->Prop)), (((member2058392318_state A_6) A_5)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_6) ((minus_2107060239tate_o A_5) ((insert2134838167_state A_6) bot_bo70021908tate_o)))) A_5))).
% Axiom fact_694_Diff__insert__absorb:(forall (X_1:pname) (A_4:(pname->Prop)), ((((member_pname X_1) A_4)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_1) A_4)) ((insert_pname X_1) bot_bot_pname_o))) A_4))).
% Axiom fact_695_Diff__insert__absorb:(forall (X_1:hoare_1167836817_state) (A_4:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_1) A_4)->False)->(((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((insert2134838167_state X_1) A_4)) ((insert2134838167_state X_1) bot_bo70021908tate_o))) A_4))).
% Axiom fact_696_insert__Diff__single:(forall (A_3:pname) (A_2:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_3) ((minus_minus_pname_o A_2) ((insert_pname A_3) bot_bot_pname_o)))) ((insert_pname A_3) A_2))).
% Axiom fact_697_insert__Diff__single:(forall (A_3:hoare_1167836817_state) (A_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_3) ((minus_2107060239tate_o A_2) ((insert2134838167_state A_3) bot_bo70021908tate_o)))) ((insert2134838167_state A_3) A_2))).
% Axiom fact_698_Diff__insert2:(forall (A_1:(hoare_1167836817_state->Prop)) (A:hoare_1167836817_state) (B:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o A_1) ((insert2134838167_state A) B))) ((minus_2107060239tate_o ((minus_2107060239tate_o A_1) ((insert2134838167_state A) bot_bo70021908tate_o))) B))).
% 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____srushsumbx__Otriple_Itc__Com__Ostate:(forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_state True) X) Y)) X)).
% Axiom help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate:(forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_state False) X) Y)) Y)).
% Axiom help_If_3_1_If_000tc__Hoare____Mirabelle____srushsumbx__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____srushsumbx__Otriple_Itc__Com:(forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), ((or (((fequal1831255762_state X) Y)->False)) (((eq hoare_1167836817_state) X) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com:(forall (X:hoare_1167836817_state) (Y:hoare_1167836817_state), ((or (not (((eq hoare_1167836817_state) X) Y))) ((fequal1831255762_state X) Y))).
% Axiom help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It:(forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), ((or (((fequal1486222077tate_o X) Y)->False)) (((eq (hoare_1167836817_state->Prop)) X) Y))).
% Axiom help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It:(forall (X:(hoare_1167836817_state->Prop)) (Y:(hoare_1167836817_state->Prop)), ((or (not (((eq (hoare_1167836817_state->Prop)) X) Y))) ((fequal1486222077tate_o X) Y))).
% Axiom conj_0:hoare_1201148605gleton.
% Axiom conj_1:wT_bodies.
% Axiom conj_2:(finite1084549118_state fa).
% Axiom conj_3:(((member2058392318_state (hoare_Mirabelle_MGT y)) fa)->False).
% Axiom conj_4:((ord_le827224136tate_o fa) ((image_575578384_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_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa).
% Trying to prove ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o))
% Found conj_5:(((eq option_com) (body pn)) (some_com y))
% Instantiate: A_75:=(body pn):option_com
% Found conj_5 as proof of (((eq option_com) A_75) (some_com y))
% Found conj_0:hoare_1201148605gleton
% Found conj_0 as proof of hoare_1201148605gleton
% Found fact_21_empty__subsetI0:=(fact_21_empty__subsetI (fun (x1:pname)=> ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)))):((ord_less_eq_pname_o bot_bot_pname_o) (fun (x1:pname)=> ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o))))
% Found (fact_21_empty__subsetI (fun (x1:pname)=> ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)))) as proof of ((ord_less_eq_pname_o P_16) (fun (x1:pname)=> ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o))))
% Found (fact_21_empty__subsetI (fun (x1:pname)=> ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)))) as proof of ((ord_less_eq_pname_o P_16) (fun (x1:pname)=> ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o))))
% Found (fact_21_empty__subsetI (fun (x1:pname)=> ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)))) as proof of ((ord_less_eq_pname_o P_16) (fun (x1:pname)=> ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o))))
% Found conj_6:((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa)
% Instantiate: G_30:=fa:(hoare_1167836817_state->Prop)
% Found conj_6 as proof of ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_30)
% Found conj_0:hoare_1201148605gleton
% Found conj_0 as proof of hoare_1201148605gleton
% Found conj_5:(((eq option_com) (body pn)) (some_com y))
% Instantiate: A_75:=(body pn):option_com
% Found conj_5 as proof of (((eq option_com) A_75) (some_com y))
% Found conj_0:hoare_1201148605gleton
% Found conj_0 as proof of hoare_1201148605gleton
% Found conj_5:(((eq option_com) (body pn)) (some_com y))
% Instantiate: A_75:=(body pn):option_com
% Found conj_5 as proof of (((eq option_com) A_75) (some_com y))
% Found conj_5:(((eq option_com) (body pn)) (some_com y))
% Instantiate: A_75:=(body pn):option_com
% Found conj_5 as proof of (((eq option_com) A_75) (some_com y))
% Found conj_5:(((eq option_com) (body pn)) (some_com y))
% Instantiate: A_75:=(body pn):option_com
% Found conj_5 as proof of (((eq option_com) A_75) (some_com y))
% Found conj_0:hoare_1201148605gleton
% Found conj_0 as proof of hoare_1201148605gleton
% Found conj_6:((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa)
% Instantiate: Ts_5:=fa:(hoare_1167836817_state->Prop)
% Found conj_6 as proof of ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) Ts_5)
% Found fact_0_empty0:=(fact_0_empty ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))):((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) bot_bo70021908tate_o)
% Found (fact_0_empty ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) as proof of ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) bot_bo70021908tate_o)
% Found (fact_0_empty ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) as proof of ((hoare_123228589_state ((image_575578384_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) bot_bo70021908tate_o)
% Found fact_127_subset__refl0:=(fact_127_subset__refl ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)):((ord_le827224136tate_o ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)) ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o))
% Found (fact_127_subset__refl ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)) Ts_5)
% Found (fact_127_subset__refl ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)) Ts_5)
% Found (fact_127_subset__refl ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)) as proof of ((ord_le827224136tate_o ((insert2134838167_state (hoare_Mirabelle_MGT y)) bot_bo70021908tate_o)) Ts_5)
% Found functional_extensionality_dep:(forall (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x))) (g:(forall (x:A), (B x))), ((forall (x:A), (((eq (B x)) (f x)) (g x)))->(((eq (forall (x:A), (B x))) f) g)))
% Found functional_extensionality_dep as proof of (forall (A:Type) (B:(A->Type)) (f:(forall (x2:A), (B x2))) (g:(forall (x2:A), (B x2))), ((forall (x2:A), (((eq (B x2)) (f x2)) (g x2)))->(((eq (forall (x2:A), (B x2))) f) g)))
% Found eta_expansion_dep:=(fun (A:Type) (B:(A->Type)) (f:(forall (x:A), (B x)))=> (((((functional_extensionality_dep A) (fun (x1:A)=> (B x1))) f) (fun (x:A)=> (f x))) (fu
% EOF
%------------------------------------------------------------------------------