%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SWW471^2 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n190.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 13:37:21 EDT 2014

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SWW471^2 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n190.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 09:14:56 CDT 2014
% % CPUTime  : 300.01 
% 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 0x17c48c0>, <kernel.Type object at 0x17c45a8>) of role type named ty_ty_t__a
% Using role type
% Declaring x_a:Type
% FOF formula (<kernel.Constant object at 0x13e7c68>, <kernel.Type object at 0x17c4050>) of role type named ty_ty_tc__Com__Ocom
% Using role type
% Declaring com:Type
% FOF formula (<kernel.Constant object at 0x17c42d8>, <kernel.Type object at 0x17c44d0>) of role type named ty_ty_tc__Com__Opname
% Using role type
% Declaring pname:Type
% FOF formula (<kernel.Constant object at 0x17c45a8>, <kernel.Type object at 0x17c40e0>) of role type named ty_ty_tc__Com__Ostate
% Using role type
% Declaring state:Type
% FOF formula (<kernel.Constant object at 0x17c4050>, <kernel.Type object at 0x17c4290>) of role type named ty_ty_tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J
% Using role type
% Declaring hoare_1775062406iple_a:Type
% FOF formula (<kernel.Constant object at 0x17c44d0>, <kernel.Type object at 0x17c4488>) 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 0x17c40e0>, <kernel.Type object at 0x17c4368>) of role type named ty_ty_tc__Nat__Onat
% Using role type
% Declaring nat:Type
% FOF formula (<kernel.Constant object at 0x17c4290>, <kernel.Type object at 0x17c4680>) 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 0x17c4098>, <kernel.DependentProduct object at 0x17c3878>) of role type named sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring big_la1126801287name_o:(((pname->Prop)->Prop)->(pname->Prop))
% FOF formula (<kernel.Constant object at 0x17c46c8>, <kernel.DependentProduct object at 0x17c3128>) of role type named sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Hoare____Mirabelle___
% Using role type
% Declaring big_la447547205le_a_o:(((hoare_1775062406iple_a->Prop)->Prop)->(hoare_1775062406iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x17c4368>, <kernel.DependentProduct object at 0x17c3128>) of role type named sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Hoare____Mirabelle____001
% Using role type
% Declaring big_la831793456tate_o:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))
% FOF formula (<kernel.Constant object at 0x17c4098>, <kernel.DependentProduct object at 0x17c3fc8>) of role type named sy_c_Big__Operators_Olattice__class_OInf__fin_000_Eo
% Using role type
% Declaring big_la1690136417_fin_o:((Prop->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x17c4a70>, <kernel.DependentProduct object at 0x17c3128>) of role type named sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Com__Opname_M_Eo_J
% Using role type
% Declaring big_la1286884090name_o:(((pname->Prop)->Prop)->(pname->Prop))
% FOF formula (<kernel.Constant object at 0x17c4098>, <kernel.DependentProduct object at 0x17c3170>) of role type named sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Hoare____Mirabelle___
% Using role type
% Declaring big_la1843772984le_a_o:(((hoare_1775062406iple_a->Prop)->Prop)->(hoare_1775062406iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x17c4a70>, <kernel.DependentProduct object at 0x17c3fc8>) of role type named sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Hoare____Mirabelle____002
% Using role type
% Declaring big_la1138507389tate_o:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop))
% FOF formula (<kernel.Constant object at 0x17c4368>, <kernel.DependentProduct object at 0x17c3680>) of role type named sy_c_Big__Operators_Olattice__class_OSup__fin_000_Eo
% Using role type
% Declaring big_la727467310_fin_o:((Prop->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x17c4368>, <kernel.DependentProduct object at 0x17c3248>) of role type named sy_c_Com_Obody
% Using role type
% Declaring body_1:(pname->option_com)
% FOF formula (<kernel.Constant object at 0x17c3170>, <kernel.DependentProduct object at 0x17c37a0>) of role type named sy_c_Com_Ocom_OBODY
% Using role type
% Declaring body:(pname->com)
% FOF formula (<kernel.Constant object at 0x17c3680>, <kernel.DependentProduct object at 0x17c3fc8>) of role type named sy_c_Com_Ocom_OCond
% Using role type
% Declaring cond:((state->Prop)->(com->(com->com)))
% FOF formula (<kernel.Constant object at 0x17c3248>, <kernel.Constant object at 0x17c3fc8>) of role type named sy_c_Com_Ocom_OSKIP
% Using role type
% Declaring skip:com
% FOF formula (<kernel.Constant object at 0x17c3170>, <kernel.DependentProduct object at 0x17c3998>) of role type named sy_c_Com_Ocom_OSemi
% Using role type
% Declaring semi:(com->(com->com))
% FOF formula (<kernel.Constant object at 0x17c3cf8>, <kernel.DependentProduct object at 0x17c37e8>) of role type named sy_c_Com_Ocom_OWhile
% Using role type
% Declaring while:((state->Prop)->(com->com))
% FOF formula (<kernel.Constant object at 0x17c3fc8>, <kernel.DependentProduct object at 0x17c3680>) of role type named sy_c_Com_Ocom_Ocom__size
% Using role type
% Declaring com_size:(com->nat)
% FOF formula (<kernel.Constant object at 0x17c37a0>, <kernel.DependentProduct object at 0x17c3680>) 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 0x17c37e8>, <kernel.DependentProduct object at 0x17c3680>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_
% Using role type
% Declaring finite789576932le_a_o:(((hoare_1775062406iple_a->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x17c3d40>, <kernel.DependentProduct object at 0x17c3680>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple__003
% Using role type
% Declaring finite1380128977tate_o:(((hoare_1167836817_state->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x17c3878>, <kernel.DependentProduct object at 0x17c3908>) of role type named sy_c_Finite__Set_Ofinite_000_Eo
% Using role type
% Declaring finite_finite_o:((Prop->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x17c3248>, <kernel.DependentProduct object at 0x17c3dd0>) 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 0x17c3680>, <kernel.DependentProduct object at 0x17c3878>) of role type named sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_
% Using role type
% Declaring finite2063573081iple_a:((hoare_1775062406iple_a->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x17c3f38>, <kernel.DependentProduct object at 0x17c3dd0>) 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 0x17c3f80>, <kernel.DependentProduct object at 0x17c3878>) of role type named sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otr
% Using role type
% Declaring finite1805141964_pname:(((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop)))->((pname->(hoare_1775062406iple_a->Prop))->((hoare_1775062406iple_a->Prop)->((pname->Prop)->(hoare_1775062406iple_a->Prop)))))
% FOF formula (<kernel.Constant object at 0x17c35a8>, <kernel.DependentProduct object at 0x17c3ea8>) of role type named sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otr_004
% Using role type
% Declaring finite1068437657_pname:(((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))->((pname->(hoare_1167836817_state->Prop))->((hoare_1167836817_state->Prop)->((pname->Prop)->(hoare_1167836817_state->Prop)))))
% FOF formula (<kernel.Constant object at 0x17c35f0>, <kernel.DependentProduct object at 0x17c3f80>) 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 0x17c3bd8>, <kernel.DependentProduct object at 0x17c35a8>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____srushsumbx__Otriple_
% Using role type
% Declaring finite2078349315iple_a:((hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))->(((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)->Prop))
% FOF formula (<kernel.Constant object at 0x17c3518>, <kernel.DependentProduct object at 0x17c35f0>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____srushsumbx__Otriple__005
% 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 0x17c3680>, <kernel.DependentProduct object at 0x17c3bd8>) 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 0x17c3050>, <kernel.DependentProduct object at 0x17c3518>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____srushsumbx__Ot
% Using role type
% Declaring finite1358382848iple_a:((hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))->(((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)->Prop))
% FOF formula (<kernel.Constant object at 0x17c35a8>, <kernel.DependentProduct object at 0x17c3680>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____srushsumbx__Ot_006
% 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 0x17c3878>, <kernel.DependentProduct object at 0x17c3560>) 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 0x17c3ef0>, <kernel.DependentProduct object at 0x17c34d0>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____srushsumbx__
% Using role type
% Declaring minus_1944206118le_a_o:((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x17c3518>, <kernel.DependentProduct object at 0x17c33b0>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____srushsumbx___007
% 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 0x17c3050>, <kernel.DependentProduct object at 0x17c35a8>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat
% Using role type
% Declaring minus_minus_nat:(nat->(nat->nat))
% FOF formula (<kernel.Constant object at 0x17c3488>, <kernel.Constant object at 0x17c35a8>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat
% Using role type
% Declaring one_one_nat:nat
% FOF formula (<kernel.Constant object at 0x17c3518>, <kernel.DependentProduct object at 0x17c33b0>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat
% Using role type
% Declaring plus_plus_nat:(nat->(nat->nat))
% FOF formula (<kernel.Constant object at 0x17c34d0>, <kernel.Constant object at 0x17c33b0>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat
% Using role type
% Declaring zero_zero_nat:nat
% FOF formula (<kernel.Constant object at 0x17c3320>, <kernel.DependentProduct object at 0x17c3a70>) 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 0x17c3c68>, <kernel.DependentProduct object at 0x17c34d0>) of role type named sy_c_HOL_OThe_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J
% Using role type
% Declaring the_Ho1155011127iple_a:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)
% FOF formula (<kernel.Constant object at 0x17c33b0>, <kernel.DependentProduct object at 0x12b2518>) 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 0x17c3cb0>, <kernel.DependentProduct object at 0x12b2cf8>) 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 0x12b2518>, <kernel.DependentProduct object at 0x17c3c68>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__derivs_000t__a
% Using role type
% Declaring hoare_1508237396rivs_a:((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x181fbd8>, <kernel.DependentProduct object at 0x17c3a70>) 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 0x181fbd8>, <kernel.DependentProduct object at 0x17c3c68>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__valids_000t__a
% Using role type
% Declaring hoare_1846070742lids_a:((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1823248>, <kernel.DependentProduct object at 0x17c33f8>) 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 0x1823248>, <kernel.DependentProduct object at 0x17c3c68>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple_000t__a
% Using role type
% Declaring hoare_1766022166iple_a:((x_a->(state->Prop))->(com->((x_a->(state->Prop))->hoare_1775062406iple_a)))
% FOF formula (<kernel.Constant object at 0x17c34d0>, <kernel.DependentProduct object at 0x17c33f8>) 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 0x17c3cb0>, <kernel.DependentProduct object at 0x17c33f8>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple__size_000t__a
% Using role type
% Declaring hoare_1118907895size_a:((x_a->nat)->(hoare_1775062406iple_a->nat))
% FOF formula (<kernel.Constant object at 0x17c3c68>, <kernel.DependentProduct object at 0x17c33b0>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple__size_000tc__Com__Ostate
% Using role type
% Declaring hoare_545207370_state:((state->nat)->(hoare_1167836817_state->nat))
% FOF formula (<kernel.Constant object at 0x17c33f8>, <kernel.DependentProduct object at 0x17a4518>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Otriple__valid_000t__a
% Using role type
% Declaring hoare_1462269968alid_a:(nat->(hoare_1775062406iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x17c3cb0>, <kernel.DependentProduct object at 0x17a4050>) of role type named sy_c_Hoare__Mirabelle__srushsumbx_Otriple__valid_000tc__Com__Ostate
% Using role type
% Declaring hoare_56934129_state:(nat->(hoare_1167836817_state->Prop))
% FOF formula (<kernel.Constant object at 0x17c33f8>, <kernel.DependentProduct object at 0x17a43b0>) of role type named sy_c_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J
% Using role type
% Declaring if_Hoa1047340790iple_a:(Prop->(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a)))
% FOF formula (<kernel.Constant object at 0x17c3cb0>, <kernel.DependentProduct object at 0x17a43b0>) 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 0x17c33f8>, <kernel.DependentProduct object at 0x17a4290>) 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 0x17c33f8>, <kernel.DependentProduct object at 0x17a4170>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell
% Using role type
% Declaring semila1691990438_a_o_o:(((hoare_1775062406iple_a->Prop)->Prop)->(((hoare_1775062406iple_a->Prop)->Prop)->((hoare_1775062406iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x17a4518>, <kernel.DependentProduct object at 0x17a4908>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell_008
% 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 0x17a4200>, <kernel.DependentProduct object at 0x17a48c0>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_Eo_M_Eo_J
% Using role type
% Declaring semila232696320nf_o_o:((Prop->Prop)->((Prop->Prop)->(Prop->Prop)))
% FOF formula (<kernel.Constant object at 0x17a4560>, <kernel.DependentProduct object at 0x17a48c0>) 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 0x17a45f0>, <kernel.DependentProduct object at 0x17a48c0>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____s
% Using role type
% Declaring semila966743401le_a_o:((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x17a4320>, <kernel.DependentProduct object at 0x17a48c0>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____s_009
% Using role type
% Declaring semila179895820tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x17a4518>, <kernel.DependentProduct object at 0x17c2d40>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_Eo
% Using role type
% Declaring semila854092349_inf_o:(Prop->(Prop->Prop))
% FOF formula (<kernel.Constant object at 0x17a45f0>, <kernel.DependentProduct object at 0x17c2cf8>) 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 0x17a4320>, <kernel.DependentProduct object at 0x17c2128>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell
% Using role type
% Declaring semila2069193356_a_o_o:(((hoare_1775062406iple_a->Prop)->Prop)->(((hoare_1775062406iple_a->Prop)->Prop)->((hoare_1775062406iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x17a45f0>, <kernel.DependentProduct object at 0x17c20e0>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell_010
% 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 0x17a4320>, <kernel.DependentProduct object at 0x17c27e8>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_Eo_M_Eo_J
% Using role type
% Declaring semila2062604954up_o_o:((Prop->Prop)->((Prop->Prop)->(Prop->Prop)))
% FOF formula (<kernel.Constant object at 0x17a4518>, <kernel.DependentProduct object at 0x17c2128>) 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 0x17a4518>, <kernel.DependentProduct object at 0x17c2128>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____s
% Using role type
% Declaring semila13410563le_a_o:((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x17c2170>, <kernel.DependentProduct object at 0x17c2128>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____s_011
% Using role type
% Declaring semila1172322802tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x17c2b48>, <kernel.DependentProduct object at 0x17c28c0>) 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 0x17c27e8>, <kernel.DependentProduct object at 0x13cc8c0>) of role type named sy_c_Nat_OSuc
% Using role type
% Declaring suc:(nat->nat)
% FOF formula (<kernel.Constant object at 0x17c2128>, <kernel.DependentProduct object at 0x13cc830>) of role type named sy_c_Nat_Onat_Onat__case_000tc__Nat__Onat
% Using role type
% Declaring nat_case_nat:(nat->((nat->nat)->(nat->nat)))
% FOF formula (<kernel.Constant object at 0x17c2b48>, <kernel.DependentProduct object at 0x13cc878>) of role type named sy_c_Nat_Osize__class_Osize_000tc__Com__Ocom
% Using role type
% Declaring size_size_com:(com->nat)
% FOF formula (<kernel.Constant object at 0x17c27e8>, <kernel.DependentProduct object at 0x13cc7a0>) of role type named sy_c_Nat_Osize__class_Osize_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It_
% Using role type
% Declaring size_s724313756iple_a:(hoare_1775062406iple_a->nat)
% FOF formula (<kernel.Constant object at 0x17c2b48>, <kernel.DependentProduct object at 0x13cc758>) of role type named sy_c_Nat_Osize__class_Osize_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc
% Using role type
% Declaring size_s645941755_state:(hoare_1167836817_state->nat)
% FOF formula (<kernel.Constant object at 0x17c2128>, <kernel.DependentProduct object at 0x13cc7e8>) of role type named sy_c_Natural_Oevalc
% Using role type
% Declaring evalc:(com->(state->(state->Prop)))
% FOF formula (<kernel.Constant object at 0x17c2b48>, <kernel.DependentProduct object at 0x13cc830>) of role type named sy_c_Natural_Oevaln
% Using role type
% Declaring evaln:(com->(state->(nat->(state->Prop))))
% FOF formula (<kernel.Constant object at 0x13cc758>, <kernel.DependentProduct object at 0x13cc908>) 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 0x13cc680>, <kernel.DependentProduct object at 0x13cc6c8>) 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 0x13cc830>, <kernel.DependentProduct object at 0x13cc758>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____srushsu
% Using role type
% Declaring bot_bo1976773294_a_o_o:((hoare_1775062406iple_a->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x13cc710>, <kernel.DependentProduct object at 0x13cc6c8>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____srushsu_012
% Using role type
% Declaring bot_bo691907561te_o_o:((hoare_1167836817_state->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x13cc638>, <kernel.DependentProduct object at 0x13cc758>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_Eo_M_Eo_J
% Using role type
% Declaring bot_bot_o_o:(Prop->Prop)
% FOF formula (<kernel.Constant object at 0x13cc830>, <kernel.DependentProduct object at 0x13cc5a8>) 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 0x13cc878>, <kernel.DependentProduct object at 0x13cc518>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____srushsumbx__O
% Using role type
% Declaring bot_bo751897185le_a_o:(hoare_1775062406iple_a->Prop)
% FOF formula (<kernel.Constant object at 0x13cc758>, <kernel.DependentProduct object at 0x13cc560>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____srushsumbx__O_013
% Using role type
% Declaring bot_bo70021908tate_o:(hoare_1167836817_state->Prop)
% FOF formula (<kernel.Constant object at 0x13cc5a8>, <kernel.Sort object at 0x12b11b8>) 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 0x13cc6c8>, <kernel.Constant object at 0x13cc758>) of role type named sy_c_Orderings_Obot__class_Obot_000tc__Nat__Onat
% Using role type
% Declaring bot_bot_nat:nat
% FOF formula (<kernel.Constant object at 0x13cc518>, <kernel.DependentProduct object at 0x13cc5f0>) 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 0x13cc488>, <kernel.DependentProduct object at 0x13cc758>) of role type named sy_c_Set_OCollect_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J
% Using role type
% Declaring collec676402587iple_a:((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x13cc3f8>, <kernel.DependentProduct object at 0x13cc5f0>) 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 0x13cc5a8>, <kernel.DependentProduct object at 0x13ccab8>) 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 0x13cc9e0>, <kernel.DependentProduct object at 0x13ccb00>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_M
% Using role type
% Declaring image_2014247585le_a_o:(((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop))->(((hoare_1775062406iple_a->Prop)->Prop)->((hoare_1775062406iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x13cc758>, <kernel.DependentProduct object at 0x13cca28>) 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 0x13cc8c0>, <kernel.DependentProduct object at 0x13cc440>) of role type named sy_c_Set_Oimage_000_Eo_000_Eo
% Using role type
% Declaring image_o_o:((Prop->Prop)->((Prop->Prop)->(Prop->Prop)))
% FOF formula (<kernel.Constant object at 0x13ccbd8>, <kernel.DependentProduct object at 0x13cc9e0>) 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 0x13cca28>, <kernel.DependentProduct object at 0x13ccc68>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____srushsumbx__Otri
% Using role type
% Declaring image_2063119815iple_a:((pname->hoare_1775062406iple_a)->((pname->Prop)->(hoare_1775062406iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x13cc758>, <kernel.DependentProduct object at 0x13cccb0>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____srushsumbx__Otri_014
% Using role type
% Declaring image_575578384_state:((pname->hoare_1167836817_state)->((pname->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x13cc8c0>, <kernel.DependentProduct object at 0x13cccf8>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_000tc__
% Using role type
% Declaring image_51246659_pname:((hoare_1775062406iple_a->pname)->((hoare_1775062406iple_a->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x13cc9e0>, <kernel.DependentProduct object at 0x13ccd40>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_000tc___015
% Using role type
% Declaring image_1170193413iple_a:((hoare_1775062406iple_a->hoare_1775062406iple_a)->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x13ccc68>, <kernel.DependentProduct object at 0x13ccd88>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_000tc___016
% Using role type
% Declaring image_1021683026_state:((hoare_1775062406iple_a->hoare_1167836817_state)->((hoare_1775062406iple_a->Prop)->(hoare_1167836817_state->Prop)))
% FOF formula (<kernel.Constant object at 0x13cca28>, <kernel.DependentProduct object at 0x13ccdd0>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat
% Using role type
% Declaring image_1802845250iple_a:((hoare_1167836817_state->hoare_1775062406iple_a)->((hoare_1167836817_state->Prop)->(hoare_1775062406iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x13cccb0>, <kernel.DependentProduct object at 0x13cce18>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_017
% 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 0x13cccf8>, <kernel.DependentProduct object at 0x13ccdd0>) 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 0x13ccd40>, <kernel.DependentProduct object at 0x13cce18>) of role type named sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_
% Using role type
% Declaring insert1210049533le_a_o:((hoare_1775062406iple_a->Prop)->(((hoare_1775062406iple_a->Prop)->Prop)->((hoare_1775062406iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x13ccc68>, <kernel.DependentProduct object at 0x13ccdd0>) 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 0x13ccea8>, <kernel.DependentProduct object at 0x13ccf38>) of role type named sy_c_Set_Oinsert_000_Eo
% Using role type
% Declaring insert_o:(Prop->((Prop->Prop)->(Prop->Prop)))
% FOF formula (<kernel.Constant object at 0x13ccb90>, <kernel.DependentProduct object at 0x13ccf80>) 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 0x13cce18>, <kernel.DependentProduct object at 0x13ccdd0>) of role type named sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J
% Using role type
% Declaring insert1281456128iple_a:(hoare_1775062406iple_a->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x13ccf38>, <kernel.DependentProduct object at 0x13ccfc8>) 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 0x13ccf80>, <kernel.DependentProduct object at 0x13ccb90>) 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 0x13cccf8>, <kernel.DependentProduct object at 0x17bc098>) of role type named sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J
% Using role type
% Declaring the_el1844711461iple_a:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)
% FOF formula (<kernel.Constant object at 0x13ccb00>, <kernel.DependentProduct object at 0x17bc050>) 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 0x13ccd40>, <kernel.DependentProduct object at 0x17bc0e0>) 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 0x13ccdd0>, <kernel.DependentProduct object at 0x17bc170>) 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 0x13cccf8>, <kernel.DependentProduct object at 0x17bc0e0>) of role type named sy_c_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J
% Using role type
% Declaring fequal1288209029iple_a:(hoare_1775062406iple_a->(hoare_1775062406iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x13ccd40>, <kernel.DependentProduct object at 0x17bc128>) 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 0x13cccf8>, <kernel.DependentProduct object at 0x17bc1b8>) 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 0x13ccd40>, <kernel.DependentProduct object at 0x17bc248>) of role type named sy_c_member_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_M_Eo_
% Using role type
% Declaring member1207314404le_a_o:((hoare_1775062406iple_a->Prop)->(((hoare_1775062406iple_a->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x13ccdd0>, <kernel.DependentProduct object at 0x17bc290>) 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 0x13ccdd0>, <kernel.DependentProduct object at 0x17bc170>) of role type named sy_c_member_000_Eo
% Using role type
% Declaring member_o:(Prop->((Prop->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x17bc1b8>, <kernel.DependentProduct object at 0x17bc3b0>) 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 0x17bc2d8>, <kernel.DependentProduct object at 0x17bc128>) of role type named sy_c_member_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J
% Using role type
% Declaring member2122167641iple_a:(hoare_1775062406iple_a->((hoare_1775062406iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x17bc170>, <kernel.DependentProduct object at 0x17bc3f8>) 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 0x17bc1b8>, <kernel.DependentProduct object at 0x17bc0e0>) of role type named sy_v_G
% Using role type
% Declaring g:(hoare_1775062406iple_a->Prop)
% FOF formula (<kernel.Constant object at 0x17bc128>, <kernel.DependentProduct object at 0x17bc3b0>) of role type named sy_v_P
% Using role type
% Declaring p:(pname->(x_a->(state->Prop)))
% FOF formula (<kernel.Constant object at 0x17bc3f8>, <kernel.DependentProduct object at 0x17bc170>) of role type named sy_v_Procs
% Using role type
% Declaring procs:(pname->Prop)
% FOF formula (<kernel.Constant object at 0x17bc0e0>, <kernel.DependentProduct object at 0x17bc488>) of role type named sy_v_Q
% Using role type
% Declaring q:(pname->(x_a->(state->Prop)))
% FOF formula (<kernel.Constant object at 0x17bc3b0>, <kernel.Constant object at 0x17bc488>) of role type named sy_v_n
% Using role type
% Declaring n:nat
% FOF formula (forall (Fun1_4:(x_a->(state->Prop))) (Com:com) (Fun2_4:(x_a->(state->Prop))) (Fun1_3:(x_a->(state->Prop))) (Com_1:com) (Fun2_3:(x_a->(state->Prop))), ((iff (((eq hoare_1775062406iple_a) (((hoare_1766022166iple_a Fun1_4) Com) Fun2_4)) (((hoare_1766022166iple_a Fun1_3) Com_1) Fun2_3))) ((and ((and (((eq (x_a->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com) Com_1))) (((eq (x_a->(state->Prop))) Fun2_4) Fun2_3)))) of role axiom named fact_0_triple_Oinject
% A new axiom: (forall (Fun1_4:(x_a->(state->Prop))) (Com:com) (Fun2_4:(x_a->(state->Prop))) (Fun1_3:(x_a->(state->Prop))) (Com_1:com) (Fun2_3:(x_a->(state->Prop))), ((iff (((eq hoare_1775062406iple_a) (((hoare_1766022166iple_a Fun1_4) Com) Fun2_4)) (((hoare_1766022166iple_a Fun1_3) Com_1) Fun2_3))) ((and ((and (((eq (x_a->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com) Com_1))) (((eq (x_a->(state->Prop))) Fun2_4) Fun2_3))))
% FOF formula (forall (Fun1_4:(state->(state->Prop))) (Com:com) (Fun2_4:(state->(state->Prop))) (Fun1_3:(state->(state->Prop))) (Com_1:com) (Fun2_3:(state->(state->Prop))), ((iff (((eq hoare_1167836817_state) (((hoare_908217195_state Fun1_4) Com) Fun2_4)) (((hoare_908217195_state Fun1_3) Com_1) Fun2_3))) ((and ((and (((eq (state->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com) Com_1))) (((eq (state->(state->Prop))) Fun2_4) Fun2_3)))) of role axiom named fact_1_triple_Oinject
% A new axiom: (forall (Fun1_4:(state->(state->Prop))) (Com:com) (Fun2_4:(state->(state->Prop))) (Fun1_3:(state->(state->Prop))) (Com_1:com) (Fun2_3:(state->(state->Prop))), ((iff (((eq hoare_1167836817_state) (((hoare_908217195_state Fun1_4) Com) Fun2_4)) (((hoare_908217195_state Fun1_3) Com_1) Fun2_3))) ((and ((and (((eq (state->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com) Com_1))) (((eq (state->(state->Prop))) Fun2_4) Fun2_3))))
% FOF formula (forall (G_25:(hoare_1167836817_state->Prop)) (Ts_4:(hoare_1167836817_state->Prop)), ((iff ((hoare_529639851_state G_25) Ts_4)) (forall (N:nat), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) G_25)->((hoare_56934129_state N) X)))->(forall (X:hoare_1167836817_state), (((member2058392318_state X) Ts_4)->((hoare_56934129_state N) X))))))) of role axiom named fact_2_hoare__valids__def
% A new axiom: (forall (G_25:(hoare_1167836817_state->Prop)) (Ts_4:(hoare_1167836817_state->Prop)), ((iff ((hoare_529639851_state G_25) Ts_4)) (forall (N:nat), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) G_25)->((hoare_56934129_state N) X)))->(forall (X:hoare_1167836817_state), (((member2058392318_state X) Ts_4)->((hoare_56934129_state N) X)))))))
% FOF formula (forall (G_25:(hoare_1775062406iple_a->Prop)) (Ts_4:(hoare_1775062406iple_a->Prop)), ((iff ((hoare_1846070742lids_a G_25) Ts_4)) (forall (N:nat), ((forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) G_25)->((hoare_1462269968alid_a N) X)))->(forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) Ts_4)->((hoare_1462269968alid_a N) X))))))) of role axiom named fact_3_hoare__valids__def
% A new axiom: (forall (G_25:(hoare_1775062406iple_a->Prop)) (Ts_4:(hoare_1775062406iple_a->Prop)), ((iff ((hoare_1846070742lids_a G_25) Ts_4)) (forall (N:nat), ((forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) G_25)->((hoare_1462269968alid_a N) X)))->(forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) Ts_4)->((hoare_1462269968alid_a N) X)))))))
% FOF formula (forall (G_24:(hoare_1167836817_state->Prop)) (P_37:(pname->(state->(state->Prop)))) (Q_20:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_24) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1))) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_37 P_10)) (the_com (body_1 P_10))) (Q_20 P_10)))) Procs_1))->((hoare_123228589_state G_24) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1)))) of role axiom named fact_4_hoare__derivs_OBody
% A new axiom: (forall (G_24:(hoare_1167836817_state->Prop)) (P_37:(pname->(state->(state->Prop)))) (Q_20:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_24) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1))) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_37 P_10)) (the_com (body_1 P_10))) (Q_20 P_10)))) Procs_1))->((hoare_123228589_state G_24) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1))))
% FOF formula (forall (G_24:(hoare_1775062406iple_a->Prop)) (P_37:(pname->(x_a->(state->Prop)))) (Q_20:(pname->(x_a->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_1508237396rivs_a ((semila13410563le_a_o G_24) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1))) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_37 P_10)) (the_com (body_1 P_10))) (Q_20 P_10)))) Procs_1))->((hoare_1508237396rivs_a G_24) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1)))) of role axiom named fact_5_hoare__derivs_OBody
% A new axiom: (forall (G_24:(hoare_1775062406iple_a->Prop)) (P_37:(pname->(x_a->(state->Prop)))) (Q_20:(pname->(x_a->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_1508237396rivs_a ((semila13410563le_a_o G_24) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1))) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_37 P_10)) (the_com (body_1 P_10))) (Q_20 P_10)))) Procs_1))->((hoare_1508237396rivs_a G_24) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1))))
% FOF formula (forall (C_42:hoare_1167836817_state) (A_138:(hoare_1167836817_state->Prop)) (B_79:(hoare_1167836817_state->Prop)), (((member2058392318_state C_42) ((semila1172322802tate_o A_138) B_79))->((((member2058392318_state C_42) A_138)->False)->((member2058392318_state C_42) B_79)))) of role axiom named fact_6_UnE
% A new axiom: (forall (C_42:hoare_1167836817_state) (A_138:(hoare_1167836817_state->Prop)) (B_79:(hoare_1167836817_state->Prop)), (((member2058392318_state C_42) ((semila1172322802tate_o A_138) B_79))->((((member2058392318_state C_42) A_138)->False)->((member2058392318_state C_42) B_79))))
% FOF formula (forall (C_42:hoare_1775062406iple_a) (A_138:(hoare_1775062406iple_a->Prop)) (B_79:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_42) ((semila13410563le_a_o A_138) B_79))->((((member2122167641iple_a C_42) A_138)->False)->((member2122167641iple_a C_42) B_79)))) of role axiom named fact_7_UnE
% A new axiom: (forall (C_42:hoare_1775062406iple_a) (A_138:(hoare_1775062406iple_a->Prop)) (B_79:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_42) ((semila13410563le_a_o A_138) B_79))->((((member2122167641iple_a C_42) A_138)->False)->((member2122167641iple_a C_42) B_79))))
% FOF formula (forall (C_42:pname) (A_138:(pname->Prop)) (B_79:(pname->Prop)), (((member_pname C_42) ((semila1780557381name_o A_138) B_79))->((((member_pname C_42) A_138)->False)->((member_pname C_42) B_79)))) of role axiom named fact_8_UnE
% A new axiom: (forall (C_42:pname) (A_138:(pname->Prop)) (B_79:(pname->Prop)), (((member_pname C_42) ((semila1780557381name_o A_138) B_79))->((((member_pname C_42) A_138)->False)->((member_pname C_42) B_79))))
% FOF formula (forall (A_137:(hoare_1167836817_state->Prop)) (B_78:(hoare_1167836817_state->Prop)) (X_51:hoare_1167836817_state), ((((semila1172322802tate_o A_137) B_78) X_51)->(((A_137 X_51)->False)->(B_78 X_51)))) of role axiom named fact_9_sup1E
% A new axiom: (forall (A_137:(hoare_1167836817_state->Prop)) (B_78:(hoare_1167836817_state->Prop)) (X_51:hoare_1167836817_state), ((((semila1172322802tate_o A_137) B_78) X_51)->(((A_137 X_51)->False)->(B_78 X_51))))
% FOF formula (forall (A_137:(pname->Prop)) (B_78:(pname->Prop)) (X_51:pname), ((((semila1780557381name_o A_137) B_78) X_51)->(((A_137 X_51)->False)->(B_78 X_51)))) of role axiom named fact_10_sup1E
% A new axiom: (forall (A_137:(pname->Prop)) (B_78:(pname->Prop)) (X_51:pname), ((((semila1780557381name_o A_137) B_78) X_51)->(((A_137 X_51)->False)->(B_78 X_51))))
% FOF formula (forall (A_137:(hoare_1775062406iple_a->Prop)) (B_78:(hoare_1775062406iple_a->Prop)) (X_51:hoare_1775062406iple_a), ((((semila13410563le_a_o A_137) B_78) X_51)->(((A_137 X_51)->False)->(B_78 X_51)))) of role axiom named fact_11_sup1E
% A new axiom: (forall (A_137:(hoare_1775062406iple_a->Prop)) (B_78:(hoare_1775062406iple_a->Prop)) (X_51:hoare_1775062406iple_a), ((((semila13410563le_a_o A_137) B_78) X_51)->(((A_137 X_51)->False)->(B_78 X_51))))
% FOF formula (forall (A_136:(hoare_1167836817_state->Prop)) (B_77:(hoare_1167836817_state->Prop)) (X_50:hoare_1167836817_state), ((((B_77 X_50)->False)->(A_136 X_50))->(((semila1172322802tate_o A_136) B_77) X_50))) of role axiom named fact_12_sup1CI
% A new axiom: (forall (A_136:(hoare_1167836817_state->Prop)) (B_77:(hoare_1167836817_state->Prop)) (X_50:hoare_1167836817_state), ((((B_77 X_50)->False)->(A_136 X_50))->(((semila1172322802tate_o A_136) B_77) X_50)))
% FOF formula (forall (A_136:(pname->Prop)) (B_77:(pname->Prop)) (X_50:pname), ((((B_77 X_50)->False)->(A_136 X_50))->(((semila1780557381name_o A_136) B_77) X_50))) of role axiom named fact_13_sup1CI
% A new axiom: (forall (A_136:(pname->Prop)) (B_77:(pname->Prop)) (X_50:pname), ((((B_77 X_50)->False)->(A_136 X_50))->(((semila1780557381name_o A_136) B_77) X_50)))
% FOF formula (forall (A_136:(hoare_1775062406iple_a->Prop)) (B_77:(hoare_1775062406iple_a->Prop)) (X_50:hoare_1775062406iple_a), ((((B_77 X_50)->False)->(A_136 X_50))->(((semila13410563le_a_o A_136) B_77) X_50))) of role axiom named fact_14_sup1CI
% A new axiom: (forall (A_136:(hoare_1775062406iple_a->Prop)) (B_77:(hoare_1775062406iple_a->Prop)) (X_50:hoare_1775062406iple_a), ((((B_77 X_50)->False)->(A_136 X_50))->(((semila13410563le_a_o A_136) B_77) X_50)))
% FOF formula (forall (A_135:(hoare_1167836817_state->Prop)) (C_41:hoare_1167836817_state) (B_76:(hoare_1167836817_state->Prop)), (((((member2058392318_state C_41) B_76)->False)->((member2058392318_state C_41) A_135))->((member2058392318_state C_41) ((semila1172322802tate_o A_135) B_76)))) of role axiom named fact_15_UnCI
% A new axiom: (forall (A_135:(hoare_1167836817_state->Prop)) (C_41:hoare_1167836817_state) (B_76:(hoare_1167836817_state->Prop)), (((((member2058392318_state C_41) B_76)->False)->((member2058392318_state C_41) A_135))->((member2058392318_state C_41) ((semila1172322802tate_o A_135) B_76))))
% FOF formula (forall (A_135:(hoare_1775062406iple_a->Prop)) (C_41:hoare_1775062406iple_a) (B_76:(hoare_1775062406iple_a->Prop)), (((((member2122167641iple_a C_41) B_76)->False)->((member2122167641iple_a C_41) A_135))->((member2122167641iple_a C_41) ((semila13410563le_a_o A_135) B_76)))) of role axiom named fact_16_UnCI
% A new axiom: (forall (A_135:(hoare_1775062406iple_a->Prop)) (C_41:hoare_1775062406iple_a) (B_76:(hoare_1775062406iple_a->Prop)), (((((member2122167641iple_a C_41) B_76)->False)->((member2122167641iple_a C_41) A_135))->((member2122167641iple_a C_41) ((semila13410563le_a_o A_135) B_76))))
% FOF formula (forall (A_135:(pname->Prop)) (C_41:pname) (B_76:(pname->Prop)), (((((member_pname C_41) B_76)->False)->((member_pname C_41) A_135))->((member_pname C_41) ((semila1780557381name_o A_135) B_76)))) of role axiom named fact_17_UnCI
% A new axiom: (forall (A_135:(pname->Prop)) (C_41:pname) (B_76:(pname->Prop)), (((((member_pname C_41) B_76)->False)->((member_pname C_41) A_135))->((member_pname C_41) ((semila1780557381name_o A_135) B_76))))
% FOF formula (forall (A_134:(pname->Prop)) (B_75:hoare_1167836817_state) (F_41:(pname->hoare_1167836817_state)) (X_49:pname), ((((eq hoare_1167836817_state) B_75) (F_41 X_49))->(((member_pname X_49) A_134)->((member2058392318_state B_75) ((image_575578384_state F_41) A_134))))) of role axiom named fact_18_image__eqI
% A new axiom: (forall (A_134:(pname->Prop)) (B_75:hoare_1167836817_state) (F_41:(pname->hoare_1167836817_state)) (X_49:pname), ((((eq hoare_1167836817_state) B_75) (F_41 X_49))->(((member_pname X_49) A_134)->((member2058392318_state B_75) ((image_575578384_state F_41) A_134)))))
% FOF formula (forall (A_134:(hoare_1775062406iple_a->Prop)) (B_75:pname) (F_41:(hoare_1775062406iple_a->pname)) (X_49:hoare_1775062406iple_a), ((((eq pname) B_75) (F_41 X_49))->(((member2122167641iple_a X_49) A_134)->((member_pname B_75) ((image_51246659_pname F_41) A_134))))) of role axiom named fact_19_image__eqI
% A new axiom: (forall (A_134:(hoare_1775062406iple_a->Prop)) (B_75:pname) (F_41:(hoare_1775062406iple_a->pname)) (X_49:hoare_1775062406iple_a), ((((eq pname) B_75) (F_41 X_49))->(((member2122167641iple_a X_49) A_134)->((member_pname B_75) ((image_51246659_pname F_41) A_134)))))
% FOF formula (forall (A_134:(pname->Prop)) (B_75:hoare_1775062406iple_a) (F_41:(pname->hoare_1775062406iple_a)) (X_49:pname), ((((eq hoare_1775062406iple_a) B_75) (F_41 X_49))->(((member_pname X_49) A_134)->((member2122167641iple_a B_75) ((image_2063119815iple_a F_41) A_134))))) of role axiom named fact_20_image__eqI
% A new axiom: (forall (A_134:(pname->Prop)) (B_75:hoare_1775062406iple_a) (F_41:(pname->hoare_1775062406iple_a)) (X_49:pname), ((((eq hoare_1775062406iple_a) B_75) (F_41 X_49))->(((member_pname X_49) A_134)->((member2122167641iple_a B_75) ((image_2063119815iple_a F_41) A_134)))))
% FOF formula (forall (F_40:(pname->hoare_1167836817_state)) (A_133:(pname->Prop)) (B_74:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_40) ((semila1780557381name_o A_133) B_74))) ((semila1172322802tate_o ((image_575578384_state F_40) A_133)) ((image_575578384_state F_40) B_74)))) of role axiom named fact_21_image__Un
% A new axiom: (forall (F_40:(pname->hoare_1167836817_state)) (A_133:(pname->Prop)) (B_74:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_40) ((semila1780557381name_o A_133) B_74))) ((semila1172322802tate_o ((image_575578384_state F_40) A_133)) ((image_575578384_state F_40) B_74))))
% FOF formula (forall (F_40:(hoare_1775062406iple_a->hoare_1167836817_state)) (A_133:(hoare_1775062406iple_a->Prop)) (B_74:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_1021683026_state F_40) ((semila13410563le_a_o A_133) B_74))) ((semila1172322802tate_o ((image_1021683026_state F_40) A_133)) ((image_1021683026_state F_40) B_74)))) of role axiom named fact_22_image__Un
% A new axiom: (forall (F_40:(hoare_1775062406iple_a->hoare_1167836817_state)) (A_133:(hoare_1775062406iple_a->Prop)) (B_74:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_1021683026_state F_40) ((semila13410563le_a_o A_133) B_74))) ((semila1172322802tate_o ((image_1021683026_state F_40) A_133)) ((image_1021683026_state F_40) B_74))))
% FOF formula (forall (F_40:(hoare_1775062406iple_a->pname)) (A_133:(hoare_1775062406iple_a->Prop)) (B_74:(hoare_1775062406iple_a->Prop)), (((eq (pname->Prop)) ((image_51246659_pname F_40) ((semila13410563le_a_o A_133) B_74))) ((semila1780557381name_o ((image_51246659_pname F_40) A_133)) ((image_51246659_pname F_40) B_74)))) of role axiom named fact_23_image__Un
% A new axiom: (forall (F_40:(hoare_1775062406iple_a->pname)) (A_133:(hoare_1775062406iple_a->Prop)) (B_74:(hoare_1775062406iple_a->Prop)), (((eq (pname->Prop)) ((image_51246659_pname F_40) ((semila13410563le_a_o A_133) B_74))) ((semila1780557381name_o ((image_51246659_pname F_40) A_133)) ((image_51246659_pname F_40) B_74))))
% FOF formula (forall (F_40:(hoare_1167836817_state->hoare_1775062406iple_a)) (A_133:(hoare_1167836817_state->Prop)) (B_74:(hoare_1167836817_state->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_1802845250iple_a F_40) ((semila1172322802tate_o A_133) B_74))) ((semila13410563le_a_o ((image_1802845250iple_a F_40) A_133)) ((image_1802845250iple_a F_40) B_74)))) of role axiom named fact_24_image__Un
% A new axiom: (forall (F_40:(hoare_1167836817_state->hoare_1775062406iple_a)) (A_133:(hoare_1167836817_state->Prop)) (B_74:(hoare_1167836817_state->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_1802845250iple_a F_40) ((semila1172322802tate_o A_133) B_74))) ((semila13410563le_a_o ((image_1802845250iple_a F_40) A_133)) ((image_1802845250iple_a F_40) B_74))))
% FOF formula (forall (F_40:(pname->hoare_1775062406iple_a)) (A_133:(pname->Prop)) (B_74:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_40) ((semila1780557381name_o A_133) B_74))) ((semila13410563le_a_o ((image_2063119815iple_a F_40) A_133)) ((image_2063119815iple_a F_40) B_74)))) of role axiom named fact_25_image__Un
% A new axiom: (forall (F_40:(pname->hoare_1775062406iple_a)) (A_133:(pname->Prop)) (B_74:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_40) ((semila1780557381name_o A_133) B_74))) ((semila13410563le_a_o ((image_2063119815iple_a F_40) A_133)) ((image_2063119815iple_a F_40) B_74))))
% FOF formula (forall (F_39:(hoare_1167836817_state->Prop)) (G_23:(hoare_1167836817_state->Prop)) (X:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_39) G_23) X)) ((semila10642723_sup_o (F_39 X)) (G_23 X)))) of role axiom named fact_26_sup__fun__def
% A new axiom: (forall (F_39:(hoare_1167836817_state->Prop)) (G_23:(hoare_1167836817_state->Prop)) (X:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_39) G_23) X)) ((semila10642723_sup_o (F_39 X)) (G_23 X))))
% FOF formula (forall (F_39:(pname->Prop)) (G_23:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o F_39) G_23) X)) ((semila10642723_sup_o (F_39 X)) (G_23 X)))) of role axiom named fact_27_sup__fun__def
% A new axiom: (forall (F_39:(pname->Prop)) (G_23:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o F_39) G_23) X)) ((semila10642723_sup_o (F_39 X)) (G_23 X))))
% FOF formula (forall (F_39:(hoare_1775062406iple_a->Prop)) (G_23:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), ((iff (((semila13410563le_a_o F_39) G_23) X)) ((semila10642723_sup_o (F_39 X)) (G_23 X)))) of role axiom named fact_28_sup__fun__def
% A new axiom: (forall (F_39:(hoare_1775062406iple_a->Prop)) (G_23:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), ((iff (((semila13410563le_a_o F_39) G_23) X)) ((semila10642723_sup_o (F_39 X)) (G_23 X))))
% FOF formula (forall (F_38:(hoare_1167836817_state->Prop)) (G_22:(hoare_1167836817_state->Prop)) (X_48:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_38) G_22) X_48)) ((semila10642723_sup_o (F_38 X_48)) (G_22 X_48)))) of role axiom named fact_29_sup__apply
% A new axiom: (forall (F_38:(hoare_1167836817_state->Prop)) (G_22:(hoare_1167836817_state->Prop)) (X_48:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_38) G_22) X_48)) ((semila10642723_sup_o (F_38 X_48)) (G_22 X_48))))
% FOF formula (forall (F_38:(pname->Prop)) (G_22:(pname->Prop)) (X_48:pname), ((iff (((semila1780557381name_o F_38) G_22) X_48)) ((semila10642723_sup_o (F_38 X_48)) (G_22 X_48)))) of role axiom named fact_30_sup__apply
% A new axiom: (forall (F_38:(pname->Prop)) (G_22:(pname->Prop)) (X_48:pname), ((iff (((semila1780557381name_o F_38) G_22) X_48)) ((semila10642723_sup_o (F_38 X_48)) (G_22 X_48))))
% FOF formula (forall (F_38:(hoare_1775062406iple_a->Prop)) (G_22:(hoare_1775062406iple_a->Prop)) (X_48:hoare_1775062406iple_a), ((iff (((semila13410563le_a_o F_38) G_22) X_48)) ((semila10642723_sup_o (F_38 X_48)) (G_22 X_48)))) of role axiom named fact_31_sup__apply
% A new axiom: (forall (F_38:(hoare_1775062406iple_a->Prop)) (G_22:(hoare_1775062406iple_a->Prop)) (X_48:hoare_1775062406iple_a), ((iff (((semila13410563le_a_o F_38) G_22) X_48)) ((semila10642723_sup_o (F_38 X_48)) (G_22 X_48))))
% FOF formula (forall (G_21:(hoare_1167836817_state->Prop)) (G_20:(hoare_1167836817_state->Prop)) (Ts_3:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_20) Ts_3)->(((hoare_123228589_state G_21) G_20)->((hoare_123228589_state G_21) Ts_3)))) of role axiom named fact_32_cut
% A new axiom: (forall (G_21:(hoare_1167836817_state->Prop)) (G_20:(hoare_1167836817_state->Prop)) (Ts_3:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_20) Ts_3)->(((hoare_123228589_state G_21) G_20)->((hoare_123228589_state G_21) Ts_3))))
% FOF formula (forall (G_21:(hoare_1775062406iple_a->Prop)) (G_20:(hoare_1775062406iple_a->Prop)) (Ts_3:(hoare_1775062406iple_a->Prop)), (((hoare_1508237396rivs_a G_20) Ts_3)->(((hoare_1508237396rivs_a G_21) G_20)->((hoare_1508237396rivs_a G_21) Ts_3)))) of role axiom named fact_33_cut
% A new axiom: (forall (G_21:(hoare_1775062406iple_a->Prop)) (G_20:(hoare_1775062406iple_a->Prop)) (Ts_3:(hoare_1775062406iple_a->Prop)), (((hoare_1508237396rivs_a G_20) Ts_3)->(((hoare_1508237396rivs_a G_21) G_20)->((hoare_1508237396rivs_a G_21) Ts_3))))
% FOF formula (forall (X_47:(hoare_1167836817_state->Prop)) (Y_21:(hoare_1167836817_state->Prop)) (Z_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_47) Y_21)) Z_14)) ((semila1172322802tate_o X_47) ((semila1172322802tate_o Y_21) Z_14)))) of role axiom named fact_34_sup__assoc
% A new axiom: (forall (X_47:(hoare_1167836817_state->Prop)) (Y_21:(hoare_1167836817_state->Prop)) (Z_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_47) Y_21)) Z_14)) ((semila1172322802tate_o X_47) ((semila1172322802tate_o Y_21) Z_14))))
% FOF formula (forall (X_47:(pname->Prop)) (Y_21:(pname->Prop)) (Z_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_47) Y_21)) Z_14)) ((semila1780557381name_o X_47) ((semila1780557381name_o Y_21) Z_14)))) of role axiom named fact_35_sup__assoc
% A new axiom: (forall (X_47:(pname->Prop)) (Y_21:(pname->Prop)) (Z_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_47) Y_21)) Z_14)) ((semila1780557381name_o X_47) ((semila1780557381name_o Y_21) Z_14))))
% FOF formula (forall (X_47:Prop) (Y_21:Prop) (Z_14:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_47) Y_21)) Z_14)) ((semila10642723_sup_o X_47) ((semila10642723_sup_o Y_21) Z_14)))) of role axiom named fact_36_sup__assoc
% A new axiom: (forall (X_47:Prop) (Y_21:Prop) (Z_14:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_47) Y_21)) Z_14)) ((semila10642723_sup_o X_47) ((semila10642723_sup_o Y_21) Z_14))))
% FOF formula (forall (X_47:(hoare_1775062406iple_a->Prop)) (Y_21:(hoare_1775062406iple_a->Prop)) (Z_14:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o X_47) Y_21)) Z_14)) ((semila13410563le_a_o X_47) ((semila13410563le_a_o Y_21) Z_14)))) of role axiom named fact_37_sup__assoc
% A new axiom: (forall (X_47:(hoare_1775062406iple_a->Prop)) (Y_21:(hoare_1775062406iple_a->Prop)) (Z_14:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o X_47) Y_21)) Z_14)) ((semila13410563le_a_o X_47) ((semila13410563le_a_o Y_21) Z_14))))
% FOF formula (forall (X_46:(hoare_1167836817_state->Prop)) (Y_20:(hoare_1167836817_state->Prop)) (Z_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_46) Y_20)) Z_13)) ((semila1172322802tate_o X_46) ((semila1172322802tate_o Y_20) Z_13)))) of role axiom named fact_38_inf__sup__aci_I6_J
% A new axiom: (forall (X_46:(hoare_1167836817_state->Prop)) (Y_20:(hoare_1167836817_state->Prop)) (Z_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_46) Y_20)) Z_13)) ((semila1172322802tate_o X_46) ((semila1172322802tate_o Y_20) Z_13))))
% FOF formula (forall (X_46:(pname->Prop)) (Y_20:(pname->Prop)) (Z_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_46) Y_20)) Z_13)) ((semila1780557381name_o X_46) ((semila1780557381name_o Y_20) Z_13)))) of role axiom named fact_39_inf__sup__aci_I6_J
% A new axiom: (forall (X_46:(pname->Prop)) (Y_20:(pname->Prop)) (Z_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_46) Y_20)) Z_13)) ((semila1780557381name_o X_46) ((semila1780557381name_o Y_20) Z_13))))
% FOF formula (forall (X_46:Prop) (Y_20:Prop) (Z_13:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_46) Y_20)) Z_13)) ((semila10642723_sup_o X_46) ((semila10642723_sup_o Y_20) Z_13)))) of role axiom named fact_40_inf__sup__aci_I6_J
% A new axiom: (forall (X_46:Prop) (Y_20:Prop) (Z_13:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_46) Y_20)) Z_13)) ((semila10642723_sup_o X_46) ((semila10642723_sup_o Y_20) Z_13))))
% FOF formula (forall (X_46:(hoare_1775062406iple_a->Prop)) (Y_20:(hoare_1775062406iple_a->Prop)) (Z_13:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o X_46) Y_20)) Z_13)) ((semila13410563le_a_o X_46) ((semila13410563le_a_o Y_20) Z_13)))) of role axiom named fact_41_inf__sup__aci_I6_J
% A new axiom: (forall (X_46:(hoare_1775062406iple_a->Prop)) (Y_20:(hoare_1775062406iple_a->Prop)) (Z_13:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o X_46) Y_20)) Z_13)) ((semila13410563le_a_o X_46) ((semila13410563le_a_o Y_20) Z_13))))
% FOF formula (forall (A_132:(hoare_1167836817_state->Prop)) (B_73:(hoare_1167836817_state->Prop)) (C_40:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_132) B_73)) C_40)) ((semila1172322802tate_o A_132) ((semila1172322802tate_o B_73) C_40)))) of role axiom named fact_42_sup_Oassoc
% A new axiom: (forall (A_132:(hoare_1167836817_state->Prop)) (B_73:(hoare_1167836817_state->Prop)) (C_40:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_132) B_73)) C_40)) ((semila1172322802tate_o A_132) ((semila1172322802tate_o B_73) C_40))))
% FOF formula (forall (A_132:(pname->Prop)) (B_73:(pname->Prop)) (C_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_132) B_73)) C_40)) ((semila1780557381name_o A_132) ((semila1780557381name_o B_73) C_40)))) of role axiom named fact_43_sup_Oassoc
% A new axiom: (forall (A_132:(pname->Prop)) (B_73:(pname->Prop)) (C_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_132) B_73)) C_40)) ((semila1780557381name_o A_132) ((semila1780557381name_o B_73) C_40))))
% FOF formula (forall (A_132:Prop) (B_73:Prop) (C_40:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_132) B_73)) C_40)) ((semila10642723_sup_o A_132) ((semila10642723_sup_o B_73) C_40)))) of role axiom named fact_44_sup_Oassoc
% A new axiom: (forall (A_132:Prop) (B_73:Prop) (C_40:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_132) B_73)) C_40)) ((semila10642723_sup_o A_132) ((semila10642723_sup_o B_73) C_40))))
% FOF formula (forall (A_132:(hoare_1775062406iple_a->Prop)) (B_73:(hoare_1775062406iple_a->Prop)) (C_40:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o A_132) B_73)) C_40)) ((semila13410563le_a_o A_132) ((semila13410563le_a_o B_73) C_40)))) of role axiom named fact_45_sup_Oassoc
% A new axiom: (forall (A_132:(hoare_1775062406iple_a->Prop)) (B_73:(hoare_1775062406iple_a->Prop)) (C_40:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o A_132) B_73)) C_40)) ((semila13410563le_a_o A_132) ((semila13410563le_a_o B_73) C_40))))
% FOF formula (forall (X_45:(hoare_1167836817_state->Prop)) (Y_19:(hoare_1167836817_state->Prop)) (Z_12:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_45) ((semila1172322802tate_o Y_19) Z_12))) ((semila1172322802tate_o Y_19) ((semila1172322802tate_o X_45) Z_12)))) of role axiom named fact_46_sup__left__commute
% A new axiom: (forall (X_45:(hoare_1167836817_state->Prop)) (Y_19:(hoare_1167836817_state->Prop)) (Z_12:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_45) ((semila1172322802tate_o Y_19) Z_12))) ((semila1172322802tate_o Y_19) ((semila1172322802tate_o X_45) Z_12))))
% FOF formula (forall (X_45:(pname->Prop)) (Y_19:(pname->Prop)) (Z_12:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_45) ((semila1780557381name_o Y_19) Z_12))) ((semila1780557381name_o Y_19) ((semila1780557381name_o X_45) Z_12)))) of role axiom named fact_47_sup__left__commute
% A new axiom: (forall (X_45:(pname->Prop)) (Y_19:(pname->Prop)) (Z_12:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_45) ((semila1780557381name_o Y_19) Z_12))) ((semila1780557381name_o Y_19) ((semila1780557381name_o X_45) Z_12))))
% FOF formula (forall (X_45:Prop) (Y_19:Prop) (Z_12:Prop), ((iff ((semila10642723_sup_o X_45) ((semila10642723_sup_o Y_19) Z_12))) ((semila10642723_sup_o Y_19) ((semila10642723_sup_o X_45) Z_12)))) of role axiom named fact_48_sup__left__commute
% A new axiom: (forall (X_45:Prop) (Y_19:Prop) (Z_12:Prop), ((iff ((semila10642723_sup_o X_45) ((semila10642723_sup_o Y_19) Z_12))) ((semila10642723_sup_o Y_19) ((semila10642723_sup_o X_45) Z_12))))
% FOF formula (forall (X_45:(hoare_1775062406iple_a->Prop)) (Y_19:(hoare_1775062406iple_a->Prop)) (Z_12:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_45) ((semila13410563le_a_o Y_19) Z_12))) ((semila13410563le_a_o Y_19) ((semila13410563le_a_o X_45) Z_12)))) of role axiom named fact_49_sup__left__commute
% A new axiom: (forall (X_45:(hoare_1775062406iple_a->Prop)) (Y_19:(hoare_1775062406iple_a->Prop)) (Z_12:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_45) ((semila13410563le_a_o Y_19) Z_12))) ((semila13410563le_a_o Y_19) ((semila13410563le_a_o X_45) Z_12))))
% FOF formula (forall (X_44:(hoare_1167836817_state->Prop)) (Y_18:(hoare_1167836817_state->Prop)) (Z_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_44) ((semila1172322802tate_o Y_18) Z_11))) ((semila1172322802tate_o Y_18) ((semila1172322802tate_o X_44) Z_11)))) of role axiom named fact_50_inf__sup__aci_I7_J
% A new axiom: (forall (X_44:(hoare_1167836817_state->Prop)) (Y_18:(hoare_1167836817_state->Prop)) (Z_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_44) ((semila1172322802tate_o Y_18) Z_11))) ((semila1172322802tate_o Y_18) ((semila1172322802tate_o X_44) Z_11))))
% FOF formula (forall (X_44:(pname->Prop)) (Y_18:(pname->Prop)) (Z_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_44) ((semila1780557381name_o Y_18) Z_11))) ((semila1780557381name_o Y_18) ((semila1780557381name_o X_44) Z_11)))) of role axiom named fact_51_inf__sup__aci_I7_J
% A new axiom: (forall (X_44:(pname->Prop)) (Y_18:(pname->Prop)) (Z_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_44) ((semila1780557381name_o Y_18) Z_11))) ((semila1780557381name_o Y_18) ((semila1780557381name_o X_44) Z_11))))
% FOF formula (forall (X_44:Prop) (Y_18:Prop) (Z_11:Prop), ((iff ((semila10642723_sup_o X_44) ((semila10642723_sup_o Y_18) Z_11))) ((semila10642723_sup_o Y_18) ((semila10642723_sup_o X_44) Z_11)))) of role axiom named fact_52_inf__sup__aci_I7_J
% A new axiom: (forall (X_44:Prop) (Y_18:Prop) (Z_11:Prop), ((iff ((semila10642723_sup_o X_44) ((semila10642723_sup_o Y_18) Z_11))) ((semila10642723_sup_o Y_18) ((semila10642723_sup_o X_44) Z_11))))
% FOF formula (forall (X_44:(hoare_1775062406iple_a->Prop)) (Y_18:(hoare_1775062406iple_a->Prop)) (Z_11:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_44) ((semila13410563le_a_o Y_18) Z_11))) ((semila13410563le_a_o Y_18) ((semila13410563le_a_o X_44) Z_11)))) of role axiom named fact_53_inf__sup__aci_I7_J
% A new axiom: (forall (X_44:(hoare_1775062406iple_a->Prop)) (Y_18:(hoare_1775062406iple_a->Prop)) (Z_11:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_44) ((semila13410563le_a_o Y_18) Z_11))) ((semila13410563le_a_o Y_18) ((semila13410563le_a_o X_44) Z_11))))
% FOF formula (forall (B_72:(hoare_1167836817_state->Prop)) (A_131:(hoare_1167836817_state->Prop)) (C_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o B_72) ((semila1172322802tate_o A_131) C_39))) ((semila1172322802tate_o A_131) ((semila1172322802tate_o B_72) C_39)))) of role axiom named fact_54_sup_Oleft__commute
% A new axiom: (forall (B_72:(hoare_1167836817_state->Prop)) (A_131:(hoare_1167836817_state->Prop)) (C_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o B_72) ((semila1172322802tate_o A_131) C_39))) ((semila1172322802tate_o A_131) ((semila1172322802tate_o B_72) C_39))))
% FOF formula (forall (B_72:(pname->Prop)) (A_131:(pname->Prop)) (C_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_72) ((semila1780557381name_o A_131) C_39))) ((semila1780557381name_o A_131) ((semila1780557381name_o B_72) C_39)))) of role axiom named fact_55_sup_Oleft__commute
% A new axiom: (forall (B_72:(pname->Prop)) (A_131:(pname->Prop)) (C_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_72) ((semila1780557381name_o A_131) C_39))) ((semila1780557381name_o A_131) ((semila1780557381name_o B_72) C_39))))
% FOF formula (forall (B_72:Prop) (A_131:Prop) (C_39:Prop), ((iff ((semila10642723_sup_o B_72) ((semila10642723_sup_o A_131) C_39))) ((semila10642723_sup_o A_131) ((semila10642723_sup_o B_72) C_39)))) of role axiom named fact_56_sup_Oleft__commute
% A new axiom: (forall (B_72:Prop) (A_131:Prop) (C_39:Prop), ((iff ((semila10642723_sup_o B_72) ((semila10642723_sup_o A_131) C_39))) ((semila10642723_sup_o A_131) ((semila10642723_sup_o B_72) C_39))))
% FOF formula (forall (B_72:(hoare_1775062406iple_a->Prop)) (A_131:(hoare_1775062406iple_a->Prop)) (C_39:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o B_72) ((semila13410563le_a_o A_131) C_39))) ((semila13410563le_a_o A_131) ((semila13410563le_a_o B_72) C_39)))) of role axiom named fact_57_sup_Oleft__commute
% A new axiom: (forall (B_72:(hoare_1775062406iple_a->Prop)) (A_131:(hoare_1775062406iple_a->Prop)) (C_39:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o B_72) ((semila13410563le_a_o A_131) C_39))) ((semila13410563le_a_o A_131) ((semila13410563le_a_o B_72) C_39))))
% FOF formula (forall (X_43:(hoare_1167836817_state->Prop)) (Y_17:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_43) ((semila1172322802tate_o X_43) Y_17))) ((semila1172322802tate_o X_43) Y_17))) of role axiom named fact_58_sup__left__idem
% A new axiom: (forall (X_43:(hoare_1167836817_state->Prop)) (Y_17:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_43) ((semila1172322802tate_o X_43) Y_17))) ((semila1172322802tate_o X_43) Y_17)))
% FOF formula (forall (X_43:(pname->Prop)) (Y_17:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_43) ((semila1780557381name_o X_43) Y_17))) ((semila1780557381name_o X_43) Y_17))) of role axiom named fact_59_sup__left__idem
% A new axiom: (forall (X_43:(pname->Prop)) (Y_17:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_43) ((semila1780557381name_o X_43) Y_17))) ((semila1780557381name_o X_43) Y_17)))
% FOF formula (forall (X_43:Prop) (Y_17:Prop), ((iff ((semila10642723_sup_o X_43) ((semila10642723_sup_o X_43) Y_17))) ((semila10642723_sup_o X_43) Y_17))) of role axiom named fact_60_sup__left__idem
% A new axiom: (forall (X_43:Prop) (Y_17:Prop), ((iff ((semila10642723_sup_o X_43) ((semila10642723_sup_o X_43) Y_17))) ((semila10642723_sup_o X_43) Y_17)))
% FOF formula (forall (X_43:(hoare_1775062406iple_a->Prop)) (Y_17:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_43) ((semila13410563le_a_o X_43) Y_17))) ((semila13410563le_a_o X_43) Y_17))) of role axiom named fact_61_sup__left__idem
% A new axiom: (forall (X_43:(hoare_1775062406iple_a->Prop)) (Y_17:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_43) ((semila13410563le_a_o X_43) Y_17))) ((semila13410563le_a_o X_43) Y_17)))
% FOF formula (forall (X_42:(hoare_1167836817_state->Prop)) (Y_16:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_42) ((semila1172322802tate_o X_42) Y_16))) ((semila1172322802tate_o X_42) Y_16))) of role axiom named fact_62_inf__sup__aci_I8_J
% A new axiom: (forall (X_42:(hoare_1167836817_state->Prop)) (Y_16:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_42) ((semila1172322802tate_o X_42) Y_16))) ((semila1172322802tate_o X_42) Y_16)))
% FOF formula (forall (X_42:(pname->Prop)) (Y_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_42) ((semila1780557381name_o X_42) Y_16))) ((semila1780557381name_o X_42) Y_16))) of role axiom named fact_63_inf__sup__aci_I8_J
% A new axiom: (forall (X_42:(pname->Prop)) (Y_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_42) ((semila1780557381name_o X_42) Y_16))) ((semila1780557381name_o X_42) Y_16)))
% FOF formula (forall (X_42:Prop) (Y_16:Prop), ((iff ((semila10642723_sup_o X_42) ((semila10642723_sup_o X_42) Y_16))) ((semila10642723_sup_o X_42) Y_16))) of role axiom named fact_64_inf__sup__aci_I8_J
% A new axiom: (forall (X_42:Prop) (Y_16:Prop), ((iff ((semila10642723_sup_o X_42) ((semila10642723_sup_o X_42) Y_16))) ((semila10642723_sup_o X_42) Y_16)))
% FOF formula (forall (X_42:(hoare_1775062406iple_a->Prop)) (Y_16:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_42) ((semila13410563le_a_o X_42) Y_16))) ((semila13410563le_a_o X_42) Y_16))) of role axiom named fact_65_inf__sup__aci_I8_J
% A new axiom: (forall (X_42:(hoare_1775062406iple_a->Prop)) (Y_16:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_42) ((semila13410563le_a_o X_42) Y_16))) ((semila13410563le_a_o X_42) Y_16)))
% FOF formula (forall (A_130:(hoare_1167836817_state->Prop)) (B_71:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_130) ((semila1172322802tate_o A_130) B_71))) ((semila1172322802tate_o A_130) B_71))) of role axiom named fact_66_sup_Oleft__idem
% A new axiom: (forall (A_130:(hoare_1167836817_state->Prop)) (B_71:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_130) ((semila1172322802tate_o A_130) B_71))) ((semila1172322802tate_o A_130) B_71)))
% FOF formula (forall (A_130:(pname->Prop)) (B_71:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_130) ((semila1780557381name_o A_130) B_71))) ((semila1780557381name_o A_130) B_71))) of role axiom named fact_67_sup_Oleft__idem
% A new axiom: (forall (A_130:(pname->Prop)) (B_71:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_130) ((semila1780557381name_o A_130) B_71))) ((semila1780557381name_o A_130) B_71)))
% FOF formula (forall (A_130:Prop) (B_71:Prop), ((iff ((semila10642723_sup_o A_130) ((semila10642723_sup_o A_130) B_71))) ((semila10642723_sup_o A_130) B_71))) of role axiom named fact_68_sup_Oleft__idem
% A new axiom: (forall (A_130:Prop) (B_71:Prop), ((iff ((semila10642723_sup_o A_130) ((semila10642723_sup_o A_130) B_71))) ((semila10642723_sup_o A_130) B_71)))
% FOF formula (forall (A_130:(hoare_1775062406iple_a->Prop)) (B_71:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_130) ((semila13410563le_a_o A_130) B_71))) ((semila13410563le_a_o A_130) B_71))) of role axiom named fact_69_sup_Oleft__idem
% A new axiom: (forall (A_130:(hoare_1775062406iple_a->Prop)) (B_71:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_130) ((semila13410563le_a_o A_130) B_71))) ((semila13410563le_a_o A_130) B_71)))
% FOF formula (forall (X_41:(hoare_1167836817_state->Prop)) (Y_15:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_41) Y_15)) ((semila1172322802tate_o Y_15) X_41))) of role axiom named fact_70_sup__commute
% A new axiom: (forall (X_41:(hoare_1167836817_state->Prop)) (Y_15:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_41) Y_15)) ((semila1172322802tate_o Y_15) X_41)))
% FOF formula (forall (X_41:(pname->Prop)) (Y_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_41) Y_15)) ((semila1780557381name_o Y_15) X_41))) of role axiom named fact_71_sup__commute
% A new axiom: (forall (X_41:(pname->Prop)) (Y_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_41) Y_15)) ((semila1780557381name_o Y_15) X_41)))
% FOF formula (forall (X_41:Prop) (Y_15:Prop), ((iff ((semila10642723_sup_o X_41) Y_15)) ((semila10642723_sup_o Y_15) X_41))) of role axiom named fact_72_sup__commute
% A new axiom: (forall (X_41:Prop) (Y_15:Prop), ((iff ((semila10642723_sup_o X_41) Y_15)) ((semila10642723_sup_o Y_15) X_41)))
% FOF formula (forall (X_41:(hoare_1775062406iple_a->Prop)) (Y_15:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_41) Y_15)) ((semila13410563le_a_o Y_15) X_41))) of role axiom named fact_73_sup__commute
% A new axiom: (forall (X_41:(hoare_1775062406iple_a->Prop)) (Y_15:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_41) Y_15)) ((semila13410563le_a_o Y_15) X_41)))
% FOF formula (forall (X_40:(hoare_1167836817_state->Prop)) (Y_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_40) Y_14)) ((semila1172322802tate_o Y_14) X_40))) of role axiom named fact_74_inf__sup__aci_I5_J
% A new axiom: (forall (X_40:(hoare_1167836817_state->Prop)) (Y_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_40) Y_14)) ((semila1172322802tate_o Y_14) X_40)))
% FOF formula (forall (X_40:(pname->Prop)) (Y_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_40) Y_14)) ((semila1780557381name_o Y_14) X_40))) of role axiom named fact_75_inf__sup__aci_I5_J
% A new axiom: (forall (X_40:(pname->Prop)) (Y_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_40) Y_14)) ((semila1780557381name_o Y_14) X_40)))
% FOF formula (forall (X_40:Prop) (Y_14:Prop), ((iff ((semila10642723_sup_o X_40) Y_14)) ((semila10642723_sup_o Y_14) X_40))) of role axiom named fact_76_inf__sup__aci_I5_J
% A new axiom: (forall (X_40:Prop) (Y_14:Prop), ((iff ((semila10642723_sup_o X_40) Y_14)) ((semila10642723_sup_o Y_14) X_40)))
% FOF formula (forall (X_40:(hoare_1775062406iple_a->Prop)) (Y_14:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_40) Y_14)) ((semila13410563le_a_o Y_14) X_40))) of role axiom named fact_77_inf__sup__aci_I5_J
% A new axiom: (forall (X_40:(hoare_1775062406iple_a->Prop)) (Y_14:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_40) Y_14)) ((semila13410563le_a_o Y_14) X_40)))
% FOF formula (forall (A_129:(hoare_1167836817_state->Prop)) (B_70:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_129) B_70)) ((semila1172322802tate_o B_70) A_129))) of role axiom named fact_78_sup_Ocommute
% A new axiom: (forall (A_129:(hoare_1167836817_state->Prop)) (B_70:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_129) B_70)) ((semila1172322802tate_o B_70) A_129)))
% FOF formula (forall (A_129:(pname->Prop)) (B_70:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_129) B_70)) ((semila1780557381name_o B_70) A_129))) of role axiom named fact_79_sup_Ocommute
% A new axiom: (forall (A_129:(pname->Prop)) (B_70:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_129) B_70)) ((semila1780557381name_o B_70) A_129)))
% FOF formula (forall (A_129:Prop) (B_70:Prop), ((iff ((semila10642723_sup_o A_129) B_70)) ((semila10642723_sup_o B_70) A_129))) of role axiom named fact_80_sup_Ocommute
% A new axiom: (forall (A_129:Prop) (B_70:Prop), ((iff ((semila10642723_sup_o A_129) B_70)) ((semila10642723_sup_o B_70) A_129)))
% FOF formula (forall (A_129:(hoare_1775062406iple_a->Prop)) (B_70:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_129) B_70)) ((semila13410563le_a_o B_70) A_129))) of role axiom named fact_81_sup_Ocommute
% A new axiom: (forall (A_129:(hoare_1775062406iple_a->Prop)) (B_70:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_129) B_70)) ((semila13410563le_a_o B_70) A_129)))
% FOF formula (forall (X_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_39) X_39)) X_39)) of role axiom named fact_82_sup__idem
% A new axiom: (forall (X_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_39) X_39)) X_39))
% FOF formula (forall (X_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_39) X_39)) X_39)) of role axiom named fact_83_sup__idem
% A new axiom: (forall (X_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_39) X_39)) X_39))
% FOF formula (forall (X_39:Prop), ((iff ((semila10642723_sup_o X_39) X_39)) X_39)) of role axiom named fact_84_sup__idem
% A new axiom: (forall (X_39:Prop), ((iff ((semila10642723_sup_o X_39) X_39)) X_39))
% FOF formula (forall (X_39:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_39) X_39)) X_39)) of role axiom named fact_85_sup__idem
% A new axiom: (forall (X_39:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_39) X_39)) X_39))
% FOF formula (forall (A_128:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_128) A_128)) A_128)) of role axiom named fact_86_sup_Oidem
% A new axiom: (forall (A_128:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_128) A_128)) A_128))
% FOF formula (forall (A_128:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_128) A_128)) A_128)) of role axiom named fact_87_sup_Oidem
% A new axiom: (forall (A_128:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_128) A_128)) A_128))
% FOF formula (forall (A_128:Prop), ((iff ((semila10642723_sup_o A_128) A_128)) A_128)) of role axiom named fact_88_sup_Oidem
% A new axiom: (forall (A_128:Prop), ((iff ((semila10642723_sup_o A_128) A_128)) A_128))
% FOF formula (forall (A_128:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_128) A_128)) A_128)) of role axiom named fact_89_sup_Oidem
% A new axiom: (forall (A_128:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_128) A_128)) A_128))
% FOF formula (forall (B_69:hoare_1167836817_state) (F_37:(pname->hoare_1167836817_state)) (X_38:pname) (A_127:(pname->Prop)), (((member_pname X_38) A_127)->((((eq hoare_1167836817_state) B_69) (F_37 X_38))->((member2058392318_state B_69) ((image_575578384_state F_37) A_127))))) of role axiom named fact_90_rev__image__eqI
% A new axiom: (forall (B_69:hoare_1167836817_state) (F_37:(pname->hoare_1167836817_state)) (X_38:pname) (A_127:(pname->Prop)), (((member_pname X_38) A_127)->((((eq hoare_1167836817_state) B_69) (F_37 X_38))->((member2058392318_state B_69) ((image_575578384_state F_37) A_127)))))
% FOF formula (forall (B_69:pname) (F_37:(hoare_1775062406iple_a->pname)) (X_38:hoare_1775062406iple_a) (A_127:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a X_38) A_127)->((((eq pname) B_69) (F_37 X_38))->((member_pname B_69) ((image_51246659_pname F_37) A_127))))) of role axiom named fact_91_rev__image__eqI
% A new axiom: (forall (B_69:pname) (F_37:(hoare_1775062406iple_a->pname)) (X_38:hoare_1775062406iple_a) (A_127:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a X_38) A_127)->((((eq pname) B_69) (F_37 X_38))->((member_pname B_69) ((image_51246659_pname F_37) A_127)))))
% FOF formula (forall (B_69:hoare_1775062406iple_a) (F_37:(pname->hoare_1775062406iple_a)) (X_38:pname) (A_127:(pname->Prop)), (((member_pname X_38) A_127)->((((eq hoare_1775062406iple_a) B_69) (F_37 X_38))->((member2122167641iple_a B_69) ((image_2063119815iple_a F_37) A_127))))) of role axiom named fact_92_rev__image__eqI
% A new axiom: (forall (B_69:hoare_1775062406iple_a) (F_37:(pname->hoare_1775062406iple_a)) (X_38:pname) (A_127:(pname->Prop)), (((member_pname X_38) A_127)->((((eq hoare_1775062406iple_a) B_69) (F_37 X_38))->((member2122167641iple_a B_69) ((image_2063119815iple_a F_37) A_127)))))
% FOF formula (forall (F_36:(pname->hoare_1167836817_state)) (X_37:pname) (A_126:(pname->Prop)), (((member_pname X_37) A_126)->((member2058392318_state (F_36 X_37)) ((image_575578384_state F_36) A_126)))) of role axiom named fact_93_imageI
% A new axiom: (forall (F_36:(pname->hoare_1167836817_state)) (X_37:pname) (A_126:(pname->Prop)), (((member_pname X_37) A_126)->((member2058392318_state (F_36 X_37)) ((image_575578384_state F_36) A_126))))
% FOF formula (forall (F_36:(hoare_1775062406iple_a->pname)) (X_37:hoare_1775062406iple_a) (A_126:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a X_37) A_126)->((member_pname (F_36 X_37)) ((image_51246659_pname F_36) A_126)))) of role axiom named fact_94_imageI
% A new axiom: (forall (F_36:(hoare_1775062406iple_a->pname)) (X_37:hoare_1775062406iple_a) (A_126:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a X_37) A_126)->((member_pname (F_36 X_37)) ((image_51246659_pname F_36) A_126))))
% FOF formula (forall (F_36:(pname->hoare_1775062406iple_a)) (X_37:pname) (A_126:(pname->Prop)), (((member_pname X_37) A_126)->((member2122167641iple_a (F_36 X_37)) ((image_2063119815iple_a F_36) A_126)))) of role axiom named fact_95_imageI
% A new axiom: (forall (F_36:(pname->hoare_1775062406iple_a)) (X_37:pname) (A_126:(pname->Prop)), (((member_pname X_37) A_126)->((member2122167641iple_a (F_36 X_37)) ((image_2063119815iple_a F_36) A_126))))
% FOF formula (forall (Z_10:hoare_1167836817_state) (F_35:(pname->hoare_1167836817_state)) (A_125:(pname->Prop)), ((iff ((member2058392318_state Z_10) ((image_575578384_state F_35) A_125))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_125)) (((eq hoare_1167836817_state) Z_10) (F_35 X))))))) of role axiom named fact_96_image__iff
% A new axiom: (forall (Z_10:hoare_1167836817_state) (F_35:(pname->hoare_1167836817_state)) (A_125:(pname->Prop)), ((iff ((member2058392318_state Z_10) ((image_575578384_state F_35) A_125))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_125)) (((eq hoare_1167836817_state) Z_10) (F_35 X)))))))
% FOF formula (forall (Z_10:hoare_1775062406iple_a) (F_35:(pname->hoare_1775062406iple_a)) (A_125:(pname->Prop)), ((iff ((member2122167641iple_a Z_10) ((image_2063119815iple_a F_35) A_125))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_125)) (((eq hoare_1775062406iple_a) Z_10) (F_35 X))))))) of role axiom named fact_97_image__iff
% A new axiom: (forall (Z_10:hoare_1775062406iple_a) (F_35:(pname->hoare_1775062406iple_a)) (A_125:(pname->Prop)), ((iff ((member2122167641iple_a Z_10) ((image_2063119815iple_a F_35) A_125))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_125)) (((eq hoare_1775062406iple_a) Z_10) (F_35 X)))))))
% FOF formula (forall (A_124:(hoare_1167836817_state->Prop)) (C_38:hoare_1167836817_state) (B_68:(hoare_1167836817_state->Prop)), (((member2058392318_state C_38) B_68)->((member2058392318_state C_38) ((semila1172322802tate_o A_124) B_68)))) of role axiom named fact_98_UnI2
% A new axiom: (forall (A_124:(hoare_1167836817_state->Prop)) (C_38:hoare_1167836817_state) (B_68:(hoare_1167836817_state->Prop)), (((member2058392318_state C_38) B_68)->((member2058392318_state C_38) ((semila1172322802tate_o A_124) B_68))))
% FOF formula (forall (A_124:(hoare_1775062406iple_a->Prop)) (C_38:hoare_1775062406iple_a) (B_68:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_38) B_68)->((member2122167641iple_a C_38) ((semila13410563le_a_o A_124) B_68)))) of role axiom named fact_99_UnI2
% A new axiom: (forall (A_124:(hoare_1775062406iple_a->Prop)) (C_38:hoare_1775062406iple_a) (B_68:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_38) B_68)->((member2122167641iple_a C_38) ((semila13410563le_a_o A_124) B_68))))
% FOF formula (forall (A_124:(pname->Prop)) (C_38:pname) (B_68:(pname->Prop)), (((member_pname C_38) B_68)->((member_pname C_38) ((semila1780557381name_o A_124) B_68)))) of role axiom named fact_100_UnI2
% A new axiom: (forall (A_124:(pname->Prop)) (C_38:pname) (B_68:(pname->Prop)), (((member_pname C_38) B_68)->((member_pname C_38) ((semila1780557381name_o A_124) B_68))))
% FOF formula (forall (B_67:(hoare_1167836817_state->Prop)) (C_37:hoare_1167836817_state) (A_123:(hoare_1167836817_state->Prop)), (((member2058392318_state C_37) A_123)->((member2058392318_state C_37) ((semila1172322802tate_o A_123) B_67)))) of role axiom named fact_101_UnI1
% A new axiom: (forall (B_67:(hoare_1167836817_state->Prop)) (C_37:hoare_1167836817_state) (A_123:(hoare_1167836817_state->Prop)), (((member2058392318_state C_37) A_123)->((member2058392318_state C_37) ((semila1172322802tate_o A_123) B_67))))
% FOF formula (forall (B_67:(hoare_1775062406iple_a->Prop)) (C_37:hoare_1775062406iple_a) (A_123:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_37) A_123)->((member2122167641iple_a C_37) ((semila13410563le_a_o A_123) B_67)))) of role axiom named fact_102_UnI1
% A new axiom: (forall (B_67:(hoare_1775062406iple_a->Prop)) (C_37:hoare_1775062406iple_a) (A_123:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_37) A_123)->((member2122167641iple_a C_37) ((semila13410563le_a_o A_123) B_67))))
% FOF formula (forall (B_67:(pname->Prop)) (C_37:pname) (A_123:(pname->Prop)), (((member_pname C_37) A_123)->((member_pname C_37) ((semila1780557381name_o A_123) B_67)))) of role axiom named fact_103_UnI1
% A new axiom: (forall (B_67:(pname->Prop)) (C_37:pname) (A_123:(pname->Prop)), (((member_pname C_37) A_123)->((member_pname C_37) ((semila1780557381name_o A_123) B_67))))
% FOF formula (forall (A_122:(hoare_1167836817_state->Prop)) (B_66:(hoare_1167836817_state->Prop)) (X_36:hoare_1167836817_state), ((B_66 X_36)->(((semila1172322802tate_o A_122) B_66) X_36))) of role axiom named fact_104_sup1I2
% A new axiom: (forall (A_122:(hoare_1167836817_state->Prop)) (B_66:(hoare_1167836817_state->Prop)) (X_36:hoare_1167836817_state), ((B_66 X_36)->(((semila1172322802tate_o A_122) B_66) X_36)))
% FOF formula (forall (A_122:(pname->Prop)) (B_66:(pname->Prop)) (X_36:pname), ((B_66 X_36)->(((semila1780557381name_o A_122) B_66) X_36))) of role axiom named fact_105_sup1I2
% A new axiom: (forall (A_122:(pname->Prop)) (B_66:(pname->Prop)) (X_36:pname), ((B_66 X_36)->(((semila1780557381name_o A_122) B_66) X_36)))
% FOF formula (forall (A_122:(hoare_1775062406iple_a->Prop)) (B_66:(hoare_1775062406iple_a->Prop)) (X_36:hoare_1775062406iple_a), ((B_66 X_36)->(((semila13410563le_a_o A_122) B_66) X_36))) of role axiom named fact_106_sup1I2
% A new axiom: (forall (A_122:(hoare_1775062406iple_a->Prop)) (B_66:(hoare_1775062406iple_a->Prop)) (X_36:hoare_1775062406iple_a), ((B_66 X_36)->(((semila13410563le_a_o A_122) B_66) X_36)))
% FOF formula (forall (B_65:(hoare_1167836817_state->Prop)) (A_121:(hoare_1167836817_state->Prop)) (X_35:hoare_1167836817_state), ((A_121 X_35)->(((semila1172322802tate_o A_121) B_65) X_35))) of role axiom named fact_107_sup1I1
% A new axiom: (forall (B_65:(hoare_1167836817_state->Prop)) (A_121:(hoare_1167836817_state->Prop)) (X_35:hoare_1167836817_state), ((A_121 X_35)->(((semila1172322802tate_o A_121) B_65) X_35)))
% FOF formula (forall (B_65:(pname->Prop)) (A_121:(pname->Prop)) (X_35:pname), ((A_121 X_35)->(((semila1780557381name_o A_121) B_65) X_35))) of role axiom named fact_108_sup1I1
% A new axiom: (forall (B_65:(pname->Prop)) (A_121:(pname->Prop)) (X_35:pname), ((A_121 X_35)->(((semila1780557381name_o A_121) B_65) X_35)))
% FOF formula (forall (B_65:(hoare_1775062406iple_a->Prop)) (A_121:(hoare_1775062406iple_a->Prop)) (X_35:hoare_1775062406iple_a), ((A_121 X_35)->(((semila13410563le_a_o A_121) B_65) X_35))) of role axiom named fact_109_sup1I1
% A new axiom: (forall (B_65:(hoare_1775062406iple_a->Prop)) (A_121:(hoare_1775062406iple_a->Prop)) (X_35:hoare_1775062406iple_a), ((A_121 X_35)->(((semila13410563le_a_o A_121) B_65) X_35)))
% FOF formula (forall (P_36:(hoare_1167836817_state->Prop)) (A_120:(hoare_1167836817_state->Prop)) (B_64:(hoare_1167836817_state->Prop)), ((iff (forall (X:hoare_1167836817_state), (((member2058392318_state X) ((semila1172322802tate_o A_120) B_64))->(P_36 X)))) ((and (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_120)->(P_36 X)))) (forall (X:hoare_1167836817_state), (((member2058392318_state X) B_64)->(P_36 X)))))) of role axiom named fact_110_ball__Un
% A new axiom: (forall (P_36:(hoare_1167836817_state->Prop)) (A_120:(hoare_1167836817_state->Prop)) (B_64:(hoare_1167836817_state->Prop)), ((iff (forall (X:hoare_1167836817_state), (((member2058392318_state X) ((semila1172322802tate_o A_120) B_64))->(P_36 X)))) ((and (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_120)->(P_36 X)))) (forall (X:hoare_1167836817_state), (((member2058392318_state X) B_64)->(P_36 X))))))
% FOF formula (forall (P_36:(pname->Prop)) (A_120:(pname->Prop)) (B_64:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) ((semila1780557381name_o A_120) B_64))->(P_36 X)))) ((and (forall (X:pname), (((member_pname X) A_120)->(P_36 X)))) (forall (X:pname), (((member_pname X) B_64)->(P_36 X)))))) of role axiom named fact_111_ball__Un
% A new axiom: (forall (P_36:(pname->Prop)) (A_120:(pname->Prop)) (B_64:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) ((semila1780557381name_o A_120) B_64))->(P_36 X)))) ((and (forall (X:pname), (((member_pname X) A_120)->(P_36 X)))) (forall (X:pname), (((member_pname X) B_64)->(P_36 X))))))
% FOF formula (forall (P_36:(hoare_1775062406iple_a->Prop)) (A_120:(hoare_1775062406iple_a->Prop)) (B_64:(hoare_1775062406iple_a->Prop)), ((iff (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) ((semila13410563le_a_o A_120) B_64))->(P_36 X)))) ((and (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) A_120)->(P_36 X)))) (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) B_64)->(P_36 X)))))) of role axiom named fact_112_ball__Un
% A new axiom: (forall (P_36:(hoare_1775062406iple_a->Prop)) (A_120:(hoare_1775062406iple_a->Prop)) (B_64:(hoare_1775062406iple_a->Prop)), ((iff (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) ((semila13410563le_a_o A_120) B_64))->(P_36 X)))) ((and (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) A_120)->(P_36 X)))) (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) B_64)->(P_36 X))))))
% FOF formula (forall (P_35:(hoare_1167836817_state->Prop)) (A_119:(hoare_1167836817_state->Prop)) (B_63:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) ((semila1172322802tate_o A_119) B_63))) (P_35 X))))) ((or ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) A_119)) (P_35 X))))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) B_63)) (P_35 X))))))) of role axiom named fact_113_bex__Un
% A new axiom: (forall (P_35:(hoare_1167836817_state->Prop)) (A_119:(hoare_1167836817_state->Prop)) (B_63:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) ((semila1172322802tate_o A_119) B_63))) (P_35 X))))) ((or ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) A_119)) (P_35 X))))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) B_63)) (P_35 X)))))))
% FOF formula (forall (P_35:(pname->Prop)) (A_119:(pname->Prop)) (B_63:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((and ((member_pname X) ((semila1780557381name_o A_119) B_63))) (P_35 X))))) ((or ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_119)) (P_35 X))))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) B_63)) (P_35 X))))))) of role axiom named fact_114_bex__Un
% A new axiom: (forall (P_35:(pname->Prop)) (A_119:(pname->Prop)) (B_63:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((and ((member_pname X) ((semila1780557381name_o A_119) B_63))) (P_35 X))))) ((or ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_119)) (P_35 X))))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) B_63)) (P_35 X)))))))
% FOF formula (forall (P_35:(hoare_1775062406iple_a->Prop)) (A_119:(hoare_1775062406iple_a->Prop)) (B_63:(hoare_1775062406iple_a->Prop)), ((iff ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) ((semila13410563le_a_o A_119) B_63))) (P_35 X))))) ((or ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) A_119)) (P_35 X))))) ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) B_63)) (P_35 X))))))) of role axiom named fact_115_bex__Un
% A new axiom: (forall (P_35:(hoare_1775062406iple_a->Prop)) (A_119:(hoare_1775062406iple_a->Prop)) (B_63:(hoare_1775062406iple_a->Prop)), ((iff ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) ((semila13410563le_a_o A_119) B_63))) (P_35 X))))) ((or ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) A_119)) (P_35 X))))) ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) B_63)) (P_35 X)))))))
% FOF formula (forall (A_118:(hoare_1167836817_state->Prop)) (B_62:(hoare_1167836817_state->Prop)) (C_36:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_118) B_62)) C_36)) ((semila1172322802tate_o A_118) ((semila1172322802tate_o B_62) C_36)))) of role axiom named fact_116_Un__assoc
% A new axiom: (forall (A_118:(hoare_1167836817_state->Prop)) (B_62:(hoare_1167836817_state->Prop)) (C_36:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_118) B_62)) C_36)) ((semila1172322802tate_o A_118) ((semila1172322802tate_o B_62) C_36))))
% FOF formula (forall (A_118:(pname->Prop)) (B_62:(pname->Prop)) (C_36:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_118) B_62)) C_36)) ((semila1780557381name_o A_118) ((semila1780557381name_o B_62) C_36)))) of role axiom named fact_117_Un__assoc
% A new axiom: (forall (A_118:(pname->Prop)) (B_62:(pname->Prop)) (C_36:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_118) B_62)) C_36)) ((semila1780557381name_o A_118) ((semila1780557381name_o B_62) C_36))))
% FOF formula (forall (A_118:(hoare_1775062406iple_a->Prop)) (B_62:(hoare_1775062406iple_a->Prop)) (C_36:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o A_118) B_62)) C_36)) ((semila13410563le_a_o A_118) ((semila13410563le_a_o B_62) C_36)))) of role axiom named fact_118_Un__assoc
% A new axiom: (forall (A_118:(hoare_1775062406iple_a->Prop)) (B_62:(hoare_1775062406iple_a->Prop)) (C_36:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o A_118) B_62)) C_36)) ((semila13410563le_a_o A_118) ((semila13410563le_a_o B_62) C_36))))
% FOF formula (forall (C_35:hoare_1167836817_state) (A_117:(hoare_1167836817_state->Prop)) (B_61:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_35) ((semila1172322802tate_o A_117) B_61))) ((or ((member2058392318_state C_35) A_117)) ((member2058392318_state C_35) B_61)))) of role axiom named fact_119_Un__iff
% A new axiom: (forall (C_35:hoare_1167836817_state) (A_117:(hoare_1167836817_state->Prop)) (B_61:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_35) ((semila1172322802tate_o A_117) B_61))) ((or ((member2058392318_state C_35) A_117)) ((member2058392318_state C_35) B_61))))
% FOF formula (forall (C_35:hoare_1775062406iple_a) (A_117:(hoare_1775062406iple_a->Prop)) (B_61:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a C_35) ((semila13410563le_a_o A_117) B_61))) ((or ((member2122167641iple_a C_35) A_117)) ((member2122167641iple_a C_35) B_61)))) of role axiom named fact_120_Un__iff
% A new axiom: (forall (C_35:hoare_1775062406iple_a) (A_117:(hoare_1775062406iple_a->Prop)) (B_61:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a C_35) ((semila13410563le_a_o A_117) B_61))) ((or ((member2122167641iple_a C_35) A_117)) ((member2122167641iple_a C_35) B_61))))
% FOF formula (forall (C_35:pname) (A_117:(pname->Prop)) (B_61:(pname->Prop)), ((iff ((member_pname C_35) ((semila1780557381name_o A_117) B_61))) ((or ((member_pname C_35) A_117)) ((member_pname C_35) B_61)))) of role axiom named fact_121_Un__iff
% A new axiom: (forall (C_35:pname) (A_117:(pname->Prop)) (B_61:(pname->Prop)), ((iff ((member_pname C_35) ((semila1780557381name_o A_117) B_61))) ((or ((member_pname C_35) A_117)) ((member_pname C_35) B_61))))
% FOF formula (forall (A_116:(hoare_1167836817_state->Prop)) (B_60:(hoare_1167836817_state->Prop)) (C_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_116) ((semila1172322802tate_o B_60) C_34))) ((semila1172322802tate_o B_60) ((semila1172322802tate_o A_116) C_34)))) of role axiom named fact_122_Un__left__commute
% A new axiom: (forall (A_116:(hoare_1167836817_state->Prop)) (B_60:(hoare_1167836817_state->Prop)) (C_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_116) ((semila1172322802tate_o B_60) C_34))) ((semila1172322802tate_o B_60) ((semila1172322802tate_o A_116) C_34))))
% FOF formula (forall (A_116:(pname->Prop)) (B_60:(pname->Prop)) (C_34:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_116) ((semila1780557381name_o B_60) C_34))) ((semila1780557381name_o B_60) ((semila1780557381name_o A_116) C_34)))) of role axiom named fact_123_Un__left__commute
% A new axiom: (forall (A_116:(pname->Prop)) (B_60:(pname->Prop)) (C_34:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_116) ((semila1780557381name_o B_60) C_34))) ((semila1780557381name_o B_60) ((semila1780557381name_o A_116) C_34))))
% FOF formula (forall (A_116:(hoare_1775062406iple_a->Prop)) (B_60:(hoare_1775062406iple_a->Prop)) (C_34:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_116) ((semila13410563le_a_o B_60) C_34))) ((semila13410563le_a_o B_60) ((semila13410563le_a_o A_116) C_34)))) of role axiom named fact_124_Un__left__commute
% A new axiom: (forall (A_116:(hoare_1775062406iple_a->Prop)) (B_60:(hoare_1775062406iple_a->Prop)) (C_34:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_116) ((semila13410563le_a_o B_60) C_34))) ((semila13410563le_a_o B_60) ((semila13410563le_a_o A_116) C_34))))
% FOF formula (forall (A_115:(hoare_1167836817_state->Prop)) (B_59:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_115) ((semila1172322802tate_o A_115) B_59))) ((semila1172322802tate_o A_115) B_59))) of role axiom named fact_125_Un__left__absorb
% A new axiom: (forall (A_115:(hoare_1167836817_state->Prop)) (B_59:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_115) ((semila1172322802tate_o A_115) B_59))) ((semila1172322802tate_o A_115) B_59)))
% FOF formula (forall (A_115:(pname->Prop)) (B_59:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_115) ((semila1780557381name_o A_115) B_59))) ((semila1780557381name_o A_115) B_59))) of role axiom named fact_126_Un__left__absorb
% A new axiom: (forall (A_115:(pname->Prop)) (B_59:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_115) ((semila1780557381name_o A_115) B_59))) ((semila1780557381name_o A_115) B_59)))
% FOF formula (forall (A_115:(hoare_1775062406iple_a->Prop)) (B_59:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_115) ((semila13410563le_a_o A_115) B_59))) ((semila13410563le_a_o A_115) B_59))) of role axiom named fact_127_Un__left__absorb
% A new axiom: (forall (A_115:(hoare_1775062406iple_a->Prop)) (B_59:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_115) ((semila13410563le_a_o A_115) B_59))) ((semila13410563le_a_o A_115) B_59)))
% FOF formula (forall (A_114:(hoare_1167836817_state->Prop)) (B_58:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_114) B_58)) ((semila1172322802tate_o B_58) A_114))) of role axiom named fact_128_Un__commute
% A new axiom: (forall (A_114:(hoare_1167836817_state->Prop)) (B_58:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_114) B_58)) ((semila1172322802tate_o B_58) A_114)))
% FOF formula (forall (A_114:(pname->Prop)) (B_58:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_114) B_58)) ((semila1780557381name_o B_58) A_114))) of role axiom named fact_129_Un__commute
% A new axiom: (forall (A_114:(pname->Prop)) (B_58:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_114) B_58)) ((semila1780557381name_o B_58) A_114)))
% FOF formula (forall (A_114:(hoare_1775062406iple_a->Prop)) (B_58:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_114) B_58)) ((semila13410563le_a_o B_58) A_114))) of role axiom named fact_130_Un__commute
% A new axiom: (forall (A_114:(hoare_1775062406iple_a->Prop)) (B_58:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_114) B_58)) ((semila13410563le_a_o B_58) A_114)))
% FOF formula (forall (A_113:(hoare_1167836817_state->Prop)) (B_57:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_113) B_57)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or ((member2058392318_state X) A_113)) ((member2058392318_state X) B_57)))))) of role axiom named fact_131_Un__def
% A new axiom: (forall (A_113:(hoare_1167836817_state->Prop)) (B_57:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_113) B_57)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or ((member2058392318_state X) A_113)) ((member2058392318_state X) B_57))))))
% FOF formula (forall (A_113:(hoare_1775062406iple_a->Prop)) (B_57:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_113) B_57)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or ((member2122167641iple_a X) A_113)) ((member2122167641iple_a X) B_57)))))) of role axiom named fact_132_Un__def
% A new axiom: (forall (A_113:(hoare_1775062406iple_a->Prop)) (B_57:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_113) B_57)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or ((member2122167641iple_a X) A_113)) ((member2122167641iple_a X) B_57))))))
% FOF formula (forall (A_113:(pname->Prop)) (B_57:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_113) B_57)) (collect_pname (fun (X:pname)=> ((or ((member_pname X) A_113)) ((member_pname X) B_57)))))) of role axiom named fact_133_Un__def
% A new axiom: (forall (A_113:(pname->Prop)) (B_57:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_113) B_57)) (collect_pname (fun (X:pname)=> ((or ((member_pname X) A_113)) ((member_pname X) B_57))))))
% FOF formula (forall (A_112:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_112) A_112)) A_112)) of role axiom named fact_134_Un__absorb
% A new axiom: (forall (A_112:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_112) A_112)) A_112))
% FOF formula (forall (A_112:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_112) A_112)) A_112)) of role axiom named fact_135_Un__absorb
% A new axiom: (forall (A_112:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_112) A_112)) A_112))
% FOF formula (forall (A_112:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_112) A_112)) A_112)) of role axiom named fact_136_Un__absorb
% A new axiom: (forall (A_112:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_112) A_112)) A_112))
% FOF formula (forall (F_34:(hoare_1775062406iple_a->hoare_1167836817_state)) (G_19:(pname->hoare_1775062406iple_a)) (A_111:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_1021683026_state F_34) ((image_2063119815iple_a G_19) A_111))) ((image_575578384_state (fun (X:pname)=> (F_34 (G_19 X)))) A_111))) of role axiom named fact_137_image__image
% A new axiom: (forall (F_34:(hoare_1775062406iple_a->hoare_1167836817_state)) (G_19:(pname->hoare_1775062406iple_a)) (A_111:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_1021683026_state F_34) ((image_2063119815iple_a G_19) A_111))) ((image_575578384_state (fun (X:pname)=> (F_34 (G_19 X)))) A_111)))
% FOF formula (forall (F_34:(hoare_1167836817_state->hoare_1775062406iple_a)) (G_19:(pname->hoare_1167836817_state)) (A_111:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_1802845250iple_a F_34) ((image_575578384_state G_19) A_111))) ((image_2063119815iple_a (fun (X:pname)=> (F_34 (G_19 X)))) A_111))) of role axiom named fact_138_image__image
% A new axiom: (forall (F_34:(hoare_1167836817_state->hoare_1775062406iple_a)) (G_19:(pname->hoare_1167836817_state)) (A_111:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_1802845250iple_a F_34) ((image_575578384_state G_19) A_111))) ((image_2063119815iple_a (fun (X:pname)=> (F_34 (G_19 X)))) A_111)))
% FOF formula (forall (R_2:(hoare_1167836817_state->Prop)) (S_6:(hoare_1167836817_state->Prop)) (X: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_6))) X)) ((member2058392318_state X) ((semila1172322802tate_o R_2) S_6)))) of role axiom named fact_139_sup__Un__eq
% A new axiom: (forall (R_2:(hoare_1167836817_state->Prop)) (S_6:(hoare_1167836817_state->Prop)) (X: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_6))) X)) ((member2058392318_state X) ((semila1172322802tate_o R_2) S_6))))
% FOF formula (forall (R_2:(hoare_1775062406iple_a->Prop)) (S_6:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), ((iff (((semila13410563le_a_o (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) R_2))) (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) S_6))) X)) ((member2122167641iple_a X) ((semila13410563le_a_o R_2) S_6)))) of role axiom named fact_140_sup__Un__eq
% A new axiom: (forall (R_2:(hoare_1775062406iple_a->Prop)) (S_6:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), ((iff (((semila13410563le_a_o (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) R_2))) (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) S_6))) X)) ((member2122167641iple_a X) ((semila13410563le_a_o R_2) S_6))))
% FOF formula (forall (R_2:(pname->Prop)) (S_6:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o (fun (Y_2:pname)=> ((member_pname Y_2) R_2))) (fun (Y_2:pname)=> ((member_pname Y_2) S_6))) X)) ((member_pname X) ((semila1780557381name_o R_2) S_6)))) of role axiom named fact_141_sup__Un__eq
% A new axiom: (forall (R_2:(pname->Prop)) (S_6:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o (fun (Y_2:pname)=> ((member_pname Y_2) R_2))) (fun (Y_2:pname)=> ((member_pname Y_2) S_6))) X)) ((member_pname X) ((semila1780557381name_o R_2) S_6))))
% FOF formula (forall (P_34:(pname->Prop)) (Q_19:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((or (P_34 X)) (Q_19 X))))) ((semila1780557381name_o (collect_pname P_34)) (collect_pname Q_19)))) of role axiom named fact_142_Collect__disj__eq
% A new axiom: (forall (P_34:(pname->Prop)) (Q_19:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((or (P_34 X)) (Q_19 X))))) ((semila1780557381name_o (collect_pname P_34)) (collect_pname Q_19))))
% FOF formula (forall (P_34:(hoare_1167836817_state->Prop)) (Q_19:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or (P_34 X)) (Q_19 X))))) ((semila1172322802tate_o (collec1027672124_state P_34)) (collec1027672124_state Q_19)))) of role axiom named fact_143_Collect__disj__eq
% A new axiom: (forall (P_34:(hoare_1167836817_state->Prop)) (Q_19:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or (P_34 X)) (Q_19 X))))) ((semila1172322802tate_o (collec1027672124_state P_34)) (collec1027672124_state Q_19))))
% FOF formula (forall (P_34:(hoare_1775062406iple_a->Prop)) (Q_19:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or (P_34 X)) (Q_19 X))))) ((semila13410563le_a_o (collec676402587iple_a P_34)) (collec676402587iple_a Q_19)))) of role axiom named fact_144_Collect__disj__eq
% A new axiom: (forall (P_34:(hoare_1775062406iple_a->Prop)) (Q_19:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or (P_34 X)) (Q_19 X))))) ((semila13410563le_a_o (collec676402587iple_a P_34)) (collec676402587iple_a Q_19))))
% FOF formula (forall (B_56:pname) (F_33:(hoare_1775062406iple_a->pname)) (A_110:(hoare_1775062406iple_a->Prop)), (((member_pname B_56) ((image_51246659_pname F_33) A_110))->((forall (X:hoare_1775062406iple_a), ((((eq pname) B_56) (F_33 X))->(((member2122167641iple_a X) A_110)->False)))->False))) of role axiom named fact_145_imageE
% A new axiom: (forall (B_56:pname) (F_33:(hoare_1775062406iple_a->pname)) (A_110:(hoare_1775062406iple_a->Prop)), (((member_pname B_56) ((image_51246659_pname F_33) A_110))->((forall (X:hoare_1775062406iple_a), ((((eq pname) B_56) (F_33 X))->(((member2122167641iple_a X) A_110)->False)))->False)))
% FOF formula (forall (B_56:hoare_1167836817_state) (F_33:(pname->hoare_1167836817_state)) (A_110:(pname->Prop)), (((member2058392318_state B_56) ((image_575578384_state F_33) A_110))->((forall (X:pname), ((((eq hoare_1167836817_state) B_56) (F_33 X))->(((member_pname X) A_110)->False)))->False))) of role axiom named fact_146_imageE
% A new axiom: (forall (B_56:hoare_1167836817_state) (F_33:(pname->hoare_1167836817_state)) (A_110:(pname->Prop)), (((member2058392318_state B_56) ((image_575578384_state F_33) A_110))->((forall (X:pname), ((((eq hoare_1167836817_state) B_56) (F_33 X))->(((member_pname X) A_110)->False)))->False)))
% FOF formula (forall (B_56:hoare_1775062406iple_a) (F_33:(pname->hoare_1775062406iple_a)) (A_110:(pname->Prop)), (((member2122167641iple_a B_56) ((image_2063119815iple_a F_33) A_110))->((forall (X:pname), ((((eq hoare_1775062406iple_a) B_56) (F_33 X))->(((member_pname X) A_110)->False)))->False))) of role axiom named fact_147_imageE
% A new axiom: (forall (B_56:hoare_1775062406iple_a) (F_33:(pname->hoare_1775062406iple_a)) (A_110:(pname->Prop)), (((member2122167641iple_a B_56) ((image_2063119815iple_a F_33) A_110))->((forall (X:pname), ((((eq hoare_1775062406iple_a) B_56) (F_33 X))->(((member_pname X) A_110)->False)))->False)))
% FOF formula (forall (N_8:nat) (P_33:(state->(state->Prop))) (Pn_6:pname) (Q_18:(state->(state->Prop))), ((iff ((hoare_56934129_state N_8) (((hoare_908217195_state P_33) (the_com (body_1 Pn_6))) Q_18))) ((hoare_56934129_state (suc N_8)) (((hoare_908217195_state P_33) (body Pn_6)) Q_18)))) of role axiom named fact_148_Body__triple__valid__Suc
% A new axiom: (forall (N_8:nat) (P_33:(state->(state->Prop))) (Pn_6:pname) (Q_18:(state->(state->Prop))), ((iff ((hoare_56934129_state N_8) (((hoare_908217195_state P_33) (the_com (body_1 Pn_6))) Q_18))) ((hoare_56934129_state (suc N_8)) (((hoare_908217195_state P_33) (body Pn_6)) Q_18))))
% FOF formula (forall (N_8:nat) (P_33:(x_a->(state->Prop))) (Pn_6:pname) (Q_18:(x_a->(state->Prop))), ((iff ((hoare_1462269968alid_a N_8) (((hoare_1766022166iple_a P_33) (the_com (body_1 Pn_6))) Q_18))) ((hoare_1462269968alid_a (suc N_8)) (((hoare_1766022166iple_a P_33) (body Pn_6)) Q_18)))) of role axiom named fact_149_Body__triple__valid__Suc
% A new axiom: (forall (N_8:nat) (P_33:(x_a->(state->Prop))) (Pn_6:pname) (Q_18:(x_a->(state->Prop))), ((iff ((hoare_1462269968alid_a N_8) (((hoare_1766022166iple_a P_33) (the_com (body_1 Pn_6))) Q_18))) ((hoare_1462269968alid_a (suc N_8)) (((hoare_1766022166iple_a P_33) (body Pn_6)) Q_18))))
% FOF formula (forall (Y_13:hoare_1775062406iple_a), ((forall (Fun1_2:(x_a->(state->Prop))) (Com_4:com) (Fun2_2:(x_a->(state->Prop))), (not (((eq hoare_1775062406iple_a) Y_13) (((hoare_1766022166iple_a Fun1_2) Com_4) Fun2_2))))->False)) of role axiom named fact_150_triple_Oexhaust
% A new axiom: (forall (Y_13:hoare_1775062406iple_a), ((forall (Fun1_2:(x_a->(state->Prop))) (Com_4:com) (Fun2_2:(x_a->(state->Prop))), (not (((eq hoare_1775062406iple_a) Y_13) (((hoare_1766022166iple_a Fun1_2) Com_4) Fun2_2))))->False))
% FOF formula (forall (Y_13:hoare_1167836817_state), ((forall (Fun1_2:(state->(state->Prop))) (Com_4:com) (Fun2_2:(state->(state->Prop))), (not (((eq hoare_1167836817_state) Y_13) (((hoare_908217195_state Fun1_2) Com_4) Fun2_2))))->False)) of role axiom named fact_151_triple_Oexhaust
% A new axiom: (forall (Y_13:hoare_1167836817_state), ((forall (Fun1_2:(state->(state->Prop))) (Com_4:com) (Fun2_2:(state->(state->Prop))), (not (((eq hoare_1167836817_state) Y_13) (((hoare_908217195_state Fun1_2) Com_4) Fun2_2))))->False))
% FOF formula (forall (Pn_5:pname) (G_18:(hoare_1167836817_state->Prop)) (P_32:(pname->(state->(state->Prop)))) (Q_17:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_18) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_32 P_10)) (body P_10)) (Q_17 P_10)))) Procs))) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_32 P_10)) (the_com (body_1 P_10))) (Q_17 P_10)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state (P_32 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo70021908tate_o))))) of role axiom named fact_152_Body1
% A new axiom: (forall (Pn_5:pname) (G_18:(hoare_1167836817_state->Prop)) (P_32:(pname->(state->(state->Prop)))) (Q_17:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_18) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_32 P_10)) (body P_10)) (Q_17 P_10)))) Procs))) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_32 P_10)) (the_com (body_1 P_10))) (Q_17 P_10)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state (P_32 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo70021908tate_o)))))
% FOF formula (forall (Pn_5:pname) (G_18:(hoare_1775062406iple_a->Prop)) (P_32:(pname->(x_a->(state->Prop)))) (Q_17:(pname->(x_a->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_1508237396rivs_a ((semila13410563le_a_o G_18) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_32 P_10)) (body P_10)) (Q_17 P_10)))) Procs))) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_32 P_10)) (the_com (body_1 P_10))) (Q_17 P_10)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_1508237396rivs_a G_18) ((insert1281456128iple_a (((hoare_1766022166iple_a (P_32 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo751897185le_a_o))))) of role axiom named fact_153_Body1
% A new axiom: (forall (Pn_5:pname) (G_18:(hoare_1775062406iple_a->Prop)) (P_32:(pname->(x_a->(state->Prop)))) (Q_17:(pname->(x_a->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_1508237396rivs_a ((semila13410563le_a_o G_18) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_32 P_10)) (body P_10)) (Q_17 P_10)))) Procs))) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_32 P_10)) (the_com (body_1 P_10))) (Q_17 P_10)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_1508237396rivs_a G_18) ((insert1281456128iple_a (((hoare_1766022166iple_a (P_32 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo751897185le_a_o)))))
% FOF formula (forall (F_32:(pname->hoare_1167836817_state)) (G_17:(pname->hoare_1167836817_state)) (M_2:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_2) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_1167836817_state) (F_32 X)) (G_17 X))))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_32) M_2)) ((image_575578384_state G_17) N_7))))) of role axiom named fact_154_image__cong
% A new axiom: (forall (F_32:(pname->hoare_1167836817_state)) (G_17:(pname->hoare_1167836817_state)) (M_2:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_2) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_1167836817_state) (F_32 X)) (G_17 X))))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_32) M_2)) ((image_575578384_state G_17) N_7)))))
% FOF formula (forall (F_32:(pname->hoare_1775062406iple_a)) (G_17:(pname->hoare_1775062406iple_a)) (M_2:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_2) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_1775062406iple_a) (F_32 X)) (G_17 X))))->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_32) M_2)) ((image_2063119815iple_a G_17) N_7))))) of role axiom named fact_155_image__cong
% A new axiom: (forall (F_32:(pname->hoare_1775062406iple_a)) (G_17:(pname->hoare_1775062406iple_a)) (M_2:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_2) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_1775062406iple_a) (F_32 X)) (G_17 X))))->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_32) M_2)) ((image_2063119815iple_a G_17) N_7)))))
% FOF formula (forall (P_31:(state->(state->Prop))) (Pn_4:pname) (Q_16:(state->(state->Prop))), ((hoare_56934129_state zero_zero_nat) (((hoare_908217195_state P_31) (body Pn_4)) Q_16))) of role axiom named fact_156_Body__triple__valid__0
% A new axiom: (forall (P_31:(state->(state->Prop))) (Pn_4:pname) (Q_16:(state->(state->Prop))), ((hoare_56934129_state zero_zero_nat) (((hoare_908217195_state P_31) (body Pn_4)) Q_16)))
% FOF formula (forall (P_31:(x_a->(state->Prop))) (Pn_4:pname) (Q_16:(x_a->(state->Prop))), ((hoare_1462269968alid_a zero_zero_nat) (((hoare_1766022166iple_a P_31) (body Pn_4)) Q_16))) of role axiom named fact_157_Body__triple__valid__0
% A new axiom: (forall (P_31:(x_a->(state->Prop))) (Pn_4:pname) (Q_16:(x_a->(state->Prop))), ((hoare_1462269968alid_a zero_zero_nat) (((hoare_1766022166iple_a P_31) (body Pn_4)) Q_16)))
% FOF formula (forall (Pname:pname) (Pname_1:pname), ((iff (((eq com) (body Pname)) (body Pname_1))) (((eq pname) Pname) Pname_1))) of role axiom named fact_158_com_Osimps_I6_J
% A new axiom: (forall (Pname:pname) (Pname_1:pname), ((iff (((eq com) (body Pname)) (body Pname_1))) (((eq pname) Pname) Pname_1)))
% FOF formula (forall (Pn_1:pname) (S0:state) (S1:state), ((((evalc (the_com (body_1 Pn_1))) S0) S1)->(((evalc (body Pn_1)) S0) S1))) of role axiom named fact_159_evalc_OBody
% A new axiom: (forall (Pn_1:pname) (S0:state) (S1:state), ((((evalc (the_com (body_1 Pn_1))) S0) S1)->(((evalc (body Pn_1)) S0) S1)))
% FOF formula (forall (P:pname) (S:state) (S1:state), ((((evalc (body P)) S) S1)->(((evalc (the_com (body_1 P))) S) S1))) of role axiom named fact_160_evalc__elim__cases_I6_J
% A new axiom: (forall (P:pname) (S:state) (S1:state), ((((evalc (body P)) S) S1)->(((evalc (the_com (body_1 P))) S) S1)))
% FOF formula (forall (X_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_34) X_34)) X_34)) of role axiom named fact_161_Sup__fin_Oidem
% A new axiom: (forall (X_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_34) X_34)) X_34))
% FOF formula (forall (X_34:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_34) X_34)) X_34)) of role axiom named fact_162_Sup__fin_Oidem
% A new axiom: (forall (X_34:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_34) X_34)) X_34))
% FOF formula (forall (X_34:Prop), ((iff ((semila10642723_sup_o X_34) X_34)) X_34)) of role axiom named fact_163_Sup__fin_Oidem
% A new axiom: (forall (X_34:Prop), ((iff ((semila10642723_sup_o X_34) X_34)) X_34))
% FOF formula (forall (X_34:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_34) X_34)) X_34)) of role axiom named fact_164_Sup__fin_Oidem
% A new axiom: (forall (X_34:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_34) X_34)) X_34))
% FOF formula (forall (A_109:hoare_1775062406iple_a), (((member2122167641iple_a A_109) bot_bo751897185le_a_o)->False)) of role axiom named fact_165_emptyE
% A new axiom: (forall (A_109:hoare_1775062406iple_a), (((member2122167641iple_a A_109) bot_bo751897185le_a_o)->False))
% FOF formula (forall (A_109:hoare_1167836817_state), (((member2058392318_state A_109) bot_bo70021908tate_o)->False)) of role axiom named fact_166_emptyE
% A new axiom: (forall (A_109:hoare_1167836817_state), (((member2058392318_state A_109) bot_bo70021908tate_o)->False))
% FOF formula (forall (A_109:pname), (((member_pname A_109) bot_bot_pname_o)->False)) of role axiom named fact_167_emptyE
% A new axiom: (forall (A_109:pname), (((member_pname A_109) bot_bot_pname_o)->False))
% FOF formula (forall (A_108:hoare_1167836817_state) (B_55:hoare_1167836817_state) (A_107:(hoare_1167836817_state->Prop)), (((member2058392318_state A_108) ((insert2134838167_state B_55) A_107))->((not (((eq hoare_1167836817_state) A_108) B_55))->((member2058392318_state A_108) A_107)))) of role axiom named fact_168_insertE
% A new axiom: (forall (A_108:hoare_1167836817_state) (B_55:hoare_1167836817_state) (A_107:(hoare_1167836817_state->Prop)), (((member2058392318_state A_108) ((insert2134838167_state B_55) A_107))->((not (((eq hoare_1167836817_state) A_108) B_55))->((member2058392318_state A_108) A_107))))
% FOF formula (forall (A_108:hoare_1775062406iple_a) (B_55:hoare_1775062406iple_a) (A_107:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_108) ((insert1281456128iple_a B_55) A_107))->((not (((eq hoare_1775062406iple_a) A_108) B_55))->((member2122167641iple_a A_108) A_107)))) of role axiom named fact_169_insertE
% A new axiom: (forall (A_108:hoare_1775062406iple_a) (B_55:hoare_1775062406iple_a) (A_107:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_108) ((insert1281456128iple_a B_55) A_107))->((not (((eq hoare_1775062406iple_a) A_108) B_55))->((member2122167641iple_a A_108) A_107))))
% FOF formula (forall (A_108:pname) (B_55:pname) (A_107:(pname->Prop)), (((member_pname A_108) ((insert_pname B_55) A_107))->((not (((eq pname) A_108) B_55))->((member_pname A_108) A_107)))) of role axiom named fact_170_insertE
% A new axiom: (forall (A_108:pname) (B_55:pname) (A_107:(pname->Prop)), (((member_pname A_108) ((insert_pname B_55) A_107))->((not (((eq pname) A_108) B_55))->((member_pname A_108) A_107))))
% FOF formula (forall (B_54:hoare_1167836817_state) (A_106:hoare_1167836817_state) (B_53:(hoare_1167836817_state->Prop)), (((((member2058392318_state A_106) B_53)->False)->(((eq hoare_1167836817_state) A_106) B_54))->((member2058392318_state A_106) ((insert2134838167_state B_54) B_53)))) of role axiom named fact_171_insertCI
% A new axiom: (forall (B_54:hoare_1167836817_state) (A_106:hoare_1167836817_state) (B_53:(hoare_1167836817_state->Prop)), (((((member2058392318_state A_106) B_53)->False)->(((eq hoare_1167836817_state) A_106) B_54))->((member2058392318_state A_106) ((insert2134838167_state B_54) B_53))))
% FOF formula (forall (B_54:hoare_1775062406iple_a) (A_106:hoare_1775062406iple_a) (B_53:(hoare_1775062406iple_a->Prop)), (((((member2122167641iple_a A_106) B_53)->False)->(((eq hoare_1775062406iple_a) A_106) B_54))->((member2122167641iple_a A_106) ((insert1281456128iple_a B_54) B_53)))) of role axiom named fact_172_insertCI
% A new axiom: (forall (B_54:hoare_1775062406iple_a) (A_106:hoare_1775062406iple_a) (B_53:(hoare_1775062406iple_a->Prop)), (((((member2122167641iple_a A_106) B_53)->False)->(((eq hoare_1775062406iple_a) A_106) B_54))->((member2122167641iple_a A_106) ((insert1281456128iple_a B_54) B_53))))
% FOF formula (forall (B_54:pname) (A_106:pname) (B_53:(pname->Prop)), (((((member_pname A_106) B_53)->False)->(((eq pname) A_106) B_54))->((member_pname A_106) ((insert_pname B_54) B_53)))) of role axiom named fact_173_insertCI
% A new axiom: (forall (B_54:pname) (A_106:pname) (B_53:(pname->Prop)), (((((member_pname A_106) B_53)->False)->(((eq pname) A_106) B_54))->((member_pname A_106) ((insert_pname B_54) B_53))))
% FOF formula (forall (A_105:hoare_1167836817_state) (A_104:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((insert2134838167_state A_105) A_104)))) of role axiom named fact_174_empty__not__insert
% A new axiom: (forall (A_105:hoare_1167836817_state) (A_104:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((insert2134838167_state A_105) A_104))))
% FOF formula (forall (A_105:hoare_1775062406iple_a) (A_104:(hoare_1775062406iple_a->Prop)), (not (((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) ((insert1281456128iple_a A_105) A_104)))) of role axiom named fact_175_empty__not__insert
% A new axiom: (forall (A_105:hoare_1775062406iple_a) (A_104:(hoare_1775062406iple_a->Prop)), (not (((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) ((insert1281456128iple_a A_105) A_104))))
% FOF formula (forall (A_105:pname) (A_104:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_105) A_104)))) of role axiom named fact_176_empty__not__insert
% A new axiom: (forall (A_105:pname) (A_104:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_105) A_104))))
% FOF formula (forall (A_103:hoare_1167836817_state) (A_102:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_103) A_102)) bot_bo70021908tate_o))) of role axiom named fact_177_insert__not__empty
% A new axiom: (forall (A_103:hoare_1167836817_state) (A_102:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_103) A_102)) bot_bo70021908tate_o)))
% FOF formula (forall (A_103:hoare_1775062406iple_a) (A_102:(hoare_1775062406iple_a->Prop)), (not (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_103) A_102)) bot_bo751897185le_a_o))) of role axiom named fact_178_insert__not__empty
% A new axiom: (forall (A_103:hoare_1775062406iple_a) (A_102:(hoare_1775062406iple_a->Prop)), (not (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_103) A_102)) bot_bo751897185le_a_o)))
% FOF formula (forall (A_103:pname) (A_102:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_103) A_102)) bot_bot_pname_o))) of role axiom named fact_179_insert__not__empty
% A new axiom: (forall (A_103:pname) (A_102:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_103) A_102)) bot_bot_pname_o)))
% FOF formula (forall (X:hoare_1775062406iple_a), ((iff (bot_bo751897185le_a_o X)) ((member2122167641iple_a X) bot_bo751897185le_a_o))) of role axiom named fact_180_bot__empty__eq
% A new axiom: (forall (X:hoare_1775062406iple_a), ((iff (bot_bo751897185le_a_o X)) ((member2122167641iple_a X) bot_bo751897185le_a_o)))
% FOF formula (forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) ((member2058392318_state X) bot_bo70021908tate_o))) of role axiom named fact_181_bot__empty__eq
% A new axiom: (forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) ((member2058392318_state X) bot_bo70021908tate_o)))
% FOF formula (forall (X:pname), ((iff (bot_bot_pname_o X)) ((member_pname X) bot_bot_pname_o))) of role axiom named fact_182_bot__empty__eq
% A new axiom: (forall (X:pname), ((iff (bot_bot_pname_o X)) ((member_pname X) bot_bot_pname_o)))
% FOF formula (((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> False))) of role axiom named fact_183_empty__def
% A new axiom: (((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> False)))
% FOF formula (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X:pname)=> False))) of role axiom named fact_184_empty__def
% A new axiom: (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X:pname)=> False)))
% FOF formula (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state (fun (X:hoare_1167836817_state)=> False))) of role axiom named fact_185_empty__def
% A new axiom: (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state (fun (X:hoare_1167836817_state)=> False)))
% FOF formula (forall (A_101:hoare_1167836817_state) (B_52:(hoare_1167836817_state->Prop)), ((member2058392318_state A_101) ((insert2134838167_state A_101) B_52))) of role axiom named fact_186_insertI1
% A new axiom: (forall (A_101:hoare_1167836817_state) (B_52:(hoare_1167836817_state->Prop)), ((member2058392318_state A_101) ((insert2134838167_state A_101) B_52)))
% FOF formula (forall (A_101:hoare_1775062406iple_a) (B_52:(hoare_1775062406iple_a->Prop)), ((member2122167641iple_a A_101) ((insert1281456128iple_a A_101) B_52))) of role axiom named fact_187_insertI1
% A new axiom: (forall (A_101:hoare_1775062406iple_a) (B_52:(hoare_1775062406iple_a->Prop)), ((member2122167641iple_a A_101) ((insert1281456128iple_a A_101) B_52)))
% FOF formula (forall (A_101:pname) (B_52:(pname->Prop)), ((member_pname A_101) ((insert_pname A_101) B_52))) of role axiom named fact_188_insertI1
% A new axiom: (forall (A_101:pname) (B_52:(pname->Prop)), ((member_pname A_101) ((insert_pname A_101) B_52)))
% FOF formula (forall (A_100:(hoare_1775062406iple_a->Prop)), ((iff (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) A_100)->False))) (((eq (hoare_1775062406iple_a->Prop)) A_100) bot_bo751897185le_a_o))) of role axiom named fact_189_all__not__in__conv
% A new axiom: (forall (A_100:(hoare_1775062406iple_a->Prop)), ((iff (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) A_100)->False))) (((eq (hoare_1775062406iple_a->Prop)) A_100) bot_bo751897185le_a_o)))
% FOF formula (forall (A_100:(hoare_1167836817_state->Prop)), ((iff (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_100)->False))) (((eq (hoare_1167836817_state->Prop)) A_100) bot_bo70021908tate_o))) of role axiom named fact_190_all__not__in__conv
% A new axiom: (forall (A_100:(hoare_1167836817_state->Prop)), ((iff (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_100)->False))) (((eq (hoare_1167836817_state->Prop)) A_100) bot_bo70021908tate_o)))
% FOF formula (forall (A_100:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) A_100)->False))) (((eq (pname->Prop)) A_100) bot_bot_pname_o))) of role axiom named fact_191_all__not__in__conv
% A new axiom: (forall (A_100:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) A_100)->False))) (((eq (pname->Prop)) A_100) bot_bot_pname_o)))
% FOF formula (forall (A_99:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fequal1831255762_state A_99))) ((insert2134838167_state A_99) bot_bo70021908tate_o))) of role axiom named fact_192_singleton__conv2
% A new axiom: (forall (A_99:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fequal1831255762_state A_99))) ((insert2134838167_state A_99) bot_bo70021908tate_o)))
% FOF formula (forall (A_99:hoare_1775062406iple_a), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fequal1288209029iple_a A_99))) ((insert1281456128iple_a A_99) bot_bo751897185le_a_o))) of role axiom named fact_193_singleton__conv2
% A new axiom: (forall (A_99:hoare_1775062406iple_a), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fequal1288209029iple_a A_99))) ((insert1281456128iple_a A_99) bot_bo751897185le_a_o)))
% FOF formula (forall (A_99:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_99))) ((insert_pname A_99) bot_bot_pname_o))) of role axiom named fact_194_singleton__conv2
% A new axiom: (forall (A_99:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_99))) ((insert_pname A_99) bot_bot_pname_o)))
% FOF formula (forall (A_98:(hoare_1775062406iple_a->Prop)), ((iff ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((member2122167641iple_a X) A_98)))) (not (((eq (hoare_1775062406iple_a->Prop)) A_98) bot_bo751897185le_a_o)))) of role axiom named fact_195_ex__in__conv
% A new axiom: (forall (A_98:(hoare_1775062406iple_a->Prop)), ((iff ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((member2122167641iple_a X) A_98)))) (not (((eq (hoare_1775062406iple_a->Prop)) A_98) bot_bo751897185le_a_o))))
% FOF formula (forall (A_98:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((member2058392318_state X) A_98)))) (not (((eq (hoare_1167836817_state->Prop)) A_98) bot_bo70021908tate_o)))) of role axiom named fact_196_ex__in__conv
% A new axiom: (forall (A_98:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((member2058392318_state X) A_98)))) (not (((eq (hoare_1167836817_state->Prop)) A_98) bot_bo70021908tate_o))))
% FOF formula (forall (A_98:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((member_pname X) A_98)))) (not (((eq (pname->Prop)) A_98) bot_bot_pname_o)))) of role axiom named fact_197_ex__in__conv
% A new axiom: (forall (A_98:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((member_pname X) A_98)))) (not (((eq (pname->Prop)) A_98) bot_bot_pname_o))))
% FOF formula (forall (A_97:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X) A_97)))) ((insert2134838167_state A_97) bot_bo70021908tate_o))) of role axiom named fact_198_singleton__conv
% A new axiom: (forall (A_97:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X) A_97)))) ((insert2134838167_state A_97) bot_bo70021908tate_o)))
% FOF formula (forall (A_97:hoare_1775062406iple_a), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> (((eq hoare_1775062406iple_a) X) A_97)))) ((insert1281456128iple_a A_97) bot_bo751897185le_a_o))) of role axiom named fact_199_singleton__conv
% A new axiom: (forall (A_97:hoare_1775062406iple_a), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> (((eq hoare_1775062406iple_a) X) A_97)))) ((insert1281456128iple_a A_97) bot_bo751897185le_a_o)))
% FOF formula (forall (A_97:pname), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> (((eq pname) X) A_97)))) ((insert_pname A_97) bot_bot_pname_o))) of role axiom named fact_200_singleton__conv
% A new axiom: (forall (A_97:pname), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> (((eq pname) X) A_97)))) ((insert_pname A_97) bot_bot_pname_o)))
% FOF formula (forall (P_30:(hoare_1167836817_state->Prop)) (A_96:hoare_1167836817_state), ((and ((P_30 A_96)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_96) X)) (P_30 X))))) ((insert2134838167_state A_96) bot_bo70021908tate_o)))) (((P_30 A_96)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_96) X)) (P_30 X))))) bot_bo70021908tate_o)))) of role axiom named fact_201_Collect__conv__if2
% A new axiom: (forall (P_30:(hoare_1167836817_state->Prop)) (A_96:hoare_1167836817_state), ((and ((P_30 A_96)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_96) X)) (P_30 X))))) ((insert2134838167_state A_96) bot_bo70021908tate_o)))) (((P_30 A_96)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_96) X)) (P_30 X))))) bot_bo70021908tate_o))))
% FOF formula (forall (P_30:(hoare_1775062406iple_a->Prop)) (A_96:hoare_1775062406iple_a), ((and ((P_30 A_96)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) A_96) X)) (P_30 X))))) ((insert1281456128iple_a A_96) bot_bo751897185le_a_o)))) (((P_30 A_96)->False)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) A_96) X)) (P_30 X))))) bot_bo751897185le_a_o)))) of role axiom named fact_202_Collect__conv__if2
% A new axiom: (forall (P_30:(hoare_1775062406iple_a->Prop)) (A_96:hoare_1775062406iple_a), ((and ((P_30 A_96)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) A_96) X)) (P_30 X))))) ((insert1281456128iple_a A_96) bot_bo751897185le_a_o)))) (((P_30 A_96)->False)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) A_96) X)) (P_30 X))))) bot_bo751897185le_a_o))))
% FOF formula (forall (P_30:(pname->Prop)) (A_96:pname), ((and ((P_30 A_96)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_96) X)) (P_30 X))))) ((insert_pname A_96) bot_bot_pname_o)))) (((P_30 A_96)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_96) X)) (P_30 X))))) bot_bot_pname_o)))) of role axiom named fact_203_Collect__conv__if2
% A new axiom: (forall (P_30:(pname->Prop)) (A_96:pname), ((and ((P_30 A_96)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_96) X)) (P_30 X))))) ((insert_pname A_96) bot_bot_pname_o)))) (((P_30 A_96)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_96) X)) (P_30 X))))) bot_bot_pname_o))))
% FOF formula (forall (P_29:(hoare_1167836817_state->Prop)) (A_95:hoare_1167836817_state), ((and ((P_29 A_95)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X) A_95)) (P_29 X))))) ((insert2134838167_state A_95) bot_bo70021908tate_o)))) (((P_29 A_95)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X) A_95)) (P_29 X))))) bot_bo70021908tate_o)))) of role axiom named fact_204_Collect__conv__if
% A new axiom: (forall (P_29:(hoare_1167836817_state->Prop)) (A_95:hoare_1167836817_state), ((and ((P_29 A_95)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X) A_95)) (P_29 X))))) ((insert2134838167_state A_95) bot_bo70021908tate_o)))) (((P_29 A_95)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X) A_95)) (P_29 X))))) bot_bo70021908tate_o))))
% FOF formula (forall (P_29:(hoare_1775062406iple_a->Prop)) (A_95:hoare_1775062406iple_a), ((and ((P_29 A_95)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) X) A_95)) (P_29 X))))) ((insert1281456128iple_a A_95) bot_bo751897185le_a_o)))) (((P_29 A_95)->False)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) X) A_95)) (P_29 X))))) bot_bo751897185le_a_o)))) of role axiom named fact_205_Collect__conv__if
% A new axiom: (forall (P_29:(hoare_1775062406iple_a->Prop)) (A_95:hoare_1775062406iple_a), ((and ((P_29 A_95)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) X) A_95)) (P_29 X))))) ((insert1281456128iple_a A_95) bot_bo751897185le_a_o)))) (((P_29 A_95)->False)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) X) A_95)) (P_29 X))))) bot_bo751897185le_a_o))))
% FOF formula (forall (P_29:(pname->Prop)) (A_95:pname), ((and ((P_29 A_95)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_95)) (P_29 X))))) ((insert_pname A_95) bot_bot_pname_o)))) (((P_29 A_95)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_95)) (P_29 X))))) bot_bot_pname_o)))) of role axiom named fact_206_Collect__conv__if
% A new axiom: (forall (P_29:(pname->Prop)) (A_95:pname), ((and ((P_29 A_95)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_95)) (P_29 X))))) ((insert_pname A_95) bot_bot_pname_o)))) (((P_29 A_95)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_95)) (P_29 X))))) bot_bot_pname_o))))
% FOF formula (forall (P_28:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) (collec676402587iple_a P_28))) (forall (X:hoare_1775062406iple_a), ((P_28 X)->False)))) of role axiom named fact_207_empty__Collect__eq
% A new axiom: (forall (P_28:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) (collec676402587iple_a P_28))) (forall (X:hoare_1775062406iple_a), ((P_28 X)->False))))
% FOF formula (forall (P_28:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_28))) (forall (X:pname), ((P_28 X)->False)))) of role axiom named fact_208_empty__Collect__eq
% A new axiom: (forall (P_28:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_28))) (forall (X:pname), ((P_28 X)->False))))
% FOF formula (forall (P_28:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state P_28))) (forall (X:hoare_1167836817_state), ((P_28 X)->False)))) of role axiom named fact_209_empty__Collect__eq
% A new axiom: (forall (P_28:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state P_28))) (forall (X:hoare_1167836817_state), ((P_28 X)->False))))
% FOF formula (forall (X_33:hoare_1775062406iple_a) (A_94:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a X_33) A_94)) (A_94 X_33))) of role axiom named fact_210_mem__def
% A new axiom: (forall (X_33:hoare_1775062406iple_a) (A_94:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a X_33) A_94)) (A_94 X_33)))
% FOF formula (forall (X_33:pname) (A_94:(pname->Prop)), ((iff ((member_pname X_33) A_94)) (A_94 X_33))) of role axiom named fact_211_mem__def
% A new axiom: (forall (X_33:pname) (A_94:(pname->Prop)), ((iff ((member_pname X_33) A_94)) (A_94 X_33)))
% FOF formula (forall (P_27:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a P_27)) P_27)) of role axiom named fact_212_Collect__def
% A new axiom: (forall (P_27:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a P_27)) P_27))
% FOF formula (forall (P_27:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_27)) P_27)) of role axiom named fact_213_Collect__def
% A new axiom: (forall (P_27:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_27)) P_27))
% FOF formula (forall (C_33:hoare_1775062406iple_a), (((member2122167641iple_a C_33) bot_bo751897185le_a_o)->False)) of role axiom named fact_214_empty__iff
% A new axiom: (forall (C_33:hoare_1775062406iple_a), (((member2122167641iple_a C_33) bot_bo751897185le_a_o)->False))
% FOF formula (forall (C_33:hoare_1167836817_state), (((member2058392318_state C_33) bot_bo70021908tate_o)->False)) of role axiom named fact_215_empty__iff
% A new axiom: (forall (C_33:hoare_1167836817_state), (((member2058392318_state C_33) bot_bo70021908tate_o)->False))
% FOF formula (forall (C_33:pname), (((member_pname C_33) bot_bot_pname_o)->False)) of role axiom named fact_216_empty__iff
% A new axiom: (forall (C_33:pname), (((member_pname C_33) bot_bot_pname_o)->False))
% FOF formula (forall (A_93:hoare_1167836817_state) (B_51:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_93) B_51)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) X) A_93)) ((member2058392318_state X) B_51)))))) of role axiom named fact_217_insert__compr
% A new axiom: (forall (A_93:hoare_1167836817_state) (B_51:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_93) B_51)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) X) A_93)) ((member2058392318_state X) B_51))))))
% FOF formula (forall (A_93:hoare_1775062406iple_a) (B_51:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_93) B_51)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or (((eq hoare_1775062406iple_a) X) A_93)) ((member2122167641iple_a X) B_51)))))) of role axiom named fact_218_insert__compr
% A new axiom: (forall (A_93:hoare_1775062406iple_a) (B_51:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_93) B_51)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or (((eq hoare_1775062406iple_a) X) A_93)) ((member2122167641iple_a X) B_51))))))
% FOF formula (forall (A_93:pname) (B_51:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_93) B_51)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_93)) ((member_pname X) B_51)))))) of role axiom named fact_219_insert__compr
% A new axiom: (forall (A_93:pname) (B_51:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_93) B_51)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_93)) ((member_pname X) B_51))))))
% FOF formula (forall (A_92:hoare_1167836817_state) (P_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_92) (collec1027672124_state P_26))) (collec1027672124_state (fun (U_2:hoare_1167836817_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1167836817_state) U_2) A_92))) (P_26 U_2)))))) of role axiom named fact_220_insert__Collect
% A new axiom: (forall (A_92:hoare_1167836817_state) (P_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_92) (collec1027672124_state P_26))) (collec1027672124_state (fun (U_2:hoare_1167836817_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1167836817_state) U_2) A_92))) (P_26 U_2))))))
% FOF formula (forall (A_92:hoare_1775062406iple_a) (P_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_92) (collec676402587iple_a P_26))) (collec676402587iple_a (fun (U_2:hoare_1775062406iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1775062406iple_a) U_2) A_92))) (P_26 U_2)))))) of role axiom named fact_221_insert__Collect
% A new axiom: (forall (A_92:hoare_1775062406iple_a) (P_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_92) (collec676402587iple_a P_26))) (collec676402587iple_a (fun (U_2:hoare_1775062406iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1775062406iple_a) U_2) A_92))) (P_26 U_2))))))
% FOF formula (forall (A_92:pname) (P_26:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_92) (collect_pname P_26))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_92))) (P_26 U_2)))))) of role axiom named fact_222_insert__Collect
% A new axiom: (forall (A_92:pname) (P_26:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_92) (collect_pname P_26))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_92))) (P_26 U_2))))))
% FOF formula (forall (B_50:hoare_1167836817_state) (A_91:hoare_1167836817_state), ((iff ((member2058392318_state B_50) ((insert2134838167_state A_91) bot_bo70021908tate_o))) (((eq hoare_1167836817_state) B_50) A_91))) of role axiom named fact_223_singleton__iff
% A new axiom: (forall (B_50:hoare_1167836817_state) (A_91:hoare_1167836817_state), ((iff ((member2058392318_state B_50) ((insert2134838167_state A_91) bot_bo70021908tate_o))) (((eq hoare_1167836817_state) B_50) A_91)))
% FOF formula (forall (B_50:hoare_1775062406iple_a) (A_91:hoare_1775062406iple_a), ((iff ((member2122167641iple_a B_50) ((insert1281456128iple_a A_91) bot_bo751897185le_a_o))) (((eq hoare_1775062406iple_a) B_50) A_91))) of role axiom named fact_224_singleton__iff
% A new axiom: (forall (B_50:hoare_1775062406iple_a) (A_91:hoare_1775062406iple_a), ((iff ((member2122167641iple_a B_50) ((insert1281456128iple_a A_91) bot_bo751897185le_a_o))) (((eq hoare_1775062406iple_a) B_50) A_91)))
% FOF formula (forall (B_50:pname) (A_91:pname), ((iff ((member_pname B_50) ((insert_pname A_91) bot_bot_pname_o))) (((eq pname) B_50) A_91))) of role axiom named fact_225_singleton__iff
% A new axiom: (forall (B_50:pname) (A_91:pname), ((iff ((member_pname B_50) ((insert_pname A_91) bot_bot_pname_o))) (((eq pname) B_50) A_91)))
% FOF formula (forall (X_32:hoare_1167836817_state) (A_90:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_32) ((insert2134838167_state X_32) A_90))) ((insert2134838167_state X_32) A_90))) of role axiom named fact_226_insert__absorb2
% A new axiom: (forall (X_32:hoare_1167836817_state) (A_90:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_32) ((insert2134838167_state X_32) A_90))) ((insert2134838167_state X_32) A_90)))
% FOF formula (forall (X_32:hoare_1775062406iple_a) (A_90:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X_32) ((insert1281456128iple_a X_32) A_90))) ((insert1281456128iple_a X_32) A_90))) of role axiom named fact_227_insert__absorb2
% A new axiom: (forall (X_32:hoare_1775062406iple_a) (A_90:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X_32) ((insert1281456128iple_a X_32) A_90))) ((insert1281456128iple_a X_32) A_90)))
% FOF formula (forall (X_32:pname) (A_90:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_32) ((insert_pname X_32) A_90))) ((insert_pname X_32) A_90))) of role axiom named fact_228_insert__absorb2
% A new axiom: (forall (X_32:pname) (A_90:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_32) ((insert_pname X_32) A_90))) ((insert_pname X_32) A_90)))
% FOF formula (forall (X_31:hoare_1167836817_state) (Y_12:hoare_1167836817_state) (A_89:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_31) ((insert2134838167_state Y_12) A_89))) ((insert2134838167_state Y_12) ((insert2134838167_state X_31) A_89)))) of role axiom named fact_229_insert__commute
% A new axiom: (forall (X_31:hoare_1167836817_state) (Y_12:hoare_1167836817_state) (A_89:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_31) ((insert2134838167_state Y_12) A_89))) ((insert2134838167_state Y_12) ((insert2134838167_state X_31) A_89))))
% FOF formula (forall (X_31:hoare_1775062406iple_a) (Y_12:hoare_1775062406iple_a) (A_89:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X_31) ((insert1281456128iple_a Y_12) A_89))) ((insert1281456128iple_a Y_12) ((insert1281456128iple_a X_31) A_89)))) of role axiom named fact_230_insert__commute
% A new axiom: (forall (X_31:hoare_1775062406iple_a) (Y_12:hoare_1775062406iple_a) (A_89:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X_31) ((insert1281456128iple_a Y_12) A_89))) ((insert1281456128iple_a Y_12) ((insert1281456128iple_a X_31) A_89))))
% FOF formula (forall (X_31:pname) (Y_12:pname) (A_89:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_31) ((insert_pname Y_12) A_89))) ((insert_pname Y_12) ((insert_pname X_31) A_89)))) of role axiom named fact_231_insert__commute
% A new axiom: (forall (X_31:pname) (Y_12:pname) (A_89:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_31) ((insert_pname Y_12) A_89))) ((insert_pname Y_12) ((insert_pname X_31) A_89))))
% FOF formula (forall (A_88:hoare_1167836817_state) (B_49:hoare_1167836817_state) (A_87:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state A_88) ((insert2134838167_state B_49) A_87))) ((or (((eq hoare_1167836817_state) A_88) B_49)) ((member2058392318_state A_88) A_87)))) of role axiom named fact_232_insert__iff
% A new axiom: (forall (A_88:hoare_1167836817_state) (B_49:hoare_1167836817_state) (A_87:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state A_88) ((insert2134838167_state B_49) A_87))) ((or (((eq hoare_1167836817_state) A_88) B_49)) ((member2058392318_state A_88) A_87))))
% FOF formula (forall (A_88:hoare_1775062406iple_a) (B_49:hoare_1775062406iple_a) (A_87:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a A_88) ((insert1281456128iple_a B_49) A_87))) ((or (((eq hoare_1775062406iple_a) A_88) B_49)) ((member2122167641iple_a A_88) A_87)))) of role axiom named fact_233_insert__iff
% A new axiom: (forall (A_88:hoare_1775062406iple_a) (B_49:hoare_1775062406iple_a) (A_87:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a A_88) ((insert1281456128iple_a B_49) A_87))) ((or (((eq hoare_1775062406iple_a) A_88) B_49)) ((member2122167641iple_a A_88) A_87))))
% FOF formula (forall (A_88:pname) (B_49:pname) (A_87:(pname->Prop)), ((iff ((member_pname A_88) ((insert_pname B_49) A_87))) ((or (((eq pname) A_88) B_49)) ((member_pname A_88) A_87)))) of role axiom named fact_234_insert__iff
% A new axiom: (forall (A_88:pname) (B_49:pname) (A_87:(pname->Prop)), ((iff ((member_pname A_88) ((insert_pname B_49) A_87))) ((or (((eq pname) A_88) B_49)) ((member_pname A_88) A_87))))
% FOF formula (forall (P_25:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a P_25)) bot_bo751897185le_a_o)) (forall (X:hoare_1775062406iple_a), ((P_25 X)->False)))) of role axiom named fact_235_Collect__empty__eq
% A new axiom: (forall (P_25:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a P_25)) bot_bo751897185le_a_o)) (forall (X:hoare_1775062406iple_a), ((P_25 X)->False))))
% FOF formula (forall (P_25:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_25)) bot_bot_pname_o)) (forall (X:pname), ((P_25 X)->False)))) of role axiom named fact_236_Collect__empty__eq
% A new axiom: (forall (P_25:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_25)) bot_bot_pname_o)) (forall (X:pname), ((P_25 X)->False))))
% FOF formula (forall (P_25:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_25)) bot_bo70021908tate_o)) (forall (X:hoare_1167836817_state), ((P_25 X)->False)))) of role axiom named fact_237_Collect__empty__eq
% A new axiom: (forall (P_25:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_25)) bot_bo70021908tate_o)) (forall (X:hoare_1167836817_state), ((P_25 X)->False))))
% FOF formula (forall (A_86:hoare_1167836817_state) (B_48:hoare_1167836817_state) (C_32:hoare_1167836817_state) (D_1:hoare_1167836817_state), ((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_86) ((insert2134838167_state B_48) bot_bo70021908tate_o))) ((insert2134838167_state C_32) ((insert2134838167_state D_1) bot_bo70021908tate_o)))) ((or ((and (((eq hoare_1167836817_state) A_86) C_32)) (((eq hoare_1167836817_state) B_48) D_1))) ((and (((eq hoare_1167836817_state) A_86) D_1)) (((eq hoare_1167836817_state) B_48) C_32))))) of role axiom named fact_238_doubleton__eq__iff
% A new axiom: (forall (A_86:hoare_1167836817_state) (B_48:hoare_1167836817_state) (C_32:hoare_1167836817_state) (D_1:hoare_1167836817_state), ((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_86) ((insert2134838167_state B_48) bot_bo70021908tate_o))) ((insert2134838167_state C_32) ((insert2134838167_state D_1) bot_bo70021908tate_o)))) ((or ((and (((eq hoare_1167836817_state) A_86) C_32)) (((eq hoare_1167836817_state) B_48) D_1))) ((and (((eq hoare_1167836817_state) A_86) D_1)) (((eq hoare_1167836817_state) B_48) C_32)))))
% FOF formula (forall (A_86:hoare_1775062406iple_a) (B_48:hoare_1775062406iple_a) (C_32:hoare_1775062406iple_a) (D_1:hoare_1775062406iple_a), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_86) ((insert1281456128iple_a B_48) bot_bo751897185le_a_o))) ((insert1281456128iple_a C_32) ((insert1281456128iple_a D_1) bot_bo751897185le_a_o)))) ((or ((and (((eq hoare_1775062406iple_a) A_86) C_32)) (((eq hoare_1775062406iple_a) B_48) D_1))) ((and (((eq hoare_1775062406iple_a) A_86) D_1)) (((eq hoare_1775062406iple_a) B_48) C_32))))) of role axiom named fact_239_doubleton__eq__iff
% A new axiom: (forall (A_86:hoare_1775062406iple_a) (B_48:hoare_1775062406iple_a) (C_32:hoare_1775062406iple_a) (D_1:hoare_1775062406iple_a), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_86) ((insert1281456128iple_a B_48) bot_bo751897185le_a_o))) ((insert1281456128iple_a C_32) ((insert1281456128iple_a D_1) bot_bo751897185le_a_o)))) ((or ((and (((eq hoare_1775062406iple_a) A_86) C_32)) (((eq hoare_1775062406iple_a) B_48) D_1))) ((and (((eq hoare_1775062406iple_a) A_86) D_1)) (((eq hoare_1775062406iple_a) B_48) C_32)))))
% FOF formula (forall (A_86:pname) (B_48:pname) (C_32:pname) (D_1:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_86) ((insert_pname B_48) bot_bot_pname_o))) ((insert_pname C_32) ((insert_pname D_1) bot_bot_pname_o)))) ((or ((and (((eq pname) A_86) C_32)) (((eq pname) B_48) D_1))) ((and (((eq pname) A_86) D_1)) (((eq pname) B_48) C_32))))) of role axiom named fact_240_doubleton__eq__iff
% A new axiom: (forall (A_86:pname) (B_48:pname) (C_32:pname) (D_1:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_86) ((insert_pname B_48) bot_bot_pname_o))) ((insert_pname C_32) ((insert_pname D_1) bot_bot_pname_o)))) ((or ((and (((eq pname) A_86) C_32)) (((eq pname) B_48) D_1))) ((and (((eq pname) A_86) D_1)) (((eq pname) B_48) C_32)))))
% FOF formula (forall (Y_11:hoare_1167836817_state) (A_85:(hoare_1167836817_state->Prop)) (X_30:hoare_1167836817_state), ((iff (((insert2134838167_state Y_11) A_85) X_30)) ((or (((eq hoare_1167836817_state) Y_11) X_30)) (A_85 X_30)))) of role axiom named fact_241_insert__code
% A new axiom: (forall (Y_11:hoare_1167836817_state) (A_85:(hoare_1167836817_state->Prop)) (X_30:hoare_1167836817_state), ((iff (((insert2134838167_state Y_11) A_85) X_30)) ((or (((eq hoare_1167836817_state) Y_11) X_30)) (A_85 X_30))))
% FOF formula (forall (Y_11:hoare_1775062406iple_a) (A_85:(hoare_1775062406iple_a->Prop)) (X_30:hoare_1775062406iple_a), ((iff (((insert1281456128iple_a Y_11) A_85) X_30)) ((or (((eq hoare_1775062406iple_a) Y_11) X_30)) (A_85 X_30)))) of role axiom named fact_242_insert__code
% A new axiom: (forall (Y_11:hoare_1775062406iple_a) (A_85:(hoare_1775062406iple_a->Prop)) (X_30:hoare_1775062406iple_a), ((iff (((insert1281456128iple_a Y_11) A_85) X_30)) ((or (((eq hoare_1775062406iple_a) Y_11) X_30)) (A_85 X_30))))
% FOF formula (forall (Y_11:pname) (A_85:(pname->Prop)) (X_30:pname), ((iff (((insert_pname Y_11) A_85) X_30)) ((or (((eq pname) Y_11) X_30)) (A_85 X_30)))) of role axiom named fact_243_insert__code
% A new axiom: (forall (Y_11:pname) (A_85:(pname->Prop)) (X_30:pname), ((iff (((insert_pname Y_11) A_85) X_30)) ((or (((eq pname) Y_11) X_30)) (A_85 X_30))))
% FOF formula (forall (B_47:(hoare_1167836817_state->Prop)) (X_29:hoare_1167836817_state) (A_84:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_29) A_84)->False)->((((member2058392318_state X_29) B_47)->False)->((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_29) A_84)) ((insert2134838167_state X_29) B_47))) (((eq (hoare_1167836817_state->Prop)) A_84) B_47))))) of role axiom named fact_244_insert__ident
% A new axiom: (forall (B_47:(hoare_1167836817_state->Prop)) (X_29:hoare_1167836817_state) (A_84:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_29) A_84)->False)->((((member2058392318_state X_29) B_47)->False)->((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_29) A_84)) ((insert2134838167_state X_29) B_47))) (((eq (hoare_1167836817_state->Prop)) A_84) B_47)))))
% FOF formula (forall (B_47:(hoare_1775062406iple_a->Prop)) (X_29:hoare_1775062406iple_a) (A_84:(hoare_1775062406iple_a->Prop)), ((((member2122167641iple_a X_29) A_84)->False)->((((member2122167641iple_a X_29) B_47)->False)->((iff (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X_29) A_84)) ((insert1281456128iple_a X_29) B_47))) (((eq (hoare_1775062406iple_a->Prop)) A_84) B_47))))) of role axiom named fact_245_insert__ident
% A new axiom: (forall (B_47:(hoare_1775062406iple_a->Prop)) (X_29:hoare_1775062406iple_a) (A_84:(hoare_1775062406iple_a->Prop)), ((((member2122167641iple_a X_29) A_84)->False)->((((member2122167641iple_a X_29) B_47)->False)->((iff (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X_29) A_84)) ((insert1281456128iple_a X_29) B_47))) (((eq (hoare_1775062406iple_a->Prop)) A_84) B_47)))))
% FOF formula (forall (B_47:(pname->Prop)) (X_29:pname) (A_84:(pname->Prop)), ((((member_pname X_29) A_84)->False)->((((member_pname X_29) B_47)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_29) A_84)) ((insert_pname X_29) B_47))) (((eq (pname->Prop)) A_84) B_47))))) of role axiom named fact_246_insert__ident
% A new axiom: (forall (B_47:(pname->Prop)) (X_29:pname) (A_84:(pname->Prop)), ((((member_pname X_29) A_84)->False)->((((member_pname X_29) B_47)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_29) A_84)) ((insert_pname X_29) B_47))) (((eq (pname->Prop)) A_84) B_47)))))
% FOF formula (forall (A_83:hoare_1775062406iple_a) (A_82:(hoare_1775062406iple_a->Prop)), ((((eq (hoare_1775062406iple_a->Prop)) A_82) bot_bo751897185le_a_o)->(((member2122167641iple_a A_83) A_82)->False))) of role axiom named fact_247_equals0D
% A new axiom: (forall (A_83:hoare_1775062406iple_a) (A_82:(hoare_1775062406iple_a->Prop)), ((((eq (hoare_1775062406iple_a->Prop)) A_82) bot_bo751897185le_a_o)->(((member2122167641iple_a A_83) A_82)->False)))
% FOF formula (forall (A_83:hoare_1167836817_state) (A_82:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_82) bot_bo70021908tate_o)->(((member2058392318_state A_83) A_82)->False))) of role axiom named fact_248_equals0D
% A new axiom: (forall (A_83:hoare_1167836817_state) (A_82:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_82) bot_bo70021908tate_o)->(((member2058392318_state A_83) A_82)->False)))
% FOF formula (forall (A_83:pname) (A_82:(pname->Prop)), ((((eq (pname->Prop)) A_82) bot_bot_pname_o)->(((member_pname A_83) A_82)->False))) of role axiom named fact_249_equals0D
% A new axiom: (forall (A_83:pname) (A_82:(pname->Prop)), ((((eq (pname->Prop)) A_82) bot_bot_pname_o)->(((member_pname A_83) A_82)->False)))
% FOF formula (forall (B_46:hoare_1167836817_state) (A_81:hoare_1167836817_state) (B_45:(hoare_1167836817_state->Prop)), (((member2058392318_state A_81) B_45)->((member2058392318_state A_81) ((insert2134838167_state B_46) B_45)))) of role axiom named fact_250_insertI2
% A new axiom: (forall (B_46:hoare_1167836817_state) (A_81:hoare_1167836817_state) (B_45:(hoare_1167836817_state->Prop)), (((member2058392318_state A_81) B_45)->((member2058392318_state A_81) ((insert2134838167_state B_46) B_45))))
% FOF formula (forall (B_46:hoare_1775062406iple_a) (A_81:hoare_1775062406iple_a) (B_45:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_81) B_45)->((member2122167641iple_a A_81) ((insert1281456128iple_a B_46) B_45)))) of role axiom named fact_251_insertI2
% A new axiom: (forall (B_46:hoare_1775062406iple_a) (A_81:hoare_1775062406iple_a) (B_45:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_81) B_45)->((member2122167641iple_a A_81) ((insert1281456128iple_a B_46) B_45))))
% FOF formula (forall (B_46:pname) (A_81:pname) (B_45:(pname->Prop)), (((member_pname A_81) B_45)->((member_pname A_81) ((insert_pname B_46) B_45)))) of role axiom named fact_252_insertI2
% A new axiom: (forall (B_46:pname) (A_81:pname) (B_45:(pname->Prop)), (((member_pname A_81) B_45)->((member_pname A_81) ((insert_pname B_46) B_45))))
% FOF formula (forall (A_80:hoare_1167836817_state) (A_79:(hoare_1167836817_state->Prop)), (((member2058392318_state A_80) A_79)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_80) A_79)) A_79))) of role axiom named fact_253_insert__absorb
% A new axiom: (forall (A_80:hoare_1167836817_state) (A_79:(hoare_1167836817_state->Prop)), (((member2058392318_state A_80) A_79)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_80) A_79)) A_79)))
% FOF formula (forall (A_80:hoare_1775062406iple_a) (A_79:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_80) A_79)->(((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_80) A_79)) A_79))) of role axiom named fact_254_insert__absorb
% A new axiom: (forall (A_80:hoare_1775062406iple_a) (A_79:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_80) A_79)->(((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_80) A_79)) A_79)))
% FOF formula (forall (A_80:pname) (A_79:(pname->Prop)), (((member_pname A_80) A_79)->(((eq (pname->Prop)) ((insert_pname A_80) A_79)) A_79))) of role axiom named fact_255_insert__absorb
% A new axiom: (forall (A_80:pname) (A_79:(pname->Prop)), (((member_pname A_80) A_79)->(((eq (pname->Prop)) ((insert_pname A_80) A_79)) A_79)))
% FOF formula (forall (B_44:hoare_1167836817_state) (A_78:hoare_1167836817_state), (((member2058392318_state B_44) ((insert2134838167_state A_78) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) B_44) A_78))) of role axiom named fact_256_singletonE
% A new axiom: (forall (B_44:hoare_1167836817_state) (A_78:hoare_1167836817_state), (((member2058392318_state B_44) ((insert2134838167_state A_78) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) B_44) A_78)))
% FOF formula (forall (B_44:hoare_1775062406iple_a) (A_78:hoare_1775062406iple_a), (((member2122167641iple_a B_44) ((insert1281456128iple_a A_78) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) B_44) A_78))) of role axiom named fact_257_singletonE
% A new axiom: (forall (B_44:hoare_1775062406iple_a) (A_78:hoare_1775062406iple_a), (((member2122167641iple_a B_44) ((insert1281456128iple_a A_78) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) B_44) A_78)))
% FOF formula (forall (B_44:pname) (A_78:pname), (((member_pname B_44) ((insert_pname A_78) bot_bot_pname_o))->(((eq pname) B_44) A_78))) of role axiom named fact_258_singletonE
% A new axiom: (forall (B_44:pname) (A_78:pname), (((member_pname B_44) ((insert_pname A_78) bot_bot_pname_o))->(((eq pname) B_44) A_78)))
% FOF formula (forall (A_77:hoare_1167836817_state) (B_43:hoare_1167836817_state), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_77) bot_bo70021908tate_o)) ((insert2134838167_state B_43) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) A_77) B_43))) of role axiom named fact_259_singleton__inject
% A new axiom: (forall (A_77:hoare_1167836817_state) (B_43:hoare_1167836817_state), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_77) bot_bo70021908tate_o)) ((insert2134838167_state B_43) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) A_77) B_43)))
% FOF formula (forall (A_77:hoare_1775062406iple_a) (B_43:hoare_1775062406iple_a), ((((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_77) bot_bo751897185le_a_o)) ((insert1281456128iple_a B_43) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) A_77) B_43))) of role axiom named fact_260_singleton__inject
% A new axiom: (forall (A_77:hoare_1775062406iple_a) (B_43:hoare_1775062406iple_a), ((((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_77) bot_bo751897185le_a_o)) ((insert1281456128iple_a B_43) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) A_77) B_43)))
% FOF formula (forall (A_77:pname) (B_43:pname), ((((eq (pname->Prop)) ((insert_pname A_77) bot_bot_pname_o)) ((insert_pname B_43) bot_bot_pname_o))->(((eq pname) A_77) B_43))) of role axiom named fact_261_singleton__inject
% A new axiom: (forall (A_77:pname) (B_43:pname), ((((eq (pname->Prop)) ((insert_pname A_77) bot_bot_pname_o)) ((insert_pname B_43) bot_bot_pname_o))->(((eq pname) A_77) B_43)))
% FOF formula (forall (U_1:state) (C_19:com) (S:state) (T:state), ((((evalc C_19) S) T)->((((evalc C_19) S) U_1)->(((eq state) U_1) T)))) of role axiom named fact_262_com__det
% A new axiom: (forall (U_1:state) (C_19:com) (S:state) (T:state), ((((evalc C_19) S) T)->((((evalc C_19) S) U_1)->(((eq state) U_1) T))))
% FOF formula (forall (A_76:hoare_1167836817_state) (A_75:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_76) A_75)) ((semila1172322802tate_o ((insert2134838167_state A_76) bot_bo70021908tate_o)) A_75))) of role axiom named fact_263_insert__is__Un
% A new axiom: (forall (A_76:hoare_1167836817_state) (A_75:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_76) A_75)) ((semila1172322802tate_o ((insert2134838167_state A_76) bot_bo70021908tate_o)) A_75)))
% FOF formula (forall (A_76:pname) (A_75:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_76) A_75)) ((semila1780557381name_o ((insert_pname A_76) bot_bot_pname_o)) A_75))) of role axiom named fact_264_insert__is__Un
% A new axiom: (forall (A_76:pname) (A_75:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_76) A_75)) ((semila1780557381name_o ((insert_pname A_76) bot_bot_pname_o)) A_75)))
% FOF formula (forall (A_76:hoare_1775062406iple_a) (A_75:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_76) A_75)) ((semila13410563le_a_o ((insert1281456128iple_a A_76) bot_bo751897185le_a_o)) A_75))) of role axiom named fact_265_insert__is__Un
% A new axiom: (forall (A_76:hoare_1775062406iple_a) (A_75:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_76) A_75)) ((semila13410563le_a_o ((insert1281456128iple_a A_76) bot_bo751897185le_a_o)) A_75)))
% FOF formula (forall (X:hoare_1167836817_state) (Xa:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X) Xa)) (collec1027672124_state (fun (Y_2:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) Y_2) X)) ((member2058392318_state Y_2) Xa)))))) of role axiom named fact_266_insert__compr__raw
% A new axiom: (forall (X:hoare_1167836817_state) (Xa:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X) Xa)) (collec1027672124_state (fun (Y_2:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) Y_2) X)) ((member2058392318_state Y_2) Xa))))))
% FOF formula (forall (X:hoare_1775062406iple_a) (Xa:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X) Xa)) (collec676402587iple_a (fun (Y_2:hoare_1775062406iple_a)=> ((or (((eq hoare_1775062406iple_a) Y_2) X)) ((member2122167641iple_a Y_2) Xa)))))) of role axiom named fact_267_insert__compr__raw
% A new axiom: (forall (X:hoare_1775062406iple_a) (Xa:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X) Xa)) (collec676402587iple_a (fun (Y_2:hoare_1775062406iple_a)=> ((or (((eq hoare_1775062406iple_a) Y_2) X)) ((member2122167641iple_a Y_2) Xa))))))
% FOF formula (forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y_2:pname)=> ((or (((eq pname) Y_2) X)) ((member_pname Y_2) Xa)))))) of role axiom named fact_268_insert__compr__raw
% A new axiom: (forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y_2:pname)=> ((or (((eq pname) Y_2) X)) ((member_pname Y_2) Xa))))))
% FOF formula (forall (G_16:(hoare_1167836817_state->Prop)) (T_3:hoare_1167836817_state) (Ts_2:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_16) ((insert2134838167_state T_3) Ts_2))->((and ((hoare_123228589_state G_16) ((insert2134838167_state T_3) bot_bo70021908tate_o))) ((hoare_123228589_state G_16) Ts_2)))) of role axiom named fact_269_derivs__insertD
% A new axiom: (forall (G_16:(hoare_1167836817_state->Prop)) (T_3:hoare_1167836817_state) (Ts_2:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_16) ((insert2134838167_state T_3) Ts_2))->((and ((hoare_123228589_state G_16) ((insert2134838167_state T_3) bot_bo70021908tate_o))) ((hoare_123228589_state G_16) Ts_2))))
% FOF formula (forall (G_16:(hoare_1775062406iple_a->Prop)) (T_3:hoare_1775062406iple_a) (Ts_2:(hoare_1775062406iple_a->Prop)), (((hoare_1508237396rivs_a G_16) ((insert1281456128iple_a T_3) Ts_2))->((and ((hoare_1508237396rivs_a G_16) ((insert1281456128iple_a T_3) bot_bo751897185le_a_o))) ((hoare_1508237396rivs_a G_16) Ts_2)))) of role axiom named fact_270_derivs__insertD
% A new axiom: (forall (G_16:(hoare_1775062406iple_a->Prop)) (T_3:hoare_1775062406iple_a) (Ts_2:(hoare_1775062406iple_a->Prop)), (((hoare_1508237396rivs_a G_16) ((insert1281456128iple_a T_3) Ts_2))->((and ((hoare_1508237396rivs_a G_16) ((insert1281456128iple_a T_3) bot_bo751897185le_a_o))) ((hoare_1508237396rivs_a G_16) Ts_2))))
% FOF formula (forall (Ts_1:(hoare_1167836817_state->Prop)) (G_15:(hoare_1167836817_state->Prop)) (T_2:hoare_1167836817_state), (((hoare_123228589_state G_15) ((insert2134838167_state T_2) bot_bo70021908tate_o))->(((hoare_123228589_state G_15) Ts_1)->((hoare_123228589_state G_15) ((insert2134838167_state T_2) Ts_1))))) of role axiom named fact_271_hoare__derivs_Oinsert
% A new axiom: (forall (Ts_1:(hoare_1167836817_state->Prop)) (G_15:(hoare_1167836817_state->Prop)) (T_2:hoare_1167836817_state), (((hoare_123228589_state G_15) ((insert2134838167_state T_2) bot_bo70021908tate_o))->(((hoare_123228589_state G_15) Ts_1)->((hoare_123228589_state G_15) ((insert2134838167_state T_2) Ts_1)))))
% FOF formula (forall (Ts_1:(hoare_1775062406iple_a->Prop)) (G_15:(hoare_1775062406iple_a->Prop)) (T_2:hoare_1775062406iple_a), (((hoare_1508237396rivs_a G_15) ((insert1281456128iple_a T_2) bot_bo751897185le_a_o))->(((hoare_1508237396rivs_a G_15) Ts_1)->((hoare_1508237396rivs_a G_15) ((insert1281456128iple_a T_2) Ts_1))))) of role axiom named fact_272_hoare__derivs_Oinsert
% A new axiom: (forall (Ts_1:(hoare_1775062406iple_a->Prop)) (G_15:(hoare_1775062406iple_a->Prop)) (T_2:hoare_1775062406iple_a), (((hoare_1508237396rivs_a G_15) ((insert1281456128iple_a T_2) bot_bo751897185le_a_o))->(((hoare_1508237396rivs_a G_15) Ts_1)->((hoare_1508237396rivs_a G_15) ((insert1281456128iple_a T_2) Ts_1)))))
% FOF formula (forall (C_31:hoare_1167836817_state) (A_74:(pname->Prop)), ((and ((((eq (pname->Prop)) A_74) bot_bot_pname_o)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> C_31)) A_74)) bot_bo70021908tate_o))) ((not (((eq (pname->Prop)) A_74) bot_bot_pname_o))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> C_31)) A_74)) ((insert2134838167_state C_31) bot_bo70021908tate_o))))) of role axiom named fact_273_image__constant__conv
% A new axiom: (forall (C_31:hoare_1167836817_state) (A_74:(pname->Prop)), ((and ((((eq (pname->Prop)) A_74) bot_bot_pname_o)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> C_31)) A_74)) bot_bo70021908tate_o))) ((not (((eq (pname->Prop)) A_74) bot_bot_pname_o))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> C_31)) A_74)) ((insert2134838167_state C_31) bot_bo70021908tate_o)))))
% FOF formula (forall (C_31:hoare_1775062406iple_a) (A_74:(pname->Prop)), ((and ((((eq (pname->Prop)) A_74) bot_bot_pname_o)->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> C_31)) A_74)) bot_bo751897185le_a_o))) ((not (((eq (pname->Prop)) A_74) bot_bot_pname_o))->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> C_31)) A_74)) ((insert1281456128iple_a C_31) bot_bo751897185le_a_o))))) of role axiom named fact_274_image__constant__conv
% A new axiom: (forall (C_31:hoare_1775062406iple_a) (A_74:(pname->Prop)), ((and ((((eq (pname->Prop)) A_74) bot_bot_pname_o)->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> C_31)) A_74)) bot_bo751897185le_a_o))) ((not (((eq (pname->Prop)) A_74) bot_bot_pname_o))->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> C_31)) A_74)) ((insert1281456128iple_a C_31) bot_bo751897185le_a_o)))))
% FOF formula (forall (C_30:hoare_1167836817_state) (X_28:pname) (A_73:(pname->Prop)), (((member_pname X_28) A_73)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> C_30)) A_73)) ((insert2134838167_state C_30) bot_bo70021908tate_o)))) of role axiom named fact_275_image__constant
% A new axiom: (forall (C_30:hoare_1167836817_state) (X_28:pname) (A_73:(pname->Prop)), (((member_pname X_28) A_73)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> C_30)) A_73)) ((insert2134838167_state C_30) bot_bo70021908tate_o))))
% FOF formula (forall (C_30:pname) (X_28:pname) (A_73:(pname->Prop)), (((member_pname X_28) A_73)->(((eq (pname->Prop)) ((image_pname_pname (fun (X:pname)=> C_30)) A_73)) ((insert_pname C_30) bot_bot_pname_o)))) of role axiom named fact_276_image__constant
% A new axiom: (forall (C_30:pname) (X_28:pname) (A_73:(pname->Prop)), (((member_pname X_28) A_73)->(((eq (pname->Prop)) ((image_pname_pname (fun (X:pname)=> C_30)) A_73)) ((insert_pname C_30) bot_bot_pname_o))))
% FOF formula (forall (C_30:hoare_1775062406iple_a) (X_28:pname) (A_73:(pname->Prop)), (((member_pname X_28) A_73)->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> C_30)) A_73)) ((insert1281456128iple_a C_30) bot_bo751897185le_a_o)))) of role axiom named fact_277_image__constant
% A new axiom: (forall (C_30:hoare_1775062406iple_a) (X_28:pname) (A_73:(pname->Prop)), (((member_pname X_28) A_73)->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> C_30)) A_73)) ((insert1281456128iple_a C_30) bot_bo751897185le_a_o))))
% FOF formula (forall (F_31:(pname->hoare_1167836817_state)) (A_72:pname) (B_42:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_31) ((insert_pname A_72) B_42))) ((insert2134838167_state (F_31 A_72)) ((image_575578384_state F_31) B_42)))) of role axiom named fact_278_image__insert
% A new axiom: (forall (F_31:(pname->hoare_1167836817_state)) (A_72:pname) (B_42:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_31) ((insert_pname A_72) B_42))) ((insert2134838167_state (F_31 A_72)) ((image_575578384_state F_31) B_42))))
% FOF formula (forall (F_31:(pname->hoare_1775062406iple_a)) (A_72:pname) (B_42:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_31) ((insert_pname A_72) B_42))) ((insert1281456128iple_a (F_31 A_72)) ((image_2063119815iple_a F_31) B_42)))) of role axiom named fact_279_image__insert
% A new axiom: (forall (F_31:(pname->hoare_1775062406iple_a)) (A_72:pname) (B_42:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_31) ((insert_pname A_72) B_42))) ((insert1281456128iple_a (F_31 A_72)) ((image_2063119815iple_a F_31) B_42))))
% FOF formula (forall (F_30:(pname->hoare_1167836817_state)) (X_27:pname) (A_71:(pname->Prop)), (((member_pname X_27) A_71)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state (F_30 X_27)) ((image_575578384_state F_30) A_71))) ((image_575578384_state F_30) A_71)))) of role axiom named fact_280_insert__image
% A new axiom: (forall (F_30:(pname->hoare_1167836817_state)) (X_27:pname) (A_71:(pname->Prop)), (((member_pname X_27) A_71)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state (F_30 X_27)) ((image_575578384_state F_30) A_71))) ((image_575578384_state F_30) A_71))))
% FOF formula (forall (F_30:(pname->pname)) (X_27:pname) (A_71:(pname->Prop)), (((member_pname X_27) A_71)->(((eq (pname->Prop)) ((insert_pname (F_30 X_27)) ((image_pname_pname F_30) A_71))) ((image_pname_pname F_30) A_71)))) of role axiom named fact_281_insert__image
% A new axiom: (forall (F_30:(pname->pname)) (X_27:pname) (A_71:(pname->Prop)), (((member_pname X_27) A_71)->(((eq (pname->Prop)) ((insert_pname (F_30 X_27)) ((image_pname_pname F_30) A_71))) ((image_pname_pname F_30) A_71))))
% FOF formula (forall (F_30:(pname->hoare_1775062406iple_a)) (X_27:pname) (A_71:(pname->Prop)), (((member_pname X_27) A_71)->(((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a (F_30 X_27)) ((image_2063119815iple_a F_30) A_71))) ((image_2063119815iple_a F_30) A_71)))) of role axiom named fact_282_insert__image
% A new axiom: (forall (F_30:(pname->hoare_1775062406iple_a)) (X_27:pname) (A_71:(pname->Prop)), (((member_pname X_27) A_71)->(((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a (F_30 X_27)) ((image_2063119815iple_a F_30) A_71))) ((image_2063119815iple_a F_30) A_71))))
% FOF formula (forall (A_70:(hoare_1167836817_state->Prop)) (A_69:hoare_1167836817_state) (B_41:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_70) ((insert2134838167_state A_69) B_41))) ((insert2134838167_state A_69) ((semila1172322802tate_o A_70) B_41)))) of role axiom named fact_283_Un__insert__right
% A new axiom: (forall (A_70:(hoare_1167836817_state->Prop)) (A_69:hoare_1167836817_state) (B_41:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_70) ((insert2134838167_state A_69) B_41))) ((insert2134838167_state A_69) ((semila1172322802tate_o A_70) B_41))))
% FOF formula (forall (A_70:(pname->Prop)) (A_69:pname) (B_41:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_70) ((insert_pname A_69) B_41))) ((insert_pname A_69) ((semila1780557381name_o A_70) B_41)))) of role axiom named fact_284_Un__insert__right
% A new axiom: (forall (A_70:(pname->Prop)) (A_69:pname) (B_41:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_70) ((insert_pname A_69) B_41))) ((insert_pname A_69) ((semila1780557381name_o A_70) B_41))))
% FOF formula (forall (A_70:(hoare_1775062406iple_a->Prop)) (A_69:hoare_1775062406iple_a) (B_41:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_70) ((insert1281456128iple_a A_69) B_41))) ((insert1281456128iple_a A_69) ((semila13410563le_a_o A_70) B_41)))) of role axiom named fact_285_Un__insert__right
% A new axiom: (forall (A_70:(hoare_1775062406iple_a->Prop)) (A_69:hoare_1775062406iple_a) (B_41:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_70) ((insert1281456128iple_a A_69) B_41))) ((insert1281456128iple_a A_69) ((semila13410563le_a_o A_70) B_41))))
% FOF formula (forall (A_68:hoare_1167836817_state) (B_40:(hoare_1167836817_state->Prop)) (C_29:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((insert2134838167_state A_68) B_40)) C_29)) ((insert2134838167_state A_68) ((semila1172322802tate_o B_40) C_29)))) of role axiom named fact_286_Un__insert__left
% A new axiom: (forall (A_68:hoare_1167836817_state) (B_40:(hoare_1167836817_state->Prop)) (C_29:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((insert2134838167_state A_68) B_40)) C_29)) ((insert2134838167_state A_68) ((semila1172322802tate_o B_40) C_29))))
% FOF formula (forall (A_68:pname) (B_40:(pname->Prop)) (C_29:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_68) B_40)) C_29)) ((insert_pname A_68) ((semila1780557381name_o B_40) C_29)))) of role axiom named fact_287_Un__insert__left
% A new axiom: (forall (A_68:pname) (B_40:(pname->Prop)) (C_29:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_68) B_40)) C_29)) ((insert_pname A_68) ((semila1780557381name_o B_40) C_29))))
% FOF formula (forall (A_68:hoare_1775062406iple_a) (B_40:(hoare_1775062406iple_a->Prop)) (C_29:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((insert1281456128iple_a A_68) B_40)) C_29)) ((insert1281456128iple_a A_68) ((semila13410563le_a_o B_40) C_29)))) of role axiom named fact_288_Un__insert__left
% A new axiom: (forall (A_68:hoare_1775062406iple_a) (B_40:(hoare_1775062406iple_a->Prop)) (C_29:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((insert1281456128iple_a A_68) B_40)) C_29)) ((insert1281456128iple_a A_68) ((semila13410563le_a_o B_40) C_29))))
% FOF formula (forall (F_29:(pname->hoare_1167836817_state)) (A_67:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((image_575578384_state F_29) A_67))) (((eq (pname->Prop)) A_67) bot_bot_pname_o))) of role axiom named fact_289_empty__is__image
% A new axiom: (forall (F_29:(pname->hoare_1167836817_state)) (A_67:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((image_575578384_state F_29) A_67))) (((eq (pname->Prop)) A_67) bot_bot_pname_o)))
% FOF formula (forall (F_29:(pname->hoare_1775062406iple_a)) (A_67:(pname->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) ((image_2063119815iple_a F_29) A_67))) (((eq (pname->Prop)) A_67) bot_bot_pname_o))) of role axiom named fact_290_empty__is__image
% A new axiom: (forall (F_29:(pname->hoare_1775062406iple_a)) (A_67:(pname->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) ((image_2063119815iple_a F_29) A_67))) (((eq (pname->Prop)) A_67) bot_bot_pname_o)))
% FOF formula (forall (F_28:(pname->hoare_1167836817_state)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_28) bot_bot_pname_o)) bot_bo70021908tate_o)) of role axiom named fact_291_image__empty
% A new axiom: (forall (F_28:(pname->hoare_1167836817_state)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_28) bot_bot_pname_o)) bot_bo70021908tate_o))
% FOF formula (forall (F_28:(pname->hoare_1775062406iple_a)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_28) bot_bot_pname_o)) bot_bo751897185le_a_o)) of role axiom named fact_292_image__empty
% A new axiom: (forall (F_28:(pname->hoare_1775062406iple_a)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_28) bot_bot_pname_o)) bot_bo751897185le_a_o))
% FOF formula (forall (F_27:(pname->hoare_1167836817_state)) (A_66:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_27) A_66)) bot_bo70021908tate_o)) (((eq (pname->Prop)) A_66) bot_bot_pname_o))) of role axiom named fact_293_image__is__empty
% A new axiom: (forall (F_27:(pname->hoare_1167836817_state)) (A_66:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_27) A_66)) bot_bo70021908tate_o)) (((eq (pname->Prop)) A_66) bot_bot_pname_o)))
% FOF formula (forall (F_27:(pname->hoare_1775062406iple_a)) (A_66:(pname->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_27) A_66)) bot_bo751897185le_a_o)) (((eq (pname->Prop)) A_66) bot_bot_pname_o))) of role axiom named fact_294_image__is__empty
% A new axiom: (forall (F_27:(pname->hoare_1775062406iple_a)) (A_66:(pname->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_27) A_66)) bot_bo751897185le_a_o)) (((eq (pname->Prop)) A_66) bot_bot_pname_o)))
% FOF formula (forall (P_24:(hoare_1167836817_state->Prop)) (X:hoare_1167836817_state), (((member2058392318_state X) bot_bo70021908tate_o)->(P_24 X))) of role axiom named fact_295_ball__empty
% A new axiom: (forall (P_24:(hoare_1167836817_state->Prop)) (X:hoare_1167836817_state), (((member2058392318_state X) bot_bo70021908tate_o)->(P_24 X)))
% FOF formula (forall (P_24:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), (((member2122167641iple_a X) bot_bo751897185le_a_o)->(P_24 X))) of role axiom named fact_296_ball__empty
% A new axiom: (forall (P_24:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), (((member2122167641iple_a X) bot_bo751897185le_a_o)->(P_24 X)))
% FOF formula (forall (P_24:(pname->Prop)) (X:pname), (((member_pname X) bot_bot_pname_o)->(P_24 X))) of role axiom named fact_297_ball__empty
% A new axiom: (forall (P_24:(pname->Prop)) (X:pname), (((member_pname X) bot_bot_pname_o)->(P_24 X)))
% FOF formula (forall (B_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) B_39)) B_39)) of role axiom named fact_298_Un__empty__left
% A new axiom: (forall (B_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) B_39)) B_39))
% FOF formula (forall (B_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_39)) B_39)) of role axiom named fact_299_Un__empty__left
% A new axiom: (forall (B_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_39)) B_39))
% FOF formula (forall (B_39:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o bot_bo751897185le_a_o) B_39)) B_39)) of role axiom named fact_300_Un__empty__left
% A new axiom: (forall (B_39:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o bot_bo751897185le_a_o) B_39)) B_39))
% FOF formula (forall (A_65:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_65) bot_bo70021908tate_o)) A_65)) of role axiom named fact_301_Un__empty__right
% A new axiom: (forall (A_65:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_65) bot_bo70021908tate_o)) A_65))
% FOF formula (forall (A_65:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_65) bot_bot_pname_o)) A_65)) of role axiom named fact_302_Un__empty__right
% A new axiom: (forall (A_65:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_65) bot_bot_pname_o)) A_65))
% FOF formula (forall (A_65:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_65) bot_bo751897185le_a_o)) A_65)) of role axiom named fact_303_Un__empty__right
% A new axiom: (forall (A_65:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_65) bot_bo751897185le_a_o)) A_65))
% FOF formula (forall (A_64:(hoare_1167836817_state->Prop)) (B_38:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_64) B_38)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) A_64) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) B_38) bot_bo70021908tate_o)))) of role axiom named fact_304_Un__empty
% A new axiom: (forall (A_64:(hoare_1167836817_state->Prop)) (B_38:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_64) B_38)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) A_64) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) B_38) bot_bo70021908tate_o))))
% FOF formula (forall (A_64:(pname->Prop)) (B_38:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_64) B_38)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_64) bot_bot_pname_o)) (((eq (pname->Prop)) B_38) bot_bot_pname_o)))) of role axiom named fact_305_Un__empty
% A new axiom: (forall (A_64:(pname->Prop)) (B_38:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_64) B_38)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_64) bot_bot_pname_o)) (((eq (pname->Prop)) B_38) bot_bot_pname_o))))
% FOF formula (forall (A_64:(hoare_1775062406iple_a->Prop)) (B_38:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_64) B_38)) bot_bo751897185le_a_o)) ((and (((eq (hoare_1775062406iple_a->Prop)) A_64) bot_bo751897185le_a_o)) (((eq (hoare_1775062406iple_a->Prop)) B_38) bot_bo751897185le_a_o)))) of role axiom named fact_306_Un__empty
% A new axiom: (forall (A_64:(hoare_1775062406iple_a->Prop)) (B_38:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_64) B_38)) bot_bo751897185le_a_o)) ((and (((eq (hoare_1775062406iple_a->Prop)) A_64) bot_bo751897185le_a_o)) (((eq (hoare_1775062406iple_a->Prop)) B_38) bot_bo751897185le_a_o))))
% FOF formula (forall (G_14:(hoare_1775062406iple_a->Prop)) (P_23:(x_a->(state->Prop))) (C_28:com) (Q_15:(x_a->(state->Prop))) (C_27:Prop), ((C_27->((hoare_1508237396rivs_a G_14) ((insert1281456128iple_a (((hoare_1766022166iple_a P_23) C_28) Q_15)) bot_bo751897185le_a_o)))->((hoare_1508237396rivs_a G_14) ((insert1281456128iple_a (((hoare_1766022166iple_a (fun (Z_8:x_a) (S_3:state)=> ((and ((P_23 Z_8) S_3)) C_27))) C_28) Q_15)) bot_bo751897185le_a_o)))) of role axiom named fact_307_constant
% A new axiom: (forall (G_14:(hoare_1775062406iple_a->Prop)) (P_23:(x_a->(state->Prop))) (C_28:com) (Q_15:(x_a->(state->Prop))) (C_27:Prop), ((C_27->((hoare_1508237396rivs_a G_14) ((insert1281456128iple_a (((hoare_1766022166iple_a P_23) C_28) Q_15)) bot_bo751897185le_a_o)))->((hoare_1508237396rivs_a G_14) ((insert1281456128iple_a (((hoare_1766022166iple_a (fun (Z_8:x_a) (S_3:state)=> ((and ((P_23 Z_8) S_3)) C_27))) C_28) Q_15)) bot_bo751897185le_a_o))))
% FOF formula (forall (G_14:(hoare_1167836817_state->Prop)) (P_23:(state->(state->Prop))) (C_28:com) (Q_15:(state->(state->Prop))) (C_27:Prop), ((C_27->((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state P_23) C_28) Q_15)) bot_bo70021908tate_o)))->((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state (fun (Z_8:state) (S_3:state)=> ((and ((P_23 Z_8) S_3)) C_27))) C_28) Q_15)) bot_bo70021908tate_o)))) of role axiom named fact_308_constant
% A new axiom: (forall (G_14:(hoare_1167836817_state->Prop)) (P_23:(state->(state->Prop))) (C_28:com) (Q_15:(state->(state->Prop))) (C_27:Prop), ((C_27->((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state P_23) C_28) Q_15)) bot_bo70021908tate_o)))->((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state (fun (Z_8:state) (S_3:state)=> ((and ((P_23 Z_8) S_3)) C_27))) C_28) Q_15)) bot_bo70021908tate_o))))
% FOF formula (forall (G_13:(hoare_1167836817_state->Prop)), ((hoare_123228589_state G_13) bot_bo70021908tate_o)) of role axiom named fact_309_empty
% A new axiom: (forall (G_13:(hoare_1167836817_state->Prop)), ((hoare_123228589_state G_13) bot_bo70021908tate_o))
% FOF formula (forall (G_13:(hoare_1775062406iple_a->Prop)), ((hoare_1508237396rivs_a G_13) bot_bo751897185le_a_o)) of role axiom named fact_310_empty
% A new axiom: (forall (G_13:(hoare_1775062406iple_a->Prop)), ((hoare_1508237396rivs_a G_13) bot_bo751897185le_a_o))
% FOF formula (forall (X_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) X_26)) X_26)) of role axiom named fact_311_sup__bot__left
% A new axiom: (forall (X_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) X_26)) X_26))
% FOF formula (forall (X_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) X_26)) X_26)) of role axiom named fact_312_sup__bot__left
% A new axiom: (forall (X_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) X_26)) X_26))
% FOF formula (forall (X_26:Prop), ((iff ((semila10642723_sup_o bot_bot_o) X_26)) X_26)) of role axiom named fact_313_sup__bot__left
% A new axiom: (forall (X_26:Prop), ((iff ((semila10642723_sup_o bot_bot_o) X_26)) X_26))
% FOF formula (forall (X_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o bot_bo751897185le_a_o) X_26)) X_26)) of role axiom named fact_314_sup__bot__left
% A new axiom: (forall (X_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o bot_bo751897185le_a_o) X_26)) X_26))
% FOF formula (forall (X_25:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_25) bot_bo70021908tate_o)) X_25)) of role axiom named fact_315_sup__bot__right
% A new axiom: (forall (X_25:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_25) bot_bo70021908tate_o)) X_25))
% FOF formula (forall (X_25:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_25) bot_bot_pname_o)) X_25)) of role axiom named fact_316_sup__bot__right
% A new axiom: (forall (X_25:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_25) bot_bot_pname_o)) X_25))
% FOF formula (forall (X_25:Prop), ((iff ((semila10642723_sup_o X_25) bot_bot_o)) X_25)) of role axiom named fact_317_sup__bot__right
% A new axiom: (forall (X_25:Prop), ((iff ((semila10642723_sup_o X_25) bot_bot_o)) X_25))
% FOF formula (forall (X_25:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_25) bot_bo751897185le_a_o)) X_25)) of role axiom named fact_318_sup__bot__right
% A new axiom: (forall (X_25:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_25) bot_bo751897185le_a_o)) X_25))
% FOF formula (forall (X_24:(hoare_1167836817_state->Prop)) (Y_10:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_24) Y_10)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) X_24) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) Y_10) bot_bo70021908tate_o)))) of role axiom named fact_319_sup__eq__bot__iff
% A new axiom: (forall (X_24:(hoare_1167836817_state->Prop)) (Y_10:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_24) Y_10)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) X_24) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) Y_10) bot_bo70021908tate_o))))
% FOF formula (forall (X_24:(pname->Prop)) (Y_10:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_24) Y_10)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_24) bot_bot_pname_o)) (((eq (pname->Prop)) Y_10) bot_bot_pname_o)))) of role axiom named fact_320_sup__eq__bot__iff
% A new axiom: (forall (X_24:(pname->Prop)) (Y_10:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_24) Y_10)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_24) bot_bot_pname_o)) (((eq (pname->Prop)) Y_10) bot_bot_pname_o))))
% FOF formula (forall (X_24:Prop) (Y_10:Prop), ((iff ((iff ((semila10642723_sup_o X_24) Y_10)) bot_bot_o)) ((and ((iff X_24) bot_bot_o)) ((iff Y_10) bot_bot_o)))) of role axiom named fact_321_sup__eq__bot__iff
% A new axiom: (forall (X_24:Prop) (Y_10:Prop), ((iff ((iff ((semila10642723_sup_o X_24) Y_10)) bot_bot_o)) ((and ((iff X_24) bot_bot_o)) ((iff Y_10) bot_bot_o))))
% FOF formula (forall (X_24:(hoare_1775062406iple_a->Prop)) (Y_10:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_24) Y_10)) bot_bo751897185le_a_o)) ((and (((eq (hoare_1775062406iple_a->Prop)) X_24) bot_bo751897185le_a_o)) (((eq (hoare_1775062406iple_a->Prop)) Y_10) bot_bo751897185le_a_o)))) of role axiom named fact_322_sup__eq__bot__iff
% A new axiom: (forall (X_24:(hoare_1775062406iple_a->Prop)) (Y_10:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_24) Y_10)) bot_bo751897185le_a_o)) ((and (((eq (hoare_1775062406iple_a->Prop)) X_24) bot_bo751897185le_a_o)) (((eq (hoare_1775062406iple_a->Prop)) Y_10) bot_bo751897185le_a_o))))
% FOF formula (forall (N_6:nat) (T_1:hoare_1167836817_state), (((hoare_56934129_state (suc N_6)) T_1)->((hoare_56934129_state N_6) T_1))) of role axiom named fact_323_triple__valid__Suc
% A new axiom: (forall (N_6:nat) (T_1:hoare_1167836817_state), (((hoare_56934129_state (suc N_6)) T_1)->((hoare_56934129_state N_6) T_1)))
% FOF formula (forall (N_6:nat) (T_1:hoare_1775062406iple_a), (((hoare_1462269968alid_a (suc N_6)) T_1)->((hoare_1462269968alid_a N_6) T_1))) of role axiom named fact_324_triple__valid__Suc
% A new axiom: (forall (N_6:nat) (T_1:hoare_1775062406iple_a), (((hoare_1462269968alid_a (suc N_6)) T_1)->((hoare_1462269968alid_a N_6) T_1)))
% FOF formula (forall (A_63:hoare_1167836817_state) (B_37:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_63) B_37)) ((semila1172322802tate_o (collec1027672124_state (fun (X:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X) A_63)))) B_37))) of role axiom named fact_325_insert__def
% A new axiom: (forall (A_63:hoare_1167836817_state) (B_37:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_63) B_37)) ((semila1172322802tate_o (collec1027672124_state (fun (X:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X) A_63)))) B_37)))
% FOF formula (forall (A_63:pname) (B_37:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_63) B_37)) ((semila1780557381name_o (collect_pname (fun (X:pname)=> (((eq pname) X) A_63)))) B_37))) of role axiom named fact_326_insert__def
% A new axiom: (forall (A_63:pname) (B_37:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_63) B_37)) ((semila1780557381name_o (collect_pname (fun (X:pname)=> (((eq pname) X) A_63)))) B_37)))
% FOF formula (forall (A_63:hoare_1775062406iple_a) (B_37:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_63) B_37)) ((semila13410563le_a_o (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> (((eq hoare_1775062406iple_a) X) A_63)))) B_37))) of role axiom named fact_327_insert__def
% A new axiom: (forall (A_63:hoare_1775062406iple_a) (B_37:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_63) B_37)) ((semila13410563le_a_o (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> (((eq hoare_1775062406iple_a) X) A_63)))) B_37)))
% FOF formula (forall (G_12:(hoare_1775062406iple_a->Prop)) (P_22:(x_a->(state->Prop))) (Pn_3:pname) (Q_14:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_12) ((insert1281456128iple_a (((hoare_1766022166iple_a P_22) (the_com (body_1 Pn_3))) Q_14)) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_12) ((insert1281456128iple_a (((hoare_1766022166iple_a P_22) (body Pn_3)) Q_14)) bot_bo751897185le_a_o)))) of role axiom named fact_328_weak__Body
% A new axiom: (forall (G_12:(hoare_1775062406iple_a->Prop)) (P_22:(x_a->(state->Prop))) (Pn_3:pname) (Q_14:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_12) ((insert1281456128iple_a (((hoare_1766022166iple_a P_22) (the_com (body_1 Pn_3))) Q_14)) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_12) ((insert1281456128iple_a (((hoare_1766022166iple_a P_22) (body Pn_3)) Q_14)) bot_bo751897185le_a_o))))
% FOF formula (forall (G_12:(hoare_1167836817_state->Prop)) (P_22:(state->(state->Prop))) (Pn_3:pname) (Q_14:(state->(state->Prop))), (((hoare_123228589_state G_12) ((insert2134838167_state (((hoare_908217195_state P_22) (the_com (body_1 Pn_3))) Q_14)) bot_bo70021908tate_o))->((hoare_123228589_state G_12) ((insert2134838167_state (((hoare_908217195_state P_22) (body Pn_3)) Q_14)) bot_bo70021908tate_o)))) of role axiom named fact_329_weak__Body
% A new axiom: (forall (G_12:(hoare_1167836817_state->Prop)) (P_22:(state->(state->Prop))) (Pn_3:pname) (Q_14:(state->(state->Prop))), (((hoare_123228589_state G_12) ((insert2134838167_state (((hoare_908217195_state P_22) (the_com (body_1 Pn_3))) Q_14)) bot_bo70021908tate_o))->((hoare_123228589_state G_12) ((insert2134838167_state (((hoare_908217195_state P_22) (body Pn_3)) Q_14)) bot_bo70021908tate_o))))
% FOF formula (forall (P_21:(x_a->(state->Prop))) (Pn_2:pname) (Q_13:(x_a->(state->Prop))) (G_11:(hoare_1775062406iple_a->Prop)), (((hoare_1508237396rivs_a ((insert1281456128iple_a (((hoare_1766022166iple_a P_21) (body Pn_2)) Q_13)) G_11)) ((insert1281456128iple_a (((hoare_1766022166iple_a P_21) (the_com (body_1 Pn_2))) Q_13)) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_11) ((insert1281456128iple_a (((hoare_1766022166iple_a P_21) (body Pn_2)) Q_13)) bot_bo751897185le_a_o)))) of role axiom named fact_330_BodyN
% A new axiom: (forall (P_21:(x_a->(state->Prop))) (Pn_2:pname) (Q_13:(x_a->(state->Prop))) (G_11:(hoare_1775062406iple_a->Prop)), (((hoare_1508237396rivs_a ((insert1281456128iple_a (((hoare_1766022166iple_a P_21) (body Pn_2)) Q_13)) G_11)) ((insert1281456128iple_a (((hoare_1766022166iple_a P_21) (the_com (body_1 Pn_2))) Q_13)) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_11) ((insert1281456128iple_a (((hoare_1766022166iple_a P_21) (body Pn_2)) Q_13)) bot_bo751897185le_a_o))))
% FOF formula (forall (P_21:(state->(state->Prop))) (Pn_2:pname) (Q_13:(state->(state->Prop))) (G_11:(hoare_1167836817_state->Prop)), (((hoare_123228589_state ((insert2134838167_state (((hoare_908217195_state P_21) (body Pn_2)) Q_13)) G_11)) ((insert2134838167_state (((hoare_908217195_state P_21) (the_com (body_1 Pn_2))) Q_13)) bot_bo70021908tate_o))->((hoare_123228589_state G_11) ((insert2134838167_state (((hoare_908217195_state P_21) (body Pn_2)) Q_13)) bot_bo70021908tate_o)))) of role axiom named fact_331_BodyN
% A new axiom: (forall (P_21:(state->(state->Prop))) (Pn_2:pname) (Q_13:(state->(state->Prop))) (G_11:(hoare_1167836817_state->Prop)), (((hoare_123228589_state ((insert2134838167_state (((hoare_908217195_state P_21) (body Pn_2)) Q_13)) G_11)) ((insert2134838167_state (((hoare_908217195_state P_21) (the_com (body_1 Pn_2))) Q_13)) bot_bo70021908tate_o))->((hoare_123228589_state G_11) ((insert2134838167_state (((hoare_908217195_state P_21) (body Pn_2)) Q_13)) bot_bo70021908tate_o))))
% FOF formula (forall (N_5:nat) (Ts:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) Ts)->((hoare_56934129_state (suc N_5)) X)))->(forall (X:hoare_1167836817_state), (((member2058392318_state X) Ts)->((hoare_56934129_state N_5) X))))) of role axiom named fact_332_triples__valid__Suc
% A new axiom: (forall (N_5:nat) (Ts:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) Ts)->((hoare_56934129_state (suc N_5)) X)))->(forall (X:hoare_1167836817_state), (((member2058392318_state X) Ts)->((hoare_56934129_state N_5) X)))))
% FOF formula (forall (N_5:nat) (Ts:(hoare_1775062406iple_a->Prop)), ((forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) Ts)->((hoare_1462269968alid_a (suc N_5)) X)))->(forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) Ts)->((hoare_1462269968alid_a N_5) X))))) of role axiom named fact_333_triples__valid__Suc
% A new axiom: (forall (N_5:nat) (Ts:(hoare_1775062406iple_a->Prop)), ((forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) Ts)->((hoare_1462269968alid_a (suc N_5)) X)))->(forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) Ts)->((hoare_1462269968alid_a N_5) X)))))
% FOF formula (forall (G_10:(hoare_1775062406iple_a->Prop)) (C_26:com) (Q_12:(x_a->(state->Prop))) (P_20:(x_a->(state->Prop))), ((forall (Z_8:x_a) (S_3:state), (((P_20 Z_8) S_3)->((hoare_1508237396rivs_a G_10) ((insert1281456128iple_a (((hoare_1766022166iple_a (fun (Za:x_a) (S_4:state)=> (((eq state) S_4) S_3))) C_26) (fun (Z_9:x_a)=> (Q_12 Z_8)))) bot_bo751897185le_a_o))))->((hoare_1508237396rivs_a G_10) ((insert1281456128iple_a (((hoare_1766022166iple_a P_20) C_26) Q_12)) bot_bo751897185le_a_o)))) of role axiom named fact_334_escape
% A new axiom: (forall (G_10:(hoare_1775062406iple_a->Prop)) (C_26:com) (Q_12:(x_a->(state->Prop))) (P_20:(x_a->(state->Prop))), ((forall (Z_8:x_a) (S_3:state), (((P_20 Z_8) S_3)->((hoare_1508237396rivs_a G_10) ((insert1281456128iple_a (((hoare_1766022166iple_a (fun (Za:x_a) (S_4:state)=> (((eq state) S_4) S_3))) C_26) (fun (Z_9:x_a)=> (Q_12 Z_8)))) bot_bo751897185le_a_o))))->((hoare_1508237396rivs_a G_10) ((insert1281456128iple_a (((hoare_1766022166iple_a P_20) C_26) Q_12)) bot_bo751897185le_a_o))))
% FOF formula (forall (G_10:(hoare_1167836817_state->Prop)) (C_26:com) (Q_12:(state->(state->Prop))) (P_20:(state->(state->Prop))), ((forall (Z_8:state) (S_3:state), (((P_20 Z_8) S_3)->((hoare_123228589_state G_10) ((insert2134838167_state (((hoare_908217195_state (fun (Za:state) (S_4:state)=> (((eq state) S_4) S_3))) C_26) (fun (Z_9:state)=> (Q_12 Z_8)))) bot_bo70021908tate_o))))->((hoare_123228589_state G_10) ((insert2134838167_state (((hoare_908217195_state P_20) C_26) Q_12)) bot_bo70021908tate_o)))) of role axiom named fact_335_escape
% A new axiom: (forall (G_10:(hoare_1167836817_state->Prop)) (C_26:com) (Q_12:(state->(state->Prop))) (P_20:(state->(state->Prop))), ((forall (Z_8:state) (S_3:state), (((P_20 Z_8) S_3)->((hoare_123228589_state G_10) ((insert2134838167_state (((hoare_908217195_state (fun (Za:state) (S_4:state)=> (((eq state) S_4) S_3))) C_26) (fun (Z_9:state)=> (Q_12 Z_8)))) bot_bo70021908tate_o))))->((hoare_123228589_state G_10) ((insert2134838167_state (((hoare_908217195_state P_20) C_26) Q_12)) bot_bo70021908tate_o))))
% FOF formula (forall (P_19:(x_a->(state->Prop))) (G_9:(hoare_1775062406iple_a->Prop)) (P_18:(x_a->(state->Prop))) (C_25:com) (Q_11:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_9) ((insert1281456128iple_a (((hoare_1766022166iple_a P_18) C_25) Q_11)) bot_bo751897185le_a_o))->((forall (Z_8:x_a) (S_3:state), (((P_19 Z_8) S_3)->((P_18 Z_8) S_3)))->((hoare_1508237396rivs_a G_9) ((insert1281456128iple_a (((hoare_1766022166iple_a P_19) C_25) Q_11)) bot_bo751897185le_a_o))))) of role axiom named fact_336_conseq1
% A new axiom: (forall (P_19:(x_a->(state->Prop))) (G_9:(hoare_1775062406iple_a->Prop)) (P_18:(x_a->(state->Prop))) (C_25:com) (Q_11:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_9) ((insert1281456128iple_a (((hoare_1766022166iple_a P_18) C_25) Q_11)) bot_bo751897185le_a_o))->((forall (Z_8:x_a) (S_3:state), (((P_19 Z_8) S_3)->((P_18 Z_8) S_3)))->((hoare_1508237396rivs_a G_9) ((insert1281456128iple_a (((hoare_1766022166iple_a P_19) C_25) Q_11)) bot_bo751897185le_a_o)))))
% FOF formula (forall (P_19:(state->(state->Prop))) (G_9:(hoare_1167836817_state->Prop)) (P_18:(state->(state->Prop))) (C_25:com) (Q_11:(state->(state->Prop))), (((hoare_123228589_state G_9) ((insert2134838167_state (((hoare_908217195_state P_18) C_25) Q_11)) bot_bo70021908tate_o))->((forall (Z_8:state) (S_3:state), (((P_19 Z_8) S_3)->((P_18 Z_8) S_3)))->((hoare_123228589_state G_9) ((insert2134838167_state (((hoare_908217195_state P_19) C_25) Q_11)) bot_bo70021908tate_o))))) of role axiom named fact_337_conseq1
% A new axiom: (forall (P_19:(state->(state->Prop))) (G_9:(hoare_1167836817_state->Prop)) (P_18:(state->(state->Prop))) (C_25:com) (Q_11:(state->(state->Prop))), (((hoare_123228589_state G_9) ((insert2134838167_state (((hoare_908217195_state P_18) C_25) Q_11)) bot_bo70021908tate_o))->((forall (Z_8:state) (S_3:state), (((P_19 Z_8) S_3)->((P_18 Z_8) S_3)))->((hoare_123228589_state G_9) ((insert2134838167_state (((hoare_908217195_state P_19) C_25) Q_11)) bot_bo70021908tate_o)))))
% FOF formula (forall (Q_10:(x_a->(state->Prop))) (G_8:(hoare_1775062406iple_a->Prop)) (P_17:(x_a->(state->Prop))) (C_24:com) (Q_9:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_8) ((insert1281456128iple_a (((hoare_1766022166iple_a P_17) C_24) Q_9)) bot_bo751897185le_a_o))->((forall (Z_8:x_a) (S_3:state), (((Q_9 Z_8) S_3)->((Q_10 Z_8) S_3)))->((hoare_1508237396rivs_a G_8) ((insert1281456128iple_a (((hoare_1766022166iple_a P_17) C_24) Q_10)) bot_bo751897185le_a_o))))) of role axiom named fact_338_conseq2
% A new axiom: (forall (Q_10:(x_a->(state->Prop))) (G_8:(hoare_1775062406iple_a->Prop)) (P_17:(x_a->(state->Prop))) (C_24:com) (Q_9:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_8) ((insert1281456128iple_a (((hoare_1766022166iple_a P_17) C_24) Q_9)) bot_bo751897185le_a_o))->((forall (Z_8:x_a) (S_3:state), (((Q_9 Z_8) S_3)->((Q_10 Z_8) S_3)))->((hoare_1508237396rivs_a G_8) ((insert1281456128iple_a (((hoare_1766022166iple_a P_17) C_24) Q_10)) bot_bo751897185le_a_o)))))
% FOF formula (forall (Q_10:(state->(state->Prop))) (G_8:(hoare_1167836817_state->Prop)) (P_17:(state->(state->Prop))) (C_24:com) (Q_9:(state->(state->Prop))), (((hoare_123228589_state G_8) ((insert2134838167_state (((hoare_908217195_state P_17) C_24) Q_9)) bot_bo70021908tate_o))->((forall (Z_8:state) (S_3:state), (((Q_9 Z_8) S_3)->((Q_10 Z_8) S_3)))->((hoare_123228589_state G_8) ((insert2134838167_state (((hoare_908217195_state P_17) C_24) Q_10)) bot_bo70021908tate_o))))) of role axiom named fact_339_conseq2
% A new axiom: (forall (Q_10:(state->(state->Prop))) (G_8:(hoare_1167836817_state->Prop)) (P_17:(state->(state->Prop))) (C_24:com) (Q_9:(state->(state->Prop))), (((hoare_123228589_state G_8) ((insert2134838167_state (((hoare_908217195_state P_17) C_24) Q_9)) bot_bo70021908tate_o))->((forall (Z_8:state) (S_3:state), (((Q_9 Z_8) S_3)->((Q_10 Z_8) S_3)))->((hoare_123228589_state G_8) ((insert2134838167_state (((hoare_908217195_state P_17) C_24) Q_10)) bot_bo70021908tate_o)))))
% FOF formula (forall (Fa:(state->nat)) (Fun1_1:(state->(state->Prop))) (Com_3:com) (Fun2_1:(state->(state->Prop))), (((eq nat) ((hoare_545207370_state Fa) (((hoare_908217195_state Fun1_1) Com_3) Fun2_1))) zero_zero_nat)) of role axiom named fact_340_triple_Osize_I1_J
% A new axiom: (forall (Fa:(state->nat)) (Fun1_1:(state->(state->Prop))) (Com_3:com) (Fun2_1:(state->(state->Prop))), (((eq nat) ((hoare_545207370_state Fa) (((hoare_908217195_state Fun1_1) Com_3) Fun2_1))) zero_zero_nat))
% FOF formula (forall (Fa:(x_a->nat)) (Fun1_1:(x_a->(state->Prop))) (Com_3:com) (Fun2_1:(x_a->(state->Prop))), (((eq nat) ((hoare_1118907895size_a Fa) (((hoare_1766022166iple_a Fun1_1) Com_3) Fun2_1))) zero_zero_nat)) of role axiom named fact_341_triple_Osize_I1_J
% A new axiom: (forall (Fa:(x_a->nat)) (Fun1_1:(x_a->(state->Prop))) (Com_3:com) (Fun2_1:(x_a->(state->Prop))), (((eq nat) ((hoare_1118907895size_a Fa) (((hoare_1766022166iple_a Fun1_1) Com_3) Fun2_1))) zero_zero_nat))
% FOF formula (forall (C_19:com), (((eq hoare_1167836817_state) (hoare_Mirabelle_MGT C_19)) (((hoare_908217195_state fequal_state) C_19) (evalc C_19)))) of role axiom named fact_342_MGT__def
% A new axiom: (forall (C_19:com), (((eq hoare_1167836817_state) (hoare_Mirabelle_MGT C_19)) (((hoare_908217195_state fequal_state) C_19) (evalc C_19))))
% FOF formula (forall (Fun1:(state->(state->Prop))) (Com_2:com) (Fun2:(state->(state->Prop))), (((eq nat) (size_s645941755_state (((hoare_908217195_state Fun1) Com_2) Fun2))) zero_zero_nat)) of role axiom named fact_343_triple_Osize_I2_J
% A new axiom: (forall (Fun1:(state->(state->Prop))) (Com_2:com) (Fun2:(state->(state->Prop))), (((eq nat) (size_s645941755_state (((hoare_908217195_state Fun1) Com_2) Fun2))) zero_zero_nat))
% FOF formula (forall (Fun1:(x_a->(state->Prop))) (Com_2:com) (Fun2:(x_a->(state->Prop))), (((eq nat) (size_s724313756iple_a (((hoare_1766022166iple_a Fun1) Com_2) Fun2))) zero_zero_nat)) of role axiom named fact_344_triple_Osize_I2_J
% A new axiom: (forall (Fun1:(x_a->(state->Prop))) (Com_2:com) (Fun2:(x_a->(state->Prop))), (((eq nat) (size_s724313756iple_a (((hoare_1766022166iple_a Fun1) Com_2) Fun2))) zero_zero_nat))
% FOF formula (forall (Q_8:(state->(state->Prop))) (P_16:(state->(state->Prop))) (G_7:(hoare_1167836817_state->Prop)) (P_15:(state->(state->Prop))) (C_23:com) (Q_7:(state->(state->Prop))), (((hoare_123228589_state G_7) ((insert2134838167_state (((hoare_908217195_state P_15) C_23) Q_7)) bot_bo70021908tate_o))->((forall (Z_8:state) (S_3:state), (((P_16 Z_8) S_3)->(forall (S_4:state), ((forall (Z_9:state), (((P_15 Z_9) S_3)->((Q_7 Z_9) S_4)))->((Q_8 Z_8) S_4)))))->((hoare_123228589_state G_7) ((insert2134838167_state (((hoare_908217195_state P_16) C_23) Q_8)) bot_bo70021908tate_o))))) of role axiom named fact_345_conseq12
% A new axiom: (forall (Q_8:(state->(state->Prop))) (P_16:(state->(state->Prop))) (G_7:(hoare_1167836817_state->Prop)) (P_15:(state->(state->Prop))) (C_23:com) (Q_7:(state->(state->Prop))), (((hoare_123228589_state G_7) ((insert2134838167_state (((hoare_908217195_state P_15) C_23) Q_7)) bot_bo70021908tate_o))->((forall (Z_8:state) (S_3:state), (((P_16 Z_8) S_3)->(forall (S_4:state), ((forall (Z_9:state), (((P_15 Z_9) S_3)->((Q_7 Z_9) S_4)))->((Q_8 Z_8) S_4)))))->((hoare_123228589_state G_7) ((insert2134838167_state (((hoare_908217195_state P_16) C_23) Q_8)) bot_bo70021908tate_o)))))
% FOF formula (forall (Q_8:(x_a->(state->Prop))) (P_16:(x_a->(state->Prop))) (G_7:(hoare_1775062406iple_a->Prop)) (P_15:(x_a->(state->Prop))) (C_23:com) (Q_7:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_7) ((insert1281456128iple_a (((hoare_1766022166iple_a P_15) C_23) Q_7)) bot_bo751897185le_a_o))->((forall (Z_8:x_a) (S_3:state), (((P_16 Z_8) S_3)->(forall (S_4:state), ((forall (Z_9:x_a), (((P_15 Z_9) S_3)->((Q_7 Z_9) S_4)))->((Q_8 Z_8) S_4)))))->((hoare_1508237396rivs_a G_7) ((insert1281456128iple_a (((hoare_1766022166iple_a P_16) C_23) Q_8)) bot_bo751897185le_a_o))))) of role axiom named fact_346_conseq12
% A new axiom: (forall (Q_8:(x_a->(state->Prop))) (P_16:(x_a->(state->Prop))) (G_7:(hoare_1775062406iple_a->Prop)) (P_15:(x_a->(state->Prop))) (C_23:com) (Q_7:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_7) ((insert1281456128iple_a (((hoare_1766022166iple_a P_15) C_23) Q_7)) bot_bo751897185le_a_o))->((forall (Z_8:x_a) (S_3:state), (((P_16 Z_8) S_3)->(forall (S_4:state), ((forall (Z_9:x_a), (((P_15 Z_9) S_3)->((Q_7 Z_9) S_4)))->((Q_8 Z_8) S_4)))))->((hoare_1508237396rivs_a G_7) ((insert1281456128iple_a (((hoare_1766022166iple_a P_16) C_23) Q_8)) bot_bo751897185le_a_o)))))
% FOF formula (forall (X_23:hoare_1167836817_state), (((eq hoare_1167836817_state) (the_el323660082_state ((insert2134838167_state X_23) bot_bo70021908tate_o))) X_23)) of role axiom named fact_347_the__elem__eq
% A new axiom: (forall (X_23:hoare_1167836817_state), (((eq hoare_1167836817_state) (the_el323660082_state ((insert2134838167_state X_23) bot_bo70021908tate_o))) X_23))
% FOF formula (forall (X_23:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (the_el1844711461iple_a ((insert1281456128iple_a X_23) bot_bo751897185le_a_o))) X_23)) of role axiom named fact_348_the__elem__eq
% A new axiom: (forall (X_23:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (the_el1844711461iple_a ((insert1281456128iple_a X_23) bot_bo751897185le_a_o))) X_23))
% FOF formula (forall (X_23:pname), (((eq pname) (the_elem_pname ((insert_pname X_23) bot_bot_pname_o))) X_23)) of role axiom named fact_349_the__elem__eq
% A new axiom: (forall (X_23:pname), (((eq pname) (the_elem_pname ((insert_pname X_23) bot_bot_pname_o))) X_23))
% FOF formula (forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))) of role axiom named fact_350_Zero__not__Suc
% A new axiom: (forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M))))
% FOF formula (forall (Nat_1:nat), (not (((eq nat) zero_zero_nat) (suc Nat_1)))) of role axiom named fact_351_nat_Osimps_I2_J
% A new axiom: (forall (Nat_1:nat), (not (((eq nat) zero_zero_nat) (suc Nat_1))))
% FOF formula (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))) of role axiom named fact_352_Suc__not__Zero
% A new axiom: (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat)))
% FOF formula (forall (Nat_3:nat), (not (((eq nat) (suc Nat_3)) zero_zero_nat))) of role axiom named fact_353_nat_Osimps_I3_J
% A new axiom: (forall (Nat_3:nat), (not (((eq nat) (suc Nat_3)) zero_zero_nat)))
% FOF formula (forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))) of role axiom named fact_354_Zero__neq__Suc
% A new axiom: (forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M))))
% FOF formula (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))) of role axiom named fact_355_Suc__neq__Zero
% A new axiom: (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat)))
% FOF formula (forall (X:pname), ((iff (bot_bot_pname_o X)) bot_bot_o)) of role axiom named fact_356_bot__fun__def
% A new axiom: (forall (X:pname), ((iff (bot_bot_pname_o X)) bot_bot_o))
% FOF formula (forall (X:hoare_1775062406iple_a), ((iff (bot_bo751897185le_a_o X)) bot_bot_o)) of role axiom named fact_357_bot__fun__def
% A new axiom: (forall (X:hoare_1775062406iple_a), ((iff (bot_bo751897185le_a_o X)) bot_bot_o))
% FOF formula (forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) bot_bot_o)) of role axiom named fact_358_bot__fun__def
% A new axiom: (forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) bot_bot_o))
% FOF formula (((eq nat) bot_bot_nat) zero_zero_nat) of role axiom named fact_359_bot__nat__def
% A new axiom: (((eq nat) bot_bot_nat) zero_zero_nat)
% FOF formula (forall (X_1:nat) (Y:nat), ((((eq nat) (suc X_1)) (suc Y))->(((eq nat) X_1) Y))) of role axiom named fact_360_Suc__inject
% A new axiom: (forall (X_1:nat) (Y:nat), ((((eq nat) (suc X_1)) (suc Y))->(((eq nat) X_1) Y)))
% FOF formula (forall (Nat_2:nat) (Nat_1:nat), ((iff (((eq nat) (suc Nat_2)) (suc Nat_1))) (((eq nat) Nat_2) Nat_1))) of role axiom named fact_361_nat_Oinject
% A new axiom: (forall (Nat_2:nat) (Nat_1:nat), ((iff (((eq nat) (suc Nat_2)) (suc Nat_1))) (((eq nat) Nat_2) Nat_1)))
% FOF formula (forall (N_1:nat), (not (((eq nat) (suc N_1)) N_1))) of role axiom named fact_362_Suc__n__not__n
% A new axiom: (forall (N_1:nat), (not (((eq nat) (suc N_1)) N_1)))
% FOF formula (forall (N_1:nat), (not (((eq nat) N_1) (suc N_1)))) of role axiom named fact_363_n__not__Suc__n
% A new axiom: (forall (N_1:nat), (not (((eq nat) N_1) (suc N_1))))
% FOF formula (forall (X_22:pname), ((iff (bot_bot_pname_o X_22)) bot_bot_o)) of role axiom named fact_364_bot__apply
% A new axiom: (forall (X_22:pname), ((iff (bot_bot_pname_o X_22)) bot_bot_o))
% FOF formula (forall (X_22:hoare_1775062406iple_a), ((iff (bot_bo751897185le_a_o X_22)) bot_bot_o)) of role axiom named fact_365_bot__apply
% A new axiom: (forall (X_22:hoare_1775062406iple_a), ((iff (bot_bo751897185le_a_o X_22)) bot_bot_o))
% FOF formula (forall (X_22:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_22)) bot_bot_o)) of role axiom named fact_366_bot__apply
% A new axiom: (forall (X_22:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_22)) bot_bot_o))
% FOF formula (forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat:nat), (not (((eq nat) Y) (suc Nat))))->False))) of role axiom named fact_367_nat_Oexhaust
% A new axiom: (forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat:nat), (not (((eq nat) Y) (suc Nat))))->False)))
% FOF formula (forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N:nat), ((P (suc N))->(P N)))->(P zero_zero_nat)))) of role axiom named fact_368_zero__induct
% A new axiom: (forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N:nat), ((P (suc N))->(P N)))->(P zero_zero_nat))))
% FOF formula (forall (N_1:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N:nat), ((P N)->(P (suc N))))->(P N_1)))) of role axiom named fact_369_nat__induct
% A new axiom: (forall (N_1:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N:nat), ((P N)->(P (suc N))))->(P N_1))))
% FOF formula (forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ex nat) (fun (M_1:nat)=> (((eq nat) N_1) (suc M_1)))))) of role axiom named fact_370_not0__implies__Suc
% A new axiom: (forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ex nat) (fun (M_1:nat)=> (((eq nat) N_1) (suc M_1))))))
% FOF formula (forall (Pn_1:pname) (S0:state) (N_1:nat) (S1:state), (((((evaln (the_com (body_1 Pn_1))) S0) N_1) S1)->((((evaln (body Pn_1)) S0) (suc N_1)) S1))) of role axiom named fact_371_evaln_OBody
% A new axiom: (forall (Pn_1:pname) (S0:state) (N_1:nat) (S1:state), (((((evaln (the_com (body_1 Pn_1))) S0) N_1) S1)->((((evaln (body Pn_1)) S0) (suc N_1)) S1)))
% FOF formula (forall (G_6:(hoare_1167836817_state->Prop)) (P_14:(state->(state->Prop))), ((hoare_123228589_state G_6) ((insert2134838167_state (((hoare_908217195_state P_14) skip) P_14)) bot_bo70021908tate_o))) of role axiom named fact_372_hoare__derivs_OSkip
% A new axiom: (forall (G_6:(hoare_1167836817_state->Prop)) (P_14:(state->(state->Prop))), ((hoare_123228589_state G_6) ((insert2134838167_state (((hoare_908217195_state P_14) skip) P_14)) bot_bo70021908tate_o)))
% FOF formula (forall (G_6:(hoare_1775062406iple_a->Prop)) (P_14:(x_a->(state->Prop))), ((hoare_1508237396rivs_a G_6) ((insert1281456128iple_a (((hoare_1766022166iple_a P_14) skip) P_14)) bot_bo751897185le_a_o))) of role axiom named fact_373_hoare__derivs_OSkip
% A new axiom: (forall (G_6:(hoare_1775062406iple_a->Prop)) (P_14:(x_a->(state->Prop))), ((hoare_1508237396rivs_a G_6) ((insert1281456128iple_a (((hoare_1766022166iple_a P_14) skip) P_14)) bot_bo751897185le_a_o)))
% FOF formula (forall (S:state) (N_1:nat) (T:state), (((((evaln skip) S) N_1) T)->(((eq state) T) S))) of role axiom named fact_374_evaln__elim__cases_I1_J
% A new axiom: (forall (S:state) (N_1:nat) (T:state), (((((evaln skip) S) N_1) T)->(((eq state) T) S)))
% FOF formula (forall (S:state) (N_1:nat), ((((evaln skip) S) N_1) S)) of role axiom named fact_375_evaln_OSkip
% A new axiom: (forall (S:state) (N_1:nat), ((((evaln skip) S) N_1) S))
% FOF formula (forall (S:state), (((evalc skip) S) S)) of role axiom named fact_376_evalc_OSkip
% A new axiom: (forall (S:state), (((evalc skip) S) S))
% FOF formula (forall (S:state) (T:state), ((((evalc skip) S) T)->(((eq state) T) S))) of role axiom named fact_377_evalc__elim__cases_I1_J
% A new axiom: (forall (S:state) (T:state), ((((evalc skip) S) T)->(((eq state) T) S)))
% FOF formula (forall (C_19:com) (S:state) (N_1:nat) (S_5:state), (((((evaln C_19) S) N_1) S_5)->((((evaln C_19) S) (suc N_1)) S_5))) of role axiom named fact_378_evaln__Suc
% A new axiom: (forall (C_19:com) (S:state) (N_1:nat) (S_5:state), (((((evaln C_19) S) N_1) S_5)->((((evaln C_19) S) (suc N_1)) S_5)))
% FOF formula (forall (C_19:com) (S:state) (T:state), ((iff (((evalc C_19) S) T)) ((ex nat) (fun (N:nat)=> ((((evaln C_19) S) N) T))))) of role axiom named fact_379_eval__eq
% A new axiom: (forall (C_19:com) (S:state) (T:state), ((iff (((evalc C_19) S) T)) ((ex nat) (fun (N:nat)=> ((((evaln C_19) S) N) T)))))
% FOF formula (forall (C_19:com) (S:state) (N_1:nat) (T:state), (((((evaln C_19) S) N_1) T)->(((evalc C_19) S) T))) of role axiom named fact_380_evaln__evalc
% A new axiom: (forall (C_19:com) (S:state) (N_1:nat) (T:state), (((((evaln C_19) S) N_1) T)->(((evalc C_19) S) T)))
% FOF formula (forall (Pname_1:pname), (not (((eq com) (body Pname_1)) skip))) of role axiom named fact_381_com_Osimps_I19_J
% A new axiom: (forall (Pname_1:pname), (not (((eq com) (body Pname_1)) skip)))
% FOF formula (forall (Pname_1:pname), (not (((eq com) skip) (body Pname_1)))) of role axiom named fact_382_com_Osimps_I18_J
% A new axiom: (forall (Pname_1:pname), (not (((eq com) skip) (body Pname_1))))
% FOF formula (forall (N_4:nat) (P_13:(state->(state->Prop))) (C_22:com) (Q_6:(state->(state->Prop))), ((iff ((hoare_56934129_state N_4) (((hoare_908217195_state P_13) C_22) Q_6))) (forall (Z_8:state) (S_3:state), (((P_13 Z_8) S_3)->(forall (S_4:state), (((((evaln C_22) S_3) N_4) S_4)->((Q_6 Z_8) S_4))))))) of role axiom named fact_383_triple__valid__def2
% A new axiom: (forall (N_4:nat) (P_13:(state->(state->Prop))) (C_22:com) (Q_6:(state->(state->Prop))), ((iff ((hoare_56934129_state N_4) (((hoare_908217195_state P_13) C_22) Q_6))) (forall (Z_8:state) (S_3:state), (((P_13 Z_8) S_3)->(forall (S_4:state), (((((evaln C_22) S_3) N_4) S_4)->((Q_6 Z_8) S_4)))))))
% FOF formula (forall (N_4:nat) (P_13:(x_a->(state->Prop))) (C_22:com) (Q_6:(x_a->(state->Prop))), ((iff ((hoare_1462269968alid_a N_4) (((hoare_1766022166iple_a P_13) C_22) Q_6))) (forall (Z_8:x_a) (S_3:state), (((P_13 Z_8) S_3)->(forall (S_4:state), (((((evaln C_22) S_3) N_4) S_4)->((Q_6 Z_8) S_4))))))) of role axiom named fact_384_triple__valid__def2
% A new axiom: (forall (N_4:nat) (P_13:(x_a->(state->Prop))) (C_22:com) (Q_6:(x_a->(state->Prop))), ((iff ((hoare_1462269968alid_a N_4) (((hoare_1766022166iple_a P_13) C_22) Q_6))) (forall (Z_8:x_a) (S_3:state), (((P_13 Z_8) S_3)->(forall (S_4:state), (((((evaln C_22) S_3) N_4) S_4)->((Q_6 Z_8) S_4)))))))
% FOF formula (forall (P:pname) (S:state) (N_1:nat) (S1:state), (((((evaln (body P)) S) N_1) S1)->((forall (N:nat), ((((eq nat) N_1) (suc N))->(((((evaln (the_com (body_1 P))) S) N) S1)->False)))->False))) of role axiom named fact_385_evaln__elim__cases_I6_J
% A new axiom: (forall (P:pname) (S:state) (N_1:nat) (S1:state), (((((evaln (body P)) S) N_1) S1)->((forall (N:nat), ((((eq nat) N_1) (suc N))->(((((evaln (the_com (body_1 P))) S) N) S1)->False)))->False)))
% FOF formula (forall (C_19:com) (S:state) (T:state), ((((evalc C_19) S) T)->((ex nat) (fun (N:nat)=> ((((evaln C_19) S) N) T))))) of role axiom named fact_386_evalc__evaln
% A new axiom: (forall (C_19:com) (S:state) (T:state), ((((evalc C_19) S) T)->((ex nat) (fun (N:nat)=> ((((evaln C_19) S) N) T)))))
% FOF formula (forall (G_5:(hoare_1167836817_state->Prop)) (P_12:(state->(state->Prop))) (B_36:(state->Prop)) (C_21:com), ((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state (fun (Z_8:state) (S_3:state)=> ((and ((P_12 Z_8) S_3)) (not (B_36 S_3))))) ((while B_36) C_21)) P_12)) bot_bo70021908tate_o))) of role axiom named fact_387_LoopF
% A new axiom: (forall (G_5:(hoare_1167836817_state->Prop)) (P_12:(state->(state->Prop))) (B_36:(state->Prop)) (C_21:com), ((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state (fun (Z_8:state) (S_3:state)=> ((and ((P_12 Z_8) S_3)) (not (B_36 S_3))))) ((while B_36) C_21)) P_12)) bot_bo70021908tate_o)))
% FOF formula (forall (G_5:(hoare_1775062406iple_a->Prop)) (P_12:(x_a->(state->Prop))) (B_36:(state->Prop)) (C_21:com), ((hoare_1508237396rivs_a G_5) ((insert1281456128iple_a (((hoare_1766022166iple_a (fun (Z_8:x_a) (S_3:state)=> ((and ((P_12 Z_8) S_3)) (not (B_36 S_3))))) ((while B_36) C_21)) P_12)) bot_bo751897185le_a_o))) of role axiom named fact_388_LoopF
% A new axiom: (forall (G_5:(hoare_1775062406iple_a->Prop)) (P_12:(x_a->(state->Prop))) (B_36:(state->Prop)) (C_21:com), ((hoare_1508237396rivs_a G_5) ((insert1281456128iple_a (((hoare_1766022166iple_a (fun (Z_8:x_a) (S_3:state)=> ((and ((P_12 Z_8) S_3)) (not (B_36 S_3))))) ((while B_36) C_21)) P_12)) bot_bo751897185le_a_o)))
% FOF formula (forall (D:com) (R_1:(state->(state->Prop))) (G_4:(hoare_1167836817_state->Prop)) (P_11:(state->(state->Prop))) (C_20:com) (Q_5:(state->(state->Prop))), (((hoare_123228589_state G_4) ((insert2134838167_state (((hoare_908217195_state P_11) C_20) Q_5)) bot_bo70021908tate_o))->(((hoare_123228589_state G_4) ((insert2134838167_state (((hoare_908217195_state Q_5) D) R_1)) bot_bo70021908tate_o))->((hoare_123228589_state G_4) ((insert2134838167_state (((hoare_908217195_state P_11) ((semi C_20) D)) R_1)) bot_bo70021908tate_o))))) of role axiom named fact_389_Comp
% A new axiom: (forall (D:com) (R_1:(state->(state->Prop))) (G_4:(hoare_1167836817_state->Prop)) (P_11:(state->(state->Prop))) (C_20:com) (Q_5:(state->(state->Prop))), (((hoare_123228589_state G_4) ((insert2134838167_state (((hoare_908217195_state P_11) C_20) Q_5)) bot_bo70021908tate_o))->(((hoare_123228589_state G_4) ((insert2134838167_state (((hoare_908217195_state Q_5) D) R_1)) bot_bo70021908tate_o))->((hoare_123228589_state G_4) ((insert2134838167_state (((hoare_908217195_state P_11) ((semi C_20) D)) R_1)) bot_bo70021908tate_o)))))
% FOF formula (forall (D:com) (R_1:(x_a->(state->Prop))) (G_4:(hoare_1775062406iple_a->Prop)) (P_11:(x_a->(state->Prop))) (C_20:com) (Q_5:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_4) ((insert1281456128iple_a (((hoare_1766022166iple_a P_11) C_20) Q_5)) bot_bo751897185le_a_o))->(((hoare_1508237396rivs_a G_4) ((insert1281456128iple_a (((hoare_1766022166iple_a Q_5) D) R_1)) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_4) ((insert1281456128iple_a (((hoare_1766022166iple_a P_11) ((semi C_20) D)) R_1)) bot_bo751897185le_a_o))))) of role axiom named fact_390_Comp
% A new axiom: (forall (D:com) (R_1:(x_a->(state->Prop))) (G_4:(hoare_1775062406iple_a->Prop)) (P_11:(x_a->(state->Prop))) (C_20:com) (Q_5:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_4) ((insert1281456128iple_a (((hoare_1766022166iple_a P_11) C_20) Q_5)) bot_bo751897185le_a_o))->(((hoare_1508237396rivs_a G_4) ((insert1281456128iple_a (((hoare_1766022166iple_a Q_5) D) R_1)) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_4) ((insert1281456128iple_a (((hoare_1766022166iple_a P_11) ((semi C_20) D)) R_1)) bot_bo751897185le_a_o)))))
% FOF formula (forall (X_21:(hoare_1167836817_state->Prop)), (((eq hoare_1167836817_state) (the_el323660082_state X_21)) (the_Ho310147232_state (fun (X:hoare_1167836817_state)=> (((eq (hoare_1167836817_state->Prop)) X_21) ((insert2134838167_state X) bot_bo70021908tate_o)))))) of role axiom named fact_391_the__elem__def
% A new axiom: (forall (X_21:(hoare_1167836817_state->Prop)), (((eq hoare_1167836817_state) (the_el323660082_state X_21)) (the_Ho310147232_state (fun (X:hoare_1167836817_state)=> (((eq (hoare_1167836817_state->Prop)) X_21) ((insert2134838167_state X) bot_bo70021908tate_o))))))
% FOF formula (forall (X_21:(hoare_1775062406iple_a->Prop)), (((eq hoare_1775062406iple_a) (the_el1844711461iple_a X_21)) (the_Ho1155011127iple_a (fun (X:hoare_1775062406iple_a)=> (((eq (hoare_1775062406iple_a->Prop)) X_21) ((insert1281456128iple_a X) bot_bo751897185le_a_o)))))) of role axiom named fact_392_the__elem__def
% A new axiom: (forall (X_21:(hoare_1775062406iple_a->Prop)), (((eq hoare_1775062406iple_a) (the_el1844711461iple_a X_21)) (the_Ho1155011127iple_a (fun (X:hoare_1775062406iple_a)=> (((eq (hoare_1775062406iple_a->Prop)) X_21) ((insert1281456128iple_a X) bot_bo751897185le_a_o))))))
% FOF formula (forall (X_21:(pname->Prop)), (((eq pname) (the_elem_pname X_21)) (the_pname (fun (X:pname)=> (((eq (pname->Prop)) X_21) ((insert_pname X) bot_bot_pname_o)))))) of role axiom named fact_393_the__elem__def
% A new axiom: (forall (X_21:(pname->Prop)), (((eq pname) (the_elem_pname X_21)) (the_pname (fun (X:pname)=> (((eq (pname->Prop)) X_21) ((insert_pname X) bot_bot_pname_o))))))
% FOF formula (forall (P_9:(pname->(state->(state->Prop)))) (Q_4:(pname->(state->(state->Prop)))) (G_3:(hoare_1167836817_state->Prop)) (P_8:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(state->(state->Prop)))) (U:(pname->Prop)), ((finite_finite_pname U)->((forall (P_10:pname), (((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10))) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10))) bot_bo70021908tate_o))))->(((hoare_123228589_state G_3) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10)))) U))->((hoare_123228589_state G_3) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10)))) U)))))) of role axiom named fact_394_finite__pointwise
% A new axiom: (forall (P_9:(pname->(state->(state->Prop)))) (Q_4:(pname->(state->(state->Prop)))) (G_3:(hoare_1167836817_state->Prop)) (P_8:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(state->(state->Prop)))) (U:(pname->Prop)), ((finite_finite_pname U)->((forall (P_10:pname), (((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10))) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10))) bot_bo70021908tate_o))))->(((hoare_123228589_state G_3) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10)))) U))->((hoare_123228589_state G_3) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10)))) U))))))
% FOF formula (forall (P_9:(pname->(x_a->(state->Prop)))) (Q_4:(pname->(x_a->(state->Prop)))) (G_3:(hoare_1775062406iple_a->Prop)) (P_8:(pname->(x_a->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(x_a->(state->Prop)))) (U:(pname->Prop)), ((finite_finite_pname U)->((forall (P_10:pname), (((hoare_1508237396rivs_a G_3) ((insert1281456128iple_a (((hoare_1766022166iple_a (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10))) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_3) ((insert1281456128iple_a (((hoare_1766022166iple_a (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10))) bot_bo751897185le_a_o))))->(((hoare_1508237396rivs_a G_3) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10)))) U))->((hoare_1508237396rivs_a G_3) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10)))) U)))))) of role axiom named fact_395_finite__pointwise
% A new axiom: (forall (P_9:(pname->(x_a->(state->Prop)))) (Q_4:(pname->(x_a->(state->Prop)))) (G_3:(hoare_1775062406iple_a->Prop)) (P_8:(pname->(x_a->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(x_a->(state->Prop)))) (U:(pname->Prop)), ((finite_finite_pname U)->((forall (P_10:pname), (((hoare_1508237396rivs_a G_3) ((insert1281456128iple_a (((hoare_1766022166iple_a (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10))) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_3) ((insert1281456128iple_a (((hoare_1766022166iple_a (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10))) bot_bo751897185le_a_o))))->(((hoare_1508237396rivs_a G_3) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10)))) U))->((hoare_1508237396rivs_a G_3) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10)))) U))))))
% FOF formula (forall (C_19:com) (N_1:nat) (B:(state->Prop)) (S:state), (((B S)->False)->((((evaln ((while B) C_19)) S) N_1) S))) of role axiom named fact_396_evaln_OWhileFalse
% A new axiom: (forall (C_19:com) (N_1:nat) (B:(state->Prop)) (S:state), (((B S)->False)->((((evaln ((while B) C_19)) S) N_1) S)))
% FOF formula (forall (S2:state) (C_19:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->(((((evaln C_19) S0) N_1) S1)->(((((evaln ((while B) C_19)) S1) N_1) S2)->((((evaln ((while B) C_19)) S0) N_1) S2))))) of role axiom named fact_397_evaln_OWhileTrue
% A new axiom: (forall (S2:state) (C_19:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->(((((evaln C_19) S0) N_1) S1)->(((((evaln ((while B) C_19)) S1) N_1) S2)->((((evaln ((while B) C_19)) S0) N_1) S2)))))
% FOF formula (forall (S2:state) (C_19:com) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->((((evalc C_19) S0) S1)->((((evalc ((while B) C_19)) S1) S2)->(((evalc ((while B) C_19)) S0) S2))))) of role axiom named fact_398_evalc_OWhileTrue
% A new axiom: (forall (S2:state) (C_19:com) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->((((evalc C_19) S0) S1)->((((evalc ((while B) C_19)) S1) S2)->(((evalc ((while B) C_19)) S0) S2)))))
% FOF formula (forall (C_19:com) (B:(state->Prop)) (S:state), (((B S)->False)->(((evalc ((while B) C_19)) S) S))) of role axiom named fact_399_evalc_OWhileFalse
% A new axiom: (forall (C_19:com) (B:(state->Prop)) (S:state), (((B S)->False)->(((evalc ((while B) C_19)) S) S)))
% FOF formula (forall (C1:com) (S2:state) (C0:com) (S0:state) (N_1:nat) (S1:state), (((((evaln C0) S0) N_1) S1)->(((((evaln C1) S1) N_1) S2)->((((evaln ((semi C0) C1)) S0) N_1) S2)))) of role axiom named fact_400_evaln_OSemi
% A new axiom: (forall (C1:com) (S2:state) (C0:com) (S0:state) (N_1:nat) (S1:state), (((((evaln C0) S0) N_1) S1)->(((((evaln C1) S1) N_1) S2)->((((evaln ((semi C0) C1)) S0) N_1) S2))))
% FOF formula (forall (C1:com) (S2:state) (C0:com) (S0:state) (S1:state), ((((evalc C0) S0) S1)->((((evalc C1) S1) S2)->(((evalc ((semi C0) C1)) S0) S2)))) of role axiom named fact_401_evalc_OSemi
% A new axiom: (forall (C1:com) (S2:state) (C0:com) (S0:state) (S1:state), ((((evalc C0) S0) S1)->((((evalc C1) S1) S2)->(((evalc ((semi C0) C1)) S0) S2))))
% FOF formula (forall (Com1:com) (Com2:com) (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) ((semi Com1) Com2)) ((while Fun_1) Com_1)))) of role axiom named fact_402_com_Osimps_I46_J
% A new axiom: (forall (Com1:com) (Com2:com) (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) ((semi Com1) Com2)) ((while Fun_1) Com_1))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_1:com) (Com1:com) (Com2:com), (not (((eq com) ((while Fun_1) Com_1)) ((semi Com1) Com2)))) of role axiom named fact_403_com_Osimps_I47_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_1:com) (Com1:com) (Com2:com), (not (((eq com) ((while Fun_1) Com_1)) ((semi Com1) Com2))))
% FOF formula (forall (Com1:com) (Com2:com) (Com1_1:com) (Com2_1:com), ((iff (((eq com) ((semi Com1) Com2)) ((semi Com1_1) Com2_1))) ((and (((eq com) Com1) Com1_1)) (((eq com) Com2) Com2_1)))) of role axiom named fact_404_com_Osimps_I3_J
% A new axiom: (forall (Com1:com) (Com2:com) (Com1_1:com) (Com2_1:com), ((iff (((eq com) ((semi Com1) Com2)) ((semi Com1_1) Com2_1))) ((and (((eq com) Com1) Com1_1)) (((eq com) Com2) Com2_1))))
% FOF formula (forall (Fun:(state->Prop)) (Com:com) (Fun_1:(state->Prop)) (Com_1:com), ((iff (((eq com) ((while Fun) Com)) ((while Fun_1) Com_1))) ((and (((eq (state->Prop)) Fun) Fun_1)) (((eq com) Com) Com_1)))) of role axiom named fact_405_com_Osimps_I5_J
% A new axiom: (forall (Fun:(state->Prop)) (Com:com) (Fun_1:(state->Prop)) (Com_1:com), ((iff (((eq com) ((while Fun) Com)) ((while Fun_1) Com_1))) ((and (((eq (state->Prop)) Fun) Fun_1)) (((eq com) Com) Com_1))))
% FOF formula (forall (Pname_1:pname) (Fun:(state->Prop)) (Com:com), (not (((eq com) (body Pname_1)) ((while Fun) Com)))) of role axiom named fact_406_com_Osimps_I59_J
% A new axiom: (forall (Pname_1:pname) (Fun:(state->Prop)) (Com:com), (not (((eq com) (body Pname_1)) ((while Fun) Com))))
% FOF formula (forall (Fun:(state->Prop)) (Com:com) (Pname_1:pname), (not (((eq com) ((while Fun) Com)) (body Pname_1)))) of role axiom named fact_407_com_Osimps_I58_J
% A new axiom: (forall (Fun:(state->Prop)) (Com:com) (Pname_1:pname), (not (((eq com) ((while Fun) Com)) (body Pname_1))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) skip) ((while Fun_1) Com_1)))) of role axiom named fact_408_com_Osimps_I16_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) skip) ((while Fun_1) Com_1))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) ((while Fun_1) Com_1)) skip))) of role axiom named fact_409_com_Osimps_I17_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) ((while Fun_1) Com_1)) skip)))
% FOF formula (forall (Pname_1:pname) (Com1:com) (Com2:com), (not (((eq com) (body Pname_1)) ((semi Com1) Com2)))) of role axiom named fact_410_com_Osimps_I49_J
% A new axiom: (forall (Pname_1:pname) (Com1:com) (Com2:com), (not (((eq com) (body Pname_1)) ((semi Com1) Com2))))
% FOF formula (forall (Com1:com) (Com2:com) (Pname_1:pname), (not (((eq com) ((semi Com1) Com2)) (body Pname_1)))) of role axiom named fact_411_com_Osimps_I48_J
% A new axiom: (forall (Com1:com) (Com2:com) (Pname_1:pname), (not (((eq com) ((semi Com1) Com2)) (body Pname_1))))
% FOF formula (forall (Com1_1:com) (Com2_1:com), (not (((eq com) skip) ((semi Com1_1) Com2_1)))) of role axiom named fact_412_com_Osimps_I12_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com), (not (((eq com) skip) ((semi Com1_1) Com2_1))))
% FOF formula (forall (Com1_1:com) (Com2_1:com), (not (((eq com) ((semi Com1_1) Com2_1)) skip))) of role axiom named fact_413_com_Osimps_I13_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com), (not (((eq com) ((semi Com1_1) Com2_1)) skip)))
% FOF formula (forall (C1:com) (C2:com) (S:state) (T:state), ((((evalc ((semi C1) C2)) S) T)->((forall (S1_1:state), ((((evalc C1) S) S1_1)->((((evalc C2) S1_1) T)->False)))->False))) of role axiom named fact_414_evalc__elim__cases_I4_J
% A new axiom: (forall (C1:com) (C2:com) (S:state) (T:state), ((((evalc ((semi C1) C2)) S) T)->((forall (S1_1:state), ((((evalc C1) S) S1_1)->((((evalc C2) S1_1) T)->False)))->False)))
% FOF formula (forall (C1:com) (C2:com) (S:state) (N_1:nat) (T:state), (((((evaln ((semi C1) C2)) S) N_1) T)->((forall (S1_1:state), (((((evaln C1) S) N_1) S1_1)->(((((evaln C2) S1_1) N_1) T)->False)))->False))) of role axiom named fact_415_evaln__elim__cases_I4_J
% A new axiom: (forall (C1:com) (C2:com) (S:state) (N_1:nat) (T:state), (((((evaln ((semi C1) C2)) S) N_1) T)->((forall (S1_1:state), (((((evaln C1) S) N_1) S1_1)->(((((evaln C2) S1_1) N_1) T)->False)))->False)))
% FOF formula (forall (H_2:(pname->hoare_1167836817_state)) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->(finite1084549118_state ((image_575578384_state H_2) F_26)))) of role axiom named fact_416_finite__imageI
% A new axiom: (forall (H_2:(pname->hoare_1167836817_state)) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->(finite1084549118_state ((image_575578384_state H_2) F_26))))
% FOF formula (forall (H_2:(pname->hoare_1775062406iple_a)) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->(finite2063573081iple_a ((image_2063119815iple_a H_2) F_26)))) of role axiom named fact_417_finite__imageI
% A new axiom: (forall (H_2:(pname->hoare_1775062406iple_a)) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->(finite2063573081iple_a ((image_2063119815iple_a H_2) F_26))))
% FOF formula (forall (A_62:hoare_1167836817_state) (A_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_61)->(finite1084549118_state ((insert2134838167_state A_62) A_61)))) of role axiom named fact_418_finite_OinsertI
% A new axiom: (forall (A_62:hoare_1167836817_state) (A_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_61)->(finite1084549118_state ((insert2134838167_state A_62) A_61))))
% FOF formula (forall (A_62:hoare_1775062406iple_a) (A_61:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a A_61)->(finite2063573081iple_a ((insert1281456128iple_a A_62) A_61)))) of role axiom named fact_419_finite_OinsertI
% A new axiom: (forall (A_62:hoare_1775062406iple_a) (A_61:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a A_61)->(finite2063573081iple_a ((insert1281456128iple_a A_62) A_61))))
% FOF formula (forall (A_62:pname) (A_61:(pname->Prop)), ((finite_finite_pname A_61)->(finite_finite_pname ((insert_pname A_62) A_61)))) of role axiom named fact_420_finite_OinsertI
% A new axiom: (forall (A_62:pname) (A_61:(pname->Prop)), ((finite_finite_pname A_61)->(finite_finite_pname ((insert_pname A_62) A_61))))
% FOF formula (finite_finite_pname bot_bot_pname_o) of role axiom named fact_421_finite_OemptyI
% A new axiom: (finite_finite_pname bot_bot_pname_o)
% FOF formula (finite2063573081iple_a bot_bo751897185le_a_o) of role axiom named fact_422_finite_OemptyI
% A new axiom: (finite2063573081iple_a bot_bo751897185le_a_o)
% FOF formula (finite1084549118_state bot_bo70021908tate_o) of role axiom named fact_423_finite_OemptyI
% A new axiom: (finite1084549118_state bot_bo70021908tate_o)
% FOF formula (forall (Q_2:(hoare_1775062406iple_a->Prop)) (P_7:(hoare_1775062406iple_a->Prop)), (((or (finite2063573081iple_a (collec676402587iple_a P_7))) (finite2063573081iple_a (collec676402587iple_a Q_2)))->(finite2063573081iple_a (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (P_7 X)) (Q_2 X))))))) of role axiom named fact_424_finite__Collect__conjI
% A new axiom: (forall (Q_2:(hoare_1775062406iple_a->Prop)) (P_7:(hoare_1775062406iple_a->Prop)), (((or (finite2063573081iple_a (collec676402587iple_a P_7))) (finite2063573081iple_a (collec676402587iple_a Q_2)))->(finite2063573081iple_a (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (P_7 X)) (Q_2 X)))))))
% FOF formula (forall (Q_2:(pname->Prop)) (P_7:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_7))) (finite_finite_pname (collect_pname Q_2)))->(finite_finite_pname (collect_pname (fun (X:pname)=> ((and (P_7 X)) (Q_2 X))))))) of role axiom named fact_425_finite__Collect__conjI
% A new axiom: (forall (Q_2:(pname->Prop)) (P_7:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_7))) (finite_finite_pname (collect_pname Q_2)))->(finite_finite_pname (collect_pname (fun (X:pname)=> ((and (P_7 X)) (Q_2 X)))))))
% FOF formula (forall (P_6:(hoare_1775062406iple_a->Prop)) (Q_1:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or (P_6 X)) (Q_1 X)))))) ((and (finite2063573081iple_a (collec676402587iple_a P_6))) (finite2063573081iple_a (collec676402587iple_a Q_1))))) of role axiom named fact_426_finite__Collect__disjI
% A new axiom: (forall (P_6:(hoare_1775062406iple_a->Prop)) (Q_1:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or (P_6 X)) (Q_1 X)))))) ((and (finite2063573081iple_a (collec676402587iple_a P_6))) (finite2063573081iple_a (collec676402587iple_a Q_1)))))
% FOF formula (forall (P_6:(pname->Prop)) (Q_1:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X:pname)=> ((or (P_6 X)) (Q_1 X)))))) ((and (finite_finite_pname (collect_pname P_6))) (finite_finite_pname (collect_pname Q_1))))) of role axiom named fact_427_finite__Collect__disjI
% A new axiom: (forall (P_6:(pname->Prop)) (Q_1:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X:pname)=> ((or (P_6 X)) (Q_1 X)))))) ((and (finite_finite_pname (collect_pname P_6))) (finite_finite_pname (collect_pname Q_1)))))
% FOF formula (forall (A_60:hoare_1167836817_state) (A_59:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((insert2134838167_state A_60) A_59))) (finite1084549118_state A_59))) of role axiom named fact_428_finite__insert
% A new axiom: (forall (A_60:hoare_1167836817_state) (A_59:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((insert2134838167_state A_60) A_59))) (finite1084549118_state A_59)))
% FOF formula (forall (A_60:hoare_1775062406iple_a) (A_59:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a ((insert1281456128iple_a A_60) A_59))) (finite2063573081iple_a A_59))) of role axiom named fact_429_finite__insert
% A new axiom: (forall (A_60:hoare_1775062406iple_a) (A_59:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a ((insert1281456128iple_a A_60) A_59))) (finite2063573081iple_a A_59)))
% FOF formula (forall (A_60:pname) (A_59:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_60) A_59))) (finite_finite_pname A_59))) of role axiom named fact_430_finite__insert
% A new axiom: (forall (A_60:pname) (A_59:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_60) A_59))) (finite_finite_pname A_59)))
% FOF formula (forall (F_25:(pname->Prop)) (G_2:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_25) G_2))) ((and (finite_finite_pname F_25)) (finite_finite_pname G_2)))) of role axiom named fact_431_finite__Un
% A new axiom: (forall (F_25:(pname->Prop)) (G_2:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_25) G_2))) ((and (finite_finite_pname F_25)) (finite_finite_pname G_2))))
% FOF formula (forall (F_25:(hoare_1167836817_state->Prop)) (G_2:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((semila1172322802tate_o F_25) G_2))) ((and (finite1084549118_state F_25)) (finite1084549118_state G_2)))) of role axiom named fact_432_finite__Un
% A new axiom: (forall (F_25:(hoare_1167836817_state->Prop)) (G_2:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((semila1172322802tate_o F_25) G_2))) ((and (finite1084549118_state F_25)) (finite1084549118_state G_2))))
% FOF formula (forall (F_25:(hoare_1775062406iple_a->Prop)) (G_2:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a ((semila13410563le_a_o F_25) G_2))) ((and (finite2063573081iple_a F_25)) (finite2063573081iple_a G_2)))) of role axiom named fact_433_finite__Un
% A new axiom: (forall (F_25:(hoare_1775062406iple_a->Prop)) (G_2:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a ((semila13410563le_a_o F_25) G_2))) ((and (finite2063573081iple_a F_25)) (finite2063573081iple_a G_2))))
% FOF formula (forall (G_1:(pname->Prop)) (F_24:(pname->Prop)), ((finite_finite_pname F_24)->((finite_finite_pname G_1)->(finite_finite_pname ((semila1780557381name_o F_24) G_1))))) of role axiom named fact_434_finite__UnI
% A new axiom: (forall (G_1:(pname->Prop)) (F_24:(pname->Prop)), ((finite_finite_pname F_24)->((finite_finite_pname G_1)->(finite_finite_pname ((semila1780557381name_o F_24) G_1)))))
% FOF formula (forall (G_1:(hoare_1167836817_state->Prop)) (F_24:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_24)->((finite1084549118_state G_1)->(finite1084549118_state ((semila1172322802tate_o F_24) G_1))))) of role axiom named fact_435_finite__UnI
% A new axiom: (forall (G_1:(hoare_1167836817_state->Prop)) (F_24:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_24)->((finite1084549118_state G_1)->(finite1084549118_state ((semila1172322802tate_o F_24) G_1)))))
% FOF formula (forall (G_1:(hoare_1775062406iple_a->Prop)) (F_24:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_24)->((finite2063573081iple_a G_1)->(finite2063573081iple_a ((semila13410563le_a_o F_24) G_1))))) of role axiom named fact_436_finite__UnI
% A new axiom: (forall (G_1:(hoare_1775062406iple_a->Prop)) (F_24:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_24)->((finite2063573081iple_a G_1)->(finite2063573081iple_a ((semila13410563le_a_o F_24) G_1)))))
% FOF formula (forall (A_57:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state A_57)) ((or (((eq (hoare_1167836817_state->Prop)) A_57) bot_bo70021908tate_o)) ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (A_56:hoare_1167836817_state)=> ((and (((eq (hoare_1167836817_state->Prop)) A_57) ((insert2134838167_state A_56) A_58))) (finite1084549118_state A_58))))))))) of role axiom named fact_437_finite_Osimps
% A new axiom: (forall (A_57:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state A_57)) ((or (((eq (hoare_1167836817_state->Prop)) A_57) bot_bo70021908tate_o)) ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (A_56:hoare_1167836817_state)=> ((and (((eq (hoare_1167836817_state->Prop)) A_57) ((insert2134838167_state A_56) A_58))) (finite1084549118_state A_58)))))))))
% FOF formula (forall (A_57:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a A_57)) ((or (((eq (hoare_1775062406iple_a->Prop)) A_57) bot_bo751897185le_a_o)) ((ex (hoare_1775062406iple_a->Prop)) (fun (A_58:(hoare_1775062406iple_a->Prop))=> ((ex hoare_1775062406iple_a) (fun (A_56:hoare_1775062406iple_a)=> ((and (((eq (hoare_1775062406iple_a->Prop)) A_57) ((insert1281456128iple_a A_56) A_58))) (finite2063573081iple_a A_58))))))))) of role axiom named fact_438_finite_Osimps
% A new axiom: (forall (A_57:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a A_57)) ((or (((eq (hoare_1775062406iple_a->Prop)) A_57) bot_bo751897185le_a_o)) ((ex (hoare_1775062406iple_a->Prop)) (fun (A_58:(hoare_1775062406iple_a->Prop))=> ((ex hoare_1775062406iple_a) (fun (A_56:hoare_1775062406iple_a)=> ((and (((eq (hoare_1775062406iple_a->Prop)) A_57) ((insert1281456128iple_a A_56) A_58))) (finite2063573081iple_a A_58)))))))))
% FOF formula (forall (A_57:(pname->Prop)), ((iff (finite_finite_pname A_57)) ((or (((eq (pname->Prop)) A_57) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_58:(pname->Prop))=> ((ex pname) (fun (A_56:pname)=> ((and (((eq (pname->Prop)) A_57) ((insert_pname A_56) A_58))) (finite_finite_pname A_58))))))))) of role axiom named fact_439_finite_Osimps
% A new axiom: (forall (A_57:(pname->Prop)), ((iff (finite_finite_pname A_57)) ((or (((eq (pname->Prop)) A_57) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_58:(pname->Prop))=> ((ex pname) (fun (A_56:pname)=> ((and (((eq (pname->Prop)) A_57) ((insert_pname A_56) A_58))) (finite_finite_pname A_58)))))))))
% FOF formula (forall (P_5:((hoare_1167836817_state->Prop)->Prop)) (F_23:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_23)->((P_5 bot_bo70021908tate_o)->((forall (X:hoare_1167836817_state) (F_16:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_16)->((((member2058392318_state X) F_16)->False)->((P_5 F_16)->(P_5 ((insert2134838167_state X) F_16))))))->(P_5 F_23))))) of role axiom named fact_440_finite__induct
% A new axiom: (forall (P_5:((hoare_1167836817_state->Prop)->Prop)) (F_23:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_23)->((P_5 bot_bo70021908tate_o)->((forall (X:hoare_1167836817_state) (F_16:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_16)->((((member2058392318_state X) F_16)->False)->((P_5 F_16)->(P_5 ((insert2134838167_state X) F_16))))))->(P_5 F_23)))))
% FOF formula (forall (P_5:((hoare_1775062406iple_a->Prop)->Prop)) (F_23:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_23)->((P_5 bot_bo751897185le_a_o)->((forall (X:hoare_1775062406iple_a) (F_16:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_16)->((((member2122167641iple_a X) F_16)->False)->((P_5 F_16)->(P_5 ((insert1281456128iple_a X) F_16))))))->(P_5 F_23))))) of role axiom named fact_441_finite__induct
% A new axiom: (forall (P_5:((hoare_1775062406iple_a->Prop)->Prop)) (F_23:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_23)->((P_5 bot_bo751897185le_a_o)->((forall (X:hoare_1775062406iple_a) (F_16:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_16)->((((member2122167641iple_a X) F_16)->False)->((P_5 F_16)->(P_5 ((insert1281456128iple_a X) F_16))))))->(P_5 F_23)))))
% FOF formula (forall (P_5:((pname->Prop)->Prop)) (F_23:(pname->Prop)), ((finite_finite_pname F_23)->((P_5 bot_bot_pname_o)->((forall (X:pname) (F_16:(pname->Prop)), ((finite_finite_pname F_16)->((((member_pname X) F_16)->False)->((P_5 F_16)->(P_5 ((insert_pname X) F_16))))))->(P_5 F_23))))) of role axiom named fact_442_finite__induct
% A new axiom: (forall (P_5:((pname->Prop)->Prop)) (F_23:(pname->Prop)), ((finite_finite_pname F_23)->((P_5 bot_bot_pname_o)->((forall (X:pname) (F_16:(pname->Prop)), ((finite_finite_pname F_16)->((((member_pname X) F_16)->False)->((P_5 F_16)->(P_5 ((insert_pname X) F_16))))))->(P_5 F_23)))))
% FOF formula (forall (F_22:(pname->hoare_1167836817_state)) (A_55:(pname->Prop)), (((finite_finite_pname A_55)->False)->((finite1084549118_state ((image_575578384_state F_22) A_55))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_55)) ((finite_finite_pname (collect_pname (fun (A_56:pname)=> ((and ((member_pname A_56) A_55)) (((eq hoare_1167836817_state) (F_22 A_56)) (F_22 X))))))->False))))))) of role axiom named fact_443_pigeonhole__infinite
% A new axiom: (forall (F_22:(pname->hoare_1167836817_state)) (A_55:(pname->Prop)), (((finite_finite_pname A_55)->False)->((finite1084549118_state ((image_575578384_state F_22) A_55))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_55)) ((finite_finite_pname (collect_pname (fun (A_56:pname)=> ((and ((member_pname A_56) A_55)) (((eq hoare_1167836817_state) (F_22 A_56)) (F_22 X))))))->False)))))))
% FOF formula (forall (F_22:(pname->hoare_1775062406iple_a)) (A_55:(pname->Prop)), (((finite_finite_pname A_55)->False)->((finite2063573081iple_a ((image_2063119815iple_a F_22) A_55))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_55)) ((finite_finite_pname (collect_pname (fun (A_56:pname)=> ((and ((member_pname A_56) A_55)) (((eq hoare_1775062406iple_a) (F_22 A_56)) (F_22 X))))))->False))))))) of role axiom named fact_444_pigeonhole__infinite
% A new axiom: (forall (F_22:(pname->hoare_1775062406iple_a)) (A_55:(pname->Prop)), (((finite_finite_pname A_55)->False)->((finite2063573081iple_a ((image_2063119815iple_a F_22) A_55))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_55)) ((finite_finite_pname (collect_pname (fun (A_56:pname)=> ((and ((member_pname A_56) A_55)) (((eq hoare_1775062406iple_a) (F_22 A_56)) (F_22 X))))))->False)))))))
% FOF formula (forall (B:(state->Prop)) (C_19:com) (S:state) (T:state), ((((evalc ((while B) C_19)) S) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), ((((evalc C_19) S) S1_1)->((((evalc ((while B) C_19)) S1_1) T)->False))))->False)))) of role axiom named fact_445_evalc__WHILE__case
% A new axiom: (forall (B:(state->Prop)) (C_19:com) (S:state) (T:state), ((((evalc ((while B) C_19)) S) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), ((((evalc C_19) S) S1_1)->((((evalc ((while B) C_19)) S1_1) T)->False))))->False))))
% FOF formula (forall (B:(state->Prop)) (C_19:com) (S:state) (N_1:nat) (T:state), (((((evaln ((while B) C_19)) S) N_1) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), (((((evaln C_19) S) N_1) S1_1)->(((((evaln ((while B) C_19)) S1_1) N_1) T)->False))))->False)))) of role axiom named fact_446_evaln__WHILE__case
% A new axiom: (forall (B:(state->Prop)) (C_19:com) (S:state) (N_1:nat) (T:state), (((((evaln ((while B) C_19)) S) N_1) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), (((((evaln C_19) S) N_1) S1_1)->(((((evaln ((while B) C_19)) S1_1) N_1) T)->False))))->False))))
% FOF formula (forall (A_54:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_54) bot_bo70021908tate_o))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (B_34:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_54) ((insert2134838167_state X) B_34))) (((member2058392318_state X) B_34)->False)))))))) of role axiom named fact_447_nonempty__iff
% A new axiom: (forall (A_54:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_54) bot_bo70021908tate_o))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (B_34:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_54) ((insert2134838167_state X) B_34))) (((member2058392318_state X) B_34)->False))))))))
% FOF formula (forall (A_54:(hoare_1775062406iple_a->Prop)), ((iff (not (((eq (hoare_1775062406iple_a->Prop)) A_54) bot_bo751897185le_a_o))) ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((ex (hoare_1775062406iple_a->Prop)) (fun (B_34:(hoare_1775062406iple_a->Prop))=> ((and (((eq (hoare_1775062406iple_a->Prop)) A_54) ((insert1281456128iple_a X) B_34))) (((member2122167641iple_a X) B_34)->False)))))))) of role axiom named fact_448_nonempty__iff
% A new axiom: (forall (A_54:(hoare_1775062406iple_a->Prop)), ((iff (not (((eq (hoare_1775062406iple_a->Prop)) A_54) bot_bo751897185le_a_o))) ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((ex (hoare_1775062406iple_a->Prop)) (fun (B_34:(hoare_1775062406iple_a->Prop))=> ((and (((eq (hoare_1775062406iple_a->Prop)) A_54) ((insert1281456128iple_a X) B_34))) (((member2122167641iple_a X) B_34)->False))))))))
% FOF formula (forall (A_54:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_54) bot_bot_pname_o))) ((ex pname) (fun (X:pname)=> ((ex (pname->Prop)) (fun (B_34:(pname->Prop))=> ((and (((eq (pname->Prop)) A_54) ((insert_pname X) B_34))) (((member_pname X) B_34)->False)))))))) of role axiom named fact_449_nonempty__iff
% A new axiom: (forall (A_54:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_54) bot_bot_pname_o))) ((ex pname) (fun (X:pname)=> ((ex (pname->Prop)) (fun (B_34:(pname->Prop))=> ((and (((eq (pname->Prop)) A_54) ((insert_pname X) B_34))) (((member_pname X) B_34)->False))))))))
% FOF formula (forall (B_35:(pname->Prop)) (A_53:(pname->Prop)) (F_21:(pname->(pname->pname))) (F_20:((pname->Prop)->pname)), (((finite89670078_pname F_21) F_20)->((finite_finite_pname A_53)->((not (((eq (pname->Prop)) A_53) bot_bot_pname_o))->((finite_finite_pname B_35)->((not (((eq (pname->Prop)) B_35) bot_bot_pname_o))->(((eq pname) (F_20 ((semila1780557381name_o A_53) B_35))) ((F_21 (F_20 A_53)) (F_20 B_35))))))))) of role axiom named fact_450_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_35:(pname->Prop)) (A_53:(pname->Prop)) (F_21:(pname->(pname->pname))) (F_20:((pname->Prop)->pname)), (((finite89670078_pname F_21) F_20)->((finite_finite_pname A_53)->((not (((eq (pname->Prop)) A_53) bot_bot_pname_o))->((finite_finite_pname B_35)->((not (((eq (pname->Prop)) B_35) bot_bot_pname_o))->(((eq pname) (F_20 ((semila1780557381name_o A_53) B_35))) ((F_21 (F_20 A_53)) (F_20 B_35)))))))))
% FOF formula (forall (B_35:(hoare_1775062406iple_a->Prop)) (A_53:(hoare_1775062406iple_a->Prop)) (F_21:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_20:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_21) F_20)->((finite2063573081iple_a A_53)->((not (((eq (hoare_1775062406iple_a->Prop)) A_53) bot_bo751897185le_a_o))->((finite2063573081iple_a B_35)->((not (((eq (hoare_1775062406iple_a->Prop)) B_35) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (F_20 ((semila13410563le_a_o A_53) B_35))) ((F_21 (F_20 A_53)) (F_20 B_35))))))))) of role axiom named fact_451_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_35:(hoare_1775062406iple_a->Prop)) (A_53:(hoare_1775062406iple_a->Prop)) (F_21:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_20:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_21) F_20)->((finite2063573081iple_a A_53)->((not (((eq (hoare_1775062406iple_a->Prop)) A_53) bot_bo751897185le_a_o))->((finite2063573081iple_a B_35)->((not (((eq (hoare_1775062406iple_a->Prop)) B_35) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (F_20 ((semila13410563le_a_o A_53) B_35))) ((F_21 (F_20 A_53)) (F_20 B_35)))))))))
% FOF formula (forall (B_35:(hoare_1167836817_state->Prop)) (A_53:(hoare_1167836817_state->Prop)) (F_21:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_20:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_21) F_20)->((finite1084549118_state A_53)->((not (((eq (hoare_1167836817_state->Prop)) A_53) bot_bo70021908tate_o))->((finite1084549118_state B_35)->((not (((eq (hoare_1167836817_state->Prop)) B_35) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_20 ((semila1172322802tate_o A_53) B_35))) ((F_21 (F_20 A_53)) (F_20 B_35))))))))) of role axiom named fact_452_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_35:(hoare_1167836817_state->Prop)) (A_53:(hoare_1167836817_state->Prop)) (F_21:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_20:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_21) F_20)->((finite1084549118_state A_53)->((not (((eq (hoare_1167836817_state->Prop)) A_53) bot_bo70021908tate_o))->((finite1084549118_state B_35)->((not (((eq (hoare_1167836817_state->Prop)) B_35) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_20 ((semila1172322802tate_o A_53) B_35))) ((F_21 (F_20 A_53)) (F_20 B_35)))))))))
% FOF formula (forall (X_20:hoare_1167836817_state) (A_52:(hoare_1167836817_state->Prop)) (F_19:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_18:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_19) F_18)->((finite1084549118_state A_52)->((not (((eq (hoare_1167836817_state->Prop)) A_52) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_18 ((insert2134838167_state X_20) A_52))) ((F_19 X_20) (F_18 A_52))))))) of role axiom named fact_453_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_20:hoare_1167836817_state) (A_52:(hoare_1167836817_state->Prop)) (F_19:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_18:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_19) F_18)->((finite1084549118_state A_52)->((not (((eq (hoare_1167836817_state->Prop)) A_52) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_18 ((insert2134838167_state X_20) A_52))) ((F_19 X_20) (F_18 A_52)))))))
% FOF formula (forall (X_20:hoare_1775062406iple_a) (A_52:(hoare_1775062406iple_a->Prop)) (F_19:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_18:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_19) F_18)->((finite2063573081iple_a A_52)->((not (((eq (hoare_1775062406iple_a->Prop)) A_52) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (F_18 ((insert1281456128iple_a X_20) A_52))) ((F_19 X_20) (F_18 A_52))))))) of role axiom named fact_454_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_20:hoare_1775062406iple_a) (A_52:(hoare_1775062406iple_a->Prop)) (F_19:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_18:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_19) F_18)->((finite2063573081iple_a A_52)->((not (((eq (hoare_1775062406iple_a->Prop)) A_52) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (F_18 ((insert1281456128iple_a X_20) A_52))) ((F_19 X_20) (F_18 A_52)))))))
% FOF formula (forall (X_20:pname) (A_52:(pname->Prop)) (F_19:(pname->(pname->pname))) (F_18:((pname->Prop)->pname)), (((finite89670078_pname F_19) F_18)->((finite_finite_pname A_52)->((not (((eq (pname->Prop)) A_52) bot_bot_pname_o))->(((eq pname) (F_18 ((insert_pname X_20) A_52))) ((F_19 X_20) (F_18 A_52))))))) of role axiom named fact_455_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_20:pname) (A_52:(pname->Prop)) (F_19:(pname->(pname->pname))) (F_18:((pname->Prop)->pname)), (((finite89670078_pname F_19) F_18)->((finite_finite_pname A_52)->((not (((eq (pname->Prop)) A_52) bot_bot_pname_o))->(((eq pname) (F_18 ((insert_pname X_20) A_52))) ((F_19 X_20) (F_18 A_52)))))))
% FOF formula (forall (F_17:(pname->hoare_1167836817_state)) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_17) A_51)) ((((finite1068437657_pname semila1172322802tate_o) (fun (X:pname)=> ((insert2134838167_state (F_17 X)) bot_bo70021908tate_o))) bot_bo70021908tate_o) A_51)))) of role axiom named fact_456_image__eq__fold__image
% A new axiom: (forall (F_17:(pname->hoare_1167836817_state)) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_17) A_51)) ((((finite1068437657_pname semila1172322802tate_o) (fun (X:pname)=> ((insert2134838167_state (F_17 X)) bot_bo70021908tate_o))) bot_bo70021908tate_o) A_51))))
% FOF formula (forall (F_17:(pname->hoare_1775062406iple_a)) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_17) A_51)) ((((finite1805141964_pname semila13410563le_a_o) (fun (X:pname)=> ((insert1281456128iple_a (F_17 X)) bot_bo751897185le_a_o))) bot_bo751897185le_a_o) A_51)))) of role axiom named fact_457_image__eq__fold__image
% A new axiom: (forall (F_17:(pname->hoare_1775062406iple_a)) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_17) A_51)) ((((finite1805141964_pname semila13410563le_a_o) (fun (X:pname)=> ((insert1281456128iple_a (F_17 X)) bot_bo751897185le_a_o))) bot_bo751897185le_a_o) A_51))))
% FOF formula (forall (P_4:((hoare_1167836817_state->Prop)->Prop)) (F_15:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_15)->((not (((eq (hoare_1167836817_state->Prop)) F_15) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state), (P_4 ((insert2134838167_state X) bot_bo70021908tate_o)))->((forall (X:hoare_1167836817_state) (F_16:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_16)->((not (((eq (hoare_1167836817_state->Prop)) F_16) bot_bo70021908tate_o))->((((member2058392318_state X) F_16)->False)->((P_4 F_16)->(P_4 ((insert2134838167_state X) F_16)))))))->(P_4 F_15)))))) of role axiom named fact_458_finite__ne__induct
% A new axiom: (forall (P_4:((hoare_1167836817_state->Prop)->Prop)) (F_15:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_15)->((not (((eq (hoare_1167836817_state->Prop)) F_15) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state), (P_4 ((insert2134838167_state X) bot_bo70021908tate_o)))->((forall (X:hoare_1167836817_state) (F_16:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_16)->((not (((eq (hoare_1167836817_state->Prop)) F_16) bot_bo70021908tate_o))->((((member2058392318_state X) F_16)->False)->((P_4 F_16)->(P_4 ((insert2134838167_state X) F_16)))))))->(P_4 F_15))))))
% FOF formula (forall (P_4:((hoare_1775062406iple_a->Prop)->Prop)) (F_15:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_15)->((not (((eq (hoare_1775062406iple_a->Prop)) F_15) bot_bo751897185le_a_o))->((forall (X:hoare_1775062406iple_a), (P_4 ((insert1281456128iple_a X) bot_bo751897185le_a_o)))->((forall (X:hoare_1775062406iple_a) (F_16:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_16)->((not (((eq (hoare_1775062406iple_a->Prop)) F_16) bot_bo751897185le_a_o))->((((member2122167641iple_a X) F_16)->False)->((P_4 F_16)->(P_4 ((insert1281456128iple_a X) F_16)))))))->(P_4 F_15)))))) of role axiom named fact_459_finite__ne__induct
% A new axiom: (forall (P_4:((hoare_1775062406iple_a->Prop)->Prop)) (F_15:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_15)->((not (((eq (hoare_1775062406iple_a->Prop)) F_15) bot_bo751897185le_a_o))->((forall (X:hoare_1775062406iple_a), (P_4 ((insert1281456128iple_a X) bot_bo751897185le_a_o)))->((forall (X:hoare_1775062406iple_a) (F_16:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_16)->((not (((eq (hoare_1775062406iple_a->Prop)) F_16) bot_bo751897185le_a_o))->((((member2122167641iple_a X) F_16)->False)->((P_4 F_16)->(P_4 ((insert1281456128iple_a X) F_16)))))))->(P_4 F_15))))))
% FOF formula (forall (P_4:((pname->Prop)->Prop)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->((not (((eq (pname->Prop)) F_15) bot_bot_pname_o))->((forall (X:pname), (P_4 ((insert_pname X) bot_bot_pname_o)))->((forall (X:pname) (F_16:(pname->Prop)), ((finite_finite_pname F_16)->((not (((eq (pname->Prop)) F_16) bot_bot_pname_o))->((((member_pname X) F_16)->False)->((P_4 F_16)->(P_4 ((insert_pname X) F_16)))))))->(P_4 F_15)))))) of role axiom named fact_460_finite__ne__induct
% A new axiom: (forall (P_4:((pname->Prop)->Prop)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->((not (((eq (pname->Prop)) F_15) bot_bot_pname_o))->((forall (X:pname), (P_4 ((insert_pname X) bot_bot_pname_o)))->((forall (X:pname) (F_16:(pname->Prop)), ((finite_finite_pname F_16)->((not (((eq (pname->Prop)) F_16) bot_bot_pname_o))->((((member_pname X) F_16)->False)->((P_4 F_16)->(P_4 ((insert_pname X) F_16)))))))->(P_4 F_15))))))
% FOF formula (forall (X_19:hoare_1775062406iple_a) (A_50:(hoare_1775062406iple_a->Prop)) (F_14:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_13:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_14) F_13)->((finite2063573081iple_a A_50)->(((member2122167641iple_a X_19) A_50)->(((eq hoare_1775062406iple_a) ((F_14 X_19) (F_13 A_50))) (F_13 A_50)))))) of role axiom named fact_461_folding__one__idem_Oin__idem
% A new axiom: (forall (X_19:hoare_1775062406iple_a) (A_50:(hoare_1775062406iple_a->Prop)) (F_14:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_13:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_14) F_13)->((finite2063573081iple_a A_50)->(((member2122167641iple_a X_19) A_50)->(((eq hoare_1775062406iple_a) ((F_14 X_19) (F_13 A_50))) (F_13 A_50))))))
% FOF formula (forall (X_19:pname) (A_50:(pname->Prop)) (F_14:(pname->(pname->pname))) (F_13:((pname->Prop)->pname)), (((finite89670078_pname F_14) F_13)->((finite_finite_pname A_50)->(((member_pname X_19) A_50)->(((eq pname) ((F_14 X_19) (F_13 A_50))) (F_13 A_50)))))) of role axiom named fact_462_folding__one__idem_Oin__idem
% A new axiom: (forall (X_19:pname) (A_50:(pname->Prop)) (F_14:(pname->(pname->pname))) (F_13:((pname->Prop)->pname)), (((finite89670078_pname F_14) F_13)->((finite_finite_pname A_50)->(((member_pname X_19) A_50)->(((eq pname) ((F_14 X_19) (F_13 A_50))) (F_13 A_50))))))
% FOF formula (forall (N_3:(pname->Prop)) (H_1:(pname->pname)) (F_12:(pname->(pname->pname))) (F_11:((pname->Prop)->pname)), (((finite89670078_pname F_12) F_11)->((forall (X:pname) (Y_2:pname), (((eq pname) (H_1 ((F_12 X) Y_2))) ((F_12 (H_1 X)) (H_1 Y_2))))->((finite_finite_pname N_3)->((not (((eq (pname->Prop)) N_3) bot_bot_pname_o))->(((eq pname) (H_1 (F_11 N_3))) (F_11 ((image_pname_pname H_1) N_3)))))))) of role axiom named fact_463_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_3:(pname->Prop)) (H_1:(pname->pname)) (F_12:(pname->(pname->pname))) (F_11:((pname->Prop)->pname)), (((finite89670078_pname F_12) F_11)->((forall (X:pname) (Y_2:pname), (((eq pname) (H_1 ((F_12 X) Y_2))) ((F_12 (H_1 X)) (H_1 Y_2))))->((finite_finite_pname N_3)->((not (((eq (pname->Prop)) N_3) bot_bot_pname_o))->(((eq pname) (H_1 (F_11 N_3))) (F_11 ((image_pname_pname H_1) N_3))))))))
% FOF formula (forall (N_3:(hoare_1775062406iple_a->Prop)) (H_1:(hoare_1775062406iple_a->hoare_1775062406iple_a)) (F_12:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_11:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_12) F_11)->((forall (X:hoare_1775062406iple_a) (Y_2:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (H_1 ((F_12 X) Y_2))) ((F_12 (H_1 X)) (H_1 Y_2))))->((finite2063573081iple_a N_3)->((not (((eq (hoare_1775062406iple_a->Prop)) N_3) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (H_1 (F_11 N_3))) (F_11 ((image_1170193413iple_a H_1) N_3)))))))) of role axiom named fact_464_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_3:(hoare_1775062406iple_a->Prop)) (H_1:(hoare_1775062406iple_a->hoare_1775062406iple_a)) (F_12:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_11:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_12) F_11)->((forall (X:hoare_1775062406iple_a) (Y_2:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (H_1 ((F_12 X) Y_2))) ((F_12 (H_1 X)) (H_1 Y_2))))->((finite2063573081iple_a N_3)->((not (((eq (hoare_1775062406iple_a->Prop)) N_3) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (H_1 (F_11 N_3))) (F_11 ((image_1170193413iple_a H_1) N_3))))))))
% FOF formula (forall (N_3:(hoare_1167836817_state->Prop)) (H_1:(hoare_1167836817_state->hoare_1167836817_state)) (F_12:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_11:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_12) F_11)->((forall (X:hoare_1167836817_state) (Y_2:hoare_1167836817_state), (((eq hoare_1167836817_state) (H_1 ((F_12 X) Y_2))) ((F_12 (H_1 X)) (H_1 Y_2))))->((finite1084549118_state N_3)->((not (((eq (hoare_1167836817_state->Prop)) N_3) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (H_1 (F_11 N_3))) (F_11 ((image_31595733_state H_1) N_3)))))))) of role axiom named fact_465_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_3:(hoare_1167836817_state->Prop)) (H_1:(hoare_1167836817_state->hoare_1167836817_state)) (F_12:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_11:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_12) F_11)->((forall (X:hoare_1167836817_state) (Y_2:hoare_1167836817_state), (((eq hoare_1167836817_state) (H_1 ((F_12 X) Y_2))) ((F_12 (H_1 X)) (H_1 Y_2))))->((finite1084549118_state N_3)->((not (((eq (hoare_1167836817_state->Prop)) N_3) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (H_1 (F_11 N_3))) (F_11 ((image_31595733_state H_1) N_3))))))))
% FOF formula (forall (X_18:hoare_1167836817_state) (A_49:(hoare_1167836817_state->Prop)) (F_10:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_9:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_10) F_9)->((finite1084549118_state A_49)->((((member2058392318_state X_18) A_49)->False)->((not (((eq (hoare_1167836817_state->Prop)) A_49) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_9 ((insert2134838167_state X_18) A_49))) ((F_10 X_18) (F_9 A_49)))))))) of role axiom named fact_466_folding__one_Oinsert
% A new axiom: (forall (X_18:hoare_1167836817_state) (A_49:(hoare_1167836817_state->Prop)) (F_10:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_9:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_10) F_9)->((finite1084549118_state A_49)->((((member2058392318_state X_18) A_49)->False)->((not (((eq (hoare_1167836817_state->Prop)) A_49) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_9 ((insert2134838167_state X_18) A_49))) ((F_10 X_18) (F_9 A_49))))))))
% FOF formula (forall (X_18:hoare_1775062406iple_a) (A_49:(hoare_1775062406iple_a->Prop)) (F_10:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_9:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_10) F_9)->((finite2063573081iple_a A_49)->((((member2122167641iple_a X_18) A_49)->False)->((not (((eq (hoare_1775062406iple_a->Prop)) A_49) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (F_9 ((insert1281456128iple_a X_18) A_49))) ((F_10 X_18) (F_9 A_49)))))))) of role axiom named fact_467_folding__one_Oinsert
% A new axiom: (forall (X_18:hoare_1775062406iple_a) (A_49:(hoare_1775062406iple_a->Prop)) (F_10:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_9:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_10) F_9)->((finite2063573081iple_a A_49)->((((member2122167641iple_a X_18) A_49)->False)->((not (((eq (hoare_1775062406iple_a->Prop)) A_49) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (F_9 ((insert1281456128iple_a X_18) A_49))) ((F_10 X_18) (F_9 A_49))))))))
% FOF formula (forall (X_18:pname) (A_49:(pname->Prop)) (F_10:(pname->(pname->pname))) (F_9:((pname->Prop)->pname)), (((finite1282449217_pname F_10) F_9)->((finite_finite_pname A_49)->((((member_pname X_18) A_49)->False)->((not (((eq (pname->Prop)) A_49) bot_bot_pname_o))->(((eq pname) (F_9 ((insert_pname X_18) A_49))) ((F_10 X_18) (F_9 A_49)))))))) of role axiom named fact_468_folding__one_Oinsert
% A new axiom: (forall (X_18:pname) (A_49:(pname->Prop)) (F_10:(pname->(pname->pname))) (F_9:((pname->Prop)->pname)), (((finite1282449217_pname F_10) F_9)->((finite_finite_pname A_49)->((((member_pname X_18) A_49)->False)->((not (((eq (pname->Prop)) A_49) bot_bot_pname_o))->(((eq pname) (F_9 ((insert_pname X_18) A_49))) ((F_10 X_18) (F_9 A_49))))))))
% FOF formula (forall (X_17:hoare_1167836817_state) (F_8:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_7:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_8) F_7)->(((eq hoare_1167836817_state) (F_7 ((insert2134838167_state X_17) bot_bo70021908tate_o))) X_17))) of role axiom named fact_469_folding__one_Osingleton
% A new axiom: (forall (X_17:hoare_1167836817_state) (F_8:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_7:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_8) F_7)->(((eq hoare_1167836817_state) (F_7 ((insert2134838167_state X_17) bot_bo70021908tate_o))) X_17)))
% FOF formula (forall (X_17:hoare_1775062406iple_a) (F_8:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_7:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_8) F_7)->(((eq hoare_1775062406iple_a) (F_7 ((insert1281456128iple_a X_17) bot_bo751897185le_a_o))) X_17))) of role axiom named fact_470_folding__one_Osingleton
% A new axiom: (forall (X_17:hoare_1775062406iple_a) (F_8:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_7:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_8) F_7)->(((eq hoare_1775062406iple_a) (F_7 ((insert1281456128iple_a X_17) bot_bo751897185le_a_o))) X_17)))
% FOF formula (forall (X_17:pname) (F_8:(pname->(pname->pname))) (F_7:((pname->Prop)->pname)), (((finite1282449217_pname F_8) F_7)->(((eq pname) (F_7 ((insert_pname X_17) bot_bot_pname_o))) X_17))) of role axiom named fact_471_folding__one_Osingleton
% A new axiom: (forall (X_17:pname) (F_8:(pname->(pname->pname))) (F_7:((pname->Prop)->pname)), (((finite1282449217_pname F_8) F_7)->(((eq pname) (F_7 ((insert_pname X_17) bot_bot_pname_o))) X_17)))
% FOF formula (forall (A_48:(hoare_1167836817_state->Prop)) (F_6:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_5:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_6) F_5)->((finite1084549118_state A_48)->((not (((eq (hoare_1167836817_state->Prop)) A_48) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state) (Y_2:hoare_1167836817_state), ((member2058392318_state ((F_6 X) Y_2)) ((insert2134838167_state X) ((insert2134838167_state Y_2) bot_bo70021908tate_o))))->((member2058392318_state (F_5 A_48)) A_48)))))) of role axiom named fact_472_folding__one_Oclosed
% A new axiom: (forall (A_48:(hoare_1167836817_state->Prop)) (F_6:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_5:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_6) F_5)->((finite1084549118_state A_48)->((not (((eq (hoare_1167836817_state->Prop)) A_48) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state) (Y_2:hoare_1167836817_state), ((member2058392318_state ((F_6 X) Y_2)) ((insert2134838167_state X) ((insert2134838167_state Y_2) bot_bo70021908tate_o))))->((member2058392318_state (F_5 A_48)) A_48))))))
% FOF formula (forall (A_48:(hoare_1775062406iple_a->Prop)) (F_6:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_5:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_6) F_5)->((finite2063573081iple_a A_48)->((not (((eq (hoare_1775062406iple_a->Prop)) A_48) bot_bo751897185le_a_o))->((forall (X:hoare_1775062406iple_a) (Y_2:hoare_1775062406iple_a), ((member2122167641iple_a ((F_6 X) Y_2)) ((insert1281456128iple_a X) ((insert1281456128iple_a Y_2) bot_bo751897185le_a_o))))->((member2122167641iple_a (F_5 A_48)) A_48)))))) of role axiom named fact_473_folding__one_Oclosed
% A new axiom: (forall (A_48:(hoare_1775062406iple_a->Prop)) (F_6:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_5:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_6) F_5)->((finite2063573081iple_a A_48)->((not (((eq (hoare_1775062406iple_a->Prop)) A_48) bot_bo751897185le_a_o))->((forall (X:hoare_1775062406iple_a) (Y_2:hoare_1775062406iple_a), ((member2122167641iple_a ((F_6 X) Y_2)) ((insert1281456128iple_a X) ((insert1281456128iple_a Y_2) bot_bo751897185le_a_o))))->((member2122167641iple_a (F_5 A_48)) A_48))))))
% FOF formula (forall (A_48:(pname->Prop)) (F_6:(pname->(pname->pname))) (F_5:((pname->Prop)->pname)), (((finite1282449217_pname F_6) F_5)->((finite_finite_pname A_48)->((not (((eq (pname->Prop)) A_48) bot_bot_pname_o))->((forall (X:pname) (Y_2:pname), ((member_pname ((F_6 X) Y_2)) ((insert_pname X) ((insert_pname Y_2) bot_bot_pname_o))))->((member_pname (F_5 A_48)) A_48)))))) of role axiom named fact_474_folding__one_Oclosed
% A new axiom: (forall (A_48:(pname->Prop)) (F_6:(pname->(pname->pname))) (F_5:((pname->Prop)->pname)), (((finite1282449217_pname F_6) F_5)->((finite_finite_pname A_48)->((not (((eq (pname->Prop)) A_48) bot_bot_pname_o))->((forall (X:pname) (Y_2:pname), ((member_pname ((F_6 X) Y_2)) ((insert_pname X) ((insert_pname Y_2) bot_bot_pname_o))))->((member_pname (F_5 A_48)) A_48))))))
% FOF formula (forall (C2:com) (S2:state) (N2:nat) (T2:state) (C1:com) (S1:state) (N1:nat) (T1:state), (((((evaln C1) S1) N1) T1)->(((((evaln C2) S2) N2) T2)->((ex nat) (fun (N:nat)=> ((and ((((evaln C1) S1) N) T1)) ((((evaln C2) S2) N) T2))))))) of role axiom named fact_475_evaln__max2
% A new axiom: (forall (C2:com) (S2:state) (N2:nat) (T2:state) (C1:com) (S1:state) (N1:nat) (T1:state), (((((evaln C1) S1) N1) T1)->(((((evaln C2) S2) N2) T2)->((ex nat) (fun (N:nat)=> ((and ((((evaln C1) S1) N) T1)) ((((evaln C2) S2) N) T2)))))))
% FOF formula (forall (A_47:hoare_1167836817_state) (A_46:(hoare_1167836817_state->Prop)), (((member2058392318_state A_47) A_46)->((ex (hoare_1167836817_state->Prop)) (fun (B_34:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_46) ((insert2134838167_state A_47) B_34))) (((member2058392318_state A_47) B_34)->False)))))) of role axiom named fact_476_mk__disjoint__insert
% A new axiom: (forall (A_47:hoare_1167836817_state) (A_46:(hoare_1167836817_state->Prop)), (((member2058392318_state A_47) A_46)->((ex (hoare_1167836817_state->Prop)) (fun (B_34:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_46) ((insert2134838167_state A_47) B_34))) (((member2058392318_state A_47) B_34)->False))))))
% FOF formula (forall (A_47:hoare_1775062406iple_a) (A_46:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_47) A_46)->((ex (hoare_1775062406iple_a->Prop)) (fun (B_34:(hoare_1775062406iple_a->Prop))=> ((and (((eq (hoare_1775062406iple_a->Prop)) A_46) ((insert1281456128iple_a A_47) B_34))) (((member2122167641iple_a A_47) B_34)->False)))))) of role axiom named fact_477_mk__disjoint__insert
% A new axiom: (forall (A_47:hoare_1775062406iple_a) (A_46:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_47) A_46)->((ex (hoare_1775062406iple_a->Prop)) (fun (B_34:(hoare_1775062406iple_a->Prop))=> ((and (((eq (hoare_1775062406iple_a->Prop)) A_46) ((insert1281456128iple_a A_47) B_34))) (((member2122167641iple_a A_47) B_34)->False))))))
% FOF formula (forall (A_47:pname) (A_46:(pname->Prop)), (((member_pname A_47) A_46)->((ex (pname->Prop)) (fun (B_34:(pname->Prop))=> ((and (((eq (pname->Prop)) A_46) ((insert_pname A_47) B_34))) (((member_pname A_47) B_34)->False)))))) of role axiom named fact_478_mk__disjoint__insert
% A new axiom: (forall (A_47:pname) (A_46:(pname->Prop)), (((member_pname A_47) A_46)->((ex (pname->Prop)) (fun (B_34:(pname->Prop))=> ((and (((eq (pname->Prop)) A_46) ((insert_pname A_47) B_34))) (((member_pname A_47) B_34)->False))))))
% FOF formula (forall (X_16:hoare_1167836817_state) (A_45:(hoare_1167836817_state->Prop)), (((member2058392318_state X_16) A_45)->((forall (B_34:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_45) ((insert2134838167_state X_16) B_34))->((member2058392318_state X_16) B_34)))->False))) of role axiom named fact_479_Set_Oset__insert
% A new axiom: (forall (X_16:hoare_1167836817_state) (A_45:(hoare_1167836817_state->Prop)), (((member2058392318_state X_16) A_45)->((forall (B_34:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_45) ((insert2134838167_state X_16) B_34))->((member2058392318_state X_16) B_34)))->False)))
% FOF formula (forall (X_16:hoare_1775062406iple_a) (A_45:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a X_16) A_45)->((forall (B_34:(hoare_1775062406iple_a->Prop)), ((((eq (hoare_1775062406iple_a->Prop)) A_45) ((insert1281456128iple_a X_16) B_34))->((member2122167641iple_a X_16) B_34)))->False))) of role axiom named fact_480_Set_Oset__insert
% A new axiom: (forall (X_16:hoare_1775062406iple_a) (A_45:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a X_16) A_45)->((forall (B_34:(hoare_1775062406iple_a->Prop)), ((((eq (hoare_1775062406iple_a->Prop)) A_45) ((insert1281456128iple_a X_16) B_34))->((member2122167641iple_a X_16) B_34)))->False)))
% FOF formula (forall (X_16:pname) (A_45:(pname->Prop)), (((member_pname X_16) A_45)->((forall (B_34:(pname->Prop)), ((((eq (pname->Prop)) A_45) ((insert_pname X_16) B_34))->((member_pname X_16) B_34)))->False))) of role axiom named fact_481_Set_Oset__insert
% A new axiom: (forall (X_16:pname) (A_45:(pname->Prop)), (((member_pname X_16) A_45)->((forall (B_34:(pname->Prop)), ((((eq (pname->Prop)) A_45) ((insert_pname X_16) B_34))->((member_pname X_16) B_34)))->False)))
% FOF formula (forall (A_44:(hoare_1775062406iple_a->Prop)), ((forall (Y_2:hoare_1775062406iple_a), (((member2122167641iple_a Y_2) A_44)->False))->(((eq (hoare_1775062406iple_a->Prop)) A_44) bot_bo751897185le_a_o))) of role axiom named fact_482_equals0I
% A new axiom: (forall (A_44:(hoare_1775062406iple_a->Prop)), ((forall (Y_2:hoare_1775062406iple_a), (((member2122167641iple_a Y_2) A_44)->False))->(((eq (hoare_1775062406iple_a->Prop)) A_44) bot_bo751897185le_a_o)))
% FOF formula (forall (A_44:(pname->Prop)), ((forall (Y_2:pname), (((member_pname Y_2) A_44)->False))->(((eq (pname->Prop)) A_44) bot_bot_pname_o))) of role axiom named fact_483_equals0I
% A new axiom: (forall (A_44:(pname->Prop)), ((forall (Y_2:pname), (((member_pname Y_2) A_44)->False))->(((eq (pname->Prop)) A_44) bot_bot_pname_o)))
% FOF formula (forall (A_44:(hoare_1167836817_state->Prop)), ((forall (Y_2:hoare_1167836817_state), (((member2058392318_state Y_2) A_44)->False))->(((eq (hoare_1167836817_state->Prop)) A_44) bot_bo70021908tate_o))) of role axiom named fact_484_equals0I
% A new axiom: (forall (A_44:(hoare_1167836817_state->Prop)), ((forall (Y_2:hoare_1167836817_state), (((member2058392318_state Y_2) A_44)->False))->(((eq (hoare_1167836817_state->Prop)) A_44) bot_bo70021908tate_o)))
% FOF formula (forall (B_33:(Prop->Prop)) (A_43:(Prop->Prop)), ((finite_finite_o A_43)->((not (((eq (Prop->Prop)) A_43) bot_bot_o_o))->((finite_finite_o B_33)->((not (((eq (Prop->Prop)) B_33) bot_bot_o_o))->((iff (big_la727467310_fin_o ((semila2062604954up_o_o A_43) B_33))) ((semila10642723_sup_o (big_la727467310_fin_o A_43)) (big_la727467310_fin_o B_33)))))))) of role axiom named fact_485_Sup__fin_Ounion__idem
% A new axiom: (forall (B_33:(Prop->Prop)) (A_43:(Prop->Prop)), ((finite_finite_o A_43)->((not (((eq (Prop->Prop)) A_43) bot_bot_o_o))->((finite_finite_o B_33)->((not (((eq (Prop->Prop)) B_33) bot_bot_o_o))->((iff (big_la727467310_fin_o ((semila2062604954up_o_o A_43) B_33))) ((semila10642723_sup_o (big_la727467310_fin_o A_43)) (big_la727467310_fin_o B_33))))))))
% FOF formula (forall (B_33:((pname->Prop)->Prop)) (A_43:((pname->Prop)->Prop)), ((finite297249702name_o A_43)->((not (((eq ((pname->Prop)->Prop)) A_43) bot_bot_pname_o_o))->((finite297249702name_o B_33)->((not (((eq ((pname->Prop)->Prop)) B_33) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((semila181081674me_o_o A_43) B_33))) ((semila1780557381name_o (big_la1286884090name_o A_43)) (big_la1286884090name_o B_33)))))))) of role axiom named fact_486_Sup__fin_Ounion__idem
% A new axiom: (forall (B_33:((pname->Prop)->Prop)) (A_43:((pname->Prop)->Prop)), ((finite297249702name_o A_43)->((not (((eq ((pname->Prop)->Prop)) A_43) bot_bot_pname_o_o))->((finite297249702name_o B_33)->((not (((eq ((pname->Prop)->Prop)) B_33) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((semila181081674me_o_o A_43) B_33))) ((semila1780557381name_o (big_la1286884090name_o A_43)) (big_la1286884090name_o B_33))))))))
% FOF formula (forall (B_33:((hoare_1167836817_state->Prop)->Prop)) (A_43:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_43)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_43) bot_bo691907561te_o_o))->((finite1380128977tate_o B_33)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_33) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((semila866907787te_o_o A_43) B_33))) ((semila1172322802tate_o (big_la1138507389tate_o A_43)) (big_la1138507389tate_o B_33)))))))) of role axiom named fact_487_Sup__fin_Ounion__idem
% A new axiom: (forall (B_33:((hoare_1167836817_state->Prop)->Prop)) (A_43:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_43)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_43) bot_bo691907561te_o_o))->((finite1380128977tate_o B_33)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_33) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((semila866907787te_o_o A_43) B_33))) ((semila1172322802tate_o (big_la1138507389tate_o A_43)) (big_la1138507389tate_o B_33))))))))
% FOF formula (forall (B_33:((hoare_1775062406iple_a->Prop)->Prop)) (A_43:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_43)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_43) bot_bo1976773294_a_o_o))->((finite789576932le_a_o B_33)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) B_33) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((semila2069193356_a_o_o A_43) B_33))) ((semila13410563le_a_o (big_la1843772984le_a_o A_43)) (big_la1843772984le_a_o B_33)))))))) of role axiom named fact_488_Sup__fin_Ounion__idem
% A new axiom: (forall (B_33:((hoare_1775062406iple_a->Prop)->Prop)) (A_43:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_43)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_43) bot_bo1976773294_a_o_o))->((finite789576932le_a_o B_33)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) B_33) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((semila2069193356_a_o_o A_43) B_33))) ((semila13410563le_a_o (big_la1843772984le_a_o A_43)) (big_la1843772984le_a_o B_33))))))))
% FOF formula (forall (X_15:Prop) (A_42:(Prop->Prop)), ((finite_finite_o A_42)->(((member_o X_15) A_42)->((iff ((semila10642723_sup_o X_15) (big_la727467310_fin_o A_42))) (big_la727467310_fin_o A_42))))) of role axiom named fact_489_Sup__fin_Oin__idem
% A new axiom: (forall (X_15:Prop) (A_42:(Prop->Prop)), ((finite_finite_o A_42)->(((member_o X_15) A_42)->((iff ((semila10642723_sup_o X_15) (big_la727467310_fin_o A_42))) (big_la727467310_fin_o A_42)))))
% FOF formula (forall (X_15:(pname->Prop)) (A_42:((pname->Prop)->Prop)), ((finite297249702name_o A_42)->(((member_pname_o X_15) A_42)->(((eq (pname->Prop)) ((semila1780557381name_o X_15) (big_la1286884090name_o A_42))) (big_la1286884090name_o A_42))))) of role axiom named fact_490_Sup__fin_Oin__idem
% A new axiom: (forall (X_15:(pname->Prop)) (A_42:((pname->Prop)->Prop)), ((finite297249702name_o A_42)->(((member_pname_o X_15) A_42)->(((eq (pname->Prop)) ((semila1780557381name_o X_15) (big_la1286884090name_o A_42))) (big_la1286884090name_o A_42)))))
% FOF formula (forall (X_15:(hoare_1167836817_state->Prop)) (A_42:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_42)->(((member864234961tate_o X_15) A_42)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_15) (big_la1138507389tate_o A_42))) (big_la1138507389tate_o A_42))))) of role axiom named fact_491_Sup__fin_Oin__idem
% A new axiom: (forall (X_15:(hoare_1167836817_state->Prop)) (A_42:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_42)->(((member864234961tate_o X_15) A_42)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_15) (big_la1138507389tate_o A_42))) (big_la1138507389tate_o A_42)))))
% FOF formula (forall (X_15:(hoare_1775062406iple_a->Prop)) (A_42:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_42)->(((member1207314404le_a_o X_15) A_42)->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_15) (big_la1843772984le_a_o A_42))) (big_la1843772984le_a_o A_42))))) of role axiom named fact_492_Sup__fin_Oin__idem
% A new axiom: (forall (X_15:(hoare_1775062406iple_a->Prop)) (A_42:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_42)->(((member1207314404le_a_o X_15) A_42)->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_15) (big_la1843772984le_a_o A_42))) (big_la1843772984le_a_o A_42)))))
% FOF formula (forall (X_14:Prop) (A_41:(Prop->Prop)), ((finite_finite_o A_41)->((((member_o X_14) A_41)->False)->((not (((eq (Prop->Prop)) A_41) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_14) A_41))) ((semila10642723_sup_o X_14) (big_la727467310_fin_o A_41))))))) of role axiom named fact_493_Sup__fin_Oinsert
% A new axiom: (forall (X_14:Prop) (A_41:(Prop->Prop)), ((finite_finite_o A_41)->((((member_o X_14) A_41)->False)->((not (((eq (Prop->Prop)) A_41) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_14) A_41))) ((semila10642723_sup_o X_14) (big_la727467310_fin_o A_41)))))))
% FOF formula (forall (X_14:(pname->Prop)) (A_41:((pname->Prop)->Prop)), ((finite297249702name_o A_41)->((((member_pname_o X_14) A_41)->False)->((not (((eq ((pname->Prop)->Prop)) A_41) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_14) A_41))) ((semila1780557381name_o X_14) (big_la1286884090name_o A_41))))))) of role axiom named fact_494_Sup__fin_Oinsert
% A new axiom: (forall (X_14:(pname->Prop)) (A_41:((pname->Prop)->Prop)), ((finite297249702name_o A_41)->((((member_pname_o X_14) A_41)->False)->((not (((eq ((pname->Prop)->Prop)) A_41) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_14) A_41))) ((semila1780557381name_o X_14) (big_la1286884090name_o A_41)))))))
% FOF formula (forall (X_14:(hoare_1167836817_state->Prop)) (A_41:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_41)->((((member864234961tate_o X_14) A_41)->False)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_41) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((insert999278200tate_o X_14) A_41))) ((semila1172322802tate_o X_14) (big_la1138507389tate_o A_41))))))) of role axiom named fact_495_Sup__fin_Oinsert
% A new axiom: (forall (X_14:(hoare_1167836817_state->Prop)) (A_41:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_41)->((((member864234961tate_o X_14) A_41)->False)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_41) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((insert999278200tate_o X_14) A_41))) ((semila1172322802tate_o X_14) (big_la1138507389tate_o A_41)))))))
% FOF formula (forall (X_14:(hoare_1775062406iple_a->Prop)) (A_41:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_41)->((((member1207314404le_a_o X_14) A_41)->False)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_41) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((insert1210049533le_a_o X_14) A_41))) ((semila13410563le_a_o X_14) (big_la1843772984le_a_o A_41))))))) of role axiom named fact_496_Sup__fin_Oinsert
% A new axiom: (forall (X_14:(hoare_1775062406iple_a->Prop)) (A_41:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_41)->((((member1207314404le_a_o X_14) A_41)->False)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_41) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((insert1210049533le_a_o X_14) A_41))) ((semila13410563le_a_o X_14) (big_la1843772984le_a_o A_41)))))))
% FOF formula (forall (X_13:Prop) (A_40:(Prop->Prop)), ((finite_finite_o A_40)->((not (((eq (Prop->Prop)) A_40) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_13) A_40))) ((semila10642723_sup_o X_13) (big_la727467310_fin_o A_40)))))) of role axiom named fact_497_Sup__fin_Oinsert__idem
% A new axiom: (forall (X_13:Prop) (A_40:(Prop->Prop)), ((finite_finite_o A_40)->((not (((eq (Prop->Prop)) A_40) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_13) A_40))) ((semila10642723_sup_o X_13) (big_la727467310_fin_o A_40))))))
% FOF formula (forall (X_13:(pname->Prop)) (A_40:((pname->Prop)->Prop)), ((finite297249702name_o A_40)->((not (((eq ((pname->Prop)->Prop)) A_40) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_13) A_40))) ((semila1780557381name_o X_13) (big_la1286884090name_o A_40)))))) of role axiom named fact_498_Sup__fin_Oinsert__idem
% A new axiom: (forall (X_13:(pname->Prop)) (A_40:((pname->Prop)->Prop)), ((finite297249702name_o A_40)->((not (((eq ((pname->Prop)->Prop)) A_40) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_13) A_40))) ((semila1780557381name_o X_13) (big_la1286884090name_o A_40))))))
% FOF formula (forall (X_13:(hoare_1167836817_state->Prop)) (A_40:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_40)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_40) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((insert999278200tate_o X_13) A_40))) ((semila1172322802tate_o X_13) (big_la1138507389tate_o A_40)))))) of role axiom named fact_499_Sup__fin_Oinsert__idem
% A new axiom: (forall (X_13:(hoare_1167836817_state->Prop)) (A_40:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_40)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_40) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((insert999278200tate_o X_13) A_40))) ((semila1172322802tate_o X_13) (big_la1138507389tate_o A_40))))))
% FOF formula (forall (X_13:(hoare_1775062406iple_a->Prop)) (A_40:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_40)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_40) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((insert1210049533le_a_o X_13) A_40))) ((semila13410563le_a_o X_13) (big_la1843772984le_a_o A_40)))))) of role axiom named fact_500_Sup__fin_Oinsert__idem
% A new axiom: (forall (X_13:(hoare_1775062406iple_a->Prop)) (A_40:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_40)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_40) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((insert1210049533le_a_o X_13) A_40))) ((semila13410563le_a_o X_13) (big_la1843772984le_a_o A_40))))))
% FOF formula (forall (N_2:(Prop->Prop)) (H:(Prop->Prop)), ((forall (X:Prop) (Y_2:Prop), ((iff (H ((semila10642723_sup_o X) Y_2))) ((semila10642723_sup_o (H X)) (H Y_2))))->((finite_finite_o N_2)->((not (((eq (Prop->Prop)) N_2) bot_bot_o_o))->((iff (H (big_la727467310_fin_o N_2))) (big_la727467310_fin_o ((image_o_o H) N_2))))))) of role axiom named fact_501_Sup__fin_Ohom__commute
% A new axiom: (forall (N_2:(Prop->Prop)) (H:(Prop->Prop)), ((forall (X:Prop) (Y_2:Prop), ((iff (H ((semila10642723_sup_o X) Y_2))) ((semila10642723_sup_o (H X)) (H Y_2))))->((finite_finite_o N_2)->((not (((eq (Prop->Prop)) N_2) bot_bot_o_o))->((iff (H (big_la727467310_fin_o N_2))) (big_la727467310_fin_o ((image_o_o H) N_2)))))))
% FOF formula (forall (N_2:((pname->Prop)->Prop)) (H:((pname->Prop)->(pname->Prop))), ((forall (X:(pname->Prop)) (Y_2:(pname->Prop)), (((eq (pname->Prop)) (H ((semila1780557381name_o X) Y_2))) ((semila1780557381name_o (H X)) (H Y_2))))->((finite297249702name_o N_2)->((not (((eq ((pname->Prop)->Prop)) N_2) bot_bot_pname_o_o))->(((eq (pname->Prop)) (H (big_la1286884090name_o N_2))) (big_la1286884090name_o ((image_1085733413name_o H) N_2))))))) of role axiom named fact_502_Sup__fin_Ohom__commute
% A new axiom: (forall (N_2:((pname->Prop)->Prop)) (H:((pname->Prop)->(pname->Prop))), ((forall (X:(pname->Prop)) (Y_2:(pname->Prop)), (((eq (pname->Prop)) (H ((semila1780557381name_o X) Y_2))) ((semila1780557381name_o (H X)) (H Y_2))))->((finite297249702name_o N_2)->((not (((eq ((pname->Prop)->Prop)) N_2) bot_bot_pname_o_o))->(((eq (pname->Prop)) (H (big_la1286884090name_o N_2))) (big_la1286884090name_o ((image_1085733413name_o H) N_2)))))))
% FOF formula (forall (N_2:((hoare_1167836817_state->Prop)->Prop)) (H:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))), ((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (H ((semila1172322802tate_o X) Y_2))) ((semila1172322802tate_o (H X)) (H Y_2))))->((finite1380128977tate_o N_2)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) N_2) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (H (big_la1138507389tate_o N_2))) (big_la1138507389tate_o ((image_1488525317tate_o H) N_2))))))) of role axiom named fact_503_Sup__fin_Ohom__commute
% A new axiom: (forall (N_2:((hoare_1167836817_state->Prop)->Prop)) (H:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))), ((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (H ((semila1172322802tate_o X) Y_2))) ((semila1172322802tate_o (H X)) (H Y_2))))->((finite1380128977tate_o N_2)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) N_2) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (H (big_la1138507389tate_o N_2))) (big_la1138507389tate_o ((image_1488525317tate_o H) N_2)))))))
% FOF formula (forall (N_2:((hoare_1775062406iple_a->Prop)->Prop)) (H:((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop))), ((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (H ((semila13410563le_a_o X) Y_2))) ((semila13410563le_a_o (H X)) (H Y_2))))->((finite789576932le_a_o N_2)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) N_2) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (H (big_la1843772984le_a_o N_2))) (big_la1843772984le_a_o ((image_2014247585le_a_o H) N_2))))))) of role axiom named fact_504_Sup__fin_Ohom__commute
% A new axiom: (forall (N_2:((hoare_1775062406iple_a->Prop)->Prop)) (H:((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop))), ((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (H ((semila13410563le_a_o X) Y_2))) ((semila13410563le_a_o (H X)) (H Y_2))))->((finite789576932le_a_o N_2)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) N_2) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (H (big_la1843772984le_a_o N_2))) (big_la1843772984le_a_o ((image_2014247585le_a_o H) N_2)))))))
% FOF formula (forall (A_39:(Prop->Prop)), ((finite_finite_o A_39)->((not (((eq (Prop->Prop)) A_39) bot_bot_o_o))->((forall (X:Prop) (Y_2:Prop), ((member_o ((semila10642723_sup_o X) Y_2)) ((insert_o X) ((insert_o Y_2) bot_bot_o_o))))->((member_o (big_la727467310_fin_o A_39)) A_39))))) of role axiom named fact_505_Sup__fin_Oclosed
% A new axiom: (forall (A_39:(Prop->Prop)), ((finite_finite_o A_39)->((not (((eq (Prop->Prop)) A_39) bot_bot_o_o))->((forall (X:Prop) (Y_2:Prop), ((member_o ((semila10642723_sup_o X) Y_2)) ((insert_o X) ((insert_o Y_2) bot_bot_o_o))))->((member_o (big_la727467310_fin_o A_39)) A_39)))))
% FOF formula (forall (A_39:((pname->Prop)->Prop)), ((finite297249702name_o A_39)->((not (((eq ((pname->Prop)->Prop)) A_39) bot_bot_pname_o_o))->((forall (X:(pname->Prop)) (Y_2:(pname->Prop)), ((member_pname_o ((semila1780557381name_o X) Y_2)) ((insert_pname_o X) ((insert_pname_o Y_2) bot_bot_pname_o_o))))->((member_pname_o (big_la1286884090name_o A_39)) A_39))))) of role axiom named fact_506_Sup__fin_Oclosed
% A new axiom: (forall (A_39:((pname->Prop)->Prop)), ((finite297249702name_o A_39)->((not (((eq ((pname->Prop)->Prop)) A_39) bot_bot_pname_o_o))->((forall (X:(pname->Prop)) (Y_2:(pname->Prop)), ((member_pname_o ((semila1780557381name_o X) Y_2)) ((insert_pname_o X) ((insert_pname_o Y_2) bot_bot_pname_o_o))))->((member_pname_o (big_la1286884090name_o A_39)) A_39)))))
% FOF formula (forall (A_39:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_39)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_39) bot_bo691907561te_o_o))->((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), ((member864234961tate_o ((semila1172322802tate_o X) Y_2)) ((insert999278200tate_o X) ((insert999278200tate_o Y_2) bot_bo691907561te_o_o))))->((member864234961tate_o (big_la1138507389tate_o A_39)) A_39))))) of role axiom named fact_507_Sup__fin_Oclosed
% A new axiom: (forall (A_39:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_39)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_39) bot_bo691907561te_o_o))->((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), ((member864234961tate_o ((semila1172322802tate_o X) Y_2)) ((insert999278200tate_o X) ((insert999278200tate_o Y_2) bot_bo691907561te_o_o))))->((member864234961tate_o (big_la1138507389tate_o A_39)) A_39)))))
% FOF formula (forall (A_39:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_39)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_39) bot_bo1976773294_a_o_o))->((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)), ((member1207314404le_a_o ((semila13410563le_a_o X) Y_2)) ((insert1210049533le_a_o X) ((insert1210049533le_a_o Y_2) bot_bo1976773294_a_o_o))))->((member1207314404le_a_o (big_la1843772984le_a_o A_39)) A_39))))) of role axiom named fact_508_Sup__fin_Oclosed
% A new axiom: (forall (A_39:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_39)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_39) bot_bo1976773294_a_o_o))->((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)), ((member1207314404le_a_o ((semila13410563le_a_o X) Y_2)) ((insert1210049533le_a_o X) ((insert1210049533le_a_o Y_2) bot_bo1976773294_a_o_o))))->((member1207314404le_a_o (big_la1843772984le_a_o A_39)) A_39)))))
% FOF formula (forall (B_32:(Prop->Prop)) (A_38:(Prop->Prop)), ((finite_finite_o A_38)->((finite_finite_o B_32)->((not (((eq (Prop->Prop)) ((semila232696320nf_o_o A_38) B_32)) bot_bot_o_o))->((iff ((semila10642723_sup_o (big_la727467310_fin_o ((semila2062604954up_o_o A_38) B_32))) (big_la727467310_fin_o ((semila232696320nf_o_o A_38) B_32)))) ((semila10642723_sup_o (big_la727467310_fin_o A_38)) (big_la727467310_fin_o B_32))))))) of role axiom named fact_509_Sup__fin_Ounion__inter
% A new axiom: (forall (B_32:(Prop->Prop)) (A_38:(Prop->Prop)), ((finite_finite_o A_38)->((finite_finite_o B_32)->((not (((eq (Prop->Prop)) ((semila232696320nf_o_o A_38) B_32)) bot_bot_o_o))->((iff ((semila10642723_sup_o (big_la727467310_fin_o ((semila2062604954up_o_o A_38) B_32))) (big_la727467310_fin_o ((semila232696320nf_o_o A_38) B_32)))) ((semila10642723_sup_o (big_la727467310_fin_o A_38)) (big_la727467310_fin_o B_32)))))))
% FOF formula (forall (B_32:((pname->Prop)->Prop)) (A_38:((pname->Prop)->Prop)), ((finite297249702name_o A_38)->((finite297249702name_o B_32)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_38) B_32)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((semila1780557381name_o (big_la1286884090name_o ((semila181081674me_o_o A_38) B_32))) (big_la1286884090name_o ((semila2013987940me_o_o A_38) B_32)))) ((semila1780557381name_o (big_la1286884090name_o A_38)) (big_la1286884090name_o B_32))))))) of role axiom named fact_510_Sup__fin_Ounion__inter
% A new axiom: (forall (B_32:((pname->Prop)->Prop)) (A_38:((pname->Prop)->Prop)), ((finite297249702name_o A_38)->((finite297249702name_o B_32)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_38) B_32)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((semila1780557381name_o (big_la1286884090name_o ((semila181081674me_o_o A_38) B_32))) (big_la1286884090name_o ((semila2013987940me_o_o A_38) B_32)))) ((semila1780557381name_o (big_la1286884090name_o A_38)) (big_la1286884090name_o B_32)))))))
% FOF formula (forall (B_32:((hoare_1167836817_state->Prop)->Prop)) (A_38:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_38)->((finite1380128977tate_o B_32)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_38) B_32)) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o (big_la1138507389tate_o ((semila866907787te_o_o A_38) B_32))) (big_la1138507389tate_o ((semila1758709489te_o_o A_38) B_32)))) ((semila1172322802tate_o (big_la1138507389tate_o A_38)) (big_la1138507389tate_o B_32))))))) of role axiom named fact_511_Sup__fin_Ounion__inter
% A new axiom: (forall (B_32:((hoare_1167836817_state->Prop)->Prop)) (A_38:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_38)->((finite1380128977tate_o B_32)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_38) B_32)) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o (big_la1138507389tate_o ((semila866907787te_o_o A_38) B_32))) (big_la1138507389tate_o ((semila1758709489te_o_o A_38) B_32)))) ((semila1172322802tate_o (big_la1138507389tate_o A_38)) (big_la1138507389tate_o B_32)))))))
% FOF formula (forall (B_32:((hoare_1775062406iple_a->Prop)->Prop)) (A_38:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_38)->((finite789576932le_a_o B_32)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) ((semila1691990438_a_o_o A_38) B_32)) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o (big_la1843772984le_a_o ((semila2069193356_a_o_o A_38) B_32))) (big_la1843772984le_a_o ((semila1691990438_a_o_o A_38) B_32)))) ((semila13410563le_a_o (big_la1843772984le_a_o A_38)) (big_la1843772984le_a_o B_32))))))) of role axiom named fact_512_Sup__fin_Ounion__inter
% A new axiom: (forall (B_32:((hoare_1775062406iple_a->Prop)->Prop)) (A_38:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_38)->((finite789576932le_a_o B_32)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) ((semila1691990438_a_o_o A_38) B_32)) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o (big_la1843772984le_a_o ((semila2069193356_a_o_o A_38) B_32))) (big_la1843772984le_a_o ((semila1691990438_a_o_o A_38) B_32)))) ((semila13410563le_a_o (big_la1843772984le_a_o A_38)) (big_la1843772984le_a_o B_32)))))))
% FOF formula (forall (B_31:(Prop->Prop)) (A_37:(Prop->Prop)), ((finite_finite_o A_37)->((not (((eq (Prop->Prop)) A_37) bot_bot_o_o))->((finite_finite_o B_31)->((not (((eq (Prop->Prop)) B_31) bot_bot_o_o))->((((eq (Prop->Prop)) ((semila232696320nf_o_o A_37) B_31)) bot_bot_o_o)->((iff (big_la727467310_fin_o ((semila2062604954up_o_o A_37) B_31))) ((semila10642723_sup_o (big_la727467310_fin_o A_37)) (big_la727467310_fin_o B_31))))))))) of role axiom named fact_513_Sup__fin_Ounion__disjoint
% A new axiom: (forall (B_31:(Prop->Prop)) (A_37:(Prop->Prop)), ((finite_finite_o A_37)->((not (((eq (Prop->Prop)) A_37) bot_bot_o_o))->((finite_finite_o B_31)->((not (((eq (Prop->Prop)) B_31) bot_bot_o_o))->((((eq (Prop->Prop)) ((semila232696320nf_o_o A_37) B_31)) bot_bot_o_o)->((iff (big_la727467310_fin_o ((semila2062604954up_o_o A_37) B_31))) ((semila10642723_sup_o (big_la727467310_fin_o A_37)) (big_la727467310_fin_o B_31)))))))))
% FOF formula (forall (B_31:((pname->Prop)->Prop)) (A_37:((pname->Prop)->Prop)), ((finite297249702name_o A_37)->((not (((eq ((pname->Prop)->Prop)) A_37) bot_bot_pname_o_o))->((finite297249702name_o B_31)->((not (((eq ((pname->Prop)->Prop)) B_31) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_37) B_31)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (big_la1286884090name_o ((semila181081674me_o_o A_37) B_31))) ((semila1780557381name_o (big_la1286884090name_o A_37)) (big_la1286884090name_o B_31))))))))) of role axiom named fact_514_Sup__fin_Ounion__disjoint
% A new axiom: (forall (B_31:((pname->Prop)->Prop)) (A_37:((pname->Prop)->Prop)), ((finite297249702name_o A_37)->((not (((eq ((pname->Prop)->Prop)) A_37) bot_bot_pname_o_o))->((finite297249702name_o B_31)->((not (((eq ((pname->Prop)->Prop)) B_31) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_37) B_31)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (big_la1286884090name_o ((semila181081674me_o_o A_37) B_31))) ((semila1780557381name_o (big_la1286884090name_o A_37)) (big_la1286884090name_o B_31)))))))))
% FOF formula (forall (B_31:((hoare_1167836817_state->Prop)->Prop)) (A_37:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_37)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_37) bot_bo691907561te_o_o))->((finite1380128977tate_o B_31)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_31) bot_bo691907561te_o_o))->((((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_37) B_31)) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((semila866907787te_o_o A_37) B_31))) ((semila1172322802tate_o (big_la1138507389tate_o A_37)) (big_la1138507389tate_o B_31))))))))) of role axiom named fact_515_Sup__fin_Ounion__disjoint
% A new axiom: (forall (B_31:((hoare_1167836817_state->Prop)->Prop)) (A_37:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_37)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_37) bot_bo691907561te_o_o))->((finite1380128977tate_o B_31)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_31) bot_bo691907561te_o_o))->((((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_37) B_31)) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((semila866907787te_o_o A_37) B_31))) ((semila1172322802tate_o (big_la1138507389tate_o A_37)) (big_la1138507389tate_o B_31)))))))))
% FOF formula (forall (B_31:((hoare_1775062406iple_a->Prop)->Prop)) (A_37:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_37)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_37) bot_bo1976773294_a_o_o))->((finite789576932le_a_o B_31)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) B_31) bot_bo1976773294_a_o_o))->((((eq ((hoare_1775062406iple_a->Prop)->Prop)) ((semila1691990438_a_o_o A_37) B_31)) bot_bo1976773294_a_o_o)->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((semila2069193356_a_o_o A_37) B_31))) ((semila13410563le_a_o (big_la1843772984le_a_o A_37)) (big_la1843772984le_a_o B_31))))))))) of role axiom named fact_516_Sup__fin_Ounion__disjoint
% A new axiom: (forall (B_31:((hoare_1775062406iple_a->Prop)->Prop)) (A_37:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_37)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_37) bot_bo1976773294_a_o_o))->((finite789576932le_a_o B_31)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) B_31) bot_bo1976773294_a_o_o))->((((eq ((hoare_1775062406iple_a->Prop)->Prop)) ((semila1691990438_a_o_o A_37) B_31)) bot_bo1976773294_a_o_o)->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((semila2069193356_a_o_o A_37) B_31))) ((semila13410563le_a_o (big_la1843772984le_a_o A_37)) (big_la1843772984le_a_o B_31)))))))))
% FOF formula (forall (B_30:(hoare_1775062406iple_a->Prop)) (C_18:hoare_1775062406iple_a) (A_36:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_18) A_36)->(((member2122167641iple_a C_18) B_30)->((member2122167641iple_a C_18) ((semila966743401le_a_o A_36) B_30))))) of role axiom named fact_517_IntI
% A new axiom: (forall (B_30:(hoare_1775062406iple_a->Prop)) (C_18:hoare_1775062406iple_a) (A_36:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_18) A_36)->(((member2122167641iple_a C_18) B_30)->((member2122167641iple_a C_18) ((semila966743401le_a_o A_36) B_30)))))
% FOF formula (forall (B_30:(pname->Prop)) (C_18:pname) (A_36:(pname->Prop)), (((member_pname C_18) A_36)->(((member_pname C_18) B_30)->((member_pname C_18) ((semila1673364395name_o A_36) B_30))))) of role axiom named fact_518_IntI
% A new axiom: (forall (B_30:(pname->Prop)) (C_18:pname) (A_36:(pname->Prop)), (((member_pname C_18) A_36)->(((member_pname C_18) B_30)->((member_pname C_18) ((semila1673364395name_o A_36) B_30)))))
% FOF formula (forall (C_17:hoare_1775062406iple_a) (A_35:(hoare_1775062406iple_a->Prop)) (B_29:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_17) ((semila966743401le_a_o A_35) B_29))->((((member2122167641iple_a C_17) A_35)->(((member2122167641iple_a C_17) B_29)->False))->False))) of role axiom named fact_519_IntE
% A new axiom: (forall (C_17:hoare_1775062406iple_a) (A_35:(hoare_1775062406iple_a->Prop)) (B_29:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_17) ((semila966743401le_a_o A_35) B_29))->((((member2122167641iple_a C_17) A_35)->(((member2122167641iple_a C_17) B_29)->False))->False)))
% FOF formula (forall (C_17:pname) (A_35:(pname->Prop)) (B_29:(pname->Prop)), (((member_pname C_17) ((semila1673364395name_o A_35) B_29))->((((member_pname C_17) A_35)->(((member_pname C_17) B_29)->False))->False))) of role axiom named fact_520_IntE
% A new axiom: (forall (C_17:pname) (A_35:(pname->Prop)) (B_29:(pname->Prop)), (((member_pname C_17) ((semila1673364395name_o A_35) B_29))->((((member_pname C_17) A_35)->(((member_pname C_17) B_29)->False))->False)))
% FOF formula (forall (X_12:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_12) bot_bot_pname_o)) bot_bot_pname_o)) of role axiom named fact_521_inf__bot__right
% A new axiom: (forall (X_12:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_12) bot_bot_pname_o)) bot_bot_pname_o))
% FOF formula (forall (X_12:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_12) bot_bo751897185le_a_o)) bot_bo751897185le_a_o)) of role axiom named fact_522_inf__bot__right
% A new axiom: (forall (X_12:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_12) bot_bo751897185le_a_o)) bot_bo751897185le_a_o))
% FOF formula (forall (X_12:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_12) bot_bo70021908tate_o)) bot_bo70021908tate_o)) of role axiom named fact_523_inf__bot__right
% A new axiom: (forall (X_12:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_12) bot_bo70021908tate_o)) bot_bo70021908tate_o))
% FOF formula (forall (X_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) X_11)) bot_bot_pname_o)) of role axiom named fact_524_inf__bot__left
% A new axiom: (forall (X_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) X_11)) bot_bot_pname_o))
% FOF formula (forall (X_11:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o bot_bo751897185le_a_o) X_11)) bot_bo751897185le_a_o)) of role axiom named fact_525_inf__bot__left
% A new axiom: (forall (X_11:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o bot_bo751897185le_a_o) X_11)) bot_bo751897185le_a_o))
% FOF formula (forall (X_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) X_11)) bot_bo70021908tate_o)) of role axiom named fact_526_inf__bot__left
% A new axiom: (forall (X_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) X_11)) bot_bo70021908tate_o))
% FOF formula (forall (Y_9:Prop) (Z_7:Prop) (X_10:Prop), ((iff ((semila10642723_sup_o ((semila854092349_inf_o Y_9) Z_7)) X_10)) ((semila854092349_inf_o ((semila10642723_sup_o Y_9) X_10)) ((semila10642723_sup_o Z_7) X_10)))) of role axiom named fact_527_sup__inf__distrib2
% A new axiom: (forall (Y_9:Prop) (Z_7:Prop) (X_10:Prop), ((iff ((semila10642723_sup_o ((semila854092349_inf_o Y_9) Z_7)) X_10)) ((semila854092349_inf_o ((semila10642723_sup_o Y_9) X_10)) ((semila10642723_sup_o Z_7) X_10))))
% FOF formula (forall (Y_9:(pname->Prop)) (Z_7:(pname->Prop)) (X_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o Y_9) Z_7)) X_10)) ((semila1673364395name_o ((semila1780557381name_o Y_9) X_10)) ((semila1780557381name_o Z_7) X_10)))) of role axiom named fact_528_sup__inf__distrib2
% A new axiom: (forall (Y_9:(pname->Prop)) (Z_7:(pname->Prop)) (X_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o Y_9) Z_7)) X_10)) ((semila1673364395name_o ((semila1780557381name_o Y_9) X_10)) ((semila1780557381name_o Z_7) X_10))))
% FOF formula (forall (Y_9:(hoare_1167836817_state->Prop)) (Z_7:(hoare_1167836817_state->Prop)) (X_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o Y_9) Z_7)) X_10)) ((semila179895820tate_o ((semila1172322802tate_o Y_9) X_10)) ((semila1172322802tate_o Z_7) X_10)))) of role axiom named fact_529_sup__inf__distrib2
% A new axiom: (forall (Y_9:(hoare_1167836817_state->Prop)) (Z_7:(hoare_1167836817_state->Prop)) (X_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o Y_9) Z_7)) X_10)) ((semila179895820tate_o ((semila1172322802tate_o Y_9) X_10)) ((semila1172322802tate_o Z_7) X_10))))
% FOF formula (forall (Y_9:(hoare_1775062406iple_a->Prop)) (Z_7:(hoare_1775062406iple_a->Prop)) (X_10:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila966743401le_a_o Y_9) Z_7)) X_10)) ((semila966743401le_a_o ((semila13410563le_a_o Y_9) X_10)) ((semila13410563le_a_o Z_7) X_10)))) of role axiom named fact_530_sup__inf__distrib2
% A new axiom: (forall (Y_9:(hoare_1775062406iple_a->Prop)) (Z_7:(hoare_1775062406iple_a->Prop)) (X_10:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila966743401le_a_o Y_9) Z_7)) X_10)) ((semila966743401le_a_o ((semila13410563le_a_o Y_9) X_10)) ((semila13410563le_a_o Z_7) X_10))))
% FOF formula (forall (Y_8:Prop) (Z_6:Prop) (X_9:Prop), ((iff ((semila854092349_inf_o ((semila10642723_sup_o Y_8) Z_6)) X_9)) ((semila10642723_sup_o ((semila854092349_inf_o Y_8) X_9)) ((semila854092349_inf_o Z_6) X_9)))) of role axiom named fact_531_inf__sup__distrib2
% A new axiom: (forall (Y_8:Prop) (Z_6:Prop) (X_9:Prop), ((iff ((semila854092349_inf_o ((semila10642723_sup_o Y_8) Z_6)) X_9)) ((semila10642723_sup_o ((semila854092349_inf_o Y_8) X_9)) ((semila854092349_inf_o Z_6) X_9))))
% FOF formula (forall (Y_8:(pname->Prop)) (Z_6:(pname->Prop)) (X_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o Y_8) Z_6)) X_9)) ((semila1780557381name_o ((semila1673364395name_o Y_8) X_9)) ((semila1673364395name_o Z_6) X_9)))) of role axiom named fact_532_inf__sup__distrib2
% A new axiom: (forall (Y_8:(pname->Prop)) (Z_6:(pname->Prop)) (X_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o Y_8) Z_6)) X_9)) ((semila1780557381name_o ((semila1673364395name_o Y_8) X_9)) ((semila1673364395name_o Z_6) X_9))))
% FOF formula (forall (Y_8:(hoare_1167836817_state->Prop)) (Z_6:(hoare_1167836817_state->Prop)) (X_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o Y_8) Z_6)) X_9)) ((semila1172322802tate_o ((semila179895820tate_o Y_8) X_9)) ((semila179895820tate_o Z_6) X_9)))) of role axiom named fact_533_inf__sup__distrib2
% A new axiom: (forall (Y_8:(hoare_1167836817_state->Prop)) (Z_6:(hoare_1167836817_state->Prop)) (X_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o Y_8) Z_6)) X_9)) ((semila1172322802tate_o ((semila179895820tate_o Y_8) X_9)) ((semila179895820tate_o Z_6) X_9))))
% FOF formula (forall (Y_8:(hoare_1775062406iple_a->Prop)) (Z_6:(hoare_1775062406iple_a->Prop)) (X_9:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((semila13410563le_a_o Y_8) Z_6)) X_9)) ((semila13410563le_a_o ((semila966743401le_a_o Y_8) X_9)) ((semila966743401le_a_o Z_6) X_9)))) of role axiom named fact_534_inf__sup__distrib2
% A new axiom: (forall (Y_8:(hoare_1775062406iple_a->Prop)) (Z_6:(hoare_1775062406iple_a->Prop)) (X_9:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((semila13410563le_a_o Y_8) Z_6)) X_9)) ((semila13410563le_a_o ((semila966743401le_a_o Y_8) X_9)) ((semila966743401le_a_o Z_6) X_9))))
% FOF formula (forall (X_8:Prop) (Y_7:Prop) (Z_5:Prop), ((iff ((semila10642723_sup_o X_8) ((semila854092349_inf_o Y_7) Z_5))) ((semila854092349_inf_o ((semila10642723_sup_o X_8) Y_7)) ((semila10642723_sup_o X_8) Z_5)))) of role axiom named fact_535_sup__inf__distrib1
% A new axiom: (forall (X_8:Prop) (Y_7:Prop) (Z_5:Prop), ((iff ((semila10642723_sup_o X_8) ((semila854092349_inf_o Y_7) Z_5))) ((semila854092349_inf_o ((semila10642723_sup_o X_8) Y_7)) ((semila10642723_sup_o X_8) Z_5))))
% FOF formula (forall (X_8:(pname->Prop)) (Y_7:(pname->Prop)) (Z_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_8) ((semila1673364395name_o Y_7) Z_5))) ((semila1673364395name_o ((semila1780557381name_o X_8) Y_7)) ((semila1780557381name_o X_8) Z_5)))) of role axiom named fact_536_sup__inf__distrib1
% A new axiom: (forall (X_8:(pname->Prop)) (Y_7:(pname->Prop)) (Z_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_8) ((semila1673364395name_o Y_7) Z_5))) ((semila1673364395name_o ((semila1780557381name_o X_8) Y_7)) ((semila1780557381name_o X_8) Z_5))))
% FOF formula (forall (X_8:(hoare_1167836817_state->Prop)) (Y_7:(hoare_1167836817_state->Prop)) (Z_5:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_8) ((semila179895820tate_o Y_7) Z_5))) ((semila179895820tate_o ((semila1172322802tate_o X_8) Y_7)) ((semila1172322802tate_o X_8) Z_5)))) of role axiom named fact_537_sup__inf__distrib1
% A new axiom: (forall (X_8:(hoare_1167836817_state->Prop)) (Y_7:(hoare_1167836817_state->Prop)) (Z_5:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_8) ((semila179895820tate_o Y_7) Z_5))) ((semila179895820tate_o ((semila1172322802tate_o X_8) Y_7)) ((semila1172322802tate_o X_8) Z_5))))
% FOF formula (forall (X_8:(hoare_1775062406iple_a->Prop)) (Y_7:(hoare_1775062406iple_a->Prop)) (Z_5:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_8) ((semila966743401le_a_o Y_7) Z_5))) ((semila966743401le_a_o ((semila13410563le_a_o X_8) Y_7)) ((semila13410563le_a_o X_8) Z_5)))) of role axiom named fact_538_sup__inf__distrib1
% A new axiom: (forall (X_8:(hoare_1775062406iple_a->Prop)) (Y_7:(hoare_1775062406iple_a->Prop)) (Z_5:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_8) ((semila966743401le_a_o Y_7) Z_5))) ((semila966743401le_a_o ((semila13410563le_a_o X_8) Y_7)) ((semila13410563le_a_o X_8) Z_5))))
% FOF formula (forall (X_7:Prop) (Y_6:Prop) (Z_4:Prop), ((iff ((semila854092349_inf_o X_7) ((semila10642723_sup_o Y_6) Z_4))) ((semila10642723_sup_o ((semila854092349_inf_o X_7) Y_6)) ((semila854092349_inf_o X_7) Z_4)))) of role axiom named fact_539_inf__sup__distrib1
% A new axiom: (forall (X_7:Prop) (Y_6:Prop) (Z_4:Prop), ((iff ((semila854092349_inf_o X_7) ((semila10642723_sup_o Y_6) Z_4))) ((semila10642723_sup_o ((semila854092349_inf_o X_7) Y_6)) ((semila854092349_inf_o X_7) Z_4))))
% FOF formula (forall (X_7:(pname->Prop)) (Y_6:(pname->Prop)) (Z_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_7) ((semila1780557381name_o Y_6) Z_4))) ((semila1780557381name_o ((semila1673364395name_o X_7) Y_6)) ((semila1673364395name_o X_7) Z_4)))) of role axiom named fact_540_inf__sup__distrib1
% A new axiom: (forall (X_7:(pname->Prop)) (Y_6:(pname->Prop)) (Z_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_7) ((semila1780557381name_o Y_6) Z_4))) ((semila1780557381name_o ((semila1673364395name_o X_7) Y_6)) ((semila1673364395name_o X_7) Z_4))))
% FOF formula (forall (X_7:(hoare_1167836817_state->Prop)) (Y_6:(hoare_1167836817_state->Prop)) (Z_4:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_7) ((semila1172322802tate_o Y_6) Z_4))) ((semila1172322802tate_o ((semila179895820tate_o X_7) Y_6)) ((semila179895820tate_o X_7) Z_4)))) of role axiom named fact_541_inf__sup__distrib1
% A new axiom: (forall (X_7:(hoare_1167836817_state->Prop)) (Y_6:(hoare_1167836817_state->Prop)) (Z_4:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_7) ((semila1172322802tate_o Y_6) Z_4))) ((semila1172322802tate_o ((semila179895820tate_o X_7) Y_6)) ((semila179895820tate_o X_7) Z_4))))
% FOF formula (forall (X_7:(hoare_1775062406iple_a->Prop)) (Y_6:(hoare_1775062406iple_a->Prop)) (Z_4:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_7) ((semila13410563le_a_o Y_6) Z_4))) ((semila13410563le_a_o ((semila966743401le_a_o X_7) Y_6)) ((semila966743401le_a_o X_7) Z_4)))) of role axiom named fact_542_inf__sup__distrib1
% A new axiom: (forall (X_7:(hoare_1775062406iple_a->Prop)) (Y_6:(hoare_1775062406iple_a->Prop)) (Z_4:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_7) ((semila13410563le_a_o Y_6) Z_4))) ((semila13410563le_a_o ((semila966743401le_a_o X_7) Y_6)) ((semila966743401le_a_o X_7) Z_4))))
% FOF formula (forall (X_6:Prop) (Y_5:Prop), ((iff ((semila10642723_sup_o X_6) ((semila854092349_inf_o X_6) Y_5))) X_6)) of role axiom named fact_543_sup__inf__absorb
% A new axiom: (forall (X_6:Prop) (Y_5:Prop), ((iff ((semila10642723_sup_o X_6) ((semila854092349_inf_o X_6) Y_5))) X_6))
% FOF formula (forall (X_6:(pname->Prop)) (Y_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_6) ((semila1673364395name_o X_6) Y_5))) X_6)) of role axiom named fact_544_sup__inf__absorb
% A new axiom: (forall (X_6:(pname->Prop)) (Y_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_6) ((semila1673364395name_o X_6) Y_5))) X_6))
% FOF formula (forall (X_6:(hoare_1167836817_state->Prop)) (Y_5:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_6) ((semila179895820tate_o X_6) Y_5))) X_6)) of role axiom named fact_545_sup__inf__absorb
% A new axiom: (forall (X_6:(hoare_1167836817_state->Prop)) (Y_5:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_6) ((semila179895820tate_o X_6) Y_5))) X_6))
% FOF formula (forall (X_6:(hoare_1775062406iple_a->Prop)) (Y_5:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_6) ((semila966743401le_a_o X_6) Y_5))) X_6)) of role axiom named fact_546_sup__inf__absorb
% A new axiom: (forall (X_6:(hoare_1775062406iple_a->Prop)) (Y_5:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_6) ((semila966743401le_a_o X_6) Y_5))) X_6))
% FOF formula (forall (X_5:Prop) (Y_4:Prop), ((iff ((semila854092349_inf_o X_5) ((semila10642723_sup_o X_5) Y_4))) X_5)) of role axiom named fact_547_inf__sup__absorb
% A new axiom: (forall (X_5:Prop) (Y_4:Prop), ((iff ((semila854092349_inf_o X_5) ((semila10642723_sup_o X_5) Y_4))) X_5))
% FOF formula (forall (X_5:(pname->Prop)) (Y_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_5) ((semila1780557381name_o X_5) Y_4))) X_5)) of role axiom named fact_548_inf__sup__absorb
% A new axiom: (forall (X_5:(pname->Prop)) (Y_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_5) ((semila1780557381name_o X_5) Y_4))) X_5))
% FOF formula (forall (X_5:(hoare_1167836817_state->Prop)) (Y_4:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_5) ((semila1172322802tate_o X_5) Y_4))) X_5)) of role axiom named fact_549_inf__sup__absorb
% A new axiom: (forall (X_5:(hoare_1167836817_state->Prop)) (Y_4:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_5) ((semila1172322802tate_o X_5) Y_4))) X_5))
% FOF formula (forall (X_5:(hoare_1775062406iple_a->Prop)) (Y_4:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_5) ((semila13410563le_a_o X_5) Y_4))) X_5)) of role axiom named fact_550_inf__sup__absorb
% A new axiom: (forall (X_5:(hoare_1775062406iple_a->Prop)) (Y_4:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_5) ((semila13410563le_a_o X_5) Y_4))) X_5))
% FOF formula (forall (A_34:(pname->Prop)) (B_28:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1673364395name_o A_34) B_28)) bot_bot_pname_o)) (forall (X:pname), (((member_pname X) A_34)->(forall (Xa:pname), (((member_pname Xa) B_28)->(not (((eq pname) X) Xa)))))))) of role axiom named fact_551_disjoint__iff__not__equal
% A new axiom: (forall (A_34:(pname->Prop)) (B_28:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1673364395name_o A_34) B_28)) bot_bot_pname_o)) (forall (X:pname), (((member_pname X) A_34)->(forall (Xa:pname), (((member_pname Xa) B_28)->(not (((eq pname) X) Xa))))))))
% FOF formula (forall (A_34:(hoare_1775062406iple_a->Prop)) (B_28:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_34) B_28)) bot_bo751897185le_a_o)) (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) A_34)->(forall (Xa:hoare_1775062406iple_a), (((member2122167641iple_a Xa) B_28)->(not (((eq hoare_1775062406iple_a) X) Xa)))))))) of role axiom named fact_552_disjoint__iff__not__equal
% A new axiom: (forall (A_34:(hoare_1775062406iple_a->Prop)) (B_28:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_34) B_28)) bot_bo751897185le_a_o)) (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) A_34)->(forall (Xa:hoare_1775062406iple_a), (((member2122167641iple_a Xa) B_28)->(not (((eq hoare_1775062406iple_a) X) Xa))))))))
% FOF formula (forall (A_34:(hoare_1167836817_state->Prop)) (B_28:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_34) B_28)) bot_bo70021908tate_o)) (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_34)->(forall (Xa:hoare_1167836817_state), (((member2058392318_state Xa) B_28)->(not (((eq hoare_1167836817_state) X) Xa)))))))) of role axiom named fact_553_disjoint__iff__not__equal
% A new axiom: (forall (A_34:(hoare_1167836817_state->Prop)) (B_28:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_34) B_28)) bot_bo70021908tate_o)) (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_34)->(forall (Xa:hoare_1167836817_state), (((member2058392318_state Xa) B_28)->(not (((eq hoare_1167836817_state) X) Xa))))))))
% FOF formula (forall (A_33:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_33) bot_bot_pname_o)) bot_bot_pname_o)) of role axiom named fact_554_Int__empty__right
% A new axiom: (forall (A_33:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_33) bot_bot_pname_o)) bot_bot_pname_o))
% FOF formula (forall (A_33:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_33) bot_bo751897185le_a_o)) bot_bo751897185le_a_o)) of role axiom named fact_555_Int__empty__right
% A new axiom: (forall (A_33:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_33) bot_bo751897185le_a_o)) bot_bo751897185le_a_o))
% FOF formula (forall (A_33:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_33) bot_bo70021908tate_o)) bot_bo70021908tate_o)) of role axiom named fact_556_Int__empty__right
% A new axiom: (forall (A_33:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_33) bot_bo70021908tate_o)) bot_bo70021908tate_o))
% FOF formula (forall (B_27:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) B_27)) bot_bot_pname_o)) of role axiom named fact_557_Int__empty__left
% A new axiom: (forall (B_27:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) B_27)) bot_bot_pname_o))
% FOF formula (forall (B_27:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o bot_bo751897185le_a_o) B_27)) bot_bo751897185le_a_o)) of role axiom named fact_558_Int__empty__left
% A new axiom: (forall (B_27:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o bot_bo751897185le_a_o) B_27)) bot_bo751897185le_a_o))
% FOF formula (forall (B_27:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) B_27)) bot_bo70021908tate_o)) of role axiom named fact_559_Int__empty__left
% A new axiom: (forall (B_27:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) B_27)) bot_bo70021908tate_o))
% FOF formula (forall (A_32:(hoare_1775062406iple_a->Prop)) (B_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_32) B_26)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) A_32)) ((member2122167641iple_a X) B_26)))))) of role axiom named fact_560_Int__def
% A new axiom: (forall (A_32:(hoare_1775062406iple_a->Prop)) (B_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_32) B_26)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) A_32)) ((member2122167641iple_a X) B_26))))))
% FOF formula (forall (A_32:(pname->Prop)) (B_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_32) B_26)) (collect_pname (fun (X:pname)=> ((and ((member_pname X) A_32)) ((member_pname X) B_26)))))) of role axiom named fact_561_Int__def
% A new axiom: (forall (A_32:(pname->Prop)) (B_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_32) B_26)) (collect_pname (fun (X:pname)=> ((and ((member_pname X) A_32)) ((member_pname X) B_26))))))
% FOF formula (forall (C_16:hoare_1775062406iple_a) (A_31:(hoare_1775062406iple_a->Prop)) (B_25:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a C_16) ((semila966743401le_a_o A_31) B_25))) ((and ((member2122167641iple_a C_16) A_31)) ((member2122167641iple_a C_16) B_25)))) of role axiom named fact_562_Int__iff
% A new axiom: (forall (C_16:hoare_1775062406iple_a) (A_31:(hoare_1775062406iple_a->Prop)) (B_25:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a C_16) ((semila966743401le_a_o A_31) B_25))) ((and ((member2122167641iple_a C_16) A_31)) ((member2122167641iple_a C_16) B_25))))
% FOF formula (forall (C_16:pname) (A_31:(pname->Prop)) (B_25:(pname->Prop)), ((iff ((member_pname C_16) ((semila1673364395name_o A_31) B_25))) ((and ((member_pname C_16) A_31)) ((member_pname C_16) B_25)))) of role axiom named fact_563_Int__iff
% A new axiom: (forall (C_16:pname) (A_31:(pname->Prop)) (B_25:(pname->Prop)), ((iff ((member_pname C_16) ((semila1673364395name_o A_31) B_25))) ((and ((member_pname C_16) A_31)) ((member_pname C_16) B_25))))
% FOF formula (forall (C_15:hoare_1775062406iple_a) (A_30:(hoare_1775062406iple_a->Prop)) (B_24:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_15) ((semila966743401le_a_o A_30) B_24))->((member2122167641iple_a C_15) A_30))) of role axiom named fact_564_IntD1
% A new axiom: (forall (C_15:hoare_1775062406iple_a) (A_30:(hoare_1775062406iple_a->Prop)) (B_24:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_15) ((semila966743401le_a_o A_30) B_24))->((member2122167641iple_a C_15) A_30)))
% FOF formula (forall (C_15:pname) (A_30:(pname->Prop)) (B_24:(pname->Prop)), (((member_pname C_15) ((semila1673364395name_o A_30) B_24))->((member_pname C_15) A_30))) of role axiom named fact_565_IntD1
% A new axiom: (forall (C_15:pname) (A_30:(pname->Prop)) (B_24:(pname->Prop)), (((member_pname C_15) ((semila1673364395name_o A_30) B_24))->((member_pname C_15) A_30)))
% FOF formula (forall (C_14:hoare_1775062406iple_a) (A_29:(hoare_1775062406iple_a->Prop)) (B_23:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_14) ((semila966743401le_a_o A_29) B_23))->((member2122167641iple_a C_14) B_23))) of role axiom named fact_566_IntD2
% A new axiom: (forall (C_14:hoare_1775062406iple_a) (A_29:(hoare_1775062406iple_a->Prop)) (B_23:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_14) ((semila966743401le_a_o A_29) B_23))->((member2122167641iple_a C_14) B_23)))
% FOF formula (forall (C_14:pname) (A_29:(pname->Prop)) (B_23:(pname->Prop)), (((member_pname C_14) ((semila1673364395name_o A_29) B_23))->((member_pname C_14) B_23))) of role axiom named fact_567_IntD2
% A new axiom: (forall (C_14:pname) (A_29:(pname->Prop)) (B_23:(pname->Prop)), (((member_pname C_14) ((semila1673364395name_o A_29) B_23))->((member_pname C_14) B_23)))
% FOF formula (forall (P_3:(hoare_1775062406iple_a->Prop)) (Q:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (P_3 X)) (Q X))))) ((semila966743401le_a_o (collec676402587iple_a P_3)) (collec676402587iple_a Q)))) of role axiom named fact_568_Collect__conj__eq
% A new axiom: (forall (P_3:(hoare_1775062406iple_a->Prop)) (Q:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (P_3 X)) (Q X))))) ((semila966743401le_a_o (collec676402587iple_a P_3)) (collec676402587iple_a Q))))
% FOF formula (forall (P_3:(pname->Prop)) (Q:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (P_3 X)) (Q X))))) ((semila1673364395name_o (collect_pname P_3)) (collect_pname Q)))) of role axiom named fact_569_Collect__conj__eq
% A new axiom: (forall (P_3:(pname->Prop)) (Q:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (P_3 X)) (Q X))))) ((semila1673364395name_o (collect_pname P_3)) (collect_pname Q))))
% FOF formula (forall (X_4:hoare_1775062406iple_a) (A_28:(hoare_1775062406iple_a->Prop)) (P_2:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a X_4) ((semila966743401le_a_o A_28) (collec676402587iple_a P_2)))) ((and ((member2122167641iple_a X_4) A_28)) (P_2 X_4)))) of role axiom named fact_570_Int__Collect
% A new axiom: (forall (X_4:hoare_1775062406iple_a) (A_28:(hoare_1775062406iple_a->Prop)) (P_2:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a X_4) ((semila966743401le_a_o A_28) (collec676402587iple_a P_2)))) ((and ((member2122167641iple_a X_4) A_28)) (P_2 X_4))))
% FOF formula (forall (X_4:pname) (A_28:(pname->Prop)) (P_2:(pname->Prop)), ((iff ((member_pname X_4) ((semila1673364395name_o A_28) (collect_pname P_2)))) ((and ((member_pname X_4) A_28)) (P_2 X_4)))) of role axiom named fact_571_Int__Collect
% A new axiom: (forall (X_4:pname) (A_28:(pname->Prop)) (P_2:(pname->Prop)), ((iff ((member_pname X_4) ((semila1673364395name_o A_28) (collect_pname P_2)))) ((and ((member_pname X_4) A_28)) (P_2 X_4))))
% FOF formula (forall (R:(hoare_1775062406iple_a->Prop)) (S_2:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), ((iff (((semila966743401le_a_o (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) R))) (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) S_2))) X)) ((member2122167641iple_a X) ((semila966743401le_a_o R) S_2)))) of role axiom named fact_572_inf__Int__eq
% A new axiom: (forall (R:(hoare_1775062406iple_a->Prop)) (S_2:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), ((iff (((semila966743401le_a_o (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) R))) (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) S_2))) X)) ((member2122167641iple_a X) ((semila966743401le_a_o R) S_2))))
% FOF formula (forall (R:(pname->Prop)) (S_2:(pname->Prop)) (X:pname), ((iff (((semila1673364395name_o (fun (Y_2:pname)=> ((member_pname Y_2) R))) (fun (Y_2:pname)=> ((member_pname Y_2) S_2))) X)) ((member_pname X) ((semila1673364395name_o R) S_2)))) of role axiom named fact_573_inf__Int__eq
% A new axiom: (forall (R:(pname->Prop)) (S_2:(pname->Prop)) (X:pname), ((iff (((semila1673364395name_o (fun (Y_2:pname)=> ((member_pname Y_2) R))) (fun (Y_2:pname)=> ((member_pname Y_2) S_2))) X)) ((member_pname X) ((semila1673364395name_o R) S_2))))
% FOF formula (forall (A_27:(pname->Prop)) (B_22:(pname->Prop)) (C_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o ((semila1673364395name_o A_27) B_22)) ((semila1673364395name_o B_22) C_13))) ((semila1673364395name_o C_13) A_27))) ((semila1673364395name_o ((semila1673364395name_o ((semila1780557381name_o A_27) B_22)) ((semila1780557381name_o B_22) C_13))) ((semila1780557381name_o C_13) A_27)))) of role axiom named fact_574_Un__Int__crazy
% A new axiom: (forall (A_27:(pname->Prop)) (B_22:(pname->Prop)) (C_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o ((semila1673364395name_o A_27) B_22)) ((semila1673364395name_o B_22) C_13))) ((semila1673364395name_o C_13) A_27))) ((semila1673364395name_o ((semila1673364395name_o ((semila1780557381name_o A_27) B_22)) ((semila1780557381name_o B_22) C_13))) ((semila1780557381name_o C_13) A_27))))
% FOF formula (forall (A_27:(hoare_1167836817_state->Prop)) (B_22:(hoare_1167836817_state->Prop)) (C_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o ((semila179895820tate_o A_27) B_22)) ((semila179895820tate_o B_22) C_13))) ((semila179895820tate_o C_13) A_27))) ((semila179895820tate_o ((semila179895820tate_o ((semila1172322802tate_o A_27) B_22)) ((semila1172322802tate_o B_22) C_13))) ((semila1172322802tate_o C_13) A_27)))) of role axiom named fact_575_Un__Int__crazy
% A new axiom: (forall (A_27:(hoare_1167836817_state->Prop)) (B_22:(hoare_1167836817_state->Prop)) (C_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o ((semila179895820tate_o A_27) B_22)) ((semila179895820tate_o B_22) C_13))) ((semila179895820tate_o C_13) A_27))) ((semila179895820tate_o ((semila179895820tate_o ((semila1172322802tate_o A_27) B_22)) ((semila1172322802tate_o B_22) C_13))) ((semila1172322802tate_o C_13) A_27))))
% FOF formula (forall (A_27:(hoare_1775062406iple_a->Prop)) (B_22:(hoare_1775062406iple_a->Prop)) (C_13:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o ((semila966743401le_a_o A_27) B_22)) ((semila966743401le_a_o B_22) C_13))) ((semila966743401le_a_o C_13) A_27))) ((semila966743401le_a_o ((semila966743401le_a_o ((semila13410563le_a_o A_27) B_22)) ((semila13410563le_a_o B_22) C_13))) ((semila13410563le_a_o C_13) A_27)))) of role axiom named fact_576_Un__Int__crazy
% A new axiom: (forall (A_27:(hoare_1775062406iple_a->Prop)) (B_22:(hoare_1775062406iple_a->Prop)) (C_13:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o ((semila966743401le_a_o A_27) B_22)) ((semila966743401le_a_o B_22) C_13))) ((semila966743401le_a_o C_13) A_27))) ((semila966743401le_a_o ((semila966743401le_a_o ((semila13410563le_a_o A_27) B_22)) ((semila13410563le_a_o B_22) C_13))) ((semila13410563le_a_o C_13) A_27))))
% FOF formula (forall (B_21:(pname->Prop)) (C_12:(pname->Prop)) (A_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o B_21) C_12)) A_26)) ((semila1673364395name_o ((semila1780557381name_o B_21) A_26)) ((semila1780557381name_o C_12) A_26)))) of role axiom named fact_577_Un__Int__distrib2
% A new axiom: (forall (B_21:(pname->Prop)) (C_12:(pname->Prop)) (A_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o B_21) C_12)) A_26)) ((semila1673364395name_o ((semila1780557381name_o B_21) A_26)) ((semila1780557381name_o C_12) A_26))))
% FOF formula (forall (B_21:(hoare_1167836817_state->Prop)) (C_12:(hoare_1167836817_state->Prop)) (A_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o B_21) C_12)) A_26)) ((semila179895820tate_o ((semila1172322802tate_o B_21) A_26)) ((semila1172322802tate_o C_12) A_26)))) of role axiom named fact_578_Un__Int__distrib2
% A new axiom: (forall (B_21:(hoare_1167836817_state->Prop)) (C_12:(hoare_1167836817_state->Prop)) (A_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o B_21) C_12)) A_26)) ((semila179895820tate_o ((semila1172322802tate_o B_21) A_26)) ((semila1172322802tate_o C_12) A_26))))
% FOF formula (forall (B_21:(hoare_1775062406iple_a->Prop)) (C_12:(hoare_1775062406iple_a->Prop)) (A_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila966743401le_a_o B_21) C_12)) A_26)) ((semila966743401le_a_o ((semila13410563le_a_o B_21) A_26)) ((semila13410563le_a_o C_12) A_26)))) of role axiom named fact_579_Un__Int__distrib2
% A new axiom: (forall (B_21:(hoare_1775062406iple_a->Prop)) (C_12:(hoare_1775062406iple_a->Prop)) (A_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila966743401le_a_o B_21) C_12)) A_26)) ((semila966743401le_a_o ((semila13410563le_a_o B_21) A_26)) ((semila13410563le_a_o C_12) A_26))))
% FOF formula (forall (B_20:(pname->Prop)) (C_11:(pname->Prop)) (A_25:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o B_20) C_11)) A_25)) ((semila1780557381name_o ((semila1673364395name_o B_20) A_25)) ((semila1673364395name_o C_11) A_25)))) of role axiom named fact_580_Int__Un__distrib2
% A new axiom: (forall (B_20:(pname->Prop)) (C_11:(pname->Prop)) (A_25:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o B_20) C_11)) A_25)) ((semila1780557381name_o ((semila1673364395name_o B_20) A_25)) ((semila1673364395name_o C_11) A_25))))
% FOF formula (forall (B_20:(hoare_1167836817_state->Prop)) (C_11:(hoare_1167836817_state->Prop)) (A_25:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o B_20) C_11)) A_25)) ((semila1172322802tate_o ((semila179895820tate_o B_20) A_25)) ((semila179895820tate_o C_11) A_25)))) of role axiom named fact_581_Int__Un__distrib2
% A new axiom: (forall (B_20:(hoare_1167836817_state->Prop)) (C_11:(hoare_1167836817_state->Prop)) (A_25:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o B_20) C_11)) A_25)) ((semila1172322802tate_o ((semila179895820tate_o B_20) A_25)) ((semila179895820tate_o C_11) A_25))))
% FOF formula (forall (B_20:(hoare_1775062406iple_a->Prop)) (C_11:(hoare_1775062406iple_a->Prop)) (A_25:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((semila13410563le_a_o B_20) C_11)) A_25)) ((semila13410563le_a_o ((semila966743401le_a_o B_20) A_25)) ((semila966743401le_a_o C_11) A_25)))) of role axiom named fact_582_Int__Un__distrib2
% A new axiom: (forall (B_20:(hoare_1775062406iple_a->Prop)) (C_11:(hoare_1775062406iple_a->Prop)) (A_25:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((semila13410563le_a_o B_20) C_11)) A_25)) ((semila13410563le_a_o ((semila966743401le_a_o B_20) A_25)) ((semila966743401le_a_o C_11) A_25))))
% FOF formula (forall (A_24:(pname->Prop)) (B_19:(pname->Prop)) (C_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_24) ((semila1673364395name_o B_19) C_10))) ((semila1673364395name_o ((semila1780557381name_o A_24) B_19)) ((semila1780557381name_o A_24) C_10)))) of role axiom named fact_583_Un__Int__distrib
% A new axiom: (forall (A_24:(pname->Prop)) (B_19:(pname->Prop)) (C_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_24) ((semila1673364395name_o B_19) C_10))) ((semila1673364395name_o ((semila1780557381name_o A_24) B_19)) ((semila1780557381name_o A_24) C_10))))
% FOF formula (forall (A_24:(hoare_1167836817_state->Prop)) (B_19:(hoare_1167836817_state->Prop)) (C_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_24) ((semila179895820tate_o B_19) C_10))) ((semila179895820tate_o ((semila1172322802tate_o A_24) B_19)) ((semila1172322802tate_o A_24) C_10)))) of role axiom named fact_584_Un__Int__distrib
% A new axiom: (forall (A_24:(hoare_1167836817_state->Prop)) (B_19:(hoare_1167836817_state->Prop)) (C_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_24) ((semila179895820tate_o B_19) C_10))) ((semila179895820tate_o ((semila1172322802tate_o A_24) B_19)) ((semila1172322802tate_o A_24) C_10))))
% FOF formula (forall (A_24:(hoare_1775062406iple_a->Prop)) (B_19:(hoare_1775062406iple_a->Prop)) (C_10:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_24) ((semila966743401le_a_o B_19) C_10))) ((semila966743401le_a_o ((semila13410563le_a_o A_24) B_19)) ((semila13410563le_a_o A_24) C_10)))) of role axiom named fact_585_Un__Int__distrib
% A new axiom: (forall (A_24:(hoare_1775062406iple_a->Prop)) (B_19:(hoare_1775062406iple_a->Prop)) (C_10:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_24) ((semila966743401le_a_o B_19) C_10))) ((semila966743401le_a_o ((semila13410563le_a_o A_24) B_19)) ((semila13410563le_a_o A_24) C_10))))
% FOF formula (forall (A_23:(pname->Prop)) (B_18:(pname->Prop)) (C_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_23) ((semila1780557381name_o B_18) C_9))) ((semila1780557381name_o ((semila1673364395name_o A_23) B_18)) ((semila1673364395name_o A_23) C_9)))) of role axiom named fact_586_Int__Un__distrib
% A new axiom: (forall (A_23:(pname->Prop)) (B_18:(pname->Prop)) (C_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_23) ((semila1780557381name_o B_18) C_9))) ((semila1780557381name_o ((semila1673364395name_o A_23) B_18)) ((semila1673364395name_o A_23) C_9))))
% FOF formula (forall (A_23:(hoare_1167836817_state->Prop)) (B_18:(hoare_1167836817_state->Prop)) (C_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_23) ((semila1172322802tate_o B_18) C_9))) ((semila1172322802tate_o ((semila179895820tate_o A_23) B_18)) ((semila179895820tate_o A_23) C_9)))) of role axiom named fact_587_Int__Un__distrib
% A new axiom: (forall (A_23:(hoare_1167836817_state->Prop)) (B_18:(hoare_1167836817_state->Prop)) (C_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_23) ((semila1172322802tate_o B_18) C_9))) ((semila1172322802tate_o ((semila179895820tate_o A_23) B_18)) ((semila179895820tate_o A_23) C_9))))
% FOF formula (forall (A_23:(hoare_1775062406iple_a->Prop)) (B_18:(hoare_1775062406iple_a->Prop)) (C_9:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_23) ((semila13410563le_a_o B_18) C_9))) ((semila13410563le_a_o ((semila966743401le_a_o A_23) B_18)) ((semila966743401le_a_o A_23) C_9)))) of role axiom named fact_588_Int__Un__distrib
% A new axiom: (forall (A_23:(hoare_1775062406iple_a->Prop)) (B_18:(hoare_1775062406iple_a->Prop)) (C_9:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_23) ((semila13410563le_a_o B_18) C_9))) ((semila13410563le_a_o ((semila966743401le_a_o A_23) B_18)) ((semila966743401le_a_o A_23) C_9))))
% FOF formula (forall (B_17:(hoare_1167836817_state->Prop)) (A_22:hoare_1167836817_state) (C_8:(hoare_1167836817_state->Prop)), (((member2058392318_state A_22) C_8)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_22) B_17)) C_8)) ((insert2134838167_state A_22) ((semila179895820tate_o B_17) C_8))))) of role axiom named fact_589_Int__insert__left__if1
% A new axiom: (forall (B_17:(hoare_1167836817_state->Prop)) (A_22:hoare_1167836817_state) (C_8:(hoare_1167836817_state->Prop)), (((member2058392318_state A_22) C_8)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_22) B_17)) C_8)) ((insert2134838167_state A_22) ((semila179895820tate_o B_17) C_8)))))
% FOF formula (forall (B_17:(hoare_1775062406iple_a->Prop)) (A_22:hoare_1775062406iple_a) (C_8:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_22) C_8)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_22) B_17)) C_8)) ((insert1281456128iple_a A_22) ((semila966743401le_a_o B_17) C_8))))) of role axiom named fact_590_Int__insert__left__if1
% A new axiom: (forall (B_17:(hoare_1775062406iple_a->Prop)) (A_22:hoare_1775062406iple_a) (C_8:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_22) C_8)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_22) B_17)) C_8)) ((insert1281456128iple_a A_22) ((semila966743401le_a_o B_17) C_8)))))
% FOF formula (forall (B_17:(pname->Prop)) (A_22:pname) (C_8:(pname->Prop)), (((member_pname A_22) C_8)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_22) B_17)) C_8)) ((insert_pname A_22) ((semila1673364395name_o B_17) C_8))))) of role axiom named fact_591_Int__insert__left__if1
% A new axiom: (forall (B_17:(pname->Prop)) (A_22:pname) (C_8:(pname->Prop)), (((member_pname A_22) C_8)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_22) B_17)) C_8)) ((insert_pname A_22) ((semila1673364395name_o B_17) C_8)))))
% FOF formula (forall (B_16:(hoare_1167836817_state->Prop)) (A_21:hoare_1167836817_state) (A_20:(hoare_1167836817_state->Prop)), (((member2058392318_state A_21) A_20)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_20) ((insert2134838167_state A_21) B_16))) ((insert2134838167_state A_21) ((semila179895820tate_o A_20) B_16))))) of role axiom named fact_592_Int__insert__right__if1
% A new axiom: (forall (B_16:(hoare_1167836817_state->Prop)) (A_21:hoare_1167836817_state) (A_20:(hoare_1167836817_state->Prop)), (((member2058392318_state A_21) A_20)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_20) ((insert2134838167_state A_21) B_16))) ((insert2134838167_state A_21) ((semila179895820tate_o A_20) B_16)))))
% FOF formula (forall (B_16:(hoare_1775062406iple_a->Prop)) (A_21:hoare_1775062406iple_a) (A_20:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_21) A_20)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_20) ((insert1281456128iple_a A_21) B_16))) ((insert1281456128iple_a A_21) ((semila966743401le_a_o A_20) B_16))))) of role axiom named fact_593_Int__insert__right__if1
% A new axiom: (forall (B_16:(hoare_1775062406iple_a->Prop)) (A_21:hoare_1775062406iple_a) (A_20:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_21) A_20)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_20) ((insert1281456128iple_a A_21) B_16))) ((insert1281456128iple_a A_21) ((semila966743401le_a_o A_20) B_16)))))
% FOF formula (forall (B_16:(pname->Prop)) (A_21:pname) (A_20:(pname->Prop)), (((member_pname A_21) A_20)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) ((insert_pname A_21) B_16))) ((insert_pname A_21) ((semila1673364395name_o A_20) B_16))))) of role axiom named fact_594_Int__insert__right__if1
% A new axiom: (forall (B_16:(pname->Prop)) (A_21:pname) (A_20:(pname->Prop)), (((member_pname A_21) A_20)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) ((insert_pname A_21) B_16))) ((insert_pname A_21) ((semila1673364395name_o A_20) B_16)))))
% FOF formula (forall (B_15:(hoare_1167836817_state->Prop)) (A_19:hoare_1167836817_state) (C_7:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_19) C_7)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_19) B_15)) C_7)) ((semila179895820tate_o B_15) C_7)))) of role axiom named fact_595_Int__insert__left__if0
% A new axiom: (forall (B_15:(hoare_1167836817_state->Prop)) (A_19:hoare_1167836817_state) (C_7:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_19) C_7)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_19) B_15)) C_7)) ((semila179895820tate_o B_15) C_7))))
% FOF formula (forall (B_15:(hoare_1775062406iple_a->Prop)) (A_19:hoare_1775062406iple_a) (C_7:(hoare_1775062406iple_a->Prop)), ((((member2122167641iple_a A_19) C_7)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_19) B_15)) C_7)) ((semila966743401le_a_o B_15) C_7)))) of role axiom named fact_596_Int__insert__left__if0
% A new axiom: (forall (B_15:(hoare_1775062406iple_a->Prop)) (A_19:hoare_1775062406iple_a) (C_7:(hoare_1775062406iple_a->Prop)), ((((member2122167641iple_a A_19) C_7)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_19) B_15)) C_7)) ((semila966743401le_a_o B_15) C_7))))
% FOF formula (forall (B_15:(pname->Prop)) (A_19:pname) (C_7:(pname->Prop)), ((((member_pname A_19) C_7)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_19) B_15)) C_7)) ((semila1673364395name_o B_15) C_7)))) of role axiom named fact_597_Int__insert__left__if0
% A new axiom: (forall (B_15:(pname->Prop)) (A_19:pname) (C_7:(pname->Prop)), ((((member_pname A_19) C_7)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_19) B_15)) C_7)) ((semila1673364395name_o B_15) C_7))))
% FOF formula (forall (B_14:(hoare_1167836817_state->Prop)) (A_18:hoare_1167836817_state) (A_17:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_18) A_17)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_17) ((insert2134838167_state A_18) B_14))) ((semila179895820tate_o A_17) B_14)))) of role axiom named fact_598_Int__insert__right__if0
% A new axiom: (forall (B_14:(hoare_1167836817_state->Prop)) (A_18:hoare_1167836817_state) (A_17:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_18) A_17)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_17) ((insert2134838167_state A_18) B_14))) ((semila179895820tate_o A_17) B_14))))
% FOF formula (forall (B_14:(hoare_1775062406iple_a->Prop)) (A_18:hoare_1775062406iple_a) (A_17:(hoare_1775062406iple_a->Prop)), ((((member2122167641iple_a A_18) A_17)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_17) ((insert1281456128iple_a A_18) B_14))) ((semila966743401le_a_o A_17) B_14)))) of role axiom named fact_599_Int__insert__right__if0
% A new axiom: (forall (B_14:(hoare_1775062406iple_a->Prop)) (A_18:hoare_1775062406iple_a) (A_17:(hoare_1775062406iple_a->Prop)), ((((member2122167641iple_a A_18) A_17)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_17) ((insert1281456128iple_a A_18) B_14))) ((semila966743401le_a_o A_17) B_14))))
% FOF formula (forall (B_14:(pname->Prop)) (A_18:pname) (A_17:(pname->Prop)), ((((member_pname A_18) A_17)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_17) ((insert_pname A_18) B_14))) ((semila1673364395name_o A_17) B_14)))) of role axiom named fact_600_Int__insert__right__if0
% A new axiom: (forall (B_14:(pname->Prop)) (A_18:pname) (A_17:(pname->Prop)), ((((member_pname A_18) A_17)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_17) ((insert_pname A_18) B_14))) ((semila1673364395name_o A_17) B_14))))
% FOF formula (forall (A_16:hoare_1167836817_state) (A_15:(hoare_1167836817_state->Prop)) (B_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_16) A_15)) ((insert2134838167_state A_16) B_13))) ((insert2134838167_state A_16) ((semila179895820tate_o A_15) B_13)))) of role axiom named fact_601_insert__inter__insert
% A new axiom: (forall (A_16:hoare_1167836817_state) (A_15:(hoare_1167836817_state->Prop)) (B_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_16) A_15)) ((insert2134838167_state A_16) B_13))) ((insert2134838167_state A_16) ((semila179895820tate_o A_15) B_13))))
% FOF formula (forall (A_16:hoare_1775062406iple_a) (A_15:(hoare_1775062406iple_a->Prop)) (B_13:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_16) A_15)) ((insert1281456128iple_a A_16) B_13))) ((insert1281456128iple_a A_16) ((semila966743401le_a_o A_15) B_13)))) of role axiom named fact_602_insert__inter__insert
% A new axiom: (forall (A_16:hoare_1775062406iple_a) (A_15:(hoare_1775062406iple_a->Prop)) (B_13:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_16) A_15)) ((insert1281456128iple_a A_16) B_13))) ((insert1281456128iple_a A_16) ((semila966743401le_a_o A_15) B_13))))
% FOF formula (forall (A_16:pname) (A_15:(pname->Prop)) (B_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_16) A_15)) ((insert_pname A_16) B_13))) ((insert_pname A_16) ((semila1673364395name_o A_15) B_13)))) of role axiom named fact_603_insert__inter__insert
% A new axiom: (forall (A_16:pname) (A_15:(pname->Prop)) (B_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_16) A_15)) ((insert_pname A_16) B_13))) ((insert_pname A_16) ((semila1673364395name_o A_15) B_13))))
% FOF formula (forall (B_12:(hoare_1167836817_state->Prop)) (A_14:hoare_1167836817_state) (C_6:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_14) C_6)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_14) B_12)) C_6)) ((insert2134838167_state A_14) ((semila179895820tate_o B_12) C_6))))) ((((member2058392318_state A_14) C_6)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_14) B_12)) C_6)) ((semila179895820tate_o B_12) C_6))))) of role axiom named fact_604_Int__insert__left
% A new axiom: (forall (B_12:(hoare_1167836817_state->Prop)) (A_14:hoare_1167836817_state) (C_6:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_14) C_6)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_14) B_12)) C_6)) ((insert2134838167_state A_14) ((semila179895820tate_o B_12) C_6))))) ((((member2058392318_state A_14) C_6)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_14) B_12)) C_6)) ((semila179895820tate_o B_12) C_6)))))
% FOF formula (forall (B_12:(hoare_1775062406iple_a->Prop)) (A_14:hoare_1775062406iple_a) (C_6:(hoare_1775062406iple_a->Prop)), ((and (((member2122167641iple_a A_14) C_6)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_14) B_12)) C_6)) ((insert1281456128iple_a A_14) ((semila966743401le_a_o B_12) C_6))))) ((((member2122167641iple_a A_14) C_6)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_14) B_12)) C_6)) ((semila966743401le_a_o B_12) C_6))))) of role axiom named fact_605_Int__insert__left
% A new axiom: (forall (B_12:(hoare_1775062406iple_a->Prop)) (A_14:hoare_1775062406iple_a) (C_6:(hoare_1775062406iple_a->Prop)), ((and (((member2122167641iple_a A_14) C_6)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_14) B_12)) C_6)) ((insert1281456128iple_a A_14) ((semila966743401le_a_o B_12) C_6))))) ((((member2122167641iple_a A_14) C_6)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_14) B_12)) C_6)) ((semila966743401le_a_o B_12) C_6)))))
% FOF formula (forall (B_12:(pname->Prop)) (A_14:pname) (C_6:(pname->Prop)), ((and (((member_pname A_14) C_6)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_14) B_12)) C_6)) ((insert_pname A_14) ((semila1673364395name_o B_12) C_6))))) ((((member_pname A_14) C_6)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_14) B_12)) C_6)) ((semila1673364395name_o B_12) C_6))))) of role axiom named fact_606_Int__insert__left
% A new axiom: (forall (B_12:(pname->Prop)) (A_14:pname) (C_6:(pname->Prop)), ((and (((member_pname A_14) C_6)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_14) B_12)) C_6)) ((insert_pname A_14) ((semila1673364395name_o B_12) C_6))))) ((((member_pname A_14) C_6)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_14) B_12)) C_6)) ((semila1673364395name_o B_12) C_6)))))
% FOF formula (forall (B_11:(hoare_1167836817_state->Prop)) (A_13:hoare_1167836817_state) (A_12:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_13) A_12)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_12) ((insert2134838167_state A_13) B_11))) ((insert2134838167_state A_13) ((semila179895820tate_o A_12) B_11))))) ((((member2058392318_state A_13) A_12)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_12) ((insert2134838167_state A_13) B_11))) ((semila179895820tate_o A_12) B_11))))) of role axiom named fact_607_Int__insert__right
% A new axiom: (forall (B_11:(hoare_1167836817_state->Prop)) (A_13:hoare_1167836817_state) (A_12:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_13) A_12)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_12) ((insert2134838167_state A_13) B_11))) ((insert2134838167_state A_13) ((semila179895820tate_o A_12) B_11))))) ((((member2058392318_state A_13) A_12)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_12) ((insert2134838167_state A_13) B_11))) ((semila179895820tate_o A_12) B_11)))))
% FOF formula (forall (B_11:(hoare_1775062406iple_a->Prop)) (A_13:hoare_1775062406iple_a) (A_12:(hoare_1775062406iple_a->Prop)), ((and (((member2122167641iple_a A_13) A_12)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_12) ((insert1281456128iple_a A_13) B_11))) ((insert1281456128iple_a A_13) ((semila966743401le_a_o A_12) B_11))))) ((((member2122167641iple_a A_13) A_12)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_12) ((insert1281456128iple_a A_13) B_11))) ((semila966743401le_a_o A_12) B_11))))) of role axiom named fact_608_Int__insert__right
% A new axiom: (forall (B_11:(hoare_1775062406iple_a->Prop)) (A_13:hoare_1775062406iple_a) (A_12:(hoare_1775062406iple_a->Prop)), ((and (((member2122167641iple_a A_13) A_12)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_12) ((insert1281456128iple_a A_13) B_11))) ((insert1281456128iple_a A_13) ((semila966743401le_a_o A_12) B_11))))) ((((member2122167641iple_a A_13) A_12)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_12) ((insert1281456128iple_a A_13) B_11))) ((semila966743401le_a_o A_12) B_11)))))
% FOF formula (forall (B_11:(pname->Prop)) (A_13:pname) (A_12:(pname->Prop)), ((and (((member_pname A_13) A_12)->(((eq (pname->Prop)) ((semila1673364395name_o A_12) ((insert_pname A_13) B_11))) ((insert_pname A_13) ((semila1673364395name_o A_12) B_11))))) ((((member_pname A_13) A_12)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_12) ((insert_pname A_13) B_11))) ((semila1673364395name_o A_12) B_11))))) of role axiom named fact_609_Int__insert__right
% A new axiom: (forall (B_11:(pname->Prop)) (A_13:pname) (A_12:(pname->Prop)), ((and (((member_pname A_13) A_12)->(((eq (pname->Prop)) ((semila1673364395name_o A_12) ((insert_pname A_13) B_11))) ((insert_pname A_13) ((semila1673364395name_o A_12) B_11))))) ((((member_pname A_13) A_12)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_12) ((insert_pname A_13) B_11))) ((semila1673364395name_o A_12) B_11)))))
% FOF formula (forall (P_1:(pname->Prop)) (F_4:(pname->hoare_1167836817_state)) (G:(pname->hoare_1167836817_state)) (S_1:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> (((if_Hoa833675553_state (P_1 X)) (F_4 X)) (G X)))) S_1)) ((semila1172322802tate_o ((image_575578384_state F_4) ((semila1673364395name_o S_1) (collect_pname P_1)))) ((image_575578384_state G) ((semila1673364395name_o S_1) (collect_pname (fun (X:pname)=> (not (P_1 X))))))))) of role axiom named fact_610_if__image__distrib
% A new axiom: (forall (P_1:(pname->Prop)) (F_4:(pname->hoare_1167836817_state)) (G:(pname->hoare_1167836817_state)) (S_1:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> (((if_Hoa833675553_state (P_1 X)) (F_4 X)) (G X)))) S_1)) ((semila1172322802tate_o ((image_575578384_state F_4) ((semila1673364395name_o S_1) (collect_pname P_1)))) ((image_575578384_state G) ((semila1673364395name_o S_1) (collect_pname (fun (X:pname)=> (not (P_1 X)))))))))
% FOF formula (forall (P_1:(pname->Prop)) (F_4:(pname->hoare_1775062406iple_a)) (G:(pname->hoare_1775062406iple_a)) (S_1:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> (((if_Hoa1047340790iple_a (P_1 X)) (F_4 X)) (G X)))) S_1)) ((semila13410563le_a_o ((image_2063119815iple_a F_4) ((semila1673364395name_o S_1) (collect_pname P_1)))) ((image_2063119815iple_a G) ((semila1673364395name_o S_1) (collect_pname (fun (X:pname)=> (not (P_1 X))))))))) of role axiom named fact_611_if__image__distrib
% A new axiom: (forall (P_1:(pname->Prop)) (F_4:(pname->hoare_1775062406iple_a)) (G:(pname->hoare_1775062406iple_a)) (S_1:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> (((if_Hoa1047340790iple_a (P_1 X)) (F_4 X)) (G X)))) S_1)) ((semila13410563le_a_o ((image_2063119815iple_a F_4) ((semila1673364395name_o S_1) (collect_pname P_1)))) ((image_2063119815iple_a G) ((semila1673364395name_o S_1) (collect_pname (fun (X:pname)=> (not (P_1 X)))))))))
% FOF formula (forall (B_10:(pname->Prop)) (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)->((finite_finite_pname B_10)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_11) B_10)) bot_bot_pname_o))->(((eq pname) ((F_3 (F_2 ((semila1780557381name_o A_11) B_10))) (F_2 ((semila1673364395name_o A_11) B_10)))) ((F_3 (F_2 A_11)) (F_2 B_10)))))))) of role axiom named fact_612_folding__one_Ounion__inter
% A new axiom: (forall (B_10:(pname->Prop)) (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)->((finite_finite_pname B_10)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_11) B_10)) bot_bot_pname_o))->(((eq pname) ((F_3 (F_2 ((semila1780557381name_o A_11) B_10))) (F_2 ((semila1673364395name_o A_11) B_10)))) ((F_3 (F_2 A_11)) (F_2 B_10))))))))
% FOF formula (forall (B_10:(hoare_1775062406iple_a->Prop)) (A_11:(hoare_1775062406iple_a->Prop)) (F_3:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_2:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_3) F_2)->((finite2063573081iple_a A_11)->((finite2063573081iple_a B_10)->((not (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_11) B_10)) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) ((F_3 (F_2 ((semila13410563le_a_o A_11) B_10))) (F_2 ((semila966743401le_a_o A_11) B_10)))) ((F_3 (F_2 A_11)) (F_2 B_10)))))))) of role axiom named fact_613_folding__one_Ounion__inter
% A new axiom: (forall (B_10:(hoare_1775062406iple_a->Prop)) (A_11:(hoare_1775062406iple_a->Prop)) (F_3:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_2:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_3) F_2)->((finite2063573081iple_a A_11)->((finite2063573081iple_a B_10)->((not (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_11) B_10)) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) ((F_3 (F_2 ((semila13410563le_a_o A_11) B_10))) (F_2 ((semila966743401le_a_o A_11) B_10)))) ((F_3 (F_2 A_11)) (F_2 B_10))))))))
% FOF formula (forall (B_10:(hoare_1167836817_state->Prop)) (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)->((finite1084549118_state B_10)->((not (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_11) B_10)) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) ((F_3 (F_2 ((semila1172322802tate_o A_11) B_10))) (F_2 ((semila179895820tate_o A_11) B_10)))) ((F_3 (F_2 A_11)) (F_2 B_10)))))))) of role axiom named fact_614_folding__one_Ounion__inter
% A new axiom: (forall (B_10:(hoare_1167836817_state->Prop)) (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)->((finite1084549118_state B_10)->((not (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_11) B_10)) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) ((F_3 (F_2 ((semila1172322802tate_o A_11) B_10))) (F_2 ((semila179895820tate_o A_11) B_10)))) ((F_3 (F_2 A_11)) (F_2 B_10))))))))
% FOF formula (forall (B_9:(pname->Prop)) (A_10:(pname->Prop)) (F_1:(pname->(pname->pname))) (F:((pname->Prop)->pname)), (((finite1282449217_pname F_1) F)->((finite_finite_pname A_10)->((not (((eq (pname->Prop)) A_10) bot_bot_pname_o))->((finite_finite_pname B_9)->((not (((eq (pname->Prop)) B_9) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_10) B_9)) bot_bot_pname_o)->(((eq pname) (F ((semila1780557381name_o A_10) B_9))) ((F_1 (F A_10)) (F B_9)))))))))) of role axiom named fact_615_folding__one_Ounion__disjoint
% A new axiom: (forall (B_9:(pname->Prop)) (A_10:(pname->Prop)) (F_1:(pname->(pname->pname))) (F:((pname->Prop)->pname)), (((finite1282449217_pname F_1) F)->((finite_finite_pname A_10)->((not (((eq (pname->Prop)) A_10) bot_bot_pname_o))->((finite_finite_pname B_9)->((not (((eq (pname->Prop)) B_9) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_10) B_9)) bot_bot_pname_o)->(((eq pname) (F ((semila1780557381name_o A_10) B_9))) ((F_1 (F A_10)) (F B_9))))))))))
% FOF formula (forall (B_9:(hoare_1775062406iple_a->Prop)) (A_10:(hoare_1775062406iple_a->Prop)) (F_1:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_1) F)->((finite2063573081iple_a A_10)->((not (((eq (hoare_1775062406iple_a->Prop)) A_10) bot_bo751897185le_a_o))->((finite2063573081iple_a B_9)->((not (((eq (hoare_1775062406iple_a->Prop)) B_9) bot_bo751897185le_a_o))->((((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_10) B_9)) bot_bo751897185le_a_o)->(((eq hoare_1775062406iple_a) (F ((semila13410563le_a_o A_10) B_9))) ((F_1 (F A_10)) (F B_9)))))))))) of role axiom named fact_616_folding__one_Ounion__disjoint
% A new axiom: (forall (B_9:(hoare_1775062406iple_a->Prop)) (A_10:(hoare_1775062406iple_a->Prop)) (F_1:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_1) F)->((finite2063573081iple_a A_10)->((not (((eq (hoare_1775062406iple_a->Prop)) A_10) bot_bo751897185le_a_o))->((finite2063573081iple_a B_9)->((not (((eq (hoare_1775062406iple_a->Prop)) B_9) bot_bo751897185le_a_o))->((((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_10) B_9)) bot_bo751897185le_a_o)->(((eq hoare_1775062406iple_a) (F ((semila13410563le_a_o A_10) B_9))) ((F_1 (F A_10)) (F B_9))))))))))
% FOF formula (forall (B_9:(hoare_1167836817_state->Prop)) (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)->((not (((eq (hoare_1167836817_state->Prop)) A_10) bot_bo70021908tate_o))->((finite1084549118_state B_9)->((not (((eq (hoare_1167836817_state->Prop)) B_9) bot_bo70021908tate_o))->((((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_10) B_9)) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F ((semila1172322802tate_o A_10) B_9))) ((F_1 (F A_10)) (F B_9)))))))))) of role axiom named fact_617_folding__one_Ounion__disjoint
% A new axiom: (forall (B_9:(hoare_1167836817_state->Prop)) (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)->((not (((eq (hoare_1167836817_state->Prop)) A_10) bot_bo70021908tate_o))->((finite1084549118_state B_9)->((not (((eq (hoare_1167836817_state->Prop)) B_9) bot_bo70021908tate_o))->((((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_10) B_9)) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F ((semila1172322802tate_o A_10) B_9))) ((F_1 (F A_10)) (F B_9))))))))))
% FOF formula (forall (X_3:Prop) (Y_3:Prop) (Z_3:Prop), ((forall (X:Prop) (Y_2:Prop) (Z_2:Prop), ((iff ((semila10642723_sup_o X) ((semila854092349_inf_o Y_2) Z_2))) ((semila854092349_inf_o ((semila10642723_sup_o X) Y_2)) ((semila10642723_sup_o X) Z_2))))->((iff ((semila854092349_inf_o X_3) ((semila10642723_sup_o Y_3) Z_3))) ((semila10642723_sup_o ((semila854092349_inf_o X_3) Y_3)) ((semila854092349_inf_o X_3) Z_3))))) of role axiom named fact_618_distrib__imp2
% A new axiom: (forall (X_3:Prop) (Y_3:Prop) (Z_3:Prop), ((forall (X:Prop) (Y_2:Prop) (Z_2:Prop), ((iff ((semila10642723_sup_o X) ((semila854092349_inf_o Y_2) Z_2))) ((semila854092349_inf_o ((semila10642723_sup_o X) Y_2)) ((semila10642723_sup_o X) Z_2))))->((iff ((semila854092349_inf_o X_3) ((semila10642723_sup_o Y_3) Z_3))) ((semila10642723_sup_o ((semila854092349_inf_o X_3) Y_3)) ((semila854092349_inf_o X_3) Z_3)))))
% FOF formula (forall (X_3:(pname->Prop)) (Y_3:(pname->Prop)) (Z_3:(pname->Prop)), ((forall (X:(pname->Prop)) (Y_2:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X) ((semila1673364395name_o Y_2) Z_2))) ((semila1673364395name_o ((semila1780557381name_o X) Y_2)) ((semila1780557381name_o X) Z_2))))->(((eq (pname->Prop)) ((semila1673364395name_o X_3) ((semila1780557381name_o Y_3) Z_3))) ((semila1780557381name_o ((semila1673364395name_o X_3) Y_3)) ((semila1673364395name_o X_3) Z_3))))) of role axiom named fact_619_distrib__imp2
% A new axiom: (forall (X_3:(pname->Prop)) (Y_3:(pname->Prop)) (Z_3:(pname->Prop)), ((forall (X:(pname->Prop)) (Y_2:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X) ((semila1673364395name_o Y_2) Z_2))) ((semila1673364395name_o ((semila1780557381name_o X) Y_2)) ((semila1780557381name_o X) Z_2))))->(((eq (pname->Prop)) ((semila1673364395name_o X_3) ((semila1780557381name_o Y_3) Z_3))) ((semila1780557381name_o ((semila1673364395name_o X_3) Y_3)) ((semila1673364395name_o X_3) Z_3)))))
% FOF formula (forall (X_3:(hoare_1167836817_state->Prop)) (Y_3:(hoare_1167836817_state->Prop)) (Z_3:(hoare_1167836817_state->Prop)), ((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X) ((semila179895820tate_o Y_2) Z_2))) ((semila179895820tate_o ((semila1172322802tate_o X) Y_2)) ((semila1172322802tate_o X) Z_2))))->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_3) ((semila1172322802tate_o Y_3) Z_3))) ((semila1172322802tate_o ((semila179895820tate_o X_3) Y_3)) ((semila179895820tate_o X_3) Z_3))))) of role axiom named fact_620_distrib__imp2
% A new axiom: (forall (X_3:(hoare_1167836817_state->Prop)) (Y_3:(hoare_1167836817_state->Prop)) (Z_3:(hoare_1167836817_state->Prop)), ((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X) ((semila179895820tate_o Y_2) Z_2))) ((semila179895820tate_o ((semila1172322802tate_o X) Y_2)) ((semila1172322802tate_o X) Z_2))))->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_3) ((semila1172322802tate_o Y_3) Z_3))) ((semila1172322802tate_o ((semila179895820tate_o X_3) Y_3)) ((semila179895820tate_o X_3) Z_3)))))
% FOF formula (forall (X_3:(hoare_1775062406iple_a->Prop)) (Y_3:(hoare_1775062406iple_a->Prop)) (Z_3:(hoare_1775062406iple_a->Prop)), ((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)) (Z_2:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X) ((semila966743401le_a_o Y_2) Z_2))) ((semila966743401le_a_o ((semila13410563le_a_o X) Y_2)) ((semila13410563le_a_o X) Z_2))))->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_3) ((semila13410563le_a_o Y_3) Z_3))) ((semila13410563le_a_o ((semila966743401le_a_o X_3) Y_3)) ((semila966743401le_a_o X_3) Z_3))))) of role axiom named fact_621_distrib__imp2
% A new axiom: (forall (X_3:(hoare_1775062406iple_a->Prop)) (Y_3:(hoare_1775062406iple_a->Prop)) (Z_3:(hoare_1775062406iple_a->Prop)), ((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)) (Z_2:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X) ((semila966743401le_a_o Y_2) Z_2))) ((semila966743401le_a_o ((semila13410563le_a_o X) Y_2)) ((semila13410563le_a_o X) Z_2))))->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_3) ((semila13410563le_a_o Y_3) Z_3))) ((semila13410563le_a_o ((semila966743401le_a_o X_3) Y_3)) ((semila966743401le_a_o X_3) Z_3)))))
% FOF formula (forall (X_2:Prop) (Y_1:Prop) (Z_1:Prop), ((forall (X:Prop) (Y_2:Prop) (Z_2:Prop), ((iff ((semila854092349_inf_o X) ((semila10642723_sup_o Y_2) Z_2))) ((semila10642723_sup_o ((semila854092349_inf_o X) Y_2)) ((semila854092349_inf_o X) Z_2))))->((iff ((semila10642723_sup_o X_2) ((semila854092349_inf_o Y_1) Z_1))) ((semila854092349_inf_o ((semila10642723_sup_o X_2) Y_1)) ((semila10642723_sup_o X_2) Z_1))))) of role axiom named fact_622_distrib__imp1
% A new axiom: (forall (X_2:Prop) (Y_1:Prop) (Z_1:Prop), ((forall (X:Prop) (Y_2:Prop) (Z_2:Prop), ((iff ((semila854092349_inf_o X) ((semila10642723_sup_o Y_2) Z_2))) ((semila10642723_sup_o ((semila854092349_inf_o X) Y_2)) ((semila854092349_inf_o X) Z_2))))->((iff ((semila10642723_sup_o X_2) ((semila854092349_inf_o Y_1) Z_1))) ((semila854092349_inf_o ((semila10642723_sup_o X_2) Y_1)) ((semila10642723_sup_o X_2) Z_1)))))
% FOF formula (forall (X_2:(pname->Prop)) (Y_1:(pname->Prop)) (Z_1:(pname->Prop)), ((forall (X:(pname->Prop)) (Y_2:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X) ((semila1780557381name_o Y_2) Z_2))) ((semila1780557381name_o ((semila1673364395name_o X) Y_2)) ((semila1673364395name_o X) Z_2))))->(((eq (pname->Prop)) ((semila1780557381name_o X_2) ((semila1673364395name_o Y_1) Z_1))) ((semila1673364395name_o ((semila1780557381name_o X_2) Y_1)) ((semila1780557381name_o X_2) Z_1))))) of role axiom named fact_623_distrib__imp1
% A new axiom: (forall (X_2:(pname->Prop)) (Y_1:(pname->Prop)) (Z_1:(pname->Prop)), ((forall (X:(pname->Prop)) (Y_2:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X) ((semila1780557381name_o Y_2) Z_2))) ((semila1780557381name_o ((semila1673364395name_o X) Y_2)) ((semila1673364395name_o X) Z_2))))->(((eq (pname->Prop)) ((semila1780557381name_o X_2) ((semila1673364395name_o Y_1) Z_1))) ((semila1673364395name_o ((semila1780557381name_o X_2) Y_1)) ((semila1780557381name_o X_2) Z_1)))))
% FOF formula (forall (X_2:(hoare_1167836817_state->Prop)) (Y_1:(hoare_1167836817_state->Prop)) (Z_1:(hoare_1167836817_state->Prop)), ((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X) ((semila1172322802tate_o Y_2) Z_2))) ((semila1172322802tate_o ((semila179895820tate_o X) Y_2)) ((semila179895820tate_o X) Z_2))))->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_2) ((semila179895820tate_o Y_1) Z_1))) ((semila179895820tate_o ((semila1172322802tate_o X_2) Y_1)) ((semila1172322802tate_o X_2) Z_1))))) of role axiom named fact_624_distrib__imp1
% A new axiom: (forall (X_2:(hoare_1167836817_state->Prop)) (Y_1:(hoare_1167836817_state->Prop)) (Z_1:(hoare_1167836817_state->Prop)), ((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X) ((semila1172322802tate_o Y_2) Z_2))) ((semila1172322802tate_o ((semila179895820tate_o X) Y_2)) ((semila179895820tate_o X) Z_2))))->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_2) ((semila179895820tate_o Y_1) Z_1))) ((semila179895820tate_o ((semila1172322802tate_o X_2) Y_1)) ((semila1172322802tate_o X_2) Z_1)))))
% FOF formula (forall (X_2:(hoare_1775062406iple_a->Prop)) (Y_1:(hoare_1775062406iple_a->Prop)) (Z_1:(hoare_1775062406iple_a->Prop)), ((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)) (Z_2:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X) ((semila13410563le_a_o Y_2) Z_2))) ((semila13410563le_a_o ((semila966743401le_a_o X) Y_2)) ((semila966743401le_a_o X) Z_2))))->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_2) ((semila966743401le_a_o Y_1) Z_1))) ((semila966743401le_a_o ((semila13410563le_a_o X_2) Y_1)) ((semila13410563le_a_o X_2) Z_1))))) of role axiom named fact_625_distrib__imp1
% A new axiom: (forall (X_2:(hoare_1775062406iple_a->Prop)) (Y_1:(hoare_1775062406iple_a->Prop)) (Z_1:(hoare_1775062406iple_a->Prop)), ((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)) (Z_2:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X) ((semila13410563le_a_o Y_2) Z_2))) ((semila13410563le_a_o ((semila966743401le_a_o X) Y_2)) ((semila966743401le_a_o X) Z_2))))->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_2) ((semila966743401le_a_o Y_1) Z_1))) ((semila966743401le_a_o ((semila13410563le_a_o X_2) Y_1)) ((semila13410563le_a_o X_2) Z_1)))))
% FOF formula (forall (A_9:Prop) (A_8:(Prop->Prop)), ((finite_finite_o A_8)->(((member_o A_9) A_8)->((iff ((semila10642723_sup_o A_9) (big_la1690136417_fin_o A_8))) A_9)))) of role axiom named fact_626_sup__Inf__absorb
% A new axiom: (forall (A_9:Prop) (A_8:(Prop->Prop)), ((finite_finite_o A_8)->(((member_o A_9) A_8)->((iff ((semila10642723_sup_o A_9) (big_la1690136417_fin_o A_8))) A_9))))
% FOF formula (forall (A_9:(pname->Prop)) (A_8:((pname->Prop)->Prop)), ((finite297249702name_o A_8)->(((member_pname_o A_9) A_8)->(((eq (pname->Prop)) ((semila1780557381name_o A_9) (big_la1126801287name_o A_8))) A_9)))) of role axiom named fact_627_sup__Inf__absorb
% A new axiom: (forall (A_9:(pname->Prop)) (A_8:((pname->Prop)->Prop)), ((finite297249702name_o A_8)->(((member_pname_o A_9) A_8)->(((eq (pname->Prop)) ((semila1780557381name_o A_9) (big_la1126801287name_o A_8))) A_9))))
% FOF formula (forall (A_9:(hoare_1167836817_state->Prop)) (A_8:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_8)->(((member864234961tate_o A_9) A_8)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_9) (big_la831793456tate_o A_8))) A_9)))) of role axiom named fact_628_sup__Inf__absorb
% A new axiom: (forall (A_9:(hoare_1167836817_state->Prop)) (A_8:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_8)->(((member864234961tate_o A_9) A_8)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_9) (big_la831793456tate_o A_8))) A_9))))
% FOF formula (forall (A_9:(hoare_1775062406iple_a->Prop)) (A_8:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_8)->(((member1207314404le_a_o A_9) A_8)->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_9) (big_la447547205le_a_o A_8))) A_9)))) of role axiom named fact_629_sup__Inf__absorb
% A new axiom: (forall (A_9:(hoare_1775062406iple_a->Prop)) (A_8:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_8)->(((member1207314404le_a_o A_9) A_8)->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_9) (big_la447547205le_a_o A_8))) A_9))))
% FOF formula (forall (C_5:hoare_1775062406iple_a) (A_7:(hoare_1775062406iple_a->Prop)) (B_8:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_5) ((minus_1944206118le_a_o A_7) B_8))->((((member2122167641iple_a C_5) A_7)->((member2122167641iple_a C_5) B_8))->False))) of role axiom named fact_630_DiffE
% A new axiom: (forall (C_5:hoare_1775062406iple_a) (A_7:(hoare_1775062406iple_a->Prop)) (B_8:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_5) ((minus_1944206118le_a_o A_7) B_8))->((((member2122167641iple_a C_5) A_7)->((member2122167641iple_a C_5) B_8))->False)))
% FOF formula (forall (C_5:pname) (A_7:(pname->Prop)) (B_8:(pname->Prop)), (((member_pname C_5) ((minus_minus_pname_o A_7) B_8))->((((member_pname C_5) A_7)->((member_pname C_5) B_8))->False))) of role axiom named fact_631_DiffE
% A new axiom: (forall (C_5:pname) (A_7:(pname->Prop)) (B_8:(pname->Prop)), (((member_pname C_5) ((minus_minus_pname_o A_7) B_8))->((((member_pname C_5) A_7)->((member_pname C_5) B_8))->False)))
% FOF formula (forall (B_7:(hoare_1775062406iple_a->Prop)) (C_4:hoare_1775062406iple_a) (A_6:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_4) A_6)->((((member2122167641iple_a C_4) B_7)->False)->((member2122167641iple_a C_4) ((minus_1944206118le_a_o A_6) B_7))))) of role axiom named fact_632_DiffI
% A new axiom: (forall (B_7:(hoare_1775062406iple_a->Prop)) (C_4:hoare_1775062406iple_a) (A_6:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_4) A_6)->((((member2122167641iple_a C_4) B_7)->False)->((member2122167641iple_a C_4) ((minus_1944206118le_a_o A_6) B_7)))))
% FOF formula (forall (B_7:(pname->Prop)) (C_4:pname) (A_6:(pname->Prop)), (((member_pname C_4) A_6)->((((member_pname C_4) B_7)->False)->((member_pname C_4) ((minus_minus_pname_o A_6) B_7))))) of role axiom named fact_633_DiffI
% A new axiom: (forall (B_7:(pname->Prop)) (C_4:pname) (A_6:(pname->Prop)), (((member_pname C_4) A_6)->((((member_pname C_4) B_7)->False)->((member_pname C_4) ((minus_minus_pname_o A_6) B_7)))))
% FOF formula (forall (A_5:(pname->Prop)) (B_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_5) ((minus_minus_pname_o B_6) A_5))) ((semila1780557381name_o A_5) B_6))) of role axiom named fact_634_Un__Diff__cancel
% A new axiom: (forall (A_5:(pname->Prop)) (B_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_5) ((minus_minus_pname_o B_6) A_5))) ((semila1780557381name_o A_5) B_6)))
% FOF formula (forall (A_5:(hoare_1167836817_state->Prop)) (B_6:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_5) ((minus_2107060239tate_o B_6) A_5))) ((semila1172322802tate_o A_5) B_6))) of role axiom named fact_635_Un__Diff__cancel
% A new axiom: (forall (A_5:(hoare_1167836817_state->Prop)) (B_6:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_5) ((minus_2107060239tate_o B_6) A_5))) ((semila1172322802tate_o A_5) B_6)))
% FOF formula (forall (A_5:(hoare_1775062406iple_a->Prop)) (B_6:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_5) ((minus_1944206118le_a_o B_6) A_5))) ((semila13410563le_a_o A_5) B_6))) of role axiom named fact_636_Un__Diff__cancel
% A new axiom: (forall (A_5:(hoare_1775062406iple_a->Prop)) (B_6:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_5) ((minus_1944206118le_a_o B_6) A_5))) ((semila13410563le_a_o A_5) B_6)))
% FOF formula (forall (B_5:(pname->Prop)) (A_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o B_5) A_4)) A_4)) ((semila1780557381name_o B_5) A_4))) of role axiom named fact_637_Un__Diff__cancel2
% A new axiom: (forall (B_5:(pname->Prop)) (A_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o B_5) A_4)) A_4)) ((semila1780557381name_o B_5) A_4)))
% FOF formula (forall (B_5:(hoare_1167836817_state->Prop)) (A_4:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((minus_2107060239tate_o B_5) A_4)) A_4)) ((semila1172322802tate_o B_5) A_4))) of role axiom named fact_638_Un__Diff__cancel2
% A new axiom: (forall (B_5:(hoare_1167836817_state->Prop)) (A_4:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((minus_2107060239tate_o B_5) A_4)) A_4)) ((semila1172322802tate_o B_5) A_4)))
% FOF formula (forall (B_5:(hoare_1775062406iple_a->Prop)) (A_4:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((minus_1944206118le_a_o B_5) A_4)) A_4)) ((semila13410563le_a_o B_5) A_4))) of role axiom named fact_639_Un__Diff__cancel2
% A new axiom: (forall (B_5:(hoare_1775062406iple_a->Prop)) (A_4:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((minus_1944206118le_a_o B_5) A_4)) A_4)) ((semila13410563le_a_o B_5) A_4)))
% FOF formula (forall (A_3:(pname->Prop)) (B_4:(pname->Prop)) (C_3:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o ((semila1780557381name_o A_3) B_4)) C_3)) ((semila1780557381name_o ((minus_minus_pname_o A_3) C_3)) ((minus_minus_pname_o B_4) C_3)))) of role axiom named fact_640_Un__Diff
% A new axiom: (forall (A_3:(pname->Prop)) (B_4:(pname->Prop)) (C_3:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o ((semila1780557381name_o A_3) B_4)) C_3)) ((semila1780557381name_o ((minus_minus_pname_o A_3) C_3)) ((minus_minus_pname_o B_4) C_3))))
% FOF formula (forall (A_3:(hoare_1167836817_state->Prop)) (B_4:(hoare_1167836817_state->Prop)) (C_3:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((semila1172322802tate_o A_3) B_4)) C_3)) ((semila1172322802tate_o ((minus_2107060239tate_o A_3) C_3)) ((minus_2107060239tate_o B_4) C_3)))) of role axiom named fact_641_Un__Diff
% A new axiom: (forall (A_3:(hoare_1167836817_state->Prop)) (B_4:(hoare_1167836817_state->Prop)) (C_3:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((semila1172322802tate_o A_3) B_4)) C_3)) ((semila1172322802tate_o ((minus_2107060239tate_o A_3) C_3)) ((minus_2107060239tate_o B_4) C_3))))
% FOF formula (forall (A_3:(hoare_1775062406iple_a->Prop)) (B_4:(hoare_1775062406iple_a->Prop)) (C_3:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((minus_1944206118le_a_o ((semila13410563le_a_o A_3) B_4)) C_3)) ((semila13410563le_a_o ((minus_1944206118le_a_o A_3) C_3)) ((minus_1944206118le_a_o B_4) C_3)))) of role axiom named fact_642_Un__Diff
% A new axiom: (forall (A_3:(hoare_1775062406iple_a->Prop)) (B_4:(hoare_1775062406iple_a->Prop)) (C_3:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((minus_1944206118le_a_o ((semila13410563le_a_o A_3) B_4)) C_3)) ((semila13410563le_a_o ((minus_1944206118le_a_o A_3) C_3)) ((minus_1944206118le_a_o B_4) C_3))))
% FOF formula (forall (C_2:hoare_1775062406iple_a) (A_2:(hoare_1775062406iple_a->Prop)) (B_3:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_2) ((minus_1944206118le_a_o A_2) B_3))->(((member2122167641iple_a C_2) B_3)->False))) of role axiom named fact_643_DiffD2
% A new axiom: (forall (C_2:hoare_1775062406iple_a) (A_2:(hoare_1775062406iple_a->Prop)) (B_3:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_2) ((minus_1944206118le_a_o A_2) B_3))->(((member2122167641iple_a C_2) B_3)->False)))
% FOF formula (forall (C_2:pname) (A_2:(pname->Prop)) (B_3:(pname->Prop)), (((member_pname C_2) ((minus_minus_pname_o A_2) B_3))->(((member_pname C_2) B_3)->False))) of role axiom named fact_644_DiffD2
% A new axiom: (forall (C_2:pname) (A_2:(pname->Prop)) (B_3:(pname->Prop)), (((member_pname C_2) ((minus_minus_pname_o A_2) B_3))->(((member_pname C_2) B_3)->False)))
% FOF formula (forall (C_1:hoare_1775062406iple_a) (A_1:(hoare_1775062406iple_a->Prop)) (B_2:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_1) ((minus_1944206118le_a_o A_1) B_2))->((member2122167641iple_a C_1) A_1))) of role axiom named fact_645_DiffD1
% A new axiom: (forall (C_1:hoare_1775062406iple_a) (A_1:(hoare_1775062406iple_a->Prop)) (B_2:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_1) ((minus_1944206118le_a_o A_1) B_2))->((member2122167641iple_a C_1) A_1)))
% FOF formula (forall (C_1:pname) (A_1:(pname->Prop)) (B_2:(pname->Prop)), (((member_pname C_1) ((minus_minus_pname_o A_1) B_2))->((member_pname C_1) A_1))) of role axiom named fact_646_DiffD1
% A new axiom: (forall (C_1:pname) (A_1:(pname->Prop)) (B_2:(pname->Prop)), (((member_pname C_1) ((minus_minus_pname_o A_1) B_2))->((member_pname C_1) A_1)))
% FOF formula (forall (C:pname) (A:(pname->Prop)) (B_1:(pname->Prop)), ((iff ((member_pname C) ((minus_minus_pname_o A) B_1))) ((and ((member_pname C) A)) (((member_pname C) B_1)->False)))) of role axiom named fact_647_Diff__iff
% A new axiom: (forall (C:pname) (A:(pname->Prop)) (B_1:(pname->Prop)), ((iff ((member_pname C) ((minus_minus_pname_o A) B_1))) ((and ((member_pname C) A)) (((member_pname C) B_1)->False))))
% FOF formula (forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat (suc M)) (suc N_1))) ((minus_minus_nat M) N_1))) of role axiom named fact_648_diff__Suc__Suc
% A new axiom: (forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat (suc M)) (suc N_1))) ((minus_minus_nat M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M)) N_1)) (suc K))) ((minus_minus_nat ((minus_minus_nat M) N_1)) K))) of role axiom named fact_649_Suc__diff__diff
% A new axiom: (forall (M:nat) (N_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M)) N_1)) (suc K))) ((minus_minus_nat ((minus_minus_nat M) N_1)) K)))
% FOF formula (forall (N_1:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N_1)) zero_zero_nat)) of role axiom named fact_650_diff__0__eq__0
% A new axiom: (forall (N_1:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N_1)) zero_zero_nat))
% FOF formula (forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)) of role axiom named fact_651_minus__nat_Odiff__0
% A new axiom: (forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M))
% FOF formula (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)) of role axiom named fact_652_diff__self__eq__0
% A new axiom: (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat))
% FOF formula (forall (M:nat) (N_1:nat), ((((eq nat) ((minus_minus_nat M) N_1)) zero_zero_nat)->((((eq nat) ((minus_minus_nat N_1) M)) zero_zero_nat)->(((eq nat) M) N_1)))) of role axiom named fact_653_diffs0__imp__equal
% A new axiom: (forall (M:nat) (N_1:nat), ((((eq nat) ((minus_minus_nat M) N_1)) zero_zero_nat)->((((eq nat) ((minus_minus_nat N_1) M)) zero_zero_nat)->(((eq nat) M) N_1))))
% FOF formula (forall (_TPTP_I:nat) (P:(nat->Prop)) (K:nat), ((P K)->((forall (N:nat), ((P (suc N))->(P N)))->(P ((minus_minus_nat K) _TPTP_I))))) of role axiom named fact_654_zero__induct__lemma
% A new axiom: (forall (_TPTP_I:nat) (P:(nat->Prop)) (K:nat), ((P K)->((forall (N:nat), ((P (suc N))->(P N)))->(P ((minus_minus_nat K) _TPTP_I)))))
% FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat _TPTP_I) J)) K)) ((minus_minus_nat ((minus_minus_nat _TPTP_I) K)) J))) of role axiom named fact_655_diff__commute
% A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat _TPTP_I) J)) K)) ((minus_minus_nat ((minus_minus_nat _TPTP_I) K)) J)))
% FOF formula (forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat M) (suc N_1))) (((nat_case_nat zero_zero_nat) (fun (K_1:nat)=> K_1)) ((minus_minus_nat M) N_1)))) of role axiom named fact_656_diff__Suc
% A new axiom: (forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat M) (suc N_1))) (((nat_case_nat zero_zero_nat) (fun (K_1:nat)=> K_1)) ((minus_minus_nat M) N_1))))
% FOF formula (forall (N_1:nat), (((eq nat) ((minus_minus_nat (suc N_1)) one_one_nat)) N_1)) of role axiom named fact_657_diff__Suc__1
% A new axiom: (forall (N_1:nat), (((eq nat) ((minus_minus_nat (suc N_1)) one_one_nat)) N_1))
% FOF formula (forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat M) (suc N_1))) ((minus_minus_nat ((minus_minus_nat M) one_one_nat)) N_1))) of role axiom named fact_658_diff__Suc__eq__diff__pred
% A new axiom: (forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat M) (suc N_1))) ((minus_minus_nat ((minus_minus_nat M) one_one_nat)) N_1)))
% FOF formula (((eq nat) one_one_nat) (suc zero_zero_nat)) of role axiom named fact_659_One__nat__def
% A new axiom: (((eq nat) one_one_nat) (suc zero_zero_nat))
% FOF formula (forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat N_1) one_one_nat))) of role axiom named fact_660_Suc__eq__plus1
% A new axiom: (forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat N_1) one_one_nat)))
% FOF formula (forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat one_one_nat) N_1))) of role axiom named fact_661_Suc__eq__plus1__left
% A new axiom: (forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat one_one_nat) N_1)))
% FOF formula (forall (M:nat) (K:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K)) ((plus_plus_nat N_1) K))) ((minus_minus_nat M) N_1))) of role axiom named fact_662_diff__cancel2
% A new axiom: (forall (M:nat) (K:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K)) ((plus_plus_nat N_1) K))) ((minus_minus_nat M) N_1)))
% FOF formula (forall (K:nat) (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N_1))) ((minus_minus_nat M) N_1))) of role axiom named fact_663_diff__cancel
% A new axiom: (forall (K:nat) (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N_1))) ((minus_minus_nat M) N_1)))
% FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat _TPTP_I) J)) K)) ((minus_minus_nat _TPTP_I) ((plus_plus_nat J) K)))) of role axiom named fact_664_diff__diff__left
% A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat _TPTP_I) J)) K)) ((minus_minus_nat _TPTP_I) ((plus_plus_nat J) K))))
% FOF formula (forall (N_1:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N_1) M)) N_1)) M)) of role axiom named fact_665_diff__add__inverse
% A new axiom: (forall (N_1:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N_1) M)) N_1)) M))
% FOF formula (forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N_1)) N_1)) M)) of role axiom named fact_666_diff__add__inverse2
% A new axiom: (forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N_1)) N_1)) M))
% FOF formula (forall (N_1:nat) (M:nat), (((eq nat) ((minus_minus_nat N_1) ((plus_plus_nat N_1) M))) zero_zero_nat)) of role axiom named fact_667_diff__add__0
% A new axiom: (forall (N_1:nat) (M:nat), (((eq nat) ((minus_minus_nat N_1) ((plus_plus_nat N_1) M))) zero_zero_nat))
% FOF formula (forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M) N_1)) ((plus_plus_nat N_1) M))) of role axiom named fact_668_nat__add__commute
% A new axiom: (forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M) N_1)) ((plus_plus_nat N_1) M)))
% FOF formula (forall (X_1:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X_1) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X_1) Z)))) of role axiom named fact_669_nat__add__left__commute
% A new axiom: (forall (X_1:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X_1) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X_1) Z))))
% FOF formula (forall (M:nat) (N_1:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N_1)) K)) ((plus_plus_nat M) ((plus_plus_nat N_1) K)))) of role axiom named fact_670_nat__add__assoc
% A new axiom: (forall (M:nat) (N_1:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N_1)) K)) ((plus_plus_nat M) ((plus_plus_nat N_1) K))))
% FOF formula (forall (K:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N_1))) (((eq nat) M) N_1))) of role axiom named fact_671_nat__add__left__cancel
% A new axiom: (forall (K:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N_1))) (((eq nat) M) N_1)))
% FOF formula (forall (M:nat) (K:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N_1) K))) (((eq nat) M) N_1))) of role axiom named fact_672_nat__add__right__cancel
% A new axiom: (forall (M:nat) (K:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N_1) K))) (((eq nat) M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M)) N_1)) ((plus_plus_nat M) (suc N_1)))) of role axiom named fact_673_add__Suc__shift
% A new axiom: (forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M)) N_1)) ((plus_plus_nat M) (suc N_1))))
% FOF formula (forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M)) N_1)) (suc ((plus_plus_nat M) N_1)))) of role axiom named fact_674_add__Suc
% A new axiom: (forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M)) N_1)) (suc ((plus_plus_nat M) N_1))))
% FOF formula (forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M) (suc N_1))) (suc ((plus_plus_nat M) N_1)))) of role axiom named fact_675_add__Suc__right
% A new axiom: (forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M) (suc N_1))) (suc ((plus_plus_nat M) N_1))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M) N_1))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat)))))) of role axiom named fact_676_one__is__add
% A new axiom: (forall (M:nat) (N_1:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M) N_1))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat))))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) N_1)) (suc zero_zero_nat))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat)))))) of role axiom named fact_677_add__is__1
% A new axiom: (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) N_1)) (suc zero_zero_nat))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat))))))
% FOF formula (forall (N_1:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N_1)) N_1)) of role axiom named fact_678_plus__nat_Oadd__0
% A new axiom: (forall (N_1:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N_1)) N_1))
% FOF formula (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)) of role axiom named fact_679_Nat_Oadd__0__right
% A new axiom: (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M))
% FOF formula (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) N_1)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat)))) of role axiom named fact_680_add__is__0
% A new axiom: (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) N_1)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat))))
% FOF formula (forall (M:nat) (N_1:nat), ((((eq nat) ((plus_plus_nat M) N_1)) M)->(((eq nat) N_1) zero_zero_nat))) of role axiom named fact_681_add__eq__self__zero
% A new axiom: (forall (M:nat) (N_1:nat), ((((eq nat) ((plus_plus_nat M) N_1)) M)->(((eq nat) N_1) zero_zero_nat)))
% FOF formula (forall (N_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((plus_plus_nat M) N_1)) N_1))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((plus_plus_nat M) N_1)) (suc ((plus_plus_nat ((minus_minus_nat M) one_one_nat)) N_1)))))) of role axiom named fact_682_add__eq__if
% A new axiom: (forall (N_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((plus_plus_nat M) N_1)) N_1))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((plus_plus_nat M) N_1)) (suc ((plus_plus_nat ((minus_minus_nat M) one_one_nat)) N_1))))))
% FOF formula (forall (Com1:com) (Com2:com), (((eq nat) (com_size ((semi Com1) Com2))) ((plus_plus_nat ((plus_plus_nat (com_size Com1)) (com_size Com2))) (suc zero_zero_nat)))) of role axiom named fact_683_com_Osize_I4_J
% A new axiom: (forall (Com1:com) (Com2:com), (((eq nat) (com_size ((semi Com1) Com2))) ((plus_plus_nat ((plus_plus_nat (com_size Com1)) (com_size Com2))) (suc zero_zero_nat))))
% FOF formula (forall (Pname:pname), (((eq nat) (com_size (body Pname))) zero_zero_nat)) of role axiom named fact_684_com_Osize_I7_J
% A new axiom: (forall (Pname:pname), (((eq nat) (com_size (body Pname))) zero_zero_nat))
% FOF formula (((eq nat) (com_size skip)) zero_zero_nat) of role axiom named fact_685_com_Osize_I1_J
% A new axiom: (((eq nat) (com_size skip)) zero_zero_nat)
% FOF formula (forall (Fun:(state->Prop)) (Com:com), (((eq nat) (com_size ((while Fun) Com))) ((plus_plus_nat (com_size Com)) (suc zero_zero_nat)))) of role axiom named fact_686_com_Osize_I6_J
% A new axiom: (forall (Fun:(state->Prop)) (Com:com), (((eq nat) (com_size ((while Fun) Com))) ((plus_plus_nat (com_size Com)) (suc zero_zero_nat))))
% FOF formula (forall (Com1:com) (Com2:com), (((eq nat) (size_size_com ((semi Com1) Com2))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1)) (size_size_com Com2))) (suc zero_zero_nat)))) of role axiom named fact_687_com_Osize_I12_J
% A new axiom: (forall (Com1:com) (Com2:com), (((eq nat) (size_size_com ((semi Com1) Com2))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1)) (size_size_com Com2))) (suc zero_zero_nat))))
% FOF formula (forall (Pname:pname), (((eq nat) (size_size_com (body Pname))) zero_zero_nat)) of role axiom named fact_688_com_Osize_I15_J
% A new axiom: (forall (Pname:pname), (((eq nat) (size_size_com (body Pname))) zero_zero_nat))
% FOF formula (((eq nat) (size_size_com skip)) zero_zero_nat) of role axiom named fact_689_com_Osize_I9_J
% A new axiom: (((eq nat) (size_size_com skip)) zero_zero_nat)
% FOF formula (forall (Fun:(state->Prop)) (Com:com), (((eq nat) (size_size_com ((while Fun) Com))) ((plus_plus_nat (size_size_com Com)) (suc zero_zero_nat)))) of role axiom named fact_690_com_Osize_I14_J
% A new axiom: (forall (Fun:(state->Prop)) (Com:com), (((eq nat) (size_size_com ((while Fun) Com))) ((plus_plus_nat (size_size_com Com)) (suc zero_zero_nat))))
% FOF formula (forall (Fun:(state->Prop)) (Com1:com) (Com2:com), (((eq nat) (size_size_com (((cond Fun) Com1) Com2))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1)) (size_size_com Com2))) (suc zero_zero_nat)))) of role axiom named fact_691_com_Osize_I13_J
% A new axiom: (forall (Fun:(state->Prop)) (Com1:com) (Com2:com), (((eq nat) (size_size_com (((cond Fun) Com1) Com2))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1)) (size_size_com Com2))) (suc zero_zero_nat))))
% FOF formula (forall (C0:com) (C1:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S:state), (((B S)->False)->(((((evaln C1) S) N_1) S1)->((((evaln (((cond B) C0) C1)) S) N_1) S1)))) of role axiom named fact_692_evaln_OIfFalse
% A new axiom: (forall (C0:com) (C1:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S:state), (((B S)->False)->(((((evaln C1) S) N_1) S1)->((((evaln (((cond B) C0) C1)) S) N_1) S1))))
% FOF formula (forall (C1:com) (C0:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S:state), ((B S)->(((((evaln C0) S) N_1) S1)->((((evaln (((cond B) C0) C1)) S) N_1) S1)))) of role axiom named fact_693_evaln_OIfTrue
% A new axiom: (forall (C1:com) (C0:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S:state), ((B S)->(((((evaln C0) S) N_1) S1)->((((evaln (((cond B) C0) C1)) S) N_1) S1))))
% FOF formula (forall (B:(state->Prop)) (C1:com) (C2:com) (S:state) (N_1:nat) (T:state), (((((evaln (((cond B) C1) C2)) S) N_1) T)->(((B S)->(((((evaln C1) S) N_1) T)->False))->((((B S)->False)->(((((evaln C2) S) N_1) T)->False))->False)))) of role axiom named fact_694_evaln__elim__cases_I5_J
% A new axiom: (forall (B:(state->Prop)) (C1:com) (C2:com) (S:state) (N_1:nat) (T:state), (((((evaln (((cond B) C1) C2)) S) N_1) T)->(((B S)->(((((evaln C1) S) N_1) T)->False))->((((B S)->False)->(((((evaln C2) S) N_1) T)->False))->False))))
% FOF formula (forall (B:(state->Prop)) (C1:com) (C2:com) (S:state) (T:state), ((((evalc (((cond B) C1) C2)) S) T)->(((B S)->((((evalc C1) S) T)->False))->((((B S)->False)->((((evalc C2) S) T)->False))->False)))) of role axiom named fact_695_evalc__elim__cases_I5_J
% A new axiom: (forall (B:(state->Prop)) (C1:com) (C2:com) (S:state) (T:state), ((((evalc (((cond B) C1) C2)) S) T)->(((B S)->((((evalc C1) S) T)->False))->((((B S)->False)->((((evalc C2) S) T)->False))->False))))
% FOF formula (forall (C1:com) (C0:com) (S1:state) (B:(state->Prop)) (S:state), ((B S)->((((evalc C0) S) S1)->(((evalc (((cond B) C0) C1)) S) S1)))) of role axiom named fact_696_evalc_OIfTrue
% A new axiom: (forall (C1:com) (C0:com) (S1:state) (B:(state->Prop)) (S:state), ((B S)->((((evalc C0) S) S1)->(((evalc (((cond B) C0) C1)) S) S1))))
% FOF formula (forall (C0:com) (C1:com) (S1:state) (B:(state->Prop)) (S:state), (((B S)->False)->((((evalc C1) S) S1)->(((evalc (((cond B) C0) C1)) S) S1)))) of role axiom named fact_697_evalc_OIfFalse
% A new axiom: (forall (C0:com) (C1:com) (S1:state) (B:(state->Prop)) (S:state), (((B S)->False)->((((evalc C1) S) S1)->(((evalc (((cond B) C0) C1)) S) S1))))
% FOF formula (forall (X_1:pname) (Y:pname), ((or (((fequal_pname X_1) Y)->False)) (((eq pname) X_1) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Com__Opname_T
% A new axiom: (forall (X_1:pname) (Y:pname), ((or (((fequal_pname X_1) Y)->False)) (((eq pname) X_1) Y)))
% FOF formula (forall (X_1:pname) (Y:pname), ((or (not (((eq pname) X_1) Y))) ((fequal_pname X_1) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Com__Opname_T
% A new axiom: (forall (X_1:pname) (Y:pname), ((or (not (((eq pname) X_1) Y))) ((fequal_pname X_1) Y)))
% FOF formula (forall (X_1:state) (Y:state), ((or (((fequal_state X_1) Y)->False)) (((eq state) X_1) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Com__Ostate_T
% A new axiom: (forall (X_1:state) (Y:state), ((or (((fequal_state X_1) Y)->False)) (((eq state) X_1) Y)))
% FOF formula (forall (X_1:state) (Y:state), ((or (not (((eq state) X_1) Y))) ((fequal_state X_1) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Com__Ostate_T
% A new axiom: (forall (X_1:state) (Y:state), ((or (not (((eq state) X_1) Y))) ((fequal_state X_1) Y)))
% FOF formula (forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (((if_Hoa1047340790iple_a True) X_1) Y)) X_1)) of role axiom named help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_T
% A new axiom: (forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (((if_Hoa1047340790iple_a True) X_1) Y)) X_1))
% FOF formula (forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (((if_Hoa1047340790iple_a False) X_1) Y)) Y)) of role axiom named help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_T
% A new axiom: (forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (((if_Hoa1047340790iple_a False) X_1) 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_It__a_J_T
% A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False)))
% FOF formula (forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), ((or (((fequal1288209029iple_a X_1) Y)->False)) (((eq hoare_1775062406iple_a) X_1) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_
% A new axiom: (forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), ((or (((fequal1288209029iple_a X_1) Y)->False)) (((eq hoare_1775062406iple_a) X_1) Y)))
% FOF formula (forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), ((or (not (((eq hoare_1775062406iple_a) X_1) Y))) ((fequal1288209029iple_a X_1) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_
% A new axiom: (forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), ((or (not (((eq hoare_1775062406iple_a) X_1) Y))) ((fequal1288209029iple_a X_1) Y)))
% FOF formula (forall (X_1:hoare_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_state True) X_1) Y)) X_1)) of role axiom named help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate
% A new axiom: (forall (X_1:hoare_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_state True) X_1) Y)) X_1))
% FOF formula (forall (X_1:hoare_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_state False) X_1) Y)) Y)) of role axiom named help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate
% A new axiom: (forall (X_1:hoare_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_state False) X_1) 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_1:hoare_1167836817_state) (Y:hoare_1167836817_state), ((or (((fequal1831255762_state X_1) Y)->False)) (((eq hoare_1167836817_state) X_1) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com
% A new axiom: (forall (X_1:hoare_1167836817_state) (Y:hoare_1167836817_state), ((or (((fequal1831255762_state X_1) Y)->False)) (((eq hoare_1167836817_state) X_1) Y)))
% FOF formula (forall (X_1:hoare_1167836817_state) (Y:hoare_1167836817_state), ((or (not (((eq hoare_1167836817_state) X_1) Y))) ((fequal1831255762_state X_1) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com
% A new axiom: (forall (X_1:hoare_1167836817_state) (Y:hoare_1167836817_state), ((or (not (((eq hoare_1167836817_state) X_1) Y))) ((fequal1831255762_state X_1) Y)))
% FOF formula (forall (N:nat), ((forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) ((semila13410563le_a_o g) ((image_2063119815iple_a (fun (Pn:pname)=> (((hoare_1766022166iple_a (p Pn)) (body Pn)) (q Pn)))) procs)))->((hoare_1462269968alid_a N) X)))->(forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) ((image_2063119815iple_a (fun (Pn:pname)=> (((hoare_1766022166iple_a (p Pn)) (the_com (body_1 Pn))) (q Pn)))) procs))->((hoare_1462269968alid_a N) X))))) of role hypothesis named conj_0
% A new axiom: (forall (N:nat), ((forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) ((semila13410563le_a_o g) ((image_2063119815iple_a (fun (Pn:pname)=> (((hoare_1766022166iple_a (p Pn)) (body Pn)) (q Pn)))) procs)))->((hoare_1462269968alid_a N) X)))->(forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) ((image_2063119815iple_a (fun (Pn:pname)=> (((hoare_1766022166iple_a (p Pn)) (the_com (body_1 Pn))) (q Pn)))) procs))->((hoare_1462269968alid_a N) X)))))
% FOF formula ((forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) g)->((hoare_1462269968alid_a n) X)))->(forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) ((image_2063119815iple_a (fun (Pn:pname)=> (((hoare_1766022166iple_a (p Pn)) (body Pn)) (q Pn)))) procs))->((hoare_1462269968alid_a n) X)))) of role conjecture named conj_1
% Conjecture to prove = ((forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) g)->((hoare_1462269968alid_a n) X)))->(forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) ((image_2063119815iple_a (fun (Pn:pname)=> (((hoare_1766022166iple_a (p Pn)) (body Pn)) (q Pn)))) procs))->((hoare_1462269968alid_a n) X)))):Prop
% Parameter x_a_DUMMY:x_a.
% Parameter pname_DUMMY:pname.
% Parameter state_DUMMY:state.
% Parameter hoare_1775062406iple_a_DUMMY:hoare_1775062406iple_a.
% Parameter hoare_1167836817_state_DUMMY:hoare_1167836817_state.
% Parameter option_com_DUMMY:option_com.
% We need to prove ['((forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) g)->((hoare_1462269968alid_a n) X)))->(forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) ((image_2063119815iple_a (fun (Pn:pname)=> (((hoare_1766022166iple_a (p Pn)) (body Pn)) (q Pn)))) procs))->((hoare_1462269968alid_a n) X))))']
% Parameter x_a:Type.
% Parameter com:Type.
% Parameter pname:Type.
% Parameter state:Type.
% Parameter hoare_1775062406iple_a:Type.
% Parameter hoare_1167836817_state:Type.
% Parameter nat:Type.
% Parameter option_com:Type.
% Parameter big_la1126801287name_o:(((pname->Prop)->Prop)->(pname->Prop)).
% Parameter big_la447547205le_a_o:(((hoare_1775062406iple_a->Prop)->Prop)->(hoare_1775062406iple_a->Prop)).
% Parameter big_la831793456tate_o:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop)).
% Parameter big_la1690136417_fin_o:((Prop->Prop)->Prop).
% Parameter big_la1286884090name_o:(((pname->Prop)->Prop)->(pname->Prop)).
% Parameter big_la1843772984le_a_o:(((hoare_1775062406iple_a->Prop)->Prop)->(hoare_1775062406iple_a->Prop)).
% Parameter big_la1138507389tate_o:(((hoare_1167836817_state->Prop)->Prop)->(hoare_1167836817_state->Prop)).
% Parameter big_la727467310_fin_o:((Prop->Prop)->Prop).
% Parameter body_1:(pname->option_com).
% Parameter body:(pname->com).
% Parameter cond:((state->Prop)->(com->(com->com))).
% Parameter skip:com.
% Parameter semi:(com->(com->com)).
% Parameter while:((state->Prop)->(com->com)).
% Parameter com_size:(com->nat).
% Parameter finite297249702name_o:(((pname->Prop)->Prop)->Prop).
% Parameter finite789576932le_a_o:(((hoare_1775062406iple_a->Prop)->Prop)->Prop).
% Parameter finite1380128977tate_o:(((hoare_1167836817_state->Prop)->Prop)->Prop).
% Parameter finite_finite_o:((Prop->Prop)->Prop).
% Parameter finite_finite_pname:((pname->Prop)->Prop).
% Parameter finite2063573081iple_a:((hoare_1775062406iple_a->Prop)->Prop).
% Parameter finite1084549118_state:((hoare_1167836817_state->Prop)->Prop).
% Parameter finite1805141964_pname:(((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop)))->((pname->(hoare_1775062406iple_a->Prop))->((hoare_1775062406iple_a->Prop)->((pname->Prop)->(hoare_1775062406iple_a->Prop))))).
% Parameter finite1068437657_pname:(((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop)))->((pname->(hoare_1167836817_state->Prop))->((hoare_1167836817_state->Prop)->((pname->Prop)->(hoare_1167836817_state->Prop))))).
% Parameter finite1282449217_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)).
% Parameter finite2078349315iple_a:((hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))->(((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)->Prop)).
% Parameter finite1074406356_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop)).
% Parameter finite89670078_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)).
% Parameter finite1358382848iple_a:((hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))->(((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)->Prop)).
% Parameter finite806517911_state:((hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))->(((hoare_1167836817_state->Prop)->hoare_1167836817_state)->Prop)).
% Parameter minus_minus_pname_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter minus_1944206118le_a_o:((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop))).
% Parameter minus_2107060239tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))).
% Parameter minus_minus_nat:(nat->(nat->nat)).
% Parameter one_one_nat:nat.
% Parameter plus_plus_nat:(nat->(nat->nat)).
% Parameter zero_zero_nat:nat.
% Parameter the_pname:((pname->Prop)->pname).
% Parameter the_Ho1155011127iple_a:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a).
% Parameter the_Ho310147232_state:((hoare_1167836817_state->Prop)->hoare_1167836817_state).
% Parameter hoare_Mirabelle_MGT:(com->hoare_1167836817_state).
% Parameter hoare_1508237396rivs_a:((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->Prop)).
% Parameter hoare_123228589_state:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)).
% Parameter hoare_1846070742lids_a:((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->Prop)).
% Parameter hoare_529639851_state:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->Prop)).
% Parameter hoare_1766022166iple_a:((x_a->(state->Prop))->(com->((x_a->(state->Prop))->hoare_1775062406iple_a))).
% Parameter hoare_908217195_state:((state->(state->Prop))->(com->((state->(state->Prop))->hoare_1167836817_state))).
% Parameter hoare_1118907895size_a:((x_a->nat)->(hoare_1775062406iple_a->nat)).
% Parameter hoare_545207370_state:((state->nat)->(hoare_1167836817_state->nat)).
% Parameter hoare_1462269968alid_a:(nat->(hoare_1775062406iple_a->Prop)).
% Parameter hoare_56934129_state:(nat->(hoare_1167836817_state->Prop)).
% Parameter if_Hoa1047340790iple_a:(Prop->(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))).
% Parameter if_Hoa833675553_state:(Prop->(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))).
% Parameter semila2013987940me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter semila1691990438_a_o_o:(((hoare_1775062406iple_a->Prop)->Prop)->(((hoare_1775062406iple_a->Prop)->Prop)->((hoare_1775062406iple_a->Prop)->Prop))).
% Parameter semila1758709489te_o_o:(((hoare_1167836817_state->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop))).
% Parameter semila232696320nf_o_o:((Prop->Prop)->((Prop->Prop)->(Prop->Prop))).
% Parameter semila1673364395name_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter semila966743401le_a_o:((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop))).
% Parameter semila179895820tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))).
% Parameter semila854092349_inf_o:(Prop->(Prop->Prop)).
% Parameter semila181081674me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter semila2069193356_a_o_o:(((hoare_1775062406iple_a->Prop)->Prop)->(((hoare_1775062406iple_a->Prop)->Prop)->((hoare_1775062406iple_a->Prop)->Prop))).
% Parameter semila866907787te_o_o:(((hoare_1167836817_state->Prop)->Prop)->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop))).
% Parameter semila2062604954up_o_o:((Prop->Prop)->((Prop->Prop)->(Prop->Prop))).
% Parameter semila1780557381name_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter semila13410563le_a_o:((hoare_1775062406iple_a->Prop)->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop))).
% Parameter semila1172322802tate_o:((hoare_1167836817_state->Prop)->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))).
% Parameter semila10642723_sup_o:(Prop->(Prop->Prop)).
% Parameter suc:(nat->nat).
% Parameter nat_case_nat:(nat->((nat->nat)->(nat->nat))).
% Parameter size_size_com:(com->nat).
% Parameter size_s724313756iple_a:(hoare_1775062406iple_a->nat).
% Parameter size_s645941755_state:(hoare_1167836817_state->nat).
% Parameter evalc:(com->(state->(state->Prop))).
% Parameter evaln:(com->(state->(nat->(state->Prop)))).
% Parameter the_com:(option_com->com).
% Parameter bot_bot_pname_o_o:((pname->Prop)->Prop).
% Parameter bot_bo1976773294_a_o_o:((hoare_1775062406iple_a->Prop)->Prop).
% Parameter bot_bo691907561te_o_o:((hoare_1167836817_state->Prop)->Prop).
% Parameter bot_bot_o_o:(Prop->Prop).
% Parameter bot_bot_pname_o:(pname->Prop).
% Parameter bot_bo751897185le_a_o:(hoare_1775062406iple_a->Prop).
% Parameter bot_bo70021908tate_o:(hoare_1167836817_state->Prop).
% Parameter bot_bot_o:Prop.
% Parameter bot_bot_nat:nat.
% Parameter collect_pname:((pname->Prop)->(pname->Prop)).
% Parameter collec676402587iple_a:((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->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_2014247585le_a_o:(((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop))->(((hoare_1775062406iple_a->Prop)->Prop)->((hoare_1775062406iple_a->Prop)->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_o_o:((Prop->Prop)->((Prop->Prop)->(Prop->Prop))).
% Parameter image_pname_pname:((pname->pname)->((pname->Prop)->(pname->Prop))).
% Parameter image_2063119815iple_a:((pname->hoare_1775062406iple_a)->((pname->Prop)->(hoare_1775062406iple_a->Prop))).
% Parameter image_575578384_state:((pname->hoare_1167836817_state)->((pname->Prop)->(hoare_1167836817_state->Prop))).
% Parameter image_51246659_pname:((hoare_1775062406iple_a->pname)->((hoare_1775062406iple_a->Prop)->(pname->Prop))).
% Parameter image_1170193413iple_a:((hoare_1775062406iple_a->hoare_1775062406iple_a)->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop))).
% Parameter image_1021683026_state:((hoare_1775062406iple_a->hoare_1167836817_state)->((hoare_1775062406iple_a->Prop)->(hoare_1167836817_state->Prop))).
% Parameter image_1802845250iple_a:((hoare_1167836817_state->hoare_1775062406iple_a)->((hoare_1167836817_state->Prop)->(hoare_1775062406iple_a->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 insert1210049533le_a_o:((hoare_1775062406iple_a->Prop)->(((hoare_1775062406iple_a->Prop)->Prop)->((hoare_1775062406iple_a->Prop)->Prop))).
% Parameter insert999278200tate_o:((hoare_1167836817_state->Prop)->(((hoare_1167836817_state->Prop)->Prop)->((hoare_1167836817_state->Prop)->Prop))).
% Parameter insert_o:(Prop->((Prop->Prop)->(Prop->Prop))).
% Parameter insert_pname:(pname->((pname->Prop)->(pname->Prop))).
% Parameter insert1281456128iple_a:(hoare_1775062406iple_a->((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop))).
% Parameter insert2134838167_state:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))).
% Parameter the_elem_pname:((pname->Prop)->pname).
% Parameter the_el1844711461iple_a:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a).
% Parameter the_el323660082_state:((hoare_1167836817_state->Prop)->hoare_1167836817_state).
% Parameter fequal_pname:(pname->(pname->Prop)).
% Parameter fequal_state:(state->(state->Prop)).
% Parameter fequal1288209029iple_a:(hoare_1775062406iple_a->(hoare_1775062406iple_a->Prop)).
% Parameter fequal1831255762_state:(hoare_1167836817_state->(hoare_1167836817_state->Prop)).
% Parameter member_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->Prop)).
% Parameter member1207314404le_a_o:((hoare_1775062406iple_a->Prop)->(((hoare_1775062406iple_a->Prop)->Prop)->Prop)).
% Parameter member864234961tate_o:((hoare_1167836817_state->Prop)->(((hoare_1167836817_state->Prop)->Prop)->Prop)).
% Parameter member_o:(Prop->((Prop->Prop)->Prop)).
% Parameter member_pname:(pname->((pname->Prop)->Prop)).
% Parameter member2122167641iple_a:(hoare_1775062406iple_a->((hoare_1775062406iple_a->Prop)->Prop)).
% Parameter member2058392318_state:(hoare_1167836817_state->((hoare_1167836817_state->Prop)->Prop)).
% Parameter g:(hoare_1775062406iple_a->Prop).
% Parameter p:(pname->(x_a->(state->Prop))).
% Parameter procs:(pname->Prop).
% Parameter q:(pname->(x_a->(state->Prop))).
% Parameter n:nat.
% Axiom fact_0_triple_Oinject:(forall (Fun1_4:(x_a->(state->Prop))) (Com:com) (Fun2_4:(x_a->(state->Prop))) (Fun1_3:(x_a->(state->Prop))) (Com_1:com) (Fun2_3:(x_a->(state->Prop))), ((iff (((eq hoare_1775062406iple_a) (((hoare_1766022166iple_a Fun1_4) Com) Fun2_4)) (((hoare_1766022166iple_a Fun1_3) Com_1) Fun2_3))) ((and ((and (((eq (x_a->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com) Com_1))) (((eq (x_a->(state->Prop))) Fun2_4) Fun2_3)))).
% Axiom fact_1_triple_Oinject:(forall (Fun1_4:(state->(state->Prop))) (Com:com) (Fun2_4:(state->(state->Prop))) (Fun1_3:(state->(state->Prop))) (Com_1:com) (Fun2_3:(state->(state->Prop))), ((iff (((eq hoare_1167836817_state) (((hoare_908217195_state Fun1_4) Com) Fun2_4)) (((hoare_908217195_state Fun1_3) Com_1) Fun2_3))) ((and ((and (((eq (state->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com) Com_1))) (((eq (state->(state->Prop))) Fun2_4) Fun2_3)))).
% Axiom fact_2_hoare__valids__def:(forall (G_25:(hoare_1167836817_state->Prop)) (Ts_4:(hoare_1167836817_state->Prop)), ((iff ((hoare_529639851_state G_25) Ts_4)) (forall (N:nat), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) G_25)->((hoare_56934129_state N) X)))->(forall (X:hoare_1167836817_state), (((member2058392318_state X) Ts_4)->((hoare_56934129_state N) X))))))).
% Axiom fact_3_hoare__valids__def:(forall (G_25:(hoare_1775062406iple_a->Prop)) (Ts_4:(hoare_1775062406iple_a->Prop)), ((iff ((hoare_1846070742lids_a G_25) Ts_4)) (forall (N:nat), ((forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) G_25)->((hoare_1462269968alid_a N) X)))->(forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) Ts_4)->((hoare_1462269968alid_a N) X))))))).
% Axiom fact_4_hoare__derivs_OBody:(forall (G_24:(hoare_1167836817_state->Prop)) (P_37:(pname->(state->(state->Prop)))) (Q_20:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_24) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1))) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_37 P_10)) (the_com (body_1 P_10))) (Q_20 P_10)))) Procs_1))->((hoare_123228589_state G_24) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1)))).
% Axiom fact_5_hoare__derivs_OBody:(forall (G_24:(hoare_1775062406iple_a->Prop)) (P_37:(pname->(x_a->(state->Prop)))) (Q_20:(pname->(x_a->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_1508237396rivs_a ((semila13410563le_a_o G_24) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1))) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_37 P_10)) (the_com (body_1 P_10))) (Q_20 P_10)))) Procs_1))->((hoare_1508237396rivs_a G_24) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_37 P_10)) (body P_10)) (Q_20 P_10)))) Procs_1)))).
% Axiom fact_6_UnE:(forall (C_42:hoare_1167836817_state) (A_138:(hoare_1167836817_state->Prop)) (B_79:(hoare_1167836817_state->Prop)), (((member2058392318_state C_42) ((semila1172322802tate_o A_138) B_79))->((((member2058392318_state C_42) A_138)->False)->((member2058392318_state C_42) B_79)))).
% Axiom fact_7_UnE:(forall (C_42:hoare_1775062406iple_a) (A_138:(hoare_1775062406iple_a->Prop)) (B_79:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_42) ((semila13410563le_a_o A_138) B_79))->((((member2122167641iple_a C_42) A_138)->False)->((member2122167641iple_a C_42) B_79)))).
% Axiom fact_8_UnE:(forall (C_42:pname) (A_138:(pname->Prop)) (B_79:(pname->Prop)), (((member_pname C_42) ((semila1780557381name_o A_138) B_79))->((((member_pname C_42) A_138)->False)->((member_pname C_42) B_79)))).
% Axiom fact_9_sup1E:(forall (A_137:(hoare_1167836817_state->Prop)) (B_78:(hoare_1167836817_state->Prop)) (X_51:hoare_1167836817_state), ((((semila1172322802tate_o A_137) B_78) X_51)->(((A_137 X_51)->False)->(B_78 X_51)))).
% Axiom fact_10_sup1E:(forall (A_137:(pname->Prop)) (B_78:(pname->Prop)) (X_51:pname), ((((semila1780557381name_o A_137) B_78) X_51)->(((A_137 X_51)->False)->(B_78 X_51)))).
% Axiom fact_11_sup1E:(forall (A_137:(hoare_1775062406iple_a->Prop)) (B_78:(hoare_1775062406iple_a->Prop)) (X_51:hoare_1775062406iple_a), ((((semila13410563le_a_o A_137) B_78) X_51)->(((A_137 X_51)->False)->(B_78 X_51)))).
% Axiom fact_12_sup1CI:(forall (A_136:(hoare_1167836817_state->Prop)) (B_77:(hoare_1167836817_state->Prop)) (X_50:hoare_1167836817_state), ((((B_77 X_50)->False)->(A_136 X_50))->(((semila1172322802tate_o A_136) B_77) X_50))).
% Axiom fact_13_sup1CI:(forall (A_136:(pname->Prop)) (B_77:(pname->Prop)) (X_50:pname), ((((B_77 X_50)->False)->(A_136 X_50))->(((semila1780557381name_o A_136) B_77) X_50))).
% Axiom fact_14_sup1CI:(forall (A_136:(hoare_1775062406iple_a->Prop)) (B_77:(hoare_1775062406iple_a->Prop)) (X_50:hoare_1775062406iple_a), ((((B_77 X_50)->False)->(A_136 X_50))->(((semila13410563le_a_o A_136) B_77) X_50))).
% Axiom fact_15_UnCI:(forall (A_135:(hoare_1167836817_state->Prop)) (C_41:hoare_1167836817_state) (B_76:(hoare_1167836817_state->Prop)), (((((member2058392318_state C_41) B_76)->False)->((member2058392318_state C_41) A_135))->((member2058392318_state C_41) ((semila1172322802tate_o A_135) B_76)))).
% Axiom fact_16_UnCI:(forall (A_135:(hoare_1775062406iple_a->Prop)) (C_41:hoare_1775062406iple_a) (B_76:(hoare_1775062406iple_a->Prop)), (((((member2122167641iple_a C_41) B_76)->False)->((member2122167641iple_a C_41) A_135))->((member2122167641iple_a C_41) ((semila13410563le_a_o A_135) B_76)))).
% Axiom fact_17_UnCI:(forall (A_135:(pname->Prop)) (C_41:pname) (B_76:(pname->Prop)), (((((member_pname C_41) B_76)->False)->((member_pname C_41) A_135))->((member_pname C_41) ((semila1780557381name_o A_135) B_76)))).
% Axiom fact_18_image__eqI:(forall (A_134:(pname->Prop)) (B_75:hoare_1167836817_state) (F_41:(pname->hoare_1167836817_state)) (X_49:pname), ((((eq hoare_1167836817_state) B_75) (F_41 X_49))->(((member_pname X_49) A_134)->((member2058392318_state B_75) ((image_575578384_state F_41) A_134))))).
% Axiom fact_19_image__eqI:(forall (A_134:(hoare_1775062406iple_a->Prop)) (B_75:pname) (F_41:(hoare_1775062406iple_a->pname)) (X_49:hoare_1775062406iple_a), ((((eq pname) B_75) (F_41 X_49))->(((member2122167641iple_a X_49) A_134)->((member_pname B_75) ((image_51246659_pname F_41) A_134))))).
% Axiom fact_20_image__eqI:(forall (A_134:(pname->Prop)) (B_75:hoare_1775062406iple_a) (F_41:(pname->hoare_1775062406iple_a)) (X_49:pname), ((((eq hoare_1775062406iple_a) B_75) (F_41 X_49))->(((member_pname X_49) A_134)->((member2122167641iple_a B_75) ((image_2063119815iple_a F_41) A_134))))).
% Axiom fact_21_image__Un:(forall (F_40:(pname->hoare_1167836817_state)) (A_133:(pname->Prop)) (B_74:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_40) ((semila1780557381name_o A_133) B_74))) ((semila1172322802tate_o ((image_575578384_state F_40) A_133)) ((image_575578384_state F_40) B_74)))).
% Axiom fact_22_image__Un:(forall (F_40:(hoare_1775062406iple_a->hoare_1167836817_state)) (A_133:(hoare_1775062406iple_a->Prop)) (B_74:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_1021683026_state F_40) ((semila13410563le_a_o A_133) B_74))) ((semila1172322802tate_o ((image_1021683026_state F_40) A_133)) ((image_1021683026_state F_40) B_74)))).
% Axiom fact_23_image__Un:(forall (F_40:(hoare_1775062406iple_a->pname)) (A_133:(hoare_1775062406iple_a->Prop)) (B_74:(hoare_1775062406iple_a->Prop)), (((eq (pname->Prop)) ((image_51246659_pname F_40) ((semila13410563le_a_o A_133) B_74))) ((semila1780557381name_o ((image_51246659_pname F_40) A_133)) ((image_51246659_pname F_40) B_74)))).
% Axiom fact_24_image__Un:(forall (F_40:(hoare_1167836817_state->hoare_1775062406iple_a)) (A_133:(hoare_1167836817_state->Prop)) (B_74:(hoare_1167836817_state->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_1802845250iple_a F_40) ((semila1172322802tate_o A_133) B_74))) ((semila13410563le_a_o ((image_1802845250iple_a F_40) A_133)) ((image_1802845250iple_a F_40) B_74)))).
% Axiom fact_25_image__Un:(forall (F_40:(pname->hoare_1775062406iple_a)) (A_133:(pname->Prop)) (B_74:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_40) ((semila1780557381name_o A_133) B_74))) ((semila13410563le_a_o ((image_2063119815iple_a F_40) A_133)) ((image_2063119815iple_a F_40) B_74)))).
% Axiom fact_26_sup__fun__def:(forall (F_39:(hoare_1167836817_state->Prop)) (G_23:(hoare_1167836817_state->Prop)) (X:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_39) G_23) X)) ((semila10642723_sup_o (F_39 X)) (G_23 X)))).
% Axiom fact_27_sup__fun__def:(forall (F_39:(pname->Prop)) (G_23:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o F_39) G_23) X)) ((semila10642723_sup_o (F_39 X)) (G_23 X)))).
% Axiom fact_28_sup__fun__def:(forall (F_39:(hoare_1775062406iple_a->Prop)) (G_23:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), ((iff (((semila13410563le_a_o F_39) G_23) X)) ((semila10642723_sup_o (F_39 X)) (G_23 X)))).
% Axiom fact_29_sup__apply:(forall (F_38:(hoare_1167836817_state->Prop)) (G_22:(hoare_1167836817_state->Prop)) (X_48:hoare_1167836817_state), ((iff (((semila1172322802tate_o F_38) G_22) X_48)) ((semila10642723_sup_o (F_38 X_48)) (G_22 X_48)))).
% Axiom fact_30_sup__apply:(forall (F_38:(pname->Prop)) (G_22:(pname->Prop)) (X_48:pname), ((iff (((semila1780557381name_o F_38) G_22) X_48)) ((semila10642723_sup_o (F_38 X_48)) (G_22 X_48)))).
% Axiom fact_31_sup__apply:(forall (F_38:(hoare_1775062406iple_a->Prop)) (G_22:(hoare_1775062406iple_a->Prop)) (X_48:hoare_1775062406iple_a), ((iff (((semila13410563le_a_o F_38) G_22) X_48)) ((semila10642723_sup_o (F_38 X_48)) (G_22 X_48)))).
% Axiom fact_32_cut:(forall (G_21:(hoare_1167836817_state->Prop)) (G_20:(hoare_1167836817_state->Prop)) (Ts_3:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_20) Ts_3)->(((hoare_123228589_state G_21) G_20)->((hoare_123228589_state G_21) Ts_3)))).
% Axiom fact_33_cut:(forall (G_21:(hoare_1775062406iple_a->Prop)) (G_20:(hoare_1775062406iple_a->Prop)) (Ts_3:(hoare_1775062406iple_a->Prop)), (((hoare_1508237396rivs_a G_20) Ts_3)->(((hoare_1508237396rivs_a G_21) G_20)->((hoare_1508237396rivs_a G_21) Ts_3)))).
% Axiom fact_34_sup__assoc:(forall (X_47:(hoare_1167836817_state->Prop)) (Y_21:(hoare_1167836817_state->Prop)) (Z_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_47) Y_21)) Z_14)) ((semila1172322802tate_o X_47) ((semila1172322802tate_o Y_21) Z_14)))).
% Axiom fact_35_sup__assoc:(forall (X_47:(pname->Prop)) (Y_21:(pname->Prop)) (Z_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_47) Y_21)) Z_14)) ((semila1780557381name_o X_47) ((semila1780557381name_o Y_21) Z_14)))).
% Axiom fact_36_sup__assoc:(forall (X_47:Prop) (Y_21:Prop) (Z_14:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_47) Y_21)) Z_14)) ((semila10642723_sup_o X_47) ((semila10642723_sup_o Y_21) Z_14)))).
% Axiom fact_37_sup__assoc:(forall (X_47:(hoare_1775062406iple_a->Prop)) (Y_21:(hoare_1775062406iple_a->Prop)) (Z_14:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o X_47) Y_21)) Z_14)) ((semila13410563le_a_o X_47) ((semila13410563le_a_o Y_21) Z_14)))).
% Axiom fact_38_inf__sup__aci_I6_J:(forall (X_46:(hoare_1167836817_state->Prop)) (Y_20:(hoare_1167836817_state->Prop)) (Z_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o X_46) Y_20)) Z_13)) ((semila1172322802tate_o X_46) ((semila1172322802tate_o Y_20) Z_13)))).
% Axiom fact_39_inf__sup__aci_I6_J:(forall (X_46:(pname->Prop)) (Y_20:(pname->Prop)) (Z_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_46) Y_20)) Z_13)) ((semila1780557381name_o X_46) ((semila1780557381name_o Y_20) Z_13)))).
% Axiom fact_40_inf__sup__aci_I6_J:(forall (X_46:Prop) (Y_20:Prop) (Z_13:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_46) Y_20)) Z_13)) ((semila10642723_sup_o X_46) ((semila10642723_sup_o Y_20) Z_13)))).
% Axiom fact_41_inf__sup__aci_I6_J:(forall (X_46:(hoare_1775062406iple_a->Prop)) (Y_20:(hoare_1775062406iple_a->Prop)) (Z_13:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o X_46) Y_20)) Z_13)) ((semila13410563le_a_o X_46) ((semila13410563le_a_o Y_20) Z_13)))).
% Axiom fact_42_sup_Oassoc:(forall (A_132:(hoare_1167836817_state->Prop)) (B_73:(hoare_1167836817_state->Prop)) (C_40:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_132) B_73)) C_40)) ((semila1172322802tate_o A_132) ((semila1172322802tate_o B_73) C_40)))).
% Axiom fact_43_sup_Oassoc:(forall (A_132:(pname->Prop)) (B_73:(pname->Prop)) (C_40:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_132) B_73)) C_40)) ((semila1780557381name_o A_132) ((semila1780557381name_o B_73) C_40)))).
% Axiom fact_44_sup_Oassoc:(forall (A_132:Prop) (B_73:Prop) (C_40:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_132) B_73)) C_40)) ((semila10642723_sup_o A_132) ((semila10642723_sup_o B_73) C_40)))).
% Axiom fact_45_sup_Oassoc:(forall (A_132:(hoare_1775062406iple_a->Prop)) (B_73:(hoare_1775062406iple_a->Prop)) (C_40:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o A_132) B_73)) C_40)) ((semila13410563le_a_o A_132) ((semila13410563le_a_o B_73) C_40)))).
% Axiom fact_46_sup__left__commute:(forall (X_45:(hoare_1167836817_state->Prop)) (Y_19:(hoare_1167836817_state->Prop)) (Z_12:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_45) ((semila1172322802tate_o Y_19) Z_12))) ((semila1172322802tate_o Y_19) ((semila1172322802tate_o X_45) Z_12)))).
% Axiom fact_47_sup__left__commute:(forall (X_45:(pname->Prop)) (Y_19:(pname->Prop)) (Z_12:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_45) ((semila1780557381name_o Y_19) Z_12))) ((semila1780557381name_o Y_19) ((semila1780557381name_o X_45) Z_12)))).
% Axiom fact_48_sup__left__commute:(forall (X_45:Prop) (Y_19:Prop) (Z_12:Prop), ((iff ((semila10642723_sup_o X_45) ((semila10642723_sup_o Y_19) Z_12))) ((semila10642723_sup_o Y_19) ((semila10642723_sup_o X_45) Z_12)))).
% Axiom fact_49_sup__left__commute:(forall (X_45:(hoare_1775062406iple_a->Prop)) (Y_19:(hoare_1775062406iple_a->Prop)) (Z_12:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_45) ((semila13410563le_a_o Y_19) Z_12))) ((semila13410563le_a_o Y_19) ((semila13410563le_a_o X_45) Z_12)))).
% Axiom fact_50_inf__sup__aci_I7_J:(forall (X_44:(hoare_1167836817_state->Prop)) (Y_18:(hoare_1167836817_state->Prop)) (Z_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_44) ((semila1172322802tate_o Y_18) Z_11))) ((semila1172322802tate_o Y_18) ((semila1172322802tate_o X_44) Z_11)))).
% Axiom fact_51_inf__sup__aci_I7_J:(forall (X_44:(pname->Prop)) (Y_18:(pname->Prop)) (Z_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_44) ((semila1780557381name_o Y_18) Z_11))) ((semila1780557381name_o Y_18) ((semila1780557381name_o X_44) Z_11)))).
% Axiom fact_52_inf__sup__aci_I7_J:(forall (X_44:Prop) (Y_18:Prop) (Z_11:Prop), ((iff ((semila10642723_sup_o X_44) ((semila10642723_sup_o Y_18) Z_11))) ((semila10642723_sup_o Y_18) ((semila10642723_sup_o X_44) Z_11)))).
% Axiom fact_53_inf__sup__aci_I7_J:(forall (X_44:(hoare_1775062406iple_a->Prop)) (Y_18:(hoare_1775062406iple_a->Prop)) (Z_11:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_44) ((semila13410563le_a_o Y_18) Z_11))) ((semila13410563le_a_o Y_18) ((semila13410563le_a_o X_44) Z_11)))).
% Axiom fact_54_sup_Oleft__commute:(forall (B_72:(hoare_1167836817_state->Prop)) (A_131:(hoare_1167836817_state->Prop)) (C_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o B_72) ((semila1172322802tate_o A_131) C_39))) ((semila1172322802tate_o A_131) ((semila1172322802tate_o B_72) C_39)))).
% Axiom fact_55_sup_Oleft__commute:(forall (B_72:(pname->Prop)) (A_131:(pname->Prop)) (C_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_72) ((semila1780557381name_o A_131) C_39))) ((semila1780557381name_o A_131) ((semila1780557381name_o B_72) C_39)))).
% Axiom fact_56_sup_Oleft__commute:(forall (B_72:Prop) (A_131:Prop) (C_39:Prop), ((iff ((semila10642723_sup_o B_72) ((semila10642723_sup_o A_131) C_39))) ((semila10642723_sup_o A_131) ((semila10642723_sup_o B_72) C_39)))).
% Axiom fact_57_sup_Oleft__commute:(forall (B_72:(hoare_1775062406iple_a->Prop)) (A_131:(hoare_1775062406iple_a->Prop)) (C_39:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o B_72) ((semila13410563le_a_o A_131) C_39))) ((semila13410563le_a_o A_131) ((semila13410563le_a_o B_72) C_39)))).
% Axiom fact_58_sup__left__idem:(forall (X_43:(hoare_1167836817_state->Prop)) (Y_17:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_43) ((semila1172322802tate_o X_43) Y_17))) ((semila1172322802tate_o X_43) Y_17))).
% Axiom fact_59_sup__left__idem:(forall (X_43:(pname->Prop)) (Y_17:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_43) ((semila1780557381name_o X_43) Y_17))) ((semila1780557381name_o X_43) Y_17))).
% Axiom fact_60_sup__left__idem:(forall (X_43:Prop) (Y_17:Prop), ((iff ((semila10642723_sup_o X_43) ((semila10642723_sup_o X_43) Y_17))) ((semila10642723_sup_o X_43) Y_17))).
% Axiom fact_61_sup__left__idem:(forall (X_43:(hoare_1775062406iple_a->Prop)) (Y_17:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_43) ((semila13410563le_a_o X_43) Y_17))) ((semila13410563le_a_o X_43) Y_17))).
% Axiom fact_62_inf__sup__aci_I8_J:(forall (X_42:(hoare_1167836817_state->Prop)) (Y_16:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_42) ((semila1172322802tate_o X_42) Y_16))) ((semila1172322802tate_o X_42) Y_16))).
% Axiom fact_63_inf__sup__aci_I8_J:(forall (X_42:(pname->Prop)) (Y_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_42) ((semila1780557381name_o X_42) Y_16))) ((semila1780557381name_o X_42) Y_16))).
% Axiom fact_64_inf__sup__aci_I8_J:(forall (X_42:Prop) (Y_16:Prop), ((iff ((semila10642723_sup_o X_42) ((semila10642723_sup_o X_42) Y_16))) ((semila10642723_sup_o X_42) Y_16))).
% Axiom fact_65_inf__sup__aci_I8_J:(forall (X_42:(hoare_1775062406iple_a->Prop)) (Y_16:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_42) ((semila13410563le_a_o X_42) Y_16))) ((semila13410563le_a_o X_42) Y_16))).
% Axiom fact_66_sup_Oleft__idem:(forall (A_130:(hoare_1167836817_state->Prop)) (B_71:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_130) ((semila1172322802tate_o A_130) B_71))) ((semila1172322802tate_o A_130) B_71))).
% Axiom fact_67_sup_Oleft__idem:(forall (A_130:(pname->Prop)) (B_71:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_130) ((semila1780557381name_o A_130) B_71))) ((semila1780557381name_o A_130) B_71))).
% Axiom fact_68_sup_Oleft__idem:(forall (A_130:Prop) (B_71:Prop), ((iff ((semila10642723_sup_o A_130) ((semila10642723_sup_o A_130) B_71))) ((semila10642723_sup_o A_130) B_71))).
% Axiom fact_69_sup_Oleft__idem:(forall (A_130:(hoare_1775062406iple_a->Prop)) (B_71:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_130) ((semila13410563le_a_o A_130) B_71))) ((semila13410563le_a_o A_130) B_71))).
% Axiom fact_70_sup__commute:(forall (X_41:(hoare_1167836817_state->Prop)) (Y_15:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_41) Y_15)) ((semila1172322802tate_o Y_15) X_41))).
% Axiom fact_71_sup__commute:(forall (X_41:(pname->Prop)) (Y_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_41) Y_15)) ((semila1780557381name_o Y_15) X_41))).
% Axiom fact_72_sup__commute:(forall (X_41:Prop) (Y_15:Prop), ((iff ((semila10642723_sup_o X_41) Y_15)) ((semila10642723_sup_o Y_15) X_41))).
% Axiom fact_73_sup__commute:(forall (X_41:(hoare_1775062406iple_a->Prop)) (Y_15:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_41) Y_15)) ((semila13410563le_a_o Y_15) X_41))).
% Axiom fact_74_inf__sup__aci_I5_J:(forall (X_40:(hoare_1167836817_state->Prop)) (Y_14:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_40) Y_14)) ((semila1172322802tate_o Y_14) X_40))).
% Axiom fact_75_inf__sup__aci_I5_J:(forall (X_40:(pname->Prop)) (Y_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_40) Y_14)) ((semila1780557381name_o Y_14) X_40))).
% Axiom fact_76_inf__sup__aci_I5_J:(forall (X_40:Prop) (Y_14:Prop), ((iff ((semila10642723_sup_o X_40) Y_14)) ((semila10642723_sup_o Y_14) X_40))).
% Axiom fact_77_inf__sup__aci_I5_J:(forall (X_40:(hoare_1775062406iple_a->Prop)) (Y_14:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_40) Y_14)) ((semila13410563le_a_o Y_14) X_40))).
% Axiom fact_78_sup_Ocommute:(forall (A_129:(hoare_1167836817_state->Prop)) (B_70:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_129) B_70)) ((semila1172322802tate_o B_70) A_129))).
% Axiom fact_79_sup_Ocommute:(forall (A_129:(pname->Prop)) (B_70:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_129) B_70)) ((semila1780557381name_o B_70) A_129))).
% Axiom fact_80_sup_Ocommute:(forall (A_129:Prop) (B_70:Prop), ((iff ((semila10642723_sup_o A_129) B_70)) ((semila10642723_sup_o B_70) A_129))).
% Axiom fact_81_sup_Ocommute:(forall (A_129:(hoare_1775062406iple_a->Prop)) (B_70:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_129) B_70)) ((semila13410563le_a_o B_70) A_129))).
% Axiom fact_82_sup__idem:(forall (X_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_39) X_39)) X_39)).
% Axiom fact_83_sup__idem:(forall (X_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_39) X_39)) X_39)).
% Axiom fact_84_sup__idem:(forall (X_39:Prop), ((iff ((semila10642723_sup_o X_39) X_39)) X_39)).
% Axiom fact_85_sup__idem:(forall (X_39:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_39) X_39)) X_39)).
% Axiom fact_86_sup_Oidem:(forall (A_128:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_128) A_128)) A_128)).
% Axiom fact_87_sup_Oidem:(forall (A_128:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_128) A_128)) A_128)).
% Axiom fact_88_sup_Oidem:(forall (A_128:Prop), ((iff ((semila10642723_sup_o A_128) A_128)) A_128)).
% Axiom fact_89_sup_Oidem:(forall (A_128:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_128) A_128)) A_128)).
% Axiom fact_90_rev__image__eqI:(forall (B_69:hoare_1167836817_state) (F_37:(pname->hoare_1167836817_state)) (X_38:pname) (A_127:(pname->Prop)), (((member_pname X_38) A_127)->((((eq hoare_1167836817_state) B_69) (F_37 X_38))->((member2058392318_state B_69) ((image_575578384_state F_37) A_127))))).
% Axiom fact_91_rev__image__eqI:(forall (B_69:pname) (F_37:(hoare_1775062406iple_a->pname)) (X_38:hoare_1775062406iple_a) (A_127:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a X_38) A_127)->((((eq pname) B_69) (F_37 X_38))->((member_pname B_69) ((image_51246659_pname F_37) A_127))))).
% Axiom fact_92_rev__image__eqI:(forall (B_69:hoare_1775062406iple_a) (F_37:(pname->hoare_1775062406iple_a)) (X_38:pname) (A_127:(pname->Prop)), (((member_pname X_38) A_127)->((((eq hoare_1775062406iple_a) B_69) (F_37 X_38))->((member2122167641iple_a B_69) ((image_2063119815iple_a F_37) A_127))))).
% Axiom fact_93_imageI:(forall (F_36:(pname->hoare_1167836817_state)) (X_37:pname) (A_126:(pname->Prop)), (((member_pname X_37) A_126)->((member2058392318_state (F_36 X_37)) ((image_575578384_state F_36) A_126)))).
% Axiom fact_94_imageI:(forall (F_36:(hoare_1775062406iple_a->pname)) (X_37:hoare_1775062406iple_a) (A_126:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a X_37) A_126)->((member_pname (F_36 X_37)) ((image_51246659_pname F_36) A_126)))).
% Axiom fact_95_imageI:(forall (F_36:(pname->hoare_1775062406iple_a)) (X_37:pname) (A_126:(pname->Prop)), (((member_pname X_37) A_126)->((member2122167641iple_a (F_36 X_37)) ((image_2063119815iple_a F_36) A_126)))).
% Axiom fact_96_image__iff:(forall (Z_10:hoare_1167836817_state) (F_35:(pname->hoare_1167836817_state)) (A_125:(pname->Prop)), ((iff ((member2058392318_state Z_10) ((image_575578384_state F_35) A_125))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_125)) (((eq hoare_1167836817_state) Z_10) (F_35 X))))))).
% Axiom fact_97_image__iff:(forall (Z_10:hoare_1775062406iple_a) (F_35:(pname->hoare_1775062406iple_a)) (A_125:(pname->Prop)), ((iff ((member2122167641iple_a Z_10) ((image_2063119815iple_a F_35) A_125))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_125)) (((eq hoare_1775062406iple_a) Z_10) (F_35 X))))))).
% Axiom fact_98_UnI2:(forall (A_124:(hoare_1167836817_state->Prop)) (C_38:hoare_1167836817_state) (B_68:(hoare_1167836817_state->Prop)), (((member2058392318_state C_38) B_68)->((member2058392318_state C_38) ((semila1172322802tate_o A_124) B_68)))).
% Axiom fact_99_UnI2:(forall (A_124:(hoare_1775062406iple_a->Prop)) (C_38:hoare_1775062406iple_a) (B_68:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_38) B_68)->((member2122167641iple_a C_38) ((semila13410563le_a_o A_124) B_68)))).
% Axiom fact_100_UnI2:(forall (A_124:(pname->Prop)) (C_38:pname) (B_68:(pname->Prop)), (((member_pname C_38) B_68)->((member_pname C_38) ((semila1780557381name_o A_124) B_68)))).
% Axiom fact_101_UnI1:(forall (B_67:(hoare_1167836817_state->Prop)) (C_37:hoare_1167836817_state) (A_123:(hoare_1167836817_state->Prop)), (((member2058392318_state C_37) A_123)->((member2058392318_state C_37) ((semila1172322802tate_o A_123) B_67)))).
% Axiom fact_102_UnI1:(forall (B_67:(hoare_1775062406iple_a->Prop)) (C_37:hoare_1775062406iple_a) (A_123:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_37) A_123)->((member2122167641iple_a C_37) ((semila13410563le_a_o A_123) B_67)))).
% Axiom fact_103_UnI1:(forall (B_67:(pname->Prop)) (C_37:pname) (A_123:(pname->Prop)), (((member_pname C_37) A_123)->((member_pname C_37) ((semila1780557381name_o A_123) B_67)))).
% Axiom fact_104_sup1I2:(forall (A_122:(hoare_1167836817_state->Prop)) (B_66:(hoare_1167836817_state->Prop)) (X_36:hoare_1167836817_state), ((B_66 X_36)->(((semila1172322802tate_o A_122) B_66) X_36))).
% Axiom fact_105_sup1I2:(forall (A_122:(pname->Prop)) (B_66:(pname->Prop)) (X_36:pname), ((B_66 X_36)->(((semila1780557381name_o A_122) B_66) X_36))).
% Axiom fact_106_sup1I2:(forall (A_122:(hoare_1775062406iple_a->Prop)) (B_66:(hoare_1775062406iple_a->Prop)) (X_36:hoare_1775062406iple_a), ((B_66 X_36)->(((semila13410563le_a_o A_122) B_66) X_36))).
% Axiom fact_107_sup1I1:(forall (B_65:(hoare_1167836817_state->Prop)) (A_121:(hoare_1167836817_state->Prop)) (X_35:hoare_1167836817_state), ((A_121 X_35)->(((semila1172322802tate_o A_121) B_65) X_35))).
% Axiom fact_108_sup1I1:(forall (B_65:(pname->Prop)) (A_121:(pname->Prop)) (X_35:pname), ((A_121 X_35)->(((semila1780557381name_o A_121) B_65) X_35))).
% Axiom fact_109_sup1I1:(forall (B_65:(hoare_1775062406iple_a->Prop)) (A_121:(hoare_1775062406iple_a->Prop)) (X_35:hoare_1775062406iple_a), ((A_121 X_35)->(((semila13410563le_a_o A_121) B_65) X_35))).
% Axiom fact_110_ball__Un:(forall (P_36:(hoare_1167836817_state->Prop)) (A_120:(hoare_1167836817_state->Prop)) (B_64:(hoare_1167836817_state->Prop)), ((iff (forall (X:hoare_1167836817_state), (((member2058392318_state X) ((semila1172322802tate_o A_120) B_64))->(P_36 X)))) ((and (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_120)->(P_36 X)))) (forall (X:hoare_1167836817_state), (((member2058392318_state X) B_64)->(P_36 X)))))).
% Axiom fact_111_ball__Un:(forall (P_36:(pname->Prop)) (A_120:(pname->Prop)) (B_64:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) ((semila1780557381name_o A_120) B_64))->(P_36 X)))) ((and (forall (X:pname), (((member_pname X) A_120)->(P_36 X)))) (forall (X:pname), (((member_pname X) B_64)->(P_36 X)))))).
% Axiom fact_112_ball__Un:(forall (P_36:(hoare_1775062406iple_a->Prop)) (A_120:(hoare_1775062406iple_a->Prop)) (B_64:(hoare_1775062406iple_a->Prop)), ((iff (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) ((semila13410563le_a_o A_120) B_64))->(P_36 X)))) ((and (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) A_120)->(P_36 X)))) (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) B_64)->(P_36 X)))))).
% Axiom fact_113_bex__Un:(forall (P_35:(hoare_1167836817_state->Prop)) (A_119:(hoare_1167836817_state->Prop)) (B_63:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) ((semila1172322802tate_o A_119) B_63))) (P_35 X))))) ((or ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) A_119)) (P_35 X))))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((and ((member2058392318_state X) B_63)) (P_35 X))))))).
% Axiom fact_114_bex__Un:(forall (P_35:(pname->Prop)) (A_119:(pname->Prop)) (B_63:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((and ((member_pname X) ((semila1780557381name_o A_119) B_63))) (P_35 X))))) ((or ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_119)) (P_35 X))))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) B_63)) (P_35 X))))))).
% Axiom fact_115_bex__Un:(forall (P_35:(hoare_1775062406iple_a->Prop)) (A_119:(hoare_1775062406iple_a->Prop)) (B_63:(hoare_1775062406iple_a->Prop)), ((iff ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) ((semila13410563le_a_o A_119) B_63))) (P_35 X))))) ((or ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) A_119)) (P_35 X))))) ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) B_63)) (P_35 X))))))).
% Axiom fact_116_Un__assoc:(forall (A_118:(hoare_1167836817_state->Prop)) (B_62:(hoare_1167836817_state->Prop)) (C_36:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o A_118) B_62)) C_36)) ((semila1172322802tate_o A_118) ((semila1172322802tate_o B_62) C_36)))).
% Axiom fact_117_Un__assoc:(forall (A_118:(pname->Prop)) (B_62:(pname->Prop)) (C_36:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_118) B_62)) C_36)) ((semila1780557381name_o A_118) ((semila1780557381name_o B_62) C_36)))).
% Axiom fact_118_Un__assoc:(forall (A_118:(hoare_1775062406iple_a->Prop)) (B_62:(hoare_1775062406iple_a->Prop)) (C_36:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o A_118) B_62)) C_36)) ((semila13410563le_a_o A_118) ((semila13410563le_a_o B_62) C_36)))).
% Axiom fact_119_Un__iff:(forall (C_35:hoare_1167836817_state) (A_117:(hoare_1167836817_state->Prop)) (B_61:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state C_35) ((semila1172322802tate_o A_117) B_61))) ((or ((member2058392318_state C_35) A_117)) ((member2058392318_state C_35) B_61)))).
% Axiom fact_120_Un__iff:(forall (C_35:hoare_1775062406iple_a) (A_117:(hoare_1775062406iple_a->Prop)) (B_61:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a C_35) ((semila13410563le_a_o A_117) B_61))) ((or ((member2122167641iple_a C_35) A_117)) ((member2122167641iple_a C_35) B_61)))).
% Axiom fact_121_Un__iff:(forall (C_35:pname) (A_117:(pname->Prop)) (B_61:(pname->Prop)), ((iff ((member_pname C_35) ((semila1780557381name_o A_117) B_61))) ((or ((member_pname C_35) A_117)) ((member_pname C_35) B_61)))).
% Axiom fact_122_Un__left__commute:(forall (A_116:(hoare_1167836817_state->Prop)) (B_60:(hoare_1167836817_state->Prop)) (C_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_116) ((semila1172322802tate_o B_60) C_34))) ((semila1172322802tate_o B_60) ((semila1172322802tate_o A_116) C_34)))).
% Axiom fact_123_Un__left__commute:(forall (A_116:(pname->Prop)) (B_60:(pname->Prop)) (C_34:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_116) ((semila1780557381name_o B_60) C_34))) ((semila1780557381name_o B_60) ((semila1780557381name_o A_116) C_34)))).
% Axiom fact_124_Un__left__commute:(forall (A_116:(hoare_1775062406iple_a->Prop)) (B_60:(hoare_1775062406iple_a->Prop)) (C_34:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_116) ((semila13410563le_a_o B_60) C_34))) ((semila13410563le_a_o B_60) ((semila13410563le_a_o A_116) C_34)))).
% Axiom fact_125_Un__left__absorb:(forall (A_115:(hoare_1167836817_state->Prop)) (B_59:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_115) ((semila1172322802tate_o A_115) B_59))) ((semila1172322802tate_o A_115) B_59))).
% Axiom fact_126_Un__left__absorb:(forall (A_115:(pname->Prop)) (B_59:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_115) ((semila1780557381name_o A_115) B_59))) ((semila1780557381name_o A_115) B_59))).
% Axiom fact_127_Un__left__absorb:(forall (A_115:(hoare_1775062406iple_a->Prop)) (B_59:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_115) ((semila13410563le_a_o A_115) B_59))) ((semila13410563le_a_o A_115) B_59))).
% Axiom fact_128_Un__commute:(forall (A_114:(hoare_1167836817_state->Prop)) (B_58:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_114) B_58)) ((semila1172322802tate_o B_58) A_114))).
% Axiom fact_129_Un__commute:(forall (A_114:(pname->Prop)) (B_58:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_114) B_58)) ((semila1780557381name_o B_58) A_114))).
% Axiom fact_130_Un__commute:(forall (A_114:(hoare_1775062406iple_a->Prop)) (B_58:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_114) B_58)) ((semila13410563le_a_o B_58) A_114))).
% Axiom fact_131_Un__def:(forall (A_113:(hoare_1167836817_state->Prop)) (B_57:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_113) B_57)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or ((member2058392318_state X) A_113)) ((member2058392318_state X) B_57)))))).
% Axiom fact_132_Un__def:(forall (A_113:(hoare_1775062406iple_a->Prop)) (B_57:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_113) B_57)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or ((member2122167641iple_a X) A_113)) ((member2122167641iple_a X) B_57)))))).
% Axiom fact_133_Un__def:(forall (A_113:(pname->Prop)) (B_57:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_113) B_57)) (collect_pname (fun (X:pname)=> ((or ((member_pname X) A_113)) ((member_pname X) B_57)))))).
% Axiom fact_134_Un__absorb:(forall (A_112:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_112) A_112)) A_112)).
% Axiom fact_135_Un__absorb:(forall (A_112:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_112) A_112)) A_112)).
% Axiom fact_136_Un__absorb:(forall (A_112:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_112) A_112)) A_112)).
% Axiom fact_137_image__image:(forall (F_34:(hoare_1775062406iple_a->hoare_1167836817_state)) (G_19:(pname->hoare_1775062406iple_a)) (A_111:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_1021683026_state F_34) ((image_2063119815iple_a G_19) A_111))) ((image_575578384_state (fun (X:pname)=> (F_34 (G_19 X)))) A_111))).
% Axiom fact_138_image__image:(forall (F_34:(hoare_1167836817_state->hoare_1775062406iple_a)) (G_19:(pname->hoare_1167836817_state)) (A_111:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_1802845250iple_a F_34) ((image_575578384_state G_19) A_111))) ((image_2063119815iple_a (fun (X:pname)=> (F_34 (G_19 X)))) A_111))).
% Axiom fact_139_sup__Un__eq:(forall (R_2:(hoare_1167836817_state->Prop)) (S_6:(hoare_1167836817_state->Prop)) (X: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_6))) X)) ((member2058392318_state X) ((semila1172322802tate_o R_2) S_6)))).
% Axiom fact_140_sup__Un__eq:(forall (R_2:(hoare_1775062406iple_a->Prop)) (S_6:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), ((iff (((semila13410563le_a_o (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) R_2))) (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) S_6))) X)) ((member2122167641iple_a X) ((semila13410563le_a_o R_2) S_6)))).
% Axiom fact_141_sup__Un__eq:(forall (R_2:(pname->Prop)) (S_6:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o (fun (Y_2:pname)=> ((member_pname Y_2) R_2))) (fun (Y_2:pname)=> ((member_pname Y_2) S_6))) X)) ((member_pname X) ((semila1780557381name_o R_2) S_6)))).
% Axiom fact_142_Collect__disj__eq:(forall (P_34:(pname->Prop)) (Q_19:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((or (P_34 X)) (Q_19 X))))) ((semila1780557381name_o (collect_pname P_34)) (collect_pname Q_19)))).
% Axiom fact_143_Collect__disj__eq:(forall (P_34:(hoare_1167836817_state->Prop)) (Q_19:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or (P_34 X)) (Q_19 X))))) ((semila1172322802tate_o (collec1027672124_state P_34)) (collec1027672124_state Q_19)))).
% Axiom fact_144_Collect__disj__eq:(forall (P_34:(hoare_1775062406iple_a->Prop)) (Q_19:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or (P_34 X)) (Q_19 X))))) ((semila13410563le_a_o (collec676402587iple_a P_34)) (collec676402587iple_a Q_19)))).
% Axiom fact_145_imageE:(forall (B_56:pname) (F_33:(hoare_1775062406iple_a->pname)) (A_110:(hoare_1775062406iple_a->Prop)), (((member_pname B_56) ((image_51246659_pname F_33) A_110))->((forall (X:hoare_1775062406iple_a), ((((eq pname) B_56) (F_33 X))->(((member2122167641iple_a X) A_110)->False)))->False))).
% Axiom fact_146_imageE:(forall (B_56:hoare_1167836817_state) (F_33:(pname->hoare_1167836817_state)) (A_110:(pname->Prop)), (((member2058392318_state B_56) ((image_575578384_state F_33) A_110))->((forall (X:pname), ((((eq hoare_1167836817_state) B_56) (F_33 X))->(((member_pname X) A_110)->False)))->False))).
% Axiom fact_147_imageE:(forall (B_56:hoare_1775062406iple_a) (F_33:(pname->hoare_1775062406iple_a)) (A_110:(pname->Prop)), (((member2122167641iple_a B_56) ((image_2063119815iple_a F_33) A_110))->((forall (X:pname), ((((eq hoare_1775062406iple_a) B_56) (F_33 X))->(((member_pname X) A_110)->False)))->False))).
% Axiom fact_148_Body__triple__valid__Suc:(forall (N_8:nat) (P_33:(state->(state->Prop))) (Pn_6:pname) (Q_18:(state->(state->Prop))), ((iff ((hoare_56934129_state N_8) (((hoare_908217195_state P_33) (the_com (body_1 Pn_6))) Q_18))) ((hoare_56934129_state (suc N_8)) (((hoare_908217195_state P_33) (body Pn_6)) Q_18)))).
% Axiom fact_149_Body__triple__valid__Suc:(forall (N_8:nat) (P_33:(x_a->(state->Prop))) (Pn_6:pname) (Q_18:(x_a->(state->Prop))), ((iff ((hoare_1462269968alid_a N_8) (((hoare_1766022166iple_a P_33) (the_com (body_1 Pn_6))) Q_18))) ((hoare_1462269968alid_a (suc N_8)) (((hoare_1766022166iple_a P_33) (body Pn_6)) Q_18)))).
% Axiom fact_150_triple_Oexhaust:(forall (Y_13:hoare_1775062406iple_a), ((forall (Fun1_2:(x_a->(state->Prop))) (Com_4:com) (Fun2_2:(x_a->(state->Prop))), (not (((eq hoare_1775062406iple_a) Y_13) (((hoare_1766022166iple_a Fun1_2) Com_4) Fun2_2))))->False)).
% Axiom fact_151_triple_Oexhaust:(forall (Y_13:hoare_1167836817_state), ((forall (Fun1_2:(state->(state->Prop))) (Com_4:com) (Fun2_2:(state->(state->Prop))), (not (((eq hoare_1167836817_state) Y_13) (((hoare_908217195_state Fun1_2) Com_4) Fun2_2))))->False)).
% Axiom fact_152_Body1:(forall (Pn_5:pname) (G_18:(hoare_1167836817_state->Prop)) (P_32:(pname->(state->(state->Prop)))) (Q_17:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_123228589_state ((semila1172322802tate_o G_18) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_32 P_10)) (body P_10)) (Q_17 P_10)))) Procs))) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_32 P_10)) (the_com (body_1 P_10))) (Q_17 P_10)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_123228589_state G_18) ((insert2134838167_state (((hoare_908217195_state (P_32 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo70021908tate_o))))).
% Axiom fact_153_Body1:(forall (Pn_5:pname) (G_18:(hoare_1775062406iple_a->Prop)) (P_32:(pname->(x_a->(state->Prop)))) (Q_17:(pname->(x_a->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_1508237396rivs_a ((semila13410563le_a_o G_18) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_32 P_10)) (body P_10)) (Q_17 P_10)))) Procs))) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_32 P_10)) (the_com (body_1 P_10))) (Q_17 P_10)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_1508237396rivs_a G_18) ((insert1281456128iple_a (((hoare_1766022166iple_a (P_32 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo751897185le_a_o))))).
% Axiom fact_154_image__cong:(forall (F_32:(pname->hoare_1167836817_state)) (G_17:(pname->hoare_1167836817_state)) (M_2:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_2) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_1167836817_state) (F_32 X)) (G_17 X))))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_32) M_2)) ((image_575578384_state G_17) N_7))))).
% Axiom fact_155_image__cong:(forall (F_32:(pname->hoare_1775062406iple_a)) (G_17:(pname->hoare_1775062406iple_a)) (M_2:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_2) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_1775062406iple_a) (F_32 X)) (G_17 X))))->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_32) M_2)) ((image_2063119815iple_a G_17) N_7))))).
% Axiom fact_156_Body__triple__valid__0:(forall (P_31:(state->(state->Prop))) (Pn_4:pname) (Q_16:(state->(state->Prop))), ((hoare_56934129_state zero_zero_nat) (((hoare_908217195_state P_31) (body Pn_4)) Q_16))).
% Axiom fact_157_Body__triple__valid__0:(forall (P_31:(x_a->(state->Prop))) (Pn_4:pname) (Q_16:(x_a->(state->Prop))), ((hoare_1462269968alid_a zero_zero_nat) (((hoare_1766022166iple_a P_31) (body Pn_4)) Q_16))).
% Axiom fact_158_com_Osimps_I6_J:(forall (Pname:pname) (Pname_1:pname), ((iff (((eq com) (body Pname)) (body Pname_1))) (((eq pname) Pname) Pname_1))).
% Axiom fact_159_evalc_OBody:(forall (Pn_1:pname) (S0:state) (S1:state), ((((evalc (the_com (body_1 Pn_1))) S0) S1)->(((evalc (body Pn_1)) S0) S1))).
% Axiom fact_160_evalc__elim__cases_I6_J:(forall (P:pname) (S:state) (S1:state), ((((evalc (body P)) S) S1)->(((evalc (the_com (body_1 P))) S) S1))).
% Axiom fact_161_Sup__fin_Oidem:(forall (X_34:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_34) X_34)) X_34)).
% Axiom fact_162_Sup__fin_Oidem:(forall (X_34:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_34) X_34)) X_34)).
% Axiom fact_163_Sup__fin_Oidem:(forall (X_34:Prop), ((iff ((semila10642723_sup_o X_34) X_34)) X_34)).
% Axiom fact_164_Sup__fin_Oidem:(forall (X_34:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_34) X_34)) X_34)).
% Axiom fact_165_emptyE:(forall (A_109:hoare_1775062406iple_a), (((member2122167641iple_a A_109) bot_bo751897185le_a_o)->False)).
% Axiom fact_166_emptyE:(forall (A_109:hoare_1167836817_state), (((member2058392318_state A_109) bot_bo70021908tate_o)->False)).
% Axiom fact_167_emptyE:(forall (A_109:pname), (((member_pname A_109) bot_bot_pname_o)->False)).
% Axiom fact_168_insertE:(forall (A_108:hoare_1167836817_state) (B_55:hoare_1167836817_state) (A_107:(hoare_1167836817_state->Prop)), (((member2058392318_state A_108) ((insert2134838167_state B_55) A_107))->((not (((eq hoare_1167836817_state) A_108) B_55))->((member2058392318_state A_108) A_107)))).
% Axiom fact_169_insertE:(forall (A_108:hoare_1775062406iple_a) (B_55:hoare_1775062406iple_a) (A_107:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_108) ((insert1281456128iple_a B_55) A_107))->((not (((eq hoare_1775062406iple_a) A_108) B_55))->((member2122167641iple_a A_108) A_107)))).
% Axiom fact_170_insertE:(forall (A_108:pname) (B_55:pname) (A_107:(pname->Prop)), (((member_pname A_108) ((insert_pname B_55) A_107))->((not (((eq pname) A_108) B_55))->((member_pname A_108) A_107)))).
% Axiom fact_171_insertCI:(forall (B_54:hoare_1167836817_state) (A_106:hoare_1167836817_state) (B_53:(hoare_1167836817_state->Prop)), (((((member2058392318_state A_106) B_53)->False)->(((eq hoare_1167836817_state) A_106) B_54))->((member2058392318_state A_106) ((insert2134838167_state B_54) B_53)))).
% Axiom fact_172_insertCI:(forall (B_54:hoare_1775062406iple_a) (A_106:hoare_1775062406iple_a) (B_53:(hoare_1775062406iple_a->Prop)), (((((member2122167641iple_a A_106) B_53)->False)->(((eq hoare_1775062406iple_a) A_106) B_54))->((member2122167641iple_a A_106) ((insert1281456128iple_a B_54) B_53)))).
% Axiom fact_173_insertCI:(forall (B_54:pname) (A_106:pname) (B_53:(pname->Prop)), (((((member_pname A_106) B_53)->False)->(((eq pname) A_106) B_54))->((member_pname A_106) ((insert_pname B_54) B_53)))).
% Axiom fact_174_empty__not__insert:(forall (A_105:hoare_1167836817_state) (A_104:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((insert2134838167_state A_105) A_104)))).
% Axiom fact_175_empty__not__insert:(forall (A_105:hoare_1775062406iple_a) (A_104:(hoare_1775062406iple_a->Prop)), (not (((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) ((insert1281456128iple_a A_105) A_104)))).
% Axiom fact_176_empty__not__insert:(forall (A_105:pname) (A_104:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_105) A_104)))).
% Axiom fact_177_insert__not__empty:(forall (A_103:hoare_1167836817_state) (A_102:(hoare_1167836817_state->Prop)), (not (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_103) A_102)) bot_bo70021908tate_o))).
% Axiom fact_178_insert__not__empty:(forall (A_103:hoare_1775062406iple_a) (A_102:(hoare_1775062406iple_a->Prop)), (not (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_103) A_102)) bot_bo751897185le_a_o))).
% Axiom fact_179_insert__not__empty:(forall (A_103:pname) (A_102:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_103) A_102)) bot_bot_pname_o))).
% Axiom fact_180_bot__empty__eq:(forall (X:hoare_1775062406iple_a), ((iff (bot_bo751897185le_a_o X)) ((member2122167641iple_a X) bot_bo751897185le_a_o))).
% Axiom fact_181_bot__empty__eq:(forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) ((member2058392318_state X) bot_bo70021908tate_o))).
% Axiom fact_182_bot__empty__eq:(forall (X:pname), ((iff (bot_bot_pname_o X)) ((member_pname X) bot_bot_pname_o))).
% Axiom fact_183_empty__def:(((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> False))).
% Axiom fact_184_empty__def:(((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X:pname)=> False))).
% Axiom fact_185_empty__def:(((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state (fun (X:hoare_1167836817_state)=> False))).
% Axiom fact_186_insertI1:(forall (A_101:hoare_1167836817_state) (B_52:(hoare_1167836817_state->Prop)), ((member2058392318_state A_101) ((insert2134838167_state A_101) B_52))).
% Axiom fact_187_insertI1:(forall (A_101:hoare_1775062406iple_a) (B_52:(hoare_1775062406iple_a->Prop)), ((member2122167641iple_a A_101) ((insert1281456128iple_a A_101) B_52))).
% Axiom fact_188_insertI1:(forall (A_101:pname) (B_52:(pname->Prop)), ((member_pname A_101) ((insert_pname A_101) B_52))).
% Axiom fact_189_all__not__in__conv:(forall (A_100:(hoare_1775062406iple_a->Prop)), ((iff (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) A_100)->False))) (((eq (hoare_1775062406iple_a->Prop)) A_100) bot_bo751897185le_a_o))).
% Axiom fact_190_all__not__in__conv:(forall (A_100:(hoare_1167836817_state->Prop)), ((iff (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_100)->False))) (((eq (hoare_1167836817_state->Prop)) A_100) bot_bo70021908tate_o))).
% Axiom fact_191_all__not__in__conv:(forall (A_100:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) A_100)->False))) (((eq (pname->Prop)) A_100) bot_bot_pname_o))).
% Axiom fact_192_singleton__conv2:(forall (A_99:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fequal1831255762_state A_99))) ((insert2134838167_state A_99) bot_bo70021908tate_o))).
% Axiom fact_193_singleton__conv2:(forall (A_99:hoare_1775062406iple_a), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fequal1288209029iple_a A_99))) ((insert1281456128iple_a A_99) bot_bo751897185le_a_o))).
% Axiom fact_194_singleton__conv2:(forall (A_99:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_99))) ((insert_pname A_99) bot_bot_pname_o))).
% Axiom fact_195_ex__in__conv:(forall (A_98:(hoare_1775062406iple_a->Prop)), ((iff ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((member2122167641iple_a X) A_98)))) (not (((eq (hoare_1775062406iple_a->Prop)) A_98) bot_bo751897185le_a_o)))).
% Axiom fact_196_ex__in__conv:(forall (A_98:(hoare_1167836817_state->Prop)), ((iff ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((member2058392318_state X) A_98)))) (not (((eq (hoare_1167836817_state->Prop)) A_98) bot_bo70021908tate_o)))).
% Axiom fact_197_ex__in__conv:(forall (A_98:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((member_pname X) A_98)))) (not (((eq (pname->Prop)) A_98) bot_bot_pname_o)))).
% Axiom fact_198_singleton__conv:(forall (A_97:hoare_1167836817_state), (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X) A_97)))) ((insert2134838167_state A_97) bot_bo70021908tate_o))).
% Axiom fact_199_singleton__conv:(forall (A_97:hoare_1775062406iple_a), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> (((eq hoare_1775062406iple_a) X) A_97)))) ((insert1281456128iple_a A_97) bot_bo751897185le_a_o))).
% Axiom fact_200_singleton__conv:(forall (A_97:pname), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> (((eq pname) X) A_97)))) ((insert_pname A_97) bot_bot_pname_o))).
% Axiom fact_201_Collect__conv__if2:(forall (P_30:(hoare_1167836817_state->Prop)) (A_96:hoare_1167836817_state), ((and ((P_30 A_96)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_96) X)) (P_30 X))))) ((insert2134838167_state A_96) bot_bo70021908tate_o)))) (((P_30 A_96)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) A_96) X)) (P_30 X))))) bot_bo70021908tate_o)))).
% Axiom fact_202_Collect__conv__if2:(forall (P_30:(hoare_1775062406iple_a->Prop)) (A_96:hoare_1775062406iple_a), ((and ((P_30 A_96)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) A_96) X)) (P_30 X))))) ((insert1281456128iple_a A_96) bot_bo751897185le_a_o)))) (((P_30 A_96)->False)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) A_96) X)) (P_30 X))))) bot_bo751897185le_a_o)))).
% Axiom fact_203_Collect__conv__if2:(forall (P_30:(pname->Prop)) (A_96:pname), ((and ((P_30 A_96)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_96) X)) (P_30 X))))) ((insert_pname A_96) bot_bot_pname_o)))) (((P_30 A_96)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_96) X)) (P_30 X))))) bot_bot_pname_o)))).
% Axiom fact_204_Collect__conv__if:(forall (P_29:(hoare_1167836817_state->Prop)) (A_95:hoare_1167836817_state), ((and ((P_29 A_95)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X) A_95)) (P_29 X))))) ((insert2134838167_state A_95) bot_bo70021908tate_o)))) (((P_29 A_95)->False)->(((eq (hoare_1167836817_state->Prop)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((and (((eq hoare_1167836817_state) X) A_95)) (P_29 X))))) bot_bo70021908tate_o)))).
% Axiom fact_205_Collect__conv__if:(forall (P_29:(hoare_1775062406iple_a->Prop)) (A_95:hoare_1775062406iple_a), ((and ((P_29 A_95)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) X) A_95)) (P_29 X))))) ((insert1281456128iple_a A_95) bot_bo751897185le_a_o)))) (((P_29 A_95)->False)->(((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (((eq hoare_1775062406iple_a) X) A_95)) (P_29 X))))) bot_bo751897185le_a_o)))).
% Axiom fact_206_Collect__conv__if:(forall (P_29:(pname->Prop)) (A_95:pname), ((and ((P_29 A_95)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_95)) (P_29 X))))) ((insert_pname A_95) bot_bot_pname_o)))) (((P_29 A_95)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_95)) (P_29 X))))) bot_bot_pname_o)))).
% Axiom fact_207_empty__Collect__eq:(forall (P_28:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) (collec676402587iple_a P_28))) (forall (X:hoare_1775062406iple_a), ((P_28 X)->False)))).
% Axiom fact_208_empty__Collect__eq:(forall (P_28:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_28))) (forall (X:pname), ((P_28 X)->False)))).
% Axiom fact_209_empty__Collect__eq:(forall (P_28:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) (collec1027672124_state P_28))) (forall (X:hoare_1167836817_state), ((P_28 X)->False)))).
% Axiom fact_210_mem__def:(forall (X_33:hoare_1775062406iple_a) (A_94:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a X_33) A_94)) (A_94 X_33))).
% Axiom fact_211_mem__def:(forall (X_33:pname) (A_94:(pname->Prop)), ((iff ((member_pname X_33) A_94)) (A_94 X_33))).
% Axiom fact_212_Collect__def:(forall (P_27:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a P_27)) P_27)).
% Axiom fact_213_Collect__def:(forall (P_27:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_27)) P_27)).
% Axiom fact_214_empty__iff:(forall (C_33:hoare_1775062406iple_a), (((member2122167641iple_a C_33) bot_bo751897185le_a_o)->False)).
% Axiom fact_215_empty__iff:(forall (C_33:hoare_1167836817_state), (((member2058392318_state C_33) bot_bo70021908tate_o)->False)).
% Axiom fact_216_empty__iff:(forall (C_33:pname), (((member_pname C_33) bot_bot_pname_o)->False)).
% Axiom fact_217_insert__compr:(forall (A_93:hoare_1167836817_state) (B_51:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_93) B_51)) (collec1027672124_state (fun (X:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) X) A_93)) ((member2058392318_state X) B_51)))))).
% Axiom fact_218_insert__compr:(forall (A_93:hoare_1775062406iple_a) (B_51:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_93) B_51)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or (((eq hoare_1775062406iple_a) X) A_93)) ((member2122167641iple_a X) B_51)))))).
% Axiom fact_219_insert__compr:(forall (A_93:pname) (B_51:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_93) B_51)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_93)) ((member_pname X) B_51)))))).
% Axiom fact_220_insert__Collect:(forall (A_92:hoare_1167836817_state) (P_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_92) (collec1027672124_state P_26))) (collec1027672124_state (fun (U_2:hoare_1167836817_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1167836817_state) U_2) A_92))) (P_26 U_2)))))).
% Axiom fact_221_insert__Collect:(forall (A_92:hoare_1775062406iple_a) (P_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_92) (collec676402587iple_a P_26))) (collec676402587iple_a (fun (U_2:hoare_1775062406iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1775062406iple_a) U_2) A_92))) (P_26 U_2)))))).
% Axiom fact_222_insert__Collect:(forall (A_92:pname) (P_26:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_92) (collect_pname P_26))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_92))) (P_26 U_2)))))).
% Axiom fact_223_singleton__iff:(forall (B_50:hoare_1167836817_state) (A_91:hoare_1167836817_state), ((iff ((member2058392318_state B_50) ((insert2134838167_state A_91) bot_bo70021908tate_o))) (((eq hoare_1167836817_state) B_50) A_91))).
% Axiom fact_224_singleton__iff:(forall (B_50:hoare_1775062406iple_a) (A_91:hoare_1775062406iple_a), ((iff ((member2122167641iple_a B_50) ((insert1281456128iple_a A_91) bot_bo751897185le_a_o))) (((eq hoare_1775062406iple_a) B_50) A_91))).
% Axiom fact_225_singleton__iff:(forall (B_50:pname) (A_91:pname), ((iff ((member_pname B_50) ((insert_pname A_91) bot_bot_pname_o))) (((eq pname) B_50) A_91))).
% Axiom fact_226_insert__absorb2:(forall (X_32:hoare_1167836817_state) (A_90:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_32) ((insert2134838167_state X_32) A_90))) ((insert2134838167_state X_32) A_90))).
% Axiom fact_227_insert__absorb2:(forall (X_32:hoare_1775062406iple_a) (A_90:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X_32) ((insert1281456128iple_a X_32) A_90))) ((insert1281456128iple_a X_32) A_90))).
% Axiom fact_228_insert__absorb2:(forall (X_32:pname) (A_90:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_32) ((insert_pname X_32) A_90))) ((insert_pname X_32) A_90))).
% Axiom fact_229_insert__commute:(forall (X_31:hoare_1167836817_state) (Y_12:hoare_1167836817_state) (A_89:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_31) ((insert2134838167_state Y_12) A_89))) ((insert2134838167_state Y_12) ((insert2134838167_state X_31) A_89)))).
% Axiom fact_230_insert__commute:(forall (X_31:hoare_1775062406iple_a) (Y_12:hoare_1775062406iple_a) (A_89:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X_31) ((insert1281456128iple_a Y_12) A_89))) ((insert1281456128iple_a Y_12) ((insert1281456128iple_a X_31) A_89)))).
% Axiom fact_231_insert__commute:(forall (X_31:pname) (Y_12:pname) (A_89:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_31) ((insert_pname Y_12) A_89))) ((insert_pname Y_12) ((insert_pname X_31) A_89)))).
% Axiom fact_232_insert__iff:(forall (A_88:hoare_1167836817_state) (B_49:hoare_1167836817_state) (A_87:(hoare_1167836817_state->Prop)), ((iff ((member2058392318_state A_88) ((insert2134838167_state B_49) A_87))) ((or (((eq hoare_1167836817_state) A_88) B_49)) ((member2058392318_state A_88) A_87)))).
% Axiom fact_233_insert__iff:(forall (A_88:hoare_1775062406iple_a) (B_49:hoare_1775062406iple_a) (A_87:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a A_88) ((insert1281456128iple_a B_49) A_87))) ((or (((eq hoare_1775062406iple_a) A_88) B_49)) ((member2122167641iple_a A_88) A_87)))).
% Axiom fact_234_insert__iff:(forall (A_88:pname) (B_49:pname) (A_87:(pname->Prop)), ((iff ((member_pname A_88) ((insert_pname B_49) A_87))) ((or (((eq pname) A_88) B_49)) ((member_pname A_88) A_87)))).
% Axiom fact_235_Collect__empty__eq:(forall (P_25:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a P_25)) bot_bo751897185le_a_o)) (forall (X:hoare_1775062406iple_a), ((P_25 X)->False)))).
% Axiom fact_236_Collect__empty__eq:(forall (P_25:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_25)) bot_bot_pname_o)) (forall (X:pname), ((P_25 X)->False)))).
% Axiom fact_237_Collect__empty__eq:(forall (P_25:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) (collec1027672124_state P_25)) bot_bo70021908tate_o)) (forall (X:hoare_1167836817_state), ((P_25 X)->False)))).
% Axiom fact_238_doubleton__eq__iff:(forall (A_86:hoare_1167836817_state) (B_48:hoare_1167836817_state) (C_32:hoare_1167836817_state) (D_1:hoare_1167836817_state), ((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_86) ((insert2134838167_state B_48) bot_bo70021908tate_o))) ((insert2134838167_state C_32) ((insert2134838167_state D_1) bot_bo70021908tate_o)))) ((or ((and (((eq hoare_1167836817_state) A_86) C_32)) (((eq hoare_1167836817_state) B_48) D_1))) ((and (((eq hoare_1167836817_state) A_86) D_1)) (((eq hoare_1167836817_state) B_48) C_32))))).
% Axiom fact_239_doubleton__eq__iff:(forall (A_86:hoare_1775062406iple_a) (B_48:hoare_1775062406iple_a) (C_32:hoare_1775062406iple_a) (D_1:hoare_1775062406iple_a), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_86) ((insert1281456128iple_a B_48) bot_bo751897185le_a_o))) ((insert1281456128iple_a C_32) ((insert1281456128iple_a D_1) bot_bo751897185le_a_o)))) ((or ((and (((eq hoare_1775062406iple_a) A_86) C_32)) (((eq hoare_1775062406iple_a) B_48) D_1))) ((and (((eq hoare_1775062406iple_a) A_86) D_1)) (((eq hoare_1775062406iple_a) B_48) C_32))))).
% Axiom fact_240_doubleton__eq__iff:(forall (A_86:pname) (B_48:pname) (C_32:pname) (D_1:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_86) ((insert_pname B_48) bot_bot_pname_o))) ((insert_pname C_32) ((insert_pname D_1) bot_bot_pname_o)))) ((or ((and (((eq pname) A_86) C_32)) (((eq pname) B_48) D_1))) ((and (((eq pname) A_86) D_1)) (((eq pname) B_48) C_32))))).
% Axiom fact_241_insert__code:(forall (Y_11:hoare_1167836817_state) (A_85:(hoare_1167836817_state->Prop)) (X_30:hoare_1167836817_state), ((iff (((insert2134838167_state Y_11) A_85) X_30)) ((or (((eq hoare_1167836817_state) Y_11) X_30)) (A_85 X_30)))).
% Axiom fact_242_insert__code:(forall (Y_11:hoare_1775062406iple_a) (A_85:(hoare_1775062406iple_a->Prop)) (X_30:hoare_1775062406iple_a), ((iff (((insert1281456128iple_a Y_11) A_85) X_30)) ((or (((eq hoare_1775062406iple_a) Y_11) X_30)) (A_85 X_30)))).
% Axiom fact_243_insert__code:(forall (Y_11:pname) (A_85:(pname->Prop)) (X_30:pname), ((iff (((insert_pname Y_11) A_85) X_30)) ((or (((eq pname) Y_11) X_30)) (A_85 X_30)))).
% Axiom fact_244_insert__ident:(forall (B_47:(hoare_1167836817_state->Prop)) (X_29:hoare_1167836817_state) (A_84:(hoare_1167836817_state->Prop)), ((((member2058392318_state X_29) A_84)->False)->((((member2058392318_state X_29) B_47)->False)->((iff (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X_29) A_84)) ((insert2134838167_state X_29) B_47))) (((eq (hoare_1167836817_state->Prop)) A_84) B_47))))).
% Axiom fact_245_insert__ident:(forall (B_47:(hoare_1775062406iple_a->Prop)) (X_29:hoare_1775062406iple_a) (A_84:(hoare_1775062406iple_a->Prop)), ((((member2122167641iple_a X_29) A_84)->False)->((((member2122167641iple_a X_29) B_47)->False)->((iff (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X_29) A_84)) ((insert1281456128iple_a X_29) B_47))) (((eq (hoare_1775062406iple_a->Prop)) A_84) B_47))))).
% Axiom fact_246_insert__ident:(forall (B_47:(pname->Prop)) (X_29:pname) (A_84:(pname->Prop)), ((((member_pname X_29) A_84)->False)->((((member_pname X_29) B_47)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_29) A_84)) ((insert_pname X_29) B_47))) (((eq (pname->Prop)) A_84) B_47))))).
% Axiom fact_247_equals0D:(forall (A_83:hoare_1775062406iple_a) (A_82:(hoare_1775062406iple_a->Prop)), ((((eq (hoare_1775062406iple_a->Prop)) A_82) bot_bo751897185le_a_o)->(((member2122167641iple_a A_83) A_82)->False))).
% Axiom fact_248_equals0D:(forall (A_83:hoare_1167836817_state) (A_82:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_82) bot_bo70021908tate_o)->(((member2058392318_state A_83) A_82)->False))).
% Axiom fact_249_equals0D:(forall (A_83:pname) (A_82:(pname->Prop)), ((((eq (pname->Prop)) A_82) bot_bot_pname_o)->(((member_pname A_83) A_82)->False))).
% Axiom fact_250_insertI2:(forall (B_46:hoare_1167836817_state) (A_81:hoare_1167836817_state) (B_45:(hoare_1167836817_state->Prop)), (((member2058392318_state A_81) B_45)->((member2058392318_state A_81) ((insert2134838167_state B_46) B_45)))).
% Axiom fact_251_insertI2:(forall (B_46:hoare_1775062406iple_a) (A_81:hoare_1775062406iple_a) (B_45:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_81) B_45)->((member2122167641iple_a A_81) ((insert1281456128iple_a B_46) B_45)))).
% Axiom fact_252_insertI2:(forall (B_46:pname) (A_81:pname) (B_45:(pname->Prop)), (((member_pname A_81) B_45)->((member_pname A_81) ((insert_pname B_46) B_45)))).
% Axiom fact_253_insert__absorb:(forall (A_80:hoare_1167836817_state) (A_79:(hoare_1167836817_state->Prop)), (((member2058392318_state A_80) A_79)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_80) A_79)) A_79))).
% Axiom fact_254_insert__absorb:(forall (A_80:hoare_1775062406iple_a) (A_79:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_80) A_79)->(((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_80) A_79)) A_79))).
% Axiom fact_255_insert__absorb:(forall (A_80:pname) (A_79:(pname->Prop)), (((member_pname A_80) A_79)->(((eq (pname->Prop)) ((insert_pname A_80) A_79)) A_79))).
% Axiom fact_256_singletonE:(forall (B_44:hoare_1167836817_state) (A_78:hoare_1167836817_state), (((member2058392318_state B_44) ((insert2134838167_state A_78) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) B_44) A_78))).
% Axiom fact_257_singletonE:(forall (B_44:hoare_1775062406iple_a) (A_78:hoare_1775062406iple_a), (((member2122167641iple_a B_44) ((insert1281456128iple_a A_78) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) B_44) A_78))).
% Axiom fact_258_singletonE:(forall (B_44:pname) (A_78:pname), (((member_pname B_44) ((insert_pname A_78) bot_bot_pname_o))->(((eq pname) B_44) A_78))).
% Axiom fact_259_singleton__inject:(forall (A_77:hoare_1167836817_state) (B_43:hoare_1167836817_state), ((((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_77) bot_bo70021908tate_o)) ((insert2134838167_state B_43) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) A_77) B_43))).
% Axiom fact_260_singleton__inject:(forall (A_77:hoare_1775062406iple_a) (B_43:hoare_1775062406iple_a), ((((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_77) bot_bo751897185le_a_o)) ((insert1281456128iple_a B_43) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) A_77) B_43))).
% Axiom fact_261_singleton__inject:(forall (A_77:pname) (B_43:pname), ((((eq (pname->Prop)) ((insert_pname A_77) bot_bot_pname_o)) ((insert_pname B_43) bot_bot_pname_o))->(((eq pname) A_77) B_43))).
% Axiom fact_262_com__det:(forall (U_1:state) (C_19:com) (S:state) (T:state), ((((evalc C_19) S) T)->((((evalc C_19) S) U_1)->(((eq state) U_1) T)))).
% Axiom fact_263_insert__is__Un:(forall (A_76:hoare_1167836817_state) (A_75:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_76) A_75)) ((semila1172322802tate_o ((insert2134838167_state A_76) bot_bo70021908tate_o)) A_75))).
% Axiom fact_264_insert__is__Un:(forall (A_76:pname) (A_75:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_76) A_75)) ((semila1780557381name_o ((insert_pname A_76) bot_bot_pname_o)) A_75))).
% Axiom fact_265_insert__is__Un:(forall (A_76:hoare_1775062406iple_a) (A_75:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_76) A_75)) ((semila13410563le_a_o ((insert1281456128iple_a A_76) bot_bo751897185le_a_o)) A_75))).
% Axiom fact_266_insert__compr__raw:(forall (X:hoare_1167836817_state) (Xa:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state X) Xa)) (collec1027672124_state (fun (Y_2:hoare_1167836817_state)=> ((or (((eq hoare_1167836817_state) Y_2) X)) ((member2058392318_state Y_2) Xa)))))).
% Axiom fact_267_insert__compr__raw:(forall (X:hoare_1775062406iple_a) (Xa:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a X) Xa)) (collec676402587iple_a (fun (Y_2:hoare_1775062406iple_a)=> ((or (((eq hoare_1775062406iple_a) Y_2) X)) ((member2122167641iple_a Y_2) Xa)))))).
% Axiom fact_268_insert__compr__raw:(forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y_2:pname)=> ((or (((eq pname) Y_2) X)) ((member_pname Y_2) Xa)))))).
% Axiom fact_269_derivs__insertD:(forall (G_16:(hoare_1167836817_state->Prop)) (T_3:hoare_1167836817_state) (Ts_2:(hoare_1167836817_state->Prop)), (((hoare_123228589_state G_16) ((insert2134838167_state T_3) Ts_2))->((and ((hoare_123228589_state G_16) ((insert2134838167_state T_3) bot_bo70021908tate_o))) ((hoare_123228589_state G_16) Ts_2)))).
% Axiom fact_270_derivs__insertD:(forall (G_16:(hoare_1775062406iple_a->Prop)) (T_3:hoare_1775062406iple_a) (Ts_2:(hoare_1775062406iple_a->Prop)), (((hoare_1508237396rivs_a G_16) ((insert1281456128iple_a T_3) Ts_2))->((and ((hoare_1508237396rivs_a G_16) ((insert1281456128iple_a T_3) bot_bo751897185le_a_o))) ((hoare_1508237396rivs_a G_16) Ts_2)))).
% Axiom fact_271_hoare__derivs_Oinsert:(forall (Ts_1:(hoare_1167836817_state->Prop)) (G_15:(hoare_1167836817_state->Prop)) (T_2:hoare_1167836817_state), (((hoare_123228589_state G_15) ((insert2134838167_state T_2) bot_bo70021908tate_o))->(((hoare_123228589_state G_15) Ts_1)->((hoare_123228589_state G_15) ((insert2134838167_state T_2) Ts_1))))).
% Axiom fact_272_hoare__derivs_Oinsert:(forall (Ts_1:(hoare_1775062406iple_a->Prop)) (G_15:(hoare_1775062406iple_a->Prop)) (T_2:hoare_1775062406iple_a), (((hoare_1508237396rivs_a G_15) ((insert1281456128iple_a T_2) bot_bo751897185le_a_o))->(((hoare_1508237396rivs_a G_15) Ts_1)->((hoare_1508237396rivs_a G_15) ((insert1281456128iple_a T_2) Ts_1))))).
% Axiom fact_273_image__constant__conv:(forall (C_31:hoare_1167836817_state) (A_74:(pname->Prop)), ((and ((((eq (pname->Prop)) A_74) bot_bot_pname_o)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> C_31)) A_74)) bot_bo70021908tate_o))) ((not (((eq (pname->Prop)) A_74) bot_bot_pname_o))->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> C_31)) A_74)) ((insert2134838167_state C_31) bot_bo70021908tate_o))))).
% Axiom fact_274_image__constant__conv:(forall (C_31:hoare_1775062406iple_a) (A_74:(pname->Prop)), ((and ((((eq (pname->Prop)) A_74) bot_bot_pname_o)->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> C_31)) A_74)) bot_bo751897185le_a_o))) ((not (((eq (pname->Prop)) A_74) bot_bot_pname_o))->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> C_31)) A_74)) ((insert1281456128iple_a C_31) bot_bo751897185le_a_o))))).
% Axiom fact_275_image__constant:(forall (C_30:hoare_1167836817_state) (X_28:pname) (A_73:(pname->Prop)), (((member_pname X_28) A_73)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> C_30)) A_73)) ((insert2134838167_state C_30) bot_bo70021908tate_o)))).
% Axiom fact_276_image__constant:(forall (C_30:pname) (X_28:pname) (A_73:(pname->Prop)), (((member_pname X_28) A_73)->(((eq (pname->Prop)) ((image_pname_pname (fun (X:pname)=> C_30)) A_73)) ((insert_pname C_30) bot_bot_pname_o)))).
% Axiom fact_277_image__constant:(forall (C_30:hoare_1775062406iple_a) (X_28:pname) (A_73:(pname->Prop)), (((member_pname X_28) A_73)->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> C_30)) A_73)) ((insert1281456128iple_a C_30) bot_bo751897185le_a_o)))).
% Axiom fact_278_image__insert:(forall (F_31:(pname->hoare_1167836817_state)) (A_72:pname) (B_42:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_31) ((insert_pname A_72) B_42))) ((insert2134838167_state (F_31 A_72)) ((image_575578384_state F_31) B_42)))).
% Axiom fact_279_image__insert:(forall (F_31:(pname->hoare_1775062406iple_a)) (A_72:pname) (B_42:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_31) ((insert_pname A_72) B_42))) ((insert1281456128iple_a (F_31 A_72)) ((image_2063119815iple_a F_31) B_42)))).
% Axiom fact_280_insert__image:(forall (F_30:(pname->hoare_1167836817_state)) (X_27:pname) (A_71:(pname->Prop)), (((member_pname X_27) A_71)->(((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state (F_30 X_27)) ((image_575578384_state F_30) A_71))) ((image_575578384_state F_30) A_71)))).
% Axiom fact_281_insert__image:(forall (F_30:(pname->pname)) (X_27:pname) (A_71:(pname->Prop)), (((member_pname X_27) A_71)->(((eq (pname->Prop)) ((insert_pname (F_30 X_27)) ((image_pname_pname F_30) A_71))) ((image_pname_pname F_30) A_71)))).
% Axiom fact_282_insert__image:(forall (F_30:(pname->hoare_1775062406iple_a)) (X_27:pname) (A_71:(pname->Prop)), (((member_pname X_27) A_71)->(((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a (F_30 X_27)) ((image_2063119815iple_a F_30) A_71))) ((image_2063119815iple_a F_30) A_71)))).
% Axiom fact_283_Un__insert__right:(forall (A_70:(hoare_1167836817_state->Prop)) (A_69:hoare_1167836817_state) (B_41:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_70) ((insert2134838167_state A_69) B_41))) ((insert2134838167_state A_69) ((semila1172322802tate_o A_70) B_41)))).
% Axiom fact_284_Un__insert__right:(forall (A_70:(pname->Prop)) (A_69:pname) (B_41:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_70) ((insert_pname A_69) B_41))) ((insert_pname A_69) ((semila1780557381name_o A_70) B_41)))).
% Axiom fact_285_Un__insert__right:(forall (A_70:(hoare_1775062406iple_a->Prop)) (A_69:hoare_1775062406iple_a) (B_41:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_70) ((insert1281456128iple_a A_69) B_41))) ((insert1281456128iple_a A_69) ((semila13410563le_a_o A_70) B_41)))).
% Axiom fact_286_Un__insert__left:(forall (A_68:hoare_1167836817_state) (B_40:(hoare_1167836817_state->Prop)) (C_29:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((insert2134838167_state A_68) B_40)) C_29)) ((insert2134838167_state A_68) ((semila1172322802tate_o B_40) C_29)))).
% Axiom fact_287_Un__insert__left:(forall (A_68:pname) (B_40:(pname->Prop)) (C_29:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_68) B_40)) C_29)) ((insert_pname A_68) ((semila1780557381name_o B_40) C_29)))).
% Axiom fact_288_Un__insert__left:(forall (A_68:hoare_1775062406iple_a) (B_40:(hoare_1775062406iple_a->Prop)) (C_29:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((insert1281456128iple_a A_68) B_40)) C_29)) ((insert1281456128iple_a A_68) ((semila13410563le_a_o B_40) C_29)))).
% Axiom fact_289_empty__is__image:(forall (F_29:(pname->hoare_1167836817_state)) (A_67:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) bot_bo70021908tate_o) ((image_575578384_state F_29) A_67))) (((eq (pname->Prop)) A_67) bot_bot_pname_o))).
% Axiom fact_290_empty__is__image:(forall (F_29:(pname->hoare_1775062406iple_a)) (A_67:(pname->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) bot_bo751897185le_a_o) ((image_2063119815iple_a F_29) A_67))) (((eq (pname->Prop)) A_67) bot_bot_pname_o))).
% Axiom fact_291_image__empty:(forall (F_28:(pname->hoare_1167836817_state)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_28) bot_bot_pname_o)) bot_bo70021908tate_o)).
% Axiom fact_292_image__empty:(forall (F_28:(pname->hoare_1775062406iple_a)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_28) bot_bot_pname_o)) bot_bo751897185le_a_o)).
% Axiom fact_293_image__is__empty:(forall (F_27:(pname->hoare_1167836817_state)) (A_66:(pname->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_27) A_66)) bot_bo70021908tate_o)) (((eq (pname->Prop)) A_66) bot_bot_pname_o))).
% Axiom fact_294_image__is__empty:(forall (F_27:(pname->hoare_1775062406iple_a)) (A_66:(pname->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_27) A_66)) bot_bo751897185le_a_o)) (((eq (pname->Prop)) A_66) bot_bot_pname_o))).
% Axiom fact_295_ball__empty:(forall (P_24:(hoare_1167836817_state->Prop)) (X:hoare_1167836817_state), (((member2058392318_state X) bot_bo70021908tate_o)->(P_24 X))).
% Axiom fact_296_ball__empty:(forall (P_24:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), (((member2122167641iple_a X) bot_bo751897185le_a_o)->(P_24 X))).
% Axiom fact_297_ball__empty:(forall (P_24:(pname->Prop)) (X:pname), (((member_pname X) bot_bot_pname_o)->(P_24 X))).
% Axiom fact_298_Un__empty__left:(forall (B_39:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) B_39)) B_39)).
% Axiom fact_299_Un__empty__left:(forall (B_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_39)) B_39)).
% Axiom fact_300_Un__empty__left:(forall (B_39:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o bot_bo751897185le_a_o) B_39)) B_39)).
% Axiom fact_301_Un__empty__right:(forall (A_65:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_65) bot_bo70021908tate_o)) A_65)).
% Axiom fact_302_Un__empty__right:(forall (A_65:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_65) bot_bot_pname_o)) A_65)).
% Axiom fact_303_Un__empty__right:(forall (A_65:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_65) bot_bo751897185le_a_o)) A_65)).
% Axiom fact_304_Un__empty:(forall (A_64:(hoare_1167836817_state->Prop)) (B_38:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_64) B_38)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) A_64) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) B_38) bot_bo70021908tate_o)))).
% Axiom fact_305_Un__empty:(forall (A_64:(pname->Prop)) (B_38:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_64) B_38)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_64) bot_bot_pname_o)) (((eq (pname->Prop)) B_38) bot_bot_pname_o)))).
% Axiom fact_306_Un__empty:(forall (A_64:(hoare_1775062406iple_a->Prop)) (B_38:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_64) B_38)) bot_bo751897185le_a_o)) ((and (((eq (hoare_1775062406iple_a->Prop)) A_64) bot_bo751897185le_a_o)) (((eq (hoare_1775062406iple_a->Prop)) B_38) bot_bo751897185le_a_o)))).
% Axiom fact_307_constant:(forall (G_14:(hoare_1775062406iple_a->Prop)) (P_23:(x_a->(state->Prop))) (C_28:com) (Q_15:(x_a->(state->Prop))) (C_27:Prop), ((C_27->((hoare_1508237396rivs_a G_14) ((insert1281456128iple_a (((hoare_1766022166iple_a P_23) C_28) Q_15)) bot_bo751897185le_a_o)))->((hoare_1508237396rivs_a G_14) ((insert1281456128iple_a (((hoare_1766022166iple_a (fun (Z_8:x_a) (S_3:state)=> ((and ((P_23 Z_8) S_3)) C_27))) C_28) Q_15)) bot_bo751897185le_a_o)))).
% Axiom fact_308_constant:(forall (G_14:(hoare_1167836817_state->Prop)) (P_23:(state->(state->Prop))) (C_28:com) (Q_15:(state->(state->Prop))) (C_27:Prop), ((C_27->((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state P_23) C_28) Q_15)) bot_bo70021908tate_o)))->((hoare_123228589_state G_14) ((insert2134838167_state (((hoare_908217195_state (fun (Z_8:state) (S_3:state)=> ((and ((P_23 Z_8) S_3)) C_27))) C_28) Q_15)) bot_bo70021908tate_o)))).
% Axiom fact_309_empty:(forall (G_13:(hoare_1167836817_state->Prop)), ((hoare_123228589_state G_13) bot_bo70021908tate_o)).
% Axiom fact_310_empty:(forall (G_13:(hoare_1775062406iple_a->Prop)), ((hoare_1508237396rivs_a G_13) bot_bo751897185le_a_o)).
% Axiom fact_311_sup__bot__left:(forall (X_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o bot_bo70021908tate_o) X_26)) X_26)).
% Axiom fact_312_sup__bot__left:(forall (X_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) X_26)) X_26)).
% Axiom fact_313_sup__bot__left:(forall (X_26:Prop), ((iff ((semila10642723_sup_o bot_bot_o) X_26)) X_26)).
% Axiom fact_314_sup__bot__left:(forall (X_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o bot_bo751897185le_a_o) X_26)) X_26)).
% Axiom fact_315_sup__bot__right:(forall (X_25:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_25) bot_bo70021908tate_o)) X_25)).
% Axiom fact_316_sup__bot__right:(forall (X_25:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_25) bot_bot_pname_o)) X_25)).
% Axiom fact_317_sup__bot__right:(forall (X_25:Prop), ((iff ((semila10642723_sup_o X_25) bot_bot_o)) X_25)).
% Axiom fact_318_sup__bot__right:(forall (X_25:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_25) bot_bo751897185le_a_o)) X_25)).
% Axiom fact_319_sup__eq__bot__iff:(forall (X_24:(hoare_1167836817_state->Prop)) (Y_10:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_24) Y_10)) bot_bo70021908tate_o)) ((and (((eq (hoare_1167836817_state->Prop)) X_24) bot_bo70021908tate_o)) (((eq (hoare_1167836817_state->Prop)) Y_10) bot_bo70021908tate_o)))).
% Axiom fact_320_sup__eq__bot__iff:(forall (X_24:(pname->Prop)) (Y_10:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_24) Y_10)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_24) bot_bot_pname_o)) (((eq (pname->Prop)) Y_10) bot_bot_pname_o)))).
% Axiom fact_321_sup__eq__bot__iff:(forall (X_24:Prop) (Y_10:Prop), ((iff ((iff ((semila10642723_sup_o X_24) Y_10)) bot_bot_o)) ((and ((iff X_24) bot_bot_o)) ((iff Y_10) bot_bot_o)))).
% Axiom fact_322_sup__eq__bot__iff:(forall (X_24:(hoare_1775062406iple_a->Prop)) (Y_10:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_24) Y_10)) bot_bo751897185le_a_o)) ((and (((eq (hoare_1775062406iple_a->Prop)) X_24) bot_bo751897185le_a_o)) (((eq (hoare_1775062406iple_a->Prop)) Y_10) bot_bo751897185le_a_o)))).
% Axiom fact_323_triple__valid__Suc:(forall (N_6:nat) (T_1:hoare_1167836817_state), (((hoare_56934129_state (suc N_6)) T_1)->((hoare_56934129_state N_6) T_1))).
% Axiom fact_324_triple__valid__Suc:(forall (N_6:nat) (T_1:hoare_1775062406iple_a), (((hoare_1462269968alid_a (suc N_6)) T_1)->((hoare_1462269968alid_a N_6) T_1))).
% Axiom fact_325_insert__def:(forall (A_63:hoare_1167836817_state) (B_37:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((insert2134838167_state A_63) B_37)) ((semila1172322802tate_o (collec1027672124_state (fun (X:hoare_1167836817_state)=> (((eq hoare_1167836817_state) X) A_63)))) B_37))).
% Axiom fact_326_insert__def:(forall (A_63:pname) (B_37:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_63) B_37)) ((semila1780557381name_o (collect_pname (fun (X:pname)=> (((eq pname) X) A_63)))) B_37))).
% Axiom fact_327_insert__def:(forall (A_63:hoare_1775062406iple_a) (B_37:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((insert1281456128iple_a A_63) B_37)) ((semila13410563le_a_o (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> (((eq hoare_1775062406iple_a) X) A_63)))) B_37))).
% Axiom fact_328_weak__Body:(forall (G_12:(hoare_1775062406iple_a->Prop)) (P_22:(x_a->(state->Prop))) (Pn_3:pname) (Q_14:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_12) ((insert1281456128iple_a (((hoare_1766022166iple_a P_22) (the_com (body_1 Pn_3))) Q_14)) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_12) ((insert1281456128iple_a (((hoare_1766022166iple_a P_22) (body Pn_3)) Q_14)) bot_bo751897185le_a_o)))).
% Axiom fact_329_weak__Body:(forall (G_12:(hoare_1167836817_state->Prop)) (P_22:(state->(state->Prop))) (Pn_3:pname) (Q_14:(state->(state->Prop))), (((hoare_123228589_state G_12) ((insert2134838167_state (((hoare_908217195_state P_22) (the_com (body_1 Pn_3))) Q_14)) bot_bo70021908tate_o))->((hoare_123228589_state G_12) ((insert2134838167_state (((hoare_908217195_state P_22) (body Pn_3)) Q_14)) bot_bo70021908tate_o)))).
% Axiom fact_330_BodyN:(forall (P_21:(x_a->(state->Prop))) (Pn_2:pname) (Q_13:(x_a->(state->Prop))) (G_11:(hoare_1775062406iple_a->Prop)), (((hoare_1508237396rivs_a ((insert1281456128iple_a (((hoare_1766022166iple_a P_21) (body Pn_2)) Q_13)) G_11)) ((insert1281456128iple_a (((hoare_1766022166iple_a P_21) (the_com (body_1 Pn_2))) Q_13)) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_11) ((insert1281456128iple_a (((hoare_1766022166iple_a P_21) (body Pn_2)) Q_13)) bot_bo751897185le_a_o)))).
% Axiom fact_331_BodyN:(forall (P_21:(state->(state->Prop))) (Pn_2:pname) (Q_13:(state->(state->Prop))) (G_11:(hoare_1167836817_state->Prop)), (((hoare_123228589_state ((insert2134838167_state (((hoare_908217195_state P_21) (body Pn_2)) Q_13)) G_11)) ((insert2134838167_state (((hoare_908217195_state P_21) (the_com (body_1 Pn_2))) Q_13)) bot_bo70021908tate_o))->((hoare_123228589_state G_11) ((insert2134838167_state (((hoare_908217195_state P_21) (body Pn_2)) Q_13)) bot_bo70021908tate_o)))).
% Axiom fact_332_triples__valid__Suc:(forall (N_5:nat) (Ts:(hoare_1167836817_state->Prop)), ((forall (X:hoare_1167836817_state), (((member2058392318_state X) Ts)->((hoare_56934129_state (suc N_5)) X)))->(forall (X:hoare_1167836817_state), (((member2058392318_state X) Ts)->((hoare_56934129_state N_5) X))))).
% Axiom fact_333_triples__valid__Suc:(forall (N_5:nat) (Ts:(hoare_1775062406iple_a->Prop)), ((forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) Ts)->((hoare_1462269968alid_a (suc N_5)) X)))->(forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) Ts)->((hoare_1462269968alid_a N_5) X))))).
% Axiom fact_334_escape:(forall (G_10:(hoare_1775062406iple_a->Prop)) (C_26:com) (Q_12:(x_a->(state->Prop))) (P_20:(x_a->(state->Prop))), ((forall (Z_8:x_a) (S_3:state), (((P_20 Z_8) S_3)->((hoare_1508237396rivs_a G_10) ((insert1281456128iple_a (((hoare_1766022166iple_a (fun (Za:x_a) (S_4:state)=> (((eq state) S_4) S_3))) C_26) (fun (Z_9:x_a)=> (Q_12 Z_8)))) bot_bo751897185le_a_o))))->((hoare_1508237396rivs_a G_10) ((insert1281456128iple_a (((hoare_1766022166iple_a P_20) C_26) Q_12)) bot_bo751897185le_a_o)))).
% Axiom fact_335_escape:(forall (G_10:(hoare_1167836817_state->Prop)) (C_26:com) (Q_12:(state->(state->Prop))) (P_20:(state->(state->Prop))), ((forall (Z_8:state) (S_3:state), (((P_20 Z_8) S_3)->((hoare_123228589_state G_10) ((insert2134838167_state (((hoare_908217195_state (fun (Za:state) (S_4:state)=> (((eq state) S_4) S_3))) C_26) (fun (Z_9:state)=> (Q_12 Z_8)))) bot_bo70021908tate_o))))->((hoare_123228589_state G_10) ((insert2134838167_state (((hoare_908217195_state P_20) C_26) Q_12)) bot_bo70021908tate_o)))).
% Axiom fact_336_conseq1:(forall (P_19:(x_a->(state->Prop))) (G_9:(hoare_1775062406iple_a->Prop)) (P_18:(x_a->(state->Prop))) (C_25:com) (Q_11:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_9) ((insert1281456128iple_a (((hoare_1766022166iple_a P_18) C_25) Q_11)) bot_bo751897185le_a_o))->((forall (Z_8:x_a) (S_3:state), (((P_19 Z_8) S_3)->((P_18 Z_8) S_3)))->((hoare_1508237396rivs_a G_9) ((insert1281456128iple_a (((hoare_1766022166iple_a P_19) C_25) Q_11)) bot_bo751897185le_a_o))))).
% Axiom fact_337_conseq1:(forall (P_19:(state->(state->Prop))) (G_9:(hoare_1167836817_state->Prop)) (P_18:(state->(state->Prop))) (C_25:com) (Q_11:(state->(state->Prop))), (((hoare_123228589_state G_9) ((insert2134838167_state (((hoare_908217195_state P_18) C_25) Q_11)) bot_bo70021908tate_o))->((forall (Z_8:state) (S_3:state), (((P_19 Z_8) S_3)->((P_18 Z_8) S_3)))->((hoare_123228589_state G_9) ((insert2134838167_state (((hoare_908217195_state P_19) C_25) Q_11)) bot_bo70021908tate_o))))).
% Axiom fact_338_conseq2:(forall (Q_10:(x_a->(state->Prop))) (G_8:(hoare_1775062406iple_a->Prop)) (P_17:(x_a->(state->Prop))) (C_24:com) (Q_9:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_8) ((insert1281456128iple_a (((hoare_1766022166iple_a P_17) C_24) Q_9)) bot_bo751897185le_a_o))->((forall (Z_8:x_a) (S_3:state), (((Q_9 Z_8) S_3)->((Q_10 Z_8) S_3)))->((hoare_1508237396rivs_a G_8) ((insert1281456128iple_a (((hoare_1766022166iple_a P_17) C_24) Q_10)) bot_bo751897185le_a_o))))).
% Axiom fact_339_conseq2:(forall (Q_10:(state->(state->Prop))) (G_8:(hoare_1167836817_state->Prop)) (P_17:(state->(state->Prop))) (C_24:com) (Q_9:(state->(state->Prop))), (((hoare_123228589_state G_8) ((insert2134838167_state (((hoare_908217195_state P_17) C_24) Q_9)) bot_bo70021908tate_o))->((forall (Z_8:state) (S_3:state), (((Q_9 Z_8) S_3)->((Q_10 Z_8) S_3)))->((hoare_123228589_state G_8) ((insert2134838167_state (((hoare_908217195_state P_17) C_24) Q_10)) bot_bo70021908tate_o))))).
% Axiom fact_340_triple_Osize_I1_J:(forall (Fa:(state->nat)) (Fun1_1:(state->(state->Prop))) (Com_3:com) (Fun2_1:(state->(state->Prop))), (((eq nat) ((hoare_545207370_state Fa) (((hoare_908217195_state Fun1_1) Com_3) Fun2_1))) zero_zero_nat)).
% Axiom fact_341_triple_Osize_I1_J:(forall (Fa:(x_a->nat)) (Fun1_1:(x_a->(state->Prop))) (Com_3:com) (Fun2_1:(x_a->(state->Prop))), (((eq nat) ((hoare_1118907895size_a Fa) (((hoare_1766022166iple_a Fun1_1) Com_3) Fun2_1))) zero_zero_nat)).
% Axiom fact_342_MGT__def:(forall (C_19:com), (((eq hoare_1167836817_state) (hoare_Mirabelle_MGT C_19)) (((hoare_908217195_state fequal_state) C_19) (evalc C_19)))).
% Axiom fact_343_triple_Osize_I2_J:(forall (Fun1:(state->(state->Prop))) (Com_2:com) (Fun2:(state->(state->Prop))), (((eq nat) (size_s645941755_state (((hoare_908217195_state Fun1) Com_2) Fun2))) zero_zero_nat)).
% Axiom fact_344_triple_Osize_I2_J:(forall (Fun1:(x_a->(state->Prop))) (Com_2:com) (Fun2:(x_a->(state->Prop))), (((eq nat) (size_s724313756iple_a (((hoare_1766022166iple_a Fun1) Com_2) Fun2))) zero_zero_nat)).
% Axiom fact_345_conseq12:(forall (Q_8:(state->(state->Prop))) (P_16:(state->(state->Prop))) (G_7:(hoare_1167836817_state->Prop)) (P_15:(state->(state->Prop))) (C_23:com) (Q_7:(state->(state->Prop))), (((hoare_123228589_state G_7) ((insert2134838167_state (((hoare_908217195_state P_15) C_23) Q_7)) bot_bo70021908tate_o))->((forall (Z_8:state) (S_3:state), (((P_16 Z_8) S_3)->(forall (S_4:state), ((forall (Z_9:state), (((P_15 Z_9) S_3)->((Q_7 Z_9) S_4)))->((Q_8 Z_8) S_4)))))->((hoare_123228589_state G_7) ((insert2134838167_state (((hoare_908217195_state P_16) C_23) Q_8)) bot_bo70021908tate_o))))).
% Axiom fact_346_conseq12:(forall (Q_8:(x_a->(state->Prop))) (P_16:(x_a->(state->Prop))) (G_7:(hoare_1775062406iple_a->Prop)) (P_15:(x_a->(state->Prop))) (C_23:com) (Q_7:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_7) ((insert1281456128iple_a (((hoare_1766022166iple_a P_15) C_23) Q_7)) bot_bo751897185le_a_o))->((forall (Z_8:x_a) (S_3:state), (((P_16 Z_8) S_3)->(forall (S_4:state), ((forall (Z_9:x_a), (((P_15 Z_9) S_3)->((Q_7 Z_9) S_4)))->((Q_8 Z_8) S_4)))))->((hoare_1508237396rivs_a G_7) ((insert1281456128iple_a (((hoare_1766022166iple_a P_16) C_23) Q_8)) bot_bo751897185le_a_o))))).
% Axiom fact_347_the__elem__eq:(forall (X_23:hoare_1167836817_state), (((eq hoare_1167836817_state) (the_el323660082_state ((insert2134838167_state X_23) bot_bo70021908tate_o))) X_23)).
% Axiom fact_348_the__elem__eq:(forall (X_23:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (the_el1844711461iple_a ((insert1281456128iple_a X_23) bot_bo751897185le_a_o))) X_23)).
% Axiom fact_349_the__elem__eq:(forall (X_23:pname), (((eq pname) (the_elem_pname ((insert_pname X_23) bot_bot_pname_o))) X_23)).
% Axiom fact_350_Zero__not__Suc:(forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))).
% Axiom fact_351_nat_Osimps_I2_J:(forall (Nat_1:nat), (not (((eq nat) zero_zero_nat) (suc Nat_1)))).
% Axiom fact_352_Suc__not__Zero:(forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))).
% Axiom fact_353_nat_Osimps_I3_J:(forall (Nat_3:nat), (not (((eq nat) (suc Nat_3)) zero_zero_nat))).
% Axiom fact_354_Zero__neq__Suc:(forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))).
% Axiom fact_355_Suc__neq__Zero:(forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))).
% Axiom fact_356_bot__fun__def:(forall (X:pname), ((iff (bot_bot_pname_o X)) bot_bot_o)).
% Axiom fact_357_bot__fun__def:(forall (X:hoare_1775062406iple_a), ((iff (bot_bo751897185le_a_o X)) bot_bot_o)).
% Axiom fact_358_bot__fun__def:(forall (X:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X)) bot_bot_o)).
% Axiom fact_359_bot__nat__def:(((eq nat) bot_bot_nat) zero_zero_nat).
% Axiom fact_360_Suc__inject:(forall (X_1:nat) (Y:nat), ((((eq nat) (suc X_1)) (suc Y))->(((eq nat) X_1) Y))).
% Axiom fact_361_nat_Oinject:(forall (Nat_2:nat) (Nat_1:nat), ((iff (((eq nat) (suc Nat_2)) (suc Nat_1))) (((eq nat) Nat_2) Nat_1))).
% Axiom fact_362_Suc__n__not__n:(forall (N_1:nat), (not (((eq nat) (suc N_1)) N_1))).
% Axiom fact_363_n__not__Suc__n:(forall (N_1:nat), (not (((eq nat) N_1) (suc N_1)))).
% Axiom fact_364_bot__apply:(forall (X_22:pname), ((iff (bot_bot_pname_o X_22)) bot_bot_o)).
% Axiom fact_365_bot__apply:(forall (X_22:hoare_1775062406iple_a), ((iff (bot_bo751897185le_a_o X_22)) bot_bot_o)).
% Axiom fact_366_bot__apply:(forall (X_22:hoare_1167836817_state), ((iff (bot_bo70021908tate_o X_22)) bot_bot_o)).
% Axiom fact_367_nat_Oexhaust:(forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat:nat), (not (((eq nat) Y) (suc Nat))))->False))).
% Axiom fact_368_zero__induct:(forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N:nat), ((P (suc N))->(P N)))->(P zero_zero_nat)))).
% Axiom fact_369_nat__induct:(forall (N_1:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N:nat), ((P N)->(P (suc N))))->(P N_1)))).
% Axiom fact_370_not0__implies__Suc:(forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ex nat) (fun (M_1:nat)=> (((eq nat) N_1) (suc M_1)))))).
% Axiom fact_371_evaln_OBody:(forall (Pn_1:pname) (S0:state) (N_1:nat) (S1:state), (((((evaln (the_com (body_1 Pn_1))) S0) N_1) S1)->((((evaln (body Pn_1)) S0) (suc N_1)) S1))).
% Axiom fact_372_hoare__derivs_OSkip:(forall (G_6:(hoare_1167836817_state->Prop)) (P_14:(state->(state->Prop))), ((hoare_123228589_state G_6) ((insert2134838167_state (((hoare_908217195_state P_14) skip) P_14)) bot_bo70021908tate_o))).
% Axiom fact_373_hoare__derivs_OSkip:(forall (G_6:(hoare_1775062406iple_a->Prop)) (P_14:(x_a->(state->Prop))), ((hoare_1508237396rivs_a G_6) ((insert1281456128iple_a (((hoare_1766022166iple_a P_14) skip) P_14)) bot_bo751897185le_a_o))).
% Axiom fact_374_evaln__elim__cases_I1_J:(forall (S:state) (N_1:nat) (T:state), (((((evaln skip) S) N_1) T)->(((eq state) T) S))).
% Axiom fact_375_evaln_OSkip:(forall (S:state) (N_1:nat), ((((evaln skip) S) N_1) S)).
% Axiom fact_376_evalc_OSkip:(forall (S:state), (((evalc skip) S) S)).
% Axiom fact_377_evalc__elim__cases_I1_J:(forall (S:state) (T:state), ((((evalc skip) S) T)->(((eq state) T) S))).
% Axiom fact_378_evaln__Suc:(forall (C_19:com) (S:state) (N_1:nat) (S_5:state), (((((evaln C_19) S) N_1) S_5)->((((evaln C_19) S) (suc N_1)) S_5))).
% Axiom fact_379_eval__eq:(forall (C_19:com) (S:state) (T:state), ((iff (((evalc C_19) S) T)) ((ex nat) (fun (N:nat)=> ((((evaln C_19) S) N) T))))).
% Axiom fact_380_evaln__evalc:(forall (C_19:com) (S:state) (N_1:nat) (T:state), (((((evaln C_19) S) N_1) T)->(((evalc C_19) S) T))).
% Axiom fact_381_com_Osimps_I19_J:(forall (Pname_1:pname), (not (((eq com) (body Pname_1)) skip))).
% Axiom fact_382_com_Osimps_I18_J:(forall (Pname_1:pname), (not (((eq com) skip) (body Pname_1)))).
% Axiom fact_383_triple__valid__def2:(forall (N_4:nat) (P_13:(state->(state->Prop))) (C_22:com) (Q_6:(state->(state->Prop))), ((iff ((hoare_56934129_state N_4) (((hoare_908217195_state P_13) C_22) Q_6))) (forall (Z_8:state) (S_3:state), (((P_13 Z_8) S_3)->(forall (S_4:state), (((((evaln C_22) S_3) N_4) S_4)->((Q_6 Z_8) S_4))))))).
% Axiom fact_384_triple__valid__def2:(forall (N_4:nat) (P_13:(x_a->(state->Prop))) (C_22:com) (Q_6:(x_a->(state->Prop))), ((iff ((hoare_1462269968alid_a N_4) (((hoare_1766022166iple_a P_13) C_22) Q_6))) (forall (Z_8:x_a) (S_3:state), (((P_13 Z_8) S_3)->(forall (S_4:state), (((((evaln C_22) S_3) N_4) S_4)->((Q_6 Z_8) S_4))))))).
% Axiom fact_385_evaln__elim__cases_I6_J:(forall (P:pname) (S:state) (N_1:nat) (S1:state), (((((evaln (body P)) S) N_1) S1)->((forall (N:nat), ((((eq nat) N_1) (suc N))->(((((evaln (the_com (body_1 P))) S) N) S1)->False)))->False))).
% Axiom fact_386_evalc__evaln:(forall (C_19:com) (S:state) (T:state), ((((evalc C_19) S) T)->((ex nat) (fun (N:nat)=> ((((evaln C_19) S) N) T))))).
% Axiom fact_387_LoopF:(forall (G_5:(hoare_1167836817_state->Prop)) (P_12:(state->(state->Prop))) (B_36:(state->Prop)) (C_21:com), ((hoare_123228589_state G_5) ((insert2134838167_state (((hoare_908217195_state (fun (Z_8:state) (S_3:state)=> ((and ((P_12 Z_8) S_3)) (not (B_36 S_3))))) ((while B_36) C_21)) P_12)) bot_bo70021908tate_o))).
% Axiom fact_388_LoopF:(forall (G_5:(hoare_1775062406iple_a->Prop)) (P_12:(x_a->(state->Prop))) (B_36:(state->Prop)) (C_21:com), ((hoare_1508237396rivs_a G_5) ((insert1281456128iple_a (((hoare_1766022166iple_a (fun (Z_8:x_a) (S_3:state)=> ((and ((P_12 Z_8) S_3)) (not (B_36 S_3))))) ((while B_36) C_21)) P_12)) bot_bo751897185le_a_o))).
% Axiom fact_389_Comp:(forall (D:com) (R_1:(state->(state->Prop))) (G_4:(hoare_1167836817_state->Prop)) (P_11:(state->(state->Prop))) (C_20:com) (Q_5:(state->(state->Prop))), (((hoare_123228589_state G_4) ((insert2134838167_state (((hoare_908217195_state P_11) C_20) Q_5)) bot_bo70021908tate_o))->(((hoare_123228589_state G_4) ((insert2134838167_state (((hoare_908217195_state Q_5) D) R_1)) bot_bo70021908tate_o))->((hoare_123228589_state G_4) ((insert2134838167_state (((hoare_908217195_state P_11) ((semi C_20) D)) R_1)) bot_bo70021908tate_o))))).
% Axiom fact_390_Comp:(forall (D:com) (R_1:(x_a->(state->Prop))) (G_4:(hoare_1775062406iple_a->Prop)) (P_11:(x_a->(state->Prop))) (C_20:com) (Q_5:(x_a->(state->Prop))), (((hoare_1508237396rivs_a G_4) ((insert1281456128iple_a (((hoare_1766022166iple_a P_11) C_20) Q_5)) bot_bo751897185le_a_o))->(((hoare_1508237396rivs_a G_4) ((insert1281456128iple_a (((hoare_1766022166iple_a Q_5) D) R_1)) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_4) ((insert1281456128iple_a (((hoare_1766022166iple_a P_11) ((semi C_20) D)) R_1)) bot_bo751897185le_a_o))))).
% Axiom fact_391_the__elem__def:(forall (X_21:(hoare_1167836817_state->Prop)), (((eq hoare_1167836817_state) (the_el323660082_state X_21)) (the_Ho310147232_state (fun (X:hoare_1167836817_state)=> (((eq (hoare_1167836817_state->Prop)) X_21) ((insert2134838167_state X) bot_bo70021908tate_o)))))).
% Axiom fact_392_the__elem__def:(forall (X_21:(hoare_1775062406iple_a->Prop)), (((eq hoare_1775062406iple_a) (the_el1844711461iple_a X_21)) (the_Ho1155011127iple_a (fun (X:hoare_1775062406iple_a)=> (((eq (hoare_1775062406iple_a->Prop)) X_21) ((insert1281456128iple_a X) bot_bo751897185le_a_o)))))).
% Axiom fact_393_the__elem__def:(forall (X_21:(pname->Prop)), (((eq pname) (the_elem_pname X_21)) (the_pname (fun (X:pname)=> (((eq (pname->Prop)) X_21) ((insert_pname X) bot_bot_pname_o)))))).
% Axiom fact_394_finite__pointwise:(forall (P_9:(pname->(state->(state->Prop)))) (Q_4:(pname->(state->(state->Prop)))) (G_3:(hoare_1167836817_state->Prop)) (P_8:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(state->(state->Prop)))) (U:(pname->Prop)), ((finite_finite_pname U)->((forall (P_10:pname), (((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10))) bot_bo70021908tate_o))->((hoare_123228589_state G_3) ((insert2134838167_state (((hoare_908217195_state (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10))) bot_bo70021908tate_o))))->(((hoare_123228589_state G_3) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10)))) U))->((hoare_123228589_state G_3) ((image_575578384_state (fun (P_10:pname)=> (((hoare_908217195_state (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10)))) U)))))).
% Axiom fact_395_finite__pointwise:(forall (P_9:(pname->(x_a->(state->Prop)))) (Q_4:(pname->(x_a->(state->Prop)))) (G_3:(hoare_1775062406iple_a->Prop)) (P_8:(pname->(x_a->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(x_a->(state->Prop)))) (U:(pname->Prop)), ((finite_finite_pname U)->((forall (P_10:pname), (((hoare_1508237396rivs_a G_3) ((insert1281456128iple_a (((hoare_1766022166iple_a (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10))) bot_bo751897185le_a_o))->((hoare_1508237396rivs_a G_3) ((insert1281456128iple_a (((hoare_1766022166iple_a (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10))) bot_bo751897185le_a_o))))->(((hoare_1508237396rivs_a G_3) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_8 P_10)) (C0_1 P_10)) (Q_3 P_10)))) U))->((hoare_1508237396rivs_a G_3) ((image_2063119815iple_a (fun (P_10:pname)=> (((hoare_1766022166iple_a (P_9 P_10)) (C0_1 P_10)) (Q_4 P_10)))) U)))))).
% Axiom fact_396_evaln_OWhileFalse:(forall (C_19:com) (N_1:nat) (B:(state->Prop)) (S:state), (((B S)->False)->((((evaln ((while B) C_19)) S) N_1) S))).
% Axiom fact_397_evaln_OWhileTrue:(forall (S2:state) (C_19:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->(((((evaln C_19) S0) N_1) S1)->(((((evaln ((while B) C_19)) S1) N_1) S2)->((((evaln ((while B) C_19)) S0) N_1) S2))))).
% Axiom fact_398_evalc_OWhileTrue:(forall (S2:state) (C_19:com) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->((((evalc C_19) S0) S1)->((((evalc ((while B) C_19)) S1) S2)->(((evalc ((while B) C_19)) S0) S2))))).
% Axiom fact_399_evalc_OWhileFalse:(forall (C_19:com) (B:(state->Prop)) (S:state), (((B S)->False)->(((evalc ((while B) C_19)) S) S))).
% Axiom fact_400_evaln_OSemi:(forall (C1:com) (S2:state) (C0:com) (S0:state) (N_1:nat) (S1:state), (((((evaln C0) S0) N_1) S1)->(((((evaln C1) S1) N_1) S2)->((((evaln ((semi C0) C1)) S0) N_1) S2)))).
% Axiom fact_401_evalc_OSemi:(forall (C1:com) (S2:state) (C0:com) (S0:state) (S1:state), ((((evalc C0) S0) S1)->((((evalc C1) S1) S2)->(((evalc ((semi C0) C1)) S0) S2)))).
% Axiom fact_402_com_Osimps_I46_J:(forall (Com1:com) (Com2:com) (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) ((semi Com1) Com2)) ((while Fun_1) Com_1)))).
% Axiom fact_403_com_Osimps_I47_J:(forall (Fun_1:(state->Prop)) (Com_1:com) (Com1:com) (Com2:com), (not (((eq com) ((while Fun_1) Com_1)) ((semi Com1) Com2)))).
% Axiom fact_404_com_Osimps_I3_J:(forall (Com1:com) (Com2:com) (Com1_1:com) (Com2_1:com), ((iff (((eq com) ((semi Com1) Com2)) ((semi Com1_1) Com2_1))) ((and (((eq com) Com1) Com1_1)) (((eq com) Com2) Com2_1)))).
% Axiom fact_405_com_Osimps_I5_J:(forall (Fun:(state->Prop)) (Com:com) (Fun_1:(state->Prop)) (Com_1:com), ((iff (((eq com) ((while Fun) Com)) ((while Fun_1) Com_1))) ((and (((eq (state->Prop)) Fun) Fun_1)) (((eq com) Com) Com_1)))).
% Axiom fact_406_com_Osimps_I59_J:(forall (Pname_1:pname) (Fun:(state->Prop)) (Com:com), (not (((eq com) (body Pname_1)) ((while Fun) Com)))).
% Axiom fact_407_com_Osimps_I58_J:(forall (Fun:(state->Prop)) (Com:com) (Pname_1:pname), (not (((eq com) ((while Fun) Com)) (body Pname_1)))).
% Axiom fact_408_com_Osimps_I16_J:(forall (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) skip) ((while Fun_1) Com_1)))).
% Axiom fact_409_com_Osimps_I17_J:(forall (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) ((while Fun_1) Com_1)) skip))).
% Axiom fact_410_com_Osimps_I49_J:(forall (Pname_1:pname) (Com1:com) (Com2:com), (not (((eq com) (body Pname_1)) ((semi Com1) Com2)))).
% Axiom fact_411_com_Osimps_I48_J:(forall (Com1:com) (Com2:com) (Pname_1:pname), (not (((eq com) ((semi Com1) Com2)) (body Pname_1)))).
% Axiom fact_412_com_Osimps_I12_J:(forall (Com1_1:com) (Com2_1:com), (not (((eq com) skip) ((semi Com1_1) Com2_1)))).
% Axiom fact_413_com_Osimps_I13_J:(forall (Com1_1:com) (Com2_1:com), (not (((eq com) ((semi Com1_1) Com2_1)) skip))).
% Axiom fact_414_evalc__elim__cases_I4_J:(forall (C1:com) (C2:com) (S:state) (T:state), ((((evalc ((semi C1) C2)) S) T)->((forall (S1_1:state), ((((evalc C1) S) S1_1)->((((evalc C2) S1_1) T)->False)))->False))).
% Axiom fact_415_evaln__elim__cases_I4_J:(forall (C1:com) (C2:com) (S:state) (N_1:nat) (T:state), (((((evaln ((semi C1) C2)) S) N_1) T)->((forall (S1_1:state), (((((evaln C1) S) N_1) S1_1)->(((((evaln C2) S1_1) N_1) T)->False)))->False))).
% Axiom fact_416_finite__imageI:(forall (H_2:(pname->hoare_1167836817_state)) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->(finite1084549118_state ((image_575578384_state H_2) F_26)))).
% Axiom fact_417_finite__imageI:(forall (H_2:(pname->hoare_1775062406iple_a)) (F_26:(pname->Prop)), ((finite_finite_pname F_26)->(finite2063573081iple_a ((image_2063119815iple_a H_2) F_26)))).
% Axiom fact_418_finite_OinsertI:(forall (A_62:hoare_1167836817_state) (A_61:(hoare_1167836817_state->Prop)), ((finite1084549118_state A_61)->(finite1084549118_state ((insert2134838167_state A_62) A_61)))).
% Axiom fact_419_finite_OinsertI:(forall (A_62:hoare_1775062406iple_a) (A_61:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a A_61)->(finite2063573081iple_a ((insert1281456128iple_a A_62) A_61)))).
% Axiom fact_420_finite_OinsertI:(forall (A_62:pname) (A_61:(pname->Prop)), ((finite_finite_pname A_61)->(finite_finite_pname ((insert_pname A_62) A_61)))).
% Axiom fact_421_finite_OemptyI:(finite_finite_pname bot_bot_pname_o).
% Axiom fact_422_finite_OemptyI:(finite2063573081iple_a bot_bo751897185le_a_o).
% Axiom fact_423_finite_OemptyI:(finite1084549118_state bot_bo70021908tate_o).
% Axiom fact_424_finite__Collect__conjI:(forall (Q_2:(hoare_1775062406iple_a->Prop)) (P_7:(hoare_1775062406iple_a->Prop)), (((or (finite2063573081iple_a (collec676402587iple_a P_7))) (finite2063573081iple_a (collec676402587iple_a Q_2)))->(finite2063573081iple_a (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (P_7 X)) (Q_2 X))))))).
% Axiom fact_425_finite__Collect__conjI:(forall (Q_2:(pname->Prop)) (P_7:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_7))) (finite_finite_pname (collect_pname Q_2)))->(finite_finite_pname (collect_pname (fun (X:pname)=> ((and (P_7 X)) (Q_2 X))))))).
% Axiom fact_426_finite__Collect__disjI:(forall (P_6:(hoare_1775062406iple_a->Prop)) (Q_1:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((or (P_6 X)) (Q_1 X)))))) ((and (finite2063573081iple_a (collec676402587iple_a P_6))) (finite2063573081iple_a (collec676402587iple_a Q_1))))).
% Axiom fact_427_finite__Collect__disjI:(forall (P_6:(pname->Prop)) (Q_1:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X:pname)=> ((or (P_6 X)) (Q_1 X)))))) ((and (finite_finite_pname (collect_pname P_6))) (finite_finite_pname (collect_pname Q_1))))).
% Axiom fact_428_finite__insert:(forall (A_60:hoare_1167836817_state) (A_59:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((insert2134838167_state A_60) A_59))) (finite1084549118_state A_59))).
% Axiom fact_429_finite__insert:(forall (A_60:hoare_1775062406iple_a) (A_59:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a ((insert1281456128iple_a A_60) A_59))) (finite2063573081iple_a A_59))).
% Axiom fact_430_finite__insert:(forall (A_60:pname) (A_59:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_60) A_59))) (finite_finite_pname A_59))).
% Axiom fact_431_finite__Un:(forall (F_25:(pname->Prop)) (G_2:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_25) G_2))) ((and (finite_finite_pname F_25)) (finite_finite_pname G_2)))).
% Axiom fact_432_finite__Un:(forall (F_25:(hoare_1167836817_state->Prop)) (G_2:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state ((semila1172322802tate_o F_25) G_2))) ((and (finite1084549118_state F_25)) (finite1084549118_state G_2)))).
% Axiom fact_433_finite__Un:(forall (F_25:(hoare_1775062406iple_a->Prop)) (G_2:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a ((semila13410563le_a_o F_25) G_2))) ((and (finite2063573081iple_a F_25)) (finite2063573081iple_a G_2)))).
% Axiom fact_434_finite__UnI:(forall (G_1:(pname->Prop)) (F_24:(pname->Prop)), ((finite_finite_pname F_24)->((finite_finite_pname G_1)->(finite_finite_pname ((semila1780557381name_o F_24) G_1))))).
% Axiom fact_435_finite__UnI:(forall (G_1:(hoare_1167836817_state->Prop)) (F_24:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_24)->((finite1084549118_state G_1)->(finite1084549118_state ((semila1172322802tate_o F_24) G_1))))).
% Axiom fact_436_finite__UnI:(forall (G_1:(hoare_1775062406iple_a->Prop)) (F_24:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_24)->((finite2063573081iple_a G_1)->(finite2063573081iple_a ((semila13410563le_a_o F_24) G_1))))).
% Axiom fact_437_finite_Osimps:(forall (A_57:(hoare_1167836817_state->Prop)), ((iff (finite1084549118_state A_57)) ((or (((eq (hoare_1167836817_state->Prop)) A_57) bot_bo70021908tate_o)) ((ex (hoare_1167836817_state->Prop)) (fun (A_58:(hoare_1167836817_state->Prop))=> ((ex hoare_1167836817_state) (fun (A_56:hoare_1167836817_state)=> ((and (((eq (hoare_1167836817_state->Prop)) A_57) ((insert2134838167_state A_56) A_58))) (finite1084549118_state A_58))))))))).
% Axiom fact_438_finite_Osimps:(forall (A_57:(hoare_1775062406iple_a->Prop)), ((iff (finite2063573081iple_a A_57)) ((or (((eq (hoare_1775062406iple_a->Prop)) A_57) bot_bo751897185le_a_o)) ((ex (hoare_1775062406iple_a->Prop)) (fun (A_58:(hoare_1775062406iple_a->Prop))=> ((ex hoare_1775062406iple_a) (fun (A_56:hoare_1775062406iple_a)=> ((and (((eq (hoare_1775062406iple_a->Prop)) A_57) ((insert1281456128iple_a A_56) A_58))) (finite2063573081iple_a A_58))))))))).
% Axiom fact_439_finite_Osimps:(forall (A_57:(pname->Prop)), ((iff (finite_finite_pname A_57)) ((or (((eq (pname->Prop)) A_57) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_58:(pname->Prop))=> ((ex pname) (fun (A_56:pname)=> ((and (((eq (pname->Prop)) A_57) ((insert_pname A_56) A_58))) (finite_finite_pname A_58))))))))).
% Axiom fact_440_finite__induct:(forall (P_5:((hoare_1167836817_state->Prop)->Prop)) (F_23:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_23)->((P_5 bot_bo70021908tate_o)->((forall (X:hoare_1167836817_state) (F_16:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_16)->((((member2058392318_state X) F_16)->False)->((P_5 F_16)->(P_5 ((insert2134838167_state X) F_16))))))->(P_5 F_23))))).
% Axiom fact_441_finite__induct:(forall (P_5:((hoare_1775062406iple_a->Prop)->Prop)) (F_23:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_23)->((P_5 bot_bo751897185le_a_o)->((forall (X:hoare_1775062406iple_a) (F_16:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_16)->((((member2122167641iple_a X) F_16)->False)->((P_5 F_16)->(P_5 ((insert1281456128iple_a X) F_16))))))->(P_5 F_23))))).
% Axiom fact_442_finite__induct:(forall (P_5:((pname->Prop)->Prop)) (F_23:(pname->Prop)), ((finite_finite_pname F_23)->((P_5 bot_bot_pname_o)->((forall (X:pname) (F_16:(pname->Prop)), ((finite_finite_pname F_16)->((((member_pname X) F_16)->False)->((P_5 F_16)->(P_5 ((insert_pname X) F_16))))))->(P_5 F_23))))).
% Axiom fact_443_pigeonhole__infinite:(forall (F_22:(pname->hoare_1167836817_state)) (A_55:(pname->Prop)), (((finite_finite_pname A_55)->False)->((finite1084549118_state ((image_575578384_state F_22) A_55))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_55)) ((finite_finite_pname (collect_pname (fun (A_56:pname)=> ((and ((member_pname A_56) A_55)) (((eq hoare_1167836817_state) (F_22 A_56)) (F_22 X))))))->False))))))).
% Axiom fact_444_pigeonhole__infinite:(forall (F_22:(pname->hoare_1775062406iple_a)) (A_55:(pname->Prop)), (((finite_finite_pname A_55)->False)->((finite2063573081iple_a ((image_2063119815iple_a F_22) A_55))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_55)) ((finite_finite_pname (collect_pname (fun (A_56:pname)=> ((and ((member_pname A_56) A_55)) (((eq hoare_1775062406iple_a) (F_22 A_56)) (F_22 X))))))->False))))))).
% Axiom fact_445_evalc__WHILE__case:(forall (B:(state->Prop)) (C_19:com) (S:state) (T:state), ((((evalc ((while B) C_19)) S) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), ((((evalc C_19) S) S1_1)->((((evalc ((while B) C_19)) S1_1) T)->False))))->False)))).
% Axiom fact_446_evaln__WHILE__case:(forall (B:(state->Prop)) (C_19:com) (S:state) (N_1:nat) (T:state), (((((evaln ((while B) C_19)) S) N_1) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), (((((evaln C_19) S) N_1) S1_1)->(((((evaln ((while B) C_19)) S1_1) N_1) T)->False))))->False)))).
% Axiom fact_447_nonempty__iff:(forall (A_54:(hoare_1167836817_state->Prop)), ((iff (not (((eq (hoare_1167836817_state->Prop)) A_54) bot_bo70021908tate_o))) ((ex hoare_1167836817_state) (fun (X:hoare_1167836817_state)=> ((ex (hoare_1167836817_state->Prop)) (fun (B_34:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_54) ((insert2134838167_state X) B_34))) (((member2058392318_state X) B_34)->False)))))))).
% Axiom fact_448_nonempty__iff:(forall (A_54:(hoare_1775062406iple_a->Prop)), ((iff (not (((eq (hoare_1775062406iple_a->Prop)) A_54) bot_bo751897185le_a_o))) ((ex hoare_1775062406iple_a) (fun (X:hoare_1775062406iple_a)=> ((ex (hoare_1775062406iple_a->Prop)) (fun (B_34:(hoare_1775062406iple_a->Prop))=> ((and (((eq (hoare_1775062406iple_a->Prop)) A_54) ((insert1281456128iple_a X) B_34))) (((member2122167641iple_a X) B_34)->False)))))))).
% Axiom fact_449_nonempty__iff:(forall (A_54:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_54) bot_bot_pname_o))) ((ex pname) (fun (X:pname)=> ((ex (pname->Prop)) (fun (B_34:(pname->Prop))=> ((and (((eq (pname->Prop)) A_54) ((insert_pname X) B_34))) (((member_pname X) B_34)->False)))))))).
% Axiom fact_450_folding__one__idem_Ounion__idem:(forall (B_35:(pname->Prop)) (A_53:(pname->Prop)) (F_21:(pname->(pname->pname))) (F_20:((pname->Prop)->pname)), (((finite89670078_pname F_21) F_20)->((finite_finite_pname A_53)->((not (((eq (pname->Prop)) A_53) bot_bot_pname_o))->((finite_finite_pname B_35)->((not (((eq (pname->Prop)) B_35) bot_bot_pname_o))->(((eq pname) (F_20 ((semila1780557381name_o A_53) B_35))) ((F_21 (F_20 A_53)) (F_20 B_35))))))))).
% Axiom fact_451_folding__one__idem_Ounion__idem:(forall (B_35:(hoare_1775062406iple_a->Prop)) (A_53:(hoare_1775062406iple_a->Prop)) (F_21:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_20:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_21) F_20)->((finite2063573081iple_a A_53)->((not (((eq (hoare_1775062406iple_a->Prop)) A_53) bot_bo751897185le_a_o))->((finite2063573081iple_a B_35)->((not (((eq (hoare_1775062406iple_a->Prop)) B_35) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (F_20 ((semila13410563le_a_o A_53) B_35))) ((F_21 (F_20 A_53)) (F_20 B_35))))))))).
% Axiom fact_452_folding__one__idem_Ounion__idem:(forall (B_35:(hoare_1167836817_state->Prop)) (A_53:(hoare_1167836817_state->Prop)) (F_21:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_20:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_21) F_20)->((finite1084549118_state A_53)->((not (((eq (hoare_1167836817_state->Prop)) A_53) bot_bo70021908tate_o))->((finite1084549118_state B_35)->((not (((eq (hoare_1167836817_state->Prop)) B_35) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_20 ((semila1172322802tate_o A_53) B_35))) ((F_21 (F_20 A_53)) (F_20 B_35))))))))).
% Axiom fact_453_folding__one__idem_Oinsert__idem:(forall (X_20:hoare_1167836817_state) (A_52:(hoare_1167836817_state->Prop)) (F_19:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_18:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_19) F_18)->((finite1084549118_state A_52)->((not (((eq (hoare_1167836817_state->Prop)) A_52) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_18 ((insert2134838167_state X_20) A_52))) ((F_19 X_20) (F_18 A_52))))))).
% Axiom fact_454_folding__one__idem_Oinsert__idem:(forall (X_20:hoare_1775062406iple_a) (A_52:(hoare_1775062406iple_a->Prop)) (F_19:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_18:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_19) F_18)->((finite2063573081iple_a A_52)->((not (((eq (hoare_1775062406iple_a->Prop)) A_52) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (F_18 ((insert1281456128iple_a X_20) A_52))) ((F_19 X_20) (F_18 A_52))))))).
% Axiom fact_455_folding__one__idem_Oinsert__idem:(forall (X_20:pname) (A_52:(pname->Prop)) (F_19:(pname->(pname->pname))) (F_18:((pname->Prop)->pname)), (((finite89670078_pname F_19) F_18)->((finite_finite_pname A_52)->((not (((eq (pname->Prop)) A_52) bot_bot_pname_o))->(((eq pname) (F_18 ((insert_pname X_20) A_52))) ((F_19 X_20) (F_18 A_52))))))).
% Axiom fact_456_image__eq__fold__image:(forall (F_17:(pname->hoare_1167836817_state)) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->(((eq (hoare_1167836817_state->Prop)) ((image_575578384_state F_17) A_51)) ((((finite1068437657_pname semila1172322802tate_o) (fun (X:pname)=> ((insert2134838167_state (F_17 X)) bot_bo70021908tate_o))) bot_bo70021908tate_o) A_51)))).
% Axiom fact_457_image__eq__fold__image:(forall (F_17:(pname->hoare_1775062406iple_a)) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->(((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a F_17) A_51)) ((((finite1805141964_pname semila13410563le_a_o) (fun (X:pname)=> ((insert1281456128iple_a (F_17 X)) bot_bo751897185le_a_o))) bot_bo751897185le_a_o) A_51)))).
% Axiom fact_458_finite__ne__induct:(forall (P_4:((hoare_1167836817_state->Prop)->Prop)) (F_15:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_15)->((not (((eq (hoare_1167836817_state->Prop)) F_15) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state), (P_4 ((insert2134838167_state X) bot_bo70021908tate_o)))->((forall (X:hoare_1167836817_state) (F_16:(hoare_1167836817_state->Prop)), ((finite1084549118_state F_16)->((not (((eq (hoare_1167836817_state->Prop)) F_16) bot_bo70021908tate_o))->((((member2058392318_state X) F_16)->False)->((P_4 F_16)->(P_4 ((insert2134838167_state X) F_16)))))))->(P_4 F_15)))))).
% Axiom fact_459_finite__ne__induct:(forall (P_4:((hoare_1775062406iple_a->Prop)->Prop)) (F_15:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_15)->((not (((eq (hoare_1775062406iple_a->Prop)) F_15) bot_bo751897185le_a_o))->((forall (X:hoare_1775062406iple_a), (P_4 ((insert1281456128iple_a X) bot_bo751897185le_a_o)))->((forall (X:hoare_1775062406iple_a) (F_16:(hoare_1775062406iple_a->Prop)), ((finite2063573081iple_a F_16)->((not (((eq (hoare_1775062406iple_a->Prop)) F_16) bot_bo751897185le_a_o))->((((member2122167641iple_a X) F_16)->False)->((P_4 F_16)->(P_4 ((insert1281456128iple_a X) F_16)))))))->(P_4 F_15)))))).
% Axiom fact_460_finite__ne__induct:(forall (P_4:((pname->Prop)->Prop)) (F_15:(pname->Prop)), ((finite_finite_pname F_15)->((not (((eq (pname->Prop)) F_15) bot_bot_pname_o))->((forall (X:pname), (P_4 ((insert_pname X) bot_bot_pname_o)))->((forall (X:pname) (F_16:(pname->Prop)), ((finite_finite_pname F_16)->((not (((eq (pname->Prop)) F_16) bot_bot_pname_o))->((((member_pname X) F_16)->False)->((P_4 F_16)->(P_4 ((insert_pname X) F_16)))))))->(P_4 F_15)))))).
% Axiom fact_461_folding__one__idem_Oin__idem:(forall (X_19:hoare_1775062406iple_a) (A_50:(hoare_1775062406iple_a->Prop)) (F_14:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_13:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_14) F_13)->((finite2063573081iple_a A_50)->(((member2122167641iple_a X_19) A_50)->(((eq hoare_1775062406iple_a) ((F_14 X_19) (F_13 A_50))) (F_13 A_50)))))).
% Axiom fact_462_folding__one__idem_Oin__idem:(forall (X_19:pname) (A_50:(pname->Prop)) (F_14:(pname->(pname->pname))) (F_13:((pname->Prop)->pname)), (((finite89670078_pname F_14) F_13)->((finite_finite_pname A_50)->(((member_pname X_19) A_50)->(((eq pname) ((F_14 X_19) (F_13 A_50))) (F_13 A_50)))))).
% Axiom fact_463_folding__one__idem_Ohom__commute:(forall (N_3:(pname->Prop)) (H_1:(pname->pname)) (F_12:(pname->(pname->pname))) (F_11:((pname->Prop)->pname)), (((finite89670078_pname F_12) F_11)->((forall (X:pname) (Y_2:pname), (((eq pname) (H_1 ((F_12 X) Y_2))) ((F_12 (H_1 X)) (H_1 Y_2))))->((finite_finite_pname N_3)->((not (((eq (pname->Prop)) N_3) bot_bot_pname_o))->(((eq pname) (H_1 (F_11 N_3))) (F_11 ((image_pname_pname H_1) N_3)))))))).
% Axiom fact_464_folding__one__idem_Ohom__commute:(forall (N_3:(hoare_1775062406iple_a->Prop)) (H_1:(hoare_1775062406iple_a->hoare_1775062406iple_a)) (F_12:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_11:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite1358382848iple_a F_12) F_11)->((forall (X:hoare_1775062406iple_a) (Y_2:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (H_1 ((F_12 X) Y_2))) ((F_12 (H_1 X)) (H_1 Y_2))))->((finite2063573081iple_a N_3)->((not (((eq (hoare_1775062406iple_a->Prop)) N_3) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (H_1 (F_11 N_3))) (F_11 ((image_1170193413iple_a H_1) N_3)))))))).
% Axiom fact_465_folding__one__idem_Ohom__commute:(forall (N_3:(hoare_1167836817_state->Prop)) (H_1:(hoare_1167836817_state->hoare_1167836817_state)) (F_12:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_11:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite806517911_state F_12) F_11)->((forall (X:hoare_1167836817_state) (Y_2:hoare_1167836817_state), (((eq hoare_1167836817_state) (H_1 ((F_12 X) Y_2))) ((F_12 (H_1 X)) (H_1 Y_2))))->((finite1084549118_state N_3)->((not (((eq (hoare_1167836817_state->Prop)) N_3) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (H_1 (F_11 N_3))) (F_11 ((image_31595733_state H_1) N_3)))))))).
% Axiom fact_466_folding__one_Oinsert:(forall (X_18:hoare_1167836817_state) (A_49:(hoare_1167836817_state->Prop)) (F_10:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_9:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_10) F_9)->((finite1084549118_state A_49)->((((member2058392318_state X_18) A_49)->False)->((not (((eq (hoare_1167836817_state->Prop)) A_49) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) (F_9 ((insert2134838167_state X_18) A_49))) ((F_10 X_18) (F_9 A_49)))))))).
% Axiom fact_467_folding__one_Oinsert:(forall (X_18:hoare_1775062406iple_a) (A_49:(hoare_1775062406iple_a->Prop)) (F_10:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_9:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_10) F_9)->((finite2063573081iple_a A_49)->((((member2122167641iple_a X_18) A_49)->False)->((not (((eq (hoare_1775062406iple_a->Prop)) A_49) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) (F_9 ((insert1281456128iple_a X_18) A_49))) ((F_10 X_18) (F_9 A_49)))))))).
% Axiom fact_468_folding__one_Oinsert:(forall (X_18:pname) (A_49:(pname->Prop)) (F_10:(pname->(pname->pname))) (F_9:((pname->Prop)->pname)), (((finite1282449217_pname F_10) F_9)->((finite_finite_pname A_49)->((((member_pname X_18) A_49)->False)->((not (((eq (pname->Prop)) A_49) bot_bot_pname_o))->(((eq pname) (F_9 ((insert_pname X_18) A_49))) ((F_10 X_18) (F_9 A_49)))))))).
% Axiom fact_469_folding__one_Osingleton:(forall (X_17:hoare_1167836817_state) (F_8:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_7:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_8) F_7)->(((eq hoare_1167836817_state) (F_7 ((insert2134838167_state X_17) bot_bo70021908tate_o))) X_17))).
% Axiom fact_470_folding__one_Osingleton:(forall (X_17:hoare_1775062406iple_a) (F_8:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_7:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_8) F_7)->(((eq hoare_1775062406iple_a) (F_7 ((insert1281456128iple_a X_17) bot_bo751897185le_a_o))) X_17))).
% Axiom fact_471_folding__one_Osingleton:(forall (X_17:pname) (F_8:(pname->(pname->pname))) (F_7:((pname->Prop)->pname)), (((finite1282449217_pname F_8) F_7)->(((eq pname) (F_7 ((insert_pname X_17) bot_bot_pname_o))) X_17))).
% Axiom fact_472_folding__one_Oclosed:(forall (A_48:(hoare_1167836817_state->Prop)) (F_6:(hoare_1167836817_state->(hoare_1167836817_state->hoare_1167836817_state))) (F_5:((hoare_1167836817_state->Prop)->hoare_1167836817_state)), (((finite1074406356_state F_6) F_5)->((finite1084549118_state A_48)->((not (((eq (hoare_1167836817_state->Prop)) A_48) bot_bo70021908tate_o))->((forall (X:hoare_1167836817_state) (Y_2:hoare_1167836817_state), ((member2058392318_state ((F_6 X) Y_2)) ((insert2134838167_state X) ((insert2134838167_state Y_2) bot_bo70021908tate_o))))->((member2058392318_state (F_5 A_48)) A_48)))))).
% Axiom fact_473_folding__one_Oclosed:(forall (A_48:(hoare_1775062406iple_a->Prop)) (F_6:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_5:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_6) F_5)->((finite2063573081iple_a A_48)->((not (((eq (hoare_1775062406iple_a->Prop)) A_48) bot_bo751897185le_a_o))->((forall (X:hoare_1775062406iple_a) (Y_2:hoare_1775062406iple_a), ((member2122167641iple_a ((F_6 X) Y_2)) ((insert1281456128iple_a X) ((insert1281456128iple_a Y_2) bot_bo751897185le_a_o))))->((member2122167641iple_a (F_5 A_48)) A_48)))))).
% Axiom fact_474_folding__one_Oclosed:(forall (A_48:(pname->Prop)) (F_6:(pname->(pname->pname))) (F_5:((pname->Prop)->pname)), (((finite1282449217_pname F_6) F_5)->((finite_finite_pname A_48)->((not (((eq (pname->Prop)) A_48) bot_bot_pname_o))->((forall (X:pname) (Y_2:pname), ((member_pname ((F_6 X) Y_2)) ((insert_pname X) ((insert_pname Y_2) bot_bot_pname_o))))->((member_pname (F_5 A_48)) A_48)))))).
% Axiom fact_475_evaln__max2:(forall (C2:com) (S2:state) (N2:nat) (T2:state) (C1:com) (S1:state) (N1:nat) (T1:state), (((((evaln C1) S1) N1) T1)->(((((evaln C2) S2) N2) T2)->((ex nat) (fun (N:nat)=> ((and ((((evaln C1) S1) N) T1)) ((((evaln C2) S2) N) T2))))))).
% Axiom fact_476_mk__disjoint__insert:(forall (A_47:hoare_1167836817_state) (A_46:(hoare_1167836817_state->Prop)), (((member2058392318_state A_47) A_46)->((ex (hoare_1167836817_state->Prop)) (fun (B_34:(hoare_1167836817_state->Prop))=> ((and (((eq (hoare_1167836817_state->Prop)) A_46) ((insert2134838167_state A_47) B_34))) (((member2058392318_state A_47) B_34)->False)))))).
% Axiom fact_477_mk__disjoint__insert:(forall (A_47:hoare_1775062406iple_a) (A_46:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_47) A_46)->((ex (hoare_1775062406iple_a->Prop)) (fun (B_34:(hoare_1775062406iple_a->Prop))=> ((and (((eq (hoare_1775062406iple_a->Prop)) A_46) ((insert1281456128iple_a A_47) B_34))) (((member2122167641iple_a A_47) B_34)->False)))))).
% Axiom fact_478_mk__disjoint__insert:(forall (A_47:pname) (A_46:(pname->Prop)), (((member_pname A_47) A_46)->((ex (pname->Prop)) (fun (B_34:(pname->Prop))=> ((and (((eq (pname->Prop)) A_46) ((insert_pname A_47) B_34))) (((member_pname A_47) B_34)->False)))))).
% Axiom fact_479_Set_Oset__insert:(forall (X_16:hoare_1167836817_state) (A_45:(hoare_1167836817_state->Prop)), (((member2058392318_state X_16) A_45)->((forall (B_34:(hoare_1167836817_state->Prop)), ((((eq (hoare_1167836817_state->Prop)) A_45) ((insert2134838167_state X_16) B_34))->((member2058392318_state X_16) B_34)))->False))).
% Axiom fact_480_Set_Oset__insert:(forall (X_16:hoare_1775062406iple_a) (A_45:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a X_16) A_45)->((forall (B_34:(hoare_1775062406iple_a->Prop)), ((((eq (hoare_1775062406iple_a->Prop)) A_45) ((insert1281456128iple_a X_16) B_34))->((member2122167641iple_a X_16) B_34)))->False))).
% Axiom fact_481_Set_Oset__insert:(forall (X_16:pname) (A_45:(pname->Prop)), (((member_pname X_16) A_45)->((forall (B_34:(pname->Prop)), ((((eq (pname->Prop)) A_45) ((insert_pname X_16) B_34))->((member_pname X_16) B_34)))->False))).
% Axiom fact_482_equals0I:(forall (A_44:(hoare_1775062406iple_a->Prop)), ((forall (Y_2:hoare_1775062406iple_a), (((member2122167641iple_a Y_2) A_44)->False))->(((eq (hoare_1775062406iple_a->Prop)) A_44) bot_bo751897185le_a_o))).
% Axiom fact_483_equals0I:(forall (A_44:(pname->Prop)), ((forall (Y_2:pname), (((member_pname Y_2) A_44)->False))->(((eq (pname->Prop)) A_44) bot_bot_pname_o))).
% Axiom fact_484_equals0I:(forall (A_44:(hoare_1167836817_state->Prop)), ((forall (Y_2:hoare_1167836817_state), (((member2058392318_state Y_2) A_44)->False))->(((eq (hoare_1167836817_state->Prop)) A_44) bot_bo70021908tate_o))).
% Axiom fact_485_Sup__fin_Ounion__idem:(forall (B_33:(Prop->Prop)) (A_43:(Prop->Prop)), ((finite_finite_o A_43)->((not (((eq (Prop->Prop)) A_43) bot_bot_o_o))->((finite_finite_o B_33)->((not (((eq (Prop->Prop)) B_33) bot_bot_o_o))->((iff (big_la727467310_fin_o ((semila2062604954up_o_o A_43) B_33))) ((semila10642723_sup_o (big_la727467310_fin_o A_43)) (big_la727467310_fin_o B_33)))))))).
% Axiom fact_486_Sup__fin_Ounion__idem:(forall (B_33:((pname->Prop)->Prop)) (A_43:((pname->Prop)->Prop)), ((finite297249702name_o A_43)->((not (((eq ((pname->Prop)->Prop)) A_43) bot_bot_pname_o_o))->((finite297249702name_o B_33)->((not (((eq ((pname->Prop)->Prop)) B_33) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((semila181081674me_o_o A_43) B_33))) ((semila1780557381name_o (big_la1286884090name_o A_43)) (big_la1286884090name_o B_33)))))))).
% Axiom fact_487_Sup__fin_Ounion__idem:(forall (B_33:((hoare_1167836817_state->Prop)->Prop)) (A_43:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_43)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_43) bot_bo691907561te_o_o))->((finite1380128977tate_o B_33)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_33) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((semila866907787te_o_o A_43) B_33))) ((semila1172322802tate_o (big_la1138507389tate_o A_43)) (big_la1138507389tate_o B_33)))))))).
% Axiom fact_488_Sup__fin_Ounion__idem:(forall (B_33:((hoare_1775062406iple_a->Prop)->Prop)) (A_43:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_43)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_43) bot_bo1976773294_a_o_o))->((finite789576932le_a_o B_33)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) B_33) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((semila2069193356_a_o_o A_43) B_33))) ((semila13410563le_a_o (big_la1843772984le_a_o A_43)) (big_la1843772984le_a_o B_33)))))))).
% Axiom fact_489_Sup__fin_Oin__idem:(forall (X_15:Prop) (A_42:(Prop->Prop)), ((finite_finite_o A_42)->(((member_o X_15) A_42)->((iff ((semila10642723_sup_o X_15) (big_la727467310_fin_o A_42))) (big_la727467310_fin_o A_42))))).
% Axiom fact_490_Sup__fin_Oin__idem:(forall (X_15:(pname->Prop)) (A_42:((pname->Prop)->Prop)), ((finite297249702name_o A_42)->(((member_pname_o X_15) A_42)->(((eq (pname->Prop)) ((semila1780557381name_o X_15) (big_la1286884090name_o A_42))) (big_la1286884090name_o A_42))))).
% Axiom fact_491_Sup__fin_Oin__idem:(forall (X_15:(hoare_1167836817_state->Prop)) (A_42:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_42)->(((member864234961tate_o X_15) A_42)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_15) (big_la1138507389tate_o A_42))) (big_la1138507389tate_o A_42))))).
% Axiom fact_492_Sup__fin_Oin__idem:(forall (X_15:(hoare_1775062406iple_a->Prop)) (A_42:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_42)->(((member1207314404le_a_o X_15) A_42)->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_15) (big_la1843772984le_a_o A_42))) (big_la1843772984le_a_o A_42))))).
% Axiom fact_493_Sup__fin_Oinsert:(forall (X_14:Prop) (A_41:(Prop->Prop)), ((finite_finite_o A_41)->((((member_o X_14) A_41)->False)->((not (((eq (Prop->Prop)) A_41) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_14) A_41))) ((semila10642723_sup_o X_14) (big_la727467310_fin_o A_41))))))).
% Axiom fact_494_Sup__fin_Oinsert:(forall (X_14:(pname->Prop)) (A_41:((pname->Prop)->Prop)), ((finite297249702name_o A_41)->((((member_pname_o X_14) A_41)->False)->((not (((eq ((pname->Prop)->Prop)) A_41) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_14) A_41))) ((semila1780557381name_o X_14) (big_la1286884090name_o A_41))))))).
% Axiom fact_495_Sup__fin_Oinsert:(forall (X_14:(hoare_1167836817_state->Prop)) (A_41:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_41)->((((member864234961tate_o X_14) A_41)->False)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_41) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((insert999278200tate_o X_14) A_41))) ((semila1172322802tate_o X_14) (big_la1138507389tate_o A_41))))))).
% Axiom fact_496_Sup__fin_Oinsert:(forall (X_14:(hoare_1775062406iple_a->Prop)) (A_41:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_41)->((((member1207314404le_a_o X_14) A_41)->False)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_41) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((insert1210049533le_a_o X_14) A_41))) ((semila13410563le_a_o X_14) (big_la1843772984le_a_o A_41))))))).
% Axiom fact_497_Sup__fin_Oinsert__idem:(forall (X_13:Prop) (A_40:(Prop->Prop)), ((finite_finite_o A_40)->((not (((eq (Prop->Prop)) A_40) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_13) A_40))) ((semila10642723_sup_o X_13) (big_la727467310_fin_o A_40)))))).
% Axiom fact_498_Sup__fin_Oinsert__idem:(forall (X_13:(pname->Prop)) (A_40:((pname->Prop)->Prop)), ((finite297249702name_o A_40)->((not (((eq ((pname->Prop)->Prop)) A_40) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_13) A_40))) ((semila1780557381name_o X_13) (big_la1286884090name_o A_40)))))).
% Axiom fact_499_Sup__fin_Oinsert__idem:(forall (X_13:(hoare_1167836817_state->Prop)) (A_40:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_40)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_40) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((insert999278200tate_o X_13) A_40))) ((semila1172322802tate_o X_13) (big_la1138507389tate_o A_40)))))).
% Axiom fact_500_Sup__fin_Oinsert__idem:(forall (X_13:(hoare_1775062406iple_a->Prop)) (A_40:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_40)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_40) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((insert1210049533le_a_o X_13) A_40))) ((semila13410563le_a_o X_13) (big_la1843772984le_a_o A_40)))))).
% Axiom fact_501_Sup__fin_Ohom__commute:(forall (N_2:(Prop->Prop)) (H:(Prop->Prop)), ((forall (X:Prop) (Y_2:Prop), ((iff (H ((semila10642723_sup_o X) Y_2))) ((semila10642723_sup_o (H X)) (H Y_2))))->((finite_finite_o N_2)->((not (((eq (Prop->Prop)) N_2) bot_bot_o_o))->((iff (H (big_la727467310_fin_o N_2))) (big_la727467310_fin_o ((image_o_o H) N_2))))))).
% Axiom fact_502_Sup__fin_Ohom__commute:(forall (N_2:((pname->Prop)->Prop)) (H:((pname->Prop)->(pname->Prop))), ((forall (X:(pname->Prop)) (Y_2:(pname->Prop)), (((eq (pname->Prop)) (H ((semila1780557381name_o X) Y_2))) ((semila1780557381name_o (H X)) (H Y_2))))->((finite297249702name_o N_2)->((not (((eq ((pname->Prop)->Prop)) N_2) bot_bot_pname_o_o))->(((eq (pname->Prop)) (H (big_la1286884090name_o N_2))) (big_la1286884090name_o ((image_1085733413name_o H) N_2))))))).
% Axiom fact_503_Sup__fin_Ohom__commute:(forall (N_2:((hoare_1167836817_state->Prop)->Prop)) (H:((hoare_1167836817_state->Prop)->(hoare_1167836817_state->Prop))), ((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) (H ((semila1172322802tate_o X) Y_2))) ((semila1172322802tate_o (H X)) (H Y_2))))->((finite1380128977tate_o N_2)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) N_2) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) (H (big_la1138507389tate_o N_2))) (big_la1138507389tate_o ((image_1488525317tate_o H) N_2))))))).
% Axiom fact_504_Sup__fin_Ohom__commute:(forall (N_2:((hoare_1775062406iple_a->Prop)->Prop)) (H:((hoare_1775062406iple_a->Prop)->(hoare_1775062406iple_a->Prop))), ((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (H ((semila13410563le_a_o X) Y_2))) ((semila13410563le_a_o (H X)) (H Y_2))))->((finite789576932le_a_o N_2)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) N_2) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) (H (big_la1843772984le_a_o N_2))) (big_la1843772984le_a_o ((image_2014247585le_a_o H) N_2))))))).
% Axiom fact_505_Sup__fin_Oclosed:(forall (A_39:(Prop->Prop)), ((finite_finite_o A_39)->((not (((eq (Prop->Prop)) A_39) bot_bot_o_o))->((forall (X:Prop) (Y_2:Prop), ((member_o ((semila10642723_sup_o X) Y_2)) ((insert_o X) ((insert_o Y_2) bot_bot_o_o))))->((member_o (big_la727467310_fin_o A_39)) A_39))))).
% Axiom fact_506_Sup__fin_Oclosed:(forall (A_39:((pname->Prop)->Prop)), ((finite297249702name_o A_39)->((not (((eq ((pname->Prop)->Prop)) A_39) bot_bot_pname_o_o))->((forall (X:(pname->Prop)) (Y_2:(pname->Prop)), ((member_pname_o ((semila1780557381name_o X) Y_2)) ((insert_pname_o X) ((insert_pname_o Y_2) bot_bot_pname_o_o))))->((member_pname_o (big_la1286884090name_o A_39)) A_39))))).
% Axiom fact_507_Sup__fin_Oclosed:(forall (A_39:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_39)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_39) bot_bo691907561te_o_o))->((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)), ((member864234961tate_o ((semila1172322802tate_o X) Y_2)) ((insert999278200tate_o X) ((insert999278200tate_o Y_2) bot_bo691907561te_o_o))))->((member864234961tate_o (big_la1138507389tate_o A_39)) A_39))))).
% Axiom fact_508_Sup__fin_Oclosed:(forall (A_39:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_39)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_39) bot_bo1976773294_a_o_o))->((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)), ((member1207314404le_a_o ((semila13410563le_a_o X) Y_2)) ((insert1210049533le_a_o X) ((insert1210049533le_a_o Y_2) bot_bo1976773294_a_o_o))))->((member1207314404le_a_o (big_la1843772984le_a_o A_39)) A_39))))).
% Axiom fact_509_Sup__fin_Ounion__inter:(forall (B_32:(Prop->Prop)) (A_38:(Prop->Prop)), ((finite_finite_o A_38)->((finite_finite_o B_32)->((not (((eq (Prop->Prop)) ((semila232696320nf_o_o A_38) B_32)) bot_bot_o_o))->((iff ((semila10642723_sup_o (big_la727467310_fin_o ((semila2062604954up_o_o A_38) B_32))) (big_la727467310_fin_o ((semila232696320nf_o_o A_38) B_32)))) ((semila10642723_sup_o (big_la727467310_fin_o A_38)) (big_la727467310_fin_o B_32))))))).
% Axiom fact_510_Sup__fin_Ounion__inter:(forall (B_32:((pname->Prop)->Prop)) (A_38:((pname->Prop)->Prop)), ((finite297249702name_o A_38)->((finite297249702name_o B_32)->((not (((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_38) B_32)) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((semila1780557381name_o (big_la1286884090name_o ((semila181081674me_o_o A_38) B_32))) (big_la1286884090name_o ((semila2013987940me_o_o A_38) B_32)))) ((semila1780557381name_o (big_la1286884090name_o A_38)) (big_la1286884090name_o B_32))))))).
% Axiom fact_511_Sup__fin_Ounion__inter:(forall (B_32:((hoare_1167836817_state->Prop)->Prop)) (A_38:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_38)->((finite1380128977tate_o B_32)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_38) B_32)) bot_bo691907561te_o_o))->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o (big_la1138507389tate_o ((semila866907787te_o_o A_38) B_32))) (big_la1138507389tate_o ((semila1758709489te_o_o A_38) B_32)))) ((semila1172322802tate_o (big_la1138507389tate_o A_38)) (big_la1138507389tate_o B_32))))))).
% Axiom fact_512_Sup__fin_Ounion__inter:(forall (B_32:((hoare_1775062406iple_a->Prop)->Prop)) (A_38:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_38)->((finite789576932le_a_o B_32)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) ((semila1691990438_a_o_o A_38) B_32)) bot_bo1976773294_a_o_o))->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o (big_la1843772984le_a_o ((semila2069193356_a_o_o A_38) B_32))) (big_la1843772984le_a_o ((semila1691990438_a_o_o A_38) B_32)))) ((semila13410563le_a_o (big_la1843772984le_a_o A_38)) (big_la1843772984le_a_o B_32))))))).
% Axiom fact_513_Sup__fin_Ounion__disjoint:(forall (B_31:(Prop->Prop)) (A_37:(Prop->Prop)), ((finite_finite_o A_37)->((not (((eq (Prop->Prop)) A_37) bot_bot_o_o))->((finite_finite_o B_31)->((not (((eq (Prop->Prop)) B_31) bot_bot_o_o))->((((eq (Prop->Prop)) ((semila232696320nf_o_o A_37) B_31)) bot_bot_o_o)->((iff (big_la727467310_fin_o ((semila2062604954up_o_o A_37) B_31))) ((semila10642723_sup_o (big_la727467310_fin_o A_37)) (big_la727467310_fin_o B_31))))))))).
% Axiom fact_514_Sup__fin_Ounion__disjoint:(forall (B_31:((pname->Prop)->Prop)) (A_37:((pname->Prop)->Prop)), ((finite297249702name_o A_37)->((not (((eq ((pname->Prop)->Prop)) A_37) bot_bot_pname_o_o))->((finite297249702name_o B_31)->((not (((eq ((pname->Prop)->Prop)) B_31) bot_bot_pname_o_o))->((((eq ((pname->Prop)->Prop)) ((semila2013987940me_o_o A_37) B_31)) bot_bot_pname_o_o)->(((eq (pname->Prop)) (big_la1286884090name_o ((semila181081674me_o_o A_37) B_31))) ((semila1780557381name_o (big_la1286884090name_o A_37)) (big_la1286884090name_o B_31))))))))).
% Axiom fact_515_Sup__fin_Ounion__disjoint:(forall (B_31:((hoare_1167836817_state->Prop)->Prop)) (A_37:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_37)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) A_37) bot_bo691907561te_o_o))->((finite1380128977tate_o B_31)->((not (((eq ((hoare_1167836817_state->Prop)->Prop)) B_31) bot_bo691907561te_o_o))->((((eq ((hoare_1167836817_state->Prop)->Prop)) ((semila1758709489te_o_o A_37) B_31)) bot_bo691907561te_o_o)->(((eq (hoare_1167836817_state->Prop)) (big_la1138507389tate_o ((semila866907787te_o_o A_37) B_31))) ((semila1172322802tate_o (big_la1138507389tate_o A_37)) (big_la1138507389tate_o B_31))))))))).
% Axiom fact_516_Sup__fin_Ounion__disjoint:(forall (B_31:((hoare_1775062406iple_a->Prop)->Prop)) (A_37:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_37)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) A_37) bot_bo1976773294_a_o_o))->((finite789576932le_a_o B_31)->((not (((eq ((hoare_1775062406iple_a->Prop)->Prop)) B_31) bot_bo1976773294_a_o_o))->((((eq ((hoare_1775062406iple_a->Prop)->Prop)) ((semila1691990438_a_o_o A_37) B_31)) bot_bo1976773294_a_o_o)->(((eq (hoare_1775062406iple_a->Prop)) (big_la1843772984le_a_o ((semila2069193356_a_o_o A_37) B_31))) ((semila13410563le_a_o (big_la1843772984le_a_o A_37)) (big_la1843772984le_a_o B_31))))))))).
% Axiom fact_517_IntI:(forall (B_30:(hoare_1775062406iple_a->Prop)) (C_18:hoare_1775062406iple_a) (A_36:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_18) A_36)->(((member2122167641iple_a C_18) B_30)->((member2122167641iple_a C_18) ((semila966743401le_a_o A_36) B_30))))).
% Axiom fact_518_IntI:(forall (B_30:(pname->Prop)) (C_18:pname) (A_36:(pname->Prop)), (((member_pname C_18) A_36)->(((member_pname C_18) B_30)->((member_pname C_18) ((semila1673364395name_o A_36) B_30))))).
% Axiom fact_519_IntE:(forall (C_17:hoare_1775062406iple_a) (A_35:(hoare_1775062406iple_a->Prop)) (B_29:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_17) ((semila966743401le_a_o A_35) B_29))->((((member2122167641iple_a C_17) A_35)->(((member2122167641iple_a C_17) B_29)->False))->False))).
% Axiom fact_520_IntE:(forall (C_17:pname) (A_35:(pname->Prop)) (B_29:(pname->Prop)), (((member_pname C_17) ((semila1673364395name_o A_35) B_29))->((((member_pname C_17) A_35)->(((member_pname C_17) B_29)->False))->False))).
% Axiom fact_521_inf__bot__right:(forall (X_12:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_12) bot_bot_pname_o)) bot_bot_pname_o)).
% Axiom fact_522_inf__bot__right:(forall (X_12:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_12) bot_bo751897185le_a_o)) bot_bo751897185le_a_o)).
% Axiom fact_523_inf__bot__right:(forall (X_12:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_12) bot_bo70021908tate_o)) bot_bo70021908tate_o)).
% Axiom fact_524_inf__bot__left:(forall (X_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) X_11)) bot_bot_pname_o)).
% Axiom fact_525_inf__bot__left:(forall (X_11:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o bot_bo751897185le_a_o) X_11)) bot_bo751897185le_a_o)).
% Axiom fact_526_inf__bot__left:(forall (X_11:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) X_11)) bot_bo70021908tate_o)).
% Axiom fact_527_sup__inf__distrib2:(forall (Y_9:Prop) (Z_7:Prop) (X_10:Prop), ((iff ((semila10642723_sup_o ((semila854092349_inf_o Y_9) Z_7)) X_10)) ((semila854092349_inf_o ((semila10642723_sup_o Y_9) X_10)) ((semila10642723_sup_o Z_7) X_10)))).
% Axiom fact_528_sup__inf__distrib2:(forall (Y_9:(pname->Prop)) (Z_7:(pname->Prop)) (X_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o Y_9) Z_7)) X_10)) ((semila1673364395name_o ((semila1780557381name_o Y_9) X_10)) ((semila1780557381name_o Z_7) X_10)))).
% Axiom fact_529_sup__inf__distrib2:(forall (Y_9:(hoare_1167836817_state->Prop)) (Z_7:(hoare_1167836817_state->Prop)) (X_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o Y_9) Z_7)) X_10)) ((semila179895820tate_o ((semila1172322802tate_o Y_9) X_10)) ((semila1172322802tate_o Z_7) X_10)))).
% Axiom fact_530_sup__inf__distrib2:(forall (Y_9:(hoare_1775062406iple_a->Prop)) (Z_7:(hoare_1775062406iple_a->Prop)) (X_10:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila966743401le_a_o Y_9) Z_7)) X_10)) ((semila966743401le_a_o ((semila13410563le_a_o Y_9) X_10)) ((semila13410563le_a_o Z_7) X_10)))).
% Axiom fact_531_inf__sup__distrib2:(forall (Y_8:Prop) (Z_6:Prop) (X_9:Prop), ((iff ((semila854092349_inf_o ((semila10642723_sup_o Y_8) Z_6)) X_9)) ((semila10642723_sup_o ((semila854092349_inf_o Y_8) X_9)) ((semila854092349_inf_o Z_6) X_9)))).
% Axiom fact_532_inf__sup__distrib2:(forall (Y_8:(pname->Prop)) (Z_6:(pname->Prop)) (X_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o Y_8) Z_6)) X_9)) ((semila1780557381name_o ((semila1673364395name_o Y_8) X_9)) ((semila1673364395name_o Z_6) X_9)))).
% Axiom fact_533_inf__sup__distrib2:(forall (Y_8:(hoare_1167836817_state->Prop)) (Z_6:(hoare_1167836817_state->Prop)) (X_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o Y_8) Z_6)) X_9)) ((semila1172322802tate_o ((semila179895820tate_o Y_8) X_9)) ((semila179895820tate_o Z_6) X_9)))).
% Axiom fact_534_inf__sup__distrib2:(forall (Y_8:(hoare_1775062406iple_a->Prop)) (Z_6:(hoare_1775062406iple_a->Prop)) (X_9:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((semila13410563le_a_o Y_8) Z_6)) X_9)) ((semila13410563le_a_o ((semila966743401le_a_o Y_8) X_9)) ((semila966743401le_a_o Z_6) X_9)))).
% Axiom fact_535_sup__inf__distrib1:(forall (X_8:Prop) (Y_7:Prop) (Z_5:Prop), ((iff ((semila10642723_sup_o X_8) ((semila854092349_inf_o Y_7) Z_5))) ((semila854092349_inf_o ((semila10642723_sup_o X_8) Y_7)) ((semila10642723_sup_o X_8) Z_5)))).
% Axiom fact_536_sup__inf__distrib1:(forall (X_8:(pname->Prop)) (Y_7:(pname->Prop)) (Z_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_8) ((semila1673364395name_o Y_7) Z_5))) ((semila1673364395name_o ((semila1780557381name_o X_8) Y_7)) ((semila1780557381name_o X_8) Z_5)))).
% Axiom fact_537_sup__inf__distrib1:(forall (X_8:(hoare_1167836817_state->Prop)) (Y_7:(hoare_1167836817_state->Prop)) (Z_5:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_8) ((semila179895820tate_o Y_7) Z_5))) ((semila179895820tate_o ((semila1172322802tate_o X_8) Y_7)) ((semila1172322802tate_o X_8) Z_5)))).
% Axiom fact_538_sup__inf__distrib1:(forall (X_8:(hoare_1775062406iple_a->Prop)) (Y_7:(hoare_1775062406iple_a->Prop)) (Z_5:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_8) ((semila966743401le_a_o Y_7) Z_5))) ((semila966743401le_a_o ((semila13410563le_a_o X_8) Y_7)) ((semila13410563le_a_o X_8) Z_5)))).
% Axiom fact_539_inf__sup__distrib1:(forall (X_7:Prop) (Y_6:Prop) (Z_4:Prop), ((iff ((semila854092349_inf_o X_7) ((semila10642723_sup_o Y_6) Z_4))) ((semila10642723_sup_o ((semila854092349_inf_o X_7) Y_6)) ((semila854092349_inf_o X_7) Z_4)))).
% Axiom fact_540_inf__sup__distrib1:(forall (X_7:(pname->Prop)) (Y_6:(pname->Prop)) (Z_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_7) ((semila1780557381name_o Y_6) Z_4))) ((semila1780557381name_o ((semila1673364395name_o X_7) Y_6)) ((semila1673364395name_o X_7) Z_4)))).
% Axiom fact_541_inf__sup__distrib1:(forall (X_7:(hoare_1167836817_state->Prop)) (Y_6:(hoare_1167836817_state->Prop)) (Z_4:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_7) ((semila1172322802tate_o Y_6) Z_4))) ((semila1172322802tate_o ((semila179895820tate_o X_7) Y_6)) ((semila179895820tate_o X_7) Z_4)))).
% Axiom fact_542_inf__sup__distrib1:(forall (X_7:(hoare_1775062406iple_a->Prop)) (Y_6:(hoare_1775062406iple_a->Prop)) (Z_4:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_7) ((semila13410563le_a_o Y_6) Z_4))) ((semila13410563le_a_o ((semila966743401le_a_o X_7) Y_6)) ((semila966743401le_a_o X_7) Z_4)))).
% Axiom fact_543_sup__inf__absorb:(forall (X_6:Prop) (Y_5:Prop), ((iff ((semila10642723_sup_o X_6) ((semila854092349_inf_o X_6) Y_5))) X_6)).
% Axiom fact_544_sup__inf__absorb:(forall (X_6:(pname->Prop)) (Y_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_6) ((semila1673364395name_o X_6) Y_5))) X_6)).
% Axiom fact_545_sup__inf__absorb:(forall (X_6:(hoare_1167836817_state->Prop)) (Y_5:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_6) ((semila179895820tate_o X_6) Y_5))) X_6)).
% Axiom fact_546_sup__inf__absorb:(forall (X_6:(hoare_1775062406iple_a->Prop)) (Y_5:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_6) ((semila966743401le_a_o X_6) Y_5))) X_6)).
% Axiom fact_547_inf__sup__absorb:(forall (X_5:Prop) (Y_4:Prop), ((iff ((semila854092349_inf_o X_5) ((semila10642723_sup_o X_5) Y_4))) X_5)).
% Axiom fact_548_inf__sup__absorb:(forall (X_5:(pname->Prop)) (Y_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_5) ((semila1780557381name_o X_5) Y_4))) X_5)).
% Axiom fact_549_inf__sup__absorb:(forall (X_5:(hoare_1167836817_state->Prop)) (Y_4:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_5) ((semila1172322802tate_o X_5) Y_4))) X_5)).
% Axiom fact_550_inf__sup__absorb:(forall (X_5:(hoare_1775062406iple_a->Prop)) (Y_4:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_5) ((semila13410563le_a_o X_5) Y_4))) X_5)).
% Axiom fact_551_disjoint__iff__not__equal:(forall (A_34:(pname->Prop)) (B_28:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1673364395name_o A_34) B_28)) bot_bot_pname_o)) (forall (X:pname), (((member_pname X) A_34)->(forall (Xa:pname), (((member_pname Xa) B_28)->(not (((eq pname) X) Xa)))))))).
% Axiom fact_552_disjoint__iff__not__equal:(forall (A_34:(hoare_1775062406iple_a->Prop)) (B_28:(hoare_1775062406iple_a->Prop)), ((iff (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_34) B_28)) bot_bo751897185le_a_o)) (forall (X:hoare_1775062406iple_a), (((member2122167641iple_a X) A_34)->(forall (Xa:hoare_1775062406iple_a), (((member2122167641iple_a Xa) B_28)->(not (((eq hoare_1775062406iple_a) X) Xa)))))))).
% Axiom fact_553_disjoint__iff__not__equal:(forall (A_34:(hoare_1167836817_state->Prop)) (B_28:(hoare_1167836817_state->Prop)), ((iff (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_34) B_28)) bot_bo70021908tate_o)) (forall (X:hoare_1167836817_state), (((member2058392318_state X) A_34)->(forall (Xa:hoare_1167836817_state), (((member2058392318_state Xa) B_28)->(not (((eq hoare_1167836817_state) X) Xa)))))))).
% Axiom fact_554_Int__empty__right:(forall (A_33:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_33) bot_bot_pname_o)) bot_bot_pname_o)).
% Axiom fact_555_Int__empty__right:(forall (A_33:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_33) bot_bo751897185le_a_o)) bot_bo751897185le_a_o)).
% Axiom fact_556_Int__empty__right:(forall (A_33:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_33) bot_bo70021908tate_o)) bot_bo70021908tate_o)).
% Axiom fact_557_Int__empty__left:(forall (B_27:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o bot_bot_pname_o) B_27)) bot_bot_pname_o)).
% Axiom fact_558_Int__empty__left:(forall (B_27:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o bot_bo751897185le_a_o) B_27)) bot_bo751897185le_a_o)).
% Axiom fact_559_Int__empty__left:(forall (B_27:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o bot_bo70021908tate_o) B_27)) bot_bo70021908tate_o)).
% Axiom fact_560_Int__def:(forall (A_32:(hoare_1775062406iple_a->Prop)) (B_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_32) B_26)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and ((member2122167641iple_a X) A_32)) ((member2122167641iple_a X) B_26)))))).
% Axiom fact_561_Int__def:(forall (A_32:(pname->Prop)) (B_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_32) B_26)) (collect_pname (fun (X:pname)=> ((and ((member_pname X) A_32)) ((member_pname X) B_26)))))).
% Axiom fact_562_Int__iff:(forall (C_16:hoare_1775062406iple_a) (A_31:(hoare_1775062406iple_a->Prop)) (B_25:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a C_16) ((semila966743401le_a_o A_31) B_25))) ((and ((member2122167641iple_a C_16) A_31)) ((member2122167641iple_a C_16) B_25)))).
% Axiom fact_563_Int__iff:(forall (C_16:pname) (A_31:(pname->Prop)) (B_25:(pname->Prop)), ((iff ((member_pname C_16) ((semila1673364395name_o A_31) B_25))) ((and ((member_pname C_16) A_31)) ((member_pname C_16) B_25)))).
% Axiom fact_564_IntD1:(forall (C_15:hoare_1775062406iple_a) (A_30:(hoare_1775062406iple_a->Prop)) (B_24:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_15) ((semila966743401le_a_o A_30) B_24))->((member2122167641iple_a C_15) A_30))).
% Axiom fact_565_IntD1:(forall (C_15:pname) (A_30:(pname->Prop)) (B_24:(pname->Prop)), (((member_pname C_15) ((semila1673364395name_o A_30) B_24))->((member_pname C_15) A_30))).
% Axiom fact_566_IntD2:(forall (C_14:hoare_1775062406iple_a) (A_29:(hoare_1775062406iple_a->Prop)) (B_23:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_14) ((semila966743401le_a_o A_29) B_23))->((member2122167641iple_a C_14) B_23))).
% Axiom fact_567_IntD2:(forall (C_14:pname) (A_29:(pname->Prop)) (B_23:(pname->Prop)), (((member_pname C_14) ((semila1673364395name_o A_29) B_23))->((member_pname C_14) B_23))).
% Axiom fact_568_Collect__conj__eq:(forall (P_3:(hoare_1775062406iple_a->Prop)) (Q:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) (collec676402587iple_a (fun (X:hoare_1775062406iple_a)=> ((and (P_3 X)) (Q X))))) ((semila966743401le_a_o (collec676402587iple_a P_3)) (collec676402587iple_a Q)))).
% Axiom fact_569_Collect__conj__eq:(forall (P_3:(pname->Prop)) (Q:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (P_3 X)) (Q X))))) ((semila1673364395name_o (collect_pname P_3)) (collect_pname Q)))).
% Axiom fact_570_Int__Collect:(forall (X_4:hoare_1775062406iple_a) (A_28:(hoare_1775062406iple_a->Prop)) (P_2:(hoare_1775062406iple_a->Prop)), ((iff ((member2122167641iple_a X_4) ((semila966743401le_a_o A_28) (collec676402587iple_a P_2)))) ((and ((member2122167641iple_a X_4) A_28)) (P_2 X_4)))).
% Axiom fact_571_Int__Collect:(forall (X_4:pname) (A_28:(pname->Prop)) (P_2:(pname->Prop)), ((iff ((member_pname X_4) ((semila1673364395name_o A_28) (collect_pname P_2)))) ((and ((member_pname X_4) A_28)) (P_2 X_4)))).
% Axiom fact_572_inf__Int__eq:(forall (R:(hoare_1775062406iple_a->Prop)) (S_2:(hoare_1775062406iple_a->Prop)) (X:hoare_1775062406iple_a), ((iff (((semila966743401le_a_o (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) R))) (fun (Y_2:hoare_1775062406iple_a)=> ((member2122167641iple_a Y_2) S_2))) X)) ((member2122167641iple_a X) ((semila966743401le_a_o R) S_2)))).
% Axiom fact_573_inf__Int__eq:(forall (R:(pname->Prop)) (S_2:(pname->Prop)) (X:pname), ((iff (((semila1673364395name_o (fun (Y_2:pname)=> ((member_pname Y_2) R))) (fun (Y_2:pname)=> ((member_pname Y_2) S_2))) X)) ((member_pname X) ((semila1673364395name_o R) S_2)))).
% Axiom fact_574_Un__Int__crazy:(forall (A_27:(pname->Prop)) (B_22:(pname->Prop)) (C_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o ((semila1673364395name_o A_27) B_22)) ((semila1673364395name_o B_22) C_13))) ((semila1673364395name_o C_13) A_27))) ((semila1673364395name_o ((semila1673364395name_o ((semila1780557381name_o A_27) B_22)) ((semila1780557381name_o B_22) C_13))) ((semila1780557381name_o C_13) A_27)))).
% Axiom fact_575_Un__Int__crazy:(forall (A_27:(hoare_1167836817_state->Prop)) (B_22:(hoare_1167836817_state->Prop)) (C_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila1172322802tate_o ((semila179895820tate_o A_27) B_22)) ((semila179895820tate_o B_22) C_13))) ((semila179895820tate_o C_13) A_27))) ((semila179895820tate_o ((semila179895820tate_o ((semila1172322802tate_o A_27) B_22)) ((semila1172322802tate_o B_22) C_13))) ((semila1172322802tate_o C_13) A_27)))).
% Axiom fact_576_Un__Int__crazy:(forall (A_27:(hoare_1775062406iple_a->Prop)) (B_22:(hoare_1775062406iple_a->Prop)) (C_13:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila13410563le_a_o ((semila966743401le_a_o A_27) B_22)) ((semila966743401le_a_o B_22) C_13))) ((semila966743401le_a_o C_13) A_27))) ((semila966743401le_a_o ((semila966743401le_a_o ((semila13410563le_a_o A_27) B_22)) ((semila13410563le_a_o B_22) C_13))) ((semila13410563le_a_o C_13) A_27)))).
% Axiom fact_577_Un__Int__distrib2:(forall (B_21:(pname->Prop)) (C_12:(pname->Prop)) (A_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1673364395name_o B_21) C_12)) A_26)) ((semila1673364395name_o ((semila1780557381name_o B_21) A_26)) ((semila1780557381name_o C_12) A_26)))).
% Axiom fact_578_Un__Int__distrib2:(forall (B_21:(hoare_1167836817_state->Prop)) (C_12:(hoare_1167836817_state->Prop)) (A_26:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((semila179895820tate_o B_21) C_12)) A_26)) ((semila179895820tate_o ((semila1172322802tate_o B_21) A_26)) ((semila1172322802tate_o C_12) A_26)))).
% Axiom fact_579_Un__Int__distrib2:(forall (B_21:(hoare_1775062406iple_a->Prop)) (C_12:(hoare_1775062406iple_a->Prop)) (A_26:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((semila966743401le_a_o B_21) C_12)) A_26)) ((semila966743401le_a_o ((semila13410563le_a_o B_21) A_26)) ((semila13410563le_a_o C_12) A_26)))).
% Axiom fact_580_Int__Un__distrib2:(forall (B_20:(pname->Prop)) (C_11:(pname->Prop)) (A_25:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((semila1780557381name_o B_20) C_11)) A_25)) ((semila1780557381name_o ((semila1673364395name_o B_20) A_25)) ((semila1673364395name_o C_11) A_25)))).
% Axiom fact_581_Int__Un__distrib2:(forall (B_20:(hoare_1167836817_state->Prop)) (C_11:(hoare_1167836817_state->Prop)) (A_25:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((semila1172322802tate_o B_20) C_11)) A_25)) ((semila1172322802tate_o ((semila179895820tate_o B_20) A_25)) ((semila179895820tate_o C_11) A_25)))).
% Axiom fact_582_Int__Un__distrib2:(forall (B_20:(hoare_1775062406iple_a->Prop)) (C_11:(hoare_1775062406iple_a->Prop)) (A_25:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((semila13410563le_a_o B_20) C_11)) A_25)) ((semila13410563le_a_o ((semila966743401le_a_o B_20) A_25)) ((semila966743401le_a_o C_11) A_25)))).
% Axiom fact_583_Un__Int__distrib:(forall (A_24:(pname->Prop)) (B_19:(pname->Prop)) (C_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_24) ((semila1673364395name_o B_19) C_10))) ((semila1673364395name_o ((semila1780557381name_o A_24) B_19)) ((semila1780557381name_o A_24) C_10)))).
% Axiom fact_584_Un__Int__distrib:(forall (A_24:(hoare_1167836817_state->Prop)) (B_19:(hoare_1167836817_state->Prop)) (C_10:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_24) ((semila179895820tate_o B_19) C_10))) ((semila179895820tate_o ((semila1172322802tate_o A_24) B_19)) ((semila1172322802tate_o A_24) C_10)))).
% Axiom fact_585_Un__Int__distrib:(forall (A_24:(hoare_1775062406iple_a->Prop)) (B_19:(hoare_1775062406iple_a->Prop)) (C_10:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_24) ((semila966743401le_a_o B_19) C_10))) ((semila966743401le_a_o ((semila13410563le_a_o A_24) B_19)) ((semila13410563le_a_o A_24) C_10)))).
% Axiom fact_586_Int__Un__distrib:(forall (A_23:(pname->Prop)) (B_18:(pname->Prop)) (C_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_23) ((semila1780557381name_o B_18) C_9))) ((semila1780557381name_o ((semila1673364395name_o A_23) B_18)) ((semila1673364395name_o A_23) C_9)))).
% Axiom fact_587_Int__Un__distrib:(forall (A_23:(hoare_1167836817_state->Prop)) (B_18:(hoare_1167836817_state->Prop)) (C_9:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_23) ((semila1172322802tate_o B_18) C_9))) ((semila1172322802tate_o ((semila179895820tate_o A_23) B_18)) ((semila179895820tate_o A_23) C_9)))).
% Axiom fact_588_Int__Un__distrib:(forall (A_23:(hoare_1775062406iple_a->Prop)) (B_18:(hoare_1775062406iple_a->Prop)) (C_9:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_23) ((semila13410563le_a_o B_18) C_9))) ((semila13410563le_a_o ((semila966743401le_a_o A_23) B_18)) ((semila966743401le_a_o A_23) C_9)))).
% Axiom fact_589_Int__insert__left__if1:(forall (B_17:(hoare_1167836817_state->Prop)) (A_22:hoare_1167836817_state) (C_8:(hoare_1167836817_state->Prop)), (((member2058392318_state A_22) C_8)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_22) B_17)) C_8)) ((insert2134838167_state A_22) ((semila179895820tate_o B_17) C_8))))).
% Axiom fact_590_Int__insert__left__if1:(forall (B_17:(hoare_1775062406iple_a->Prop)) (A_22:hoare_1775062406iple_a) (C_8:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_22) C_8)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_22) B_17)) C_8)) ((insert1281456128iple_a A_22) ((semila966743401le_a_o B_17) C_8))))).
% Axiom fact_591_Int__insert__left__if1:(forall (B_17:(pname->Prop)) (A_22:pname) (C_8:(pname->Prop)), (((member_pname A_22) C_8)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_22) B_17)) C_8)) ((insert_pname A_22) ((semila1673364395name_o B_17) C_8))))).
% Axiom fact_592_Int__insert__right__if1:(forall (B_16:(hoare_1167836817_state->Prop)) (A_21:hoare_1167836817_state) (A_20:(hoare_1167836817_state->Prop)), (((member2058392318_state A_21) A_20)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_20) ((insert2134838167_state A_21) B_16))) ((insert2134838167_state A_21) ((semila179895820tate_o A_20) B_16))))).
% Axiom fact_593_Int__insert__right__if1:(forall (B_16:(hoare_1775062406iple_a->Prop)) (A_21:hoare_1775062406iple_a) (A_20:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a A_21) A_20)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_20) ((insert1281456128iple_a A_21) B_16))) ((insert1281456128iple_a A_21) ((semila966743401le_a_o A_20) B_16))))).
% Axiom fact_594_Int__insert__right__if1:(forall (B_16:(pname->Prop)) (A_21:pname) (A_20:(pname->Prop)), (((member_pname A_21) A_20)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) ((insert_pname A_21) B_16))) ((insert_pname A_21) ((semila1673364395name_o A_20) B_16))))).
% Axiom fact_595_Int__insert__left__if0:(forall (B_15:(hoare_1167836817_state->Prop)) (A_19:hoare_1167836817_state) (C_7:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_19) C_7)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_19) B_15)) C_7)) ((semila179895820tate_o B_15) C_7)))).
% Axiom fact_596_Int__insert__left__if0:(forall (B_15:(hoare_1775062406iple_a->Prop)) (A_19:hoare_1775062406iple_a) (C_7:(hoare_1775062406iple_a->Prop)), ((((member2122167641iple_a A_19) C_7)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_19) B_15)) C_7)) ((semila966743401le_a_o B_15) C_7)))).
% Axiom fact_597_Int__insert__left__if0:(forall (B_15:(pname->Prop)) (A_19:pname) (C_7:(pname->Prop)), ((((member_pname A_19) C_7)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_19) B_15)) C_7)) ((semila1673364395name_o B_15) C_7)))).
% Axiom fact_598_Int__insert__right__if0:(forall (B_14:(hoare_1167836817_state->Prop)) (A_18:hoare_1167836817_state) (A_17:(hoare_1167836817_state->Prop)), ((((member2058392318_state A_18) A_17)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_17) ((insert2134838167_state A_18) B_14))) ((semila179895820tate_o A_17) B_14)))).
% Axiom fact_599_Int__insert__right__if0:(forall (B_14:(hoare_1775062406iple_a->Prop)) (A_18:hoare_1775062406iple_a) (A_17:(hoare_1775062406iple_a->Prop)), ((((member2122167641iple_a A_18) A_17)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_17) ((insert1281456128iple_a A_18) B_14))) ((semila966743401le_a_o A_17) B_14)))).
% Axiom fact_600_Int__insert__right__if0:(forall (B_14:(pname->Prop)) (A_18:pname) (A_17:(pname->Prop)), ((((member_pname A_18) A_17)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_17) ((insert_pname A_18) B_14))) ((semila1673364395name_o A_17) B_14)))).
% Axiom fact_601_insert__inter__insert:(forall (A_16:hoare_1167836817_state) (A_15:(hoare_1167836817_state->Prop)) (B_13:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_16) A_15)) ((insert2134838167_state A_16) B_13))) ((insert2134838167_state A_16) ((semila179895820tate_o A_15) B_13)))).
% Axiom fact_602_insert__inter__insert:(forall (A_16:hoare_1775062406iple_a) (A_15:(hoare_1775062406iple_a->Prop)) (B_13:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_16) A_15)) ((insert1281456128iple_a A_16) B_13))) ((insert1281456128iple_a A_16) ((semila966743401le_a_o A_15) B_13)))).
% Axiom fact_603_insert__inter__insert:(forall (A_16:pname) (A_15:(pname->Prop)) (B_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_16) A_15)) ((insert_pname A_16) B_13))) ((insert_pname A_16) ((semila1673364395name_o A_15) B_13)))).
% Axiom fact_604_Int__insert__left:(forall (B_12:(hoare_1167836817_state->Prop)) (A_14:hoare_1167836817_state) (C_6:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_14) C_6)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_14) B_12)) C_6)) ((insert2134838167_state A_14) ((semila179895820tate_o B_12) C_6))))) ((((member2058392318_state A_14) C_6)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o ((insert2134838167_state A_14) B_12)) C_6)) ((semila179895820tate_o B_12) C_6))))).
% Axiom fact_605_Int__insert__left:(forall (B_12:(hoare_1775062406iple_a->Prop)) (A_14:hoare_1775062406iple_a) (C_6:(hoare_1775062406iple_a->Prop)), ((and (((member2122167641iple_a A_14) C_6)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_14) B_12)) C_6)) ((insert1281456128iple_a A_14) ((semila966743401le_a_o B_12) C_6))))) ((((member2122167641iple_a A_14) C_6)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o ((insert1281456128iple_a A_14) B_12)) C_6)) ((semila966743401le_a_o B_12) C_6))))).
% Axiom fact_606_Int__insert__left:(forall (B_12:(pname->Prop)) (A_14:pname) (C_6:(pname->Prop)), ((and (((member_pname A_14) C_6)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_14) B_12)) C_6)) ((insert_pname A_14) ((semila1673364395name_o B_12) C_6))))) ((((member_pname A_14) C_6)->False)->(((eq (pname->Prop)) ((semila1673364395name_o ((insert_pname A_14) B_12)) C_6)) ((semila1673364395name_o B_12) C_6))))).
% Axiom fact_607_Int__insert__right:(forall (B_11:(hoare_1167836817_state->Prop)) (A_13:hoare_1167836817_state) (A_12:(hoare_1167836817_state->Prop)), ((and (((member2058392318_state A_13) A_12)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_12) ((insert2134838167_state A_13) B_11))) ((insert2134838167_state A_13) ((semila179895820tate_o A_12) B_11))))) ((((member2058392318_state A_13) A_12)->False)->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_12) ((insert2134838167_state A_13) B_11))) ((semila179895820tate_o A_12) B_11))))).
% Axiom fact_608_Int__insert__right:(forall (B_11:(hoare_1775062406iple_a->Prop)) (A_13:hoare_1775062406iple_a) (A_12:(hoare_1775062406iple_a->Prop)), ((and (((member2122167641iple_a A_13) A_12)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_12) ((insert1281456128iple_a A_13) B_11))) ((insert1281456128iple_a A_13) ((semila966743401le_a_o A_12) B_11))))) ((((member2122167641iple_a A_13) A_12)->False)->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_12) ((insert1281456128iple_a A_13) B_11))) ((semila966743401le_a_o A_12) B_11))))).
% Axiom fact_609_Int__insert__right:(forall (B_11:(pname->Prop)) (A_13:pname) (A_12:(pname->Prop)), ((and (((member_pname A_13) A_12)->(((eq (pname->Prop)) ((semila1673364395name_o A_12) ((insert_pname A_13) B_11))) ((insert_pname A_13) ((semila1673364395name_o A_12) B_11))))) ((((member_pname A_13) A_12)->False)->(((eq (pname->Prop)) ((semila1673364395name_o A_12) ((insert_pname A_13) B_11))) ((semila1673364395name_o A_12) B_11))))).
% Axiom fact_610_if__image__distrib:(forall (P_1:(pname->Prop)) (F_4:(pname->hoare_1167836817_state)) (G:(pname->hoare_1167836817_state)) (S_1:(pname->Prop)), (((eq (hoare_1167836817_state->Prop)) ((image_575578384_state (fun (X:pname)=> (((if_Hoa833675553_state (P_1 X)) (F_4 X)) (G X)))) S_1)) ((semila1172322802tate_o ((image_575578384_state F_4) ((semila1673364395name_o S_1) (collect_pname P_1)))) ((image_575578384_state G) ((semila1673364395name_o S_1) (collect_pname (fun (X:pname)=> (not (P_1 X))))))))).
% Axiom fact_611_if__image__distrib:(forall (P_1:(pname->Prop)) (F_4:(pname->hoare_1775062406iple_a)) (G:(pname->hoare_1775062406iple_a)) (S_1:(pname->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((image_2063119815iple_a (fun (X:pname)=> (((if_Hoa1047340790iple_a (P_1 X)) (F_4 X)) (G X)))) S_1)) ((semila13410563le_a_o ((image_2063119815iple_a F_4) ((semila1673364395name_o S_1) (collect_pname P_1)))) ((image_2063119815iple_a G) ((semila1673364395name_o S_1) (collect_pname (fun (X:pname)=> (not (P_1 X))))))))).
% Axiom fact_612_folding__one_Ounion__inter:(forall (B_10:(pname->Prop)) (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)->((finite_finite_pname B_10)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_11) B_10)) bot_bot_pname_o))->(((eq pname) ((F_3 (F_2 ((semila1780557381name_o A_11) B_10))) (F_2 ((semila1673364395name_o A_11) B_10)))) ((F_3 (F_2 A_11)) (F_2 B_10)))))))).
% Axiom fact_613_folding__one_Ounion__inter:(forall (B_10:(hoare_1775062406iple_a->Prop)) (A_11:(hoare_1775062406iple_a->Prop)) (F_3:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F_2:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_3) F_2)->((finite2063573081iple_a A_11)->((finite2063573081iple_a B_10)->((not (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_11) B_10)) bot_bo751897185le_a_o))->(((eq hoare_1775062406iple_a) ((F_3 (F_2 ((semila13410563le_a_o A_11) B_10))) (F_2 ((semila966743401le_a_o A_11) B_10)))) ((F_3 (F_2 A_11)) (F_2 B_10)))))))).
% Axiom fact_614_folding__one_Ounion__inter:(forall (B_10:(hoare_1167836817_state->Prop)) (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)->((finite1084549118_state B_10)->((not (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_11) B_10)) bot_bo70021908tate_o))->(((eq hoare_1167836817_state) ((F_3 (F_2 ((semila1172322802tate_o A_11) B_10))) (F_2 ((semila179895820tate_o A_11) B_10)))) ((F_3 (F_2 A_11)) (F_2 B_10)))))))).
% Axiom fact_615_folding__one_Ounion__disjoint:(forall (B_9:(pname->Prop)) (A_10:(pname->Prop)) (F_1:(pname->(pname->pname))) (F:((pname->Prop)->pname)), (((finite1282449217_pname F_1) F)->((finite_finite_pname A_10)->((not (((eq (pname->Prop)) A_10) bot_bot_pname_o))->((finite_finite_pname B_9)->((not (((eq (pname->Prop)) B_9) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_10) B_9)) bot_bot_pname_o)->(((eq pname) (F ((semila1780557381name_o A_10) B_9))) ((F_1 (F A_10)) (F B_9)))))))))).
% Axiom fact_616_folding__one_Ounion__disjoint:(forall (B_9:(hoare_1775062406iple_a->Prop)) (A_10:(hoare_1775062406iple_a->Prop)) (F_1:(hoare_1775062406iple_a->(hoare_1775062406iple_a->hoare_1775062406iple_a))) (F:((hoare_1775062406iple_a->Prop)->hoare_1775062406iple_a)), (((finite2078349315iple_a F_1) F)->((finite2063573081iple_a A_10)->((not (((eq (hoare_1775062406iple_a->Prop)) A_10) bot_bo751897185le_a_o))->((finite2063573081iple_a B_9)->((not (((eq (hoare_1775062406iple_a->Prop)) B_9) bot_bo751897185le_a_o))->((((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o A_10) B_9)) bot_bo751897185le_a_o)->(((eq hoare_1775062406iple_a) (F ((semila13410563le_a_o A_10) B_9))) ((F_1 (F A_10)) (F B_9)))))))))).
% Axiom fact_617_folding__one_Ounion__disjoint:(forall (B_9:(hoare_1167836817_state->Prop)) (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)->((not (((eq (hoare_1167836817_state->Prop)) A_10) bot_bo70021908tate_o))->((finite1084549118_state B_9)->((not (((eq (hoare_1167836817_state->Prop)) B_9) bot_bo70021908tate_o))->((((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o A_10) B_9)) bot_bo70021908tate_o)->(((eq hoare_1167836817_state) (F ((semila1172322802tate_o A_10) B_9))) ((F_1 (F A_10)) (F B_9)))))))))).
% Axiom fact_618_distrib__imp2:(forall (X_3:Prop) (Y_3:Prop) (Z_3:Prop), ((forall (X:Prop) (Y_2:Prop) (Z_2:Prop), ((iff ((semila10642723_sup_o X) ((semila854092349_inf_o Y_2) Z_2))) ((semila854092349_inf_o ((semila10642723_sup_o X) Y_2)) ((semila10642723_sup_o X) Z_2))))->((iff ((semila854092349_inf_o X_3) ((semila10642723_sup_o Y_3) Z_3))) ((semila10642723_sup_o ((semila854092349_inf_o X_3) Y_3)) ((semila854092349_inf_o X_3) Z_3))))).
% Axiom fact_619_distrib__imp2:(forall (X_3:(pname->Prop)) (Y_3:(pname->Prop)) (Z_3:(pname->Prop)), ((forall (X:(pname->Prop)) (Y_2:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X) ((semila1673364395name_o Y_2) Z_2))) ((semila1673364395name_o ((semila1780557381name_o X) Y_2)) ((semila1780557381name_o X) Z_2))))->(((eq (pname->Prop)) ((semila1673364395name_o X_3) ((semila1780557381name_o Y_3) Z_3))) ((semila1780557381name_o ((semila1673364395name_o X_3) Y_3)) ((semila1673364395name_o X_3) Z_3))))).
% Axiom fact_620_distrib__imp2:(forall (X_3:(hoare_1167836817_state->Prop)) (Y_3:(hoare_1167836817_state->Prop)) (Z_3:(hoare_1167836817_state->Prop)), ((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X) ((semila179895820tate_o Y_2) Z_2))) ((semila179895820tate_o ((semila1172322802tate_o X) Y_2)) ((semila1172322802tate_o X) Z_2))))->(((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X_3) ((semila1172322802tate_o Y_3) Z_3))) ((semila1172322802tate_o ((semila179895820tate_o X_3) Y_3)) ((semila179895820tate_o X_3) Z_3))))).
% Axiom fact_621_distrib__imp2:(forall (X_3:(hoare_1775062406iple_a->Prop)) (Y_3:(hoare_1775062406iple_a->Prop)) (Z_3:(hoare_1775062406iple_a->Prop)), ((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)) (Z_2:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X) ((semila966743401le_a_o Y_2) Z_2))) ((semila966743401le_a_o ((semila13410563le_a_o X) Y_2)) ((semila13410563le_a_o X) Z_2))))->(((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X_3) ((semila13410563le_a_o Y_3) Z_3))) ((semila13410563le_a_o ((semila966743401le_a_o X_3) Y_3)) ((semila966743401le_a_o X_3) Z_3))))).
% Axiom fact_622_distrib__imp1:(forall (X_2:Prop) (Y_1:Prop) (Z_1:Prop), ((forall (X:Prop) (Y_2:Prop) (Z_2:Prop), ((iff ((semila854092349_inf_o X) ((semila10642723_sup_o Y_2) Z_2))) ((semila10642723_sup_o ((semila854092349_inf_o X) Y_2)) ((semila854092349_inf_o X) Z_2))))->((iff ((semila10642723_sup_o X_2) ((semila854092349_inf_o Y_1) Z_1))) ((semila854092349_inf_o ((semila10642723_sup_o X_2) Y_1)) ((semila10642723_sup_o X_2) Z_1))))).
% Axiom fact_623_distrib__imp1:(forall (X_2:(pname->Prop)) (Y_1:(pname->Prop)) (Z_1:(pname->Prop)), ((forall (X:(pname->Prop)) (Y_2:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X) ((semila1780557381name_o Y_2) Z_2))) ((semila1780557381name_o ((semila1673364395name_o X) Y_2)) ((semila1673364395name_o X) Z_2))))->(((eq (pname->Prop)) ((semila1780557381name_o X_2) ((semila1673364395name_o Y_1) Z_1))) ((semila1673364395name_o ((semila1780557381name_o X_2) Y_1)) ((semila1780557381name_o X_2) Z_1))))).
% Axiom fact_624_distrib__imp1:(forall (X_2:(hoare_1167836817_state->Prop)) (Y_1:(hoare_1167836817_state->Prop)) (Z_1:(hoare_1167836817_state->Prop)), ((forall (X:(hoare_1167836817_state->Prop)) (Y_2:(hoare_1167836817_state->Prop)) (Z_2:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila179895820tate_o X) ((semila1172322802tate_o Y_2) Z_2))) ((semila1172322802tate_o ((semila179895820tate_o X) Y_2)) ((semila179895820tate_o X) Z_2))))->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o X_2) ((semila179895820tate_o Y_1) Z_1))) ((semila179895820tate_o ((semila1172322802tate_o X_2) Y_1)) ((semila1172322802tate_o X_2) Z_1))))).
% Axiom fact_625_distrib__imp1:(forall (X_2:(hoare_1775062406iple_a->Prop)) (Y_1:(hoare_1775062406iple_a->Prop)) (Z_1:(hoare_1775062406iple_a->Prop)), ((forall (X:(hoare_1775062406iple_a->Prop)) (Y_2:(hoare_1775062406iple_a->Prop)) (Z_2:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila966743401le_a_o X) ((semila13410563le_a_o Y_2) Z_2))) ((semila13410563le_a_o ((semila966743401le_a_o X) Y_2)) ((semila966743401le_a_o X) Z_2))))->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o X_2) ((semila966743401le_a_o Y_1) Z_1))) ((semila966743401le_a_o ((semila13410563le_a_o X_2) Y_1)) ((semila13410563le_a_o X_2) Z_1))))).
% Axiom fact_626_sup__Inf__absorb:(forall (A_9:Prop) (A_8:(Prop->Prop)), ((finite_finite_o A_8)->(((member_o A_9) A_8)->((iff ((semila10642723_sup_o A_9) (big_la1690136417_fin_o A_8))) A_9)))).
% Axiom fact_627_sup__Inf__absorb:(forall (A_9:(pname->Prop)) (A_8:((pname->Prop)->Prop)), ((finite297249702name_o A_8)->(((member_pname_o A_9) A_8)->(((eq (pname->Prop)) ((semila1780557381name_o A_9) (big_la1126801287name_o A_8))) A_9)))).
% Axiom fact_628_sup__Inf__absorb:(forall (A_9:(hoare_1167836817_state->Prop)) (A_8:((hoare_1167836817_state->Prop)->Prop)), ((finite1380128977tate_o A_8)->(((member864234961tate_o A_9) A_8)->(((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_9) (big_la831793456tate_o A_8))) A_9)))).
% Axiom fact_629_sup__Inf__absorb:(forall (A_9:(hoare_1775062406iple_a->Prop)) (A_8:((hoare_1775062406iple_a->Prop)->Prop)), ((finite789576932le_a_o A_8)->(((member1207314404le_a_o A_9) A_8)->(((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_9) (big_la447547205le_a_o A_8))) A_9)))).
% Axiom fact_630_DiffE:(forall (C_5:hoare_1775062406iple_a) (A_7:(hoare_1775062406iple_a->Prop)) (B_8:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_5) ((minus_1944206118le_a_o A_7) B_8))->((((member2122167641iple_a C_5) A_7)->((member2122167641iple_a C_5) B_8))->False))).
% Axiom fact_631_DiffE:(forall (C_5:pname) (A_7:(pname->Prop)) (B_8:(pname->Prop)), (((member_pname C_5) ((minus_minus_pname_o A_7) B_8))->((((member_pname C_5) A_7)->((member_pname C_5) B_8))->False))).
% Axiom fact_632_DiffI:(forall (B_7:(hoare_1775062406iple_a->Prop)) (C_4:hoare_1775062406iple_a) (A_6:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_4) A_6)->((((member2122167641iple_a C_4) B_7)->False)->((member2122167641iple_a C_4) ((minus_1944206118le_a_o A_6) B_7))))).
% Axiom fact_633_DiffI:(forall (B_7:(pname->Prop)) (C_4:pname) (A_6:(pname->Prop)), (((member_pname C_4) A_6)->((((member_pname C_4) B_7)->False)->((member_pname C_4) ((minus_minus_pname_o A_6) B_7))))).
% Axiom fact_634_Un__Diff__cancel:(forall (A_5:(pname->Prop)) (B_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_5) ((minus_minus_pname_o B_6) A_5))) ((semila1780557381name_o A_5) B_6))).
% Axiom fact_635_Un__Diff__cancel:(forall (A_5:(hoare_1167836817_state->Prop)) (B_6:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o A_5) ((minus_2107060239tate_o B_6) A_5))) ((semila1172322802tate_o A_5) B_6))).
% Axiom fact_636_Un__Diff__cancel:(forall (A_5:(hoare_1775062406iple_a->Prop)) (B_6:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o A_5) ((minus_1944206118le_a_o B_6) A_5))) ((semila13410563le_a_o A_5) B_6))).
% Axiom fact_637_Un__Diff__cancel2:(forall (B_5:(pname->Prop)) (A_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o B_5) A_4)) A_4)) ((semila1780557381name_o B_5) A_4))).
% Axiom fact_638_Un__Diff__cancel2:(forall (B_5:(hoare_1167836817_state->Prop)) (A_4:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((semila1172322802tate_o ((minus_2107060239tate_o B_5) A_4)) A_4)) ((semila1172322802tate_o B_5) A_4))).
% Axiom fact_639_Un__Diff__cancel2:(forall (B_5:(hoare_1775062406iple_a->Prop)) (A_4:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((semila13410563le_a_o ((minus_1944206118le_a_o B_5) A_4)) A_4)) ((semila13410563le_a_o B_5) A_4))).
% Axiom fact_640_Un__Diff:(forall (A_3:(pname->Prop)) (B_4:(pname->Prop)) (C_3:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o ((semila1780557381name_o A_3) B_4)) C_3)) ((semila1780557381name_o ((minus_minus_pname_o A_3) C_3)) ((minus_minus_pname_o B_4) C_3)))).
% Axiom fact_641_Un__Diff:(forall (A_3:(hoare_1167836817_state->Prop)) (B_4:(hoare_1167836817_state->Prop)) (C_3:(hoare_1167836817_state->Prop)), (((eq (hoare_1167836817_state->Prop)) ((minus_2107060239tate_o ((semila1172322802tate_o A_3) B_4)) C_3)) ((semila1172322802tate_o ((minus_2107060239tate_o A_3) C_3)) ((minus_2107060239tate_o B_4) C_3)))).
% Axiom fact_642_Un__Diff:(forall (A_3:(hoare_1775062406iple_a->Prop)) (B_4:(hoare_1775062406iple_a->Prop)) (C_3:(hoare_1775062406iple_a->Prop)), (((eq (hoare_1775062406iple_a->Prop)) ((minus_1944206118le_a_o ((semila13410563le_a_o A_3) B_4)) C_3)) ((semila13410563le_a_o ((minus_1944206118le_a_o A_3) C_3)) ((minus_1944206118le_a_o B_4) C_3)))).
% Axiom fact_643_DiffD2:(forall (C_2:hoare_1775062406iple_a) (A_2:(hoare_1775062406iple_a->Prop)) (B_3:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_2) ((minus_1944206118le_a_o A_2) B_3))->(((member2122167641iple_a C_2) B_3)->False))).
% Axiom fact_644_DiffD2:(forall (C_2:pname) (A_2:(pname->Prop)) (B_3:(pname->Prop)), (((member_pname C_2) ((minus_minus_pname_o A_2) B_3))->(((member_pname C_2) B_3)->False))).
% Axiom fact_645_DiffD1:(forall (C_1:hoare_1775062406iple_a) (A_1:(hoare_1775062406iple_a->Prop)) (B_2:(hoare_1775062406iple_a->Prop)), (((member2122167641iple_a C_1) ((minus_1944206118le_a_o A_1) B_2))->((member2122167641iple_a C_1) A_1))).
% Axiom fact_646_DiffD1:(forall (C_1:pname) (A_1:(pname->Prop)) (B_2:(pname->Prop)), (((member_pname C_1) ((minus_minus_pname_o A_1) B_2))->((member_pname C_1) A_1))).
% Axiom fact_647_Diff__iff:(forall (C:pname) (A:(pname->Prop)) (B_1:(pname->Prop)), ((iff ((member_pname C) ((minus_minus_pname_o A) B_1))) ((and ((member_pname C) A)) (((member_pname C) B_1)->False)))).
% Axiom fact_648_diff__Suc__Suc:(forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat (suc M)) (suc N_1))) ((minus_minus_nat M) N_1))).
% Axiom fact_649_Suc__diff__diff:(forall (M:nat) (N_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M)) N_1)) (suc K))) ((minus_minus_nat ((minus_minus_nat M) N_1)) K))).
% Axiom fact_650_diff__0__eq__0:(forall (N_1:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N_1)) zero_zero_nat)).
% Axiom fact_651_minus__nat_Odiff__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)).
% Axiom fact_652_diff__self__eq__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)).
% Axiom fact_653_diffs0__imp__equal:(forall (M:nat) (N_1:nat), ((((eq nat) ((minus_minus_nat M) N_1)) zero_zero_nat)->((((eq nat) ((minus_minus_nat N_1) M)) zero_zero_nat)->(((eq nat) M) N_1)))).
% Axiom fact_654_zero__induct__lemma:(forall (_TPTP_I:nat) (P:(nat->Prop)) (K:nat), ((P K)->((forall (N:nat), ((P (suc N))->(P N)))->(P ((minus_minus_nat K) _TPTP_I))))).
% Axiom fact_655_diff__commute:(forall (_TPTP_I:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat _TPTP_I) J)) K)) ((minus_minus_nat ((minus_minus_nat _TPTP_I) K)) J))).
% Axiom fact_656_diff__Suc:(forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat M) (suc N_1))) (((nat_case_nat zero_zero_nat) (fun (K_1:nat)=> K_1)) ((minus_minus_nat M) N_1)))).
% Axiom fact_657_diff__Suc__1:(forall (N_1:nat), (((eq nat) ((minus_minus_nat (suc N_1)) one_one_nat)) N_1)).
% Axiom fact_658_diff__Suc__eq__diff__pred:(forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat M) (suc N_1))) ((minus_minus_nat ((minus_minus_nat M) one_one_nat)) N_1))).
% Axiom fact_659_One__nat__def:(((eq nat) one_one_nat) (suc zero_zero_nat)).
% Axiom fact_660_Suc__eq__plus1:(forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat N_1) one_one_nat))).
% Axiom fact_661_Suc__eq__plus1__left:(forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat one_one_nat) N_1))).
% Axiom fact_662_diff__cancel2:(forall (M:nat) (K:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K)) ((plus_plus_nat N_1) K))) ((minus_minus_nat M) N_1))).
% Axiom fact_663_diff__cancel:(forall (K:nat) (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N_1))) ((minus_minus_nat M) N_1))).
% Axiom fact_664_diff__diff__left:(forall (_TPTP_I:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat _TPTP_I) J)) K)) ((minus_minus_nat _TPTP_I) ((plus_plus_nat J) K)))).
% Axiom fact_665_diff__add__inverse:(forall (N_1:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N_1) M)) N_1)) M)).
% Axiom fact_666_diff__add__inverse2:(forall (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N_1)) N_1)) M)).
% Axiom fact_667_diff__add__0:(forall (N_1:nat) (M:nat), (((eq nat) ((minus_minus_nat N_1) ((plus_plus_nat N_1) M))) zero_zero_nat)).
% Axiom fact_668_nat__add__commute:(forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M) N_1)) ((plus_plus_nat N_1) M))).
% Axiom fact_669_nat__add__left__commute:(forall (X_1:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X_1) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X_1) Z)))).
% Axiom fact_670_nat__add__assoc:(forall (M:nat) (N_1:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N_1)) K)) ((plus_plus_nat M) ((plus_plus_nat N_1) K)))).
% Axiom fact_671_nat__add__left__cancel:(forall (K:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N_1))) (((eq nat) M) N_1))).
% Axiom fact_672_nat__add__right__cancel:(forall (M:nat) (K:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N_1) K))) (((eq nat) M) N_1))).
% Axiom fact_673_add__Suc__shift:(forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M)) N_1)) ((plus_plus_nat M) (suc N_1)))).
% Axiom fact_674_add__Suc:(forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M)) N_1)) (suc ((plus_plus_nat M) N_1)))).
% Axiom fact_675_add__Suc__right:(forall (M:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M) (suc N_1))) (suc ((plus_plus_nat M) N_1)))).
% Axiom fact_676_one__is__add:(forall (M:nat) (N_1:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M) N_1))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat)))))).
% Axiom fact_677_add__is__1:(forall (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) N_1)) (suc zero_zero_nat))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat)))))).
% Axiom fact_678_plus__nat_Oadd__0:(forall (N_1:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N_1)) N_1)).
% Axiom fact_679_Nat_Oadd__0__right:(forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)).
% Axiom fact_680_add__is__0:(forall (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) N_1)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat)))).
% Axiom fact_681_add__eq__self__zero:(forall (M:nat) (N_1:nat), ((((eq nat) ((plus_plus_nat M) N_1)) M)->(((eq nat) N_1) zero_zero_nat))).
% Axiom fact_682_add__eq__if:(forall (N_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((plus_plus_nat M) N_1)) N_1))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((plus_plus_nat M) N_1)) (suc ((plus_plus_nat ((minus_minus_nat M) one_one_nat)) N_1)))))).
% Axiom fact_683_com_Osize_I4_J:(forall (Com1:com) (Com2:com), (((eq nat) (com_size ((semi Com1) Com2))) ((plus_plus_nat ((plus_plus_nat (com_size Com1)) (com_size Com2))) (suc zero_zero_nat)))).
% Axiom fact_684_com_Osize_I7_J:(forall (Pname:pname), (((eq nat) (com_size (body Pname))) zero_zero_nat)).
% Axiom fact_685_com_Osize_I1_J:(((eq nat) (com_size skip)) zero_zero_nat).
% Axiom fact_686_com_Osize_I6_J:(forall (Fun:(state->Prop)) (Com:com), (((eq nat) (com_size ((while Fun) Com))) ((plus_plus_nat (com_size Com)) (suc zero_zero_nat)))).
% Axiom fact_687_com_Osize_I12_J:(forall (Com1:com) (Com2:com), (((eq nat) (size_size_com ((semi Com1) Com2))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1)) (size_size_com Com2))) (suc zero_zero_nat)))).
% Axiom fact_688_com_Osize_I15_J:(forall (Pname:pname), (((eq nat) (size_size_com (body Pname))) zero_zero_nat)).
% Axiom fact_689_com_Osize_I9_J:(((eq nat) (size_size_com skip)) zero_zero_nat).
% Axiom fact_690_com_Osize_I14_J:(forall (Fun:(state->Prop)) (Com:com), (((eq nat) (size_size_com ((while Fun) Com))) ((plus_plus_nat (size_size_com Com)) (suc zero_zero_nat)))).
% Axiom fact_691_com_Osize_I13_J:(forall (Fun:(state->Prop)) (Com1:com) (Com2:com), (((eq nat) (size_size_com (((cond Fun) Com1) Com2))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1)) (size_size_com Com2))) (suc zero_zero_nat)))).
% Axiom fact_692_evaln_OIfFalse:(forall (C0:com) (C1:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S:state), (((B S)->False)->(((((evaln C1) S) N_1) S1)->((((evaln (((cond B) C0) C1)) S) N_1) S1)))).
% Axiom fact_693_evaln_OIfTrue:(forall (C1:com) (C0:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S:state), ((B S)->(((((evaln C0) S) N_1) S1)->((((evaln (((cond B) C0) C1)) S) N_1) S1)))).
% Axiom fact_694_evaln__elim__cases_I5_J:(forall (B:(state->Prop)) (C1:com) (C2:com) (S:state) (N_1:nat) (T:state), (((((evaln (((cond B) C1) C2)) S) N_1) T)->(((B S)->(((((evaln C1) S) N_1) T)->False))->((((B S)->False)->(((((evaln C2) S) N_1) T)->False))->False)))).
% Axiom fact_695_evalc__elim__cases_I5_J:(forall (B:(state->Prop)) (C1:com) (C2:com) (S:state) (T:state), ((((evalc (((cond B) C1) C2)) S) T)->(((B S)->((((evalc C1) S) T)->False))->((((B S)->False)->((((evalc C2) S) T)->False))->False)))).
% Axiom fact_696_evalc_OIfTrue:(forall (C1:com) (C0:com) (S1:state) (B:(state->Prop)) (S:state), ((B S)->((((evalc C0) S) S1)->(((evalc (((cond B) C0) C1)) S) S1)))).
% Axiom fact_697_evalc_OIfFalse:(forall (C0:com) (C1:com) (S1:state) (B:(state->Prop)) (S:state), (((B S)->False)->((((evalc C1) S) S1)->(((evalc (((cond B) C0) C1)) S) S1)))).
% Axiom help_fequal_1_1_fequal_000tc__Com__Opname_T:(forall (X_1:pname) (Y:pname), ((or (((fequal_pname X_1) Y)->False)) (((eq pname) X_1) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Com__Opname_T:(forall (X_1:pname) (Y:pname), ((or (not (((eq pname) X_1) Y))) ((fequal_pname X_1) Y))).
% Axiom help_fequal_1_1_fequal_000tc__Com__Ostate_T:(forall (X_1:state) (Y:state), ((or (((fequal_state X_1) Y)->False)) (((eq state) X_1) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Com__Ostate_T:(forall (X_1:state) (Y:state), ((or (not (((eq state) X_1) Y))) ((fequal_state X_1) Y))).
% Axiom help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_T:(forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (((if_Hoa1047340790iple_a True) X_1) Y)) X_1)).
% Axiom help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_T:(forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), (((eq hoare_1775062406iple_a) (((if_Hoa1047340790iple_a False) X_1) Y)) Y)).
% Axiom help_If_3_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_T:(forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))).
% Axiom help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_:(forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), ((or (((fequal1288209029iple_a X_1) Y)->False)) (((eq hoare_1775062406iple_a) X_1) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_:(forall (X_1:hoare_1775062406iple_a) (Y:hoare_1775062406iple_a), ((or (not (((eq hoare_1775062406iple_a) X_1) Y))) ((fequal1288209029iple_a X_1) Y))).
% Axiom help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate:(forall (X_1:hoare_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_state True) X_1) Y)) X_1)).
% Axiom help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate:(forall (X_1:hoare_1167836817_state) (Y:hoare_1167836817_state), (((eq hoare_1167836817_state) (((if_Hoa833675553_state False) X_1) 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 P
% EOF
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