%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SWW471^3 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n098.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 300.04s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SWW471^3 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n098.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 09:15:21 CDT 2014
% % CPUTime  : 300.04 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1f186c8>, <kernel.Type object at 0x1f18c20>) of role type named ty_ty_t__a
% Using role type
% Declaring x_a:Type
% FOF formula (<kernel.Constant object at 0x22f3518>, <kernel.Type object at 0x1f185f0>) of role type named ty_ty_tc__Com__Ocom
% Using role type
% Declaring com:Type
% FOF formula (<kernel.Constant object at 0x1f18b90>, <kernel.Type object at 0x1f187e8>) of role type named ty_ty_tc__Com__Opname
% Using role type
% Declaring pname:Type
% FOF formula (<kernel.Constant object at 0x1f18c20>, <kernel.Type object at 0x1f184d0>) of role type named ty_ty_tc__Com__Ostate
% Using role type
% Declaring state:Type
% FOF formula (<kernel.Constant object at 0x1f185f0>, <kernel.Type object at 0x1f18560>) of role type named ty_ty_tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J
% Using role type
% Declaring hoare_2091234717iple_a:Type
% FOF formula (<kernel.Constant object at 0x1f187e8>, <kernel.Type object at 0x1f18830>) of role type named ty_ty_tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J
% Using role type
% Declaring hoare_1708887482_state:Type
% FOF formula (<kernel.Constant object at 0x1f184d0>, <kernel.Type object at 0x1f18dd0>) of role type named ty_ty_tc__Nat__Onat
% Using role type
% Declaring nat:Type
% FOF formula (<kernel.Constant object at 0x1f18560>, <kernel.Type object at 0x1f18488>) 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 0x1f18cb0>, <kernel.DependentProduct object at 0x1f18560>) of role type named sy_c_Big__Operators_Ocomm__monoid__big_000_062_Itc__Hoare____Mirabelle____nqhfsd
% Using role type
% Declaring big_co1924420859_pname:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((hoare_2091234717iple_a->Prop)->(((pname->(hoare_2091234717iple_a->Prop))->((pname->Prop)->(hoare_2091234717iple_a->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x1f18758>, <kernel.DependentProduct object at 0x21c6cf8>) of role type named sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_I_062_Itc__Hoare____Mirabe
% Using role type
% Declaring big_la1994307886_a_o_o:((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1f18440>, <kernel.DependentProduct object at 0x21c6cf8>) 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 0x1f18cb0>, <kernel.DependentProduct object at 0x21c6998>) of role type named sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Hoare____Mirabelle___
% Using role type
% Declaring big_la735727201le_a_o:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x1f18758>, <kernel.DependentProduct object at 0x1f18cb0>) of role type named sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Hoare____Mirabelle____001
% Using role type
% Declaring big_la1088302868tate_o:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop))
% FOF formula (<kernel.Constant object at 0x1f184d0>, <kernel.DependentProduct object at 0x2312248>) of role type named sy_c_Big__Operators_Olattice__class_OSup__fin_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring big_la1658356148_nat_o:(((nat->Prop)->Prop)->(nat->Prop))
% FOF formula (<kernel.Constant object at 0x1f18cb0>, <kernel.DependentProduct object at 0x2312098>) 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 0x1f18440>, <kernel.DependentProduct object at 0x2312290>) of role type named sy_c_Big__Operators_Olattice__class_OSup__fin_000tc__Nat__Onat
% Using role type
% Declaring big_la43341705in_nat:((nat->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x1f18440>, <kernel.DependentProduct object at 0x2312170>) of role type named sy_c_Com_Obody
% Using role type
% Declaring body_1:(pname->option_com)
% FOF formula (<kernel.Constant object at 0x21c6b48>, <kernel.DependentProduct object at 0x2312758>) of role type named sy_c_Com_Ocom_OBODY
% Using role type
% Declaring body:(pname->com)
% FOF formula (<kernel.Constant object at 0x21c6cf8>, <kernel.DependentProduct object at 0x2312128>) 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 0x21c6b48>, <kernel.Constant object at 0x2312f80>) of role type named sy_c_Com_Ocom_OSKIP
% Using role type
% Declaring skip:com
% FOF formula (<kernel.Constant object at 0x21c6290>, <kernel.DependentProduct object at 0x2312128>) of role type named sy_c_Com_Ocom_OSemi
% Using role type
% Declaring semi:(com->(com->com))
% FOF formula (<kernel.Constant object at 0x21c6290>, <kernel.DependentProduct object at 0x2312098>) of role type named sy_c_Com_Ocom_OWhile
% Using role type
% Declaring while:((state->Prop)->(com->com))
% FOF formula (<kernel.Constant object at 0x2312f80>, <kernel.DependentProduct object at 0x2312290>) of role type named sy_c_Com_Ocom_Ocom__size
% Using role type
% Declaring com_size:(com->nat)
% FOF formula (<kernel.Constant object at 0x2312170>, <kernel.DependentProduct object at 0x2312248>) of role type named sy_c_Finite__Set_Ocard_000tc__Nat__Onat
% Using role type
% Declaring finite_card_nat:((nat->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x2312098>, <kernel.DependentProduct object at 0x2312fc8>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot
% Using role type
% Declaring finite886417794_a_o_o:((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x23121b8>, <kernel.DependentProduct object at 0x2312fc8>) 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 0x2312248>, <kernel.DependentProduct object at 0x2312fc8>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_
% Using role type
% Declaring finite1829014797le_a_o:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x2312f38>, <kernel.DependentProduct object at 0x2312fc8>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple__002
% Using role type
% Declaring finite1329924456tate_o:(((hoare_1708887482_state->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x2312e60>, <kernel.DependentProduct object at 0x2312fc8>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring finite_finite_nat_o:(((nat->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x23120e0>, <kernel.DependentProduct object at 0x23123b0>) 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 0x23127a0>, <kernel.DependentProduct object at 0x23123f8>) 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 0x2312fc8>, <kernel.DependentProduct object at 0x23120e0>) of role type named sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_
% Using role type
% Declaring finite232261744iple_a:((hoare_2091234717iple_a->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x236f290>, <kernel.DependentProduct object at 0x23123f8>) of role type named sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__C
% Using role type
% Declaring finite1625599783_state:((hoare_1708887482_state->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x2312e18>, <kernel.DependentProduct object at 0x1f33f80>) of role type named sy_c_Finite__Set_Ofinite_000tc__Nat__Onat
% Using role type
% Declaring finite_finite_nat:((nat->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x23120e0>, <kernel.DependentProduct object at 0x1f33f80>) of role type named sy_c_Finite__Set_Ofold__image_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvy
% Using role type
% Declaring finite2009943022_o_nat:((((hoare_2091234717iple_a->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop)))->((nat->((hoare_2091234717iple_a->Prop)->Prop))->(((hoare_2091234717iple_a->Prop)->Prop)->((nat->Prop)->((hoare_2091234717iple_a->Prop)->Prop)))))
% FOF formula (<kernel.Constant object at 0x2312d88>, <kernel.DependentProduct object at 0x1f33fc8>) of role type named sy_c_Finite__Set_Ofold__image_000_062_Itc__Com__Opname_M_Eo_J_000tc__Nat__Onat
% Using role type
% Declaring finite1427591632_o_nat:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->((nat->(pname->Prop))->((pname->Prop)->((nat->Prop)->(pname->Prop)))))
% FOF formula (<kernel.Constant object at 0x2312e18>, <kernel.DependentProduct object at 0x1f33fc8>) of role type named sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr
% Using role type
% Declaring finite903029825le_a_o:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->(((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))->((hoare_2091234717iple_a->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop)))))
% FOF formula (<kernel.Constant object at 0x2312d88>, <kernel.DependentProduct object at 0x1f33dd0>) of role type named sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr_003
% Using role type
% Declaring finite1290357347_pname:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((pname->(hoare_2091234717iple_a->Prop))->((hoare_2091234717iple_a->Prop)->((pname->Prop)->(hoare_2091234717iple_a->Prop)))))
% FOF formula (<kernel.Constant object at 0x23120e0>, <kernel.DependentProduct object at 0x1f33488>) of role type named sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr_004
% Using role type
% Declaring finite1481787452iple_a:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((hoare_2091234717iple_a->(hoare_2091234717iple_a->Prop))->((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))))
% FOF formula (<kernel.Constant object at 0x2312d88>, <kernel.DependentProduct object at 0x1f333f8>) of role type named sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr_005
% Using role type
% Declaring finite2100865449_o_nat:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((nat->(hoare_2091234717iple_a->Prop))->((hoare_2091234717iple_a->Prop)->((nat->Prop)->(hoare_2091234717iple_a->Prop)))))
% FOF formula (<kernel.Constant object at 0x2312d88>, <kernel.DependentProduct object at 0x1f33560>) of role type named sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr_006
% Using role type
% Declaring finite2139561282_pname:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((pname->(hoare_1708887482_state->Prop))->((hoare_1708887482_state->Prop)->((pname->Prop)->(hoare_1708887482_state->Prop)))))
% FOF formula (<kernel.Constant object at 0x1f33c20>, <kernel.DependentProduct object at 0x1f335f0>) of role type named sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr_007
% Using role type
% Declaring finite1400355848_o_nat:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((nat->(hoare_1708887482_state->Prop))->((hoare_1708887482_state->Prop)->((nat->Prop)->(hoare_1708887482_state->Prop)))))
% FOF formula (<kernel.Constant object at 0x1f33e60>, <kernel.DependentProduct object at 0x1f337e8>) of role type named sy_c_Finite__Set_Ofold__image_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Nat__Onat
% Using role type
% Declaring finite141655318_o_nat:(((nat->Prop)->((nat->Prop)->(nat->Prop)))->((nat->(nat->Prop))->((nat->Prop)->((nat->Prop)->(nat->Prop)))))
% FOF formula (<kernel.Constant object at 0x1f33dd0>, <kernel.DependentProduct object at 0x1f33560>) of role type named sy_c_Finite__Set_Ofolding__one_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot
% Using role type
% Declaring finite14499299le_a_o:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x1f338c0>, <kernel.DependentProduct object at 0x1f33e60>) 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 0x1f333b0>, <kernel.DependentProduct object at 0x1f33dd0>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_
% Using role type
% Declaring finite247037978iple_a:((hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))->(((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)->Prop))
% FOF formula (<kernel.Constant object at 0x1f335f0>, <kernel.DependentProduct object at 0x1f338c0>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple__008
% Using role type
% Declaring finite1615457021_state:((hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))->(((hoare_1708887482_state->Prop)->hoare_1708887482_state)->Prop))
% FOF formula (<kernel.Constant object at 0x1f33a70>, <kernel.DependentProduct object at 0x1f333b0>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat
% Using role type
% Declaring finite988810631ne_nat:((nat->(nat->nat))->(((nat->Prop)->nat)->Prop))
% FOF formula (<kernel.Constant object at 0x1f33c20>, <kernel.DependentProduct object at 0x1f338c0>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Hoare____Mirabelle____nqhfsdfv
% Using role type
% Declaring finite574580006le_a_o:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x1f337e8>, <kernel.DependentProduct object at 0x1f33a70>) 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 0x1f33b48>, <kernel.DependentProduct object at 0x1f33c20>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot
% Using role type
% Declaring finite1674555159iple_a:((hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))->(((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)->Prop))
% FOF formula (<kernel.Constant object at 0x1f33ab8>, <kernel.DependentProduct object at 0x1f337e8>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot_009
% Using role type
% Declaring finite1347568576_state:((hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))->(((hoare_1708887482_state->Prop)->hoare_1708887482_state)->Prop))
% FOF formula (<kernel.Constant object at 0x1f33d40>, <kernel.DependentProduct object at 0x1f33b48>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat
% Using role type
% Declaring finite795500164em_nat:((nat->(nat->nat))->(((nat->Prop)->nat)->Prop))
% FOF formula (<kernel.Constant object at 0x1f335f0>, <kernel.DependentProduct object at 0x1f334d0>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsd
% Using role type
% Declaring minus_1746272704_a_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1f333b0>, <kernel.DependentProduct object at 0x1f334d0>) 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 0x1f337e8>, <kernel.DependentProduct object at 0x1f334d0>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__
% Using role type
% Declaring minus_836160335le_a_o:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x1f336c8>, <kernel.DependentProduct object at 0x1f334d0>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv___010
% Using role type
% Declaring minus_2056855718tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x1f33d40>, <kernel.DependentProduct object at 0x23132d8>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring minus_minus_nat_o:((nat->Prop)->((nat->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x1f334d0>, <kernel.DependentProduct object at 0x2313248>) of role type named sy_c_Groups_Ominus__class_Ominus_000_Eo
% Using role type
% Declaring minus_minus_o:(Prop->(Prop->Prop))
% FOF formula (<kernel.Constant object at 0x1f336c8>, <kernel.DependentProduct object at 0x2313998>) 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 0x1f334d0>, <kernel.Constant object at 0x2313368>) 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 0x1f336c8>, <kernel.DependentProduct object at 0x23132d8>) 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 0x1f33d40>, <kernel.DependentProduct object at 0x23139e0>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat
% Using role type
% Declaring times_times_nat:(nat->(nat->nat))
% FOF formula (<kernel.Constant object at 0x1f33d40>, <kernel.Constant object at 0x23139e0>) 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 0x2313248>, <kernel.DependentProduct object at 0x2313170>) of role type named sy_c_HOL_OThe_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_E
% Using role type
% Declaring the_Ho2077879471le_a_o:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x2313050>, <kernel.DependentProduct object at 0x1f29878>) 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 0x2313200>, <kernel.DependentProduct object at 0x1f29950>) of role type named sy_c_HOL_OThe_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J
% Using role type
% Declaring the_Ho1471183438iple_a:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)
% FOF formula (<kernel.Constant object at 0x2313248>, <kernel.DependentProduct object at 0x1f298c0>) of role type named sy_c_HOL_OThe_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_
% Using role type
% Declaring the_Ho851197897_state:((hoare_1708887482_state->Prop)->hoare_1708887482_state)
% FOF formula (<kernel.Constant object at 0x2313290>, <kernel.DependentProduct object at 0x1f29830>) of role type named sy_c_HOL_OThe_000tc__Nat__Onat
% Using role type
% Declaring the_nat:((nat->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x2313248>, <kernel.DependentProduct object at 0x1f29908>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_OMGT
% Using role type
% Declaring hoare_Mirabelle_MGT:(com->hoare_1708887482_state)
% FOF formula (<kernel.Constant object at 0x2313290>, <kernel.DependentProduct object at 0x1f297a0>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__derivs_000t__a
% Using role type
% Declaring hoare_1467856363rivs_a:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x2313248>, <kernel.DependentProduct object at 0x1f296c8>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__derivs_000tc__Com__Ostate
% Using role type
% Declaring hoare_90032982_state:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x2313200>, <kernel.DependentProduct object at 0x1f29710>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__valids_000t__a
% Using role type
% Declaring hoare_1805689709lids_a:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x2313200>, <kernel.DependentProduct object at 0x1f29638>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__valids_000tc__Com__Ostate
% Using role type
% Declaring hoare_496444244_state:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1f298c0>, <kernel.DependentProduct object at 0x1f29950>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple_000t__a
% Using role type
% Declaring hoare_657976383iple_a:((x_a->(state->Prop))->(com->((x_a->(state->Prop))->hoare_2091234717iple_a)))
% FOF formula (<kernel.Constant object at 0x1f29878>, <kernel.DependentProduct object at 0x1f297e8>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple_000tc__Com__Ostate
% Using role type
% Declaring hoare_858012674_state:((state->(state->Prop))->(com->((state->(state->Prop))->hoare_1708887482_state)))
% FOF formula (<kernel.Constant object at 0x1f29758>, <kernel.DependentProduct object at 0x1f298c0>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple__size_000t__a
% Using role type
% Declaring hoare_1169027232size_a:((x_a->nat)->(hoare_2091234717iple_a->nat))
% FOF formula (<kernel.Constant object at 0x1f29908>, <kernel.DependentProduct object at 0x1f29878>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple__size_000tc__Com__Ostate
% Using role type
% Declaring hoare_518771297_state:((state->nat)->(hoare_1708887482_state->nat))
% FOF formula (<kernel.Constant object at 0x1f29950>, <kernel.DependentProduct object at 0x1f295f0>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple__valid_000t__a
% Using role type
% Declaring hoare_1421888935alid_a:(nat->(hoare_2091234717iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x1f29560>, <kernel.DependentProduct object at 0x1f298c0>) of role type named sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple__valid_000tc__Com__Ostate
% Using role type
% Declaring hoare_23738522_state:(nat->(hoare_1708887482_state->Prop))
% FOF formula (<kernel.Constant object at 0x1f29680>, <kernel.DependentProduct object at 0x1f29638>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell
% Using role type
% Declaring semila1672913213_a_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1f297e8>, <kernel.DependentProduct object at 0x1f293f8>) 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 0x1f29908>, <kernel.DependentProduct object at 0x1f292d8>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____n
% Using role type
% Declaring semila2006181266le_a_o:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x1f294d0>, <kernel.DependentProduct object at 0x1f29320>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____n_011
% Using role type
% Declaring semila129691299tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x1f29560>, <kernel.DependentProduct object at 0x1f29248>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring semila1947288293_nat_o:((nat->Prop)->((nat->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x1f29518>, <kernel.DependentProduct object at 0x1f29680>) 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 0x1f294d0>, <kernel.DependentProduct object at 0x1f297e8>) of role type named sy_c_Lattices_Osemilattice__inf__class_Oinf_000tc__Nat__Onat
% Using role type
% Declaring semila80283416nf_nat:(nat->(nat->nat))
% FOF formula (<kernel.Constant object at 0x1f29248>, <kernel.DependentProduct object at 0x1f29290>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_I_062_Itc__Hoare____Mi
% Using role type
% Declaring semila484278426_o_o_o:((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1f29680>, <kernel.DependentProduct object at 0x1f29908>) 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 0x1f297e8>, <kernel.DependentProduct object at 0x1f29200>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell
% Using role type
% Declaring semila2050116131_a_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1f29950>, <kernel.DependentProduct object at 0x1f29170>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell_012
% Using role type
% Declaring semila1853742644te_o_o:(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1f29518>, <kernel.DependentProduct object at 0x1f29098>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Nat__Onat_M_Eo_J_
% Using role type
% Declaring semila72246288at_o_o:(((nat->Prop)->Prop)->(((nat->Prop)->Prop)->((nat->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x1f29128>, <kernel.DependentProduct object at 0x1f290e0>) 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 0x1f29950>, <kernel.DependentProduct object at 0x1f297e8>) 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 0x1f294d0>, <kernel.DependentProduct object at 0x1f29a28>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____n
% Using role type
% Declaring semila1052848428le_a_o:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x1f29560>, <kernel.DependentProduct object at 0x1f29a70>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____n_013
% Using role type
% Declaring semila1122118281tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x1f29518>, <kernel.DependentProduct object at 0x1f29ab8>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring semila848761471_nat_o:((nat->Prop)->((nat->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x1f29098>, <kernel.DependentProduct object at 0x1f29128>) 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 0x1f29560>, <kernel.DependentProduct object at 0x1f29950>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000tc__Nat__Onat
% Using role type
% Declaring semila972727038up_nat:(nat->(nat->nat))
% FOF formula (<kernel.Constant object at 0x1f29ab8>, <kernel.DependentProduct object at 0x1f299e0>) of role type named sy_c_Nat_OSuc
% Using role type
% Declaring suc:(nat->nat)
% FOF formula (<kernel.Constant object at 0x1f297a0>, <kernel.DependentProduct object at 0x1f29b90>) of role type named sy_c_Nat_Onat_Onat__case_000_Eo
% Using role type
% Declaring nat_case_o:(Prop->((nat->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x1f29950>, <kernel.DependentProduct object at 0x1f29bd8>) 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 0x1f299e0>, <kernel.DependentProduct object at 0x1f29098>) 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 0x1f297a0>, <kernel.DependentProduct object at 0x1f29cb0>) of role type named sy_c_Nat_Osize__class_Osize_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It_
% Using role type
% Declaring size_s1040486067iple_a:(hoare_2091234717iple_a->nat)
% FOF formula (<kernel.Constant object at 0x1f29bd8>, <kernel.DependentProduct object at 0x1f29c68>) of role type named sy_c_Nat_Osize__class_Osize_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc
% Using role type
% Declaring size_s1186992420_state:(hoare_1708887482_state->nat)
% FOF formula (<kernel.Constant object at 0x1f29098>, <kernel.DependentProduct object at 0x1f299e0>) of role type named sy_c_Natural_Oevalc
% Using role type
% Declaring evalc:(com->(state->(state->Prop)))
% FOF formula (<kernel.Constant object at 0x1f29cb0>, <kernel.DependentProduct object at 0x1f29cf8>) of role type named sy_c_Natural_Oevaln
% Using role type
% Declaring evaln:(com->(state->(nat->(state->Prop))))
% FOF formula (<kernel.Constant object at 0x1f29128>, <kernel.DependentProduct object at 0x1f29b48>) 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 0x1f29dd0>, <kernel.DependentProduct object at 0x1f29128>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_I_062_Itc__Hoare____Mirabelle____n
% Using role type
% Declaring bot_bo690906872_o_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1f29cf8>, <kernel.DependentProduct object at 0x1f29d40>) 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 0x1f29098>, <kernel.DependentProduct object at 0x1f29128>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdf
% Using role type
% Declaring bot_bo1957696069_a_o_o:((hoare_2091234717iple_a->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1f29cb0>, <kernel.DependentProduct object at 0x1f29d40>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdf_014
% Using role type
% Declaring bot_bo1678742418te_o_o:((hoare_1708887482_state->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1f29518>, <kernel.DependentProduct object at 0x1f29128>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J
% Using role type
% Declaring bot_bot_nat_o_o:((nat->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1f29e60>, <kernel.DependentProduct object at 0x1f29d40>) 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 0x1f29cb0>, <kernel.DependentProduct object at 0x1f29ef0>) 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 0x1f29e18>, <kernel.DependentProduct object at 0x1f29f38>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__O
% Using role type
% Declaring bot_bo1791335050le_a_o:(hoare_2091234717iple_a->Prop)
% FOF formula (<kernel.Constant object at 0x1f29d40>, <kernel.DependentProduct object at 0x1f29f80>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__O_015
% Using role type
% Declaring bot_bo19817387tate_o:(hoare_1708887482_state->Prop)
% FOF formula (<kernel.Constant object at 0x1f29ef0>, <kernel.DependentProduct object at 0x1f29fc8>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring bot_bot_nat_o:(nat->Prop)
% FOF formula (<kernel.Constant object at 0x1f29f38>, <kernel.Sort object at 0x1dfd128>) 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 0x1f29128>, <kernel.Constant object at 0x1f29ef0>) 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 0x1f29f80>, <kernel.DependentProduct object at 0x230b0e0>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat
% Using role type
% Declaring ord_less_nat:(nat->(nat->Prop))
% FOF formula (<kernel.Constant object at 0x1f29ef0>, <kernel.DependentProduct object at 0x230b170>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat
% Using role type
% Declaring ord_less_eq_nat:(nat->(nat->Prop))
% FOF formula (<kernel.Constant object at 0x1f29128>, <kernel.DependentProduct object at 0x230b200>) of role type named sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J
% Using role type
% Declaring collec1008234059le_a_o:(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1f29ef0>, <kernel.DependentProduct object at 0x230b170>) 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 0x1f29128>, <kernel.DependentProduct object at 0x230b098>) of role type named sy_c_Set_OCollect_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J
% Using role type
% Declaring collec992574898iple_a:((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x1f29f80>, <kernel.DependentProduct object at 0x230b128>) of role type named sy_c_Set_OCollect_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost
% Using role type
% Declaring collec1568722789_state:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))
% FOF formula (<kernel.Constant object at 0x230b200>, <kernel.DependentProduct object at 0x230b098>) of role type named sy_c_Set_OCollect_000tc__Nat__Onat
% Using role type
% Declaring collect_nat:((nat->Prop)->(nat->Prop))
% FOF formula (<kernel.Constant object at 0x230b290>, <kernel.DependentProduct object at 0x230b320>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M
% Using role type
% Declaring image_784579955le_a_o:(((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x230b128>, <kernel.DependentProduct object at 0x230b200>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_016
% Using role type
% Declaring image_1908519857_pname:(((hoare_2091234717iple_a->Prop)->pname)->(((hoare_2091234717iple_a->Prop)->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x230b3f8>, <kernel.DependentProduct object at 0x230b1b8>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_017
% Using role type
% Declaring image_136408202iple_a:(((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)->(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x230b248>, <kernel.DependentProduct object at 0x230b290>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_018
% Using role type
% Declaring image_1501246093_state:(((hoare_2091234717iple_a->Prop)->hoare_1708887482_state)->(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x230b440>, <kernel.DependentProduct object at 0x230b128>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_019
% Using role type
% Declaring image_75520503_o_nat:(((hoare_2091234717iple_a->Prop)->nat)->(((hoare_2091234717iple_a->Prop)->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x230b488>, <kernel.DependentProduct object at 0x230b1b8>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv
% Using role type
% Declaring image_742317343le_a_o:((pname->(hoare_2091234717iple_a->Prop))->((pname->Prop)->((hoare_2091234717iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x230b200>, <kernel.DependentProduct object at 0x230b050>) 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 0x230b4d0>, <kernel.DependentProduct object at 0x230b5a8>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otri
% Using role type
% Declaring image_231808478iple_a:((pname->hoare_2091234717iple_a)->((pname->Prop)->(hoare_2091234717iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x230b560>, <kernel.DependentProduct object at 0x230b5f0>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otri_020
% Using role type
% Declaring image_1116629049_state:((pname->hoare_1708887482_state)->((pname->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x230b1b8>, <kernel.DependentProduct object at 0x230b638>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Nat__Onat
% Using role type
% Declaring image_pname_nat:((pname->nat)->((pname->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x230b050>, <kernel.DependentProduct object at 0x230b5f0>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_000_062
% Using role type
% Declaring image_1642350072le_a_o:((hoare_2091234717iple_a->(hoare_2091234717iple_a->Prop))->((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x230b200>, <kernel.DependentProduct object at 0x230b290>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_000tc__
% Using role type
% Declaring image_924789612_pname:((hoare_2091234717iple_a->pname)->((hoare_2091234717iple_a->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x230b4d0>, <kernel.DependentProduct object at 0x230b710>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_000tc___021
% Using role type
% Declaring image_1661191109iple_a:((hoare_2091234717iple_a->hoare_2091234717iple_a)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x230b638>, <kernel.DependentProduct object at 0x230b758>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_000tc___022
% Using role type
% Declaring image_1884482962_state:((hoare_2091234717iple_a->hoare_1708887482_state)->((hoare_2091234717iple_a->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x230b1b8>, <kernel.DependentProduct object at 0x230b7a0>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_000tc___023
% Using role type
% Declaring image_1773322034_a_nat:((hoare_2091234717iple_a->nat)->((hoare_2091234717iple_a->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x230b5f0>, <kernel.DependentProduct object at 0x230b7e8>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat
% Using role type
% Declaring image_293283184iple_a:((hoare_1708887482_state->hoare_2091234717iple_a)->((hoare_1708887482_state->Prop)->(hoare_2091234717iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x230b710>, <kernel.DependentProduct object at 0x230b830>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_024
% Using role type
% Declaring image_757158439_state:((hoare_1708887482_state->hoare_1708887482_state)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x230b4d0>, <kernel.DependentProduct object at 0x230b7e8>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__
% Using role type
% Declaring image_1995609573le_a_o:((nat->(hoare_2091234717iple_a->Prop))->((nat->Prop)->((hoare_2091234717iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x230b758>, <kernel.DependentProduct object at 0x230b440>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname
% Using role type
% Declaring image_nat_pname:((nat->pname)->((nat->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x230b7a0>, <kernel.DependentProduct object at 0x230b908>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otripl
% Using role type
% Declaring image_359186840iple_a:((nat->hoare_2091234717iple_a)->((nat->Prop)->(hoare_2091234717iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x230b8c0>, <kernel.DependentProduct object at 0x230b950>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otripl_025
% Using role type
% Declaring image_514827263_state:((nat->hoare_1708887482_state)->((nat->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x230b7e8>, <kernel.DependentProduct object at 0x230b998>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Nat__Onat
% Using role type
% Declaring image_nat_nat:((nat->nat)->((nat->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x230b440>, <kernel.DependentProduct object at 0x230b878>) of role type named sy_c_Set_Oinsert_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It
% Using role type
% Declaring insert987231145_a_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x230b908>, <kernel.DependentProduct object at 0x230b710>) 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 0x230b7a0>, <kernel.DependentProduct object at 0x230b878>) of role type named sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_
% Using role type
% Declaring insert102003750le_a_o:((hoare_2091234717iple_a->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x230b1b8>, <kernel.DependentProduct object at 0x230b710>) of role type named sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com
% Using role type
% Declaring insert949073679tate_o:((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x230ba70>, <kernel.DependentProduct object at 0x230b878>) of role type named sy_c_Set_Oinsert_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring insert_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->((nat->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x230bab8>, <kernel.DependentProduct object at 0x230bb48>) 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 0x230b0e0>, <kernel.DependentProduct object at 0x230bb90>) 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 0x230b710>, <kernel.DependentProduct object at 0x230b878>) of role type named sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J
% Using role type
% Declaring insert1597628439iple_a:(hoare_2091234717iple_a->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x230bb48>, <kernel.DependentProduct object at 0x230bbd8>) of role type named sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Osta
% Using role type
% Declaring insert528405184_state:(hoare_1708887482_state->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))
% FOF formula (<kernel.Constant object at 0x230b1b8>, <kernel.DependentProduct object at 0x230bc20>) of role type named sy_c_Set_Oinsert_000tc__Nat__Onat
% Using role type
% Declaring insert_nat:(nat->((nat->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x230b878>, <kernel.DependentProduct object at 0x230b908>) of role type named sy_c_Set_Othe__elem_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a
% Using role type
% Declaring the_el1618277441le_a_o:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x230bbd8>, <kernel.DependentProduct object at 0x230b7a0>) 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 0x230b1b8>, <kernel.DependentProduct object at 0x230bcf8>) of role type named sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J
% Using role type
% Declaring the_el13400124iple_a:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)
% FOF formula (<kernel.Constant object at 0x230b9e0>, <kernel.DependentProduct object at 0x230bcb0>) of role type named sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__O
% Using role type
% Declaring the_el864710747_state:((hoare_1708887482_state->Prop)->hoare_1708887482_state)
% FOF formula (<kernel.Constant object at 0x230bb48>, <kernel.DependentProduct object at 0x230bd40>) of role type named sy_c_Set_Othe__elem_000tc__Nat__Onat
% Using role type
% Declaring the_elem_nat:((nat->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x230bc68>, <kernel.DependentProduct object at 0x230bdd0>) of role type named sy_c_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_Eo_
% Using role type
% Declaring fequal845167073le_a_o:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x230bb90>, <kernel.DependentProduct object at 0x230bc68>) 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 0x230b878>, <kernel.DependentProduct object at 0x230bd88>) 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 0x230bb48>, <kernel.DependentProduct object at 0x230bd40>) of role type named sy_c_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J
% Using role type
% Declaring fequal1604381340iple_a:(hoare_2091234717iple_a->(hoare_2091234717iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x230bb90>, <kernel.DependentProduct object at 0x230bc68>) of role type named sy_c_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J
% Using role type
% Declaring fequal224822779_state:(hoare_1708887482_state->(hoare_1708887482_state->Prop))
% FOF formula (<kernel.Constant object at 0x230b9e0>, <kernel.DependentProduct object at 0x230bb90>) of role type named sy_c_fequal_000tc__Nat__Onat
% Using role type
% Declaring fequal_nat:(nat->(nat->Prop))
% FOF formula (<kernel.Constant object at 0x230bbd8>, <kernel.DependentProduct object at 0x230bd88>) of role type named sy_c_member_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J
% Using role type
% Declaring member1297825410_a_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x230bc68>, <kernel.DependentProduct object at 0x230bf80>) 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 0x230bb48>, <kernel.DependentProduct object at 0x230bfc8>) of role type named sy_c_member_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_M_Eo_
% Using role type
% Declaring member99268621le_a_o:((hoare_2091234717iple_a->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x230bb90>, <kernel.DependentProduct object at 0x230bf80>) of role type named sy_c_member_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost
% Using role type
% Declaring member814030440tate_o:((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x230be18>, <kernel.DependentProduct object at 0x230bfc8>) of role type named sy_c_member_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring member_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x230bd88>, <kernel.DependentProduct object at 0x1f3b0e0>) 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 0x230bdd0>, <kernel.DependentProduct object at 0x1f3b1b8>) 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 0x230bfc8>, <kernel.DependentProduct object at 0x1f3b128>) of role type named sy_c_member_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J
% Using role type
% Declaring member290856304iple_a:(hoare_2091234717iple_a->((hoare_2091234717iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x230be18>, <kernel.DependentProduct object at 0x1f3b200>) of role type named sy_c_member_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J
% Using role type
% Declaring member451959335_state:(hoare_1708887482_state->((hoare_1708887482_state->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x230bd88>, <kernel.DependentProduct object at 0x1f3b290>) of role type named sy_c_member_000tc__Nat__Onat
% Using role type
% Declaring member_nat:(nat->((nat->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x230bfc8>, <kernel.DependentProduct object at 0x1f3b050>) of role type named sy_v_G
% Using role type
% Declaring g:(hoare_2091234717iple_a->Prop)
% FOF formula (<kernel.Constant object at 0x230bd88>, <kernel.DependentProduct object at 0x1f3b098>) of role type named sy_v_P
% Using role type
% Declaring p:(pname->(x_a->(state->Prop)))
% FOF formula (<kernel.Constant object at 0x230bd88>, <kernel.DependentProduct object at 0x1f3b128>) of role type named sy_v_Procs
% Using role type
% Declaring procs:(pname->Prop)
% FOF formula (<kernel.Constant object at 0x1f3b050>, <kernel.DependentProduct object at 0x1f3b0e0>) of role type named sy_v_Q
% Using role type
% Declaring q:(pname->(x_a->(state->Prop)))
% FOF formula (<kernel.Constant object at 0x1f3b098>, <kernel.Constant object at 0x1f3b0e0>) of role type named sy_v_n
% Using role type
% Declaring n:nat
% FOF formula (forall (Fun1_4:(x_a->(state->Prop))) (Com_1:com) (Fun2_4:(x_a->(state->Prop))) (Fun1_3:(x_a->(state->Prop))) (Com:com) (Fun2_3:(x_a->(state->Prop))), ((iff (((eq hoare_2091234717iple_a) (((hoare_657976383iple_a Fun1_4) Com_1) Fun2_4)) (((hoare_657976383iple_a Fun1_3) Com) Fun2_3))) ((and ((and (((eq (x_a->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com_1) Com))) (((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_1:com) (Fun2_4:(x_a->(state->Prop))) (Fun1_3:(x_a->(state->Prop))) (Com:com) (Fun2_3:(x_a->(state->Prop))), ((iff (((eq hoare_2091234717iple_a) (((hoare_657976383iple_a Fun1_4) Com_1) Fun2_4)) (((hoare_657976383iple_a Fun1_3) Com) Fun2_3))) ((and ((and (((eq (x_a->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com_1) Com))) (((eq (x_a->(state->Prop))) Fun2_4) Fun2_3))))
% FOF formula (forall (Fun1_4:(state->(state->Prop))) (Com_1:com) (Fun2_4:(state->(state->Prop))) (Fun1_3:(state->(state->Prop))) (Com:com) (Fun2_3:(state->(state->Prop))), ((iff (((eq hoare_1708887482_state) (((hoare_858012674_state Fun1_4) Com_1) Fun2_4)) (((hoare_858012674_state Fun1_3) Com) Fun2_3))) ((and ((and (((eq (state->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com_1) Com))) (((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_1:com) (Fun2_4:(state->(state->Prop))) (Fun1_3:(state->(state->Prop))) (Com:com) (Fun2_3:(state->(state->Prop))), ((iff (((eq hoare_1708887482_state) (((hoare_858012674_state Fun1_4) Com_1) Fun2_4)) (((hoare_858012674_state Fun1_3) Com) Fun2_3))) ((and ((and (((eq (state->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com_1) Com))) (((eq (state->(state->Prop))) Fun2_4) Fun2_3))))
% FOF formula (forall (G_28:(hoare_1708887482_state->Prop)) (Ts_4:(hoare_1708887482_state->Prop)), ((iff ((hoare_496444244_state G_28) Ts_4)) (forall (N:nat), ((forall (X:hoare_1708887482_state), (((member451959335_state X) G_28)->((hoare_23738522_state N) X)))->(forall (X:hoare_1708887482_state), (((member451959335_state X) Ts_4)->((hoare_23738522_state N) X))))))) of role axiom named fact_2_hoare__valids__def
% A new axiom: (forall (G_28:(hoare_1708887482_state->Prop)) (Ts_4:(hoare_1708887482_state->Prop)), ((iff ((hoare_496444244_state G_28) Ts_4)) (forall (N:nat), ((forall (X:hoare_1708887482_state), (((member451959335_state X) G_28)->((hoare_23738522_state N) X)))->(forall (X:hoare_1708887482_state), (((member451959335_state X) Ts_4)->((hoare_23738522_state N) X)))))))
% FOF formula (forall (G_28:(hoare_2091234717iple_a->Prop)) (Ts_4:(hoare_2091234717iple_a->Prop)), ((iff ((hoare_1805689709lids_a G_28) Ts_4)) (forall (N:nat), ((forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) G_28)->((hoare_1421888935alid_a N) X)))->(forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) Ts_4)->((hoare_1421888935alid_a N) X))))))) of role axiom named fact_3_hoare__valids__def
% A new axiom: (forall (G_28:(hoare_2091234717iple_a->Prop)) (Ts_4:(hoare_2091234717iple_a->Prop)), ((iff ((hoare_1805689709lids_a G_28) Ts_4)) (forall (N:nat), ((forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) G_28)->((hoare_1421888935alid_a N) X)))->(forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) Ts_4)->((hoare_1421888935alid_a N) X)))))))
% FOF formula (forall (G_27:(hoare_1708887482_state->Prop)) (P_36:(pname->(state->(state->Prop)))) (Q_20:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_27) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1))) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_36 P_9)) (the_com (body_1 P_9))) (Q_20 P_9)))) Procs_1))->((hoare_90032982_state G_27) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1)))) of role axiom named fact_4_hoare__derivs_OBody
% A new axiom: (forall (G_27:(hoare_1708887482_state->Prop)) (P_36:(pname->(state->(state->Prop)))) (Q_20:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_27) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1))) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_36 P_9)) (the_com (body_1 P_9))) (Q_20 P_9)))) Procs_1))->((hoare_90032982_state G_27) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1))))
% FOF formula (forall (G_27:(hoare_2091234717iple_a->Prop)) (P_36:(pname->(x_a->(state->Prop)))) (Q_20:(pname->(x_a->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_1467856363rivs_a ((semila1052848428le_a_o G_27) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1))) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_36 P_9)) (the_com (body_1 P_9))) (Q_20 P_9)))) Procs_1))->((hoare_1467856363rivs_a G_27) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1)))) of role axiom named fact_5_hoare__derivs_OBody
% A new axiom: (forall (G_27:(hoare_2091234717iple_a->Prop)) (P_36:(pname->(x_a->(state->Prop)))) (Q_20:(pname->(x_a->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_1467856363rivs_a ((semila1052848428le_a_o G_27) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1))) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_36 P_9)) (the_com (body_1 P_9))) (Q_20 P_9)))) Procs_1))->((hoare_1467856363rivs_a G_27) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1))))
% FOF formula (forall (C_34:nat) (A_129:(nat->Prop)) (B_71:(nat->Prop)), (((member_nat C_34) ((semila848761471_nat_o A_129) B_71))->((((member_nat C_34) A_129)->False)->((member_nat C_34) B_71)))) of role axiom named fact_6_UnE
% A new axiom: (forall (C_34:nat) (A_129:(nat->Prop)) (B_71:(nat->Prop)), (((member_nat C_34) ((semila848761471_nat_o A_129) B_71))->((((member_nat C_34) A_129)->False)->((member_nat C_34) B_71))))
% FOF formula (forall (C_34:(hoare_2091234717iple_a->Prop)) (A_129:((hoare_2091234717iple_a->Prop)->Prop)) (B_71:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_34) ((semila2050116131_a_o_o A_129) B_71))->((((member99268621le_a_o C_34) A_129)->False)->((member99268621le_a_o C_34) B_71)))) of role axiom named fact_7_UnE
% A new axiom: (forall (C_34:(hoare_2091234717iple_a->Prop)) (A_129:((hoare_2091234717iple_a->Prop)->Prop)) (B_71:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_34) ((semila2050116131_a_o_o A_129) B_71))->((((member99268621le_a_o C_34) A_129)->False)->((member99268621le_a_o C_34) B_71))))
% FOF formula (forall (C_34:hoare_1708887482_state) (A_129:(hoare_1708887482_state->Prop)) (B_71:(hoare_1708887482_state->Prop)), (((member451959335_state C_34) ((semila1122118281tate_o A_129) B_71))->((((member451959335_state C_34) A_129)->False)->((member451959335_state C_34) B_71)))) of role axiom named fact_8_UnE
% A new axiom: (forall (C_34:hoare_1708887482_state) (A_129:(hoare_1708887482_state->Prop)) (B_71:(hoare_1708887482_state->Prop)), (((member451959335_state C_34) ((semila1122118281tate_o A_129) B_71))->((((member451959335_state C_34) A_129)->False)->((member451959335_state C_34) B_71))))
% FOF formula (forall (C_34:hoare_2091234717iple_a) (A_129:(hoare_2091234717iple_a->Prop)) (B_71:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_34) ((semila1052848428le_a_o A_129) B_71))->((((member290856304iple_a C_34) A_129)->False)->((member290856304iple_a C_34) B_71)))) of role axiom named fact_9_UnE
% A new axiom: (forall (C_34:hoare_2091234717iple_a) (A_129:(hoare_2091234717iple_a->Prop)) (B_71:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_34) ((semila1052848428le_a_o A_129) B_71))->((((member290856304iple_a C_34) A_129)->False)->((member290856304iple_a C_34) B_71))))
% FOF formula (forall (C_34:pname) (A_129:(pname->Prop)) (B_71:(pname->Prop)), (((member_pname C_34) ((semila1780557381name_o A_129) B_71))->((((member_pname C_34) A_129)->False)->((member_pname C_34) B_71)))) of role axiom named fact_10_UnE
% A new axiom: (forall (C_34:pname) (A_129:(pname->Prop)) (B_71:(pname->Prop)), (((member_pname C_34) ((semila1780557381name_o A_129) B_71))->((((member_pname C_34) A_129)->False)->((member_pname C_34) B_71))))
% FOF formula (forall (A_128:(nat->Prop)) (B_70:(nat->Prop)) (X_51:nat), ((((semila848761471_nat_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51)))) of role axiom named fact_11_sup1E
% A new axiom: (forall (A_128:(nat->Prop)) (B_70:(nat->Prop)) (X_51:nat), ((((semila848761471_nat_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51))))
% FOF formula (forall (A_128:((hoare_2091234717iple_a->Prop)->Prop)) (B_70:((hoare_2091234717iple_a->Prop)->Prop)) (X_51:(hoare_2091234717iple_a->Prop)), ((((semila2050116131_a_o_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51)))) of role axiom named fact_12_sup1E
% A new axiom: (forall (A_128:((hoare_2091234717iple_a->Prop)->Prop)) (B_70:((hoare_2091234717iple_a->Prop)->Prop)) (X_51:(hoare_2091234717iple_a->Prop)), ((((semila2050116131_a_o_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51))))
% FOF formula (forall (A_128:(hoare_1708887482_state->Prop)) (B_70:(hoare_1708887482_state->Prop)) (X_51:hoare_1708887482_state), ((((semila1122118281tate_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51)))) of role axiom named fact_13_sup1E
% A new axiom: (forall (A_128:(hoare_1708887482_state->Prop)) (B_70:(hoare_1708887482_state->Prop)) (X_51:hoare_1708887482_state), ((((semila1122118281tate_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51))))
% FOF formula (forall (A_128:(pname->Prop)) (B_70:(pname->Prop)) (X_51:pname), ((((semila1780557381name_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51)))) of role axiom named fact_14_sup1E
% A new axiom: (forall (A_128:(pname->Prop)) (B_70:(pname->Prop)) (X_51:pname), ((((semila1780557381name_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51))))
% FOF formula (forall (A_128:(hoare_2091234717iple_a->Prop)) (B_70:(hoare_2091234717iple_a->Prop)) (X_51:hoare_2091234717iple_a), ((((semila1052848428le_a_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51)))) of role axiom named fact_15_sup1E
% A new axiom: (forall (A_128:(hoare_2091234717iple_a->Prop)) (B_70:(hoare_2091234717iple_a->Prop)) (X_51:hoare_2091234717iple_a), ((((semila1052848428le_a_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51))))
% FOF formula (forall (A_127:(nat->Prop)) (B_69:(nat->Prop)) (X_50:nat), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila848761471_nat_o A_127) B_69) X_50))) of role axiom named fact_16_sup1CI
% A new axiom: (forall (A_127:(nat->Prop)) (B_69:(nat->Prop)) (X_50:nat), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila848761471_nat_o A_127) B_69) X_50)))
% FOF formula (forall (A_127:((hoare_2091234717iple_a->Prop)->Prop)) (B_69:((hoare_2091234717iple_a->Prop)->Prop)) (X_50:(hoare_2091234717iple_a->Prop)), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila2050116131_a_o_o A_127) B_69) X_50))) of role axiom named fact_17_sup1CI
% A new axiom: (forall (A_127:((hoare_2091234717iple_a->Prop)->Prop)) (B_69:((hoare_2091234717iple_a->Prop)->Prop)) (X_50:(hoare_2091234717iple_a->Prop)), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila2050116131_a_o_o A_127) B_69) X_50)))
% FOF formula (forall (A_127:(hoare_1708887482_state->Prop)) (B_69:(hoare_1708887482_state->Prop)) (X_50:hoare_1708887482_state), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila1122118281tate_o A_127) B_69) X_50))) of role axiom named fact_18_sup1CI
% A new axiom: (forall (A_127:(hoare_1708887482_state->Prop)) (B_69:(hoare_1708887482_state->Prop)) (X_50:hoare_1708887482_state), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila1122118281tate_o A_127) B_69) X_50)))
% FOF formula (forall (A_127:(pname->Prop)) (B_69:(pname->Prop)) (X_50:pname), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila1780557381name_o A_127) B_69) X_50))) of role axiom named fact_19_sup1CI
% A new axiom: (forall (A_127:(pname->Prop)) (B_69:(pname->Prop)) (X_50:pname), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila1780557381name_o A_127) B_69) X_50)))
% FOF formula (forall (A_127:(hoare_2091234717iple_a->Prop)) (B_69:(hoare_2091234717iple_a->Prop)) (X_50:hoare_2091234717iple_a), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila1052848428le_a_o A_127) B_69) X_50))) of role axiom named fact_20_sup1CI
% A new axiom: (forall (A_127:(hoare_2091234717iple_a->Prop)) (B_69:(hoare_2091234717iple_a->Prop)) (X_50:hoare_2091234717iple_a), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila1052848428le_a_o A_127) B_69) X_50)))
% FOF formula (forall (A_126:(nat->Prop)) (C_33:nat) (B_68:(nat->Prop)), (((((member_nat C_33) B_68)->False)->((member_nat C_33) A_126))->((member_nat C_33) ((semila848761471_nat_o A_126) B_68)))) of role axiom named fact_21_UnCI
% A new axiom: (forall (A_126:(nat->Prop)) (C_33:nat) (B_68:(nat->Prop)), (((((member_nat C_33) B_68)->False)->((member_nat C_33) A_126))->((member_nat C_33) ((semila848761471_nat_o A_126) B_68))))
% FOF formula (forall (A_126:((hoare_2091234717iple_a->Prop)->Prop)) (C_33:(hoare_2091234717iple_a->Prop)) (B_68:((hoare_2091234717iple_a->Prop)->Prop)), (((((member99268621le_a_o C_33) B_68)->False)->((member99268621le_a_o C_33) A_126))->((member99268621le_a_o C_33) ((semila2050116131_a_o_o A_126) B_68)))) of role axiom named fact_22_UnCI
% A new axiom: (forall (A_126:((hoare_2091234717iple_a->Prop)->Prop)) (C_33:(hoare_2091234717iple_a->Prop)) (B_68:((hoare_2091234717iple_a->Prop)->Prop)), (((((member99268621le_a_o C_33) B_68)->False)->((member99268621le_a_o C_33) A_126))->((member99268621le_a_o C_33) ((semila2050116131_a_o_o A_126) B_68))))
% FOF formula (forall (A_126:(hoare_1708887482_state->Prop)) (C_33:hoare_1708887482_state) (B_68:(hoare_1708887482_state->Prop)), (((((member451959335_state C_33) B_68)->False)->((member451959335_state C_33) A_126))->((member451959335_state C_33) ((semila1122118281tate_o A_126) B_68)))) of role axiom named fact_23_UnCI
% A new axiom: (forall (A_126:(hoare_1708887482_state->Prop)) (C_33:hoare_1708887482_state) (B_68:(hoare_1708887482_state->Prop)), (((((member451959335_state C_33) B_68)->False)->((member451959335_state C_33) A_126))->((member451959335_state C_33) ((semila1122118281tate_o A_126) B_68))))
% FOF formula (forall (A_126:(hoare_2091234717iple_a->Prop)) (C_33:hoare_2091234717iple_a) (B_68:(hoare_2091234717iple_a->Prop)), (((((member290856304iple_a C_33) B_68)->False)->((member290856304iple_a C_33) A_126))->((member290856304iple_a C_33) ((semila1052848428le_a_o A_126) B_68)))) of role axiom named fact_24_UnCI
% A new axiom: (forall (A_126:(hoare_2091234717iple_a->Prop)) (C_33:hoare_2091234717iple_a) (B_68:(hoare_2091234717iple_a->Prop)), (((((member290856304iple_a C_33) B_68)->False)->((member290856304iple_a C_33) A_126))->((member290856304iple_a C_33) ((semila1052848428le_a_o A_126) B_68))))
% FOF formula (forall (A_126:(pname->Prop)) (C_33:pname) (B_68:(pname->Prop)), (((((member_pname C_33) B_68)->False)->((member_pname C_33) A_126))->((member_pname C_33) ((semila1780557381name_o A_126) B_68)))) of role axiom named fact_25_UnCI
% A new axiom: (forall (A_126:(pname->Prop)) (C_33:pname) (B_68:(pname->Prop)), (((((member_pname C_33) B_68)->False)->((member_pname C_33) A_126))->((member_pname C_33) ((semila1780557381name_o A_126) B_68))))
% FOF formula (forall (A_125:(nat->Prop)) (B_67:nat) (F_50:(nat->nat)) (X_49:nat), ((((eq nat) B_67) (F_50 X_49))->(((member_nat X_49) A_125)->((member_nat B_67) ((image_nat_nat F_50) A_125))))) of role axiom named fact_26_image__eqI
% A new axiom: (forall (A_125:(nat->Prop)) (B_67:nat) (F_50:(nat->nat)) (X_49:nat), ((((eq nat) B_67) (F_50 X_49))->(((member_nat X_49) A_125)->((member_nat B_67) ((image_nat_nat F_50) A_125)))))
% FOF formula (forall (A_125:(pname->Prop)) (B_67:hoare_1708887482_state) (F_50:(pname->hoare_1708887482_state)) (X_49:pname), ((((eq hoare_1708887482_state) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member451959335_state B_67) ((image_1116629049_state F_50) A_125))))) of role axiom named fact_27_image__eqI
% A new axiom: (forall (A_125:(pname->Prop)) (B_67:hoare_1708887482_state) (F_50:(pname->hoare_1708887482_state)) (X_49:pname), ((((eq hoare_1708887482_state) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member451959335_state B_67) ((image_1116629049_state F_50) A_125)))))
% FOF formula (forall (A_125:(pname->Prop)) (B_67:nat) (F_50:(pname->nat)) (X_49:pname), ((((eq nat) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member_nat B_67) ((image_pname_nat F_50) A_125))))) of role axiom named fact_28_image__eqI
% A new axiom: (forall (A_125:(pname->Prop)) (B_67:nat) (F_50:(pname->nat)) (X_49:pname), ((((eq nat) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member_nat B_67) ((image_pname_nat F_50) A_125)))))
% FOF formula (forall (A_125:(pname->Prop)) (B_67:(hoare_2091234717iple_a->Prop)) (F_50:(pname->(hoare_2091234717iple_a->Prop))) (X_49:pname), ((((eq (hoare_2091234717iple_a->Prop)) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member99268621le_a_o B_67) ((image_742317343le_a_o F_50) A_125))))) of role axiom named fact_29_image__eqI
% A new axiom: (forall (A_125:(pname->Prop)) (B_67:(hoare_2091234717iple_a->Prop)) (F_50:(pname->(hoare_2091234717iple_a->Prop))) (X_49:pname), ((((eq (hoare_2091234717iple_a->Prop)) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member99268621le_a_o B_67) ((image_742317343le_a_o F_50) A_125)))))
% FOF formula (forall (A_125:(nat->Prop)) (B_67:pname) (F_50:(nat->pname)) (X_49:nat), ((((eq pname) B_67) (F_50 X_49))->(((member_nat X_49) A_125)->((member_pname B_67) ((image_nat_pname F_50) A_125))))) of role axiom named fact_30_image__eqI
% A new axiom: (forall (A_125:(nat->Prop)) (B_67:pname) (F_50:(nat->pname)) (X_49:nat), ((((eq pname) B_67) (F_50 X_49))->(((member_nat X_49) A_125)->((member_pname B_67) ((image_nat_pname F_50) A_125)))))
% FOF formula (forall (A_125:((hoare_2091234717iple_a->Prop)->Prop)) (B_67:pname) (F_50:((hoare_2091234717iple_a->Prop)->pname)) (X_49:(hoare_2091234717iple_a->Prop)), ((((eq pname) B_67) (F_50 X_49))->(((member99268621le_a_o X_49) A_125)->((member_pname B_67) ((image_1908519857_pname F_50) A_125))))) of role axiom named fact_31_image__eqI
% A new axiom: (forall (A_125:((hoare_2091234717iple_a->Prop)->Prop)) (B_67:pname) (F_50:((hoare_2091234717iple_a->Prop)->pname)) (X_49:(hoare_2091234717iple_a->Prop)), ((((eq pname) B_67) (F_50 X_49))->(((member99268621le_a_o X_49) A_125)->((member_pname B_67) ((image_1908519857_pname F_50) A_125)))))
% FOF formula (forall (A_125:(hoare_2091234717iple_a->Prop)) (B_67:pname) (F_50:(hoare_2091234717iple_a->pname)) (X_49:hoare_2091234717iple_a), ((((eq pname) B_67) (F_50 X_49))->(((member290856304iple_a X_49) A_125)->((member_pname B_67) ((image_924789612_pname F_50) A_125))))) of role axiom named fact_32_image__eqI
% A new axiom: (forall (A_125:(hoare_2091234717iple_a->Prop)) (B_67:pname) (F_50:(hoare_2091234717iple_a->pname)) (X_49:hoare_2091234717iple_a), ((((eq pname) B_67) (F_50 X_49))->(((member290856304iple_a X_49) A_125)->((member_pname B_67) ((image_924789612_pname F_50) A_125)))))
% FOF formula (forall (A_125:(pname->Prop)) (B_67:hoare_2091234717iple_a) (F_50:(pname->hoare_2091234717iple_a)) (X_49:pname), ((((eq hoare_2091234717iple_a) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member290856304iple_a B_67) ((image_231808478iple_a F_50) A_125))))) of role axiom named fact_33_image__eqI
% A new axiom: (forall (A_125:(pname->Prop)) (B_67:hoare_2091234717iple_a) (F_50:(pname->hoare_2091234717iple_a)) (X_49:pname), ((((eq hoare_2091234717iple_a) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member290856304iple_a B_67) ((image_231808478iple_a F_50) A_125)))))
% FOF formula (forall (F_49:(nat->nat)) (A_124:(nat->Prop)) (B_66:(nat->Prop)), (((eq (nat->Prop)) ((image_nat_nat F_49) ((semila848761471_nat_o A_124) B_66))) ((semila848761471_nat_o ((image_nat_nat F_49) A_124)) ((image_nat_nat F_49) B_66)))) of role axiom named fact_34_image__Un
% A new axiom: (forall (F_49:(nat->nat)) (A_124:(nat->Prop)) (B_66:(nat->Prop)), (((eq (nat->Prop)) ((image_nat_nat F_49) ((semila848761471_nat_o A_124) B_66))) ((semila848761471_nat_o ((image_nat_nat F_49) A_124)) ((image_nat_nat F_49) B_66))))
% FOF formula (forall (F_49:(pname->hoare_1708887482_state)) (A_124:(pname->Prop)) (B_66:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_49) ((semila1780557381name_o A_124) B_66))) ((semila1122118281tate_o ((image_1116629049_state F_49) A_124)) ((image_1116629049_state F_49) B_66)))) of role axiom named fact_35_image__Un
% A new axiom: (forall (F_49:(pname->hoare_1708887482_state)) (A_124:(pname->Prop)) (B_66:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_49) ((semila1780557381name_o A_124) B_66))) ((semila1122118281tate_o ((image_1116629049_state F_49) A_124)) ((image_1116629049_state F_49) B_66))))
% FOF formula (forall (F_49:(hoare_2091234717iple_a->nat)) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq (nat->Prop)) ((image_1773322034_a_nat F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila848761471_nat_o ((image_1773322034_a_nat F_49) A_124)) ((image_1773322034_a_nat F_49) B_66)))) of role axiom named fact_36_image__Un
% A new axiom: (forall (F_49:(hoare_2091234717iple_a->nat)) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq (nat->Prop)) ((image_1773322034_a_nat F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila848761471_nat_o ((image_1773322034_a_nat F_49) A_124)) ((image_1773322034_a_nat F_49) B_66))))
% FOF formula (forall (F_49:(hoare_2091234717iple_a->(hoare_2091234717iple_a->Prop))) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((image_1642350072le_a_o F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila2050116131_a_o_o ((image_1642350072le_a_o F_49) A_124)) ((image_1642350072le_a_o F_49) B_66)))) of role axiom named fact_37_image__Un
% A new axiom: (forall (F_49:(hoare_2091234717iple_a->(hoare_2091234717iple_a->Prop))) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((image_1642350072le_a_o F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila2050116131_a_o_o ((image_1642350072le_a_o F_49) A_124)) ((image_1642350072le_a_o F_49) B_66))))
% FOF formula (forall (F_49:(hoare_2091234717iple_a->hoare_1708887482_state)) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1884482962_state F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila1122118281tate_o ((image_1884482962_state F_49) A_124)) ((image_1884482962_state F_49) B_66)))) of role axiom named fact_38_image__Un
% A new axiom: (forall (F_49:(hoare_2091234717iple_a->hoare_1708887482_state)) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1884482962_state F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila1122118281tate_o ((image_1884482962_state F_49) A_124)) ((image_1884482962_state F_49) B_66))))
% FOF formula (forall (F_49:(hoare_2091234717iple_a->pname)) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq (pname->Prop)) ((image_924789612_pname F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila1780557381name_o ((image_924789612_pname F_49) A_124)) ((image_924789612_pname F_49) B_66)))) of role axiom named fact_39_image__Un
% A new axiom: (forall (F_49:(hoare_2091234717iple_a->pname)) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq (pname->Prop)) ((image_924789612_pname F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila1780557381name_o ((image_924789612_pname F_49) A_124)) ((image_924789612_pname F_49) B_66))))
% FOF formula (forall (F_49:(nat->hoare_2091234717iple_a)) (A_124:(nat->Prop)) (B_66:(nat->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_359186840iple_a F_49) ((semila848761471_nat_o A_124) B_66))) ((semila1052848428le_a_o ((image_359186840iple_a F_49) A_124)) ((image_359186840iple_a F_49) B_66)))) of role axiom named fact_40_image__Un
% A new axiom: (forall (F_49:(nat->hoare_2091234717iple_a)) (A_124:(nat->Prop)) (B_66:(nat->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_359186840iple_a F_49) ((semila848761471_nat_o A_124) B_66))) ((semila1052848428le_a_o ((image_359186840iple_a F_49) A_124)) ((image_359186840iple_a F_49) B_66))))
% FOF formula (forall (F_49:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)) (A_124:((hoare_2091234717iple_a->Prop)->Prop)) (B_66:((hoare_2091234717iple_a->Prop)->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_136408202iple_a F_49) ((semila2050116131_a_o_o A_124) B_66))) ((semila1052848428le_a_o ((image_136408202iple_a F_49) A_124)) ((image_136408202iple_a F_49) B_66)))) of role axiom named fact_41_image__Un
% A new axiom: (forall (F_49:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)) (A_124:((hoare_2091234717iple_a->Prop)->Prop)) (B_66:((hoare_2091234717iple_a->Prop)->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_136408202iple_a F_49) ((semila2050116131_a_o_o A_124) B_66))) ((semila1052848428le_a_o ((image_136408202iple_a F_49) A_124)) ((image_136408202iple_a F_49) B_66))))
% FOF formula (forall (F_49:(hoare_1708887482_state->hoare_2091234717iple_a)) (A_124:(hoare_1708887482_state->Prop)) (B_66:(hoare_1708887482_state->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_293283184iple_a F_49) ((semila1122118281tate_o A_124) B_66))) ((semila1052848428le_a_o ((image_293283184iple_a F_49) A_124)) ((image_293283184iple_a F_49) B_66)))) of role axiom named fact_42_image__Un
% A new axiom: (forall (F_49:(hoare_1708887482_state->hoare_2091234717iple_a)) (A_124:(hoare_1708887482_state->Prop)) (B_66:(hoare_1708887482_state->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_293283184iple_a F_49) ((semila1122118281tate_o A_124) B_66))) ((semila1052848428le_a_o ((image_293283184iple_a F_49) A_124)) ((image_293283184iple_a F_49) B_66))))
% FOF formula (forall (F_49:(pname->hoare_2091234717iple_a)) (A_124:(pname->Prop)) (B_66:(pname->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_49) ((semila1780557381name_o A_124) B_66))) ((semila1052848428le_a_o ((image_231808478iple_a F_49) A_124)) ((image_231808478iple_a F_49) B_66)))) of role axiom named fact_43_image__Un
% A new axiom: (forall (F_49:(pname->hoare_2091234717iple_a)) (A_124:(pname->Prop)) (B_66:(pname->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_49) ((semila1780557381name_o A_124) B_66))) ((semila1052848428le_a_o ((image_231808478iple_a F_49) A_124)) ((image_231808478iple_a F_49) B_66))))
% FOF formula (forall (F_48:(nat->Prop)) (G_26:(nat->Prop)) (X:nat), ((iff (((semila848761471_nat_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X)))) of role axiom named fact_44_sup__fun__def
% A new axiom: (forall (F_48:(nat->Prop)) (G_26:(nat->Prop)) (X:nat), ((iff (((semila848761471_nat_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X))))
% FOF formula (forall (F_48:((hoare_2091234717iple_a->Prop)->Prop)) (G_26:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), ((iff (((semila2050116131_a_o_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X)))) of role axiom named fact_45_sup__fun__def
% A new axiom: (forall (F_48:((hoare_2091234717iple_a->Prop)->Prop)) (G_26:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), ((iff (((semila2050116131_a_o_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X))))
% FOF formula (forall (F_48:(hoare_1708887482_state->Prop)) (G_26:(hoare_1708887482_state->Prop)) (X:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X)))) of role axiom named fact_46_sup__fun__def
% A new axiom: (forall (F_48:(hoare_1708887482_state->Prop)) (G_26:(hoare_1708887482_state->Prop)) (X:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X))))
% FOF formula (forall (F_48:(pname->Prop)) (G_26:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X)))) of role axiom named fact_47_sup__fun__def
% A new axiom: (forall (F_48:(pname->Prop)) (G_26:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X))))
% FOF formula (forall (F_48:(hoare_2091234717iple_a->Prop)) (G_26:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila1052848428le_a_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X)))) of role axiom named fact_48_sup__fun__def
% A new axiom: (forall (F_48:(hoare_2091234717iple_a->Prop)) (G_26:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila1052848428le_a_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X))))
% FOF formula (forall (F_47:(nat->Prop)) (G_25:(nat->Prop)) (X_48:nat), ((iff (((semila848761471_nat_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48)))) of role axiom named fact_49_sup__apply
% A new axiom: (forall (F_47:(nat->Prop)) (G_25:(nat->Prop)) (X_48:nat), ((iff (((semila848761471_nat_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48))))
% FOF formula (forall (F_47:((hoare_2091234717iple_a->Prop)->Prop)) (G_25:((hoare_2091234717iple_a->Prop)->Prop)) (X_48:(hoare_2091234717iple_a->Prop)), ((iff (((semila2050116131_a_o_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48)))) of role axiom named fact_50_sup__apply
% A new axiom: (forall (F_47:((hoare_2091234717iple_a->Prop)->Prop)) (G_25:((hoare_2091234717iple_a->Prop)->Prop)) (X_48:(hoare_2091234717iple_a->Prop)), ((iff (((semila2050116131_a_o_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48))))
% FOF formula (forall (F_47:(hoare_1708887482_state->Prop)) (G_25:(hoare_1708887482_state->Prop)) (X_48:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48)))) of role axiom named fact_51_sup__apply
% A new axiom: (forall (F_47:(hoare_1708887482_state->Prop)) (G_25:(hoare_1708887482_state->Prop)) (X_48:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48))))
% FOF formula (forall (F_47:(pname->Prop)) (G_25:(pname->Prop)) (X_48:pname), ((iff (((semila1780557381name_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48)))) of role axiom named fact_52_sup__apply
% A new axiom: (forall (F_47:(pname->Prop)) (G_25:(pname->Prop)) (X_48:pname), ((iff (((semila1780557381name_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48))))
% FOF formula (forall (F_47:(hoare_2091234717iple_a->Prop)) (G_25:(hoare_2091234717iple_a->Prop)) (X_48:hoare_2091234717iple_a), ((iff (((semila1052848428le_a_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48)))) of role axiom named fact_53_sup__apply
% A new axiom: (forall (F_47:(hoare_2091234717iple_a->Prop)) (G_25:(hoare_2091234717iple_a->Prop)) (X_48:hoare_2091234717iple_a), ((iff (((semila1052848428le_a_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48))))
% FOF formula (forall (G_24:(hoare_2091234717iple_a->Prop)) (G_23:(hoare_2091234717iple_a->Prop)) (Ts_3:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a G_23) Ts_3)->(((hoare_1467856363rivs_a G_24) G_23)->((hoare_1467856363rivs_a G_24) Ts_3)))) of role axiom named fact_54_cut
% A new axiom: (forall (G_24:(hoare_2091234717iple_a->Prop)) (G_23:(hoare_2091234717iple_a->Prop)) (Ts_3:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a G_23) Ts_3)->(((hoare_1467856363rivs_a G_24) G_23)->((hoare_1467856363rivs_a G_24) Ts_3))))
% FOF formula (forall (G_24:(hoare_1708887482_state->Prop)) (G_23:(hoare_1708887482_state->Prop)) (Ts_3:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_23) Ts_3)->(((hoare_90032982_state G_24) G_23)->((hoare_90032982_state G_24) Ts_3)))) of role axiom named fact_55_cut
% A new axiom: (forall (G_24:(hoare_1708887482_state->Prop)) (G_23:(hoare_1708887482_state->Prop)) (Ts_3:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_23) Ts_3)->(((hoare_90032982_state G_24) G_23)->((hoare_90032982_state G_24) Ts_3))))
% FOF formula (forall (X_47:(nat->Prop)) (Y_20:(nat->Prop)) (Z_11:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o X_47) Y_20)) Z_11)) ((semila848761471_nat_o X_47) ((semila848761471_nat_o Y_20) Z_11)))) of role axiom named fact_56_sup__assoc
% A new axiom: (forall (X_47:(nat->Prop)) (Y_20:(nat->Prop)) (Z_11:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o X_47) Y_20)) Z_11)) ((semila848761471_nat_o X_47) ((semila848761471_nat_o Y_20) Z_11))))
% FOF formula (forall (X_47:nat) (Y_20:nat) (Z_11:nat), (((eq nat) ((semila972727038up_nat ((semila972727038up_nat X_47) Y_20)) Z_11)) ((semila972727038up_nat X_47) ((semila972727038up_nat Y_20) Z_11)))) of role axiom named fact_57_sup__assoc
% A new axiom: (forall (X_47:nat) (Y_20:nat) (Z_11:nat), (((eq nat) ((semila972727038up_nat ((semila972727038up_nat X_47) Y_20)) Z_11)) ((semila972727038up_nat X_47) ((semila972727038up_nat Y_20) Z_11))))
% FOF formula (forall (X_47:((hoare_2091234717iple_a->Prop)->Prop)) (Y_20:((hoare_2091234717iple_a->Prop)->Prop)) (Z_11:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o X_47) Y_20)) Z_11)) ((semila2050116131_a_o_o X_47) ((semila2050116131_a_o_o Y_20) Z_11)))) of role axiom named fact_58_sup__assoc
% A new axiom: (forall (X_47:((hoare_2091234717iple_a->Prop)->Prop)) (Y_20:((hoare_2091234717iple_a->Prop)->Prop)) (Z_11:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o X_47) Y_20)) Z_11)) ((semila2050116131_a_o_o X_47) ((semila2050116131_a_o_o Y_20) Z_11))))
% FOF formula (forall (X_47:(hoare_1708887482_state->Prop)) (Y_20:(hoare_1708887482_state->Prop)) (Z_11:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_47) Y_20)) Z_11)) ((semila1122118281tate_o X_47) ((semila1122118281tate_o Y_20) Z_11)))) of role axiom named fact_59_sup__assoc
% A new axiom: (forall (X_47:(hoare_1708887482_state->Prop)) (Y_20:(hoare_1708887482_state->Prop)) (Z_11:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_47) Y_20)) Z_11)) ((semila1122118281tate_o X_47) ((semila1122118281tate_o Y_20) Z_11))))
% FOF formula (forall (X_47:(pname->Prop)) (Y_20:(pname->Prop)) (Z_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_47) Y_20)) Z_11)) ((semila1780557381name_o X_47) ((semila1780557381name_o Y_20) Z_11)))) of role axiom named fact_60_sup__assoc
% A new axiom: (forall (X_47:(pname->Prop)) (Y_20:(pname->Prop)) (Z_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_47) Y_20)) Z_11)) ((semila1780557381name_o X_47) ((semila1780557381name_o Y_20) Z_11))))
% FOF formula (forall (X_47:Prop) (Y_20:Prop) (Z_11:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_47) Y_20)) Z_11)) ((semila10642723_sup_o X_47) ((semila10642723_sup_o Y_20) Z_11)))) of role axiom named fact_61_sup__assoc
% A new axiom: (forall (X_47:Prop) (Y_20:Prop) (Z_11:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_47) Y_20)) Z_11)) ((semila10642723_sup_o X_47) ((semila10642723_sup_o Y_20) Z_11))))
% FOF formula (forall (X_47:(hoare_2091234717iple_a->Prop)) (Y_20:(hoare_2091234717iple_a->Prop)) (Z_11:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o X_47) Y_20)) Z_11)) ((semila1052848428le_a_o X_47) ((semila1052848428le_a_o Y_20) Z_11)))) of role axiom named fact_62_sup__assoc
% A new axiom: (forall (X_47:(hoare_2091234717iple_a->Prop)) (Y_20:(hoare_2091234717iple_a->Prop)) (Z_11:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o X_47) Y_20)) Z_11)) ((semila1052848428le_a_o X_47) ((semila1052848428le_a_o Y_20) Z_11))))
% FOF formula (forall (X_46:(nat->Prop)) (Y_19:(nat->Prop)) (Z_10:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o X_46) Y_19)) Z_10)) ((semila848761471_nat_o X_46) ((semila848761471_nat_o Y_19) Z_10)))) of role axiom named fact_63_inf__sup__aci_I6_J
% A new axiom: (forall (X_46:(nat->Prop)) (Y_19:(nat->Prop)) (Z_10:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o X_46) Y_19)) Z_10)) ((semila848761471_nat_o X_46) ((semila848761471_nat_o Y_19) Z_10))))
% FOF formula (forall (X_46:nat) (Y_19:nat) (Z_10:nat), (((eq nat) ((semila972727038up_nat ((semila972727038up_nat X_46) Y_19)) Z_10)) ((semila972727038up_nat X_46) ((semila972727038up_nat Y_19) Z_10)))) of role axiom named fact_64_inf__sup__aci_I6_J
% A new axiom: (forall (X_46:nat) (Y_19:nat) (Z_10:nat), (((eq nat) ((semila972727038up_nat ((semila972727038up_nat X_46) Y_19)) Z_10)) ((semila972727038up_nat X_46) ((semila972727038up_nat Y_19) Z_10))))
% FOF formula (forall (X_46:((hoare_2091234717iple_a->Prop)->Prop)) (Y_19:((hoare_2091234717iple_a->Prop)->Prop)) (Z_10:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o X_46) Y_19)) Z_10)) ((semila2050116131_a_o_o X_46) ((semila2050116131_a_o_o Y_19) Z_10)))) of role axiom named fact_65_inf__sup__aci_I6_J
% A new axiom: (forall (X_46:((hoare_2091234717iple_a->Prop)->Prop)) (Y_19:((hoare_2091234717iple_a->Prop)->Prop)) (Z_10:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o X_46) Y_19)) Z_10)) ((semila2050116131_a_o_o X_46) ((semila2050116131_a_o_o Y_19) Z_10))))
% FOF formula (forall (X_46:(hoare_1708887482_state->Prop)) (Y_19:(hoare_1708887482_state->Prop)) (Z_10:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_46) Y_19)) Z_10)) ((semila1122118281tate_o X_46) ((semila1122118281tate_o Y_19) Z_10)))) of role axiom named fact_66_inf__sup__aci_I6_J
% A new axiom: (forall (X_46:(hoare_1708887482_state->Prop)) (Y_19:(hoare_1708887482_state->Prop)) (Z_10:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_46) Y_19)) Z_10)) ((semila1122118281tate_o X_46) ((semila1122118281tate_o Y_19) Z_10))))
% FOF formula (forall (X_46:(pname->Prop)) (Y_19:(pname->Prop)) (Z_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_46) Y_19)) Z_10)) ((semila1780557381name_o X_46) ((semila1780557381name_o Y_19) Z_10)))) of role axiom named fact_67_inf__sup__aci_I6_J
% A new axiom: (forall (X_46:(pname->Prop)) (Y_19:(pname->Prop)) (Z_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_46) Y_19)) Z_10)) ((semila1780557381name_o X_46) ((semila1780557381name_o Y_19) Z_10))))
% FOF formula (forall (X_46:Prop) (Y_19:Prop) (Z_10:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_46) Y_19)) Z_10)) ((semila10642723_sup_o X_46) ((semila10642723_sup_o Y_19) Z_10)))) of role axiom named fact_68_inf__sup__aci_I6_J
% A new axiom: (forall (X_46:Prop) (Y_19:Prop) (Z_10:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_46) Y_19)) Z_10)) ((semila10642723_sup_o X_46) ((semila10642723_sup_o Y_19) Z_10))))
% FOF formula (forall (X_46:(hoare_2091234717iple_a->Prop)) (Y_19:(hoare_2091234717iple_a->Prop)) (Z_10:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o X_46) Y_19)) Z_10)) ((semila1052848428le_a_o X_46) ((semila1052848428le_a_o Y_19) Z_10)))) of role axiom named fact_69_inf__sup__aci_I6_J
% A new axiom: (forall (X_46:(hoare_2091234717iple_a->Prop)) (Y_19:(hoare_2091234717iple_a->Prop)) (Z_10:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o X_46) Y_19)) Z_10)) ((semila1052848428le_a_o X_46) ((semila1052848428le_a_o Y_19) Z_10))))
% FOF formula (forall (A_123:(nat->Prop)) (B_65:(nat->Prop)) (C_32:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o A_123) B_65)) C_32)) ((semila848761471_nat_o A_123) ((semila848761471_nat_o B_65) C_32)))) of role axiom named fact_70_sup_Oassoc
% A new axiom: (forall (A_123:(nat->Prop)) (B_65:(nat->Prop)) (C_32:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o A_123) B_65)) C_32)) ((semila848761471_nat_o A_123) ((semila848761471_nat_o B_65) C_32))))
% FOF formula (forall (A_123:nat) (B_65:nat) (C_32:nat), (((eq nat) ((semila972727038up_nat ((semila972727038up_nat A_123) B_65)) C_32)) ((semila972727038up_nat A_123) ((semila972727038up_nat B_65) C_32)))) of role axiom named fact_71_sup_Oassoc
% A new axiom: (forall (A_123:nat) (B_65:nat) (C_32:nat), (((eq nat) ((semila972727038up_nat ((semila972727038up_nat A_123) B_65)) C_32)) ((semila972727038up_nat A_123) ((semila972727038up_nat B_65) C_32))))
% FOF formula (forall (A_123:((hoare_2091234717iple_a->Prop)->Prop)) (B_65:((hoare_2091234717iple_a->Prop)->Prop)) (C_32:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o A_123) B_65)) C_32)) ((semila2050116131_a_o_o A_123) ((semila2050116131_a_o_o B_65) C_32)))) of role axiom named fact_72_sup_Oassoc
% A new axiom: (forall (A_123:((hoare_2091234717iple_a->Prop)->Prop)) (B_65:((hoare_2091234717iple_a->Prop)->Prop)) (C_32:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o A_123) B_65)) C_32)) ((semila2050116131_a_o_o A_123) ((semila2050116131_a_o_o B_65) C_32))))
% FOF formula (forall (A_123:(hoare_1708887482_state->Prop)) (B_65:(hoare_1708887482_state->Prop)) (C_32:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_123) B_65)) C_32)) ((semila1122118281tate_o A_123) ((semila1122118281tate_o B_65) C_32)))) of role axiom named fact_73_sup_Oassoc
% A new axiom: (forall (A_123:(hoare_1708887482_state->Prop)) (B_65:(hoare_1708887482_state->Prop)) (C_32:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_123) B_65)) C_32)) ((semila1122118281tate_o A_123) ((semila1122118281tate_o B_65) C_32))))
% FOF formula (forall (A_123:(pname->Prop)) (B_65:(pname->Prop)) (C_32:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_123) B_65)) C_32)) ((semila1780557381name_o A_123) ((semila1780557381name_o B_65) C_32)))) of role axiom named fact_74_sup_Oassoc
% A new axiom: (forall (A_123:(pname->Prop)) (B_65:(pname->Prop)) (C_32:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_123) B_65)) C_32)) ((semila1780557381name_o A_123) ((semila1780557381name_o B_65) C_32))))
% FOF formula (forall (A_123:Prop) (B_65:Prop) (C_32:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_123) B_65)) C_32)) ((semila10642723_sup_o A_123) ((semila10642723_sup_o B_65) C_32)))) of role axiom named fact_75_sup_Oassoc
% A new axiom: (forall (A_123:Prop) (B_65:Prop) (C_32:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_123) B_65)) C_32)) ((semila10642723_sup_o A_123) ((semila10642723_sup_o B_65) C_32))))
% FOF formula (forall (A_123:(hoare_2091234717iple_a->Prop)) (B_65:(hoare_2091234717iple_a->Prop)) (C_32:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o A_123) B_65)) C_32)) ((semila1052848428le_a_o A_123) ((semila1052848428le_a_o B_65) C_32)))) of role axiom named fact_76_sup_Oassoc
% A new axiom: (forall (A_123:(hoare_2091234717iple_a->Prop)) (B_65:(hoare_2091234717iple_a->Prop)) (C_32:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o A_123) B_65)) C_32)) ((semila1052848428le_a_o A_123) ((semila1052848428le_a_o B_65) C_32))))
% FOF formula (forall (X_45:(nat->Prop)) (Y_18:(nat->Prop)) (Z_9:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_45) ((semila848761471_nat_o Y_18) Z_9))) ((semila848761471_nat_o Y_18) ((semila848761471_nat_o X_45) Z_9)))) of role axiom named fact_77_sup__left__commute
% A new axiom: (forall (X_45:(nat->Prop)) (Y_18:(nat->Prop)) (Z_9:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_45) ((semila848761471_nat_o Y_18) Z_9))) ((semila848761471_nat_o Y_18) ((semila848761471_nat_o X_45) Z_9))))
% FOF formula (forall (X_45:nat) (Y_18:nat) (Z_9:nat), (((eq nat) ((semila972727038up_nat X_45) ((semila972727038up_nat Y_18) Z_9))) ((semila972727038up_nat Y_18) ((semila972727038up_nat X_45) Z_9)))) of role axiom named fact_78_sup__left__commute
% A new axiom: (forall (X_45:nat) (Y_18:nat) (Z_9:nat), (((eq nat) ((semila972727038up_nat X_45) ((semila972727038up_nat Y_18) Z_9))) ((semila972727038up_nat Y_18) ((semila972727038up_nat X_45) Z_9))))
% FOF formula (forall (X_45:((hoare_2091234717iple_a->Prop)->Prop)) (Y_18:((hoare_2091234717iple_a->Prop)->Prop)) (Z_9:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_45) ((semila2050116131_a_o_o Y_18) Z_9))) ((semila2050116131_a_o_o Y_18) ((semila2050116131_a_o_o X_45) Z_9)))) of role axiom named fact_79_sup__left__commute
% A new axiom: (forall (X_45:((hoare_2091234717iple_a->Prop)->Prop)) (Y_18:((hoare_2091234717iple_a->Prop)->Prop)) (Z_9:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_45) ((semila2050116131_a_o_o Y_18) Z_9))) ((semila2050116131_a_o_o Y_18) ((semila2050116131_a_o_o X_45) Z_9))))
% FOF formula (forall (X_45:(hoare_1708887482_state->Prop)) (Y_18:(hoare_1708887482_state->Prop)) (Z_9:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_45) ((semila1122118281tate_o Y_18) Z_9))) ((semila1122118281tate_o Y_18) ((semila1122118281tate_o X_45) Z_9)))) of role axiom named fact_80_sup__left__commute
% A new axiom: (forall (X_45:(hoare_1708887482_state->Prop)) (Y_18:(hoare_1708887482_state->Prop)) (Z_9:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_45) ((semila1122118281tate_o Y_18) Z_9))) ((semila1122118281tate_o Y_18) ((semila1122118281tate_o X_45) Z_9))))
% FOF formula (forall (X_45:(pname->Prop)) (Y_18:(pname->Prop)) (Z_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_45) ((semila1780557381name_o Y_18) Z_9))) ((semila1780557381name_o Y_18) ((semila1780557381name_o X_45) Z_9)))) of role axiom named fact_81_sup__left__commute
% A new axiom: (forall (X_45:(pname->Prop)) (Y_18:(pname->Prop)) (Z_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_45) ((semila1780557381name_o Y_18) Z_9))) ((semila1780557381name_o Y_18) ((semila1780557381name_o X_45) Z_9))))
% FOF formula (forall (X_45:Prop) (Y_18:Prop) (Z_9:Prop), ((iff ((semila10642723_sup_o X_45) ((semila10642723_sup_o Y_18) Z_9))) ((semila10642723_sup_o Y_18) ((semila10642723_sup_o X_45) Z_9)))) of role axiom named fact_82_sup__left__commute
% A new axiom: (forall (X_45:Prop) (Y_18:Prop) (Z_9:Prop), ((iff ((semila10642723_sup_o X_45) ((semila10642723_sup_o Y_18) Z_9))) ((semila10642723_sup_o Y_18) ((semila10642723_sup_o X_45) Z_9))))
% FOF formula (forall (X_45:(hoare_2091234717iple_a->Prop)) (Y_18:(hoare_2091234717iple_a->Prop)) (Z_9:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_45) ((semila1052848428le_a_o Y_18) Z_9))) ((semila1052848428le_a_o Y_18) ((semila1052848428le_a_o X_45) Z_9)))) of role axiom named fact_83_sup__left__commute
% A new axiom: (forall (X_45:(hoare_2091234717iple_a->Prop)) (Y_18:(hoare_2091234717iple_a->Prop)) (Z_9:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_45) ((semila1052848428le_a_o Y_18) Z_9))) ((semila1052848428le_a_o Y_18) ((semila1052848428le_a_o X_45) Z_9))))
% FOF formula (forall (X_44:(nat->Prop)) (Y_17:(nat->Prop)) (Z_8:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_44) ((semila848761471_nat_o Y_17) Z_8))) ((semila848761471_nat_o Y_17) ((semila848761471_nat_o X_44) Z_8)))) of role axiom named fact_84_inf__sup__aci_I7_J
% A new axiom: (forall (X_44:(nat->Prop)) (Y_17:(nat->Prop)) (Z_8:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_44) ((semila848761471_nat_o Y_17) Z_8))) ((semila848761471_nat_o Y_17) ((semila848761471_nat_o X_44) Z_8))))
% FOF formula (forall (X_44:nat) (Y_17:nat) (Z_8:nat), (((eq nat) ((semila972727038up_nat X_44) ((semila972727038up_nat Y_17) Z_8))) ((semila972727038up_nat Y_17) ((semila972727038up_nat X_44) Z_8)))) of role axiom named fact_85_inf__sup__aci_I7_J
% A new axiom: (forall (X_44:nat) (Y_17:nat) (Z_8:nat), (((eq nat) ((semila972727038up_nat X_44) ((semila972727038up_nat Y_17) Z_8))) ((semila972727038up_nat Y_17) ((semila972727038up_nat X_44) Z_8))))
% FOF formula (forall (X_44:((hoare_2091234717iple_a->Prop)->Prop)) (Y_17:((hoare_2091234717iple_a->Prop)->Prop)) (Z_8:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_44) ((semila2050116131_a_o_o Y_17) Z_8))) ((semila2050116131_a_o_o Y_17) ((semila2050116131_a_o_o X_44) Z_8)))) of role axiom named fact_86_inf__sup__aci_I7_J
% A new axiom: (forall (X_44:((hoare_2091234717iple_a->Prop)->Prop)) (Y_17:((hoare_2091234717iple_a->Prop)->Prop)) (Z_8:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_44) ((semila2050116131_a_o_o Y_17) Z_8))) ((semila2050116131_a_o_o Y_17) ((semila2050116131_a_o_o X_44) Z_8))))
% FOF formula (forall (X_44:(hoare_1708887482_state->Prop)) (Y_17:(hoare_1708887482_state->Prop)) (Z_8:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_44) ((semila1122118281tate_o Y_17) Z_8))) ((semila1122118281tate_o Y_17) ((semila1122118281tate_o X_44) Z_8)))) of role axiom named fact_87_inf__sup__aci_I7_J
% A new axiom: (forall (X_44:(hoare_1708887482_state->Prop)) (Y_17:(hoare_1708887482_state->Prop)) (Z_8:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_44) ((semila1122118281tate_o Y_17) Z_8))) ((semila1122118281tate_o Y_17) ((semila1122118281tate_o X_44) Z_8))))
% FOF formula (forall (X_44:(pname->Prop)) (Y_17:(pname->Prop)) (Z_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_44) ((semila1780557381name_o Y_17) Z_8))) ((semila1780557381name_o Y_17) ((semila1780557381name_o X_44) Z_8)))) of role axiom named fact_88_inf__sup__aci_I7_J
% A new axiom: (forall (X_44:(pname->Prop)) (Y_17:(pname->Prop)) (Z_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_44) ((semila1780557381name_o Y_17) Z_8))) ((semila1780557381name_o Y_17) ((semila1780557381name_o X_44) Z_8))))
% FOF formula (forall (X_44:Prop) (Y_17:Prop) (Z_8:Prop), ((iff ((semila10642723_sup_o X_44) ((semila10642723_sup_o Y_17) Z_8))) ((semila10642723_sup_o Y_17) ((semila10642723_sup_o X_44) Z_8)))) of role axiom named fact_89_inf__sup__aci_I7_J
% A new axiom: (forall (X_44:Prop) (Y_17:Prop) (Z_8:Prop), ((iff ((semila10642723_sup_o X_44) ((semila10642723_sup_o Y_17) Z_8))) ((semila10642723_sup_o Y_17) ((semila10642723_sup_o X_44) Z_8))))
% FOF formula (forall (X_44:(hoare_2091234717iple_a->Prop)) (Y_17:(hoare_2091234717iple_a->Prop)) (Z_8:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_44) ((semila1052848428le_a_o Y_17) Z_8))) ((semila1052848428le_a_o Y_17) ((semila1052848428le_a_o X_44) Z_8)))) of role axiom named fact_90_inf__sup__aci_I7_J
% A new axiom: (forall (X_44:(hoare_2091234717iple_a->Prop)) (Y_17:(hoare_2091234717iple_a->Prop)) (Z_8:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_44) ((semila1052848428le_a_o Y_17) Z_8))) ((semila1052848428le_a_o Y_17) ((semila1052848428le_a_o X_44) Z_8))))
% FOF formula (forall (B_64:(nat->Prop)) (A_122:(nat->Prop)) (C_31:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o B_64) ((semila848761471_nat_o A_122) C_31))) ((semila848761471_nat_o A_122) ((semila848761471_nat_o B_64) C_31)))) of role axiom named fact_91_sup_Oleft__commute
% A new axiom: (forall (B_64:(nat->Prop)) (A_122:(nat->Prop)) (C_31:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o B_64) ((semila848761471_nat_o A_122) C_31))) ((semila848761471_nat_o A_122) ((semila848761471_nat_o B_64) C_31))))
% FOF formula (forall (B_64:nat) (A_122:nat) (C_31:nat), (((eq nat) ((semila972727038up_nat B_64) ((semila972727038up_nat A_122) C_31))) ((semila972727038up_nat A_122) ((semila972727038up_nat B_64) C_31)))) of role axiom named fact_92_sup_Oleft__commute
% A new axiom: (forall (B_64:nat) (A_122:nat) (C_31:nat), (((eq nat) ((semila972727038up_nat B_64) ((semila972727038up_nat A_122) C_31))) ((semila972727038up_nat A_122) ((semila972727038up_nat B_64) C_31))))
% FOF formula (forall (B_64:((hoare_2091234717iple_a->Prop)->Prop)) (A_122:((hoare_2091234717iple_a->Prop)->Prop)) (C_31:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o B_64) ((semila2050116131_a_o_o A_122) C_31))) ((semila2050116131_a_o_o A_122) ((semila2050116131_a_o_o B_64) C_31)))) of role axiom named fact_93_sup_Oleft__commute
% A new axiom: (forall (B_64:((hoare_2091234717iple_a->Prop)->Prop)) (A_122:((hoare_2091234717iple_a->Prop)->Prop)) (C_31:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o B_64) ((semila2050116131_a_o_o A_122) C_31))) ((semila2050116131_a_o_o A_122) ((semila2050116131_a_o_o B_64) C_31))))
% FOF formula (forall (B_64:(hoare_1708887482_state->Prop)) (A_122:(hoare_1708887482_state->Prop)) (C_31:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o B_64) ((semila1122118281tate_o A_122) C_31))) ((semila1122118281tate_o A_122) ((semila1122118281tate_o B_64) C_31)))) of role axiom named fact_94_sup_Oleft__commute
% A new axiom: (forall (B_64:(hoare_1708887482_state->Prop)) (A_122:(hoare_1708887482_state->Prop)) (C_31:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o B_64) ((semila1122118281tate_o A_122) C_31))) ((semila1122118281tate_o A_122) ((semila1122118281tate_o B_64) C_31))))
% FOF formula (forall (B_64:(pname->Prop)) (A_122:(pname->Prop)) (C_31:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_64) ((semila1780557381name_o A_122) C_31))) ((semila1780557381name_o A_122) ((semila1780557381name_o B_64) C_31)))) of role axiom named fact_95_sup_Oleft__commute
% A new axiom: (forall (B_64:(pname->Prop)) (A_122:(pname->Prop)) (C_31:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_64) ((semila1780557381name_o A_122) C_31))) ((semila1780557381name_o A_122) ((semila1780557381name_o B_64) C_31))))
% FOF formula (forall (B_64:Prop) (A_122:Prop) (C_31:Prop), ((iff ((semila10642723_sup_o B_64) ((semila10642723_sup_o A_122) C_31))) ((semila10642723_sup_o A_122) ((semila10642723_sup_o B_64) C_31)))) of role axiom named fact_96_sup_Oleft__commute
% A new axiom: (forall (B_64:Prop) (A_122:Prop) (C_31:Prop), ((iff ((semila10642723_sup_o B_64) ((semila10642723_sup_o A_122) C_31))) ((semila10642723_sup_o A_122) ((semila10642723_sup_o B_64) C_31))))
% FOF formula (forall (B_64:(hoare_2091234717iple_a->Prop)) (A_122:(hoare_2091234717iple_a->Prop)) (C_31:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o B_64) ((semila1052848428le_a_o A_122) C_31))) ((semila1052848428le_a_o A_122) ((semila1052848428le_a_o B_64) C_31)))) of role axiom named fact_97_sup_Oleft__commute
% A new axiom: (forall (B_64:(hoare_2091234717iple_a->Prop)) (A_122:(hoare_2091234717iple_a->Prop)) (C_31:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o B_64) ((semila1052848428le_a_o A_122) C_31))) ((semila1052848428le_a_o A_122) ((semila1052848428le_a_o B_64) C_31))))
% FOF formula (forall (X_43:(nat->Prop)) (Y_16:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_43) ((semila848761471_nat_o X_43) Y_16))) ((semila848761471_nat_o X_43) Y_16))) of role axiom named fact_98_sup__left__idem
% A new axiom: (forall (X_43:(nat->Prop)) (Y_16:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_43) ((semila848761471_nat_o X_43) Y_16))) ((semila848761471_nat_o X_43) Y_16)))
% FOF formula (forall (X_43:nat) (Y_16:nat), (((eq nat) ((semila972727038up_nat X_43) ((semila972727038up_nat X_43) Y_16))) ((semila972727038up_nat X_43) Y_16))) of role axiom named fact_99_sup__left__idem
% A new axiom: (forall (X_43:nat) (Y_16:nat), (((eq nat) ((semila972727038up_nat X_43) ((semila972727038up_nat X_43) Y_16))) ((semila972727038up_nat X_43) Y_16)))
% FOF formula (forall (X_43:((hoare_2091234717iple_a->Prop)->Prop)) (Y_16:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_43) ((semila2050116131_a_o_o X_43) Y_16))) ((semila2050116131_a_o_o X_43) Y_16))) of role axiom named fact_100_sup__left__idem
% A new axiom: (forall (X_43:((hoare_2091234717iple_a->Prop)->Prop)) (Y_16:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_43) ((semila2050116131_a_o_o X_43) Y_16))) ((semila2050116131_a_o_o X_43) Y_16)))
% FOF formula (forall (X_43:(hoare_1708887482_state->Prop)) (Y_16:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_43) ((semila1122118281tate_o X_43) Y_16))) ((semila1122118281tate_o X_43) Y_16))) of role axiom named fact_101_sup__left__idem
% A new axiom: (forall (X_43:(hoare_1708887482_state->Prop)) (Y_16:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_43) ((semila1122118281tate_o X_43) Y_16))) ((semila1122118281tate_o X_43) Y_16)))
% FOF formula (forall (X_43:(pname->Prop)) (Y_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_43) ((semila1780557381name_o X_43) Y_16))) ((semila1780557381name_o X_43) Y_16))) of role axiom named fact_102_sup__left__idem
% A new axiom: (forall (X_43:(pname->Prop)) (Y_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_43) ((semila1780557381name_o X_43) Y_16))) ((semila1780557381name_o X_43) Y_16)))
% FOF formula (forall (X_43:Prop) (Y_16:Prop), ((iff ((semila10642723_sup_o X_43) ((semila10642723_sup_o X_43) Y_16))) ((semila10642723_sup_o X_43) Y_16))) of role axiom named fact_103_sup__left__idem
% A new axiom: (forall (X_43:Prop) (Y_16:Prop), ((iff ((semila10642723_sup_o X_43) ((semila10642723_sup_o X_43) Y_16))) ((semila10642723_sup_o X_43) Y_16)))
% FOF formula (forall (X_43:(hoare_2091234717iple_a->Prop)) (Y_16:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_43) ((semila1052848428le_a_o X_43) Y_16))) ((semila1052848428le_a_o X_43) Y_16))) of role axiom named fact_104_sup__left__idem
% A new axiom: (forall (X_43:(hoare_2091234717iple_a->Prop)) (Y_16:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_43) ((semila1052848428le_a_o X_43) Y_16))) ((semila1052848428le_a_o X_43) Y_16)))
% FOF formula (forall (X_42:(nat->Prop)) (Y_15:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_42) ((semila848761471_nat_o X_42) Y_15))) ((semila848761471_nat_o X_42) Y_15))) of role axiom named fact_105_inf__sup__aci_I8_J
% A new axiom: (forall (X_42:(nat->Prop)) (Y_15:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_42) ((semila848761471_nat_o X_42) Y_15))) ((semila848761471_nat_o X_42) Y_15)))
% FOF formula (forall (X_42:nat) (Y_15:nat), (((eq nat) ((semila972727038up_nat X_42) ((semila972727038up_nat X_42) Y_15))) ((semila972727038up_nat X_42) Y_15))) of role axiom named fact_106_inf__sup__aci_I8_J
% A new axiom: (forall (X_42:nat) (Y_15:nat), (((eq nat) ((semila972727038up_nat X_42) ((semila972727038up_nat X_42) Y_15))) ((semila972727038up_nat X_42) Y_15)))
% FOF formula (forall (X_42:((hoare_2091234717iple_a->Prop)->Prop)) (Y_15:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_42) ((semila2050116131_a_o_o X_42) Y_15))) ((semila2050116131_a_o_o X_42) Y_15))) of role axiom named fact_107_inf__sup__aci_I8_J
% A new axiom: (forall (X_42:((hoare_2091234717iple_a->Prop)->Prop)) (Y_15:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_42) ((semila2050116131_a_o_o X_42) Y_15))) ((semila2050116131_a_o_o X_42) Y_15)))
% FOF formula (forall (X_42:(hoare_1708887482_state->Prop)) (Y_15:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_42) ((semila1122118281tate_o X_42) Y_15))) ((semila1122118281tate_o X_42) Y_15))) of role axiom named fact_108_inf__sup__aci_I8_J
% A new axiom: (forall (X_42:(hoare_1708887482_state->Prop)) (Y_15:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_42) ((semila1122118281tate_o X_42) Y_15))) ((semila1122118281tate_o X_42) Y_15)))
% FOF formula (forall (X_42:(pname->Prop)) (Y_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_42) ((semila1780557381name_o X_42) Y_15))) ((semila1780557381name_o X_42) Y_15))) of role axiom named fact_109_inf__sup__aci_I8_J
% A new axiom: (forall (X_42:(pname->Prop)) (Y_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_42) ((semila1780557381name_o X_42) Y_15))) ((semila1780557381name_o X_42) Y_15)))
% FOF formula (forall (X_42:Prop) (Y_15:Prop), ((iff ((semila10642723_sup_o X_42) ((semila10642723_sup_o X_42) Y_15))) ((semila10642723_sup_o X_42) Y_15))) of role axiom named fact_110_inf__sup__aci_I8_J
% A new axiom: (forall (X_42:Prop) (Y_15:Prop), ((iff ((semila10642723_sup_o X_42) ((semila10642723_sup_o X_42) Y_15))) ((semila10642723_sup_o X_42) Y_15)))
% FOF formula (forall (X_42:(hoare_2091234717iple_a->Prop)) (Y_15:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_42) ((semila1052848428le_a_o X_42) Y_15))) ((semila1052848428le_a_o X_42) Y_15))) of role axiom named fact_111_inf__sup__aci_I8_J
% A new axiom: (forall (X_42:(hoare_2091234717iple_a->Prop)) (Y_15:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_42) ((semila1052848428le_a_o X_42) Y_15))) ((semila1052848428le_a_o X_42) Y_15)))
% FOF formula (forall (A_121:(nat->Prop)) (B_63:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_121) ((semila848761471_nat_o A_121) B_63))) ((semila848761471_nat_o A_121) B_63))) of role axiom named fact_112_sup_Oleft__idem
% A new axiom: (forall (A_121:(nat->Prop)) (B_63:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_121) ((semila848761471_nat_o A_121) B_63))) ((semila848761471_nat_o A_121) B_63)))
% FOF formula (forall (A_121:nat) (B_63:nat), (((eq nat) ((semila972727038up_nat A_121) ((semila972727038up_nat A_121) B_63))) ((semila972727038up_nat A_121) B_63))) of role axiom named fact_113_sup_Oleft__idem
% A new axiom: (forall (A_121:nat) (B_63:nat), (((eq nat) ((semila972727038up_nat A_121) ((semila972727038up_nat A_121) B_63))) ((semila972727038up_nat A_121) B_63)))
% FOF formula (forall (A_121:((hoare_2091234717iple_a->Prop)->Prop)) (B_63:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_121) ((semila2050116131_a_o_o A_121) B_63))) ((semila2050116131_a_o_o A_121) B_63))) of role axiom named fact_114_sup_Oleft__idem
% A new axiom: (forall (A_121:((hoare_2091234717iple_a->Prop)->Prop)) (B_63:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_121) ((semila2050116131_a_o_o A_121) B_63))) ((semila2050116131_a_o_o A_121) B_63)))
% FOF formula (forall (A_121:(hoare_1708887482_state->Prop)) (B_63:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_121) ((semila1122118281tate_o A_121) B_63))) ((semila1122118281tate_o A_121) B_63))) of role axiom named fact_115_sup_Oleft__idem
% A new axiom: (forall (A_121:(hoare_1708887482_state->Prop)) (B_63:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_121) ((semila1122118281tate_o A_121) B_63))) ((semila1122118281tate_o A_121) B_63)))
% FOF formula (forall (A_121:(pname->Prop)) (B_63:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_121) ((semila1780557381name_o A_121) B_63))) ((semila1780557381name_o A_121) B_63))) of role axiom named fact_116_sup_Oleft__idem
% A new axiom: (forall (A_121:(pname->Prop)) (B_63:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_121) ((semila1780557381name_o A_121) B_63))) ((semila1780557381name_o A_121) B_63)))
% FOF formula (forall (A_121:Prop) (B_63:Prop), ((iff ((semila10642723_sup_o A_121) ((semila10642723_sup_o A_121) B_63))) ((semila10642723_sup_o A_121) B_63))) of role axiom named fact_117_sup_Oleft__idem
% A new axiom: (forall (A_121:Prop) (B_63:Prop), ((iff ((semila10642723_sup_o A_121) ((semila10642723_sup_o A_121) B_63))) ((semila10642723_sup_o A_121) B_63)))
% FOF formula (forall (A_121:(hoare_2091234717iple_a->Prop)) (B_63:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_121) ((semila1052848428le_a_o A_121) B_63))) ((semila1052848428le_a_o A_121) B_63))) of role axiom named fact_118_sup_Oleft__idem
% A new axiom: (forall (A_121:(hoare_2091234717iple_a->Prop)) (B_63:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_121) ((semila1052848428le_a_o A_121) B_63))) ((semila1052848428le_a_o A_121) B_63)))
% FOF formula (forall (X_41:(nat->Prop)) (Y_14:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_41) Y_14)) ((semila848761471_nat_o Y_14) X_41))) of role axiom named fact_119_sup__commute
% A new axiom: (forall (X_41:(nat->Prop)) (Y_14:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_41) Y_14)) ((semila848761471_nat_o Y_14) X_41)))
% FOF formula (forall (X_41:nat) (Y_14:nat), (((eq nat) ((semila972727038up_nat X_41) Y_14)) ((semila972727038up_nat Y_14) X_41))) of role axiom named fact_120_sup__commute
% A new axiom: (forall (X_41:nat) (Y_14:nat), (((eq nat) ((semila972727038up_nat X_41) Y_14)) ((semila972727038up_nat Y_14) X_41)))
% FOF formula (forall (X_41:((hoare_2091234717iple_a->Prop)->Prop)) (Y_14:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_41) Y_14)) ((semila2050116131_a_o_o Y_14) X_41))) of role axiom named fact_121_sup__commute
% A new axiom: (forall (X_41:((hoare_2091234717iple_a->Prop)->Prop)) (Y_14:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_41) Y_14)) ((semila2050116131_a_o_o Y_14) X_41)))
% FOF formula (forall (X_41:(hoare_1708887482_state->Prop)) (Y_14:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_41) Y_14)) ((semila1122118281tate_o Y_14) X_41))) of role axiom named fact_122_sup__commute
% A new axiom: (forall (X_41:(hoare_1708887482_state->Prop)) (Y_14:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_41) Y_14)) ((semila1122118281tate_o Y_14) X_41)))
% FOF formula (forall (X_41:(pname->Prop)) (Y_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_41) Y_14)) ((semila1780557381name_o Y_14) X_41))) of role axiom named fact_123_sup__commute
% A new axiom: (forall (X_41:(pname->Prop)) (Y_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_41) Y_14)) ((semila1780557381name_o Y_14) X_41)))
% FOF formula (forall (X_41:Prop) (Y_14:Prop), ((iff ((semila10642723_sup_o X_41) Y_14)) ((semila10642723_sup_o Y_14) X_41))) of role axiom named fact_124_sup__commute
% A new axiom: (forall (X_41:Prop) (Y_14:Prop), ((iff ((semila10642723_sup_o X_41) Y_14)) ((semila10642723_sup_o Y_14) X_41)))
% FOF formula (forall (X_41:(hoare_2091234717iple_a->Prop)) (Y_14:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_41) Y_14)) ((semila1052848428le_a_o Y_14) X_41))) of role axiom named fact_125_sup__commute
% A new axiom: (forall (X_41:(hoare_2091234717iple_a->Prop)) (Y_14:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_41) Y_14)) ((semila1052848428le_a_o Y_14) X_41)))
% FOF formula (forall (X_40:(nat->Prop)) (Y_13:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_40) Y_13)) ((semila848761471_nat_o Y_13) X_40))) of role axiom named fact_126_inf__sup__aci_I5_J
% A new axiom: (forall (X_40:(nat->Prop)) (Y_13:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_40) Y_13)) ((semila848761471_nat_o Y_13) X_40)))
% FOF formula (forall (X_40:nat) (Y_13:nat), (((eq nat) ((semila972727038up_nat X_40) Y_13)) ((semila972727038up_nat Y_13) X_40))) of role axiom named fact_127_inf__sup__aci_I5_J
% A new axiom: (forall (X_40:nat) (Y_13:nat), (((eq nat) ((semila972727038up_nat X_40) Y_13)) ((semila972727038up_nat Y_13) X_40)))
% FOF formula (forall (X_40:((hoare_2091234717iple_a->Prop)->Prop)) (Y_13:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_40) Y_13)) ((semila2050116131_a_o_o Y_13) X_40))) of role axiom named fact_128_inf__sup__aci_I5_J
% A new axiom: (forall (X_40:((hoare_2091234717iple_a->Prop)->Prop)) (Y_13:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_40) Y_13)) ((semila2050116131_a_o_o Y_13) X_40)))
% FOF formula (forall (X_40:(hoare_1708887482_state->Prop)) (Y_13:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_40) Y_13)) ((semila1122118281tate_o Y_13) X_40))) of role axiom named fact_129_inf__sup__aci_I5_J
% A new axiom: (forall (X_40:(hoare_1708887482_state->Prop)) (Y_13:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_40) Y_13)) ((semila1122118281tate_o Y_13) X_40)))
% FOF formula (forall (X_40:(pname->Prop)) (Y_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_40) Y_13)) ((semila1780557381name_o Y_13) X_40))) of role axiom named fact_130_inf__sup__aci_I5_J
% A new axiom: (forall (X_40:(pname->Prop)) (Y_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_40) Y_13)) ((semila1780557381name_o Y_13) X_40)))
% FOF formula (forall (X_40:Prop) (Y_13:Prop), ((iff ((semila10642723_sup_o X_40) Y_13)) ((semila10642723_sup_o Y_13) X_40))) of role axiom named fact_131_inf__sup__aci_I5_J
% A new axiom: (forall (X_40:Prop) (Y_13:Prop), ((iff ((semila10642723_sup_o X_40) Y_13)) ((semila10642723_sup_o Y_13) X_40)))
% FOF formula (forall (X_40:(hoare_2091234717iple_a->Prop)) (Y_13:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_40) Y_13)) ((semila1052848428le_a_o Y_13) X_40))) of role axiom named fact_132_inf__sup__aci_I5_J
% A new axiom: (forall (X_40:(hoare_2091234717iple_a->Prop)) (Y_13:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_40) Y_13)) ((semila1052848428le_a_o Y_13) X_40)))
% FOF formula (forall (A_120:(nat->Prop)) (B_62:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_120) B_62)) ((semila848761471_nat_o B_62) A_120))) of role axiom named fact_133_sup_Ocommute
% A new axiom: (forall (A_120:(nat->Prop)) (B_62:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_120) B_62)) ((semila848761471_nat_o B_62) A_120)))
% FOF formula (forall (A_120:nat) (B_62:nat), (((eq nat) ((semila972727038up_nat A_120) B_62)) ((semila972727038up_nat B_62) A_120))) of role axiom named fact_134_sup_Ocommute
% A new axiom: (forall (A_120:nat) (B_62:nat), (((eq nat) ((semila972727038up_nat A_120) B_62)) ((semila972727038up_nat B_62) A_120)))
% FOF formula (forall (A_120:((hoare_2091234717iple_a->Prop)->Prop)) (B_62:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_120) B_62)) ((semila2050116131_a_o_o B_62) A_120))) of role axiom named fact_135_sup_Ocommute
% A new axiom: (forall (A_120:((hoare_2091234717iple_a->Prop)->Prop)) (B_62:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_120) B_62)) ((semila2050116131_a_o_o B_62) A_120)))
% FOF formula (forall (A_120:(hoare_1708887482_state->Prop)) (B_62:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_120) B_62)) ((semila1122118281tate_o B_62) A_120))) of role axiom named fact_136_sup_Ocommute
% A new axiom: (forall (A_120:(hoare_1708887482_state->Prop)) (B_62:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_120) B_62)) ((semila1122118281tate_o B_62) A_120)))
% FOF formula (forall (A_120:(pname->Prop)) (B_62:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_120) B_62)) ((semila1780557381name_o B_62) A_120))) of role axiom named fact_137_sup_Ocommute
% A new axiom: (forall (A_120:(pname->Prop)) (B_62:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_120) B_62)) ((semila1780557381name_o B_62) A_120)))
% FOF formula (forall (A_120:Prop) (B_62:Prop), ((iff ((semila10642723_sup_o A_120) B_62)) ((semila10642723_sup_o B_62) A_120))) of role axiom named fact_138_sup_Ocommute
% A new axiom: (forall (A_120:Prop) (B_62:Prop), ((iff ((semila10642723_sup_o A_120) B_62)) ((semila10642723_sup_o B_62) A_120)))
% FOF formula (forall (A_120:(hoare_2091234717iple_a->Prop)) (B_62:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_120) B_62)) ((semila1052848428le_a_o B_62) A_120))) of role axiom named fact_139_sup_Ocommute
% A new axiom: (forall (A_120:(hoare_2091234717iple_a->Prop)) (B_62:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_120) B_62)) ((semila1052848428le_a_o B_62) A_120)))
% FOF formula (forall (X_39:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_39) X_39)) X_39)) of role axiom named fact_140_sup__idem
% A new axiom: (forall (X_39:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_39) X_39)) X_39))
% FOF formula (forall (X_39:nat), (((eq nat) ((semila972727038up_nat X_39) X_39)) X_39)) of role axiom named fact_141_sup__idem
% A new axiom: (forall (X_39:nat), (((eq nat) ((semila972727038up_nat X_39) X_39)) X_39))
% FOF formula (forall (X_39:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_39) X_39)) X_39)) of role axiom named fact_142_sup__idem
% A new axiom: (forall (X_39:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_39) X_39)) X_39))
% FOF formula (forall (X_39:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_39) X_39)) X_39)) of role axiom named fact_143_sup__idem
% A new axiom: (forall (X_39:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_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_144_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_145_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_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_39) X_39)) X_39)) of role axiom named fact_146_sup__idem
% A new axiom: (forall (X_39:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_39) X_39)) X_39))
% FOF formula (forall (A_119:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_119) A_119)) A_119)) of role axiom named fact_147_sup_Oidem
% A new axiom: (forall (A_119:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_119) A_119)) A_119))
% FOF formula (forall (A_119:nat), (((eq nat) ((semila972727038up_nat A_119) A_119)) A_119)) of role axiom named fact_148_sup_Oidem
% A new axiom: (forall (A_119:nat), (((eq nat) ((semila972727038up_nat A_119) A_119)) A_119))
% FOF formula (forall (A_119:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_119) A_119)) A_119)) of role axiom named fact_149_sup_Oidem
% A new axiom: (forall (A_119:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_119) A_119)) A_119))
% FOF formula (forall (A_119:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_119) A_119)) A_119)) of role axiom named fact_150_sup_Oidem
% A new axiom: (forall (A_119:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_119) A_119)) A_119))
% FOF formula (forall (A_119:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_119) A_119)) A_119)) of role axiom named fact_151_sup_Oidem
% A new axiom: (forall (A_119:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_119) A_119)) A_119))
% FOF formula (forall (A_119:Prop), ((iff ((semila10642723_sup_o A_119) A_119)) A_119)) of role axiom named fact_152_sup_Oidem
% A new axiom: (forall (A_119:Prop), ((iff ((semila10642723_sup_o A_119) A_119)) A_119))
% FOF formula (forall (A_119:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_119) A_119)) A_119)) of role axiom named fact_153_sup_Oidem
% A new axiom: (forall (A_119:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_119) A_119)) A_119))
% FOF formula (forall (B_61:nat) (F_46:(nat->nat)) (X_38:nat) (A_118:(nat->Prop)), (((member_nat X_38) A_118)->((((eq nat) B_61) (F_46 X_38))->((member_nat B_61) ((image_nat_nat F_46) A_118))))) of role axiom named fact_154_rev__image__eqI
% A new axiom: (forall (B_61:nat) (F_46:(nat->nat)) (X_38:nat) (A_118:(nat->Prop)), (((member_nat X_38) A_118)->((((eq nat) B_61) (F_46 X_38))->((member_nat B_61) ((image_nat_nat F_46) A_118)))))
% FOF formula (forall (B_61:hoare_1708887482_state) (F_46:(pname->hoare_1708887482_state)) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq hoare_1708887482_state) B_61) (F_46 X_38))->((member451959335_state B_61) ((image_1116629049_state F_46) A_118))))) of role axiom named fact_155_rev__image__eqI
% A new axiom: (forall (B_61:hoare_1708887482_state) (F_46:(pname->hoare_1708887482_state)) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq hoare_1708887482_state) B_61) (F_46 X_38))->((member451959335_state B_61) ((image_1116629049_state F_46) A_118)))))
% FOF formula (forall (B_61:nat) (F_46:(pname->nat)) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq nat) B_61) (F_46 X_38))->((member_nat B_61) ((image_pname_nat F_46) A_118))))) of role axiom named fact_156_rev__image__eqI
% A new axiom: (forall (B_61:nat) (F_46:(pname->nat)) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq nat) B_61) (F_46 X_38))->((member_nat B_61) ((image_pname_nat F_46) A_118)))))
% FOF formula (forall (B_61:(hoare_2091234717iple_a->Prop)) (F_46:(pname->(hoare_2091234717iple_a->Prop))) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq (hoare_2091234717iple_a->Prop)) B_61) (F_46 X_38))->((member99268621le_a_o B_61) ((image_742317343le_a_o F_46) A_118))))) of role axiom named fact_157_rev__image__eqI
% A new axiom: (forall (B_61:(hoare_2091234717iple_a->Prop)) (F_46:(pname->(hoare_2091234717iple_a->Prop))) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq (hoare_2091234717iple_a->Prop)) B_61) (F_46 X_38))->((member99268621le_a_o B_61) ((image_742317343le_a_o F_46) A_118)))))
% FOF formula (forall (B_61:pname) (F_46:(nat->pname)) (X_38:nat) (A_118:(nat->Prop)), (((member_nat X_38) A_118)->((((eq pname) B_61) (F_46 X_38))->((member_pname B_61) ((image_nat_pname F_46) A_118))))) of role axiom named fact_158_rev__image__eqI
% A new axiom: (forall (B_61:pname) (F_46:(nat->pname)) (X_38:nat) (A_118:(nat->Prop)), (((member_nat X_38) A_118)->((((eq pname) B_61) (F_46 X_38))->((member_pname B_61) ((image_nat_pname F_46) A_118)))))
% FOF formula (forall (B_61:pname) (F_46:((hoare_2091234717iple_a->Prop)->pname)) (X_38:(hoare_2091234717iple_a->Prop)) (A_118:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o X_38) A_118)->((((eq pname) B_61) (F_46 X_38))->((member_pname B_61) ((image_1908519857_pname F_46) A_118))))) of role axiom named fact_159_rev__image__eqI
% A new axiom: (forall (B_61:pname) (F_46:((hoare_2091234717iple_a->Prop)->pname)) (X_38:(hoare_2091234717iple_a->Prop)) (A_118:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o X_38) A_118)->((((eq pname) B_61) (F_46 X_38))->((member_pname B_61) ((image_1908519857_pname F_46) A_118)))))
% FOF formula (forall (B_61:pname) (F_46:(hoare_2091234717iple_a->pname)) (X_38:hoare_2091234717iple_a) (A_118:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a X_38) A_118)->((((eq pname) B_61) (F_46 X_38))->((member_pname B_61) ((image_924789612_pname F_46) A_118))))) of role axiom named fact_160_rev__image__eqI
% A new axiom: (forall (B_61:pname) (F_46:(hoare_2091234717iple_a->pname)) (X_38:hoare_2091234717iple_a) (A_118:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a X_38) A_118)->((((eq pname) B_61) (F_46 X_38))->((member_pname B_61) ((image_924789612_pname F_46) A_118)))))
% FOF formula (forall (B_61:hoare_2091234717iple_a) (F_46:(pname->hoare_2091234717iple_a)) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq hoare_2091234717iple_a) B_61) (F_46 X_38))->((member290856304iple_a B_61) ((image_231808478iple_a F_46) A_118))))) of role axiom named fact_161_rev__image__eqI
% A new axiom: (forall (B_61:hoare_2091234717iple_a) (F_46:(pname->hoare_2091234717iple_a)) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq hoare_2091234717iple_a) B_61) (F_46 X_38))->((member290856304iple_a B_61) ((image_231808478iple_a F_46) A_118)))))
% FOF formula (forall (F_45:(nat->nat)) (X_37:nat) (A_117:(nat->Prop)), (((member_nat X_37) A_117)->((member_nat (F_45 X_37)) ((image_nat_nat F_45) A_117)))) of role axiom named fact_162_imageI
% A new axiom: (forall (F_45:(nat->nat)) (X_37:nat) (A_117:(nat->Prop)), (((member_nat X_37) A_117)->((member_nat (F_45 X_37)) ((image_nat_nat F_45) A_117))))
% FOF formula (forall (F_45:(pname->hoare_1708887482_state)) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member451959335_state (F_45 X_37)) ((image_1116629049_state F_45) A_117)))) of role axiom named fact_163_imageI
% A new axiom: (forall (F_45:(pname->hoare_1708887482_state)) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member451959335_state (F_45 X_37)) ((image_1116629049_state F_45) A_117))))
% FOF formula (forall (F_45:(pname->nat)) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member_nat (F_45 X_37)) ((image_pname_nat F_45) A_117)))) of role axiom named fact_164_imageI
% A new axiom: (forall (F_45:(pname->nat)) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member_nat (F_45 X_37)) ((image_pname_nat F_45) A_117))))
% FOF formula (forall (F_45:(pname->(hoare_2091234717iple_a->Prop))) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member99268621le_a_o (F_45 X_37)) ((image_742317343le_a_o F_45) A_117)))) of role axiom named fact_165_imageI
% A new axiom: (forall (F_45:(pname->(hoare_2091234717iple_a->Prop))) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member99268621le_a_o (F_45 X_37)) ((image_742317343le_a_o F_45) A_117))))
% FOF formula (forall (F_45:(nat->pname)) (X_37:nat) (A_117:(nat->Prop)), (((member_nat X_37) A_117)->((member_pname (F_45 X_37)) ((image_nat_pname F_45) A_117)))) of role axiom named fact_166_imageI
% A new axiom: (forall (F_45:(nat->pname)) (X_37:nat) (A_117:(nat->Prop)), (((member_nat X_37) A_117)->((member_pname (F_45 X_37)) ((image_nat_pname F_45) A_117))))
% FOF formula (forall (F_45:((hoare_2091234717iple_a->Prop)->pname)) (X_37:(hoare_2091234717iple_a->Prop)) (A_117:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o X_37) A_117)->((member_pname (F_45 X_37)) ((image_1908519857_pname F_45) A_117)))) of role axiom named fact_167_imageI
% A new axiom: (forall (F_45:((hoare_2091234717iple_a->Prop)->pname)) (X_37:(hoare_2091234717iple_a->Prop)) (A_117:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o X_37) A_117)->((member_pname (F_45 X_37)) ((image_1908519857_pname F_45) A_117))))
% FOF formula (forall (F_45:(hoare_2091234717iple_a->pname)) (X_37:hoare_2091234717iple_a) (A_117:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a X_37) A_117)->((member_pname (F_45 X_37)) ((image_924789612_pname F_45) A_117)))) of role axiom named fact_168_imageI
% A new axiom: (forall (F_45:(hoare_2091234717iple_a->pname)) (X_37:hoare_2091234717iple_a) (A_117:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a X_37) A_117)->((member_pname (F_45 X_37)) ((image_924789612_pname F_45) A_117))))
% FOF formula (forall (F_45:(pname->hoare_2091234717iple_a)) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member290856304iple_a (F_45 X_37)) ((image_231808478iple_a F_45) A_117)))) of role axiom named fact_169_imageI
% A new axiom: (forall (F_45:(pname->hoare_2091234717iple_a)) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member290856304iple_a (F_45 X_37)) ((image_231808478iple_a F_45) A_117))))
% FOF formula (forall (Z_7:nat) (F_44:(nat->nat)) (A_116:(nat->Prop)), ((iff ((member_nat Z_7) ((image_nat_nat F_44) A_116))) ((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_116)) (((eq nat) Z_7) (F_44 X))))))) of role axiom named fact_170_image__iff
% A new axiom: (forall (Z_7:nat) (F_44:(nat->nat)) (A_116:(nat->Prop)), ((iff ((member_nat Z_7) ((image_nat_nat F_44) A_116))) ((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_116)) (((eq nat) Z_7) (F_44 X)))))))
% FOF formula (forall (Z_7:hoare_1708887482_state) (F_44:(pname->hoare_1708887482_state)) (A_116:(pname->Prop)), ((iff ((member451959335_state Z_7) ((image_1116629049_state F_44) A_116))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_116)) (((eq hoare_1708887482_state) Z_7) (F_44 X))))))) of role axiom named fact_171_image__iff
% A new axiom: (forall (Z_7:hoare_1708887482_state) (F_44:(pname->hoare_1708887482_state)) (A_116:(pname->Prop)), ((iff ((member451959335_state Z_7) ((image_1116629049_state F_44) A_116))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_116)) (((eq hoare_1708887482_state) Z_7) (F_44 X)))))))
% FOF formula (forall (Z_7:hoare_2091234717iple_a) (F_44:(pname->hoare_2091234717iple_a)) (A_116:(pname->Prop)), ((iff ((member290856304iple_a Z_7) ((image_231808478iple_a F_44) A_116))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_116)) (((eq hoare_2091234717iple_a) Z_7) (F_44 X))))))) of role axiom named fact_172_image__iff
% A new axiom: (forall (Z_7:hoare_2091234717iple_a) (F_44:(pname->hoare_2091234717iple_a)) (A_116:(pname->Prop)), ((iff ((member290856304iple_a Z_7) ((image_231808478iple_a F_44) A_116))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_116)) (((eq hoare_2091234717iple_a) Z_7) (F_44 X)))))))
% FOF formula (forall (A_115:(nat->Prop)) (C_30:nat) (B_60:(nat->Prop)), (((member_nat C_30) B_60)->((member_nat C_30) ((semila848761471_nat_o A_115) B_60)))) of role axiom named fact_173_UnI2
% A new axiom: (forall (A_115:(nat->Prop)) (C_30:nat) (B_60:(nat->Prop)), (((member_nat C_30) B_60)->((member_nat C_30) ((semila848761471_nat_o A_115) B_60))))
% FOF formula (forall (A_115:((hoare_2091234717iple_a->Prop)->Prop)) (C_30:(hoare_2091234717iple_a->Prop)) (B_60:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_30) B_60)->((member99268621le_a_o C_30) ((semila2050116131_a_o_o A_115) B_60)))) of role axiom named fact_174_UnI2
% A new axiom: (forall (A_115:((hoare_2091234717iple_a->Prop)->Prop)) (C_30:(hoare_2091234717iple_a->Prop)) (B_60:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_30) B_60)->((member99268621le_a_o C_30) ((semila2050116131_a_o_o A_115) B_60))))
% FOF formula (forall (A_115:(hoare_1708887482_state->Prop)) (C_30:hoare_1708887482_state) (B_60:(hoare_1708887482_state->Prop)), (((member451959335_state C_30) B_60)->((member451959335_state C_30) ((semila1122118281tate_o A_115) B_60)))) of role axiom named fact_175_UnI2
% A new axiom: (forall (A_115:(hoare_1708887482_state->Prop)) (C_30:hoare_1708887482_state) (B_60:(hoare_1708887482_state->Prop)), (((member451959335_state C_30) B_60)->((member451959335_state C_30) ((semila1122118281tate_o A_115) B_60))))
% FOF formula (forall (A_115:(hoare_2091234717iple_a->Prop)) (C_30:hoare_2091234717iple_a) (B_60:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_30) B_60)->((member290856304iple_a C_30) ((semila1052848428le_a_o A_115) B_60)))) of role axiom named fact_176_UnI2
% A new axiom: (forall (A_115:(hoare_2091234717iple_a->Prop)) (C_30:hoare_2091234717iple_a) (B_60:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_30) B_60)->((member290856304iple_a C_30) ((semila1052848428le_a_o A_115) B_60))))
% FOF formula (forall (A_115:(pname->Prop)) (C_30:pname) (B_60:(pname->Prop)), (((member_pname C_30) B_60)->((member_pname C_30) ((semila1780557381name_o A_115) B_60)))) of role axiom named fact_177_UnI2
% A new axiom: (forall (A_115:(pname->Prop)) (C_30:pname) (B_60:(pname->Prop)), (((member_pname C_30) B_60)->((member_pname C_30) ((semila1780557381name_o A_115) B_60))))
% FOF formula (forall (B_59:(nat->Prop)) (C_29:nat) (A_114:(nat->Prop)), (((member_nat C_29) A_114)->((member_nat C_29) ((semila848761471_nat_o A_114) B_59)))) of role axiom named fact_178_UnI1
% A new axiom: (forall (B_59:(nat->Prop)) (C_29:nat) (A_114:(nat->Prop)), (((member_nat C_29) A_114)->((member_nat C_29) ((semila848761471_nat_o A_114) B_59))))
% FOF formula (forall (B_59:((hoare_2091234717iple_a->Prop)->Prop)) (C_29:(hoare_2091234717iple_a->Prop)) (A_114:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_29) A_114)->((member99268621le_a_o C_29) ((semila2050116131_a_o_o A_114) B_59)))) of role axiom named fact_179_UnI1
% A new axiom: (forall (B_59:((hoare_2091234717iple_a->Prop)->Prop)) (C_29:(hoare_2091234717iple_a->Prop)) (A_114:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_29) A_114)->((member99268621le_a_o C_29) ((semila2050116131_a_o_o A_114) B_59))))
% FOF formula (forall (B_59:(hoare_1708887482_state->Prop)) (C_29:hoare_1708887482_state) (A_114:(hoare_1708887482_state->Prop)), (((member451959335_state C_29) A_114)->((member451959335_state C_29) ((semila1122118281tate_o A_114) B_59)))) of role axiom named fact_180_UnI1
% A new axiom: (forall (B_59:(hoare_1708887482_state->Prop)) (C_29:hoare_1708887482_state) (A_114:(hoare_1708887482_state->Prop)), (((member451959335_state C_29) A_114)->((member451959335_state C_29) ((semila1122118281tate_o A_114) B_59))))
% FOF formula (forall (B_59:(hoare_2091234717iple_a->Prop)) (C_29:hoare_2091234717iple_a) (A_114:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_29) A_114)->((member290856304iple_a C_29) ((semila1052848428le_a_o A_114) B_59)))) of role axiom named fact_181_UnI1
% A new axiom: (forall (B_59:(hoare_2091234717iple_a->Prop)) (C_29:hoare_2091234717iple_a) (A_114:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_29) A_114)->((member290856304iple_a C_29) ((semila1052848428le_a_o A_114) B_59))))
% FOF formula (forall (B_59:(pname->Prop)) (C_29:pname) (A_114:(pname->Prop)), (((member_pname C_29) A_114)->((member_pname C_29) ((semila1780557381name_o A_114) B_59)))) of role axiom named fact_182_UnI1
% A new axiom: (forall (B_59:(pname->Prop)) (C_29:pname) (A_114:(pname->Prop)), (((member_pname C_29) A_114)->((member_pname C_29) ((semila1780557381name_o A_114) B_59))))
% FOF formula (forall (A_113:(nat->Prop)) (B_58:(nat->Prop)) (X_36:nat), ((B_58 X_36)->(((semila848761471_nat_o A_113) B_58) X_36))) of role axiom named fact_183_sup1I2
% A new axiom: (forall (A_113:(nat->Prop)) (B_58:(nat->Prop)) (X_36:nat), ((B_58 X_36)->(((semila848761471_nat_o A_113) B_58) X_36)))
% FOF formula (forall (A_113:((hoare_2091234717iple_a->Prop)->Prop)) (B_58:((hoare_2091234717iple_a->Prop)->Prop)) (X_36:(hoare_2091234717iple_a->Prop)), ((B_58 X_36)->(((semila2050116131_a_o_o A_113) B_58) X_36))) of role axiom named fact_184_sup1I2
% A new axiom: (forall (A_113:((hoare_2091234717iple_a->Prop)->Prop)) (B_58:((hoare_2091234717iple_a->Prop)->Prop)) (X_36:(hoare_2091234717iple_a->Prop)), ((B_58 X_36)->(((semila2050116131_a_o_o A_113) B_58) X_36)))
% FOF formula (forall (A_113:(hoare_1708887482_state->Prop)) (B_58:(hoare_1708887482_state->Prop)) (X_36:hoare_1708887482_state), ((B_58 X_36)->(((semila1122118281tate_o A_113) B_58) X_36))) of role axiom named fact_185_sup1I2
% A new axiom: (forall (A_113:(hoare_1708887482_state->Prop)) (B_58:(hoare_1708887482_state->Prop)) (X_36:hoare_1708887482_state), ((B_58 X_36)->(((semila1122118281tate_o A_113) B_58) X_36)))
% FOF formula (forall (A_113:(pname->Prop)) (B_58:(pname->Prop)) (X_36:pname), ((B_58 X_36)->(((semila1780557381name_o A_113) B_58) X_36))) of role axiom named fact_186_sup1I2
% A new axiom: (forall (A_113:(pname->Prop)) (B_58:(pname->Prop)) (X_36:pname), ((B_58 X_36)->(((semila1780557381name_o A_113) B_58) X_36)))
% FOF formula (forall (A_113:(hoare_2091234717iple_a->Prop)) (B_58:(hoare_2091234717iple_a->Prop)) (X_36:hoare_2091234717iple_a), ((B_58 X_36)->(((semila1052848428le_a_o A_113) B_58) X_36))) of role axiom named fact_187_sup1I2
% A new axiom: (forall (A_113:(hoare_2091234717iple_a->Prop)) (B_58:(hoare_2091234717iple_a->Prop)) (X_36:hoare_2091234717iple_a), ((B_58 X_36)->(((semila1052848428le_a_o A_113) B_58) X_36)))
% FOF formula (forall (B_57:(nat->Prop)) (A_112:(nat->Prop)) (X_35:nat), ((A_112 X_35)->(((semila848761471_nat_o A_112) B_57) X_35))) of role axiom named fact_188_sup1I1
% A new axiom: (forall (B_57:(nat->Prop)) (A_112:(nat->Prop)) (X_35:nat), ((A_112 X_35)->(((semila848761471_nat_o A_112) B_57) X_35)))
% FOF formula (forall (B_57:((hoare_2091234717iple_a->Prop)->Prop)) (A_112:((hoare_2091234717iple_a->Prop)->Prop)) (X_35:(hoare_2091234717iple_a->Prop)), ((A_112 X_35)->(((semila2050116131_a_o_o A_112) B_57) X_35))) of role axiom named fact_189_sup1I1
% A new axiom: (forall (B_57:((hoare_2091234717iple_a->Prop)->Prop)) (A_112:((hoare_2091234717iple_a->Prop)->Prop)) (X_35:(hoare_2091234717iple_a->Prop)), ((A_112 X_35)->(((semila2050116131_a_o_o A_112) B_57) X_35)))
% FOF formula (forall (B_57:(hoare_1708887482_state->Prop)) (A_112:(hoare_1708887482_state->Prop)) (X_35:hoare_1708887482_state), ((A_112 X_35)->(((semila1122118281tate_o A_112) B_57) X_35))) of role axiom named fact_190_sup1I1
% A new axiom: (forall (B_57:(hoare_1708887482_state->Prop)) (A_112:(hoare_1708887482_state->Prop)) (X_35:hoare_1708887482_state), ((A_112 X_35)->(((semila1122118281tate_o A_112) B_57) X_35)))
% FOF formula (forall (B_57:(pname->Prop)) (A_112:(pname->Prop)) (X_35:pname), ((A_112 X_35)->(((semila1780557381name_o A_112) B_57) X_35))) of role axiom named fact_191_sup1I1
% A new axiom: (forall (B_57:(pname->Prop)) (A_112:(pname->Prop)) (X_35:pname), ((A_112 X_35)->(((semila1780557381name_o A_112) B_57) X_35)))
% FOF formula (forall (B_57:(hoare_2091234717iple_a->Prop)) (A_112:(hoare_2091234717iple_a->Prop)) (X_35:hoare_2091234717iple_a), ((A_112 X_35)->(((semila1052848428le_a_o A_112) B_57) X_35))) of role axiom named fact_192_sup1I1
% A new axiom: (forall (B_57:(hoare_2091234717iple_a->Prop)) (A_112:(hoare_2091234717iple_a->Prop)) (X_35:hoare_2091234717iple_a), ((A_112 X_35)->(((semila1052848428le_a_o A_112) B_57) X_35)))
% FOF formula (forall (P_35:(nat->Prop)) (A_111:(nat->Prop)) (B_56:(nat->Prop)), ((iff (forall (X:nat), (((member_nat X) ((semila848761471_nat_o A_111) B_56))->(P_35 X)))) ((and (forall (X:nat), (((member_nat X) A_111)->(P_35 X)))) (forall (X:nat), (((member_nat X) B_56)->(P_35 X)))))) of role axiom named fact_193_ball__Un
% A new axiom: (forall (P_35:(nat->Prop)) (A_111:(nat->Prop)) (B_56:(nat->Prop)), ((iff (forall (X:nat), (((member_nat X) ((semila848761471_nat_o A_111) B_56))->(P_35 X)))) ((and (forall (X:nat), (((member_nat X) A_111)->(P_35 X)))) (forall (X:nat), (((member_nat X) B_56)->(P_35 X))))))
% FOF formula (forall (P_35:((hoare_2091234717iple_a->Prop)->Prop)) (A_111:((hoare_2091234717iple_a->Prop)->Prop)) (B_56:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) ((semila2050116131_a_o_o A_111) B_56))->(P_35 X)))) ((and (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) A_111)->(P_35 X)))) (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) B_56)->(P_35 X)))))) of role axiom named fact_194_ball__Un
% A new axiom: (forall (P_35:((hoare_2091234717iple_a->Prop)->Prop)) (A_111:((hoare_2091234717iple_a->Prop)->Prop)) (B_56:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) ((semila2050116131_a_o_o A_111) B_56))->(P_35 X)))) ((and (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) A_111)->(P_35 X)))) (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) B_56)->(P_35 X))))))
% FOF formula (forall (P_35:(hoare_1708887482_state->Prop)) (A_111:(hoare_1708887482_state->Prop)) (B_56:(hoare_1708887482_state->Prop)), ((iff (forall (X:hoare_1708887482_state), (((member451959335_state X) ((semila1122118281tate_o A_111) B_56))->(P_35 X)))) ((and (forall (X:hoare_1708887482_state), (((member451959335_state X) A_111)->(P_35 X)))) (forall (X:hoare_1708887482_state), (((member451959335_state X) B_56)->(P_35 X)))))) of role axiom named fact_195_ball__Un
% A new axiom: (forall (P_35:(hoare_1708887482_state->Prop)) (A_111:(hoare_1708887482_state->Prop)) (B_56:(hoare_1708887482_state->Prop)), ((iff (forall (X:hoare_1708887482_state), (((member451959335_state X) ((semila1122118281tate_o A_111) B_56))->(P_35 X)))) ((and (forall (X:hoare_1708887482_state), (((member451959335_state X) A_111)->(P_35 X)))) (forall (X:hoare_1708887482_state), (((member451959335_state X) B_56)->(P_35 X))))))
% FOF formula (forall (P_35:(pname->Prop)) (A_111:(pname->Prop)) (B_56:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) ((semila1780557381name_o A_111) B_56))->(P_35 X)))) ((and (forall (X:pname), (((member_pname X) A_111)->(P_35 X)))) (forall (X:pname), (((member_pname X) B_56)->(P_35 X)))))) of role axiom named fact_196_ball__Un
% A new axiom: (forall (P_35:(pname->Prop)) (A_111:(pname->Prop)) (B_56:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) ((semila1780557381name_o A_111) B_56))->(P_35 X)))) ((and (forall (X:pname), (((member_pname X) A_111)->(P_35 X)))) (forall (X:pname), (((member_pname X) B_56)->(P_35 X))))))
% FOF formula (forall (P_35:(hoare_2091234717iple_a->Prop)) (A_111:(hoare_2091234717iple_a->Prop)) (B_56:(hoare_2091234717iple_a->Prop)), ((iff (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) ((semila1052848428le_a_o A_111) B_56))->(P_35 X)))) ((and (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) A_111)->(P_35 X)))) (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) B_56)->(P_35 X)))))) of role axiom named fact_197_ball__Un
% A new axiom: (forall (P_35:(hoare_2091234717iple_a->Prop)) (A_111:(hoare_2091234717iple_a->Prop)) (B_56:(hoare_2091234717iple_a->Prop)), ((iff (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) ((semila1052848428le_a_o A_111) B_56))->(P_35 X)))) ((and (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) A_111)->(P_35 X)))) (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) B_56)->(P_35 X))))))
% FOF formula (forall (P_34:(nat->Prop)) (A_110:(nat->Prop)) (B_55:(nat->Prop)), ((iff ((ex nat) (fun (X:nat)=> ((and ((member_nat X) ((semila848761471_nat_o A_110) B_55))) (P_34 X))))) ((or ((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_110)) (P_34 X))))) ((ex nat) (fun (X:nat)=> ((and ((member_nat X) B_55)) (P_34 X))))))) of role axiom named fact_198_bex__Un
% A new axiom: (forall (P_34:(nat->Prop)) (A_110:(nat->Prop)) (B_55:(nat->Prop)), ((iff ((ex nat) (fun (X:nat)=> ((and ((member_nat X) ((semila848761471_nat_o A_110) B_55))) (P_34 X))))) ((or ((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_110)) (P_34 X))))) ((ex nat) (fun (X:nat)=> ((and ((member_nat X) B_55)) (P_34 X)))))))
% FOF formula (forall (P_34:((hoare_2091234717iple_a->Prop)->Prop)) (A_110:((hoare_2091234717iple_a->Prop)->Prop)) (B_55:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) ((semila2050116131_a_o_o A_110) B_55))) (P_34 X))))) ((or ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_110)) (P_34 X))))) ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) B_55)) (P_34 X))))))) of role axiom named fact_199_bex__Un
% A new axiom: (forall (P_34:((hoare_2091234717iple_a->Prop)->Prop)) (A_110:((hoare_2091234717iple_a->Prop)->Prop)) (B_55:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) ((semila2050116131_a_o_o A_110) B_55))) (P_34 X))))) ((or ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_110)) (P_34 X))))) ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) B_55)) (P_34 X)))))))
% FOF formula (forall (P_34:(hoare_1708887482_state->Prop)) (A_110:(hoare_1708887482_state->Prop)) (B_55:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((and ((member451959335_state X) ((semila1122118281tate_o A_110) B_55))) (P_34 X))))) ((or ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((and ((member451959335_state X) A_110)) (P_34 X))))) ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((and ((member451959335_state X) B_55)) (P_34 X))))))) of role axiom named fact_200_bex__Un
% A new axiom: (forall (P_34:(hoare_1708887482_state->Prop)) (A_110:(hoare_1708887482_state->Prop)) (B_55:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((and ((member451959335_state X) ((semila1122118281tate_o A_110) B_55))) (P_34 X))))) ((or ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((and ((member451959335_state X) A_110)) (P_34 X))))) ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((and ((member451959335_state X) B_55)) (P_34 X)))))))
% FOF formula (forall (P_34:(pname->Prop)) (A_110:(pname->Prop)) (B_55:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((and ((member_pname X) ((semila1780557381name_o A_110) B_55))) (P_34 X))))) ((or ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_110)) (P_34 X))))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) B_55)) (P_34 X))))))) of role axiom named fact_201_bex__Un
% A new axiom: (forall (P_34:(pname->Prop)) (A_110:(pname->Prop)) (B_55:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((and ((member_pname X) ((semila1780557381name_o A_110) B_55))) (P_34 X))))) ((or ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_110)) (P_34 X))))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) B_55)) (P_34 X)))))))
% FOF formula (forall (P_34:(hoare_2091234717iple_a->Prop)) (A_110:(hoare_2091234717iple_a->Prop)) (B_55:(hoare_2091234717iple_a->Prop)), ((iff ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) ((semila1052848428le_a_o A_110) B_55))) (P_34 X))))) ((or ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_110)) (P_34 X))))) ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) B_55)) (P_34 X))))))) of role axiom named fact_202_bex__Un
% A new axiom: (forall (P_34:(hoare_2091234717iple_a->Prop)) (A_110:(hoare_2091234717iple_a->Prop)) (B_55:(hoare_2091234717iple_a->Prop)), ((iff ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) ((semila1052848428le_a_o A_110) B_55))) (P_34 X))))) ((or ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_110)) (P_34 X))))) ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) B_55)) (P_34 X)))))))
% FOF formula (forall (A_109:(nat->Prop)) (B_54:(nat->Prop)) (C_28:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o A_109) B_54)) C_28)) ((semila848761471_nat_o A_109) ((semila848761471_nat_o B_54) C_28)))) of role axiom named fact_203_Un__assoc
% A new axiom: (forall (A_109:(nat->Prop)) (B_54:(nat->Prop)) (C_28:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o A_109) B_54)) C_28)) ((semila848761471_nat_o A_109) ((semila848761471_nat_o B_54) C_28))))
% FOF formula (forall (A_109:((hoare_2091234717iple_a->Prop)->Prop)) (B_54:((hoare_2091234717iple_a->Prop)->Prop)) (C_28:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o A_109) B_54)) C_28)) ((semila2050116131_a_o_o A_109) ((semila2050116131_a_o_o B_54) C_28)))) of role axiom named fact_204_Un__assoc
% A new axiom: (forall (A_109:((hoare_2091234717iple_a->Prop)->Prop)) (B_54:((hoare_2091234717iple_a->Prop)->Prop)) (C_28:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o A_109) B_54)) C_28)) ((semila2050116131_a_o_o A_109) ((semila2050116131_a_o_o B_54) C_28))))
% FOF formula (forall (A_109:(hoare_1708887482_state->Prop)) (B_54:(hoare_1708887482_state->Prop)) (C_28:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_109) B_54)) C_28)) ((semila1122118281tate_o A_109) ((semila1122118281tate_o B_54) C_28)))) of role axiom named fact_205_Un__assoc
% A new axiom: (forall (A_109:(hoare_1708887482_state->Prop)) (B_54:(hoare_1708887482_state->Prop)) (C_28:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_109) B_54)) C_28)) ((semila1122118281tate_o A_109) ((semila1122118281tate_o B_54) C_28))))
% FOF formula (forall (A_109:(pname->Prop)) (B_54:(pname->Prop)) (C_28:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_109) B_54)) C_28)) ((semila1780557381name_o A_109) ((semila1780557381name_o B_54) C_28)))) of role axiom named fact_206_Un__assoc
% A new axiom: (forall (A_109:(pname->Prop)) (B_54:(pname->Prop)) (C_28:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_109) B_54)) C_28)) ((semila1780557381name_o A_109) ((semila1780557381name_o B_54) C_28))))
% FOF formula (forall (A_109:(hoare_2091234717iple_a->Prop)) (B_54:(hoare_2091234717iple_a->Prop)) (C_28:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o A_109) B_54)) C_28)) ((semila1052848428le_a_o A_109) ((semila1052848428le_a_o B_54) C_28)))) of role axiom named fact_207_Un__assoc
% A new axiom: (forall (A_109:(hoare_2091234717iple_a->Prop)) (B_54:(hoare_2091234717iple_a->Prop)) (C_28:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o A_109) B_54)) C_28)) ((semila1052848428le_a_o A_109) ((semila1052848428le_a_o B_54) C_28))))
% FOF formula (forall (C_27:nat) (A_108:(nat->Prop)) (B_53:(nat->Prop)), ((iff ((member_nat C_27) ((semila848761471_nat_o A_108) B_53))) ((or ((member_nat C_27) A_108)) ((member_nat C_27) B_53)))) of role axiom named fact_208_Un__iff
% A new axiom: (forall (C_27:nat) (A_108:(nat->Prop)) (B_53:(nat->Prop)), ((iff ((member_nat C_27) ((semila848761471_nat_o A_108) B_53))) ((or ((member_nat C_27) A_108)) ((member_nat C_27) B_53))))
% FOF formula (forall (C_27:(hoare_2091234717iple_a->Prop)) (A_108:((hoare_2091234717iple_a->Prop)->Prop)) (B_53:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o C_27) ((semila2050116131_a_o_o A_108) B_53))) ((or ((member99268621le_a_o C_27) A_108)) ((member99268621le_a_o C_27) B_53)))) of role axiom named fact_209_Un__iff
% A new axiom: (forall (C_27:(hoare_2091234717iple_a->Prop)) (A_108:((hoare_2091234717iple_a->Prop)->Prop)) (B_53:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o C_27) ((semila2050116131_a_o_o A_108) B_53))) ((or ((member99268621le_a_o C_27) A_108)) ((member99268621le_a_o C_27) B_53))))
% FOF formula (forall (C_27:hoare_1708887482_state) (A_108:(hoare_1708887482_state->Prop)) (B_53:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_27) ((semila1122118281tate_o A_108) B_53))) ((or ((member451959335_state C_27) A_108)) ((member451959335_state C_27) B_53)))) of role axiom named fact_210_Un__iff
% A new axiom: (forall (C_27:hoare_1708887482_state) (A_108:(hoare_1708887482_state->Prop)) (B_53:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_27) ((semila1122118281tate_o A_108) B_53))) ((or ((member451959335_state C_27) A_108)) ((member451959335_state C_27) B_53))))
% FOF formula (forall (C_27:hoare_2091234717iple_a) (A_108:(hoare_2091234717iple_a->Prop)) (B_53:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a C_27) ((semila1052848428le_a_o A_108) B_53))) ((or ((member290856304iple_a C_27) A_108)) ((member290856304iple_a C_27) B_53)))) of role axiom named fact_211_Un__iff
% A new axiom: (forall (C_27:hoare_2091234717iple_a) (A_108:(hoare_2091234717iple_a->Prop)) (B_53:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a C_27) ((semila1052848428le_a_o A_108) B_53))) ((or ((member290856304iple_a C_27) A_108)) ((member290856304iple_a C_27) B_53))))
% FOF formula (forall (C_27:pname) (A_108:(pname->Prop)) (B_53:(pname->Prop)), ((iff ((member_pname C_27) ((semila1780557381name_o A_108) B_53))) ((or ((member_pname C_27) A_108)) ((member_pname C_27) B_53)))) of role axiom named fact_212_Un__iff
% A new axiom: (forall (C_27:pname) (A_108:(pname->Prop)) (B_53:(pname->Prop)), ((iff ((member_pname C_27) ((semila1780557381name_o A_108) B_53))) ((or ((member_pname C_27) A_108)) ((member_pname C_27) B_53))))
% FOF formula (forall (A_107:(nat->Prop)) (B_52:(nat->Prop)) (C_26:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_107) ((semila848761471_nat_o B_52) C_26))) ((semila848761471_nat_o B_52) ((semila848761471_nat_o A_107) C_26)))) of role axiom named fact_213_Un__left__commute
% A new axiom: (forall (A_107:(nat->Prop)) (B_52:(nat->Prop)) (C_26:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_107) ((semila848761471_nat_o B_52) C_26))) ((semila848761471_nat_o B_52) ((semila848761471_nat_o A_107) C_26))))
% FOF formula (forall (A_107:((hoare_2091234717iple_a->Prop)->Prop)) (B_52:((hoare_2091234717iple_a->Prop)->Prop)) (C_26:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_107) ((semila2050116131_a_o_o B_52) C_26))) ((semila2050116131_a_o_o B_52) ((semila2050116131_a_o_o A_107) C_26)))) of role axiom named fact_214_Un__left__commute
% A new axiom: (forall (A_107:((hoare_2091234717iple_a->Prop)->Prop)) (B_52:((hoare_2091234717iple_a->Prop)->Prop)) (C_26:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_107) ((semila2050116131_a_o_o B_52) C_26))) ((semila2050116131_a_o_o B_52) ((semila2050116131_a_o_o A_107) C_26))))
% FOF formula (forall (A_107:(hoare_1708887482_state->Prop)) (B_52:(hoare_1708887482_state->Prop)) (C_26:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_107) ((semila1122118281tate_o B_52) C_26))) ((semila1122118281tate_o B_52) ((semila1122118281tate_o A_107) C_26)))) of role axiom named fact_215_Un__left__commute
% A new axiom: (forall (A_107:(hoare_1708887482_state->Prop)) (B_52:(hoare_1708887482_state->Prop)) (C_26:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_107) ((semila1122118281tate_o B_52) C_26))) ((semila1122118281tate_o B_52) ((semila1122118281tate_o A_107) C_26))))
% FOF formula (forall (A_107:(pname->Prop)) (B_52:(pname->Prop)) (C_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_107) ((semila1780557381name_o B_52) C_26))) ((semila1780557381name_o B_52) ((semila1780557381name_o A_107) C_26)))) of role axiom named fact_216_Un__left__commute
% A new axiom: (forall (A_107:(pname->Prop)) (B_52:(pname->Prop)) (C_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_107) ((semila1780557381name_o B_52) C_26))) ((semila1780557381name_o B_52) ((semila1780557381name_o A_107) C_26))))
% FOF formula (forall (A_107:(hoare_2091234717iple_a->Prop)) (B_52:(hoare_2091234717iple_a->Prop)) (C_26:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_107) ((semila1052848428le_a_o B_52) C_26))) ((semila1052848428le_a_o B_52) ((semila1052848428le_a_o A_107) C_26)))) of role axiom named fact_217_Un__left__commute
% A new axiom: (forall (A_107:(hoare_2091234717iple_a->Prop)) (B_52:(hoare_2091234717iple_a->Prop)) (C_26:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_107) ((semila1052848428le_a_o B_52) C_26))) ((semila1052848428le_a_o B_52) ((semila1052848428le_a_o A_107) C_26))))
% FOF formula (forall (A_106:(nat->Prop)) (B_51:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_106) ((semila848761471_nat_o A_106) B_51))) ((semila848761471_nat_o A_106) B_51))) of role axiom named fact_218_Un__left__absorb
% A new axiom: (forall (A_106:(nat->Prop)) (B_51:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_106) ((semila848761471_nat_o A_106) B_51))) ((semila848761471_nat_o A_106) B_51)))
% FOF formula (forall (A_106:((hoare_2091234717iple_a->Prop)->Prop)) (B_51:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_106) ((semila2050116131_a_o_o A_106) B_51))) ((semila2050116131_a_o_o A_106) B_51))) of role axiom named fact_219_Un__left__absorb
% A new axiom: (forall (A_106:((hoare_2091234717iple_a->Prop)->Prop)) (B_51:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_106) ((semila2050116131_a_o_o A_106) B_51))) ((semila2050116131_a_o_o A_106) B_51)))
% FOF formula (forall (A_106:(hoare_1708887482_state->Prop)) (B_51:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_106) ((semila1122118281tate_o A_106) B_51))) ((semila1122118281tate_o A_106) B_51))) of role axiom named fact_220_Un__left__absorb
% A new axiom: (forall (A_106:(hoare_1708887482_state->Prop)) (B_51:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_106) ((semila1122118281tate_o A_106) B_51))) ((semila1122118281tate_o A_106) B_51)))
% FOF formula (forall (A_106:(pname->Prop)) (B_51:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_106) ((semila1780557381name_o A_106) B_51))) ((semila1780557381name_o A_106) B_51))) of role axiom named fact_221_Un__left__absorb
% A new axiom: (forall (A_106:(pname->Prop)) (B_51:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_106) ((semila1780557381name_o A_106) B_51))) ((semila1780557381name_o A_106) B_51)))
% FOF formula (forall (A_106:(hoare_2091234717iple_a->Prop)) (B_51:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_106) ((semila1052848428le_a_o A_106) B_51))) ((semila1052848428le_a_o A_106) B_51))) of role axiom named fact_222_Un__left__absorb
% A new axiom: (forall (A_106:(hoare_2091234717iple_a->Prop)) (B_51:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_106) ((semila1052848428le_a_o A_106) B_51))) ((semila1052848428le_a_o A_106) B_51)))
% FOF formula (forall (A_105:(nat->Prop)) (B_50:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_105) B_50)) ((semila848761471_nat_o B_50) A_105))) of role axiom named fact_223_Un__commute
% A new axiom: (forall (A_105:(nat->Prop)) (B_50:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_105) B_50)) ((semila848761471_nat_o B_50) A_105)))
% FOF formula (forall (A_105:((hoare_2091234717iple_a->Prop)->Prop)) (B_50:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_105) B_50)) ((semila2050116131_a_o_o B_50) A_105))) of role axiom named fact_224_Un__commute
% A new axiom: (forall (A_105:((hoare_2091234717iple_a->Prop)->Prop)) (B_50:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_105) B_50)) ((semila2050116131_a_o_o B_50) A_105)))
% FOF formula (forall (A_105:(hoare_1708887482_state->Prop)) (B_50:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_105) B_50)) ((semila1122118281tate_o B_50) A_105))) of role axiom named fact_225_Un__commute
% A new axiom: (forall (A_105:(hoare_1708887482_state->Prop)) (B_50:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_105) B_50)) ((semila1122118281tate_o B_50) A_105)))
% FOF formula (forall (A_105:(pname->Prop)) (B_50:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_105) B_50)) ((semila1780557381name_o B_50) A_105))) of role axiom named fact_226_Un__commute
% A new axiom: (forall (A_105:(pname->Prop)) (B_50:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_105) B_50)) ((semila1780557381name_o B_50) A_105)))
% FOF formula (forall (A_105:(hoare_2091234717iple_a->Prop)) (B_50:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_105) B_50)) ((semila1052848428le_a_o B_50) A_105))) of role axiom named fact_227_Un__commute
% A new axiom: (forall (A_105:(hoare_2091234717iple_a->Prop)) (B_50:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_105) B_50)) ((semila1052848428le_a_o B_50) A_105)))
% FOF formula (forall (A_104:((hoare_2091234717iple_a->Prop)->Prop)) (B_49:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_104) B_49)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or ((member99268621le_a_o X) A_104)) ((member99268621le_a_o X) B_49)))))) of role axiom named fact_228_Un__def
% A new axiom: (forall (A_104:((hoare_2091234717iple_a->Prop)->Prop)) (B_49:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_104) B_49)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or ((member99268621le_a_o X) A_104)) ((member99268621le_a_o X) B_49))))))
% FOF formula (forall (A_104:(hoare_1708887482_state->Prop)) (B_49:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_104) B_49)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((or ((member451959335_state X) A_104)) ((member451959335_state X) B_49)))))) of role axiom named fact_229_Un__def
% A new axiom: (forall (A_104:(hoare_1708887482_state->Prop)) (B_49:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_104) B_49)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((or ((member451959335_state X) A_104)) ((member451959335_state X) B_49))))))
% FOF formula (forall (A_104:(hoare_2091234717iple_a->Prop)) (B_49:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_104) B_49)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or ((member290856304iple_a X) A_104)) ((member290856304iple_a X) B_49)))))) of role axiom named fact_230_Un__def
% A new axiom: (forall (A_104:(hoare_2091234717iple_a->Prop)) (B_49:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_104) B_49)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or ((member290856304iple_a X) A_104)) ((member290856304iple_a X) B_49))))))
% FOF formula (forall (A_104:(nat->Prop)) (B_49:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_104) B_49)) (collect_nat (fun (X:nat)=> ((or ((member_nat X) A_104)) ((member_nat X) B_49)))))) of role axiom named fact_231_Un__def
% A new axiom: (forall (A_104:(nat->Prop)) (B_49:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_104) B_49)) (collect_nat (fun (X:nat)=> ((or ((member_nat X) A_104)) ((member_nat X) B_49))))))
% FOF formula (forall (A_104:(pname->Prop)) (B_49:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_104) B_49)) (collect_pname (fun (X:pname)=> ((or ((member_pname X) A_104)) ((member_pname X) B_49)))))) of role axiom named fact_232_Un__def
% A new axiom: (forall (A_104:(pname->Prop)) (B_49:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_104) B_49)) (collect_pname (fun (X:pname)=> ((or ((member_pname X) A_104)) ((member_pname X) B_49))))))
% FOF formula (forall (A_103:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_103) A_103)) A_103)) of role axiom named fact_233_Un__absorb
% A new axiom: (forall (A_103:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_103) A_103)) A_103))
% FOF formula (forall (A_103:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_103) A_103)) A_103)) of role axiom named fact_234_Un__absorb
% A new axiom: (forall (A_103:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_103) A_103)) A_103))
% FOF formula (forall (A_103:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_103) A_103)) A_103)) of role axiom named fact_235_Un__absorb
% A new axiom: (forall (A_103:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_103) A_103)) A_103))
% FOF formula (forall (A_103:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_103) A_103)) A_103)) of role axiom named fact_236_Un__absorb
% A new axiom: (forall (A_103:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_103) A_103)) A_103))
% FOF formula (forall (A_103:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_103) A_103)) A_103)) of role axiom named fact_237_Un__absorb
% A new axiom: (forall (A_103:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_103) A_103)) A_103))
% FOF formula (forall (Y_12:(nat->Prop)), (((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> X)) Y_12)) Y_12)) of role axiom named fact_238_image__ident
% A new axiom: (forall (Y_12:(nat->Prop)), (((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> X)) Y_12)) Y_12))
% FOF formula (forall (F_43:(hoare_2091234717iple_a->hoare_1708887482_state)) (G_22:(pname->hoare_2091234717iple_a)) (A_102:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1884482962_state F_43) ((image_231808478iple_a G_22) A_102))) ((image_1116629049_state (fun (X:pname)=> (F_43 (G_22 X)))) A_102))) of role axiom named fact_239_image__image
% A new axiom: (forall (F_43:(hoare_2091234717iple_a->hoare_1708887482_state)) (G_22:(pname->hoare_2091234717iple_a)) (A_102:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1884482962_state F_43) ((image_231808478iple_a G_22) A_102))) ((image_1116629049_state (fun (X:pname)=> (F_43 (G_22 X)))) A_102)))
% FOF formula (forall (F_43:(hoare_1708887482_state->hoare_2091234717iple_a)) (G_22:(pname->hoare_1708887482_state)) (A_102:(pname->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_293283184iple_a F_43) ((image_1116629049_state G_22) A_102))) ((image_231808478iple_a (fun (X:pname)=> (F_43 (G_22 X)))) A_102))) of role axiom named fact_240_image__image
% A new axiom: (forall (F_43:(hoare_1708887482_state->hoare_2091234717iple_a)) (G_22:(pname->hoare_1708887482_state)) (A_102:(pname->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_293283184iple_a F_43) ((image_1116629049_state G_22) A_102))) ((image_231808478iple_a (fun (X:pname)=> (F_43 (G_22 X)))) A_102)))
% FOF formula (forall (R_2:(nat->Prop)) (S_5:(nat->Prop)) (X:nat), ((iff (((semila848761471_nat_o (fun (Y_7:nat)=> ((member_nat Y_7) R_2))) (fun (Y_7:nat)=> ((member_nat Y_7) S_5))) X)) ((member_nat X) ((semila848761471_nat_o R_2) S_5)))) of role axiom named fact_241_sup__Un__eq
% A new axiom: (forall (R_2:(nat->Prop)) (S_5:(nat->Prop)) (X:nat), ((iff (((semila848761471_nat_o (fun (Y_7:nat)=> ((member_nat Y_7) R_2))) (fun (Y_7:nat)=> ((member_nat Y_7) S_5))) X)) ((member_nat X) ((semila848761471_nat_o R_2) S_5))))
% FOF formula (forall (R_2:((hoare_2091234717iple_a->Prop)->Prop)) (S_5:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), ((iff (((semila2050116131_a_o_o (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) R_2))) (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) S_5))) X)) ((member99268621le_a_o X) ((semila2050116131_a_o_o R_2) S_5)))) of role axiom named fact_242_sup__Un__eq
% A new axiom: (forall (R_2:((hoare_2091234717iple_a->Prop)->Prop)) (S_5:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), ((iff (((semila2050116131_a_o_o (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) R_2))) (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) S_5))) X)) ((member99268621le_a_o X) ((semila2050116131_a_o_o R_2) S_5))))
% FOF formula (forall (R_2:(hoare_1708887482_state->Prop)) (S_5:(hoare_1708887482_state->Prop)) (X:hoare_1708887482_state), ((iff (((semila1122118281tate_o (fun (Y_7:hoare_1708887482_state)=> ((member451959335_state Y_7) R_2))) (fun (Y_7:hoare_1708887482_state)=> ((member451959335_state Y_7) S_5))) X)) ((member451959335_state X) ((semila1122118281tate_o R_2) S_5)))) of role axiom named fact_243_sup__Un__eq
% A new axiom: (forall (R_2:(hoare_1708887482_state->Prop)) (S_5:(hoare_1708887482_state->Prop)) (X:hoare_1708887482_state), ((iff (((semila1122118281tate_o (fun (Y_7:hoare_1708887482_state)=> ((member451959335_state Y_7) R_2))) (fun (Y_7:hoare_1708887482_state)=> ((member451959335_state Y_7) S_5))) X)) ((member451959335_state X) ((semila1122118281tate_o R_2) S_5))))
% FOF formula (forall (R_2:(hoare_2091234717iple_a->Prop)) (S_5:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila1052848428le_a_o (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) R_2))) (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) S_5))) X)) ((member290856304iple_a X) ((semila1052848428le_a_o R_2) S_5)))) of role axiom named fact_244_sup__Un__eq
% A new axiom: (forall (R_2:(hoare_2091234717iple_a->Prop)) (S_5:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila1052848428le_a_o (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) R_2))) (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) S_5))) X)) ((member290856304iple_a X) ((semila1052848428le_a_o R_2) S_5))))
% FOF formula (forall (R_2:(pname->Prop)) (S_5:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o (fun (Y_7:pname)=> ((member_pname Y_7) R_2))) (fun (Y_7:pname)=> ((member_pname Y_7) S_5))) X)) ((member_pname X) ((semila1780557381name_o R_2) S_5)))) of role axiom named fact_245_sup__Un__eq
% A new axiom: (forall (R_2:(pname->Prop)) (S_5:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o (fun (Y_7:pname)=> ((member_pname Y_7) R_2))) (fun (Y_7:pname)=> ((member_pname Y_7) S_5))) X)) ((member_pname X) ((semila1780557381name_o R_2) S_5))))
% FOF formula (forall (P_33:(pname->Prop)) (Q_19:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((or (P_33 X)) (Q_19 X))))) ((semila1780557381name_o (collect_pname P_33)) (collect_pname Q_19)))) of role axiom named fact_246_Collect__disj__eq
% A new axiom: (forall (P_33:(pname->Prop)) (Q_19:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((or (P_33 X)) (Q_19 X))))) ((semila1780557381name_o (collect_pname P_33)) (collect_pname Q_19))))
% FOF formula (forall (P_33:((hoare_2091234717iple_a->Prop)->Prop)) (Q_19:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or (P_33 X)) (Q_19 X))))) ((semila2050116131_a_o_o (collec1008234059le_a_o P_33)) (collec1008234059le_a_o Q_19)))) of role axiom named fact_247_Collect__disj__eq
% A new axiom: (forall (P_33:((hoare_2091234717iple_a->Prop)->Prop)) (Q_19:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or (P_33 X)) (Q_19 X))))) ((semila2050116131_a_o_o (collec1008234059le_a_o P_33)) (collec1008234059le_a_o Q_19))))
% FOF formula (forall (P_33:(hoare_1708887482_state->Prop)) (Q_19:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((or (P_33 X)) (Q_19 X))))) ((semila1122118281tate_o (collec1568722789_state P_33)) (collec1568722789_state Q_19)))) of role axiom named fact_248_Collect__disj__eq
% A new axiom: (forall (P_33:(hoare_1708887482_state->Prop)) (Q_19:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((or (P_33 X)) (Q_19 X))))) ((semila1122118281tate_o (collec1568722789_state P_33)) (collec1568722789_state Q_19))))
% FOF formula (forall (P_33:(hoare_2091234717iple_a->Prop)) (Q_19:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or (P_33 X)) (Q_19 X))))) ((semila1052848428le_a_o (collec992574898iple_a P_33)) (collec992574898iple_a Q_19)))) of role axiom named fact_249_Collect__disj__eq
% A new axiom: (forall (P_33:(hoare_2091234717iple_a->Prop)) (Q_19:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or (P_33 X)) (Q_19 X))))) ((semila1052848428le_a_o (collec992574898iple_a P_33)) (collec992574898iple_a Q_19))))
% FOF formula (forall (P_33:(nat->Prop)) (Q_19:(nat->Prop)), (((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((or (P_33 X)) (Q_19 X))))) ((semila848761471_nat_o (collect_nat P_33)) (collect_nat Q_19)))) of role axiom named fact_250_Collect__disj__eq
% A new axiom: (forall (P_33:(nat->Prop)) (Q_19:(nat->Prop)), (((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((or (P_33 X)) (Q_19 X))))) ((semila848761471_nat_o (collect_nat P_33)) (collect_nat Q_19))))
% FOF formula (forall (B_48:nat) (F_42:(nat->nat)) (A_101:(nat->Prop)), (((member_nat B_48) ((image_nat_nat F_42) A_101))->((forall (X:nat), ((((eq nat) B_48) (F_42 X))->(((member_nat X) A_101)->False)))->False))) of role axiom named fact_251_imageE
% A new axiom: (forall (B_48:nat) (F_42:(nat->nat)) (A_101:(nat->Prop)), (((member_nat B_48) ((image_nat_nat F_42) A_101))->((forall (X:nat), ((((eq nat) B_48) (F_42 X))->(((member_nat X) A_101)->False)))->False)))
% FOF formula (forall (B_48:pname) (F_42:(nat->pname)) (A_101:(nat->Prop)), (((member_pname B_48) ((image_nat_pname F_42) A_101))->((forall (X:nat), ((((eq pname) B_48) (F_42 X))->(((member_nat X) A_101)->False)))->False))) of role axiom named fact_252_imageE
% A new axiom: (forall (B_48:pname) (F_42:(nat->pname)) (A_101:(nat->Prop)), (((member_pname B_48) ((image_nat_pname F_42) A_101))->((forall (X:nat), ((((eq pname) B_48) (F_42 X))->(((member_nat X) A_101)->False)))->False)))
% FOF formula (forall (B_48:pname) (F_42:((hoare_2091234717iple_a->Prop)->pname)) (A_101:((hoare_2091234717iple_a->Prop)->Prop)), (((member_pname B_48) ((image_1908519857_pname F_42) A_101))->((forall (X:(hoare_2091234717iple_a->Prop)), ((((eq pname) B_48) (F_42 X))->(((member99268621le_a_o X) A_101)->False)))->False))) of role axiom named fact_253_imageE
% A new axiom: (forall (B_48:pname) (F_42:((hoare_2091234717iple_a->Prop)->pname)) (A_101:((hoare_2091234717iple_a->Prop)->Prop)), (((member_pname B_48) ((image_1908519857_pname F_42) A_101))->((forall (X:(hoare_2091234717iple_a->Prop)), ((((eq pname) B_48) (F_42 X))->(((member99268621le_a_o X) A_101)->False)))->False)))
% FOF formula (forall (B_48:pname) (F_42:(hoare_2091234717iple_a->pname)) (A_101:(hoare_2091234717iple_a->Prop)), (((member_pname B_48) ((image_924789612_pname F_42) A_101))->((forall (X:hoare_2091234717iple_a), ((((eq pname) B_48) (F_42 X))->(((member290856304iple_a X) A_101)->False)))->False))) of role axiom named fact_254_imageE
% A new axiom: (forall (B_48:pname) (F_42:(hoare_2091234717iple_a->pname)) (A_101:(hoare_2091234717iple_a->Prop)), (((member_pname B_48) ((image_924789612_pname F_42) A_101))->((forall (X:hoare_2091234717iple_a), ((((eq pname) B_48) (F_42 X))->(((member290856304iple_a X) A_101)->False)))->False)))
% FOF formula (forall (B_48:hoare_1708887482_state) (F_42:(pname->hoare_1708887482_state)) (A_101:(pname->Prop)), (((member451959335_state B_48) ((image_1116629049_state F_42) A_101))->((forall (X:pname), ((((eq hoare_1708887482_state) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False))) of role axiom named fact_255_imageE
% A new axiom: (forall (B_48:hoare_1708887482_state) (F_42:(pname->hoare_1708887482_state)) (A_101:(pname->Prop)), (((member451959335_state B_48) ((image_1116629049_state F_42) A_101))->((forall (X:pname), ((((eq hoare_1708887482_state) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False)))
% FOF formula (forall (B_48:nat) (F_42:(pname->nat)) (A_101:(pname->Prop)), (((member_nat B_48) ((image_pname_nat F_42) A_101))->((forall (X:pname), ((((eq nat) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False))) of role axiom named fact_256_imageE
% A new axiom: (forall (B_48:nat) (F_42:(pname->nat)) (A_101:(pname->Prop)), (((member_nat B_48) ((image_pname_nat F_42) A_101))->((forall (X:pname), ((((eq nat) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False)))
% FOF formula (forall (B_48:(hoare_2091234717iple_a->Prop)) (F_42:(pname->(hoare_2091234717iple_a->Prop))) (A_101:(pname->Prop)), (((member99268621le_a_o B_48) ((image_742317343le_a_o F_42) A_101))->((forall (X:pname), ((((eq (hoare_2091234717iple_a->Prop)) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False))) of role axiom named fact_257_imageE
% A new axiom: (forall (B_48:(hoare_2091234717iple_a->Prop)) (F_42:(pname->(hoare_2091234717iple_a->Prop))) (A_101:(pname->Prop)), (((member99268621le_a_o B_48) ((image_742317343le_a_o F_42) A_101))->((forall (X:pname), ((((eq (hoare_2091234717iple_a->Prop)) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False)))
% FOF formula (forall (B_48:hoare_2091234717iple_a) (F_42:(pname->hoare_2091234717iple_a)) (A_101:(pname->Prop)), (((member290856304iple_a B_48) ((image_231808478iple_a F_42) A_101))->((forall (X:pname), ((((eq hoare_2091234717iple_a) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False))) of role axiom named fact_258_imageE
% A new axiom: (forall (B_48:hoare_2091234717iple_a) (F_42:(pname->hoare_2091234717iple_a)) (A_101:(pname->Prop)), (((member290856304iple_a B_48) ((image_231808478iple_a F_42) A_101))->((forall (X:pname), ((((eq hoare_2091234717iple_a) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False)))
% FOF formula (forall (N_8:nat) (P_32:(state->(state->Prop))) (Pn_6:pname) (Q_18:(state->(state->Prop))), ((iff ((hoare_23738522_state N_8) (((hoare_858012674_state P_32) (the_com (body_1 Pn_6))) Q_18))) ((hoare_23738522_state (suc N_8)) (((hoare_858012674_state P_32) (body Pn_6)) Q_18)))) of role axiom named fact_259_Body__triple__valid__Suc
% A new axiom: (forall (N_8:nat) (P_32:(state->(state->Prop))) (Pn_6:pname) (Q_18:(state->(state->Prop))), ((iff ((hoare_23738522_state N_8) (((hoare_858012674_state P_32) (the_com (body_1 Pn_6))) Q_18))) ((hoare_23738522_state (suc N_8)) (((hoare_858012674_state P_32) (body Pn_6)) Q_18))))
% FOF formula (forall (N_8:nat) (P_32:(x_a->(state->Prop))) (Pn_6:pname) (Q_18:(x_a->(state->Prop))), ((iff ((hoare_1421888935alid_a N_8) (((hoare_657976383iple_a P_32) (the_com (body_1 Pn_6))) Q_18))) ((hoare_1421888935alid_a (suc N_8)) (((hoare_657976383iple_a P_32) (body Pn_6)) Q_18)))) of role axiom named fact_260_Body__triple__valid__Suc
% A new axiom: (forall (N_8:nat) (P_32:(x_a->(state->Prop))) (Pn_6:pname) (Q_18:(x_a->(state->Prop))), ((iff ((hoare_1421888935alid_a N_8) (((hoare_657976383iple_a P_32) (the_com (body_1 Pn_6))) Q_18))) ((hoare_1421888935alid_a (suc N_8)) (((hoare_657976383iple_a P_32) (body Pn_6)) Q_18))))
% FOF formula (forall (Y_11:hoare_2091234717iple_a), ((forall (Fun1_2:(x_a->(state->Prop))) (Com_4:com) (Fun2_2:(x_a->(state->Prop))), (not (((eq hoare_2091234717iple_a) Y_11) (((hoare_657976383iple_a Fun1_2) Com_4) Fun2_2))))->False)) of role axiom named fact_261_triple_Oexhaust
% A new axiom: (forall (Y_11:hoare_2091234717iple_a), ((forall (Fun1_2:(x_a->(state->Prop))) (Com_4:com) (Fun2_2:(x_a->(state->Prop))), (not (((eq hoare_2091234717iple_a) Y_11) (((hoare_657976383iple_a Fun1_2) Com_4) Fun2_2))))->False))
% FOF formula (forall (Y_11:hoare_1708887482_state), ((forall (Fun1_2:(state->(state->Prop))) (Com_4:com) (Fun2_2:(state->(state->Prop))), (not (((eq hoare_1708887482_state) Y_11) (((hoare_858012674_state Fun1_2) Com_4) Fun2_2))))->False)) of role axiom named fact_262_triple_Oexhaust
% A new axiom: (forall (Y_11:hoare_1708887482_state), ((forall (Fun1_2:(state->(state->Prop))) (Com_4:com) (Fun2_2:(state->(state->Prop))), (not (((eq hoare_1708887482_state) Y_11) (((hoare_858012674_state Fun1_2) Com_4) Fun2_2))))->False))
% FOF formula (forall (Pn_5:pname) (G_21:(hoare_1708887482_state->Prop)) (P_31:(pname->(state->(state->Prop)))) (Q_17:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_21) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_31 P_9)) (body P_9)) (Q_17 P_9)))) Procs))) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_31 P_9)) (the_com (body_1 P_9))) (Q_17 P_9)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_31 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo19817387tate_o))))) of role axiom named fact_263_Body1
% A new axiom: (forall (Pn_5:pname) (G_21:(hoare_1708887482_state->Prop)) (P_31:(pname->(state->(state->Prop)))) (Q_17:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_21) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_31 P_9)) (body P_9)) (Q_17 P_9)))) Procs))) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_31 P_9)) (the_com (body_1 P_9))) (Q_17 P_9)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_31 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo19817387tate_o)))))
% FOF formula (forall (Pn_5:pname) (G_21:(hoare_2091234717iple_a->Prop)) (P_31:(pname->(x_a->(state->Prop)))) (Q_17:(pname->(x_a->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_1467856363rivs_a ((semila1052848428le_a_o G_21) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_31 P_9)) (body P_9)) (Q_17 P_9)))) Procs))) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_31 P_9)) (the_com (body_1 P_9))) (Q_17 P_9)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_1467856363rivs_a G_21) ((insert1597628439iple_a (((hoare_657976383iple_a (P_31 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo1791335050le_a_o))))) of role axiom named fact_264_Body1
% A new axiom: (forall (Pn_5:pname) (G_21:(hoare_2091234717iple_a->Prop)) (P_31:(pname->(x_a->(state->Prop)))) (Q_17:(pname->(x_a->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_1467856363rivs_a ((semila1052848428le_a_o G_21) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_31 P_9)) (body P_9)) (Q_17 P_9)))) Procs))) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_31 P_9)) (the_com (body_1 P_9))) (Q_17 P_9)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_1467856363rivs_a G_21) ((insert1597628439iple_a (((hoare_657976383iple_a (P_31 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo1791335050le_a_o)))))
% FOF formula (forall (F_41:(nat->nat)) (G_20:(nat->nat)) (M_3:(nat->Prop)) (N_7:(nat->Prop)), ((((eq (nat->Prop)) M_3) N_7)->((forall (X:nat), (((member_nat X) N_7)->(((eq nat) (F_41 X)) (G_20 X))))->(((eq (nat->Prop)) ((image_nat_nat F_41) M_3)) ((image_nat_nat G_20) N_7))))) of role axiom named fact_265_image__cong
% A new axiom: (forall (F_41:(nat->nat)) (G_20:(nat->nat)) (M_3:(nat->Prop)) (N_7:(nat->Prop)), ((((eq (nat->Prop)) M_3) N_7)->((forall (X:nat), (((member_nat X) N_7)->(((eq nat) (F_41 X)) (G_20 X))))->(((eq (nat->Prop)) ((image_nat_nat F_41) M_3)) ((image_nat_nat G_20) N_7)))))
% FOF formula (forall (F_41:(pname->hoare_1708887482_state)) (G_20:(pname->hoare_1708887482_state)) (M_3:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_3) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_1708887482_state) (F_41 X)) (G_20 X))))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_41) M_3)) ((image_1116629049_state G_20) N_7))))) of role axiom named fact_266_image__cong
% A new axiom: (forall (F_41:(pname->hoare_1708887482_state)) (G_20:(pname->hoare_1708887482_state)) (M_3:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_3) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_1708887482_state) (F_41 X)) (G_20 X))))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_41) M_3)) ((image_1116629049_state G_20) N_7)))))
% FOF formula (forall (F_41:(pname->hoare_2091234717iple_a)) (G_20:(pname->hoare_2091234717iple_a)) (M_3:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_3) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_2091234717iple_a) (F_41 X)) (G_20 X))))->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_41) M_3)) ((image_231808478iple_a G_20) N_7))))) of role axiom named fact_267_image__cong
% A new axiom: (forall (F_41:(pname->hoare_2091234717iple_a)) (G_20:(pname->hoare_2091234717iple_a)) (M_3:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_3) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_2091234717iple_a) (F_41 X)) (G_20 X))))->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_41) M_3)) ((image_231808478iple_a G_20) N_7)))))
% FOF formula (forall (P_30:(state->(state->Prop))) (Pn_4:pname) (Q_16:(state->(state->Prop))), ((hoare_23738522_state zero_zero_nat) (((hoare_858012674_state P_30) (body Pn_4)) Q_16))) of role axiom named fact_268_Body__triple__valid__0
% A new axiom: (forall (P_30:(state->(state->Prop))) (Pn_4:pname) (Q_16:(state->(state->Prop))), ((hoare_23738522_state zero_zero_nat) (((hoare_858012674_state P_30) (body Pn_4)) Q_16)))
% FOF formula (forall (P_30:(x_a->(state->Prop))) (Pn_4:pname) (Q_16:(x_a->(state->Prop))), ((hoare_1421888935alid_a zero_zero_nat) (((hoare_657976383iple_a P_30) (body Pn_4)) Q_16))) of role axiom named fact_269_Body__triple__valid__0
% A new axiom: (forall (P_30:(x_a->(state->Prop))) (Pn_4:pname) (Q_16:(x_a->(state->Prop))), ((hoare_1421888935alid_a zero_zero_nat) (((hoare_657976383iple_a P_30) (body Pn_4)) Q_16)))
% FOF formula (forall (Pname_1:pname) (Pname:pname), ((iff (((eq com) (body Pname_1)) (body Pname))) (((eq pname) Pname_1) Pname))) of role axiom named fact_270_com_Osimps_I6_J
% A new axiom: (forall (Pname_1:pname) (Pname:pname), ((iff (((eq com) (body Pname_1)) (body Pname))) (((eq pname) Pname_1) Pname)))
% 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_271_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_272_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:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_34) X_34)) X_34)) of role axiom named fact_273_Sup__fin_Oidem
% A new axiom: (forall (X_34:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_34) X_34)) X_34))
% FOF formula (forall (X_34:nat), (((eq nat) ((semila972727038up_nat X_34) X_34)) X_34)) of role axiom named fact_274_Sup__fin_Oidem
% A new axiom: (forall (X_34:nat), (((eq nat) ((semila972727038up_nat X_34) X_34)) X_34))
% FOF formula (forall (X_34:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_34) X_34)) X_34)) of role axiom named fact_275_Sup__fin_Oidem
% A new axiom: (forall (X_34:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_34) X_34)) X_34))
% FOF formula (forall (X_34:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_34) X_34)) X_34)) of role axiom named fact_276_Sup__fin_Oidem
% A new axiom: (forall (X_34:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_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_277_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_278_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_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_34) X_34)) X_34)) of role axiom named fact_279_Sup__fin_Oidem
% A new axiom: (forall (X_34:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_34) X_34)) X_34))
% FOF formula (forall (N_6:nat) (Ts_2:(hoare_1708887482_state->Prop)), ((forall (X:hoare_1708887482_state), (((member451959335_state X) Ts_2)->((hoare_23738522_state (suc N_6)) X)))->(forall (X:hoare_1708887482_state), (((member451959335_state X) Ts_2)->((hoare_23738522_state N_6) X))))) of role axiom named fact_280_triples__valid__Suc
% A new axiom: (forall (N_6:nat) (Ts_2:(hoare_1708887482_state->Prop)), ((forall (X:hoare_1708887482_state), (((member451959335_state X) Ts_2)->((hoare_23738522_state (suc N_6)) X)))->(forall (X:hoare_1708887482_state), (((member451959335_state X) Ts_2)->((hoare_23738522_state N_6) X)))))
% FOF formula (forall (N_6:nat) (Ts_2:(hoare_2091234717iple_a->Prop)), ((forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) Ts_2)->((hoare_1421888935alid_a (suc N_6)) X)))->(forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) Ts_2)->((hoare_1421888935alid_a N_6) X))))) of role axiom named fact_281_triples__valid__Suc
% A new axiom: (forall (N_6:nat) (Ts_2:(hoare_2091234717iple_a->Prop)), ((forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) Ts_2)->((hoare_1421888935alid_a (suc N_6)) X)))->(forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) Ts_2)->((hoare_1421888935alid_a N_6) X)))))
% FOF formula (forall (A_100:nat), (((member_nat A_100) bot_bot_nat_o)->False)) of role axiom named fact_282_emptyE
% A new axiom: (forall (A_100:nat), (((member_nat A_100) bot_bot_nat_o)->False))
% FOF formula (forall (A_100:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o A_100) bot_bo1957696069_a_o_o)->False)) of role axiom named fact_283_emptyE
% A new axiom: (forall (A_100:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o A_100) bot_bo1957696069_a_o_o)->False))
% FOF formula (forall (A_100:hoare_2091234717iple_a), (((member290856304iple_a A_100) bot_bo1791335050le_a_o)->False)) of role axiom named fact_284_emptyE
% A new axiom: (forall (A_100:hoare_2091234717iple_a), (((member290856304iple_a A_100) bot_bo1791335050le_a_o)->False))
% FOF formula (forall (A_100:hoare_1708887482_state), (((member451959335_state A_100) bot_bo19817387tate_o)->False)) of role axiom named fact_285_emptyE
% A new axiom: (forall (A_100:hoare_1708887482_state), (((member451959335_state A_100) bot_bo19817387tate_o)->False))
% FOF formula (forall (A_100:pname), (((member_pname A_100) bot_bot_pname_o)->False)) of role axiom named fact_286_emptyE
% A new axiom: (forall (A_100:pname), (((member_pname A_100) bot_bot_pname_o)->False))
% FOF formula (forall (A_99:nat) (B_47:nat) (A_98:(nat->Prop)), (((member_nat A_99) ((insert_nat B_47) A_98))->((not (((eq nat) A_99) B_47))->((member_nat A_99) A_98)))) of role axiom named fact_287_insertE
% A new axiom: (forall (A_99:nat) (B_47:nat) (A_98:(nat->Prop)), (((member_nat A_99) ((insert_nat B_47) A_98))->((not (((eq nat) A_99) B_47))->((member_nat A_99) A_98))))
% FOF formula (forall (A_99:(hoare_2091234717iple_a->Prop)) (B_47:(hoare_2091234717iple_a->Prop)) (A_98:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_99) ((insert102003750le_a_o B_47) A_98))->((not (((eq (hoare_2091234717iple_a->Prop)) A_99) B_47))->((member99268621le_a_o A_99) A_98)))) of role axiom named fact_288_insertE
% A new axiom: (forall (A_99:(hoare_2091234717iple_a->Prop)) (B_47:(hoare_2091234717iple_a->Prop)) (A_98:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_99) ((insert102003750le_a_o B_47) A_98))->((not (((eq (hoare_2091234717iple_a->Prop)) A_99) B_47))->((member99268621le_a_o A_99) A_98))))
% FOF formula (forall (A_99:hoare_2091234717iple_a) (B_47:hoare_2091234717iple_a) (A_98:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_99) ((insert1597628439iple_a B_47) A_98))->((not (((eq hoare_2091234717iple_a) A_99) B_47))->((member290856304iple_a A_99) A_98)))) of role axiom named fact_289_insertE
% A new axiom: (forall (A_99:hoare_2091234717iple_a) (B_47:hoare_2091234717iple_a) (A_98:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_99) ((insert1597628439iple_a B_47) A_98))->((not (((eq hoare_2091234717iple_a) A_99) B_47))->((member290856304iple_a A_99) A_98))))
% FOF formula (forall (A_99:hoare_1708887482_state) (B_47:hoare_1708887482_state) (A_98:(hoare_1708887482_state->Prop)), (((member451959335_state A_99) ((insert528405184_state B_47) A_98))->((not (((eq hoare_1708887482_state) A_99) B_47))->((member451959335_state A_99) A_98)))) of role axiom named fact_290_insertE
% A new axiom: (forall (A_99:hoare_1708887482_state) (B_47:hoare_1708887482_state) (A_98:(hoare_1708887482_state->Prop)), (((member451959335_state A_99) ((insert528405184_state B_47) A_98))->((not (((eq hoare_1708887482_state) A_99) B_47))->((member451959335_state A_99) A_98))))
% FOF formula (forall (A_99:pname) (B_47:pname) (A_98:(pname->Prop)), (((member_pname A_99) ((insert_pname B_47) A_98))->((not (((eq pname) A_99) B_47))->((member_pname A_99) A_98)))) of role axiom named fact_291_insertE
% A new axiom: (forall (A_99:pname) (B_47:pname) (A_98:(pname->Prop)), (((member_pname A_99) ((insert_pname B_47) A_98))->((not (((eq pname) A_99) B_47))->((member_pname A_99) A_98))))
% FOF formula (forall (B_46:nat) (A_97:nat) (B_45:(nat->Prop)), (((((member_nat A_97) B_45)->False)->(((eq nat) A_97) B_46))->((member_nat A_97) ((insert_nat B_46) B_45)))) of role axiom named fact_292_insertCI
% A new axiom: (forall (B_46:nat) (A_97:nat) (B_45:(nat->Prop)), (((((member_nat A_97) B_45)->False)->(((eq nat) A_97) B_46))->((member_nat A_97) ((insert_nat B_46) B_45))))
% FOF formula (forall (B_46:(hoare_2091234717iple_a->Prop)) (A_97:(hoare_2091234717iple_a->Prop)) (B_45:((hoare_2091234717iple_a->Prop)->Prop)), (((((member99268621le_a_o A_97) B_45)->False)->(((eq (hoare_2091234717iple_a->Prop)) A_97) B_46))->((member99268621le_a_o A_97) ((insert102003750le_a_o B_46) B_45)))) of role axiom named fact_293_insertCI
% A new axiom: (forall (B_46:(hoare_2091234717iple_a->Prop)) (A_97:(hoare_2091234717iple_a->Prop)) (B_45:((hoare_2091234717iple_a->Prop)->Prop)), (((((member99268621le_a_o A_97) B_45)->False)->(((eq (hoare_2091234717iple_a->Prop)) A_97) B_46))->((member99268621le_a_o A_97) ((insert102003750le_a_o B_46) B_45))))
% FOF formula (forall (B_46:hoare_2091234717iple_a) (A_97:hoare_2091234717iple_a) (B_45:(hoare_2091234717iple_a->Prop)), (((((member290856304iple_a A_97) B_45)->False)->(((eq hoare_2091234717iple_a) A_97) B_46))->((member290856304iple_a A_97) ((insert1597628439iple_a B_46) B_45)))) of role axiom named fact_294_insertCI
% A new axiom: (forall (B_46:hoare_2091234717iple_a) (A_97:hoare_2091234717iple_a) (B_45:(hoare_2091234717iple_a->Prop)), (((((member290856304iple_a A_97) B_45)->False)->(((eq hoare_2091234717iple_a) A_97) B_46))->((member290856304iple_a A_97) ((insert1597628439iple_a B_46) B_45))))
% FOF formula (forall (B_46:hoare_1708887482_state) (A_97:hoare_1708887482_state) (B_45:(hoare_1708887482_state->Prop)), (((((member451959335_state A_97) B_45)->False)->(((eq hoare_1708887482_state) A_97) B_46))->((member451959335_state A_97) ((insert528405184_state B_46) B_45)))) of role axiom named fact_295_insertCI
% A new axiom: (forall (B_46:hoare_1708887482_state) (A_97:hoare_1708887482_state) (B_45:(hoare_1708887482_state->Prop)), (((((member451959335_state A_97) B_45)->False)->(((eq hoare_1708887482_state) A_97) B_46))->((member451959335_state A_97) ((insert528405184_state B_46) B_45))))
% FOF formula (forall (B_46:pname) (A_97:pname) (B_45:(pname->Prop)), (((((member_pname A_97) B_45)->False)->(((eq pname) A_97) B_46))->((member_pname A_97) ((insert_pname B_46) B_45)))) of role axiom named fact_296_insertCI
% A new axiom: (forall (B_46:pname) (A_97:pname) (B_45:(pname->Prop)), (((((member_pname A_97) B_45)->False)->(((eq pname) A_97) B_46))->((member_pname A_97) ((insert_pname B_46) B_45))))
% FOF formula (forall (A_96:nat) (A_95:(nat->Prop)), (not (((eq (nat->Prop)) bot_bot_nat_o) ((insert_nat A_96) A_95)))) of role axiom named fact_297_empty__not__insert
% A new axiom: (forall (A_96:nat) (A_95:(nat->Prop)), (not (((eq (nat->Prop)) bot_bot_nat_o) ((insert_nat A_96) A_95))))
% FOF formula (forall (A_96:(hoare_2091234717iple_a->Prop)) (A_95:((hoare_2091234717iple_a->Prop)->Prop)), (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) bot_bo1957696069_a_o_o) ((insert102003750le_a_o A_96) A_95)))) of role axiom named fact_298_empty__not__insert
% A new axiom: (forall (A_96:(hoare_2091234717iple_a->Prop)) (A_95:((hoare_2091234717iple_a->Prop)->Prop)), (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) bot_bo1957696069_a_o_o) ((insert102003750le_a_o A_96) A_95))))
% FOF formula (forall (A_96:pname) (A_95:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_96) A_95)))) of role axiom named fact_299_empty__not__insert
% A new axiom: (forall (A_96:pname) (A_95:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_96) A_95))))
% FOF formula (forall (A_96:hoare_2091234717iple_a) (A_95:(hoare_2091234717iple_a->Prop)), (not (((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) ((insert1597628439iple_a A_96) A_95)))) of role axiom named fact_300_empty__not__insert
% A new axiom: (forall (A_96:hoare_2091234717iple_a) (A_95:(hoare_2091234717iple_a->Prop)), (not (((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) ((insert1597628439iple_a A_96) A_95))))
% FOF formula (forall (A_96:hoare_1708887482_state) (A_95:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((insert528405184_state A_96) A_95)))) of role axiom named fact_301_empty__not__insert
% A new axiom: (forall (A_96:hoare_1708887482_state) (A_95:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((insert528405184_state A_96) A_95))))
% FOF formula (forall (A_94:nat) (A_93:(nat->Prop)), (not (((eq (nat->Prop)) ((insert_nat A_94) A_93)) bot_bot_nat_o))) of role axiom named fact_302_insert__not__empty
% A new axiom: (forall (A_94:nat) (A_93:(nat->Prop)), (not (((eq (nat->Prop)) ((insert_nat A_94) A_93)) bot_bot_nat_o)))
% FOF formula (forall (A_94:(hoare_2091234717iple_a->Prop)) (A_93:((hoare_2091234717iple_a->Prop)->Prop)), (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_94) A_93)) bot_bo1957696069_a_o_o))) of role axiom named fact_303_insert__not__empty
% A new axiom: (forall (A_94:(hoare_2091234717iple_a->Prop)) (A_93:((hoare_2091234717iple_a->Prop)->Prop)), (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_94) A_93)) bot_bo1957696069_a_o_o)))
% FOF formula (forall (A_94:pname) (A_93:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_94) A_93)) bot_bot_pname_o))) of role axiom named fact_304_insert__not__empty
% A new axiom: (forall (A_94:pname) (A_93:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_94) A_93)) bot_bot_pname_o)))
% FOF formula (forall (A_94:hoare_2091234717iple_a) (A_93:(hoare_2091234717iple_a->Prop)), (not (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_94) A_93)) bot_bo1791335050le_a_o))) of role axiom named fact_305_insert__not__empty
% A new axiom: (forall (A_94:hoare_2091234717iple_a) (A_93:(hoare_2091234717iple_a->Prop)), (not (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_94) A_93)) bot_bo1791335050le_a_o)))
% FOF formula (forall (A_94:hoare_1708887482_state) (A_93:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_94) A_93)) bot_bo19817387tate_o))) of role axiom named fact_306_insert__not__empty
% A new axiom: (forall (A_94:hoare_1708887482_state) (A_93:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_94) A_93)) bot_bo19817387tate_o)))
% FOF formula (forall (X:nat), ((iff (bot_bot_nat_o X)) ((member_nat X) bot_bot_nat_o))) of role axiom named fact_307_bot__empty__eq
% A new axiom: (forall (X:nat), ((iff (bot_bot_nat_o X)) ((member_nat X) bot_bot_nat_o)))
% FOF formula (forall (X:(hoare_2091234717iple_a->Prop)), ((iff (bot_bo1957696069_a_o_o X)) ((member99268621le_a_o X) bot_bo1957696069_a_o_o))) of role axiom named fact_308_bot__empty__eq
% A new axiom: (forall (X:(hoare_2091234717iple_a->Prop)), ((iff (bot_bo1957696069_a_o_o X)) ((member99268621le_a_o X) bot_bo1957696069_a_o_o)))
% FOF formula (forall (X:hoare_2091234717iple_a), ((iff (bot_bo1791335050le_a_o X)) ((member290856304iple_a X) bot_bo1791335050le_a_o))) of role axiom named fact_309_bot__empty__eq
% A new axiom: (forall (X:hoare_2091234717iple_a), ((iff (bot_bo1791335050le_a_o X)) ((member290856304iple_a X) bot_bo1791335050le_a_o)))
% FOF formula (forall (X:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X)) ((member451959335_state X) bot_bo19817387tate_o))) of role axiom named fact_310_bot__empty__eq
% A new axiom: (forall (X:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X)) ((member451959335_state X) bot_bo19817387tate_o)))
% FOF formula (forall (X:pname), ((iff (bot_bot_pname_o X)) ((member_pname X) bot_bot_pname_o))) of role axiom named fact_311_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 (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X:pname)=> False))) of role axiom named fact_312_empty__def
% A new axiom: (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X:pname)=> False)))
% FOF formula (((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> False))) of role axiom named fact_313_empty__def
% A new axiom: (((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> False)))
% FOF formula (((eq ((hoare_2091234717iple_a->Prop)->Prop)) bot_bo1957696069_a_o_o) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> False))) of role axiom named fact_314_empty__def
% A new axiom: (((eq ((hoare_2091234717iple_a->Prop)->Prop)) bot_bo1957696069_a_o_o) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> False)))
% FOF formula (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state (fun (X:hoare_1708887482_state)=> False))) of role axiom named fact_315_empty__def
% A new axiom: (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state (fun (X:hoare_1708887482_state)=> False)))
% FOF formula (((eq (nat->Prop)) bot_bot_nat_o) (collect_nat (fun (X:nat)=> False))) of role axiom named fact_316_empty__def
% A new axiom: (((eq (nat->Prop)) bot_bot_nat_o) (collect_nat (fun (X:nat)=> False)))
% FOF formula (forall (A_92:nat) (B_44:(nat->Prop)), ((member_nat A_92) ((insert_nat A_92) B_44))) of role axiom named fact_317_insertI1
% A new axiom: (forall (A_92:nat) (B_44:(nat->Prop)), ((member_nat A_92) ((insert_nat A_92) B_44)))
% FOF formula (forall (A_92:(hoare_2091234717iple_a->Prop)) (B_44:((hoare_2091234717iple_a->Prop)->Prop)), ((member99268621le_a_o A_92) ((insert102003750le_a_o A_92) B_44))) of role axiom named fact_318_insertI1
% A new axiom: (forall (A_92:(hoare_2091234717iple_a->Prop)) (B_44:((hoare_2091234717iple_a->Prop)->Prop)), ((member99268621le_a_o A_92) ((insert102003750le_a_o A_92) B_44)))
% FOF formula (forall (A_92:hoare_2091234717iple_a) (B_44:(hoare_2091234717iple_a->Prop)), ((member290856304iple_a A_92) ((insert1597628439iple_a A_92) B_44))) of role axiom named fact_319_insertI1
% A new axiom: (forall (A_92:hoare_2091234717iple_a) (B_44:(hoare_2091234717iple_a->Prop)), ((member290856304iple_a A_92) ((insert1597628439iple_a A_92) B_44)))
% FOF formula (forall (A_92:hoare_1708887482_state) (B_44:(hoare_1708887482_state->Prop)), ((member451959335_state A_92) ((insert528405184_state A_92) B_44))) of role axiom named fact_320_insertI1
% A new axiom: (forall (A_92:hoare_1708887482_state) (B_44:(hoare_1708887482_state->Prop)), ((member451959335_state A_92) ((insert528405184_state A_92) B_44)))
% FOF formula (forall (A_92:pname) (B_44:(pname->Prop)), ((member_pname A_92) ((insert_pname A_92) B_44))) of role axiom named fact_321_insertI1
% A new axiom: (forall (A_92:pname) (B_44:(pname->Prop)), ((member_pname A_92) ((insert_pname A_92) B_44)))
% FOF formula (forall (A_91:(nat->Prop)), ((iff (forall (X:nat), (((member_nat X) A_91)->False))) (((eq (nat->Prop)) A_91) bot_bot_nat_o))) of role axiom named fact_322_all__not__in__conv
% A new axiom: (forall (A_91:(nat->Prop)), ((iff (forall (X:nat), (((member_nat X) A_91)->False))) (((eq (nat->Prop)) A_91) bot_bot_nat_o)))
% FOF formula (forall (A_91:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) A_91)->False))) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_91) bot_bo1957696069_a_o_o))) of role axiom named fact_323_all__not__in__conv
% A new axiom: (forall (A_91:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) A_91)->False))) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_91) bot_bo1957696069_a_o_o)))
% FOF formula (forall (A_91:(hoare_2091234717iple_a->Prop)), ((iff (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) A_91)->False))) (((eq (hoare_2091234717iple_a->Prop)) A_91) bot_bo1791335050le_a_o))) of role axiom named fact_324_all__not__in__conv
% A new axiom: (forall (A_91:(hoare_2091234717iple_a->Prop)), ((iff (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) A_91)->False))) (((eq (hoare_2091234717iple_a->Prop)) A_91) bot_bo1791335050le_a_o)))
% FOF formula (forall (A_91:(hoare_1708887482_state->Prop)), ((iff (forall (X:hoare_1708887482_state), (((member451959335_state X) A_91)->False))) (((eq (hoare_1708887482_state->Prop)) A_91) bot_bo19817387tate_o))) of role axiom named fact_325_all__not__in__conv
% A new axiom: (forall (A_91:(hoare_1708887482_state->Prop)), ((iff (forall (X:hoare_1708887482_state), (((member451959335_state X) A_91)->False))) (((eq (hoare_1708887482_state->Prop)) A_91) bot_bo19817387tate_o)))
% FOF formula (forall (A_91:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) A_91)->False))) (((eq (pname->Prop)) A_91) bot_bot_pname_o))) of role axiom named fact_326_all__not__in__conv
% A new axiom: (forall (A_91:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) A_91)->False))) (((eq (pname->Prop)) A_91) bot_bot_pname_o)))
% FOF formula (forall (A_90:(hoare_2091234717iple_a->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fequal845167073le_a_o A_90))) ((insert102003750le_a_o A_90) bot_bo1957696069_a_o_o))) of role axiom named fact_327_singleton__conv2
% A new axiom: (forall (A_90:(hoare_2091234717iple_a->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fequal845167073le_a_o A_90))) ((insert102003750le_a_o A_90) bot_bo1957696069_a_o_o)))
% FOF formula (forall (A_90:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_90))) ((insert_pname A_90) bot_bot_pname_o))) of role axiom named fact_328_singleton__conv2
% A new axiom: (forall (A_90:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_90))) ((insert_pname A_90) bot_bot_pname_o)))
% FOF formula (forall (A_90:hoare_2091234717iple_a), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fequal1604381340iple_a A_90))) ((insert1597628439iple_a A_90) bot_bo1791335050le_a_o))) of role axiom named fact_329_singleton__conv2
% A new axiom: (forall (A_90:hoare_2091234717iple_a), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fequal1604381340iple_a A_90))) ((insert1597628439iple_a A_90) bot_bo1791335050le_a_o)))
% FOF formula (forall (A_90:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fequal224822779_state A_90))) ((insert528405184_state A_90) bot_bo19817387tate_o))) of role axiom named fact_330_singleton__conv2
% A new axiom: (forall (A_90:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fequal224822779_state A_90))) ((insert528405184_state A_90) bot_bo19817387tate_o)))
% FOF formula (forall (A_90:nat), (((eq (nat->Prop)) (collect_nat (fequal_nat A_90))) ((insert_nat A_90) bot_bot_nat_o))) of role axiom named fact_331_singleton__conv2
% A new axiom: (forall (A_90:nat), (((eq (nat->Prop)) (collect_nat (fequal_nat A_90))) ((insert_nat A_90) bot_bot_nat_o)))
% FOF formula (forall (A_89:(nat->Prop)), ((iff ((ex nat) (fun (X:nat)=> ((member_nat X) A_89)))) (not (((eq (nat->Prop)) A_89) bot_bot_nat_o)))) of role axiom named fact_332_ex__in__conv
% A new axiom: (forall (A_89:(nat->Prop)), ((iff ((ex nat) (fun (X:nat)=> ((member_nat X) A_89)))) (not (((eq (nat->Prop)) A_89) bot_bot_nat_o))))
% FOF formula (forall (A_89:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o X) A_89)))) (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_89) bot_bo1957696069_a_o_o)))) of role axiom named fact_333_ex__in__conv
% A new axiom: (forall (A_89:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o X) A_89)))) (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_89) bot_bo1957696069_a_o_o))))
% FOF formula (forall (A_89:(hoare_2091234717iple_a->Prop)), ((iff ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((member290856304iple_a X) A_89)))) (not (((eq (hoare_2091234717iple_a->Prop)) A_89) bot_bo1791335050le_a_o)))) of role axiom named fact_334_ex__in__conv
% A new axiom: (forall (A_89:(hoare_2091234717iple_a->Prop)), ((iff ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((member290856304iple_a X) A_89)))) (not (((eq (hoare_2091234717iple_a->Prop)) A_89) bot_bo1791335050le_a_o))))
% FOF formula (forall (A_89:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((member451959335_state X) A_89)))) (not (((eq (hoare_1708887482_state->Prop)) A_89) bot_bo19817387tate_o)))) of role axiom named fact_335_ex__in__conv
% A new axiom: (forall (A_89:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((member451959335_state X) A_89)))) (not (((eq (hoare_1708887482_state->Prop)) A_89) bot_bo19817387tate_o))))
% FOF formula (forall (A_89:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((member_pname X) A_89)))) (not (((eq (pname->Prop)) A_89) bot_bot_pname_o)))) of role axiom named fact_336_ex__in__conv
% A new axiom: (forall (A_89:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((member_pname X) A_89)))) (not (((eq (pname->Prop)) A_89) bot_bot_pname_o))))
% FOF formula (forall (A_88:(hoare_2091234717iple_a->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> (((eq (hoare_2091234717iple_a->Prop)) X) A_88)))) ((insert102003750le_a_o A_88) bot_bo1957696069_a_o_o))) of role axiom named fact_337_singleton__conv
% A new axiom: (forall (A_88:(hoare_2091234717iple_a->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> (((eq (hoare_2091234717iple_a->Prop)) X) A_88)))) ((insert102003750le_a_o A_88) bot_bo1957696069_a_o_o)))
% FOF formula (forall (A_88:pname), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> (((eq pname) X) A_88)))) ((insert_pname A_88) bot_bot_pname_o))) of role axiom named fact_338_singleton__conv
% A new axiom: (forall (A_88:pname), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> (((eq pname) X) A_88)))) ((insert_pname A_88) bot_bot_pname_o)))
% FOF formula (forall (A_88:hoare_2091234717iple_a), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> (((eq hoare_2091234717iple_a) X) A_88)))) ((insert1597628439iple_a A_88) bot_bo1791335050le_a_o))) of role axiom named fact_339_singleton__conv
% A new axiom: (forall (A_88:hoare_2091234717iple_a), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> (((eq hoare_2091234717iple_a) X) A_88)))) ((insert1597628439iple_a A_88) bot_bo1791335050le_a_o)))
% FOF formula (forall (A_88:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X) A_88)))) ((insert528405184_state A_88) bot_bo19817387tate_o))) of role axiom named fact_340_singleton__conv
% A new axiom: (forall (A_88:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X) A_88)))) ((insert528405184_state A_88) bot_bo19817387tate_o)))
% FOF formula (forall (A_88:nat), (((eq (nat->Prop)) (collect_nat (fun (X:nat)=> (((eq nat) X) A_88)))) ((insert_nat A_88) bot_bot_nat_o))) of role axiom named fact_341_singleton__conv
% A new axiom: (forall (A_88:nat), (((eq (nat->Prop)) (collect_nat (fun (X:nat)=> (((eq nat) X) A_88)))) ((insert_nat A_88) bot_bot_nat_o)))
% FOF formula (forall (P_29:((hoare_2091234717iple_a->Prop)->Prop)) (A_87:(hoare_2091234717iple_a->Prop)), ((and ((P_29 A_87)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_87) X)) (P_29 X))))) ((insert102003750le_a_o A_87) bot_bo1957696069_a_o_o)))) (((P_29 A_87)->False)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_87) X)) (P_29 X))))) bot_bo1957696069_a_o_o)))) of role axiom named fact_342_Collect__conv__if2
% A new axiom: (forall (P_29:((hoare_2091234717iple_a->Prop)->Prop)) (A_87:(hoare_2091234717iple_a->Prop)), ((and ((P_29 A_87)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_87) X)) (P_29 X))))) ((insert102003750le_a_o A_87) bot_bo1957696069_a_o_o)))) (((P_29 A_87)->False)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_87) X)) (P_29 X))))) bot_bo1957696069_a_o_o))))
% FOF formula (forall (P_29:(pname->Prop)) (A_87:pname), ((and ((P_29 A_87)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_87) X)) (P_29 X))))) ((insert_pname A_87) bot_bot_pname_o)))) (((P_29 A_87)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_87) X)) (P_29 X))))) bot_bot_pname_o)))) of role axiom named fact_343_Collect__conv__if2
% A new axiom: (forall (P_29:(pname->Prop)) (A_87:pname), ((and ((P_29 A_87)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_87) X)) (P_29 X))))) ((insert_pname A_87) bot_bot_pname_o)))) (((P_29 A_87)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_87) X)) (P_29 X))))) bot_bot_pname_o))))
% FOF formula (forall (P_29:(hoare_2091234717iple_a->Prop)) (A_87:hoare_2091234717iple_a), ((and ((P_29 A_87)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) A_87) X)) (P_29 X))))) ((insert1597628439iple_a A_87) bot_bo1791335050le_a_o)))) (((P_29 A_87)->False)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) A_87) X)) (P_29 X))))) bot_bo1791335050le_a_o)))) of role axiom named fact_344_Collect__conv__if2
% A new axiom: (forall (P_29:(hoare_2091234717iple_a->Prop)) (A_87:hoare_2091234717iple_a), ((and ((P_29 A_87)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) A_87) X)) (P_29 X))))) ((insert1597628439iple_a A_87) bot_bo1791335050le_a_o)))) (((P_29 A_87)->False)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) A_87) X)) (P_29 X))))) bot_bo1791335050le_a_o))))
% FOF formula (forall (P_29:(hoare_1708887482_state->Prop)) (A_87:hoare_1708887482_state), ((and ((P_29 A_87)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_87) X)) (P_29 X))))) ((insert528405184_state A_87) bot_bo19817387tate_o)))) (((P_29 A_87)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_87) X)) (P_29 X))))) bot_bo19817387tate_o)))) of role axiom named fact_345_Collect__conv__if2
% A new axiom: (forall (P_29:(hoare_1708887482_state->Prop)) (A_87:hoare_1708887482_state), ((and ((P_29 A_87)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_87) X)) (P_29 X))))) ((insert528405184_state A_87) bot_bo19817387tate_o)))) (((P_29 A_87)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_87) X)) (P_29 X))))) bot_bo19817387tate_o))))
% FOF formula (forall (P_29:(nat->Prop)) (A_87:nat), ((and ((P_29 A_87)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) A_87) X)) (P_29 X))))) ((insert_nat A_87) bot_bot_nat_o)))) (((P_29 A_87)->False)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) A_87) X)) (P_29 X))))) bot_bot_nat_o)))) of role axiom named fact_346_Collect__conv__if2
% A new axiom: (forall (P_29:(nat->Prop)) (A_87:nat), ((and ((P_29 A_87)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) A_87) X)) (P_29 X))))) ((insert_nat A_87) bot_bot_nat_o)))) (((P_29 A_87)->False)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) A_87) X)) (P_29 X))))) bot_bot_nat_o))))
% FOF formula (forall (P_28:((hoare_2091234717iple_a->Prop)->Prop)) (A_86:(hoare_2091234717iple_a->Prop)), ((and ((P_28 A_86)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) X) A_86)) (P_28 X))))) ((insert102003750le_a_o A_86) bot_bo1957696069_a_o_o)))) (((P_28 A_86)->False)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) X) A_86)) (P_28 X))))) bot_bo1957696069_a_o_o)))) of role axiom named fact_347_Collect__conv__if
% A new axiom: (forall (P_28:((hoare_2091234717iple_a->Prop)->Prop)) (A_86:(hoare_2091234717iple_a->Prop)), ((and ((P_28 A_86)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) X) A_86)) (P_28 X))))) ((insert102003750le_a_o A_86) bot_bo1957696069_a_o_o)))) (((P_28 A_86)->False)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) X) A_86)) (P_28 X))))) bot_bo1957696069_a_o_o))))
% FOF formula (forall (P_28:(pname->Prop)) (A_86:pname), ((and ((P_28 A_86)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_86)) (P_28 X))))) ((insert_pname A_86) bot_bot_pname_o)))) (((P_28 A_86)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_86)) (P_28 X))))) bot_bot_pname_o)))) of role axiom named fact_348_Collect__conv__if
% A new axiom: (forall (P_28:(pname->Prop)) (A_86:pname), ((and ((P_28 A_86)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_86)) (P_28 X))))) ((insert_pname A_86) bot_bot_pname_o)))) (((P_28 A_86)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_86)) (P_28 X))))) bot_bot_pname_o))))
% FOF formula (forall (P_28:(hoare_2091234717iple_a->Prop)) (A_86:hoare_2091234717iple_a), ((and ((P_28 A_86)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) X) A_86)) (P_28 X))))) ((insert1597628439iple_a A_86) bot_bo1791335050le_a_o)))) (((P_28 A_86)->False)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) X) A_86)) (P_28 X))))) bot_bo1791335050le_a_o)))) of role axiom named fact_349_Collect__conv__if
% A new axiom: (forall (P_28:(hoare_2091234717iple_a->Prop)) (A_86:hoare_2091234717iple_a), ((and ((P_28 A_86)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) X) A_86)) (P_28 X))))) ((insert1597628439iple_a A_86) bot_bo1791335050le_a_o)))) (((P_28 A_86)->False)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) X) A_86)) (P_28 X))))) bot_bo1791335050le_a_o))))
% FOF formula (forall (P_28:(hoare_1708887482_state->Prop)) (A_86:hoare_1708887482_state), ((and ((P_28 A_86)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X) A_86)) (P_28 X))))) ((insert528405184_state A_86) bot_bo19817387tate_o)))) (((P_28 A_86)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X) A_86)) (P_28 X))))) bot_bo19817387tate_o)))) of role axiom named fact_350_Collect__conv__if
% A new axiom: (forall (P_28:(hoare_1708887482_state->Prop)) (A_86:hoare_1708887482_state), ((and ((P_28 A_86)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X) A_86)) (P_28 X))))) ((insert528405184_state A_86) bot_bo19817387tate_o)))) (((P_28 A_86)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X) A_86)) (P_28 X))))) bot_bo19817387tate_o))))
% FOF formula (forall (P_28:(nat->Prop)) (A_86:nat), ((and ((P_28 A_86)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) X) A_86)) (P_28 X))))) ((insert_nat A_86) bot_bot_nat_o)))) (((P_28 A_86)->False)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) X) A_86)) (P_28 X))))) bot_bot_nat_o)))) of role axiom named fact_351_Collect__conv__if
% A new axiom: (forall (P_28:(nat->Prop)) (A_86:nat), ((and ((P_28 A_86)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) X) A_86)) (P_28 X))))) ((insert_nat A_86) bot_bot_nat_o)))) (((P_28 A_86)->False)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) X) A_86)) (P_28 X))))) bot_bot_nat_o))))
% FOF formula (forall (X_33:nat) (A_85:(nat->Prop)), ((iff ((member_nat X_33) A_85)) (A_85 X_33))) of role axiom named fact_352_mem__def
% A new axiom: (forall (X_33:nat) (A_85:(nat->Prop)), ((iff ((member_nat X_33) A_85)) (A_85 X_33)))
% FOF formula (forall (X_33:(hoare_2091234717iple_a->Prop)) (A_85:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o X_33) A_85)) (A_85 X_33))) of role axiom named fact_353_mem__def
% A new axiom: (forall (X_33:(hoare_2091234717iple_a->Prop)) (A_85:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o X_33) A_85)) (A_85 X_33)))
% FOF formula (forall (X_33:hoare_2091234717iple_a) (A_85:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a X_33) A_85)) (A_85 X_33))) of role axiom named fact_354_mem__def
% A new axiom: (forall (X_33:hoare_2091234717iple_a) (A_85:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a X_33) A_85)) (A_85 X_33)))
% FOF formula (forall (X_33:pname) (A_85:(pname->Prop)), ((iff ((member_pname X_33) A_85)) (A_85 X_33))) of role axiom named fact_355_mem__def
% A new axiom: (forall (X_33:pname) (A_85:(pname->Prop)), ((iff ((member_pname X_33) A_85)) (A_85 X_33)))
% FOF formula (forall (P_27:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_27)) P_27)) of role axiom named fact_356_Collect__def
% A new axiom: (forall (P_27:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_27)) P_27))
% FOF formula (forall (P_27:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a P_27)) P_27)) of role axiom named fact_357_Collect__def
% A new axiom: (forall (P_27:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a P_27)) P_27))
% FOF formula (forall (P_27:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_27)) P_27)) of role axiom named fact_358_Collect__def
% A new axiom: (forall (P_27:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_27)) P_27))
% FOF formula (forall (P_26:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_26))) (forall (X:pname), ((P_26 X)->False)))) of role axiom named fact_359_empty__Collect__eq
% A new axiom: (forall (P_26:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_26))) (forall (X:pname), ((P_26 X)->False))))
% FOF formula (forall (P_26:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) (collec992574898iple_a P_26))) (forall (X:hoare_2091234717iple_a), ((P_26 X)->False)))) of role axiom named fact_360_empty__Collect__eq
% A new axiom: (forall (P_26:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) (collec992574898iple_a P_26))) (forall (X:hoare_2091234717iple_a), ((P_26 X)->False))))
% FOF formula (forall (P_26:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) bot_bo1957696069_a_o_o) (collec1008234059le_a_o P_26))) (forall (X:(hoare_2091234717iple_a->Prop)), ((P_26 X)->False)))) of role axiom named fact_361_empty__Collect__eq
% A new axiom: (forall (P_26:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) bot_bo1957696069_a_o_o) (collec1008234059le_a_o P_26))) (forall (X:(hoare_2091234717iple_a->Prop)), ((P_26 X)->False))))
% FOF formula (forall (P_26:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state P_26))) (forall (X:hoare_1708887482_state), ((P_26 X)->False)))) of role axiom named fact_362_empty__Collect__eq
% A new axiom: (forall (P_26:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state P_26))) (forall (X:hoare_1708887482_state), ((P_26 X)->False))))
% FOF formula (forall (P_26:(nat->Prop)), ((iff (((eq (nat->Prop)) bot_bot_nat_o) (collect_nat P_26))) (forall (X:nat), ((P_26 X)->False)))) of role axiom named fact_363_empty__Collect__eq
% A new axiom: (forall (P_26:(nat->Prop)), ((iff (((eq (nat->Prop)) bot_bot_nat_o) (collect_nat P_26))) (forall (X:nat), ((P_26 X)->False))))
% FOF formula (forall (C_25:nat), (((member_nat C_25) bot_bot_nat_o)->False)) of role axiom named fact_364_empty__iff
% A new axiom: (forall (C_25:nat), (((member_nat C_25) bot_bot_nat_o)->False))
% FOF formula (forall (C_25:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o C_25) bot_bo1957696069_a_o_o)->False)) of role axiom named fact_365_empty__iff
% A new axiom: (forall (C_25:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o C_25) bot_bo1957696069_a_o_o)->False))
% FOF formula (forall (C_25:hoare_2091234717iple_a), (((member290856304iple_a C_25) bot_bo1791335050le_a_o)->False)) of role axiom named fact_366_empty__iff
% A new axiom: (forall (C_25:hoare_2091234717iple_a), (((member290856304iple_a C_25) bot_bo1791335050le_a_o)->False))
% FOF formula (forall (C_25:hoare_1708887482_state), (((member451959335_state C_25) bot_bo19817387tate_o)->False)) of role axiom named fact_367_empty__iff
% A new axiom: (forall (C_25:hoare_1708887482_state), (((member451959335_state C_25) bot_bo19817387tate_o)->False))
% FOF formula (forall (C_25:pname), (((member_pname C_25) bot_bot_pname_o)->False)) of role axiom named fact_368_empty__iff
% A new axiom: (forall (C_25:pname), (((member_pname C_25) bot_bot_pname_o)->False))
% FOF formula (forall (A_84:(hoare_2091234717iple_a->Prop)) (B_43:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_84) B_43)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or (((eq (hoare_2091234717iple_a->Prop)) X) A_84)) ((member99268621le_a_o X) B_43)))))) of role axiom named fact_369_insert__compr
% A new axiom: (forall (A_84:(hoare_2091234717iple_a->Prop)) (B_43:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_84) B_43)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or (((eq (hoare_2091234717iple_a->Prop)) X) A_84)) ((member99268621le_a_o X) B_43))))))
% FOF formula (forall (A_84:hoare_2091234717iple_a) (B_43:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_84) B_43)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or (((eq hoare_2091234717iple_a) X) A_84)) ((member290856304iple_a X) B_43)))))) of role axiom named fact_370_insert__compr
% A new axiom: (forall (A_84:hoare_2091234717iple_a) (B_43:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_84) B_43)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or (((eq hoare_2091234717iple_a) X) A_84)) ((member290856304iple_a X) B_43))))))
% FOF formula (forall (A_84:hoare_1708887482_state) (B_43:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_84) B_43)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) X) A_84)) ((member451959335_state X) B_43)))))) of role axiom named fact_371_insert__compr
% A new axiom: (forall (A_84:hoare_1708887482_state) (B_43:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_84) B_43)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) X) A_84)) ((member451959335_state X) B_43))))))
% FOF formula (forall (A_84:nat) (B_43:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_84) B_43)) (collect_nat (fun (X:nat)=> ((or (((eq nat) X) A_84)) ((member_nat X) B_43)))))) of role axiom named fact_372_insert__compr
% A new axiom: (forall (A_84:nat) (B_43:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_84) B_43)) (collect_nat (fun (X:nat)=> ((or (((eq nat) X) A_84)) ((member_nat X) B_43))))))
% FOF formula (forall (A_84:pname) (B_43:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_84) B_43)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_84)) ((member_pname X) B_43)))))) of role axiom named fact_373_insert__compr
% A new axiom: (forall (A_84:pname) (B_43:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_84) B_43)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_84)) ((member_pname X) B_43))))))
% FOF formula (forall (A_83:(hoare_2091234717iple_a->Prop)) (P_25:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_83) (collec1008234059le_a_o P_25))) (collec1008234059le_a_o (fun (U_2:(hoare_2091234717iple_a->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_2091234717iple_a->Prop)) U_2) A_83))) (P_25 U_2)))))) of role axiom named fact_374_insert__Collect
% A new axiom: (forall (A_83:(hoare_2091234717iple_a->Prop)) (P_25:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_83) (collec1008234059le_a_o P_25))) (collec1008234059le_a_o (fun (U_2:(hoare_2091234717iple_a->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_2091234717iple_a->Prop)) U_2) A_83))) (P_25 U_2))))))
% FOF formula (forall (A_83:pname) (P_25:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_83) (collect_pname P_25))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_83))) (P_25 U_2)))))) of role axiom named fact_375_insert__Collect
% A new axiom: (forall (A_83:pname) (P_25:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_83) (collect_pname P_25))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_83))) (P_25 U_2))))))
% FOF formula (forall (A_83:hoare_2091234717iple_a) (P_25:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_83) (collec992574898iple_a P_25))) (collec992574898iple_a (fun (U_2:hoare_2091234717iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_2091234717iple_a) U_2) A_83))) (P_25 U_2)))))) of role axiom named fact_376_insert__Collect
% A new axiom: (forall (A_83:hoare_2091234717iple_a) (P_25:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_83) (collec992574898iple_a P_25))) (collec992574898iple_a (fun (U_2:hoare_2091234717iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_2091234717iple_a) U_2) A_83))) (P_25 U_2))))))
% FOF formula (forall (A_83:hoare_1708887482_state) (P_25:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_83) (collec1568722789_state P_25))) (collec1568722789_state (fun (U_2:hoare_1708887482_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1708887482_state) U_2) A_83))) (P_25 U_2)))))) of role axiom named fact_377_insert__Collect
% A new axiom: (forall (A_83:hoare_1708887482_state) (P_25:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_83) (collec1568722789_state P_25))) (collec1568722789_state (fun (U_2:hoare_1708887482_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1708887482_state) U_2) A_83))) (P_25 U_2))))))
% FOF formula (forall (A_83:nat) (P_25:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_83) (collect_nat P_25))) (collect_nat (fun (U_2:nat)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq nat) U_2) A_83))) (P_25 U_2)))))) of role axiom named fact_378_insert__Collect
% A new axiom: (forall (A_83:nat) (P_25:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_83) (collect_nat P_25))) (collect_nat (fun (U_2:nat)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq nat) U_2) A_83))) (P_25 U_2))))))
% FOF formula (forall (B_42:nat) (A_82:nat), ((iff ((member_nat B_42) ((insert_nat A_82) bot_bot_nat_o))) (((eq nat) B_42) A_82))) of role axiom named fact_379_singleton__iff
% A new axiom: (forall (B_42:nat) (A_82:nat), ((iff ((member_nat B_42) ((insert_nat A_82) bot_bot_nat_o))) (((eq nat) B_42) A_82)))
% FOF formula (forall (B_42:(hoare_2091234717iple_a->Prop)) (A_82:(hoare_2091234717iple_a->Prop)), ((iff ((member99268621le_a_o B_42) ((insert102003750le_a_o A_82) bot_bo1957696069_a_o_o))) (((eq (hoare_2091234717iple_a->Prop)) B_42) A_82))) of role axiom named fact_380_singleton__iff
% A new axiom: (forall (B_42:(hoare_2091234717iple_a->Prop)) (A_82:(hoare_2091234717iple_a->Prop)), ((iff ((member99268621le_a_o B_42) ((insert102003750le_a_o A_82) bot_bo1957696069_a_o_o))) (((eq (hoare_2091234717iple_a->Prop)) B_42) A_82)))
% FOF formula (forall (B_42:hoare_2091234717iple_a) (A_82:hoare_2091234717iple_a), ((iff ((member290856304iple_a B_42) ((insert1597628439iple_a A_82) bot_bo1791335050le_a_o))) (((eq hoare_2091234717iple_a) B_42) A_82))) of role axiom named fact_381_singleton__iff
% A new axiom: (forall (B_42:hoare_2091234717iple_a) (A_82:hoare_2091234717iple_a), ((iff ((member290856304iple_a B_42) ((insert1597628439iple_a A_82) bot_bo1791335050le_a_o))) (((eq hoare_2091234717iple_a) B_42) A_82)))
% FOF formula (forall (B_42:hoare_1708887482_state) (A_82:hoare_1708887482_state), ((iff ((member451959335_state B_42) ((insert528405184_state A_82) bot_bo19817387tate_o))) (((eq hoare_1708887482_state) B_42) A_82))) of role axiom named fact_382_singleton__iff
% A new axiom: (forall (B_42:hoare_1708887482_state) (A_82:hoare_1708887482_state), ((iff ((member451959335_state B_42) ((insert528405184_state A_82) bot_bo19817387tate_o))) (((eq hoare_1708887482_state) B_42) A_82)))
% FOF formula (forall (B_42:pname) (A_82:pname), ((iff ((member_pname B_42) ((insert_pname A_82) bot_bot_pname_o))) (((eq pname) B_42) A_82))) of role axiom named fact_383_singleton__iff
% A new axiom: (forall (B_42:pname) (A_82:pname), ((iff ((member_pname B_42) ((insert_pname A_82) bot_bot_pname_o))) (((eq pname) B_42) A_82)))
% FOF formula (forall (X_32:nat) (A_81:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_32) ((insert_nat X_32) A_81))) ((insert_nat X_32) A_81))) of role axiom named fact_384_insert__absorb2
% A new axiom: (forall (X_32:nat) (A_81:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_32) ((insert_nat X_32) A_81))) ((insert_nat X_32) A_81)))
% FOF formula (forall (X_32:(hoare_2091234717iple_a->Prop)) (A_81:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X_32) ((insert102003750le_a_o X_32) A_81))) ((insert102003750le_a_o X_32) A_81))) of role axiom named fact_385_insert__absorb2
% A new axiom: (forall (X_32:(hoare_2091234717iple_a->Prop)) (A_81:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X_32) ((insert102003750le_a_o X_32) A_81))) ((insert102003750le_a_o X_32) A_81)))
% FOF formula (forall (X_32:pname) (A_81:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_32) ((insert_pname X_32) A_81))) ((insert_pname X_32) A_81))) of role axiom named fact_386_insert__absorb2
% A new axiom: (forall (X_32:pname) (A_81:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_32) ((insert_pname X_32) A_81))) ((insert_pname X_32) A_81)))
% FOF formula (forall (X_32:hoare_2091234717iple_a) (A_81:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X_32) ((insert1597628439iple_a X_32) A_81))) ((insert1597628439iple_a X_32) A_81))) of role axiom named fact_387_insert__absorb2
% A new axiom: (forall (X_32:hoare_2091234717iple_a) (A_81:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X_32) ((insert1597628439iple_a X_32) A_81))) ((insert1597628439iple_a X_32) A_81)))
% FOF formula (forall (X_32:hoare_1708887482_state) (A_81:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_32) ((insert528405184_state X_32) A_81))) ((insert528405184_state X_32) A_81))) of role axiom named fact_388_insert__absorb2
% A new axiom: (forall (X_32:hoare_1708887482_state) (A_81:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_32) ((insert528405184_state X_32) A_81))) ((insert528405184_state X_32) A_81)))
% FOF formula (forall (X_31:nat) (Y_10:nat) (A_80:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_31) ((insert_nat Y_10) A_80))) ((insert_nat Y_10) ((insert_nat X_31) A_80)))) of role axiom named fact_389_insert__commute
% A new axiom: (forall (X_31:nat) (Y_10:nat) (A_80:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_31) ((insert_nat Y_10) A_80))) ((insert_nat Y_10) ((insert_nat X_31) A_80))))
% FOF formula (forall (X_31:(hoare_2091234717iple_a->Prop)) (Y_10:(hoare_2091234717iple_a->Prop)) (A_80:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X_31) ((insert102003750le_a_o Y_10) A_80))) ((insert102003750le_a_o Y_10) ((insert102003750le_a_o X_31) A_80)))) of role axiom named fact_390_insert__commute
% A new axiom: (forall (X_31:(hoare_2091234717iple_a->Prop)) (Y_10:(hoare_2091234717iple_a->Prop)) (A_80:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X_31) ((insert102003750le_a_o Y_10) A_80))) ((insert102003750le_a_o Y_10) ((insert102003750le_a_o X_31) A_80))))
% FOF formula (forall (X_31:pname) (Y_10:pname) (A_80:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_31) ((insert_pname Y_10) A_80))) ((insert_pname Y_10) ((insert_pname X_31) A_80)))) of role axiom named fact_391_insert__commute
% A new axiom: (forall (X_31:pname) (Y_10:pname) (A_80:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_31) ((insert_pname Y_10) A_80))) ((insert_pname Y_10) ((insert_pname X_31) A_80))))
% FOF formula (forall (X_31:hoare_2091234717iple_a) (Y_10:hoare_2091234717iple_a) (A_80:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X_31) ((insert1597628439iple_a Y_10) A_80))) ((insert1597628439iple_a Y_10) ((insert1597628439iple_a X_31) A_80)))) of role axiom named fact_392_insert__commute
% A new axiom: (forall (X_31:hoare_2091234717iple_a) (Y_10:hoare_2091234717iple_a) (A_80:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X_31) ((insert1597628439iple_a Y_10) A_80))) ((insert1597628439iple_a Y_10) ((insert1597628439iple_a X_31) A_80))))
% FOF formula (forall (X_31:hoare_1708887482_state) (Y_10:hoare_1708887482_state) (A_80:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_31) ((insert528405184_state Y_10) A_80))) ((insert528405184_state Y_10) ((insert528405184_state X_31) A_80)))) of role axiom named fact_393_insert__commute
% A new axiom: (forall (X_31:hoare_1708887482_state) (Y_10:hoare_1708887482_state) (A_80:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_31) ((insert528405184_state Y_10) A_80))) ((insert528405184_state Y_10) ((insert528405184_state X_31) A_80))))
% FOF formula (forall (A_79:nat) (B_41:nat) (A_78:(nat->Prop)), ((iff ((member_nat A_79) ((insert_nat B_41) A_78))) ((or (((eq nat) A_79) B_41)) ((member_nat A_79) A_78)))) of role axiom named fact_394_insert__iff
% A new axiom: (forall (A_79:nat) (B_41:nat) (A_78:(nat->Prop)), ((iff ((member_nat A_79) ((insert_nat B_41) A_78))) ((or (((eq nat) A_79) B_41)) ((member_nat A_79) A_78))))
% FOF formula (forall (A_79:(hoare_2091234717iple_a->Prop)) (B_41:(hoare_2091234717iple_a->Prop)) (A_78:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o A_79) ((insert102003750le_a_o B_41) A_78))) ((or (((eq (hoare_2091234717iple_a->Prop)) A_79) B_41)) ((member99268621le_a_o A_79) A_78)))) of role axiom named fact_395_insert__iff
% A new axiom: (forall (A_79:(hoare_2091234717iple_a->Prop)) (B_41:(hoare_2091234717iple_a->Prop)) (A_78:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o A_79) ((insert102003750le_a_o B_41) A_78))) ((or (((eq (hoare_2091234717iple_a->Prop)) A_79) B_41)) ((member99268621le_a_o A_79) A_78))))
% FOF formula (forall (A_79:hoare_2091234717iple_a) (B_41:hoare_2091234717iple_a) (A_78:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a A_79) ((insert1597628439iple_a B_41) A_78))) ((or (((eq hoare_2091234717iple_a) A_79) B_41)) ((member290856304iple_a A_79) A_78)))) of role axiom named fact_396_insert__iff
% A new axiom: (forall (A_79:hoare_2091234717iple_a) (B_41:hoare_2091234717iple_a) (A_78:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a A_79) ((insert1597628439iple_a B_41) A_78))) ((or (((eq hoare_2091234717iple_a) A_79) B_41)) ((member290856304iple_a A_79) A_78))))
% FOF formula (forall (A_79:hoare_1708887482_state) (B_41:hoare_1708887482_state) (A_78:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state A_79) ((insert528405184_state B_41) A_78))) ((or (((eq hoare_1708887482_state) A_79) B_41)) ((member451959335_state A_79) A_78)))) of role axiom named fact_397_insert__iff
% A new axiom: (forall (A_79:hoare_1708887482_state) (B_41:hoare_1708887482_state) (A_78:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state A_79) ((insert528405184_state B_41) A_78))) ((or (((eq hoare_1708887482_state) A_79) B_41)) ((member451959335_state A_79) A_78))))
% FOF formula (forall (A_79:pname) (B_41:pname) (A_78:(pname->Prop)), ((iff ((member_pname A_79) ((insert_pname B_41) A_78))) ((or (((eq pname) A_79) B_41)) ((member_pname A_79) A_78)))) of role axiom named fact_398_insert__iff
% A new axiom: (forall (A_79:pname) (B_41:pname) (A_78:(pname->Prop)), ((iff ((member_pname A_79) ((insert_pname B_41) A_78))) ((or (((eq pname) A_79) B_41)) ((member_pname A_79) A_78))))
% FOF formula (forall (P_24:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_24)) bot_bot_pname_o)) (forall (X:pname), ((P_24 X)->False)))) of role axiom named fact_399_Collect__empty__eq
% A new axiom: (forall (P_24:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_24)) bot_bot_pname_o)) (forall (X:pname), ((P_24 X)->False))))
% FOF formula (forall (P_24:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a P_24)) bot_bo1791335050le_a_o)) (forall (X:hoare_2091234717iple_a), ((P_24 X)->False)))) of role axiom named fact_400_Collect__empty__eq
% A new axiom: (forall (P_24:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a P_24)) bot_bo1791335050le_a_o)) (forall (X:hoare_2091234717iple_a), ((P_24 X)->False))))
% FOF formula (forall (P_24:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o P_24)) bot_bo1957696069_a_o_o)) (forall (X:(hoare_2091234717iple_a->Prop)), ((P_24 X)->False)))) of role axiom named fact_401_Collect__empty__eq
% A new axiom: (forall (P_24:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o P_24)) bot_bo1957696069_a_o_o)) (forall (X:(hoare_2091234717iple_a->Prop)), ((P_24 X)->False))))
% FOF formula (forall (P_24:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state P_24)) bot_bo19817387tate_o)) (forall (X:hoare_1708887482_state), ((P_24 X)->False)))) of role axiom named fact_402_Collect__empty__eq
% A new axiom: (forall (P_24:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state P_24)) bot_bo19817387tate_o)) (forall (X:hoare_1708887482_state), ((P_24 X)->False))))
% FOF formula (forall (P_24:(nat->Prop)), ((iff (((eq (nat->Prop)) (collect_nat P_24)) bot_bot_nat_o)) (forall (X:nat), ((P_24 X)->False)))) of role axiom named fact_403_Collect__empty__eq
% A new axiom: (forall (P_24:(nat->Prop)), ((iff (((eq (nat->Prop)) (collect_nat P_24)) bot_bot_nat_o)) (forall (X:nat), ((P_24 X)->False))))
% FOF formula (forall (A_77:nat) (B_40:nat) (C_24:nat) (D_1:nat), ((iff (((eq (nat->Prop)) ((insert_nat A_77) ((insert_nat B_40) bot_bot_nat_o))) ((insert_nat C_24) ((insert_nat D_1) bot_bot_nat_o)))) ((or ((and (((eq nat) A_77) C_24)) (((eq nat) B_40) D_1))) ((and (((eq nat) A_77) D_1)) (((eq nat) B_40) C_24))))) of role axiom named fact_404_doubleton__eq__iff
% A new axiom: (forall (A_77:nat) (B_40:nat) (C_24:nat) (D_1:nat), ((iff (((eq (nat->Prop)) ((insert_nat A_77) ((insert_nat B_40) bot_bot_nat_o))) ((insert_nat C_24) ((insert_nat D_1) bot_bot_nat_o)))) ((or ((and (((eq nat) A_77) C_24)) (((eq nat) B_40) D_1))) ((and (((eq nat) A_77) D_1)) (((eq nat) B_40) C_24)))))
% FOF formula (forall (A_77:(hoare_2091234717iple_a->Prop)) (B_40:(hoare_2091234717iple_a->Prop)) (C_24:(hoare_2091234717iple_a->Prop)) (D_1:(hoare_2091234717iple_a->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_77) ((insert102003750le_a_o B_40) bot_bo1957696069_a_o_o))) ((insert102003750le_a_o C_24) ((insert102003750le_a_o D_1) bot_bo1957696069_a_o_o)))) ((or ((and (((eq (hoare_2091234717iple_a->Prop)) A_77) C_24)) (((eq (hoare_2091234717iple_a->Prop)) B_40) D_1))) ((and (((eq (hoare_2091234717iple_a->Prop)) A_77) D_1)) (((eq (hoare_2091234717iple_a->Prop)) B_40) C_24))))) of role axiom named fact_405_doubleton__eq__iff
% A new axiom: (forall (A_77:(hoare_2091234717iple_a->Prop)) (B_40:(hoare_2091234717iple_a->Prop)) (C_24:(hoare_2091234717iple_a->Prop)) (D_1:(hoare_2091234717iple_a->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_77) ((insert102003750le_a_o B_40) bot_bo1957696069_a_o_o))) ((insert102003750le_a_o C_24) ((insert102003750le_a_o D_1) bot_bo1957696069_a_o_o)))) ((or ((and (((eq (hoare_2091234717iple_a->Prop)) A_77) C_24)) (((eq (hoare_2091234717iple_a->Prop)) B_40) D_1))) ((and (((eq (hoare_2091234717iple_a->Prop)) A_77) D_1)) (((eq (hoare_2091234717iple_a->Prop)) B_40) C_24)))))
% FOF formula (forall (A_77:pname) (B_40:pname) (C_24:pname) (D_1:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_77) ((insert_pname B_40) bot_bot_pname_o))) ((insert_pname C_24) ((insert_pname D_1) bot_bot_pname_o)))) ((or ((and (((eq pname) A_77) C_24)) (((eq pname) B_40) D_1))) ((and (((eq pname) A_77) D_1)) (((eq pname) B_40) C_24))))) of role axiom named fact_406_doubleton__eq__iff
% A new axiom: (forall (A_77:pname) (B_40:pname) (C_24:pname) (D_1:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_77) ((insert_pname B_40) bot_bot_pname_o))) ((insert_pname C_24) ((insert_pname D_1) bot_bot_pname_o)))) ((or ((and (((eq pname) A_77) C_24)) (((eq pname) B_40) D_1))) ((and (((eq pname) A_77) D_1)) (((eq pname) B_40) C_24)))))
% FOF formula (forall (A_77:hoare_2091234717iple_a) (B_40:hoare_2091234717iple_a) (C_24:hoare_2091234717iple_a) (D_1:hoare_2091234717iple_a), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_77) ((insert1597628439iple_a B_40) bot_bo1791335050le_a_o))) ((insert1597628439iple_a C_24) ((insert1597628439iple_a D_1) bot_bo1791335050le_a_o)))) ((or ((and (((eq hoare_2091234717iple_a) A_77) C_24)) (((eq hoare_2091234717iple_a) B_40) D_1))) ((and (((eq hoare_2091234717iple_a) A_77) D_1)) (((eq hoare_2091234717iple_a) B_40) C_24))))) of role axiom named fact_407_doubleton__eq__iff
% A new axiom: (forall (A_77:hoare_2091234717iple_a) (B_40:hoare_2091234717iple_a) (C_24:hoare_2091234717iple_a) (D_1:hoare_2091234717iple_a), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_77) ((insert1597628439iple_a B_40) bot_bo1791335050le_a_o))) ((insert1597628439iple_a C_24) ((insert1597628439iple_a D_1) bot_bo1791335050le_a_o)))) ((or ((and (((eq hoare_2091234717iple_a) A_77) C_24)) (((eq hoare_2091234717iple_a) B_40) D_1))) ((and (((eq hoare_2091234717iple_a) A_77) D_1)) (((eq hoare_2091234717iple_a) B_40) C_24)))))
% FOF formula (forall (A_77:hoare_1708887482_state) (B_40:hoare_1708887482_state) (C_24:hoare_1708887482_state) (D_1:hoare_1708887482_state), ((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_77) ((insert528405184_state B_40) bot_bo19817387tate_o))) ((insert528405184_state C_24) ((insert528405184_state D_1) bot_bo19817387tate_o)))) ((or ((and (((eq hoare_1708887482_state) A_77) C_24)) (((eq hoare_1708887482_state) B_40) D_1))) ((and (((eq hoare_1708887482_state) A_77) D_1)) (((eq hoare_1708887482_state) B_40) C_24))))) of role axiom named fact_408_doubleton__eq__iff
% A new axiom: (forall (A_77:hoare_1708887482_state) (B_40:hoare_1708887482_state) (C_24:hoare_1708887482_state) (D_1:hoare_1708887482_state), ((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_77) ((insert528405184_state B_40) bot_bo19817387tate_o))) ((insert528405184_state C_24) ((insert528405184_state D_1) bot_bo19817387tate_o)))) ((or ((and (((eq hoare_1708887482_state) A_77) C_24)) (((eq hoare_1708887482_state) B_40) D_1))) ((and (((eq hoare_1708887482_state) A_77) D_1)) (((eq hoare_1708887482_state) B_40) C_24)))))
% FOF formula (forall (Y_9:nat) (A_76:(nat->Prop)) (X_30:nat), ((iff (((insert_nat Y_9) A_76) X_30)) ((or (((eq nat) Y_9) X_30)) (A_76 X_30)))) of role axiom named fact_409_insert__code
% A new axiom: (forall (Y_9:nat) (A_76:(nat->Prop)) (X_30:nat), ((iff (((insert_nat Y_9) A_76) X_30)) ((or (((eq nat) Y_9) X_30)) (A_76 X_30))))
% FOF formula (forall (Y_9:(hoare_2091234717iple_a->Prop)) (A_76:((hoare_2091234717iple_a->Prop)->Prop)) (X_30:(hoare_2091234717iple_a->Prop)), ((iff (((insert102003750le_a_o Y_9) A_76) X_30)) ((or (((eq (hoare_2091234717iple_a->Prop)) Y_9) X_30)) (A_76 X_30)))) of role axiom named fact_410_insert__code
% A new axiom: (forall (Y_9:(hoare_2091234717iple_a->Prop)) (A_76:((hoare_2091234717iple_a->Prop)->Prop)) (X_30:(hoare_2091234717iple_a->Prop)), ((iff (((insert102003750le_a_o Y_9) A_76) X_30)) ((or (((eq (hoare_2091234717iple_a->Prop)) Y_9) X_30)) (A_76 X_30))))
% FOF formula (forall (Y_9:pname) (A_76:(pname->Prop)) (X_30:pname), ((iff (((insert_pname Y_9) A_76) X_30)) ((or (((eq pname) Y_9) X_30)) (A_76 X_30)))) of role axiom named fact_411_insert__code
% A new axiom: (forall (Y_9:pname) (A_76:(pname->Prop)) (X_30:pname), ((iff (((insert_pname Y_9) A_76) X_30)) ((or (((eq pname) Y_9) X_30)) (A_76 X_30))))
% FOF formula (forall (Y_9:hoare_2091234717iple_a) (A_76:(hoare_2091234717iple_a->Prop)) (X_30:hoare_2091234717iple_a), ((iff (((insert1597628439iple_a Y_9) A_76) X_30)) ((or (((eq hoare_2091234717iple_a) Y_9) X_30)) (A_76 X_30)))) of role axiom named fact_412_insert__code
% A new axiom: (forall (Y_9:hoare_2091234717iple_a) (A_76:(hoare_2091234717iple_a->Prop)) (X_30:hoare_2091234717iple_a), ((iff (((insert1597628439iple_a Y_9) A_76) X_30)) ((or (((eq hoare_2091234717iple_a) Y_9) X_30)) (A_76 X_30))))
% FOF formula (forall (Y_9:hoare_1708887482_state) (A_76:(hoare_1708887482_state->Prop)) (X_30:hoare_1708887482_state), ((iff (((insert528405184_state Y_9) A_76) X_30)) ((or (((eq hoare_1708887482_state) Y_9) X_30)) (A_76 X_30)))) of role axiom named fact_413_insert__code
% A new axiom: (forall (Y_9:hoare_1708887482_state) (A_76:(hoare_1708887482_state->Prop)) (X_30:hoare_1708887482_state), ((iff (((insert528405184_state Y_9) A_76) X_30)) ((or (((eq hoare_1708887482_state) Y_9) X_30)) (A_76 X_30))))
% FOF formula (forall (B_39:(nat->Prop)) (X_29:nat) (A_75:(nat->Prop)), ((((member_nat X_29) A_75)->False)->((((member_nat X_29) B_39)->False)->((iff (((eq (nat->Prop)) ((insert_nat X_29) A_75)) ((insert_nat X_29) B_39))) (((eq (nat->Prop)) A_75) B_39))))) of role axiom named fact_414_insert__ident
% A new axiom: (forall (B_39:(nat->Prop)) (X_29:nat) (A_75:(nat->Prop)), ((((member_nat X_29) A_75)->False)->((((member_nat X_29) B_39)->False)->((iff (((eq (nat->Prop)) ((insert_nat X_29) A_75)) ((insert_nat X_29) B_39))) (((eq (nat->Prop)) A_75) B_39)))))
% FOF formula (forall (B_39:((hoare_2091234717iple_a->Prop)->Prop)) (X_29:(hoare_2091234717iple_a->Prop)) (A_75:((hoare_2091234717iple_a->Prop)->Prop)), ((((member99268621le_a_o X_29) A_75)->False)->((((member99268621le_a_o X_29) B_39)->False)->((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X_29) A_75)) ((insert102003750le_a_o X_29) B_39))) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_75) B_39))))) of role axiom named fact_415_insert__ident
% A new axiom: (forall (B_39:((hoare_2091234717iple_a->Prop)->Prop)) (X_29:(hoare_2091234717iple_a->Prop)) (A_75:((hoare_2091234717iple_a->Prop)->Prop)), ((((member99268621le_a_o X_29) A_75)->False)->((((member99268621le_a_o X_29) B_39)->False)->((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X_29) A_75)) ((insert102003750le_a_o X_29) B_39))) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_75) B_39)))))
% FOF formula (forall (B_39:(hoare_2091234717iple_a->Prop)) (X_29:hoare_2091234717iple_a) (A_75:(hoare_2091234717iple_a->Prop)), ((((member290856304iple_a X_29) A_75)->False)->((((member290856304iple_a X_29) B_39)->False)->((iff (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X_29) A_75)) ((insert1597628439iple_a X_29) B_39))) (((eq (hoare_2091234717iple_a->Prop)) A_75) B_39))))) of role axiom named fact_416_insert__ident
% A new axiom: (forall (B_39:(hoare_2091234717iple_a->Prop)) (X_29:hoare_2091234717iple_a) (A_75:(hoare_2091234717iple_a->Prop)), ((((member290856304iple_a X_29) A_75)->False)->((((member290856304iple_a X_29) B_39)->False)->((iff (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X_29) A_75)) ((insert1597628439iple_a X_29) B_39))) (((eq (hoare_2091234717iple_a->Prop)) A_75) B_39)))))
% FOF formula (forall (B_39:(hoare_1708887482_state->Prop)) (X_29:hoare_1708887482_state) (A_75:(hoare_1708887482_state->Prop)), ((((member451959335_state X_29) A_75)->False)->((((member451959335_state X_29) B_39)->False)->((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_29) A_75)) ((insert528405184_state X_29) B_39))) (((eq (hoare_1708887482_state->Prop)) A_75) B_39))))) of role axiom named fact_417_insert__ident
% A new axiom: (forall (B_39:(hoare_1708887482_state->Prop)) (X_29:hoare_1708887482_state) (A_75:(hoare_1708887482_state->Prop)), ((((member451959335_state X_29) A_75)->False)->((((member451959335_state X_29) B_39)->False)->((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_29) A_75)) ((insert528405184_state X_29) B_39))) (((eq (hoare_1708887482_state->Prop)) A_75) B_39)))))
% FOF formula (forall (B_39:(pname->Prop)) (X_29:pname) (A_75:(pname->Prop)), ((((member_pname X_29) A_75)->False)->((((member_pname X_29) B_39)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_29) A_75)) ((insert_pname X_29) B_39))) (((eq (pname->Prop)) A_75) B_39))))) of role axiom named fact_418_insert__ident
% A new axiom: (forall (B_39:(pname->Prop)) (X_29:pname) (A_75:(pname->Prop)), ((((member_pname X_29) A_75)->False)->((((member_pname X_29) B_39)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_29) A_75)) ((insert_pname X_29) B_39))) (((eq (pname->Prop)) A_75) B_39)))))
% FOF formula (forall (A_74:nat) (A_73:(nat->Prop)), ((((eq (nat->Prop)) A_73) bot_bot_nat_o)->(((member_nat A_74) A_73)->False))) of role axiom named fact_419_equals0D
% A new axiom: (forall (A_74:nat) (A_73:(nat->Prop)), ((((eq (nat->Prop)) A_73) bot_bot_nat_o)->(((member_nat A_74) A_73)->False)))
% FOF formula (forall (A_74:(hoare_2091234717iple_a->Prop)) (A_73:((hoare_2091234717iple_a->Prop)->Prop)), ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_73) bot_bo1957696069_a_o_o)->(((member99268621le_a_o A_74) A_73)->False))) of role axiom named fact_420_equals0D
% A new axiom: (forall (A_74:(hoare_2091234717iple_a->Prop)) (A_73:((hoare_2091234717iple_a->Prop)->Prop)), ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_73) bot_bo1957696069_a_o_o)->(((member99268621le_a_o A_74) A_73)->False)))
% FOF formula (forall (A_74:hoare_2091234717iple_a) (A_73:(hoare_2091234717iple_a->Prop)), ((((eq (hoare_2091234717iple_a->Prop)) A_73) bot_bo1791335050le_a_o)->(((member290856304iple_a A_74) A_73)->False))) of role axiom named fact_421_equals0D
% A new axiom: (forall (A_74:hoare_2091234717iple_a) (A_73:(hoare_2091234717iple_a->Prop)), ((((eq (hoare_2091234717iple_a->Prop)) A_73) bot_bo1791335050le_a_o)->(((member290856304iple_a A_74) A_73)->False)))
% FOF formula (forall (A_74:hoare_1708887482_state) (A_73:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_73) bot_bo19817387tate_o)->(((member451959335_state A_74) A_73)->False))) of role axiom named fact_422_equals0D
% A new axiom: (forall (A_74:hoare_1708887482_state) (A_73:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_73) bot_bo19817387tate_o)->(((member451959335_state A_74) A_73)->False)))
% FOF formula (forall (A_74:pname) (A_73:(pname->Prop)), ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((member_pname A_74) A_73)->False))) of role axiom named fact_423_equals0D
% A new axiom: (forall (A_74:pname) (A_73:(pname->Prop)), ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((member_pname A_74) A_73)->False)))
% FOF formula (forall (B_38:nat) (A_72:nat) (B_37:(nat->Prop)), (((member_nat A_72) B_37)->((member_nat A_72) ((insert_nat B_38) B_37)))) of role axiom named fact_424_insertI2
% A new axiom: (forall (B_38:nat) (A_72:nat) (B_37:(nat->Prop)), (((member_nat A_72) B_37)->((member_nat A_72) ((insert_nat B_38) B_37))))
% FOF formula (forall (B_38:(hoare_2091234717iple_a->Prop)) (A_72:(hoare_2091234717iple_a->Prop)) (B_37:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_72) B_37)->((member99268621le_a_o A_72) ((insert102003750le_a_o B_38) B_37)))) of role axiom named fact_425_insertI2
% A new axiom: (forall (B_38:(hoare_2091234717iple_a->Prop)) (A_72:(hoare_2091234717iple_a->Prop)) (B_37:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_72) B_37)->((member99268621le_a_o A_72) ((insert102003750le_a_o B_38) B_37))))
% FOF formula (forall (B_38:hoare_2091234717iple_a) (A_72:hoare_2091234717iple_a) (B_37:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_72) B_37)->((member290856304iple_a A_72) ((insert1597628439iple_a B_38) B_37)))) of role axiom named fact_426_insertI2
% A new axiom: (forall (B_38:hoare_2091234717iple_a) (A_72:hoare_2091234717iple_a) (B_37:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_72) B_37)->((member290856304iple_a A_72) ((insert1597628439iple_a B_38) B_37))))
% FOF formula (forall (B_38:hoare_1708887482_state) (A_72:hoare_1708887482_state) (B_37:(hoare_1708887482_state->Prop)), (((member451959335_state A_72) B_37)->((member451959335_state A_72) ((insert528405184_state B_38) B_37)))) of role axiom named fact_427_insertI2
% A new axiom: (forall (B_38:hoare_1708887482_state) (A_72:hoare_1708887482_state) (B_37:(hoare_1708887482_state->Prop)), (((member451959335_state A_72) B_37)->((member451959335_state A_72) ((insert528405184_state B_38) B_37))))
% FOF formula (forall (B_38:pname) (A_72:pname) (B_37:(pname->Prop)), (((member_pname A_72) B_37)->((member_pname A_72) ((insert_pname B_38) B_37)))) of role axiom named fact_428_insertI2
% A new axiom: (forall (B_38:pname) (A_72:pname) (B_37:(pname->Prop)), (((member_pname A_72) B_37)->((member_pname A_72) ((insert_pname B_38) B_37))))
% FOF formula (forall (A_71:nat) (A_70:(nat->Prop)), (((member_nat A_71) A_70)->(((eq (nat->Prop)) ((insert_nat A_71) A_70)) A_70))) of role axiom named fact_429_insert__absorb
% A new axiom: (forall (A_71:nat) (A_70:(nat->Prop)), (((member_nat A_71) A_70)->(((eq (nat->Prop)) ((insert_nat A_71) A_70)) A_70)))
% FOF formula (forall (A_71:(hoare_2091234717iple_a->Prop)) (A_70:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_71) A_70)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_71) A_70)) A_70))) of role axiom named fact_430_insert__absorb
% A new axiom: (forall (A_71:(hoare_2091234717iple_a->Prop)) (A_70:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_71) A_70)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_71) A_70)) A_70)))
% FOF formula (forall (A_71:hoare_2091234717iple_a) (A_70:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_71) A_70)->(((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_71) A_70)) A_70))) of role axiom named fact_431_insert__absorb
% A new axiom: (forall (A_71:hoare_2091234717iple_a) (A_70:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_71) A_70)->(((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_71) A_70)) A_70)))
% FOF formula (forall (A_71:hoare_1708887482_state) (A_70:(hoare_1708887482_state->Prop)), (((member451959335_state A_71) A_70)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_71) A_70)) A_70))) of role axiom named fact_432_insert__absorb
% A new axiom: (forall (A_71:hoare_1708887482_state) (A_70:(hoare_1708887482_state->Prop)), (((member451959335_state A_71) A_70)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_71) A_70)) A_70)))
% FOF formula (forall (A_71:pname) (A_70:(pname->Prop)), (((member_pname A_71) A_70)->(((eq (pname->Prop)) ((insert_pname A_71) A_70)) A_70))) of role axiom named fact_433_insert__absorb
% A new axiom: (forall (A_71:pname) (A_70:(pname->Prop)), (((member_pname A_71) A_70)->(((eq (pname->Prop)) ((insert_pname A_71) A_70)) A_70)))
% FOF formula (forall (B_36:nat) (A_69:nat), (((member_nat B_36) ((insert_nat A_69) bot_bot_nat_o))->(((eq nat) B_36) A_69))) of role axiom named fact_434_singletonE
% A new axiom: (forall (B_36:nat) (A_69:nat), (((member_nat B_36) ((insert_nat A_69) bot_bot_nat_o))->(((eq nat) B_36) A_69)))
% FOF formula (forall (B_36:(hoare_2091234717iple_a->Prop)) (A_69:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o B_36) ((insert102003750le_a_o A_69) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) B_36) A_69))) of role axiom named fact_435_singletonE
% A new axiom: (forall (B_36:(hoare_2091234717iple_a->Prop)) (A_69:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o B_36) ((insert102003750le_a_o A_69) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) B_36) A_69)))
% FOF formula (forall (B_36:hoare_2091234717iple_a) (A_69:hoare_2091234717iple_a), (((member290856304iple_a B_36) ((insert1597628439iple_a A_69) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) B_36) A_69))) of role axiom named fact_436_singletonE
% A new axiom: (forall (B_36:hoare_2091234717iple_a) (A_69:hoare_2091234717iple_a), (((member290856304iple_a B_36) ((insert1597628439iple_a A_69) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) B_36) A_69)))
% FOF formula (forall (B_36:hoare_1708887482_state) (A_69:hoare_1708887482_state), (((member451959335_state B_36) ((insert528405184_state A_69) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) B_36) A_69))) of role axiom named fact_437_singletonE
% A new axiom: (forall (B_36:hoare_1708887482_state) (A_69:hoare_1708887482_state), (((member451959335_state B_36) ((insert528405184_state A_69) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) B_36) A_69)))
% FOF formula (forall (B_36:pname) (A_69:pname), (((member_pname B_36) ((insert_pname A_69) bot_bot_pname_o))->(((eq pname) B_36) A_69))) of role axiom named fact_438_singletonE
% A new axiom: (forall (B_36:pname) (A_69:pname), (((member_pname B_36) ((insert_pname A_69) bot_bot_pname_o))->(((eq pname) B_36) A_69)))
% FOF formula (forall (A_68:nat) (B_35:nat), ((((eq (nat->Prop)) ((insert_nat A_68) bot_bot_nat_o)) ((insert_nat B_35) bot_bot_nat_o))->(((eq nat) A_68) B_35))) of role axiom named fact_439_singleton__inject
% A new axiom: (forall (A_68:nat) (B_35:nat), ((((eq (nat->Prop)) ((insert_nat A_68) bot_bot_nat_o)) ((insert_nat B_35) bot_bot_nat_o))->(((eq nat) A_68) B_35)))
% FOF formula (forall (A_68:(hoare_2091234717iple_a->Prop)) (B_35:(hoare_2091234717iple_a->Prop)), ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_68) bot_bo1957696069_a_o_o)) ((insert102003750le_a_o B_35) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) A_68) B_35))) of role axiom named fact_440_singleton__inject
% A new axiom: (forall (A_68:(hoare_2091234717iple_a->Prop)) (B_35:(hoare_2091234717iple_a->Prop)), ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_68) bot_bo1957696069_a_o_o)) ((insert102003750le_a_o B_35) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) A_68) B_35)))
% FOF formula (forall (A_68:pname) (B_35:pname), ((((eq (pname->Prop)) ((insert_pname A_68) bot_bot_pname_o)) ((insert_pname B_35) bot_bot_pname_o))->(((eq pname) A_68) B_35))) of role axiom named fact_441_singleton__inject
% A new axiom: (forall (A_68:pname) (B_35:pname), ((((eq (pname->Prop)) ((insert_pname A_68) bot_bot_pname_o)) ((insert_pname B_35) bot_bot_pname_o))->(((eq pname) A_68) B_35)))
% FOF formula (forall (A_68:hoare_2091234717iple_a) (B_35:hoare_2091234717iple_a), ((((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_68) bot_bo1791335050le_a_o)) ((insert1597628439iple_a B_35) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) A_68) B_35))) of role axiom named fact_442_singleton__inject
% A new axiom: (forall (A_68:hoare_2091234717iple_a) (B_35:hoare_2091234717iple_a), ((((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_68) bot_bo1791335050le_a_o)) ((insert1597628439iple_a B_35) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) A_68) B_35)))
% FOF formula (forall (A_68:hoare_1708887482_state) (B_35:hoare_1708887482_state), ((((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_68) bot_bo19817387tate_o)) ((insert528405184_state B_35) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) A_68) B_35))) of role axiom named fact_443_singleton__inject
% A new axiom: (forall (A_68:hoare_1708887482_state) (B_35:hoare_1708887482_state), ((((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_68) bot_bo19817387tate_o)) ((insert528405184_state B_35) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) A_68) B_35)))
% FOF formula (forall (U:state) (C:com) (S:state) (T:state), ((((evalc C) S) T)->((((evalc C) S) U)->(((eq state) U) T)))) of role axiom named fact_444_com__det
% A new axiom: (forall (U:state) (C:com) (S:state) (T:state), ((((evalc C) S) T)->((((evalc C) S) U)->(((eq state) U) T))))
% FOF formula (forall (A_67:nat) (A_66:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_67) A_66)) ((semila848761471_nat_o ((insert_nat A_67) bot_bot_nat_o)) A_66))) of role axiom named fact_445_insert__is__Un
% A new axiom: (forall (A_67:nat) (A_66:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_67) A_66)) ((semila848761471_nat_o ((insert_nat A_67) bot_bot_nat_o)) A_66)))
% FOF formula (forall (A_67:(hoare_2091234717iple_a->Prop)) (A_66:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_67) A_66)) ((semila2050116131_a_o_o ((insert102003750le_a_o A_67) bot_bo1957696069_a_o_o)) A_66))) of role axiom named fact_446_insert__is__Un
% A new axiom: (forall (A_67:(hoare_2091234717iple_a->Prop)) (A_66:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_67) A_66)) ((semila2050116131_a_o_o ((insert102003750le_a_o A_67) bot_bo1957696069_a_o_o)) A_66)))
% FOF formula (forall (A_67:pname) (A_66:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_67) A_66)) ((semila1780557381name_o ((insert_pname A_67) bot_bot_pname_o)) A_66))) of role axiom named fact_447_insert__is__Un
% A new axiom: (forall (A_67:pname) (A_66:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_67) A_66)) ((semila1780557381name_o ((insert_pname A_67) bot_bot_pname_o)) A_66)))
% FOF formula (forall (A_67:hoare_1708887482_state) (A_66:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_67) A_66)) ((semila1122118281tate_o ((insert528405184_state A_67) bot_bo19817387tate_o)) A_66))) of role axiom named fact_448_insert__is__Un
% A new axiom: (forall (A_67:hoare_1708887482_state) (A_66:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_67) A_66)) ((semila1122118281tate_o ((insert528405184_state A_67) bot_bo19817387tate_o)) A_66)))
% FOF formula (forall (A_67:hoare_2091234717iple_a) (A_66:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_67) A_66)) ((semila1052848428le_a_o ((insert1597628439iple_a A_67) bot_bo1791335050le_a_o)) A_66))) of role axiom named fact_449_insert__is__Un
% A new axiom: (forall (A_67:hoare_2091234717iple_a) (A_66:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_67) A_66)) ((semila1052848428le_a_o ((insert1597628439iple_a A_67) bot_bo1791335050le_a_o)) A_66)))
% FOF formula (forall (X:(hoare_2091234717iple_a->Prop)) (Xa:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X) Xa)) (collec1008234059le_a_o (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((or (((eq (hoare_2091234717iple_a->Prop)) Y_7) X)) ((member99268621le_a_o Y_7) Xa)))))) of role axiom named fact_450_insert__compr__raw
% A new axiom: (forall (X:(hoare_2091234717iple_a->Prop)) (Xa:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X) Xa)) (collec1008234059le_a_o (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((or (((eq (hoare_2091234717iple_a->Prop)) Y_7) X)) ((member99268621le_a_o Y_7) Xa))))))
% FOF formula (forall (X:hoare_2091234717iple_a) (Xa:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X) Xa)) (collec992574898iple_a (fun (Y_7:hoare_2091234717iple_a)=> ((or (((eq hoare_2091234717iple_a) Y_7) X)) ((member290856304iple_a Y_7) Xa)))))) of role axiom named fact_451_insert__compr__raw
% A new axiom: (forall (X:hoare_2091234717iple_a) (Xa:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X) Xa)) (collec992574898iple_a (fun (Y_7:hoare_2091234717iple_a)=> ((or (((eq hoare_2091234717iple_a) Y_7) X)) ((member290856304iple_a Y_7) Xa))))))
% FOF formula (forall (X:hoare_1708887482_state) (Xa:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X) Xa)) (collec1568722789_state (fun (Y_7:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) Y_7) X)) ((member451959335_state Y_7) Xa)))))) of role axiom named fact_452_insert__compr__raw
% A new axiom: (forall (X:hoare_1708887482_state) (Xa:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X) Xa)) (collec1568722789_state (fun (Y_7:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) Y_7) X)) ((member451959335_state Y_7) Xa))))))
% FOF formula (forall (X:nat) (Xa:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X) Xa)) (collect_nat (fun (Y_7:nat)=> ((or (((eq nat) Y_7) X)) ((member_nat Y_7) Xa)))))) of role axiom named fact_453_insert__compr__raw
% A new axiom: (forall (X:nat) (Xa:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X) Xa)) (collect_nat (fun (Y_7:nat)=> ((or (((eq nat) Y_7) X)) ((member_nat Y_7) Xa))))))
% FOF formula (forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y_7:pname)=> ((or (((eq pname) Y_7) X)) ((member_pname Y_7) Xa)))))) of role axiom named fact_454_insert__compr__raw
% A new axiom: (forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y_7:pname)=> ((or (((eq pname) Y_7) X)) ((member_pname Y_7) Xa))))))
% FOF formula (forall (G_19:(hoare_2091234717iple_a->Prop)) (T_3:hoare_2091234717iple_a) (Ts_1:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a G_19) ((insert1597628439iple_a T_3) Ts_1))->((and ((hoare_1467856363rivs_a G_19) ((insert1597628439iple_a T_3) bot_bo1791335050le_a_o))) ((hoare_1467856363rivs_a G_19) Ts_1)))) of role axiom named fact_455_derivs__insertD
% A new axiom: (forall (G_19:(hoare_2091234717iple_a->Prop)) (T_3:hoare_2091234717iple_a) (Ts_1:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a G_19) ((insert1597628439iple_a T_3) Ts_1))->((and ((hoare_1467856363rivs_a G_19) ((insert1597628439iple_a T_3) bot_bo1791335050le_a_o))) ((hoare_1467856363rivs_a G_19) Ts_1))))
% FOF formula (forall (G_19:(hoare_1708887482_state->Prop)) (T_3:hoare_1708887482_state) (Ts_1:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_19) ((insert528405184_state T_3) Ts_1))->((and ((hoare_90032982_state G_19) ((insert528405184_state T_3) bot_bo19817387tate_o))) ((hoare_90032982_state G_19) Ts_1)))) of role axiom named fact_456_derivs__insertD
% A new axiom: (forall (G_19:(hoare_1708887482_state->Prop)) (T_3:hoare_1708887482_state) (Ts_1:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_19) ((insert528405184_state T_3) Ts_1))->((and ((hoare_90032982_state G_19) ((insert528405184_state T_3) bot_bo19817387tate_o))) ((hoare_90032982_state G_19) Ts_1))))
% FOF formula (forall (Ts:(hoare_2091234717iple_a->Prop)) (G_18:(hoare_2091234717iple_a->Prop)) (T_2:hoare_2091234717iple_a), (((hoare_1467856363rivs_a G_18) ((insert1597628439iple_a T_2) bot_bo1791335050le_a_o))->(((hoare_1467856363rivs_a G_18) Ts)->((hoare_1467856363rivs_a G_18) ((insert1597628439iple_a T_2) Ts))))) of role axiom named fact_457_hoare__derivs_Oinsert
% A new axiom: (forall (Ts:(hoare_2091234717iple_a->Prop)) (G_18:(hoare_2091234717iple_a->Prop)) (T_2:hoare_2091234717iple_a), (((hoare_1467856363rivs_a G_18) ((insert1597628439iple_a T_2) bot_bo1791335050le_a_o))->(((hoare_1467856363rivs_a G_18) Ts)->((hoare_1467856363rivs_a G_18) ((insert1597628439iple_a T_2) Ts)))))
% FOF formula (forall (Ts:(hoare_1708887482_state->Prop)) (G_18:(hoare_1708887482_state->Prop)) (T_2:hoare_1708887482_state), (((hoare_90032982_state G_18) ((insert528405184_state T_2) bot_bo19817387tate_o))->(((hoare_90032982_state G_18) Ts)->((hoare_90032982_state G_18) ((insert528405184_state T_2) Ts))))) of role axiom named fact_458_hoare__derivs_Oinsert
% A new axiom: (forall (Ts:(hoare_1708887482_state->Prop)) (G_18:(hoare_1708887482_state->Prop)) (T_2:hoare_1708887482_state), (((hoare_90032982_state G_18) ((insert528405184_state T_2) bot_bo19817387tate_o))->(((hoare_90032982_state G_18) Ts)->((hoare_90032982_state G_18) ((insert528405184_state T_2) Ts)))))
% FOF formula (forall (C_23:nat) (A_65:(nat->Prop)), ((and ((((eq (nat->Prop)) A_65) bot_bot_nat_o)->(((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> C_23)) A_65)) bot_bot_nat_o))) ((not (((eq (nat->Prop)) A_65) bot_bot_nat_o))->(((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> C_23)) A_65)) ((insert_nat C_23) bot_bot_nat_o))))) of role axiom named fact_459_image__constant__conv
% A new axiom: (forall (C_23:nat) (A_65:(nat->Prop)), ((and ((((eq (nat->Prop)) A_65) bot_bot_nat_o)->(((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> C_23)) A_65)) bot_bot_nat_o))) ((not (((eq (nat->Prop)) A_65) bot_bot_nat_o))->(((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> C_23)) A_65)) ((insert_nat C_23) bot_bot_nat_o)))))
% FOF formula (forall (C_23:hoare_1708887482_state) (A_65:(pname->Prop)), ((and ((((eq (pname->Prop)) A_65) bot_bot_pname_o)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X:pname)=> C_23)) A_65)) bot_bo19817387tate_o))) ((not (((eq (pname->Prop)) A_65) bot_bot_pname_o))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X:pname)=> C_23)) A_65)) ((insert528405184_state C_23) bot_bo19817387tate_o))))) of role axiom named fact_460_image__constant__conv
% A new axiom: (forall (C_23:hoare_1708887482_state) (A_65:(pname->Prop)), ((and ((((eq (pname->Prop)) A_65) bot_bot_pname_o)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X:pname)=> C_23)) A_65)) bot_bo19817387tate_o))) ((not (((eq (pname->Prop)) A_65) bot_bot_pname_o))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X:pname)=> C_23)) A_65)) ((insert528405184_state C_23) bot_bo19817387tate_o)))))
% FOF formula (forall (C_23:hoare_2091234717iple_a) (A_65:(pname->Prop)), ((and ((((eq (pname->Prop)) A_65) bot_bot_pname_o)->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a (fun (X:pname)=> C_23)) A_65)) bot_bo1791335050le_a_o))) ((not (((eq (pname->Prop)) A_65) bot_bot_pname_o))->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a (fun (X:pname)=> C_23)) A_65)) ((insert1597628439iple_a C_23) bot_bo1791335050le_a_o))))) of role axiom named fact_461_image__constant__conv
% A new axiom: (forall (C_23:hoare_2091234717iple_a) (A_65:(pname->Prop)), ((and ((((eq (pname->Prop)) A_65) bot_bot_pname_o)->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a (fun (X:pname)=> C_23)) A_65)) bot_bo1791335050le_a_o))) ((not (((eq (pname->Prop)) A_65) bot_bot_pname_o))->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a (fun (X:pname)=> C_23)) A_65)) ((insert1597628439iple_a C_23) bot_bo1791335050le_a_o)))))
% FOF formula (forall (C_22:nat) (X_28:nat) (A_64:(nat->Prop)), (((member_nat X_28) A_64)->(((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> C_22)) A_64)) ((insert_nat C_22) bot_bot_nat_o)))) of role axiom named fact_462_image__constant
% A new axiom: (forall (C_22:nat) (X_28:nat) (A_64:(nat->Prop)), (((member_nat X_28) A_64)->(((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> C_22)) A_64)) ((insert_nat C_22) bot_bot_nat_o))))
% FOF formula (forall (C_22:hoare_1708887482_state) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X:pname)=> C_22)) A_64)) ((insert528405184_state C_22) bot_bo19817387tate_o)))) of role axiom named fact_463_image__constant
% A new axiom: (forall (C_22:hoare_1708887482_state) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X:pname)=> C_22)) A_64)) ((insert528405184_state C_22) bot_bo19817387tate_o))))
% FOF formula (forall (C_22:nat) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (nat->Prop)) ((image_pname_nat (fun (X:pname)=> C_22)) A_64)) ((insert_nat C_22) bot_bot_nat_o)))) of role axiom named fact_464_image__constant
% A new axiom: (forall (C_22:nat) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (nat->Prop)) ((image_pname_nat (fun (X:pname)=> C_22)) A_64)) ((insert_nat C_22) bot_bot_nat_o))))
% FOF formula (forall (C_22:(hoare_2091234717iple_a->Prop)) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((image_742317343le_a_o (fun (X:pname)=> C_22)) A_64)) ((insert102003750le_a_o C_22) bot_bo1957696069_a_o_o)))) of role axiom named fact_465_image__constant
% A new axiom: (forall (C_22:(hoare_2091234717iple_a->Prop)) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((image_742317343le_a_o (fun (X:pname)=> C_22)) A_64)) ((insert102003750le_a_o C_22) bot_bo1957696069_a_o_o))))
% FOF formula (forall (C_22:pname) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (pname->Prop)) ((image_pname_pname (fun (X:pname)=> C_22)) A_64)) ((insert_pname C_22) bot_bot_pname_o)))) of role axiom named fact_466_image__constant
% A new axiom: (forall (C_22:pname) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (pname->Prop)) ((image_pname_pname (fun (X:pname)=> C_22)) A_64)) ((insert_pname C_22) bot_bot_pname_o))))
% FOF formula (forall (C_22:hoare_2091234717iple_a) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a (fun (X:pname)=> C_22)) A_64)) ((insert1597628439iple_a C_22) bot_bo1791335050le_a_o)))) of role axiom named fact_467_image__constant
% A new axiom: (forall (C_22:hoare_2091234717iple_a) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a (fun (X:pname)=> C_22)) A_64)) ((insert1597628439iple_a C_22) bot_bo1791335050le_a_o))))
% FOF formula (forall (F_40:(nat->nat)) (A_63:nat) (B_34:(nat->Prop)), (((eq (nat->Prop)) ((image_nat_nat F_40) ((insert_nat A_63) B_34))) ((insert_nat (F_40 A_63)) ((image_nat_nat F_40) B_34)))) of role axiom named fact_468_image__insert
% A new axiom: (forall (F_40:(nat->nat)) (A_63:nat) (B_34:(nat->Prop)), (((eq (nat->Prop)) ((image_nat_nat F_40) ((insert_nat A_63) B_34))) ((insert_nat (F_40 A_63)) ((image_nat_nat F_40) B_34))))
% FOF formula (forall (F_40:(pname->hoare_1708887482_state)) (A_63:pname) (B_34:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_40) ((insert_pname A_63) B_34))) ((insert528405184_state (F_40 A_63)) ((image_1116629049_state F_40) B_34)))) of role axiom named fact_469_image__insert
% A new axiom: (forall (F_40:(pname->hoare_1708887482_state)) (A_63:pname) (B_34:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_40) ((insert_pname A_63) B_34))) ((insert528405184_state (F_40 A_63)) ((image_1116629049_state F_40) B_34))))
% FOF formula (forall (F_40:(pname->hoare_2091234717iple_a)) (A_63:pname) (B_34:(pname->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_40) ((insert_pname A_63) B_34))) ((insert1597628439iple_a (F_40 A_63)) ((image_231808478iple_a F_40) B_34)))) of role axiom named fact_470_image__insert
% A new axiom: (forall (F_40:(pname->hoare_2091234717iple_a)) (A_63:pname) (B_34:(pname->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_40) ((insert_pname A_63) B_34))) ((insert1597628439iple_a (F_40 A_63)) ((image_231808478iple_a F_40) B_34))))
% FOF formula (forall (F_39:(nat->nat)) (X_27:nat) (A_62:(nat->Prop)), (((member_nat X_27) A_62)->(((eq (nat->Prop)) ((insert_nat (F_39 X_27)) ((image_nat_nat F_39) A_62))) ((image_nat_nat F_39) A_62)))) of role axiom named fact_471_insert__image
% A new axiom: (forall (F_39:(nat->nat)) (X_27:nat) (A_62:(nat->Prop)), (((member_nat X_27) A_62)->(((eq (nat->Prop)) ((insert_nat (F_39 X_27)) ((image_nat_nat F_39) A_62))) ((image_nat_nat F_39) A_62))))
% FOF formula (forall (F_39:(pname->hoare_1708887482_state)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state (F_39 X_27)) ((image_1116629049_state F_39) A_62))) ((image_1116629049_state F_39) A_62)))) of role axiom named fact_472_insert__image
% A new axiom: (forall (F_39:(pname->hoare_1708887482_state)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state (F_39 X_27)) ((image_1116629049_state F_39) A_62))) ((image_1116629049_state F_39) A_62))))
% FOF formula (forall (F_39:(pname->nat)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (nat->Prop)) ((insert_nat (F_39 X_27)) ((image_pname_nat F_39) A_62))) ((image_pname_nat F_39) A_62)))) of role axiom named fact_473_insert__image
% A new axiom: (forall (F_39:(pname->nat)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (nat->Prop)) ((insert_nat (F_39 X_27)) ((image_pname_nat F_39) A_62))) ((image_pname_nat F_39) A_62))))
% FOF formula (forall (F_39:(pname->(hoare_2091234717iple_a->Prop))) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o (F_39 X_27)) ((image_742317343le_a_o F_39) A_62))) ((image_742317343le_a_o F_39) A_62)))) of role axiom named fact_474_insert__image
% A new axiom: (forall (F_39:(pname->(hoare_2091234717iple_a->Prop))) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o (F_39 X_27)) ((image_742317343le_a_o F_39) A_62))) ((image_742317343le_a_o F_39) A_62))))
% FOF formula (forall (F_39:(pname->pname)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (pname->Prop)) ((insert_pname (F_39 X_27)) ((image_pname_pname F_39) A_62))) ((image_pname_pname F_39) A_62)))) of role axiom named fact_475_insert__image
% A new axiom: (forall (F_39:(pname->pname)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (pname->Prop)) ((insert_pname (F_39 X_27)) ((image_pname_pname F_39) A_62))) ((image_pname_pname F_39) A_62))))
% FOF formula (forall (F_39:(pname->hoare_2091234717iple_a)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a (F_39 X_27)) ((image_231808478iple_a F_39) A_62))) ((image_231808478iple_a F_39) A_62)))) of role axiom named fact_476_insert__image
% A new axiom: (forall (F_39:(pname->hoare_2091234717iple_a)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a (F_39 X_27)) ((image_231808478iple_a F_39) A_62))) ((image_231808478iple_a F_39) A_62))))
% FOF formula (forall (A_61:(nat->Prop)) (A_60:nat) (B_33:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_61) ((insert_nat A_60) B_33))) ((insert_nat A_60) ((semila848761471_nat_o A_61) B_33)))) of role axiom named fact_477_Un__insert__right
% A new axiom: (forall (A_61:(nat->Prop)) (A_60:nat) (B_33:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_61) ((insert_nat A_60) B_33))) ((insert_nat A_60) ((semila848761471_nat_o A_61) B_33))))
% FOF formula (forall (A_61:((hoare_2091234717iple_a->Prop)->Prop)) (A_60:(hoare_2091234717iple_a->Prop)) (B_33:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_61) ((insert102003750le_a_o A_60) B_33))) ((insert102003750le_a_o A_60) ((semila2050116131_a_o_o A_61) B_33)))) of role axiom named fact_478_Un__insert__right
% A new axiom: (forall (A_61:((hoare_2091234717iple_a->Prop)->Prop)) (A_60:(hoare_2091234717iple_a->Prop)) (B_33:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_61) ((insert102003750le_a_o A_60) B_33))) ((insert102003750le_a_o A_60) ((semila2050116131_a_o_o A_61) B_33))))
% FOF formula (forall (A_61:(pname->Prop)) (A_60:pname) (B_33:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_61) ((insert_pname A_60) B_33))) ((insert_pname A_60) ((semila1780557381name_o A_61) B_33)))) of role axiom named fact_479_Un__insert__right
% A new axiom: (forall (A_61:(pname->Prop)) (A_60:pname) (B_33:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_61) ((insert_pname A_60) B_33))) ((insert_pname A_60) ((semila1780557381name_o A_61) B_33))))
% FOF formula (forall (A_61:(hoare_1708887482_state->Prop)) (A_60:hoare_1708887482_state) (B_33:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_61) ((insert528405184_state A_60) B_33))) ((insert528405184_state A_60) ((semila1122118281tate_o A_61) B_33)))) of role axiom named fact_480_Un__insert__right
% A new axiom: (forall (A_61:(hoare_1708887482_state->Prop)) (A_60:hoare_1708887482_state) (B_33:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_61) ((insert528405184_state A_60) B_33))) ((insert528405184_state A_60) ((semila1122118281tate_o A_61) B_33))))
% FOF formula (forall (A_61:(hoare_2091234717iple_a->Prop)) (A_60:hoare_2091234717iple_a) (B_33:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_61) ((insert1597628439iple_a A_60) B_33))) ((insert1597628439iple_a A_60) ((semila1052848428le_a_o A_61) B_33)))) of role axiom named fact_481_Un__insert__right
% A new axiom: (forall (A_61:(hoare_2091234717iple_a->Prop)) (A_60:hoare_2091234717iple_a) (B_33:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_61) ((insert1597628439iple_a A_60) B_33))) ((insert1597628439iple_a A_60) ((semila1052848428le_a_o A_61) B_33))))
% FOF formula (forall (A_59:nat) (B_32:(nat->Prop)) (C_21:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((insert_nat A_59) B_32)) C_21)) ((insert_nat A_59) ((semila848761471_nat_o B_32) C_21)))) of role axiom named fact_482_Un__insert__left
% A new axiom: (forall (A_59:nat) (B_32:(nat->Prop)) (C_21:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((insert_nat A_59) B_32)) C_21)) ((insert_nat A_59) ((semila848761471_nat_o B_32) C_21))))
% FOF formula (forall (A_59:(hoare_2091234717iple_a->Prop)) (B_32:((hoare_2091234717iple_a->Prop)->Prop)) (C_21:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((insert102003750le_a_o A_59) B_32)) C_21)) ((insert102003750le_a_o A_59) ((semila2050116131_a_o_o B_32) C_21)))) of role axiom named fact_483_Un__insert__left
% A new axiom: (forall (A_59:(hoare_2091234717iple_a->Prop)) (B_32:((hoare_2091234717iple_a->Prop)->Prop)) (C_21:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((insert102003750le_a_o A_59) B_32)) C_21)) ((insert102003750le_a_o A_59) ((semila2050116131_a_o_o B_32) C_21))))
% FOF formula (forall (A_59:pname) (B_32:(pname->Prop)) (C_21:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_59) B_32)) C_21)) ((insert_pname A_59) ((semila1780557381name_o B_32) C_21)))) of role axiom named fact_484_Un__insert__left
% A new axiom: (forall (A_59:pname) (B_32:(pname->Prop)) (C_21:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_59) B_32)) C_21)) ((insert_pname A_59) ((semila1780557381name_o B_32) C_21))))
% FOF formula (forall (A_59:hoare_1708887482_state) (B_32:(hoare_1708887482_state->Prop)) (C_21:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((insert528405184_state A_59) B_32)) C_21)) ((insert528405184_state A_59) ((semila1122118281tate_o B_32) C_21)))) of role axiom named fact_485_Un__insert__left
% A new axiom: (forall (A_59:hoare_1708887482_state) (B_32:(hoare_1708887482_state->Prop)) (C_21:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((insert528405184_state A_59) B_32)) C_21)) ((insert528405184_state A_59) ((semila1122118281tate_o B_32) C_21))))
% FOF formula (forall (A_59:hoare_2091234717iple_a) (B_32:(hoare_2091234717iple_a->Prop)) (C_21:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((insert1597628439iple_a A_59) B_32)) C_21)) ((insert1597628439iple_a A_59) ((semila1052848428le_a_o B_32) C_21)))) of role axiom named fact_486_Un__insert__left
% A new axiom: (forall (A_59:hoare_2091234717iple_a) (B_32:(hoare_2091234717iple_a->Prop)) (C_21:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((insert1597628439iple_a A_59) B_32)) C_21)) ((insert1597628439iple_a A_59) ((semila1052848428le_a_o B_32) C_21))))
% FOF formula (forall (F_38:(nat->nat)) (A_58:(nat->Prop)), ((iff (((eq (nat->Prop)) bot_bot_nat_o) ((image_nat_nat F_38) A_58))) (((eq (nat->Prop)) A_58) bot_bot_nat_o))) of role axiom named fact_487_empty__is__image
% A new axiom: (forall (F_38:(nat->nat)) (A_58:(nat->Prop)), ((iff (((eq (nat->Prop)) bot_bot_nat_o) ((image_nat_nat F_38) A_58))) (((eq (nat->Prop)) A_58) bot_bot_nat_o)))
% FOF formula (forall (F_38:(pname->hoare_1708887482_state)) (A_58:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((image_1116629049_state F_38) A_58))) (((eq (pname->Prop)) A_58) bot_bot_pname_o))) of role axiom named fact_488_empty__is__image
% A new axiom: (forall (F_38:(pname->hoare_1708887482_state)) (A_58:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((image_1116629049_state F_38) A_58))) (((eq (pname->Prop)) A_58) bot_bot_pname_o)))
% FOF formula (forall (F_38:(pname->hoare_2091234717iple_a)) (A_58:(pname->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) ((image_231808478iple_a F_38) A_58))) (((eq (pname->Prop)) A_58) bot_bot_pname_o))) of role axiom named fact_489_empty__is__image
% A new axiom: (forall (F_38:(pname->hoare_2091234717iple_a)) (A_58:(pname->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) ((image_231808478iple_a F_38) A_58))) (((eq (pname->Prop)) A_58) bot_bot_pname_o)))
% FOF formula (forall (F_37:(nat->nat)), (((eq (nat->Prop)) ((image_nat_nat F_37) bot_bot_nat_o)) bot_bot_nat_o)) of role axiom named fact_490_image__empty
% A new axiom: (forall (F_37:(nat->nat)), (((eq (nat->Prop)) ((image_nat_nat F_37) bot_bot_nat_o)) bot_bot_nat_o))
% FOF formula (forall (F_37:(pname->hoare_1708887482_state)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_37) bot_bot_pname_o)) bot_bo19817387tate_o)) of role axiom named fact_491_image__empty
% A new axiom: (forall (F_37:(pname->hoare_1708887482_state)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_37) bot_bot_pname_o)) bot_bo19817387tate_o))
% FOF formula (forall (F_37:(pname->hoare_2091234717iple_a)), (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_37) bot_bot_pname_o)) bot_bo1791335050le_a_o)) of role axiom named fact_492_image__empty
% A new axiom: (forall (F_37:(pname->hoare_2091234717iple_a)), (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_37) bot_bot_pname_o)) bot_bo1791335050le_a_o))
% FOF formula (forall (F_36:(nat->nat)) (A_57:(nat->Prop)), ((iff (((eq (nat->Prop)) ((image_nat_nat F_36) A_57)) bot_bot_nat_o)) (((eq (nat->Prop)) A_57) bot_bot_nat_o))) of role axiom named fact_493_image__is__empty
% A new axiom: (forall (F_36:(nat->nat)) (A_57:(nat->Prop)), ((iff (((eq (nat->Prop)) ((image_nat_nat F_36) A_57)) bot_bot_nat_o)) (((eq (nat->Prop)) A_57) bot_bot_nat_o)))
% FOF formula (forall (F_36:(pname->hoare_1708887482_state)) (A_57:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_36) A_57)) bot_bo19817387tate_o)) (((eq (pname->Prop)) A_57) bot_bot_pname_o))) of role axiom named fact_494_image__is__empty
% A new axiom: (forall (F_36:(pname->hoare_1708887482_state)) (A_57:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_36) A_57)) bot_bo19817387tate_o)) (((eq (pname->Prop)) A_57) bot_bot_pname_o)))
% FOF formula (forall (F_36:(pname->hoare_2091234717iple_a)) (A_57:(pname->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_36) A_57)) bot_bo1791335050le_a_o)) (((eq (pname->Prop)) A_57) bot_bot_pname_o))) of role axiom named fact_495_image__is__empty
% A new axiom: (forall (F_36:(pname->hoare_2091234717iple_a)) (A_57:(pname->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_36) A_57)) bot_bo1791335050le_a_o)) (((eq (pname->Prop)) A_57) bot_bot_pname_o)))
% FOF formula (forall (P_23:(nat->Prop)) (X:nat), (((member_nat X) bot_bot_nat_o)->(P_23 X))) of role axiom named fact_496_ball__empty
% A new axiom: (forall (P_23:(nat->Prop)) (X:nat), (((member_nat X) bot_bot_nat_o)->(P_23 X)))
% FOF formula (forall (P_23:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), (((member290856304iple_a X) bot_bo1791335050le_a_o)->(P_23 X))) of role axiom named fact_497_ball__empty
% A new axiom: (forall (P_23:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), (((member290856304iple_a X) bot_bo1791335050le_a_o)->(P_23 X)))
% FOF formula (forall (P_23:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) bot_bo1957696069_a_o_o)->(P_23 X))) of role axiom named fact_498_ball__empty
% A new axiom: (forall (P_23:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) bot_bo1957696069_a_o_o)->(P_23 X)))
% FOF formula (forall (P_23:(pname->Prop)) (X:pname), (((member_pname X) bot_bot_pname_o)->(P_23 X))) of role axiom named fact_499_ball__empty
% A new axiom: (forall (P_23:(pname->Prop)) (X:pname), (((member_pname X) bot_bot_pname_o)->(P_23 X)))
% FOF formula (forall (P_23:(hoare_1708887482_state->Prop)) (X:hoare_1708887482_state), (((member451959335_state X) bot_bo19817387tate_o)->(P_23 X))) of role axiom named fact_500_ball__empty
% A new axiom: (forall (P_23:(hoare_1708887482_state->Prop)) (X:hoare_1708887482_state), (((member451959335_state X) bot_bo19817387tate_o)->(P_23 X)))
% FOF formula (forall (B_31:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o bot_bot_nat_o) B_31)) B_31)) of role axiom named fact_501_Un__empty__left
% A new axiom: (forall (B_31:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o bot_bot_nat_o) B_31)) B_31))
% FOF formula (forall (B_31:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o bot_bo1957696069_a_o_o) B_31)) B_31)) of role axiom named fact_502_Un__empty__left
% A new axiom: (forall (B_31:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o bot_bo1957696069_a_o_o) B_31)) B_31))
% FOF formula (forall (B_31:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_31)) B_31)) of role axiom named fact_503_Un__empty__left
% A new axiom: (forall (B_31:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_31)) B_31))
% FOF formula (forall (B_31:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_o) B_31)) B_31)) of role axiom named fact_504_Un__empty__left
% A new axiom: (forall (B_31:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_o) B_31)) B_31))
% FOF formula (forall (B_31:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o bot_bo1791335050le_a_o) B_31)) B_31)) of role axiom named fact_505_Un__empty__left
% A new axiom: (forall (B_31:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o bot_bo1791335050le_a_o) B_31)) B_31))
% FOF formula (forall (A_56:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_56) bot_bot_nat_o)) A_56)) of role axiom named fact_506_Un__empty__right
% A new axiom: (forall (A_56:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_56) bot_bot_nat_o)) A_56))
% FOF formula (forall (A_56:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_56) bot_bo1957696069_a_o_o)) A_56)) of role axiom named fact_507_Un__empty__right
% A new axiom: (forall (A_56:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_56) bot_bo1957696069_a_o_o)) A_56))
% FOF formula (forall (A_56:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_56) bot_bot_pname_o)) A_56)) of role axiom named fact_508_Un__empty__right
% A new axiom: (forall (A_56:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_56) bot_bot_pname_o)) A_56))
% FOF formula (forall (A_56:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_56) bot_bo19817387tate_o)) A_56)) of role axiom named fact_509_Un__empty__right
% A new axiom: (forall (A_56:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_56) bot_bo19817387tate_o)) A_56))
% FOF formula (forall (A_56:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_56) bot_bo1791335050le_a_o)) A_56)) of role axiom named fact_510_Un__empty__right
% A new axiom: (forall (A_56:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_56) bot_bo1791335050le_a_o)) A_56))
% FOF formula (forall (A_55:(nat->Prop)) (B_30:(nat->Prop)), ((iff (((eq (nat->Prop)) ((semila848761471_nat_o A_55) B_30)) bot_bot_nat_o)) ((and (((eq (nat->Prop)) A_55) bot_bot_nat_o)) (((eq (nat->Prop)) B_30) bot_bot_nat_o)))) of role axiom named fact_511_Un__empty
% A new axiom: (forall (A_55:(nat->Prop)) (B_30:(nat->Prop)), ((iff (((eq (nat->Prop)) ((semila848761471_nat_o A_55) B_30)) bot_bot_nat_o)) ((and (((eq (nat->Prop)) A_55) bot_bot_nat_o)) (((eq (nat->Prop)) B_30) bot_bot_nat_o))))
% FOF formula (forall (A_55:((hoare_2091234717iple_a->Prop)->Prop)) (B_30:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_55) B_30)) bot_bo1957696069_a_o_o)) ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_55) bot_bo1957696069_a_o_o)) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_30) bot_bo1957696069_a_o_o)))) of role axiom named fact_512_Un__empty
% A new axiom: (forall (A_55:((hoare_2091234717iple_a->Prop)->Prop)) (B_30:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_55) B_30)) bot_bo1957696069_a_o_o)) ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_55) bot_bo1957696069_a_o_o)) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_30) bot_bo1957696069_a_o_o))))
% FOF formula (forall (A_55:(pname->Prop)) (B_30:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_55) B_30)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_55) bot_bot_pname_o)) (((eq (pname->Prop)) B_30) bot_bot_pname_o)))) of role axiom named fact_513_Un__empty
% A new axiom: (forall (A_55:(pname->Prop)) (B_30:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_55) B_30)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_55) bot_bot_pname_o)) (((eq (pname->Prop)) B_30) bot_bot_pname_o))))
% FOF formula (forall (A_55:(hoare_1708887482_state->Prop)) (B_30:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_55) B_30)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) A_55) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) B_30) bot_bo19817387tate_o)))) of role axiom named fact_514_Un__empty
% A new axiom: (forall (A_55:(hoare_1708887482_state->Prop)) (B_30:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_55) B_30)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) A_55) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) B_30) bot_bo19817387tate_o))))
% FOF formula (forall (A_55:(hoare_2091234717iple_a->Prop)) (B_30:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_55) B_30)) bot_bo1791335050le_a_o)) ((and (((eq (hoare_2091234717iple_a->Prop)) A_55) bot_bo1791335050le_a_o)) (((eq (hoare_2091234717iple_a->Prop)) B_30) bot_bo1791335050le_a_o)))) of role axiom named fact_515_Un__empty
% A new axiom: (forall (A_55:(hoare_2091234717iple_a->Prop)) (B_30:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_55) B_30)) bot_bo1791335050le_a_o)) ((and (((eq (hoare_2091234717iple_a->Prop)) A_55) bot_bo1791335050le_a_o)) (((eq (hoare_2091234717iple_a->Prop)) B_30) bot_bo1791335050le_a_o))))
% FOF formula (forall (G_17:(hoare_2091234717iple_a->Prop)) (P_22:(x_a->(state->Prop))) (C_20:com) (Q_15:(x_a->(state->Prop))) (C_19:Prop), ((C_19->((hoare_1467856363rivs_a G_17) ((insert1597628439iple_a (((hoare_657976383iple_a P_22) C_20) Q_15)) bot_bo1791335050le_a_o)))->((hoare_1467856363rivs_a G_17) ((insert1597628439iple_a (((hoare_657976383iple_a (fun (Z_5:x_a) (S_2:state)=> ((and ((P_22 Z_5) S_2)) C_19))) C_20) Q_15)) bot_bo1791335050le_a_o)))) of role axiom named fact_516_constant
% A new axiom: (forall (G_17:(hoare_2091234717iple_a->Prop)) (P_22:(x_a->(state->Prop))) (C_20:com) (Q_15:(x_a->(state->Prop))) (C_19:Prop), ((C_19->((hoare_1467856363rivs_a G_17) ((insert1597628439iple_a (((hoare_657976383iple_a P_22) C_20) Q_15)) bot_bo1791335050le_a_o)))->((hoare_1467856363rivs_a G_17) ((insert1597628439iple_a (((hoare_657976383iple_a (fun (Z_5:x_a) (S_2:state)=> ((and ((P_22 Z_5) S_2)) C_19))) C_20) Q_15)) bot_bo1791335050le_a_o))))
% FOF formula (forall (G_17:(hoare_1708887482_state->Prop)) (P_22:(state->(state->Prop))) (C_20:com) (Q_15:(state->(state->Prop))) (C_19:Prop), ((C_19->((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state P_22) C_20) Q_15)) bot_bo19817387tate_o)))->((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state (fun (Z_5:state) (S_2:state)=> ((and ((P_22 Z_5) S_2)) C_19))) C_20) Q_15)) bot_bo19817387tate_o)))) of role axiom named fact_517_constant
% A new axiom: (forall (G_17:(hoare_1708887482_state->Prop)) (P_22:(state->(state->Prop))) (C_20:com) (Q_15:(state->(state->Prop))) (C_19:Prop), ((C_19->((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state P_22) C_20) Q_15)) bot_bo19817387tate_o)))->((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state (fun (Z_5:state) (S_2:state)=> ((and ((P_22 Z_5) S_2)) C_19))) C_20) Q_15)) bot_bo19817387tate_o))))
% FOF formula (forall (G_16:(hoare_2091234717iple_a->Prop)), ((hoare_1467856363rivs_a G_16) bot_bo1791335050le_a_o)) of role axiom named fact_518_empty
% A new axiom: (forall (G_16:(hoare_2091234717iple_a->Prop)), ((hoare_1467856363rivs_a G_16) bot_bo1791335050le_a_o))
% FOF formula (forall (G_16:(hoare_1708887482_state->Prop)), ((hoare_90032982_state G_16) bot_bo19817387tate_o)) of role axiom named fact_519_empty
% A new axiom: (forall (G_16:(hoare_1708887482_state->Prop)), ((hoare_90032982_state G_16) bot_bo19817387tate_o))
% FOF formula (forall (X_26:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o bot_bot_nat_o) X_26)) X_26)) of role axiom named fact_520_sup__bot__left
% A new axiom: (forall (X_26:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o bot_bot_nat_o) X_26)) X_26))
% FOF formula (forall (X_26:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o bot_bo1957696069_a_o_o) X_26)) X_26)) of role axiom named fact_521_sup__bot__left
% A new axiom: (forall (X_26:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o bot_bo1957696069_a_o_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_522_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:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_o) X_26)) X_26)) of role axiom named fact_523_sup__bot__left
% A new axiom: (forall (X_26:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_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_524_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_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o bot_bo1791335050le_a_o) X_26)) X_26)) of role axiom named fact_525_sup__bot__left
% A new axiom: (forall (X_26:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o bot_bo1791335050le_a_o) X_26)) X_26))
% FOF formula (forall (X_25:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_25) bot_bot_nat_o)) X_25)) of role axiom named fact_526_sup__bot__right
% A new axiom: (forall (X_25:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_25) bot_bot_nat_o)) X_25))
% FOF formula (forall (X_25:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_25) bot_bo1957696069_a_o_o)) X_25)) of role axiom named fact_527_sup__bot__right
% A new axiom: (forall (X_25:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_25) bot_bo1957696069_a_o_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_528_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:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_25) bot_bo19817387tate_o)) X_25)) of role axiom named fact_529_sup__bot__right
% A new axiom: (forall (X_25:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_25) bot_bo19817387tate_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_530_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_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_25) bot_bo1791335050le_a_o)) X_25)) of role axiom named fact_531_sup__bot__right
% A new axiom: (forall (X_25:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_25) bot_bo1791335050le_a_o)) X_25))
% FOF formula (forall (X_24:(nat->Prop)) (Y_8:(nat->Prop)), ((iff (((eq (nat->Prop)) ((semila848761471_nat_o X_24) Y_8)) bot_bot_nat_o)) ((and (((eq (nat->Prop)) X_24) bot_bot_nat_o)) (((eq (nat->Prop)) Y_8) bot_bot_nat_o)))) of role axiom named fact_532_sup__eq__bot__iff
% A new axiom: (forall (X_24:(nat->Prop)) (Y_8:(nat->Prop)), ((iff (((eq (nat->Prop)) ((semila848761471_nat_o X_24) Y_8)) bot_bot_nat_o)) ((and (((eq (nat->Prop)) X_24) bot_bot_nat_o)) (((eq (nat->Prop)) Y_8) bot_bot_nat_o))))
% FOF formula (forall (X_24:((hoare_2091234717iple_a->Prop)->Prop)) (Y_8:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_24) Y_8)) bot_bo1957696069_a_o_o)) ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) X_24) bot_bo1957696069_a_o_o)) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) Y_8) bot_bo1957696069_a_o_o)))) of role axiom named fact_533_sup__eq__bot__iff
% A new axiom: (forall (X_24:((hoare_2091234717iple_a->Prop)->Prop)) (Y_8:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_24) Y_8)) bot_bo1957696069_a_o_o)) ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) X_24) bot_bo1957696069_a_o_o)) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) Y_8) bot_bo1957696069_a_o_o))))
% FOF formula (forall (X_24:(pname->Prop)) (Y_8:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_24) Y_8)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_24) bot_bot_pname_o)) (((eq (pname->Prop)) Y_8) bot_bot_pname_o)))) of role axiom named fact_534_sup__eq__bot__iff
% A new axiom: (forall (X_24:(pname->Prop)) (Y_8:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_24) Y_8)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_24) bot_bot_pname_o)) (((eq (pname->Prop)) Y_8) bot_bot_pname_o))))
% FOF formula (forall (X_24:(hoare_1708887482_state->Prop)) (Y_8:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_24) Y_8)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) X_24) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) Y_8) bot_bo19817387tate_o)))) of role axiom named fact_535_sup__eq__bot__iff
% A new axiom: (forall (X_24:(hoare_1708887482_state->Prop)) (Y_8:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_24) Y_8)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) X_24) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) Y_8) bot_bo19817387tate_o))))
% FOF formula (forall (X_24:Prop) (Y_8:Prop), ((iff ((iff ((semila10642723_sup_o X_24) Y_8)) bot_bot_o)) ((and ((iff X_24) bot_bot_o)) ((iff Y_8) bot_bot_o)))) of role axiom named fact_536_sup__eq__bot__iff
% A new axiom: (forall (X_24:Prop) (Y_8:Prop), ((iff ((iff ((semila10642723_sup_o X_24) Y_8)) bot_bot_o)) ((and ((iff X_24) bot_bot_o)) ((iff Y_8) bot_bot_o))))
% FOF formula (forall (X_24:(hoare_2091234717iple_a->Prop)) (Y_8:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_24) Y_8)) bot_bo1791335050le_a_o)) ((and (((eq (hoare_2091234717iple_a->Prop)) X_24) bot_bo1791335050le_a_o)) (((eq (hoare_2091234717iple_a->Prop)) Y_8) bot_bo1791335050le_a_o)))) of role axiom named fact_537_sup__eq__bot__iff
% A new axiom: (forall (X_24:(hoare_2091234717iple_a->Prop)) (Y_8:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_24) Y_8)) bot_bo1791335050le_a_o)) ((and (((eq (hoare_2091234717iple_a->Prop)) X_24) bot_bo1791335050le_a_o)) (((eq (hoare_2091234717iple_a->Prop)) Y_8) bot_bo1791335050le_a_o))))
% FOF formula (forall (N_5:nat) (T_1:hoare_1708887482_state), (((hoare_23738522_state (suc N_5)) T_1)->((hoare_23738522_state N_5) T_1))) of role axiom named fact_538_triple__valid__Suc
% A new axiom: (forall (N_5:nat) (T_1:hoare_1708887482_state), (((hoare_23738522_state (suc N_5)) T_1)->((hoare_23738522_state N_5) T_1)))
% FOF formula (forall (N_5:nat) (T_1:hoare_2091234717iple_a), (((hoare_1421888935alid_a (suc N_5)) T_1)->((hoare_1421888935alid_a N_5) T_1))) of role axiom named fact_539_triple__valid__Suc
% A new axiom: (forall (N_5:nat) (T_1:hoare_2091234717iple_a), (((hoare_1421888935alid_a (suc N_5)) T_1)->((hoare_1421888935alid_a N_5) T_1)))
% FOF formula (forall (A_54:(hoare_2091234717iple_a->Prop)) (B_29:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_54) B_29)) ((semila2050116131_a_o_o (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> (((eq (hoare_2091234717iple_a->Prop)) X) A_54)))) B_29))) of role axiom named fact_540_insert__def
% A new axiom: (forall (A_54:(hoare_2091234717iple_a->Prop)) (B_29:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_54) B_29)) ((semila2050116131_a_o_o (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> (((eq (hoare_2091234717iple_a->Prop)) X) A_54)))) B_29)))
% FOF formula (forall (A_54:pname) (B_29:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_54) B_29)) ((semila1780557381name_o (collect_pname (fun (X:pname)=> (((eq pname) X) A_54)))) B_29))) of role axiom named fact_541_insert__def
% A new axiom: (forall (A_54:pname) (B_29:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_54) B_29)) ((semila1780557381name_o (collect_pname (fun (X:pname)=> (((eq pname) X) A_54)))) B_29)))
% FOF formula (forall (A_54:hoare_1708887482_state) (B_29:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_54) B_29)) ((semila1122118281tate_o (collec1568722789_state (fun (X:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X) A_54)))) B_29))) of role axiom named fact_542_insert__def
% A new axiom: (forall (A_54:hoare_1708887482_state) (B_29:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_54) B_29)) ((semila1122118281tate_o (collec1568722789_state (fun (X:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X) A_54)))) B_29)))
% FOF formula (forall (A_54:hoare_2091234717iple_a) (B_29:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_54) B_29)) ((semila1052848428le_a_o (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> (((eq hoare_2091234717iple_a) X) A_54)))) B_29))) of role axiom named fact_543_insert__def
% A new axiom: (forall (A_54:hoare_2091234717iple_a) (B_29:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_54) B_29)) ((semila1052848428le_a_o (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> (((eq hoare_2091234717iple_a) X) A_54)))) B_29)))
% FOF formula (forall (A_54:nat) (B_29:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_54) B_29)) ((semila848761471_nat_o (collect_nat (fun (X:nat)=> (((eq nat) X) A_54)))) B_29))) of role axiom named fact_544_insert__def
% A new axiom: (forall (A_54:nat) (B_29:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_54) B_29)) ((semila848761471_nat_o (collect_nat (fun (X:nat)=> (((eq nat) X) A_54)))) B_29)))
% FOF formula (forall (G_15:(hoare_2091234717iple_a->Prop)) (P_21:(x_a->(state->Prop))) (Pn_3:pname) (Q_14:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_15) ((insert1597628439iple_a (((hoare_657976383iple_a P_21) (the_com (body_1 Pn_3))) Q_14)) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_15) ((insert1597628439iple_a (((hoare_657976383iple_a P_21) (body Pn_3)) Q_14)) bot_bo1791335050le_a_o)))) of role axiom named fact_545_weak__Body
% A new axiom: (forall (G_15:(hoare_2091234717iple_a->Prop)) (P_21:(x_a->(state->Prop))) (Pn_3:pname) (Q_14:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_15) ((insert1597628439iple_a (((hoare_657976383iple_a P_21) (the_com (body_1 Pn_3))) Q_14)) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_15) ((insert1597628439iple_a (((hoare_657976383iple_a P_21) (body Pn_3)) Q_14)) bot_bo1791335050le_a_o))))
% FOF formula (forall (G_15:(hoare_1708887482_state->Prop)) (P_21:(state->(state->Prop))) (Pn_3:pname) (Q_14:(state->(state->Prop))), (((hoare_90032982_state G_15) ((insert528405184_state (((hoare_858012674_state P_21) (the_com (body_1 Pn_3))) Q_14)) bot_bo19817387tate_o))->((hoare_90032982_state G_15) ((insert528405184_state (((hoare_858012674_state P_21) (body Pn_3)) Q_14)) bot_bo19817387tate_o)))) of role axiom named fact_546_weak__Body
% A new axiom: (forall (G_15:(hoare_1708887482_state->Prop)) (P_21:(state->(state->Prop))) (Pn_3:pname) (Q_14:(state->(state->Prop))), (((hoare_90032982_state G_15) ((insert528405184_state (((hoare_858012674_state P_21) (the_com (body_1 Pn_3))) Q_14)) bot_bo19817387tate_o))->((hoare_90032982_state G_15) ((insert528405184_state (((hoare_858012674_state P_21) (body Pn_3)) Q_14)) bot_bo19817387tate_o))))
% FOF formula (forall (P_20:(x_a->(state->Prop))) (Pn_2:pname) (Q_13:(x_a->(state->Prop))) (G_14:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a ((insert1597628439iple_a (((hoare_657976383iple_a P_20) (body Pn_2)) Q_13)) G_14)) ((insert1597628439iple_a (((hoare_657976383iple_a P_20) (the_com (body_1 Pn_2))) Q_13)) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_14) ((insert1597628439iple_a (((hoare_657976383iple_a P_20) (body Pn_2)) Q_13)) bot_bo1791335050le_a_o)))) of role axiom named fact_547_BodyN
% A new axiom: (forall (P_20:(x_a->(state->Prop))) (Pn_2:pname) (Q_13:(x_a->(state->Prop))) (G_14:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a ((insert1597628439iple_a (((hoare_657976383iple_a P_20) (body Pn_2)) Q_13)) G_14)) ((insert1597628439iple_a (((hoare_657976383iple_a P_20) (the_com (body_1 Pn_2))) Q_13)) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_14) ((insert1597628439iple_a (((hoare_657976383iple_a P_20) (body Pn_2)) Q_13)) bot_bo1791335050le_a_o))))
% FOF formula (forall (P_20:(state->(state->Prop))) (Pn_2:pname) (Q_13:(state->(state->Prop))) (G_14:(hoare_1708887482_state->Prop)), (((hoare_90032982_state ((insert528405184_state (((hoare_858012674_state P_20) (body Pn_2)) Q_13)) G_14)) ((insert528405184_state (((hoare_858012674_state P_20) (the_com (body_1 Pn_2))) Q_13)) bot_bo19817387tate_o))->((hoare_90032982_state G_14) ((insert528405184_state (((hoare_858012674_state P_20) (body Pn_2)) Q_13)) bot_bo19817387tate_o)))) of role axiom named fact_548_BodyN
% A new axiom: (forall (P_20:(state->(state->Prop))) (Pn_2:pname) (Q_13:(state->(state->Prop))) (G_14:(hoare_1708887482_state->Prop)), (((hoare_90032982_state ((insert528405184_state (((hoare_858012674_state P_20) (body Pn_2)) Q_13)) G_14)) ((insert528405184_state (((hoare_858012674_state P_20) (the_com (body_1 Pn_2))) Q_13)) bot_bo19817387tate_o))->((hoare_90032982_state G_14) ((insert528405184_state (((hoare_858012674_state P_20) (body Pn_2)) Q_13)) bot_bo19817387tate_o))))
% FOF formula (forall (G_13:(hoare_2091234717iple_a->Prop)) (C_18:com) (Q_12:(x_a->(state->Prop))) (P_19:(x_a->(state->Prop))), ((forall (Z_5:x_a) (S_2:state), (((P_19 Z_5) S_2)->((hoare_1467856363rivs_a G_13) ((insert1597628439iple_a (((hoare_657976383iple_a (fun (Za:x_a) (S_3:state)=> (((eq state) S_3) S_2))) C_18) (fun (Z_6:x_a)=> (Q_12 Z_5)))) bot_bo1791335050le_a_o))))->((hoare_1467856363rivs_a G_13) ((insert1597628439iple_a (((hoare_657976383iple_a P_19) C_18) Q_12)) bot_bo1791335050le_a_o)))) of role axiom named fact_549_escape
% A new axiom: (forall (G_13:(hoare_2091234717iple_a->Prop)) (C_18:com) (Q_12:(x_a->(state->Prop))) (P_19:(x_a->(state->Prop))), ((forall (Z_5:x_a) (S_2:state), (((P_19 Z_5) S_2)->((hoare_1467856363rivs_a G_13) ((insert1597628439iple_a (((hoare_657976383iple_a (fun (Za:x_a) (S_3:state)=> (((eq state) S_3) S_2))) C_18) (fun (Z_6:x_a)=> (Q_12 Z_5)))) bot_bo1791335050le_a_o))))->((hoare_1467856363rivs_a G_13) ((insert1597628439iple_a (((hoare_657976383iple_a P_19) C_18) Q_12)) bot_bo1791335050le_a_o))))
% FOF formula (forall (G_13:(hoare_1708887482_state->Prop)) (C_18:com) (Q_12:(state->(state->Prop))) (P_19:(state->(state->Prop))), ((forall (Z_5:state) (S_2:state), (((P_19 Z_5) S_2)->((hoare_90032982_state G_13) ((insert528405184_state (((hoare_858012674_state (fun (Za:state) (S_3:state)=> (((eq state) S_3) S_2))) C_18) (fun (Z_6:state)=> (Q_12 Z_5)))) bot_bo19817387tate_o))))->((hoare_90032982_state G_13) ((insert528405184_state (((hoare_858012674_state P_19) C_18) Q_12)) bot_bo19817387tate_o)))) of role axiom named fact_550_escape
% A new axiom: (forall (G_13:(hoare_1708887482_state->Prop)) (C_18:com) (Q_12:(state->(state->Prop))) (P_19:(state->(state->Prop))), ((forall (Z_5:state) (S_2:state), (((P_19 Z_5) S_2)->((hoare_90032982_state G_13) ((insert528405184_state (((hoare_858012674_state (fun (Za:state) (S_3:state)=> (((eq state) S_3) S_2))) C_18) (fun (Z_6:state)=> (Q_12 Z_5)))) bot_bo19817387tate_o))))->((hoare_90032982_state G_13) ((insert528405184_state (((hoare_858012674_state P_19) C_18) Q_12)) bot_bo19817387tate_o))))
% FOF formula (forall (P_18:(x_a->(state->Prop))) (G_12:(hoare_2091234717iple_a->Prop)) (P_17:(x_a->(state->Prop))) (C_17:com) (Q_11:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_12) ((insert1597628439iple_a (((hoare_657976383iple_a P_17) C_17) Q_11)) bot_bo1791335050le_a_o))->((forall (Z_5:x_a) (S_2:state), (((P_18 Z_5) S_2)->((P_17 Z_5) S_2)))->((hoare_1467856363rivs_a G_12) ((insert1597628439iple_a (((hoare_657976383iple_a P_18) C_17) Q_11)) bot_bo1791335050le_a_o))))) of role axiom named fact_551_conseq1
% A new axiom: (forall (P_18:(x_a->(state->Prop))) (G_12:(hoare_2091234717iple_a->Prop)) (P_17:(x_a->(state->Prop))) (C_17:com) (Q_11:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_12) ((insert1597628439iple_a (((hoare_657976383iple_a P_17) C_17) Q_11)) bot_bo1791335050le_a_o))->((forall (Z_5:x_a) (S_2:state), (((P_18 Z_5) S_2)->((P_17 Z_5) S_2)))->((hoare_1467856363rivs_a G_12) ((insert1597628439iple_a (((hoare_657976383iple_a P_18) C_17) Q_11)) bot_bo1791335050le_a_o)))))
% FOF formula (forall (P_18:(state->(state->Prop))) (G_12:(hoare_1708887482_state->Prop)) (P_17:(state->(state->Prop))) (C_17:com) (Q_11:(state->(state->Prop))), (((hoare_90032982_state G_12) ((insert528405184_state (((hoare_858012674_state P_17) C_17) Q_11)) bot_bo19817387tate_o))->((forall (Z_5:state) (S_2:state), (((P_18 Z_5) S_2)->((P_17 Z_5) S_2)))->((hoare_90032982_state G_12) ((insert528405184_state (((hoare_858012674_state P_18) C_17) Q_11)) bot_bo19817387tate_o))))) of role axiom named fact_552_conseq1
% A new axiom: (forall (P_18:(state->(state->Prop))) (G_12:(hoare_1708887482_state->Prop)) (P_17:(state->(state->Prop))) (C_17:com) (Q_11:(state->(state->Prop))), (((hoare_90032982_state G_12) ((insert528405184_state (((hoare_858012674_state P_17) C_17) Q_11)) bot_bo19817387tate_o))->((forall (Z_5:state) (S_2:state), (((P_18 Z_5) S_2)->((P_17 Z_5) S_2)))->((hoare_90032982_state G_12) ((insert528405184_state (((hoare_858012674_state P_18) C_17) Q_11)) bot_bo19817387tate_o)))))
% FOF formula (forall (Q_10:(x_a->(state->Prop))) (G_11:(hoare_2091234717iple_a->Prop)) (P_16:(x_a->(state->Prop))) (C_16:com) (Q_9:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_11) ((insert1597628439iple_a (((hoare_657976383iple_a P_16) C_16) Q_9)) bot_bo1791335050le_a_o))->((forall (Z_5:x_a) (S_2:state), (((Q_9 Z_5) S_2)->((Q_10 Z_5) S_2)))->((hoare_1467856363rivs_a G_11) ((insert1597628439iple_a (((hoare_657976383iple_a P_16) C_16) Q_10)) bot_bo1791335050le_a_o))))) of role axiom named fact_553_conseq2
% A new axiom: (forall (Q_10:(x_a->(state->Prop))) (G_11:(hoare_2091234717iple_a->Prop)) (P_16:(x_a->(state->Prop))) (C_16:com) (Q_9:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_11) ((insert1597628439iple_a (((hoare_657976383iple_a P_16) C_16) Q_9)) bot_bo1791335050le_a_o))->((forall (Z_5:x_a) (S_2:state), (((Q_9 Z_5) S_2)->((Q_10 Z_5) S_2)))->((hoare_1467856363rivs_a G_11) ((insert1597628439iple_a (((hoare_657976383iple_a P_16) C_16) Q_10)) bot_bo1791335050le_a_o)))))
% FOF formula (forall (Q_10:(state->(state->Prop))) (G_11:(hoare_1708887482_state->Prop)) (P_16:(state->(state->Prop))) (C_16:com) (Q_9:(state->(state->Prop))), (((hoare_90032982_state G_11) ((insert528405184_state (((hoare_858012674_state P_16) C_16) Q_9)) bot_bo19817387tate_o))->((forall (Z_5:state) (S_2:state), (((Q_9 Z_5) S_2)->((Q_10 Z_5) S_2)))->((hoare_90032982_state G_11) ((insert528405184_state (((hoare_858012674_state P_16) C_16) Q_10)) bot_bo19817387tate_o))))) of role axiom named fact_554_conseq2
% A new axiom: (forall (Q_10:(state->(state->Prop))) (G_11:(hoare_1708887482_state->Prop)) (P_16:(state->(state->Prop))) (C_16:com) (Q_9:(state->(state->Prop))), (((hoare_90032982_state G_11) ((insert528405184_state (((hoare_858012674_state P_16) C_16) Q_9)) bot_bo19817387tate_o))->((forall (Z_5:state) (S_2:state), (((Q_9 Z_5) S_2)->((Q_10 Z_5) S_2)))->((hoare_90032982_state G_11) ((insert528405184_state (((hoare_858012674_state P_16) C_16) Q_10)) bot_bo19817387tate_o)))))
% 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_1169027232size_a Fa) (((hoare_657976383iple_a Fun1_1) Com_3) Fun2_1))) zero_zero_nat)) of role axiom named fact_555_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_1169027232size_a Fa) (((hoare_657976383iple_a Fun1_1) Com_3) Fun2_1))) zero_zero_nat))
% FOF formula (forall (Fa:(state->nat)) (Fun1_1:(state->(state->Prop))) (Com_3:com) (Fun2_1:(state->(state->Prop))), (((eq nat) ((hoare_518771297_state Fa) (((hoare_858012674_state Fun1_1) Com_3) Fun2_1))) zero_zero_nat)) of role axiom named fact_556_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_518771297_state Fa) (((hoare_858012674_state Fun1_1) Com_3) Fun2_1))) zero_zero_nat))
% FOF formula (forall (C:com), (((eq hoare_1708887482_state) (hoare_Mirabelle_MGT C)) (((hoare_858012674_state fequal_state) C) (evalc C)))) of role axiom named fact_557_MGT__def
% A new axiom: (forall (C:com), (((eq hoare_1708887482_state) (hoare_Mirabelle_MGT C)) (((hoare_858012674_state fequal_state) C) (evalc C))))
% FOF formula (forall (Fun1:(x_a->(state->Prop))) (Com_2:com) (Fun2:(x_a->(state->Prop))), (((eq nat) (size_s1040486067iple_a (((hoare_657976383iple_a Fun1) Com_2) Fun2))) zero_zero_nat)) of role axiom named fact_558_triple_Osize_I2_J
% A new axiom: (forall (Fun1:(x_a->(state->Prop))) (Com_2:com) (Fun2:(x_a->(state->Prop))), (((eq nat) (size_s1040486067iple_a (((hoare_657976383iple_a Fun1) Com_2) Fun2))) zero_zero_nat))
% FOF formula (forall (Fun1:(state->(state->Prop))) (Com_2:com) (Fun2:(state->(state->Prop))), (((eq nat) (size_s1186992420_state (((hoare_858012674_state Fun1) Com_2) Fun2))) zero_zero_nat)) of role axiom named fact_559_triple_Osize_I2_J
% A new axiom: (forall (Fun1:(state->(state->Prop))) (Com_2:com) (Fun2:(state->(state->Prop))), (((eq nat) (size_s1186992420_state (((hoare_858012674_state Fun1) Com_2) Fun2))) zero_zero_nat))
% FOF formula (forall (Q_8:(x_a->(state->Prop))) (P_15:(x_a->(state->Prop))) (G_10:(hoare_2091234717iple_a->Prop)) (P_14:(x_a->(state->Prop))) (C_15:com) (Q_7:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_10) ((insert1597628439iple_a (((hoare_657976383iple_a P_14) C_15) Q_7)) bot_bo1791335050le_a_o))->((forall (Z_5:x_a) (S_2:state), (((P_15 Z_5) S_2)->(forall (S_3:state), ((forall (Z_6:x_a), (((P_14 Z_6) S_2)->((Q_7 Z_6) S_3)))->((Q_8 Z_5) S_3)))))->((hoare_1467856363rivs_a G_10) ((insert1597628439iple_a (((hoare_657976383iple_a P_15) C_15) Q_8)) bot_bo1791335050le_a_o))))) of role axiom named fact_560_conseq12
% A new axiom: (forall (Q_8:(x_a->(state->Prop))) (P_15:(x_a->(state->Prop))) (G_10:(hoare_2091234717iple_a->Prop)) (P_14:(x_a->(state->Prop))) (C_15:com) (Q_7:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_10) ((insert1597628439iple_a (((hoare_657976383iple_a P_14) C_15) Q_7)) bot_bo1791335050le_a_o))->((forall (Z_5:x_a) (S_2:state), (((P_15 Z_5) S_2)->(forall (S_3:state), ((forall (Z_6:x_a), (((P_14 Z_6) S_2)->((Q_7 Z_6) S_3)))->((Q_8 Z_5) S_3)))))->((hoare_1467856363rivs_a G_10) ((insert1597628439iple_a (((hoare_657976383iple_a P_15) C_15) Q_8)) bot_bo1791335050le_a_o)))))
% FOF formula (forall (Q_8:(state->(state->Prop))) (P_15:(state->(state->Prop))) (G_10:(hoare_1708887482_state->Prop)) (P_14:(state->(state->Prop))) (C_15:com) (Q_7:(state->(state->Prop))), (((hoare_90032982_state G_10) ((insert528405184_state (((hoare_858012674_state P_14) C_15) Q_7)) bot_bo19817387tate_o))->((forall (Z_5:state) (S_2:state), (((P_15 Z_5) S_2)->(forall (S_3:state), ((forall (Z_6:state), (((P_14 Z_6) S_2)->((Q_7 Z_6) S_3)))->((Q_8 Z_5) S_3)))))->((hoare_90032982_state G_10) ((insert528405184_state (((hoare_858012674_state P_15) C_15) Q_8)) bot_bo19817387tate_o))))) of role axiom named fact_561_conseq12
% A new axiom: (forall (Q_8:(state->(state->Prop))) (P_15:(state->(state->Prop))) (G_10:(hoare_1708887482_state->Prop)) (P_14:(state->(state->Prop))) (C_15:com) (Q_7:(state->(state->Prop))), (((hoare_90032982_state G_10) ((insert528405184_state (((hoare_858012674_state P_14) C_15) Q_7)) bot_bo19817387tate_o))->((forall (Z_5:state) (S_2:state), (((P_15 Z_5) S_2)->(forall (S_3:state), ((forall (Z_6:state), (((P_14 Z_6) S_2)->((Q_7 Z_6) S_3)))->((Q_8 Z_5) S_3)))))->((hoare_90032982_state G_10) ((insert528405184_state (((hoare_858012674_state P_15) C_15) Q_8)) bot_bo19817387tate_o)))))
% FOF formula (forall (X_23:nat), (((eq nat) (the_elem_nat ((insert_nat X_23) bot_bot_nat_o))) X_23)) of role axiom named fact_562_the__elem__eq
% A new axiom: (forall (X_23:nat), (((eq nat) (the_elem_nat ((insert_nat X_23) bot_bot_nat_o))) X_23))
% FOF formula (forall (X_23:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (the_el1618277441le_a_o ((insert102003750le_a_o X_23) bot_bo1957696069_a_o_o))) X_23)) of role axiom named fact_563_the__elem__eq
% A new axiom: (forall (X_23:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (the_el1618277441le_a_o ((insert102003750le_a_o X_23) bot_bo1957696069_a_o_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_564_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 (X_23:hoare_2091234717iple_a), (((eq hoare_2091234717iple_a) (the_el13400124iple_a ((insert1597628439iple_a X_23) bot_bo1791335050le_a_o))) X_23)) of role axiom named fact_565_the__elem__eq
% A new axiom: (forall (X_23:hoare_2091234717iple_a), (((eq hoare_2091234717iple_a) (the_el13400124iple_a ((insert1597628439iple_a X_23) bot_bo1791335050le_a_o))) X_23))
% FOF formula (forall (X_23:hoare_1708887482_state), (((eq hoare_1708887482_state) (the_el864710747_state ((insert528405184_state X_23) bot_bo19817387tate_o))) X_23)) of role axiom named fact_566_the__elem__eq
% A new axiom: (forall (X_23:hoare_1708887482_state), (((eq hoare_1708887482_state) (the_el864710747_state ((insert528405184_state X_23) bot_bo19817387tate_o))) X_23))
% FOF formula (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))) of role axiom named fact_567_Suc__neq__Zero
% A new axiom: (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat)))
% FOF formula (((eq nat) bot_bot_nat) zero_zero_nat) of role axiom named fact_568_bot__nat__def
% A new axiom: (((eq nat) bot_bot_nat) zero_zero_nat)
% FOF formula (forall (N_1:nat), (not (((eq nat) N_1) (suc N_1)))) of role axiom named fact_569_n__not__Suc__n
% A new axiom: (forall (N_1:nat), (not (((eq nat) N_1) (suc N_1))))
% FOF formula (forall (N_1:nat), (not (((eq nat) (suc N_1)) N_1))) of role axiom named fact_570_Suc__n__not__n
% A new axiom: (forall (N_1:nat), (not (((eq nat) (suc N_1)) N_1)))
% FOF formula (forall (Nat_3:nat) (Nat_2:nat), ((iff (((eq nat) (suc Nat_3)) (suc Nat_2))) (((eq nat) Nat_3) Nat_2))) of role axiom named fact_571_nat_Oinject
% A new axiom: (forall (Nat_3:nat) (Nat_2:nat), ((iff (((eq nat) (suc Nat_3)) (suc Nat_2))) (((eq nat) Nat_3) Nat_2)))
% 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_572_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 (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))) of role axiom named fact_573_Zero__not__Suc
% A new axiom: (forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M))))
% FOF formula (forall (Nat_2:nat), (not (((eq nat) zero_zero_nat) (suc Nat_2)))) of role axiom named fact_574_nat_Osimps_I2_J
% A new axiom: (forall (Nat_2:nat), (not (((eq nat) zero_zero_nat) (suc Nat_2))))
% FOF formula (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))) of role axiom named fact_575_Suc__not__Zero
% A new axiom: (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat)))
% FOF formula (forall (Nat_1:nat), (not (((eq nat) (suc Nat_1)) zero_zero_nat))) of role axiom named fact_576_nat_Osimps_I3_J
% A new axiom: (forall (Nat_1:nat), (not (((eq nat) (suc Nat_1)) zero_zero_nat)))
% FOF formula (forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))) of role axiom named fact_577_Zero__neq__Suc
% A new axiom: (forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M))))
% 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_578_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 (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_579_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 (P:(nat->Prop)) (K_1:nat), ((P K_1)->((forall (N:nat), ((P (suc N))->(P N)))->(P zero_zero_nat)))) of role axiom named fact_580_zero__induct
% A new axiom: (forall (P:(nat->Prop)) (K_1:nat), ((P K_1)->((forall (N:nat), ((P (suc N))->(P N)))->(P zero_zero_nat))))
% 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_581_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 (X:nat), ((iff (bot_bot_nat_o X)) bot_bot_o)) of role axiom named fact_582_bot__fun__def
% A new axiom: (forall (X:nat), ((iff (bot_bot_nat_o X)) bot_bot_o))
% FOF formula (forall (X:hoare_2091234717iple_a), ((iff (bot_bo1791335050le_a_o X)) bot_bot_o)) of role axiom named fact_583_bot__fun__def
% A new axiom: (forall (X:hoare_2091234717iple_a), ((iff (bot_bo1791335050le_a_o X)) bot_bot_o))
% FOF formula (forall (X:(hoare_2091234717iple_a->Prop)), ((iff (bot_bo1957696069_a_o_o X)) bot_bot_o)) of role axiom named fact_584_bot__fun__def
% A new axiom: (forall (X:(hoare_2091234717iple_a->Prop)), ((iff (bot_bo1957696069_a_o_o X)) bot_bot_o))
% FOF formula (forall (X:pname), ((iff (bot_bot_pname_o X)) bot_bot_o)) of role axiom named fact_585_bot__fun__def
% A new axiom: (forall (X:pname), ((iff (bot_bot_pname_o X)) bot_bot_o))
% FOF formula (forall (X:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X)) bot_bot_o)) of role axiom named fact_586_bot__fun__def
% A new axiom: (forall (X:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X)) bot_bot_o))
% FOF formula (forall (X_22:nat), ((iff (bot_bot_nat_o X_22)) bot_bot_o)) of role axiom named fact_587_bot__apply
% A new axiom: (forall (X_22:nat), ((iff (bot_bot_nat_o X_22)) bot_bot_o))
% FOF formula (forall (X_22:hoare_2091234717iple_a), ((iff (bot_bo1791335050le_a_o X_22)) bot_bot_o)) of role axiom named fact_588_bot__apply
% A new axiom: (forall (X_22:hoare_2091234717iple_a), ((iff (bot_bo1791335050le_a_o X_22)) bot_bot_o))
% FOF formula (forall (X_22:(hoare_2091234717iple_a->Prop)), ((iff (bot_bo1957696069_a_o_o X_22)) bot_bot_o)) of role axiom named fact_589_bot__apply
% A new axiom: (forall (X_22:(hoare_2091234717iple_a->Prop)), ((iff (bot_bo1957696069_a_o_o X_22)) bot_bot_o))
% FOF formula (forall (X_22:pname), ((iff (bot_bot_pname_o X_22)) bot_bot_o)) of role axiom named fact_590_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_1708887482_state), ((iff (bot_bo19817387tate_o X_22)) bot_bot_o)) of role axiom named fact_591_bot__apply
% A new axiom: (forall (X_22:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X_22)) bot_bot_o))
% 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_592_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_9:(hoare_2091234717iple_a->Prop)) (P_13:(x_a->(state->Prop))), ((hoare_1467856363rivs_a G_9) ((insert1597628439iple_a (((hoare_657976383iple_a P_13) skip) P_13)) bot_bo1791335050le_a_o))) of role axiom named fact_593_hoare__derivs_OSkip
% A new axiom: (forall (G_9:(hoare_2091234717iple_a->Prop)) (P_13:(x_a->(state->Prop))), ((hoare_1467856363rivs_a G_9) ((insert1597628439iple_a (((hoare_657976383iple_a P_13) skip) P_13)) bot_bo1791335050le_a_o)))
% FOF formula (forall (G_9:(hoare_1708887482_state->Prop)) (P_13:(state->(state->Prop))), ((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state P_13) skip) P_13)) bot_bo19817387tate_o))) of role axiom named fact_594_hoare__derivs_OSkip
% A new axiom: (forall (G_9:(hoare_1708887482_state->Prop)) (P_13:(state->(state->Prop))), ((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state P_13) skip) P_13)) bot_bo19817387tate_o)))
% FOF formula (forall (G_8:(hoare_2091234717iple_a->Prop)) (P_12:(x_a->(state->Prop))) (B_28:(state->Prop)) (C_14:com), ((hoare_1467856363rivs_a G_8) ((insert1597628439iple_a (((hoare_657976383iple_a (fun (Z_5:x_a) (S_2:state)=> ((and ((P_12 Z_5) S_2)) (not (B_28 S_2))))) ((while B_28) C_14)) P_12)) bot_bo1791335050le_a_o))) of role axiom named fact_595_LoopF
% A new axiom: (forall (G_8:(hoare_2091234717iple_a->Prop)) (P_12:(x_a->(state->Prop))) (B_28:(state->Prop)) (C_14:com), ((hoare_1467856363rivs_a G_8) ((insert1597628439iple_a (((hoare_657976383iple_a (fun (Z_5:x_a) (S_2:state)=> ((and ((P_12 Z_5) S_2)) (not (B_28 S_2))))) ((while B_28) C_14)) P_12)) bot_bo1791335050le_a_o)))
% FOF formula (forall (G_8:(hoare_1708887482_state->Prop)) (P_12:(state->(state->Prop))) (B_28:(state->Prop)) (C_14:com), ((hoare_90032982_state G_8) ((insert528405184_state (((hoare_858012674_state (fun (Z_5:state) (S_2:state)=> ((and ((P_12 Z_5) S_2)) (not (B_28 S_2))))) ((while B_28) C_14)) P_12)) bot_bo19817387tate_o))) of role axiom named fact_596_LoopF
% A new axiom: (forall (G_8:(hoare_1708887482_state->Prop)) (P_12:(state->(state->Prop))) (B_28:(state->Prop)) (C_14:com), ((hoare_90032982_state G_8) ((insert528405184_state (((hoare_858012674_state (fun (Z_5:state) (S_2:state)=> ((and ((P_12 Z_5) S_2)) (not (B_28 S_2))))) ((while B_28) C_14)) P_12)) bot_bo19817387tate_o)))
% FOF formula (forall (C:com) (N_1:nat) (B:(state->Prop)) (S:state), (((B S)->False)->((((evaln ((while B) C)) S) N_1) S))) of role axiom named fact_597_evaln_OWhileFalse
% A new axiom: (forall (C:com) (N_1:nat) (B:(state->Prop)) (S:state), (((B S)->False)->((((evaln ((while B) C)) S) N_1) S)))
% FOF formula (forall (S2:state) (C:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->(((((evaln C) S0) N_1) S1)->(((((evaln ((while B) C)) S1) N_1) S2)->((((evaln ((while B) C)) S0) N_1) S2))))) of role axiom named fact_598_evaln_OWhileTrue
% A new axiom: (forall (S2:state) (C:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->(((((evaln C) S0) N_1) S1)->(((((evaln ((while B) C)) S1) N_1) S2)->((((evaln ((while B) C)) S0) N_1) S2)))))
% FOF formula (forall (S2:state) (C:com) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->((((evalc C) S0) S1)->((((evalc ((while B) C)) S1) S2)->(((evalc ((while B) C)) S0) S2))))) of role axiom named fact_599_evalc_OWhileTrue
% A new axiom: (forall (S2:state) (C:com) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->((((evalc C) S0) S1)->((((evalc ((while B) C)) S1) S2)->(((evalc ((while B) C)) S0) S2)))))
% FOF formula (forall (C:com) (B:(state->Prop)) (S:state), (((B S)->False)->(((evalc ((while B) C)) S) S))) of role axiom named fact_600_evalc_OWhileFalse
% A new axiom: (forall (C:com) (B:(state->Prop)) (S:state), (((B S)->False)->(((evalc ((while B) C)) S) S)))
% FOF formula (forall (S:state) (N_1:nat), ((((evaln skip) S) N_1) S)) of role axiom named fact_601_evaln_OSkip
% A new axiom: (forall (S:state) (N_1:nat), ((((evaln skip) S) N_1) S))
% 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_602_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) (T:state), ((((evalc skip) S) T)->(((eq state) T) S))) of role axiom named fact_603_evalc__elim__cases_I1_J
% A new axiom: (forall (S:state) (T:state), ((((evalc skip) S) T)->(((eq state) T) S)))
% FOF formula (forall (S:state), (((evalc skip) S) S)) of role axiom named fact_604_evalc_OSkip
% A new axiom: (forall (S:state), (((evalc skip) S) S))
% FOF formula (forall (Fun:(state->Prop)) (Com:com), (not (((eq com) skip) ((while Fun) Com)))) of role axiom named fact_605_com_Osimps_I16_J
% A new axiom: (forall (Fun:(state->Prop)) (Com:com), (not (((eq com) skip) ((while Fun) Com))))
% FOF formula (forall (Fun:(state->Prop)) (Com:com), (not (((eq com) ((while Fun) Com)) skip))) of role axiom named fact_606_com_Osimps_I17_J
% A new axiom: (forall (Fun:(state->Prop)) (Com:com), (not (((eq com) ((while Fun) Com)) skip)))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_1:com) (Fun:(state->Prop)) (Com:com), ((iff (((eq com) ((while Fun_1) Com_1)) ((while Fun) Com))) ((and (((eq (state->Prop)) Fun_1) Fun)) (((eq com) Com_1) Com)))) of role axiom named fact_607_com_Osimps_I5_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_1:com) (Fun:(state->Prop)) (Com:com), ((iff (((eq com) ((while Fun_1) Com_1)) ((while Fun) Com))) ((and (((eq (state->Prop)) Fun_1) Fun)) (((eq com) Com_1) Com))))
% FOF formula (forall (C:com) (S:state) (N_1:nat) (S_4:state), (((((evaln C) S) N_1) S_4)->((((evaln C) S) (suc N_1)) S_4))) of role axiom named fact_608_evaln__Suc
% A new axiom: (forall (C:com) (S:state) (N_1:nat) (S_4:state), (((((evaln C) S) N_1) S_4)->((((evaln C) S) (suc N_1)) S_4)))
% FOF formula (forall (C:com) (S:state) (N_1:nat) (T:state), (((((evaln C) S) N_1) T)->(((evalc C) S) T))) of role axiom named fact_609_evaln__evalc
% A new axiom: (forall (C:com) (S:state) (N_1:nat) (T:state), (((((evaln C) S) N_1) T)->(((evalc C) S) T)))
% FOF formula (forall (C:com) (S:state) (T:state), ((iff (((evalc C) S) T)) ((ex nat) (fun (N:nat)=> ((((evaln C) S) N) T))))) of role axiom named fact_610_eval__eq
% A new axiom: (forall (C:com) (S:state) (T:state), ((iff (((evalc C) S) T)) ((ex nat) (fun (N:nat)=> ((((evaln C) S) N) T)))))
% FOF formula (forall (Pname:pname) (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) (body Pname)) ((while Fun_1) Com_1)))) of role axiom named fact_611_com_Osimps_I59_J
% A new axiom: (forall (Pname:pname) (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) (body Pname)) ((while Fun_1) Com_1))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_1:com) (Pname:pname), (not (((eq com) ((while Fun_1) Com_1)) (body Pname)))) of role axiom named fact_612_com_Osimps_I58_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_1:com) (Pname:pname), (not (((eq com) ((while Fun_1) Com_1)) (body Pname))))
% FOF formula (forall (Pname:pname), (not (((eq com) skip) (body Pname)))) of role axiom named fact_613_com_Osimps_I18_J
% A new axiom: (forall (Pname:pname), (not (((eq com) skip) (body Pname))))
% FOF formula (forall (Pname:pname), (not (((eq com) (body Pname)) skip))) of role axiom named fact_614_com_Osimps_I19_J
% A new axiom: (forall (Pname:pname), (not (((eq com) (body Pname)) skip)))
% FOF formula (forall (N_4:nat) (P_11:(state->(state->Prop))) (C_13:com) (Q_6:(state->(state->Prop))), ((iff ((hoare_23738522_state N_4) (((hoare_858012674_state P_11) C_13) Q_6))) (forall (Z_5:state) (S_2:state), (((P_11 Z_5) S_2)->(forall (S_3:state), (((((evaln C_13) S_2) N_4) S_3)->((Q_6 Z_5) S_3))))))) of role axiom named fact_615_triple__valid__def2
% A new axiom: (forall (N_4:nat) (P_11:(state->(state->Prop))) (C_13:com) (Q_6:(state->(state->Prop))), ((iff ((hoare_23738522_state N_4) (((hoare_858012674_state P_11) C_13) Q_6))) (forall (Z_5:state) (S_2:state), (((P_11 Z_5) S_2)->(forall (S_3:state), (((((evaln C_13) S_2) N_4) S_3)->((Q_6 Z_5) S_3)))))))
% FOF formula (forall (N_4:nat) (P_11:(x_a->(state->Prop))) (C_13:com) (Q_6:(x_a->(state->Prop))), ((iff ((hoare_1421888935alid_a N_4) (((hoare_657976383iple_a P_11) C_13) Q_6))) (forall (Z_5:x_a) (S_2:state), (((P_11 Z_5) S_2)->(forall (S_3:state), (((((evaln C_13) S_2) N_4) S_3)->((Q_6 Z_5) S_3))))))) of role axiom named fact_616_triple__valid__def2
% A new axiom: (forall (N_4:nat) (P_11:(x_a->(state->Prop))) (C_13:com) (Q_6:(x_a->(state->Prop))), ((iff ((hoare_1421888935alid_a N_4) (((hoare_657976383iple_a P_11) C_13) Q_6))) (forall (Z_5:x_a) (S_2:state), (((P_11 Z_5) S_2)->(forall (S_3:state), (((((evaln C_13) S_2) N_4) S_3)->((Q_6 Z_5) S_3)))))))
% 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_617_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 (B:(state->Prop)) (C:com) (S:state) (T:state), ((((evalc ((while B) C)) S) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), ((((evalc C) S) S1_1)->((((evalc ((while B) C)) S1_1) T)->False))))->False)))) of role axiom named fact_618_evalc__WHILE__case
% A new axiom: (forall (B:(state->Prop)) (C:com) (S:state) (T:state), ((((evalc ((while B) C)) S) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), ((((evalc C) S) S1_1)->((((evalc ((while B) C)) S1_1) T)->False))))->False))))
% FOF formula (forall (B:(state->Prop)) (C:com) (S:state) (N_1:nat) (T:state), (((((evaln ((while B) C)) S) N_1) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), (((((evaln C) S) N_1) S1_1)->(((((evaln ((while B) C)) S1_1) N_1) T)->False))))->False)))) of role axiom named fact_619_evaln__WHILE__case
% A new axiom: (forall (B:(state->Prop)) (C:com) (S:state) (N_1:nat) (T:state), (((((evaln ((while B) C)) S) N_1) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), (((((evaln C) S) N_1) S1_1)->(((((evaln ((while B) C)) S1_1) N_1) T)->False))))->False))))
% FOF formula (forall (C:com) (S:state) (T:state), ((((evalc C) S) T)->((ex nat) (fun (N:nat)=> ((((evaln C) S) N) T))))) of role axiom named fact_620_evalc__evaln
% A new axiom: (forall (C:com) (S:state) (T:state), ((((evalc C) S) T)->((ex nat) (fun (N:nat)=> ((((evaln C) S) N) T)))))
% FOF formula (forall (D:com) (R_1:(x_a->(state->Prop))) (G_7:(hoare_2091234717iple_a->Prop)) (P_10:(x_a->(state->Prop))) (C_12:com) (Q_5:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_7) ((insert1597628439iple_a (((hoare_657976383iple_a P_10) C_12) Q_5)) bot_bo1791335050le_a_o))->(((hoare_1467856363rivs_a G_7) ((insert1597628439iple_a (((hoare_657976383iple_a Q_5) D) R_1)) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_7) ((insert1597628439iple_a (((hoare_657976383iple_a P_10) ((semi C_12) D)) R_1)) bot_bo1791335050le_a_o))))) of role axiom named fact_621_Comp
% A new axiom: (forall (D:com) (R_1:(x_a->(state->Prop))) (G_7:(hoare_2091234717iple_a->Prop)) (P_10:(x_a->(state->Prop))) (C_12:com) (Q_5:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_7) ((insert1597628439iple_a (((hoare_657976383iple_a P_10) C_12) Q_5)) bot_bo1791335050le_a_o))->(((hoare_1467856363rivs_a G_7) ((insert1597628439iple_a (((hoare_657976383iple_a Q_5) D) R_1)) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_7) ((insert1597628439iple_a (((hoare_657976383iple_a P_10) ((semi C_12) D)) R_1)) bot_bo1791335050le_a_o)))))
% FOF formula (forall (D:com) (R_1:(state->(state->Prop))) (G_7:(hoare_1708887482_state->Prop)) (P_10:(state->(state->Prop))) (C_12:com) (Q_5:(state->(state->Prop))), (((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state P_10) C_12) Q_5)) bot_bo19817387tate_o))->(((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state Q_5) D) R_1)) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state P_10) ((semi C_12) D)) R_1)) bot_bo19817387tate_o))))) of role axiom named fact_622_Comp
% A new axiom: (forall (D:com) (R_1:(state->(state->Prop))) (G_7:(hoare_1708887482_state->Prop)) (P_10:(state->(state->Prop))) (C_12:com) (Q_5:(state->(state->Prop))), (((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state P_10) C_12) Q_5)) bot_bo19817387tate_o))->(((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state Q_5) D) R_1)) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state P_10) ((semi C_12) D)) R_1)) bot_bo19817387tate_o)))))
% FOF formula (forall (X_21:(nat->Prop)), (((eq nat) (the_elem_nat X_21)) (the_nat (fun (X:nat)=> (((eq (nat->Prop)) X_21) ((insert_nat X) bot_bot_nat_o)))))) of role axiom named fact_623_the__elem__def
% A new axiom: (forall (X_21:(nat->Prop)), (((eq nat) (the_elem_nat X_21)) (the_nat (fun (X:nat)=> (((eq (nat->Prop)) X_21) ((insert_nat X) bot_bot_nat_o))))))
% FOF formula (forall (X_21:((hoare_2091234717iple_a->Prop)->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (the_el1618277441le_a_o X_21)) (the_Ho2077879471le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> (((eq ((hoare_2091234717iple_a->Prop)->Prop)) X_21) ((insert102003750le_a_o X) bot_bo1957696069_a_o_o)))))) of role axiom named fact_624_the__elem__def
% A new axiom: (forall (X_21:((hoare_2091234717iple_a->Prop)->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (the_el1618277441le_a_o X_21)) (the_Ho2077879471le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> (((eq ((hoare_2091234717iple_a->Prop)->Prop)) X_21) ((insert102003750le_a_o X) bot_bo1957696069_a_o_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_625_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 (X_21:(hoare_2091234717iple_a->Prop)), (((eq hoare_2091234717iple_a) (the_el13400124iple_a X_21)) (the_Ho1471183438iple_a (fun (X:hoare_2091234717iple_a)=> (((eq (hoare_2091234717iple_a->Prop)) X_21) ((insert1597628439iple_a X) bot_bo1791335050le_a_o)))))) of role axiom named fact_626_the__elem__def
% A new axiom: (forall (X_21:(hoare_2091234717iple_a->Prop)), (((eq hoare_2091234717iple_a) (the_el13400124iple_a X_21)) (the_Ho1471183438iple_a (fun (X:hoare_2091234717iple_a)=> (((eq (hoare_2091234717iple_a->Prop)) X_21) ((insert1597628439iple_a X) bot_bo1791335050le_a_o))))))
% FOF formula (forall (X_21:(hoare_1708887482_state->Prop)), (((eq hoare_1708887482_state) (the_el864710747_state X_21)) (the_Ho851197897_state (fun (X:hoare_1708887482_state)=> (((eq (hoare_1708887482_state->Prop)) X_21) ((insert528405184_state X) bot_bo19817387tate_o)))))) of role axiom named fact_627_the__elem__def
% A new axiom: (forall (X_21:(hoare_1708887482_state->Prop)), (((eq hoare_1708887482_state) (the_el864710747_state X_21)) (the_Ho851197897_state (fun (X:hoare_1708887482_state)=> (((eq (hoare_1708887482_state->Prop)) X_21) ((insert528405184_state X) bot_bo19817387tate_o))))))
% FOF formula (forall (P_8:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (Q_4:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (C0_1:(hoare_2091234717iple_a->com)) (Q_3:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (U_1:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a U_1)->((forall (P_9:hoare_2091234717iple_a), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_1661191109iple_a (fun (P_9:hoare_2091234717iple_a)=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_1661191109iple_a (fun (P_9:hoare_2091234717iple_a)=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))) of role axiom named fact_628_finite__pointwise
% A new axiom: (forall (P_8:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (Q_4:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (C0_1:(hoare_2091234717iple_a->com)) (Q_3:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (U_1:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a U_1)->((forall (P_9:hoare_2091234717iple_a), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_1661191109iple_a (fun (P_9:hoare_2091234717iple_a)=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_1661191109iple_a (fun (P_9:hoare_2091234717iple_a)=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1))))))
% FOF formula (forall (P_8:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (Q_4:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (C0_1:((hoare_2091234717iple_a->Prop)->com)) (Q_3:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (U_1:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o U_1)->((forall (P_9:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_136408202iple_a (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_136408202iple_a (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))) of role axiom named fact_629_finite__pointwise
% A new axiom: (forall (P_8:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (Q_4:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (C0_1:((hoare_2091234717iple_a->Prop)->com)) (Q_3:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (U_1:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o U_1)->((forall (P_9:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_136408202iple_a (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_136408202iple_a (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1))))))
% FOF formula (forall (P_8:(pname->(state->(state->Prop)))) (Q_4:(pname->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(state->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_9:pname), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))) of role axiom named fact_630_finite__pointwise
% A new axiom: (forall (P_8:(pname->(state->(state->Prop)))) (Q_4:(pname->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(state->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_9:pname), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1))))))
% FOF formula (forall (P_8:(hoare_2091234717iple_a->(state->(state->Prop)))) (Q_4:(hoare_2091234717iple_a->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:(hoare_2091234717iple_a->(state->(state->Prop)))) (C0_1:(hoare_2091234717iple_a->com)) (Q_3:(hoare_2091234717iple_a->(state->(state->Prop)))) (U_1:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a U_1)->((forall (P_9:hoare_2091234717iple_a), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_1884482962_state (fun (P_9:hoare_2091234717iple_a)=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_1884482962_state (fun (P_9:hoare_2091234717iple_a)=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))) of role axiom named fact_631_finite__pointwise
% A new axiom: (forall (P_8:(hoare_2091234717iple_a->(state->(state->Prop)))) (Q_4:(hoare_2091234717iple_a->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:(hoare_2091234717iple_a->(state->(state->Prop)))) (C0_1:(hoare_2091234717iple_a->com)) (Q_3:(hoare_2091234717iple_a->(state->(state->Prop)))) (U_1:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a U_1)->((forall (P_9:hoare_2091234717iple_a), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_1884482962_state (fun (P_9:hoare_2091234717iple_a)=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_1884482962_state (fun (P_9:hoare_2091234717iple_a)=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1))))))
% FOF formula (forall (P_8:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (Q_4:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (C0_1:((hoare_2091234717iple_a->Prop)->com)) (Q_3:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (U_1:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o U_1)->((forall (P_9:(hoare_2091234717iple_a->Prop)), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_1501246093_state (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_1501246093_state (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))) of role axiom named fact_632_finite__pointwise
% A new axiom: (forall (P_8:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (Q_4:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (C0_1:((hoare_2091234717iple_a->Prop)->com)) (Q_3:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (U_1:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o U_1)->((forall (P_9:(hoare_2091234717iple_a->Prop)), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_1501246093_state (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_1501246093_state (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1))))))
% FOF formula (forall (P_8:(nat->(x_a->(state->Prop)))) (Q_4:(nat->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:(nat->(x_a->(state->Prop)))) (C0_1:(nat->com)) (Q_3:(nat->(x_a->(state->Prop)))) (U_1:(nat->Prop)), ((finite_finite_nat U_1)->((forall (P_9:nat), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_359186840iple_a (fun (P_9:nat)=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_359186840iple_a (fun (P_9:nat)=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))) of role axiom named fact_633_finite__pointwise
% A new axiom: (forall (P_8:(nat->(x_a->(state->Prop)))) (Q_4:(nat->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:(nat->(x_a->(state->Prop)))) (C0_1:(nat->com)) (Q_3:(nat->(x_a->(state->Prop)))) (U_1:(nat->Prop)), ((finite_finite_nat U_1)->((forall (P_9:nat), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_359186840iple_a (fun (P_9:nat)=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_359186840iple_a (fun (P_9:nat)=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1))))))
% FOF formula (forall (P_8:(nat->(state->(state->Prop)))) (Q_4:(nat->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:(nat->(state->(state->Prop)))) (C0_1:(nat->com)) (Q_3:(nat->(state->(state->Prop)))) (U_1:(nat->Prop)), ((finite_finite_nat U_1)->((forall (P_9:nat), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_514827263_state (fun (P_9:nat)=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_514827263_state (fun (P_9:nat)=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))) of role axiom named fact_634_finite__pointwise
% A new axiom: (forall (P_8:(nat->(state->(state->Prop)))) (Q_4:(nat->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:(nat->(state->(state->Prop)))) (C0_1:(nat->com)) (Q_3:(nat->(state->(state->Prop)))) (U_1:(nat->Prop)), ((finite_finite_nat U_1)->((forall (P_9:nat), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_514827263_state (fun (P_9:nat)=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_514827263_state (fun (P_9:nat)=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1))))))
% FOF formula (forall (P_8:(pname->(x_a->(state->Prop)))) (Q_4:(pname->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:(pname->(x_a->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(x_a->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_9:pname), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))) of role axiom named fact_635_finite__pointwise
% A new axiom: (forall (P_8:(pname->(x_a->(state->Prop)))) (Q_4:(pname->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:(pname->(x_a->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(x_a->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_9:pname), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1))))))
% 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_636_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_53:nat) (A_52:(nat->Prop)), (((member_nat A_53) A_52)->((ex (nat->Prop)) (fun (B_26:(nat->Prop))=> ((and (((eq (nat->Prop)) A_52) ((insert_nat A_53) B_26))) (((member_nat A_53) B_26)->False)))))) of role axiom named fact_637_mk__disjoint__insert
% A new axiom: (forall (A_53:nat) (A_52:(nat->Prop)), (((member_nat A_53) A_52)->((ex (nat->Prop)) (fun (B_26:(nat->Prop))=> ((and (((eq (nat->Prop)) A_52) ((insert_nat A_53) B_26))) (((member_nat A_53) B_26)->False))))))
% FOF formula (forall (A_53:(hoare_2091234717iple_a->Prop)) (A_52:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_53) A_52)->((ex ((hoare_2091234717iple_a->Prop)->Prop)) (fun (B_26:((hoare_2091234717iple_a->Prop)->Prop))=> ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_52) ((insert102003750le_a_o A_53) B_26))) (((member99268621le_a_o A_53) B_26)->False)))))) of role axiom named fact_638_mk__disjoint__insert
% A new axiom: (forall (A_53:(hoare_2091234717iple_a->Prop)) (A_52:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_53) A_52)->((ex ((hoare_2091234717iple_a->Prop)->Prop)) (fun (B_26:((hoare_2091234717iple_a->Prop)->Prop))=> ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_52) ((insert102003750le_a_o A_53) B_26))) (((member99268621le_a_o A_53) B_26)->False))))))
% FOF formula (forall (A_53:hoare_2091234717iple_a) (A_52:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_53) A_52)->((ex (hoare_2091234717iple_a->Prop)) (fun (B_26:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_52) ((insert1597628439iple_a A_53) B_26))) (((member290856304iple_a A_53) B_26)->False)))))) of role axiom named fact_639_mk__disjoint__insert
% A new axiom: (forall (A_53:hoare_2091234717iple_a) (A_52:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_53) A_52)->((ex (hoare_2091234717iple_a->Prop)) (fun (B_26:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_52) ((insert1597628439iple_a A_53) B_26))) (((member290856304iple_a A_53) B_26)->False))))))
% FOF formula (forall (A_53:hoare_1708887482_state) (A_52:(hoare_1708887482_state->Prop)), (((member451959335_state A_53) A_52)->((ex (hoare_1708887482_state->Prop)) (fun (B_26:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_52) ((insert528405184_state A_53) B_26))) (((member451959335_state A_53) B_26)->False)))))) of role axiom named fact_640_mk__disjoint__insert
% A new axiom: (forall (A_53:hoare_1708887482_state) (A_52:(hoare_1708887482_state->Prop)), (((member451959335_state A_53) A_52)->((ex (hoare_1708887482_state->Prop)) (fun (B_26:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_52) ((insert528405184_state A_53) B_26))) (((member451959335_state A_53) B_26)->False))))))
% FOF formula (forall (A_53:pname) (A_52:(pname->Prop)), (((member_pname A_53) A_52)->((ex (pname->Prop)) (fun (B_26:(pname->Prop))=> ((and (((eq (pname->Prop)) A_52) ((insert_pname A_53) B_26))) (((member_pname A_53) B_26)->False)))))) of role axiom named fact_641_mk__disjoint__insert
% A new axiom: (forall (A_53:pname) (A_52:(pname->Prop)), (((member_pname A_53) A_52)->((ex (pname->Prop)) (fun (B_26:(pname->Prop))=> ((and (((eq (pname->Prop)) A_52) ((insert_pname A_53) B_26))) (((member_pname A_53) B_26)->False))))))
% 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_642_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_643_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_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2)))) of role axiom named fact_644_com_Osimps_I3_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2))))
% FOF formula (forall (Com1_1:com) (Com2_1:com) (Pname:pname), (not (((eq com) ((semi Com1_1) Com2_1)) (body Pname)))) of role axiom named fact_645_com_Osimps_I48_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com) (Pname:pname), (not (((eq com) ((semi Com1_1) Com2_1)) (body Pname))))
% FOF formula (forall (Pname:pname) (Com1_1:com) (Com2_1:com), (not (((eq com) (body Pname)) ((semi Com1_1) Com2_1)))) of role axiom named fact_646_com_Osimps_I49_J
% A new axiom: (forall (Pname:pname) (Com1_1:com) (Com2_1:com), (not (((eq com) (body Pname)) ((semi Com1_1) Com2_1))))
% FOF formula (forall (Fun:(state->Prop)) (Com:com) (Com1_1:com) (Com2_1:com), (not (((eq com) ((while Fun) Com)) ((semi Com1_1) Com2_1)))) of role axiom named fact_647_com_Osimps_I47_J
% A new axiom: (forall (Fun:(state->Prop)) (Com:com) (Com1_1:com) (Com2_1:com), (not (((eq com) ((while Fun) Com)) ((semi Com1_1) Com2_1))))
% FOF formula (forall (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com:com), (not (((eq com) ((semi Com1_1) Com2_1)) ((while Fun) Com)))) of role axiom named fact_648_com_Osimps_I46_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com:com), (not (((eq com) ((semi Com1_1) Com2_1)) ((while Fun) Com))))
% FOF formula (forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip))) of role axiom named fact_649_com_Osimps_I13_J
% A new axiom: (forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip)))
% FOF formula (forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2)))) of role axiom named fact_650_com_Osimps_I12_J
% A new axiom: (forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2))))
% 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_651_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_652_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_1:(pname->hoare_1708887482_state)) (F_35:(pname->Prop)), ((finite_finite_pname F_35)->(finite1625599783_state ((image_1116629049_state H_1) F_35)))) of role axiom named fact_653_finite__imageI
% A new axiom: (forall (H_1:(pname->hoare_1708887482_state)) (F_35:(pname->Prop)), ((finite_finite_pname F_35)->(finite1625599783_state ((image_1116629049_state H_1) F_35))))
% FOF formula (forall (H_1:(nat->hoare_2091234717iple_a)) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite232261744iple_a ((image_359186840iple_a H_1) F_35)))) of role axiom named fact_654_finite__imageI
% A new axiom: (forall (H_1:(nat->hoare_2091234717iple_a)) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite232261744iple_a ((image_359186840iple_a H_1) F_35))))
% FOF formula (forall (H_1:(nat->(hoare_2091234717iple_a->Prop))) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite1829014797le_a_o ((image_1995609573le_a_o H_1) F_35)))) of role axiom named fact_655_finite__imageI
% A new axiom: (forall (H_1:(nat->(hoare_2091234717iple_a->Prop))) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite1829014797le_a_o ((image_1995609573le_a_o H_1) F_35))))
% FOF formula (forall (H_1:(nat->pname)) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite_finite_pname ((image_nat_pname H_1) F_35)))) of role axiom named fact_656_finite__imageI
% A new axiom: (forall (H_1:(nat->pname)) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite_finite_pname ((image_nat_pname H_1) F_35))))
% FOF formula (forall (H_1:(nat->nat)) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite_finite_nat ((image_nat_nat H_1) F_35)))) of role axiom named fact_657_finite__imageI
% A new axiom: (forall (H_1:(nat->nat)) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite_finite_nat ((image_nat_nat H_1) F_35))))
% FOF formula (forall (H_1:(hoare_2091234717iple_a->nat)) (F_35:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_35)->(finite_finite_nat ((image_1773322034_a_nat H_1) F_35)))) of role axiom named fact_658_finite__imageI
% A new axiom: (forall (H_1:(hoare_2091234717iple_a->nat)) (F_35:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_35)->(finite_finite_nat ((image_1773322034_a_nat H_1) F_35))))
% FOF formula (forall (H_1:((hoare_2091234717iple_a->Prop)->nat)) (F_35:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_35)->(finite_finite_nat ((image_75520503_o_nat H_1) F_35)))) of role axiom named fact_659_finite__imageI
% A new axiom: (forall (H_1:((hoare_2091234717iple_a->Prop)->nat)) (F_35:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_35)->(finite_finite_nat ((image_75520503_o_nat H_1) F_35))))
% FOF formula (forall (H_1:(pname->nat)) (F_35:(pname->Prop)), ((finite_finite_pname F_35)->(finite_finite_nat ((image_pname_nat H_1) F_35)))) of role axiom named fact_660_finite__imageI
% A new axiom: (forall (H_1:(pname->nat)) (F_35:(pname->Prop)), ((finite_finite_pname F_35)->(finite_finite_nat ((image_pname_nat H_1) F_35))))
% FOF formula (forall (H_1:(pname->hoare_2091234717iple_a)) (F_35:(pname->Prop)), ((finite_finite_pname F_35)->(finite232261744iple_a ((image_231808478iple_a H_1) F_35)))) of role axiom named fact_661_finite__imageI
% A new axiom: (forall (H_1:(pname->hoare_2091234717iple_a)) (F_35:(pname->Prop)), ((finite_finite_pname F_35)->(finite232261744iple_a ((image_231808478iple_a H_1) F_35))))
% FOF formula (forall (A_51:(hoare_2091234717iple_a->Prop)) (A_50:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_50)->(finite1829014797le_a_o ((insert102003750le_a_o A_51) A_50)))) of role axiom named fact_662_finite_OinsertI
% A new axiom: (forall (A_51:(hoare_2091234717iple_a->Prop)) (A_50:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_50)->(finite1829014797le_a_o ((insert102003750le_a_o A_51) A_50))))
% FOF formula (forall (A_51:pname) (A_50:(pname->Prop)), ((finite_finite_pname A_50)->(finite_finite_pname ((insert_pname A_51) A_50)))) of role axiom named fact_663_finite_OinsertI
% A new axiom: (forall (A_51:pname) (A_50:(pname->Prop)), ((finite_finite_pname A_50)->(finite_finite_pname ((insert_pname A_51) A_50))))
% FOF formula (forall (A_51:hoare_2091234717iple_a) (A_50:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a A_50)->(finite232261744iple_a ((insert1597628439iple_a A_51) A_50)))) of role axiom named fact_664_finite_OinsertI
% A new axiom: (forall (A_51:hoare_2091234717iple_a) (A_50:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a A_50)->(finite232261744iple_a ((insert1597628439iple_a A_51) A_50))))
% FOF formula (forall (A_51:hoare_1708887482_state) (A_50:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_50)->(finite1625599783_state ((insert528405184_state A_51) A_50)))) of role axiom named fact_665_finite_OinsertI
% A new axiom: (forall (A_51:hoare_1708887482_state) (A_50:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_50)->(finite1625599783_state ((insert528405184_state A_51) A_50))))
% FOF formula (forall (A_51:nat) (A_50:(nat->Prop)), ((finite_finite_nat A_50)->(finite_finite_nat ((insert_nat A_51) A_50)))) of role axiom named fact_666_finite_OinsertI
% A new axiom: (forall (A_51:nat) (A_50:(nat->Prop)), ((finite_finite_nat A_50)->(finite_finite_nat ((insert_nat A_51) A_50))))
% FOF formula (finite232261744iple_a bot_bo1791335050le_a_o) of role axiom named fact_667_finite_OemptyI
% A new axiom: (finite232261744iple_a bot_bo1791335050le_a_o)
% FOF formula (finite1829014797le_a_o bot_bo1957696069_a_o_o) of role axiom named fact_668_finite_OemptyI
% A new axiom: (finite1829014797le_a_o bot_bo1957696069_a_o_o)
% FOF formula (finite_finite_pname bot_bot_pname_o) of role axiom named fact_669_finite_OemptyI
% A new axiom: (finite_finite_pname bot_bot_pname_o)
% FOF formula (finite1625599783_state bot_bo19817387tate_o) of role axiom named fact_670_finite_OemptyI
% A new axiom: (finite1625599783_state bot_bo19817387tate_o)
% FOF formula (finite_finite_nat bot_bot_nat_o) of role axiom named fact_671_finite_OemptyI
% A new axiom: (finite_finite_nat bot_bot_nat_o)
% FOF formula (forall (Q_2:(pname->Prop)) (P_6:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_6))) (finite_finite_pname (collect_pname Q_2)))->(finite_finite_pname (collect_pname (fun (X:pname)=> ((and (P_6 X)) (Q_2 X))))))) of role axiom named fact_672_finite__Collect__conjI
% A new axiom: (forall (Q_2:(pname->Prop)) (P_6:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_6))) (finite_finite_pname (collect_pname Q_2)))->(finite_finite_pname (collect_pname (fun (X:pname)=> ((and (P_6 X)) (Q_2 X)))))))
% FOF formula (forall (Q_2:(hoare_2091234717iple_a->Prop)) (P_6:(hoare_2091234717iple_a->Prop)), (((or (finite232261744iple_a (collec992574898iple_a P_6))) (finite232261744iple_a (collec992574898iple_a Q_2)))->(finite232261744iple_a (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (P_6 X)) (Q_2 X))))))) of role axiom named fact_673_finite__Collect__conjI
% A new axiom: (forall (Q_2:(hoare_2091234717iple_a->Prop)) (P_6:(hoare_2091234717iple_a->Prop)), (((or (finite232261744iple_a (collec992574898iple_a P_6))) (finite232261744iple_a (collec992574898iple_a Q_2)))->(finite232261744iple_a (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (P_6 X)) (Q_2 X)))))))
% FOF formula (forall (Q_2:((hoare_2091234717iple_a->Prop)->Prop)) (P_6:((hoare_2091234717iple_a->Prop)->Prop)), (((or (finite1829014797le_a_o (collec1008234059le_a_o P_6))) (finite1829014797le_a_o (collec1008234059le_a_o Q_2)))->(finite1829014797le_a_o (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (P_6 X)) (Q_2 X))))))) of role axiom named fact_674_finite__Collect__conjI
% A new axiom: (forall (Q_2:((hoare_2091234717iple_a->Prop)->Prop)) (P_6:((hoare_2091234717iple_a->Prop)->Prop)), (((or (finite1829014797le_a_o (collec1008234059le_a_o P_6))) (finite1829014797le_a_o (collec1008234059le_a_o Q_2)))->(finite1829014797le_a_o (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (P_6 X)) (Q_2 X)))))))
% FOF formula (forall (Q_2:(nat->Prop)) (P_6:(nat->Prop)), (((or (finite_finite_nat (collect_nat P_6))) (finite_finite_nat (collect_nat Q_2)))->(finite_finite_nat (collect_nat (fun (X:nat)=> ((and (P_6 X)) (Q_2 X))))))) of role axiom named fact_675_finite__Collect__conjI
% A new axiom: (forall (Q_2:(nat->Prop)) (P_6:(nat->Prop)), (((or (finite_finite_nat (collect_nat P_6))) (finite_finite_nat (collect_nat Q_2)))->(finite_finite_nat (collect_nat (fun (X:nat)=> ((and (P_6 X)) (Q_2 X)))))))
% FOF formula (forall (F_34:((hoare_2091234717iple_a->Prop)->Prop)) (G_5:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o ((semila2050116131_a_o_o F_34) G_5))) ((and (finite1829014797le_a_o F_34)) (finite1829014797le_a_o G_5)))) of role axiom named fact_676_finite__Un
% A new axiom: (forall (F_34:((hoare_2091234717iple_a->Prop)->Prop)) (G_5:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o ((semila2050116131_a_o_o F_34) G_5))) ((and (finite1829014797le_a_o F_34)) (finite1829014797le_a_o G_5))))
% FOF formula (forall (F_34:(pname->Prop)) (G_5:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_34) G_5))) ((and (finite_finite_pname F_34)) (finite_finite_pname G_5)))) of role axiom named fact_677_finite__Un
% A new axiom: (forall (F_34:(pname->Prop)) (G_5:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_34) G_5))) ((and (finite_finite_pname F_34)) (finite_finite_pname G_5))))
% FOF formula (forall (F_34:(hoare_1708887482_state->Prop)) (G_5:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((semila1122118281tate_o F_34) G_5))) ((and (finite1625599783_state F_34)) (finite1625599783_state G_5)))) of role axiom named fact_678_finite__Un
% A new axiom: (forall (F_34:(hoare_1708887482_state->Prop)) (G_5:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((semila1122118281tate_o F_34) G_5))) ((and (finite1625599783_state F_34)) (finite1625599783_state G_5))))
% FOF formula (forall (F_34:(hoare_2091234717iple_a->Prop)) (G_5:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a ((semila1052848428le_a_o F_34) G_5))) ((and (finite232261744iple_a F_34)) (finite232261744iple_a G_5)))) of role axiom named fact_679_finite__Un
% A new axiom: (forall (F_34:(hoare_2091234717iple_a->Prop)) (G_5:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a ((semila1052848428le_a_o F_34) G_5))) ((and (finite232261744iple_a F_34)) (finite232261744iple_a G_5))))
% FOF formula (forall (F_34:(nat->Prop)) (G_5:(nat->Prop)), ((iff (finite_finite_nat ((semila848761471_nat_o F_34) G_5))) ((and (finite_finite_nat F_34)) (finite_finite_nat G_5)))) of role axiom named fact_680_finite__Un
% A new axiom: (forall (F_34:(nat->Prop)) (G_5:(nat->Prop)), ((iff (finite_finite_nat ((semila848761471_nat_o F_34) G_5))) ((and (finite_finite_nat F_34)) (finite_finite_nat G_5))))
% FOF formula (forall (G_4:((hoare_2091234717iple_a->Prop)->Prop)) (F_33:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_33)->((finite1829014797le_a_o G_4)->(finite1829014797le_a_o ((semila2050116131_a_o_o F_33) G_4))))) of role axiom named fact_681_finite__UnI
% A new axiom: (forall (G_4:((hoare_2091234717iple_a->Prop)->Prop)) (F_33:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_33)->((finite1829014797le_a_o G_4)->(finite1829014797le_a_o ((semila2050116131_a_o_o F_33) G_4)))))
% FOF formula (forall (G_4:(pname->Prop)) (F_33:(pname->Prop)), ((finite_finite_pname F_33)->((finite_finite_pname G_4)->(finite_finite_pname ((semila1780557381name_o F_33) G_4))))) of role axiom named fact_682_finite__UnI
% A new axiom: (forall (G_4:(pname->Prop)) (F_33:(pname->Prop)), ((finite_finite_pname F_33)->((finite_finite_pname G_4)->(finite_finite_pname ((semila1780557381name_o F_33) G_4)))))
% FOF formula (forall (G_4:(hoare_1708887482_state->Prop)) (F_33:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_33)->((finite1625599783_state G_4)->(finite1625599783_state ((semila1122118281tate_o F_33) G_4))))) of role axiom named fact_683_finite__UnI
% A new axiom: (forall (G_4:(hoare_1708887482_state->Prop)) (F_33:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_33)->((finite1625599783_state G_4)->(finite1625599783_state ((semila1122118281tate_o F_33) G_4)))))
% FOF formula (forall (G_4:(hoare_2091234717iple_a->Prop)) (F_33:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_33)->((finite232261744iple_a G_4)->(finite232261744iple_a ((semila1052848428le_a_o F_33) G_4))))) of role axiom named fact_684_finite__UnI
% A new axiom: (forall (G_4:(hoare_2091234717iple_a->Prop)) (F_33:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_33)->((finite232261744iple_a G_4)->(finite232261744iple_a ((semila1052848428le_a_o F_33) G_4)))))
% FOF formula (forall (G_4:(nat->Prop)) (F_33:(nat->Prop)), ((finite_finite_nat F_33)->((finite_finite_nat G_4)->(finite_finite_nat ((semila848761471_nat_o F_33) G_4))))) of role axiom named fact_685_finite__UnI
% A new axiom: (forall (G_4:(nat->Prop)) (F_33:(nat->Prop)), ((finite_finite_nat F_33)->((finite_finite_nat G_4)->(finite_finite_nat ((semila848761471_nat_o F_33) G_4)))))
% FOF formula (forall (P_5:(pname->Prop)) (Q_1:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X:pname)=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite_finite_pname (collect_pname P_5))) (finite_finite_pname (collect_pname Q_1))))) of role axiom named fact_686_finite__Collect__disjI
% A new axiom: (forall (P_5:(pname->Prop)) (Q_1:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X:pname)=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite_finite_pname (collect_pname P_5))) (finite_finite_pname (collect_pname Q_1)))))
% FOF formula (forall (P_5:(hoare_2091234717iple_a->Prop)) (Q_1:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite232261744iple_a (collec992574898iple_a P_5))) (finite232261744iple_a (collec992574898iple_a Q_1))))) of role axiom named fact_687_finite__Collect__disjI
% A new axiom: (forall (P_5:(hoare_2091234717iple_a->Prop)) (Q_1:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite232261744iple_a (collec992574898iple_a P_5))) (finite232261744iple_a (collec992574898iple_a Q_1)))))
% FOF formula (forall (P_5:((hoare_2091234717iple_a->Prop)->Prop)) (Q_1:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite1829014797le_a_o (collec1008234059le_a_o P_5))) (finite1829014797le_a_o (collec1008234059le_a_o Q_1))))) of role axiom named fact_688_finite__Collect__disjI
% A new axiom: (forall (P_5:((hoare_2091234717iple_a->Prop)->Prop)) (Q_1:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite1829014797le_a_o (collec1008234059le_a_o P_5))) (finite1829014797le_a_o (collec1008234059le_a_o Q_1)))))
% FOF formula (forall (P_5:(nat->Prop)) (Q_1:(nat->Prop)), ((iff (finite_finite_nat (collect_nat (fun (X:nat)=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite_finite_nat (collect_nat P_5))) (finite_finite_nat (collect_nat Q_1))))) of role axiom named fact_689_finite__Collect__disjI
% A new axiom: (forall (P_5:(nat->Prop)) (Q_1:(nat->Prop)), ((iff (finite_finite_nat (collect_nat (fun (X:nat)=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite_finite_nat (collect_nat P_5))) (finite_finite_nat (collect_nat Q_1)))))
% FOF formula (forall (A_49:(hoare_2091234717iple_a->Prop)) (A_48:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o ((insert102003750le_a_o A_49) A_48))) (finite1829014797le_a_o A_48))) of role axiom named fact_690_finite__insert
% A new axiom: (forall (A_49:(hoare_2091234717iple_a->Prop)) (A_48:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o ((insert102003750le_a_o A_49) A_48))) (finite1829014797le_a_o A_48)))
% FOF formula (forall (A_49:pname) (A_48:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_49) A_48))) (finite_finite_pname A_48))) of role axiom named fact_691_finite__insert
% A new axiom: (forall (A_49:pname) (A_48:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_49) A_48))) (finite_finite_pname A_48)))
% FOF formula (forall (A_49:hoare_2091234717iple_a) (A_48:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a ((insert1597628439iple_a A_49) A_48))) (finite232261744iple_a A_48))) of role axiom named fact_692_finite__insert
% A new axiom: (forall (A_49:hoare_2091234717iple_a) (A_48:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a ((insert1597628439iple_a A_49) A_48))) (finite232261744iple_a A_48)))
% FOF formula (forall (A_49:hoare_1708887482_state) (A_48:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((insert528405184_state A_49) A_48))) (finite1625599783_state A_48))) of role axiom named fact_693_finite__insert
% A new axiom: (forall (A_49:hoare_1708887482_state) (A_48:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((insert528405184_state A_49) A_48))) (finite1625599783_state A_48)))
% FOF formula (forall (A_49:nat) (A_48:(nat->Prop)), ((iff (finite_finite_nat ((insert_nat A_49) A_48))) (finite_finite_nat A_48))) of role axiom named fact_694_finite__insert
% A new axiom: (forall (A_49:nat) (A_48:(nat->Prop)), ((iff (finite_finite_nat ((insert_nat A_49) A_48))) (finite_finite_nat A_48)))
% FOF formula (forall (P_4:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)) (F_32:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_32)->((P_4 bot_bo1957696069_a_o_o)->((forall (X:(hoare_2091234717iple_a->Prop)) (F_25:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_25)->((((member99268621le_a_o X) F_25)->False)->((P_4 F_25)->(P_4 ((insert102003750le_a_o X) F_25))))))->(P_4 F_32))))) of role axiom named fact_695_finite__induct
% A new axiom: (forall (P_4:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)) (F_32:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_32)->((P_4 bot_bo1957696069_a_o_o)->((forall (X:(hoare_2091234717iple_a->Prop)) (F_25:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_25)->((((member99268621le_a_o X) F_25)->False)->((P_4 F_25)->(P_4 ((insert102003750le_a_o X) F_25))))))->(P_4 F_32)))))
% FOF formula (forall (P_4:((hoare_2091234717iple_a->Prop)->Prop)) (F_32:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_32)->((P_4 bot_bo1791335050le_a_o)->((forall (X:hoare_2091234717iple_a) (F_25:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_25)->((((member290856304iple_a X) F_25)->False)->((P_4 F_25)->(P_4 ((insert1597628439iple_a X) F_25))))))->(P_4 F_32))))) of role axiom named fact_696_finite__induct
% A new axiom: (forall (P_4:((hoare_2091234717iple_a->Prop)->Prop)) (F_32:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_32)->((P_4 bot_bo1791335050le_a_o)->((forall (X:hoare_2091234717iple_a) (F_25:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_25)->((((member290856304iple_a X) F_25)->False)->((P_4 F_25)->(P_4 ((insert1597628439iple_a X) F_25))))))->(P_4 F_32)))))
% FOF formula (forall (P_4:((hoare_1708887482_state->Prop)->Prop)) (F_32:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_32)->((P_4 bot_bo19817387tate_o)->((forall (X:hoare_1708887482_state) (F_25:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_25)->((((member451959335_state X) F_25)->False)->((P_4 F_25)->(P_4 ((insert528405184_state X) F_25))))))->(P_4 F_32))))) of role axiom named fact_697_finite__induct
% A new axiom: (forall (P_4:((hoare_1708887482_state->Prop)->Prop)) (F_32:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_32)->((P_4 bot_bo19817387tate_o)->((forall (X:hoare_1708887482_state) (F_25:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_25)->((((member451959335_state X) F_25)->False)->((P_4 F_25)->(P_4 ((insert528405184_state X) F_25))))))->(P_4 F_32)))))
% FOF formula (forall (P_4:((nat->Prop)->Prop)) (F_32:(nat->Prop)), ((finite_finite_nat F_32)->((P_4 bot_bot_nat_o)->((forall (X:nat) (F_25:(nat->Prop)), ((finite_finite_nat F_25)->((((member_nat X) F_25)->False)->((P_4 F_25)->(P_4 ((insert_nat X) F_25))))))->(P_4 F_32))))) of role axiom named fact_698_finite__induct
% A new axiom: (forall (P_4:((nat->Prop)->Prop)) (F_32:(nat->Prop)), ((finite_finite_nat F_32)->((P_4 bot_bot_nat_o)->((forall (X:nat) (F_25:(nat->Prop)), ((finite_finite_nat F_25)->((((member_nat X) F_25)->False)->((P_4 F_25)->(P_4 ((insert_nat X) F_25))))))->(P_4 F_32)))))
% FOF formula (forall (P_4:((pname->Prop)->Prop)) (F_32:(pname->Prop)), ((finite_finite_pname F_32)->((P_4 bot_bot_pname_o)->((forall (X:pname) (F_25:(pname->Prop)), ((finite_finite_pname F_25)->((((member_pname X) F_25)->False)->((P_4 F_25)->(P_4 ((insert_pname X) F_25))))))->(P_4 F_32))))) of role axiom named fact_699_finite__induct
% A new axiom: (forall (P_4:((pname->Prop)->Prop)) (F_32:(pname->Prop)), ((finite_finite_pname F_32)->((P_4 bot_bot_pname_o)->((forall (X:pname) (F_25:(pname->Prop)), ((finite_finite_pname F_25)->((((member_pname X) F_25)->False)->((P_4 F_25)->(P_4 ((insert_pname X) F_25))))))->(P_4 F_32)))))
% FOF formula (forall (A_46:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o A_46)) ((or (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_46) bot_bo1957696069_a_o_o)) ((ex ((hoare_2091234717iple_a->Prop)->Prop)) (fun (A_47:((hoare_2091234717iple_a->Prop)->Prop))=> ((ex (hoare_2091234717iple_a->Prop)) (fun (A_45:(hoare_2091234717iple_a->Prop))=> ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_46) ((insert102003750le_a_o A_45) A_47))) (finite1829014797le_a_o A_47))))))))) of role axiom named fact_700_finite_Osimps
% A new axiom: (forall (A_46:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o A_46)) ((or (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_46) bot_bo1957696069_a_o_o)) ((ex ((hoare_2091234717iple_a->Prop)->Prop)) (fun (A_47:((hoare_2091234717iple_a->Prop)->Prop))=> ((ex (hoare_2091234717iple_a->Prop)) (fun (A_45:(hoare_2091234717iple_a->Prop))=> ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_46) ((insert102003750le_a_o A_45) A_47))) (finite1829014797le_a_o A_47)))))))))
% FOF formula (forall (A_46:(pname->Prop)), ((iff (finite_finite_pname A_46)) ((or (((eq (pname->Prop)) A_46) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_47:(pname->Prop))=> ((ex pname) (fun (A_45:pname)=> ((and (((eq (pname->Prop)) A_46) ((insert_pname A_45) A_47))) (finite_finite_pname A_47))))))))) of role axiom named fact_701_finite_Osimps
% A new axiom: (forall (A_46:(pname->Prop)), ((iff (finite_finite_pname A_46)) ((or (((eq (pname->Prop)) A_46) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_47:(pname->Prop))=> ((ex pname) (fun (A_45:pname)=> ((and (((eq (pname->Prop)) A_46) ((insert_pname A_45) A_47))) (finite_finite_pname A_47)))))))))
% FOF formula (forall (A_46:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a A_46)) ((or (((eq (hoare_2091234717iple_a->Prop)) A_46) bot_bo1791335050le_a_o)) ((ex (hoare_2091234717iple_a->Prop)) (fun (A_47:(hoare_2091234717iple_a->Prop))=> ((ex hoare_2091234717iple_a) (fun (A_45:hoare_2091234717iple_a)=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_46) ((insert1597628439iple_a A_45) A_47))) (finite232261744iple_a A_47))))))))) of role axiom named fact_702_finite_Osimps
% A new axiom: (forall (A_46:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a A_46)) ((or (((eq (hoare_2091234717iple_a->Prop)) A_46) bot_bo1791335050le_a_o)) ((ex (hoare_2091234717iple_a->Prop)) (fun (A_47:(hoare_2091234717iple_a->Prop))=> ((ex hoare_2091234717iple_a) (fun (A_45:hoare_2091234717iple_a)=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_46) ((insert1597628439iple_a A_45) A_47))) (finite232261744iple_a A_47)))))))))
% FOF formula (forall (A_46:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state A_46)) ((or (((eq (hoare_1708887482_state->Prop)) A_46) bot_bo19817387tate_o)) ((ex (hoare_1708887482_state->Prop)) (fun (A_47:(hoare_1708887482_state->Prop))=> ((ex hoare_1708887482_state) (fun (A_45:hoare_1708887482_state)=> ((and (((eq (hoare_1708887482_state->Prop)) A_46) ((insert528405184_state A_45) A_47))) (finite1625599783_state A_47))))))))) of role axiom named fact_703_finite_Osimps
% A new axiom: (forall (A_46:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state A_46)) ((or (((eq (hoare_1708887482_state->Prop)) A_46) bot_bo19817387tate_o)) ((ex (hoare_1708887482_state->Prop)) (fun (A_47:(hoare_1708887482_state->Prop))=> ((ex hoare_1708887482_state) (fun (A_45:hoare_1708887482_state)=> ((and (((eq (hoare_1708887482_state->Prop)) A_46) ((insert528405184_state A_45) A_47))) (finite1625599783_state A_47)))))))))
% FOF formula (forall (A_46:(nat->Prop)), ((iff (finite_finite_nat A_46)) ((or (((eq (nat->Prop)) A_46) bot_bot_nat_o)) ((ex (nat->Prop)) (fun (A_47:(nat->Prop))=> ((ex nat) (fun (A_45:nat)=> ((and (((eq (nat->Prop)) A_46) ((insert_nat A_45) A_47))) (finite_finite_nat A_47))))))))) of role axiom named fact_704_finite_Osimps
% A new axiom: (forall (A_46:(nat->Prop)), ((iff (finite_finite_nat A_46)) ((or (((eq (nat->Prop)) A_46) bot_bot_nat_o)) ((ex (nat->Prop)) (fun (A_47:(nat->Prop))=> ((ex nat) (fun (A_45:nat)=> ((and (((eq (nat->Prop)) A_46) ((insert_nat A_45) A_47))) (finite_finite_nat A_47)))))))))
% FOF formula (forall (F_31:((hoare_2091234717iple_a->Prop)->nat)) (A_44:((hoare_2091234717iple_a->Prop)->Prop)), (((finite1829014797le_a_o A_44)->False)->((finite_finite_nat ((image_75520503_o_nat F_31) A_44))->((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_44)) ((finite1829014797le_a_o (collec1008234059le_a_o (fun (A_45:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False))))))) of role axiom named fact_705_pigeonhole__infinite
% A new axiom: (forall (F_31:((hoare_2091234717iple_a->Prop)->nat)) (A_44:((hoare_2091234717iple_a->Prop)->Prop)), (((finite1829014797le_a_o A_44)->False)->((finite_finite_nat ((image_75520503_o_nat F_31) A_44))->((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_44)) ((finite1829014797le_a_o (collec1008234059le_a_o (fun (A_45:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False)))))))
% FOF formula (forall (F_31:(hoare_2091234717iple_a->nat)) (A_44:(hoare_2091234717iple_a->Prop)), (((finite232261744iple_a A_44)->False)->((finite_finite_nat ((image_1773322034_a_nat F_31) A_44))->((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_44)) ((finite232261744iple_a (collec992574898iple_a (fun (A_45:hoare_2091234717iple_a)=> ((and ((member290856304iple_a A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False))))))) of role axiom named fact_706_pigeonhole__infinite
% A new axiom: (forall (F_31:(hoare_2091234717iple_a->nat)) (A_44:(hoare_2091234717iple_a->Prop)), (((finite232261744iple_a A_44)->False)->((finite_finite_nat ((image_1773322034_a_nat F_31) A_44))->((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_44)) ((finite232261744iple_a (collec992574898iple_a (fun (A_45:hoare_2091234717iple_a)=> ((and ((member290856304iple_a A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False)))))))
% FOF formula (forall (F_31:(pname->nat)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite_finite_nat ((image_pname_nat F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False))))))) of role axiom named fact_707_pigeonhole__infinite
% A new axiom: (forall (F_31:(pname->nat)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite_finite_nat ((image_pname_nat F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False)))))))
% FOF formula (forall (F_31:(nat->nat)) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite_finite_nat ((image_nat_nat F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False))))))) of role axiom named fact_708_pigeonhole__infinite
% A new axiom: (forall (F_31:(nat->nat)) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite_finite_nat ((image_nat_nat F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False)))))))
% FOF formula (forall (F_31:(nat->hoare_2091234717iple_a)) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite232261744iple_a ((image_359186840iple_a F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq hoare_2091234717iple_a) (F_31 A_45)) (F_31 X))))))->False))))))) of role axiom named fact_709_pigeonhole__infinite
% A new axiom: (forall (F_31:(nat->hoare_2091234717iple_a)) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite232261744iple_a ((image_359186840iple_a F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq hoare_2091234717iple_a) (F_31 A_45)) (F_31 X))))))->False)))))))
% FOF formula (forall (F_31:(nat->(hoare_2091234717iple_a->Prop))) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite1829014797le_a_o ((image_1995609573le_a_o F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq (hoare_2091234717iple_a->Prop)) (F_31 A_45)) (F_31 X))))))->False))))))) of role axiom named fact_710_pigeonhole__infinite
% A new axiom: (forall (F_31:(nat->(hoare_2091234717iple_a->Prop))) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite1829014797le_a_o ((image_1995609573le_a_o F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq (hoare_2091234717iple_a->Prop)) (F_31 A_45)) (F_31 X))))))->False)))))))
% FOF formula (forall (F_31:(nat->pname)) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite_finite_pname ((image_nat_pname F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq pname) (F_31 A_45)) (F_31 X))))))->False))))))) of role axiom named fact_711_pigeonhole__infinite
% A new axiom: (forall (F_31:(nat->pname)) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite_finite_pname ((image_nat_pname F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq pname) (F_31 A_45)) (F_31 X))))))->False)))))))
% FOF formula (forall (F_31:(pname->hoare_1708887482_state)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite1625599783_state ((image_1116629049_state F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq hoare_1708887482_state) (F_31 A_45)) (F_31 X))))))->False))))))) of role axiom named fact_712_pigeonhole__infinite
% A new axiom: (forall (F_31:(pname->hoare_1708887482_state)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite1625599783_state ((image_1116629049_state F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq hoare_1708887482_state) (F_31 A_45)) (F_31 X))))))->False)))))))
% FOF formula (forall (F_31:(pname->(hoare_2091234717iple_a->Prop))) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite1829014797le_a_o ((image_742317343le_a_o F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq (hoare_2091234717iple_a->Prop)) (F_31 A_45)) (F_31 X))))))->False))))))) of role axiom named fact_713_pigeonhole__infinite
% A new axiom: (forall (F_31:(pname->(hoare_2091234717iple_a->Prop))) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite1829014797le_a_o ((image_742317343le_a_o F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq (hoare_2091234717iple_a->Prop)) (F_31 A_45)) (F_31 X))))))->False)))))))
% FOF formula (forall (F_31:(pname->pname)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite_finite_pname ((image_pname_pname F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq pname) (F_31 A_45)) (F_31 X))))))->False))))))) of role axiom named fact_714_pigeonhole__infinite
% A new axiom: (forall (F_31:(pname->pname)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite_finite_pname ((image_pname_pname F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq pname) (F_31 A_45)) (F_31 X))))))->False)))))))
% FOF formula (forall (F_31:(pname->hoare_2091234717iple_a)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite232261744iple_a ((image_231808478iple_a F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq hoare_2091234717iple_a) (F_31 A_45)) (F_31 X))))))->False))))))) of role axiom named fact_715_pigeonhole__infinite
% A new axiom: (forall (F_31:(pname->hoare_2091234717iple_a)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite232261744iple_a ((image_231808478iple_a F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq hoare_2091234717iple_a) (F_31 A_45)) (F_31 X))))))->False)))))))
% FOF formula (forall (A_43:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_43) bot_bot_nat_o))) ((ex nat) (fun (X:nat)=> ((ex (nat->Prop)) (fun (B_26:(nat->Prop))=> ((and (((eq (nat->Prop)) A_43) ((insert_nat X) B_26))) (((member_nat X) B_26)->False)))))))) of role axiom named fact_716_nonempty__iff
% A new axiom: (forall (A_43:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_43) bot_bot_nat_o))) ((ex nat) (fun (X:nat)=> ((ex (nat->Prop)) (fun (B_26:(nat->Prop))=> ((and (((eq (nat->Prop)) A_43) ((insert_nat X) B_26))) (((member_nat X) B_26)->False))))))))
% FOF formula (forall (A_43:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_43) bot_bo1957696069_a_o_o))) ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((ex ((hoare_2091234717iple_a->Prop)->Prop)) (fun (B_26:((hoare_2091234717iple_a->Prop)->Prop))=> ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_43) ((insert102003750le_a_o X) B_26))) (((member99268621le_a_o X) B_26)->False)))))))) of role axiom named fact_717_nonempty__iff
% A new axiom: (forall (A_43:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_43) bot_bo1957696069_a_o_o))) ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((ex ((hoare_2091234717iple_a->Prop)->Prop)) (fun (B_26:((hoare_2091234717iple_a->Prop)->Prop))=> ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_43) ((insert102003750le_a_o X) B_26))) (((member99268621le_a_o X) B_26)->False))))))))
% FOF formula (forall (A_43:(hoare_2091234717iple_a->Prop)), ((iff (not (((eq (hoare_2091234717iple_a->Prop)) A_43) bot_bo1791335050le_a_o))) ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((ex (hoare_2091234717iple_a->Prop)) (fun (B_26:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_43) ((insert1597628439iple_a X) B_26))) (((member290856304iple_a X) B_26)->False)))))))) of role axiom named fact_718_nonempty__iff
% A new axiom: (forall (A_43:(hoare_2091234717iple_a->Prop)), ((iff (not (((eq (hoare_2091234717iple_a->Prop)) A_43) bot_bo1791335050le_a_o))) ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((ex (hoare_2091234717iple_a->Prop)) (fun (B_26:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_43) ((insert1597628439iple_a X) B_26))) (((member290856304iple_a X) B_26)->False))))))))
% FOF formula (forall (A_43:(hoare_1708887482_state->Prop)), ((iff (not (((eq (hoare_1708887482_state->Prop)) A_43) bot_bo19817387tate_o))) ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((ex (hoare_1708887482_state->Prop)) (fun (B_26:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_43) ((insert528405184_state X) B_26))) (((member451959335_state X) B_26)->False)))))))) of role axiom named fact_719_nonempty__iff
% A new axiom: (forall (A_43:(hoare_1708887482_state->Prop)), ((iff (not (((eq (hoare_1708887482_state->Prop)) A_43) bot_bo19817387tate_o))) ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((ex (hoare_1708887482_state->Prop)) (fun (B_26:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_43) ((insert528405184_state X) B_26))) (((member451959335_state X) B_26)->False))))))))
% FOF formula (forall (A_43:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_43) bot_bot_pname_o))) ((ex pname) (fun (X:pname)=> ((ex (pname->Prop)) (fun (B_26:(pname->Prop))=> ((and (((eq (pname->Prop)) A_43) ((insert_pname X) B_26))) (((member_pname X) B_26)->False)))))))) of role axiom named fact_720_nonempty__iff
% A new axiom: (forall (A_43:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_43) bot_bot_pname_o))) ((ex pname) (fun (X:pname)=> ((ex (pname->Prop)) (fun (B_26:(pname->Prop))=> ((and (((eq (pname->Prop)) A_43) ((insert_pname X) B_26))) (((member_pname X) B_26)->False))))))))
% FOF formula (forall (B_27:((hoare_2091234717iple_a->Prop)->Prop)) (A_42:((hoare_2091234717iple_a->Prop)->Prop)) (F_30:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_29:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_30) F_29)->((finite1829014797le_a_o A_42)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_42) bot_bo1957696069_a_o_o))->((finite1829014797le_a_o B_27)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_27) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_29 ((semila2050116131_a_o_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27))))))))) of role axiom named fact_721_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_27:((hoare_2091234717iple_a->Prop)->Prop)) (A_42:((hoare_2091234717iple_a->Prop)->Prop)) (F_30:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_29:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_30) F_29)->((finite1829014797le_a_o A_42)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_42) bot_bo1957696069_a_o_o))->((finite1829014797le_a_o B_27)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_27) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_29 ((semila2050116131_a_o_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27)))))))))
% FOF formula (forall (B_27:(pname->Prop)) (A_42:(pname->Prop)) (F_30:(pname->(pname->pname))) (F_29:((pname->Prop)->pname)), (((finite89670078_pname F_30) F_29)->((finite_finite_pname A_42)->((not (((eq (pname->Prop)) A_42) bot_bot_pname_o))->((finite_finite_pname B_27)->((not (((eq (pname->Prop)) B_27) bot_bot_pname_o))->(((eq pname) (F_29 ((semila1780557381name_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27))))))))) of role axiom named fact_722_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_27:(pname->Prop)) (A_42:(pname->Prop)) (F_30:(pname->(pname->pname))) (F_29:((pname->Prop)->pname)), (((finite89670078_pname F_30) F_29)->((finite_finite_pname A_42)->((not (((eq (pname->Prop)) A_42) bot_bot_pname_o))->((finite_finite_pname B_27)->((not (((eq (pname->Prop)) B_27) bot_bot_pname_o))->(((eq pname) (F_29 ((semila1780557381name_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27)))))))))
% FOF formula (forall (B_27:(hoare_1708887482_state->Prop)) (A_42:(hoare_1708887482_state->Prop)) (F_30:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_29:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_30) F_29)->((finite1625599783_state A_42)->((not (((eq (hoare_1708887482_state->Prop)) A_42) bot_bo19817387tate_o))->((finite1625599783_state B_27)->((not (((eq (hoare_1708887482_state->Prop)) B_27) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_29 ((semila1122118281tate_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27))))))))) of role axiom named fact_723_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_27:(hoare_1708887482_state->Prop)) (A_42:(hoare_1708887482_state->Prop)) (F_30:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_29:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_30) F_29)->((finite1625599783_state A_42)->((not (((eq (hoare_1708887482_state->Prop)) A_42) bot_bo19817387tate_o))->((finite1625599783_state B_27)->((not (((eq (hoare_1708887482_state->Prop)) B_27) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_29 ((semila1122118281tate_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27)))))))))
% FOF formula (forall (B_27:(hoare_2091234717iple_a->Prop)) (A_42:(hoare_2091234717iple_a->Prop)) (F_30:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_29:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_30) F_29)->((finite232261744iple_a A_42)->((not (((eq (hoare_2091234717iple_a->Prop)) A_42) bot_bo1791335050le_a_o))->((finite232261744iple_a B_27)->((not (((eq (hoare_2091234717iple_a->Prop)) B_27) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_29 ((semila1052848428le_a_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27))))))))) of role axiom named fact_724_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_27:(hoare_2091234717iple_a->Prop)) (A_42:(hoare_2091234717iple_a->Prop)) (F_30:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_29:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_30) F_29)->((finite232261744iple_a A_42)->((not (((eq (hoare_2091234717iple_a->Prop)) A_42) bot_bo1791335050le_a_o))->((finite232261744iple_a B_27)->((not (((eq (hoare_2091234717iple_a->Prop)) B_27) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_29 ((semila1052848428le_a_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27)))))))))
% FOF formula (forall (B_27:(nat->Prop)) (A_42:(nat->Prop)) (F_30:(nat->(nat->nat))) (F_29:((nat->Prop)->nat)), (((finite795500164em_nat F_30) F_29)->((finite_finite_nat A_42)->((not (((eq (nat->Prop)) A_42) bot_bot_nat_o))->((finite_finite_nat B_27)->((not (((eq (nat->Prop)) B_27) bot_bot_nat_o))->(((eq nat) (F_29 ((semila848761471_nat_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27))))))))) of role axiom named fact_725_folding__one__idem_Ounion__idem
% A new axiom: (forall (B_27:(nat->Prop)) (A_42:(nat->Prop)) (F_30:(nat->(nat->nat))) (F_29:((nat->Prop)->nat)), (((finite795500164em_nat F_30) F_29)->((finite_finite_nat A_42)->((not (((eq (nat->Prop)) A_42) bot_bot_nat_o))->((finite_finite_nat B_27)->((not (((eq (nat->Prop)) B_27) bot_bot_nat_o))->(((eq nat) (F_29 ((semila848761471_nat_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27)))))))))
% FOF formula (forall (X_20:(hoare_2091234717iple_a->Prop)) (A_41:((hoare_2091234717iple_a->Prop)->Prop)) (F_28:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_27:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_28) F_27)->((finite1829014797le_a_o A_41)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_41) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_27 ((insert102003750le_a_o X_20) A_41))) ((F_28 X_20) (F_27 A_41))))))) of role axiom named fact_726_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_20:(hoare_2091234717iple_a->Prop)) (A_41:((hoare_2091234717iple_a->Prop)->Prop)) (F_28:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_27:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_28) F_27)->((finite1829014797le_a_o A_41)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_41) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_27 ((insert102003750le_a_o X_20) A_41))) ((F_28 X_20) (F_27 A_41)))))))
% FOF formula (forall (X_20:pname) (A_41:(pname->Prop)) (F_28:(pname->(pname->pname))) (F_27:((pname->Prop)->pname)), (((finite89670078_pname F_28) F_27)->((finite_finite_pname A_41)->((not (((eq (pname->Prop)) A_41) bot_bot_pname_o))->(((eq pname) (F_27 ((insert_pname X_20) A_41))) ((F_28 X_20) (F_27 A_41))))))) of role axiom named fact_727_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_20:pname) (A_41:(pname->Prop)) (F_28:(pname->(pname->pname))) (F_27:((pname->Prop)->pname)), (((finite89670078_pname F_28) F_27)->((finite_finite_pname A_41)->((not (((eq (pname->Prop)) A_41) bot_bot_pname_o))->(((eq pname) (F_27 ((insert_pname X_20) A_41))) ((F_28 X_20) (F_27 A_41)))))))
% FOF formula (forall (X_20:hoare_2091234717iple_a) (A_41:(hoare_2091234717iple_a->Prop)) (F_28:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_27:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_28) F_27)->((finite232261744iple_a A_41)->((not (((eq (hoare_2091234717iple_a->Prop)) A_41) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_27 ((insert1597628439iple_a X_20) A_41))) ((F_28 X_20) (F_27 A_41))))))) of role axiom named fact_728_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_20:hoare_2091234717iple_a) (A_41:(hoare_2091234717iple_a->Prop)) (F_28:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_27:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_28) F_27)->((finite232261744iple_a A_41)->((not (((eq (hoare_2091234717iple_a->Prop)) A_41) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_27 ((insert1597628439iple_a X_20) A_41))) ((F_28 X_20) (F_27 A_41)))))))
% FOF formula (forall (X_20:hoare_1708887482_state) (A_41:(hoare_1708887482_state->Prop)) (F_28:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_27:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_28) F_27)->((finite1625599783_state A_41)->((not (((eq (hoare_1708887482_state->Prop)) A_41) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_27 ((insert528405184_state X_20) A_41))) ((F_28 X_20) (F_27 A_41))))))) of role axiom named fact_729_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_20:hoare_1708887482_state) (A_41:(hoare_1708887482_state->Prop)) (F_28:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_27:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_28) F_27)->((finite1625599783_state A_41)->((not (((eq (hoare_1708887482_state->Prop)) A_41) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_27 ((insert528405184_state X_20) A_41))) ((F_28 X_20) (F_27 A_41)))))))
% FOF formula (forall (X_20:nat) (A_41:(nat->Prop)) (F_28:(nat->(nat->nat))) (F_27:((nat->Prop)->nat)), (((finite795500164em_nat F_28) F_27)->((finite_finite_nat A_41)->((not (((eq (nat->Prop)) A_41) bot_bot_nat_o))->(((eq nat) (F_27 ((insert_nat X_20) A_41))) ((F_28 X_20) (F_27 A_41))))))) of role axiom named fact_730_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_20:nat) (A_41:(nat->Prop)) (F_28:(nat->(nat->nat))) (F_27:((nat->Prop)->nat)), (((finite795500164em_nat F_28) F_27)->((finite_finite_nat A_41)->((not (((eq (nat->Prop)) A_41) bot_bot_nat_o))->(((eq nat) (F_27 ((insert_nat X_20) A_41))) ((F_28 X_20) (F_27 A_41)))))))
% FOF formula (forall (F_26:(pname->hoare_1708887482_state)) (A_40:(pname->Prop)), ((finite_finite_pname A_40)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_26) A_40)) ((((finite2139561282_pname semila1122118281tate_o) (fun (X:pname)=> ((insert528405184_state (F_26 X)) bot_bo19817387tate_o))) bot_bo19817387tate_o) A_40)))) of role axiom named fact_731_image__eq__fold__image
% A new axiom: (forall (F_26:(pname->hoare_1708887482_state)) (A_40:(pname->Prop)), ((finite_finite_pname A_40)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_26) A_40)) ((((finite2139561282_pname semila1122118281tate_o) (fun (X:pname)=> ((insert528405184_state (F_26 X)) bot_bo19817387tate_o))) bot_bo19817387tate_o) A_40))))
% FOF formula (forall (F_26:(hoare_2091234717iple_a->hoare_2091234717iple_a)) (A_40:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_1661191109iple_a F_26) A_40)) ((((finite1481787452iple_a semila1052848428le_a_o) (fun (X:hoare_2091234717iple_a)=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40)))) of role axiom named fact_732_image__eq__fold__image
% A new axiom: (forall (F_26:(hoare_2091234717iple_a->hoare_2091234717iple_a)) (A_40:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_1661191109iple_a F_26) A_40)) ((((finite1481787452iple_a semila1052848428le_a_o) (fun (X:hoare_2091234717iple_a)=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40))))
% FOF formula (forall (F_26:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)) (A_40:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_136408202iple_a F_26) A_40)) ((((finite903029825le_a_o semila1052848428le_a_o) (fun (X:(hoare_2091234717iple_a->Prop))=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40)))) of role axiom named fact_733_image__eq__fold__image
% A new axiom: (forall (F_26:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)) (A_40:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_136408202iple_a F_26) A_40)) ((((finite903029825le_a_o semila1052848428le_a_o) (fun (X:(hoare_2091234717iple_a->Prop))=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40))))
% FOF formula (forall (F_26:(nat->nat)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (nat->Prop)) ((image_nat_nat F_26) A_40)) ((((finite141655318_o_nat semila848761471_nat_o) (fun (X:nat)=> ((insert_nat (F_26 X)) bot_bot_nat_o))) bot_bot_nat_o) A_40)))) of role axiom named fact_734_image__eq__fold__image
% A new axiom: (forall (F_26:(nat->nat)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (nat->Prop)) ((image_nat_nat F_26) A_40)) ((((finite141655318_o_nat semila848761471_nat_o) (fun (X:nat)=> ((insert_nat (F_26 X)) bot_bot_nat_o))) bot_bot_nat_o) A_40))))
% FOF formula (forall (F_26:(nat->(hoare_2091234717iple_a->Prop))) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((image_1995609573le_a_o F_26) A_40)) ((((finite2009943022_o_nat semila2050116131_a_o_o) (fun (X:nat)=> ((insert102003750le_a_o (F_26 X)) bot_bo1957696069_a_o_o))) bot_bo1957696069_a_o_o) A_40)))) of role axiom named fact_735_image__eq__fold__image
% A new axiom: (forall (F_26:(nat->(hoare_2091234717iple_a->Prop))) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((image_1995609573le_a_o F_26) A_40)) ((((finite2009943022_o_nat semila2050116131_a_o_o) (fun (X:nat)=> ((insert102003750le_a_o (F_26 X)) bot_bo1957696069_a_o_o))) bot_bo1957696069_a_o_o) A_40))))
% FOF formula (forall (F_26:(nat->pname)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (pname->Prop)) ((image_nat_pname F_26) A_40)) ((((finite1427591632_o_nat semila1780557381name_o) (fun (X:nat)=> ((insert_pname (F_26 X)) bot_bot_pname_o))) bot_bot_pname_o) A_40)))) of role axiom named fact_736_image__eq__fold__image
% A new axiom: (forall (F_26:(nat->pname)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (pname->Prop)) ((image_nat_pname F_26) A_40)) ((((finite1427591632_o_nat semila1780557381name_o) (fun (X:nat)=> ((insert_pname (F_26 X)) bot_bot_pname_o))) bot_bot_pname_o) A_40))))
% FOF formula (forall (F_26:(nat->hoare_2091234717iple_a)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_359186840iple_a F_26) A_40)) ((((finite2100865449_o_nat semila1052848428le_a_o) (fun (X:nat)=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40)))) of role axiom named fact_737_image__eq__fold__image
% A new axiom: (forall (F_26:(nat->hoare_2091234717iple_a)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_359186840iple_a F_26) A_40)) ((((finite2100865449_o_nat semila1052848428le_a_o) (fun (X:nat)=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40))))
% FOF formula (forall (F_26:(nat->hoare_1708887482_state)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (hoare_1708887482_state->Prop)) ((image_514827263_state F_26) A_40)) ((((finite1400355848_o_nat semila1122118281tate_o) (fun (X:nat)=> ((insert528405184_state (F_26 X)) bot_bo19817387tate_o))) bot_bo19817387tate_o) A_40)))) of role axiom named fact_738_image__eq__fold__image
% A new axiom: (forall (F_26:(nat->hoare_1708887482_state)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (hoare_1708887482_state->Prop)) ((image_514827263_state F_26) A_40)) ((((finite1400355848_o_nat semila1122118281tate_o) (fun (X:nat)=> ((insert528405184_state (F_26 X)) bot_bo19817387tate_o))) bot_bo19817387tate_o) A_40))))
% FOF formula (forall (F_26:(pname->hoare_2091234717iple_a)) (A_40:(pname->Prop)), ((finite_finite_pname A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_26) A_40)) ((((finite1290357347_pname semila1052848428le_a_o) (fun (X:pname)=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40)))) of role axiom named fact_739_image__eq__fold__image
% A new axiom: (forall (F_26:(pname->hoare_2091234717iple_a)) (A_40:(pname->Prop)), ((finite_finite_pname A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_26) A_40)) ((((finite1290357347_pname semila1052848428le_a_o) (fun (X:pname)=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40))))
% FOF formula (forall (P_3:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)) (F_24:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_24)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) F_24) bot_bo1957696069_a_o_o))->((forall (X:(hoare_2091234717iple_a->Prop)), (P_3 ((insert102003750le_a_o X) bot_bo1957696069_a_o_o)))->((forall (X:(hoare_2091234717iple_a->Prop)) (F_25:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_25)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) F_25) bot_bo1957696069_a_o_o))->((((member99268621le_a_o X) F_25)->False)->((P_3 F_25)->(P_3 ((insert102003750le_a_o X) F_25)))))))->(P_3 F_24)))))) of role axiom named fact_740_finite__ne__induct
% A new axiom: (forall (P_3:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)) (F_24:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_24)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) F_24) bot_bo1957696069_a_o_o))->((forall (X:(hoare_2091234717iple_a->Prop)), (P_3 ((insert102003750le_a_o X) bot_bo1957696069_a_o_o)))->((forall (X:(hoare_2091234717iple_a->Prop)) (F_25:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_25)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) F_25) bot_bo1957696069_a_o_o))->((((member99268621le_a_o X) F_25)->False)->((P_3 F_25)->(P_3 ((insert102003750le_a_o X) F_25)))))))->(P_3 F_24))))))
% FOF formula (forall (P_3:((hoare_2091234717iple_a->Prop)->Prop)) (F_24:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_24)->((not (((eq (hoare_2091234717iple_a->Prop)) F_24) bot_bo1791335050le_a_o))->((forall (X:hoare_2091234717iple_a), (P_3 ((insert1597628439iple_a X) bot_bo1791335050le_a_o)))->((forall (X:hoare_2091234717iple_a) (F_25:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_25)->((not (((eq (hoare_2091234717iple_a->Prop)) F_25) bot_bo1791335050le_a_o))->((((member290856304iple_a X) F_25)->False)->((P_3 F_25)->(P_3 ((insert1597628439iple_a X) F_25)))))))->(P_3 F_24)))))) of role axiom named fact_741_finite__ne__induct
% A new axiom: (forall (P_3:((hoare_2091234717iple_a->Prop)->Prop)) (F_24:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_24)->((not (((eq (hoare_2091234717iple_a->Prop)) F_24) bot_bo1791335050le_a_o))->((forall (X:hoare_2091234717iple_a), (P_3 ((insert1597628439iple_a X) bot_bo1791335050le_a_o)))->((forall (X:hoare_2091234717iple_a) (F_25:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_25)->((not (((eq (hoare_2091234717iple_a->Prop)) F_25) bot_bo1791335050le_a_o))->((((member290856304iple_a X) F_25)->False)->((P_3 F_25)->(P_3 ((insert1597628439iple_a X) F_25)))))))->(P_3 F_24))))))
% FOF formula (forall (P_3:((hoare_1708887482_state->Prop)->Prop)) (F_24:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_24)->((not (((eq (hoare_1708887482_state->Prop)) F_24) bot_bo19817387tate_o))->((forall (X:hoare_1708887482_state), (P_3 ((insert528405184_state X) bot_bo19817387tate_o)))->((forall (X:hoare_1708887482_state) (F_25:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_25)->((not (((eq (hoare_1708887482_state->Prop)) F_25) bot_bo19817387tate_o))->((((member451959335_state X) F_25)->False)->((P_3 F_25)->(P_3 ((insert528405184_state X) F_25)))))))->(P_3 F_24)))))) of role axiom named fact_742_finite__ne__induct
% A new axiom: (forall (P_3:((hoare_1708887482_state->Prop)->Prop)) (F_24:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_24)->((not (((eq (hoare_1708887482_state->Prop)) F_24) bot_bo19817387tate_o))->((forall (X:hoare_1708887482_state), (P_3 ((insert528405184_state X) bot_bo19817387tate_o)))->((forall (X:hoare_1708887482_state) (F_25:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_25)->((not (((eq (hoare_1708887482_state->Prop)) F_25) bot_bo19817387tate_o))->((((member451959335_state X) F_25)->False)->((P_3 F_25)->(P_3 ((insert528405184_state X) F_25)))))))->(P_3 F_24))))))
% FOF formula (forall (P_3:((nat->Prop)->Prop)) (F_24:(nat->Prop)), ((finite_finite_nat F_24)->((not (((eq (nat->Prop)) F_24) bot_bot_nat_o))->((forall (X:nat), (P_3 ((insert_nat X) bot_bot_nat_o)))->((forall (X:nat) (F_25:(nat->Prop)), ((finite_finite_nat F_25)->((not (((eq (nat->Prop)) F_25) bot_bot_nat_o))->((((member_nat X) F_25)->False)->((P_3 F_25)->(P_3 ((insert_nat X) F_25)))))))->(P_3 F_24)))))) of role axiom named fact_743_finite__ne__induct
% A new axiom: (forall (P_3:((nat->Prop)->Prop)) (F_24:(nat->Prop)), ((finite_finite_nat F_24)->((not (((eq (nat->Prop)) F_24) bot_bot_nat_o))->((forall (X:nat), (P_3 ((insert_nat X) bot_bot_nat_o)))->((forall (X:nat) (F_25:(nat->Prop)), ((finite_finite_nat F_25)->((not (((eq (nat->Prop)) F_25) bot_bot_nat_o))->((((member_nat X) F_25)->False)->((P_3 F_25)->(P_3 ((insert_nat X) F_25)))))))->(P_3 F_24))))))
% FOF formula (forall (P_3:((pname->Prop)->Prop)) (F_24:(pname->Prop)), ((finite_finite_pname F_24)->((not (((eq (pname->Prop)) F_24) bot_bot_pname_o))->((forall (X:pname), (P_3 ((insert_pname X) bot_bot_pname_o)))->((forall (X:pname) (F_25:(pname->Prop)), ((finite_finite_pname F_25)->((not (((eq (pname->Prop)) F_25) bot_bot_pname_o))->((((member_pname X) F_25)->False)->((P_3 F_25)->(P_3 ((insert_pname X) F_25)))))))->(P_3 F_24)))))) of role axiom named fact_744_finite__ne__induct
% A new axiom: (forall (P_3:((pname->Prop)->Prop)) (F_24:(pname->Prop)), ((finite_finite_pname F_24)->((not (((eq (pname->Prop)) F_24) bot_bot_pname_o))->((forall (X:pname), (P_3 ((insert_pname X) bot_bot_pname_o)))->((forall (X:pname) (F_25:(pname->Prop)), ((finite_finite_pname F_25)->((not (((eq (pname->Prop)) F_25) bot_bot_pname_o))->((((member_pname X) F_25)->False)->((P_3 F_25)->(P_3 ((insert_pname X) F_25)))))))->(P_3 F_24))))))
% FOF formula (forall (X_19:nat) (F_23:(nat->(nat->nat))) (F_22:((nat->Prop)->nat)), (((finite795500164em_nat F_23) F_22)->(((eq nat) ((F_23 X_19) X_19)) X_19))) of role axiom named fact_745_folding__one__idem_Oidem
% A new axiom: (forall (X_19:nat) (F_23:(nat->(nat->nat))) (F_22:((nat->Prop)->nat)), (((finite795500164em_nat F_23) F_22)->(((eq nat) ((F_23 X_19) X_19)) X_19)))
% FOF formula (forall (X_19:pname) (F_23:(pname->(pname->pname))) (F_22:((pname->Prop)->pname)), (((finite89670078_pname F_23) F_22)->(((eq pname) ((F_23 X_19) X_19)) X_19))) of role axiom named fact_746_folding__one__idem_Oidem
% A new axiom: (forall (X_19:pname) (F_23:(pname->(pname->pname))) (F_22:((pname->Prop)->pname)), (((finite89670078_pname F_23) F_22)->(((eq pname) ((F_23 X_19) X_19)) X_19)))
% FOF formula (forall (X_19:hoare_2091234717iple_a) (F_23:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_22:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_23) F_22)->(((eq hoare_2091234717iple_a) ((F_23 X_19) X_19)) X_19))) of role axiom named fact_747_folding__one__idem_Oidem
% A new axiom: (forall (X_19:hoare_2091234717iple_a) (F_23:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_22:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_23) F_22)->(((eq hoare_2091234717iple_a) ((F_23 X_19) X_19)) X_19)))
% FOF formula (forall (F_21:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (G_3:(pname->(hoare_2091234717iple_a->Prop))) (Z_4:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((((finite1290357347_pname F_21) G_3) Z_4) bot_bot_pname_o)) Z_4)) of role axiom named fact_748_fold__image__empty
% A new axiom: (forall (F_21:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (G_3:(pname->(hoare_2091234717iple_a->Prop))) (Z_4:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((((finite1290357347_pname F_21) G_3) Z_4) bot_bot_pname_o)) Z_4))
% FOF formula (forall (X_18:(hoare_2091234717iple_a->Prop)) (A_39:((hoare_2091234717iple_a->Prop)->Prop)) (F_20:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_19:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_20) F_19)->((finite1829014797le_a_o A_39)->(((member99268621le_a_o X_18) A_39)->(((eq (hoare_2091234717iple_a->Prop)) ((F_20 X_18) (F_19 A_39))) (F_19 A_39)))))) of role axiom named fact_749_folding__one__idem_Oin__idem
% A new axiom: (forall (X_18:(hoare_2091234717iple_a->Prop)) (A_39:((hoare_2091234717iple_a->Prop)->Prop)) (F_20:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_19:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_20) F_19)->((finite1829014797le_a_o A_39)->(((member99268621le_a_o X_18) A_39)->(((eq (hoare_2091234717iple_a->Prop)) ((F_20 X_18) (F_19 A_39))) (F_19 A_39))))))
% FOF formula (forall (X_18:hoare_2091234717iple_a) (A_39:(hoare_2091234717iple_a->Prop)) (F_20:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_19:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_20) F_19)->((finite232261744iple_a A_39)->(((member290856304iple_a X_18) A_39)->(((eq hoare_2091234717iple_a) ((F_20 X_18) (F_19 A_39))) (F_19 A_39)))))) of role axiom named fact_750_folding__one__idem_Oin__idem
% A new axiom: (forall (X_18:hoare_2091234717iple_a) (A_39:(hoare_2091234717iple_a->Prop)) (F_20:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_19:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_20) F_19)->((finite232261744iple_a A_39)->(((member290856304iple_a X_18) A_39)->(((eq hoare_2091234717iple_a) ((F_20 X_18) (F_19 A_39))) (F_19 A_39))))))
% FOF formula (forall (X_18:nat) (A_39:(nat->Prop)) (F_20:(nat->(nat->nat))) (F_19:((nat->Prop)->nat)), (((finite795500164em_nat F_20) F_19)->((finite_finite_nat A_39)->(((member_nat X_18) A_39)->(((eq nat) ((F_20 X_18) (F_19 A_39))) (F_19 A_39)))))) of role axiom named fact_751_folding__one__idem_Oin__idem
% A new axiom: (forall (X_18:nat) (A_39:(nat->Prop)) (F_20:(nat->(nat->nat))) (F_19:((nat->Prop)->nat)), (((finite795500164em_nat F_20) F_19)->((finite_finite_nat A_39)->(((member_nat X_18) A_39)->(((eq nat) ((F_20 X_18) (F_19 A_39))) (F_19 A_39))))))
% FOF formula (forall (X_18:pname) (A_39:(pname->Prop)) (F_20:(pname->(pname->pname))) (F_19:((pname->Prop)->pname)), (((finite89670078_pname F_20) F_19)->((finite_finite_pname A_39)->(((member_pname X_18) A_39)->(((eq pname) ((F_20 X_18) (F_19 A_39))) (F_19 A_39)))))) of role axiom named fact_752_folding__one__idem_Oin__idem
% A new axiom: (forall (X_18:pname) (A_39:(pname->Prop)) (F_20:(pname->(pname->pname))) (F_19:((pname->Prop)->pname)), (((finite89670078_pname F_20) F_19)->((finite_finite_pname A_39)->(((member_pname X_18) A_39)->(((eq pname) ((F_20 X_18) (F_19 A_39))) (F_19 A_39))))))
% FOF formula (forall (N_3:(hoare_2091234717iple_a->Prop)) (H:(hoare_2091234717iple_a->hoare_2091234717iple_a)) (F_18:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_17:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_18) F_17)->((forall (X:hoare_2091234717iple_a) (Y_7:hoare_2091234717iple_a), (((eq hoare_2091234717iple_a) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite232261744iple_a N_3)->((not (((eq (hoare_2091234717iple_a->Prop)) N_3) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (H (F_17 N_3))) (F_17 ((image_1661191109iple_a H) N_3)))))))) of role axiom named fact_753_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_3:(hoare_2091234717iple_a->Prop)) (H:(hoare_2091234717iple_a->hoare_2091234717iple_a)) (F_18:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_17:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_18) F_17)->((forall (X:hoare_2091234717iple_a) (Y_7:hoare_2091234717iple_a), (((eq hoare_2091234717iple_a) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite232261744iple_a N_3)->((not (((eq (hoare_2091234717iple_a->Prop)) N_3) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (H (F_17 N_3))) (F_17 ((image_1661191109iple_a H) N_3))))))))
% FOF formula (forall (N_3:((hoare_2091234717iple_a->Prop)->Prop)) (H:((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))) (F_18:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_17:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_18) F_17)->((forall (X:(hoare_2091234717iple_a->Prop)) (Y_7:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite1829014797le_a_o N_3)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) N_3) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (H (F_17 N_3))) (F_17 ((image_784579955le_a_o H) N_3)))))))) of role axiom named fact_754_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_3:((hoare_2091234717iple_a->Prop)->Prop)) (H:((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))) (F_18:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_17:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_18) F_17)->((forall (X:(hoare_2091234717iple_a->Prop)) (Y_7:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite1829014797le_a_o N_3)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) N_3) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (H (F_17 N_3))) (F_17 ((image_784579955le_a_o H) N_3))))))))
% FOF formula (forall (N_3:(pname->Prop)) (H:(pname->pname)) (F_18:(pname->(pname->pname))) (F_17:((pname->Prop)->pname)), (((finite89670078_pname F_18) F_17)->((forall (X:pname) (Y_7:pname), (((eq pname) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite_finite_pname N_3)->((not (((eq (pname->Prop)) N_3) bot_bot_pname_o))->(((eq pname) (H (F_17 N_3))) (F_17 ((image_pname_pname H) N_3)))))))) of role axiom named fact_755_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_3:(pname->Prop)) (H:(pname->pname)) (F_18:(pname->(pname->pname))) (F_17:((pname->Prop)->pname)), (((finite89670078_pname F_18) F_17)->((forall (X:pname) (Y_7:pname), (((eq pname) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite_finite_pname N_3)->((not (((eq (pname->Prop)) N_3) bot_bot_pname_o))->(((eq pname) (H (F_17 N_3))) (F_17 ((image_pname_pname H) N_3))))))))
% FOF formula (forall (N_3:(hoare_1708887482_state->Prop)) (H:(hoare_1708887482_state->hoare_1708887482_state)) (F_18:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_17:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_18) F_17)->((forall (X:hoare_1708887482_state) (Y_7:hoare_1708887482_state), (((eq hoare_1708887482_state) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite1625599783_state N_3)->((not (((eq (hoare_1708887482_state->Prop)) N_3) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (H (F_17 N_3))) (F_17 ((image_757158439_state H) N_3)))))))) of role axiom named fact_756_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_3:(hoare_1708887482_state->Prop)) (H:(hoare_1708887482_state->hoare_1708887482_state)) (F_18:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_17:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_18) F_17)->((forall (X:hoare_1708887482_state) (Y_7:hoare_1708887482_state), (((eq hoare_1708887482_state) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite1625599783_state N_3)->((not (((eq (hoare_1708887482_state->Prop)) N_3) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (H (F_17 N_3))) (F_17 ((image_757158439_state H) N_3))))))))
% FOF formula (forall (N_3:(nat->Prop)) (H:(nat->nat)) (F_18:(nat->(nat->nat))) (F_17:((nat->Prop)->nat)), (((finite795500164em_nat F_18) F_17)->((forall (X:nat) (Y_7:nat), (((eq nat) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite_finite_nat N_3)->((not (((eq (nat->Prop)) N_3) bot_bot_nat_o))->(((eq nat) (H (F_17 N_3))) (F_17 ((image_nat_nat H) N_3)))))))) of role axiom named fact_757_folding__one__idem_Ohom__commute
% A new axiom: (forall (N_3:(nat->Prop)) (H:(nat->nat)) (F_18:(nat->(nat->nat))) (F_17:((nat->Prop)->nat)), (((finite795500164em_nat F_18) F_17)->((forall (X:nat) (Y_7:nat), (((eq nat) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite_finite_nat N_3)->((not (((eq (nat->Prop)) N_3) bot_bot_nat_o))->(((eq nat) (H (F_17 N_3))) (F_17 ((image_nat_nat H) N_3))))))))
% FOF formula (forall (G_2:(pname->(hoare_2091234717iple_a->Prop))) (A_38:(pname->Prop)) (F_16:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (Z_3:(hoare_2091234717iple_a->Prop)) (F_15:((pname->(hoare_2091234717iple_a->Prop))->((pname->Prop)->(hoare_2091234717iple_a->Prop)))), ((((big_co1924420859_pname F_16) Z_3) F_15)->((and ((finite_finite_pname A_38)->(((eq (hoare_2091234717iple_a->Prop)) ((F_15 G_2) A_38)) ((((finite1290357347_pname F_16) G_2) Z_3) A_38)))) (((finite_finite_pname A_38)->False)->(((eq (hoare_2091234717iple_a->Prop)) ((F_15 G_2) A_38)) Z_3))))) of role axiom named fact_758_comm__monoid__big_OF__eq
% A new axiom: (forall (G_2:(pname->(hoare_2091234717iple_a->Prop))) (A_38:(pname->Prop)) (F_16:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (Z_3:(hoare_2091234717iple_a->Prop)) (F_15:((pname->(hoare_2091234717iple_a->Prop))->((pname->Prop)->(hoare_2091234717iple_a->Prop)))), ((((big_co1924420859_pname F_16) Z_3) F_15)->((and ((finite_finite_pname A_38)->(((eq (hoare_2091234717iple_a->Prop)) ((F_15 G_2) A_38)) ((((finite1290357347_pname F_16) G_2) Z_3) A_38)))) (((finite_finite_pname A_38)->False)->(((eq (hoare_2091234717iple_a->Prop)) ((F_15 G_2) A_38)) Z_3)))))
% FOF formula (forall (X_17:(hoare_2091234717iple_a->Prop)) (A_37:((hoare_2091234717iple_a->Prop)->Prop)) (F_14:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_13:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_14) F_13)->((finite1829014797le_a_o A_37)->((((member99268621le_a_o X_17) A_37)->False)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_37) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_13 ((insert102003750le_a_o X_17) A_37))) ((F_14 X_17) (F_13 A_37)))))))) of role axiom named fact_759_folding__one_Oinsert
% A new axiom: (forall (X_17:(hoare_2091234717iple_a->Prop)) (A_37:((hoare_2091234717iple_a->Prop)->Prop)) (F_14:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_13:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_14) F_13)->((finite1829014797le_a_o A_37)->((((member99268621le_a_o X_17) A_37)->False)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_37) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_13 ((insert102003750le_a_o X_17) A_37))) ((F_14 X_17) (F_13 A_37))))))))
% FOF formula (forall (X_17:hoare_2091234717iple_a) (A_37:(hoare_2091234717iple_a->Prop)) (F_14:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_13:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_14) F_13)->((finite232261744iple_a A_37)->((((member290856304iple_a X_17) A_37)->False)->((not (((eq (hoare_2091234717iple_a->Prop)) A_37) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_13 ((insert1597628439iple_a X_17) A_37))) ((F_14 X_17) (F_13 A_37)))))))) of role axiom named fact_760_folding__one_Oinsert
% A new axiom: (forall (X_17:hoare_2091234717iple_a) (A_37:(hoare_2091234717iple_a->Prop)) (F_14:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_13:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_14) F_13)->((finite232261744iple_a A_37)->((((member290856304iple_a X_17) A_37)->False)->((not (((eq (hoare_2091234717iple_a->Prop)) A_37) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_13 ((insert1597628439iple_a X_17) A_37))) ((F_14 X_17) (F_13 A_37))))))))
% FOF formula (forall (X_17:hoare_1708887482_state) (A_37:(hoare_1708887482_state->Prop)) (F_14:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_13:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_14) F_13)->((finite1625599783_state A_37)->((((member451959335_state X_17) A_37)->False)->((not (((eq (hoare_1708887482_state->Prop)) A_37) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_13 ((insert528405184_state X_17) A_37))) ((F_14 X_17) (F_13 A_37)))))))) of role axiom named fact_761_folding__one_Oinsert
% A new axiom: (forall (X_17:hoare_1708887482_state) (A_37:(hoare_1708887482_state->Prop)) (F_14:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_13:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_14) F_13)->((finite1625599783_state A_37)->((((member451959335_state X_17) A_37)->False)->((not (((eq (hoare_1708887482_state->Prop)) A_37) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_13 ((insert528405184_state X_17) A_37))) ((F_14 X_17) (F_13 A_37))))))))
% FOF formula (forall (X_17:nat) (A_37:(nat->Prop)) (F_14:(nat->(nat->nat))) (F_13:((nat->Prop)->nat)), (((finite988810631ne_nat F_14) F_13)->((finite_finite_nat A_37)->((((member_nat X_17) A_37)->False)->((not (((eq (nat->Prop)) A_37) bot_bot_nat_o))->(((eq nat) (F_13 ((insert_nat X_17) A_37))) ((F_14 X_17) (F_13 A_37)))))))) of role axiom named fact_762_folding__one_Oinsert
% A new axiom: (forall (X_17:nat) (A_37:(nat->Prop)) (F_14:(nat->(nat->nat))) (F_13:((nat->Prop)->nat)), (((finite988810631ne_nat F_14) F_13)->((finite_finite_nat A_37)->((((member_nat X_17) A_37)->False)->((not (((eq (nat->Prop)) A_37) bot_bot_nat_o))->(((eq nat) (F_13 ((insert_nat X_17) A_37))) ((F_14 X_17) (F_13 A_37))))))))
% FOF formula (forall (X_17:pname) (A_37:(pname->Prop)) (F_14:(pname->(pname->pname))) (F_13:((pname->Prop)->pname)), (((finite1282449217_pname F_14) F_13)->((finite_finite_pname A_37)->((((member_pname X_17) A_37)->False)->((not (((eq (pname->Prop)) A_37) bot_bot_pname_o))->(((eq pname) (F_13 ((insert_pname X_17) A_37))) ((F_14 X_17) (F_13 A_37)))))))) of role axiom named fact_763_folding__one_Oinsert
% A new axiom: (forall (X_17:pname) (A_37:(pname->Prop)) (F_14:(pname->(pname->pname))) (F_13:((pname->Prop)->pname)), (((finite1282449217_pname F_14) F_13)->((finite_finite_pname A_37)->((((member_pname X_17) A_37)->False)->((not (((eq (pname->Prop)) A_37) bot_bot_pname_o))->(((eq pname) (F_13 ((insert_pname X_17) A_37))) ((F_14 X_17) (F_13 A_37))))))))
% FOF formula (forall (X_16:nat) (F_12:(nat->(nat->nat))) (F_11:((nat->Prop)->nat)), (((finite988810631ne_nat F_12) F_11)->(((eq nat) (F_11 ((insert_nat X_16) bot_bot_nat_o))) X_16))) of role axiom named fact_764_folding__one_Osingleton
% A new axiom: (forall (X_16:nat) (F_12:(nat->(nat->nat))) (F_11:((nat->Prop)->nat)), (((finite988810631ne_nat F_12) F_11)->(((eq nat) (F_11 ((insert_nat X_16) bot_bot_nat_o))) X_16)))
% FOF formula (forall (X_16:(hoare_2091234717iple_a->Prop)) (F_12:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_11:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_12) F_11)->(((eq (hoare_2091234717iple_a->Prop)) (F_11 ((insert102003750le_a_o X_16) bot_bo1957696069_a_o_o))) X_16))) of role axiom named fact_765_folding__one_Osingleton
% A new axiom: (forall (X_16:(hoare_2091234717iple_a->Prop)) (F_12:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_11:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_12) F_11)->(((eq (hoare_2091234717iple_a->Prop)) (F_11 ((insert102003750le_a_o X_16) bot_bo1957696069_a_o_o))) X_16)))
% FOF formula (forall (X_16:pname) (F_12:(pname->(pname->pname))) (F_11:((pname->Prop)->pname)), (((finite1282449217_pname F_12) F_11)->(((eq pname) (F_11 ((insert_pname X_16) bot_bot_pname_o))) X_16))) of role axiom named fact_766_folding__one_Osingleton
% A new axiom: (forall (X_16:pname) (F_12:(pname->(pname->pname))) (F_11:((pname->Prop)->pname)), (((finite1282449217_pname F_12) F_11)->(((eq pname) (F_11 ((insert_pname X_16) bot_bot_pname_o))) X_16)))
% FOF formula (forall (X_16:hoare_2091234717iple_a) (F_12:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_11:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_12) F_11)->(((eq hoare_2091234717iple_a) (F_11 ((insert1597628439iple_a X_16) bot_bo1791335050le_a_o))) X_16))) of role axiom named fact_767_folding__one_Osingleton
% A new axiom: (forall (X_16:hoare_2091234717iple_a) (F_12:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_11:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_12) F_11)->(((eq hoare_2091234717iple_a) (F_11 ((insert1597628439iple_a X_16) bot_bo1791335050le_a_o))) X_16)))
% FOF formula (forall (X_16:hoare_1708887482_state) (F_12:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_11:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_12) F_11)->(((eq hoare_1708887482_state) (F_11 ((insert528405184_state X_16) bot_bo19817387tate_o))) X_16))) of role axiom named fact_768_folding__one_Osingleton
% A new axiom: (forall (X_16:hoare_1708887482_state) (F_12:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_11:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_12) F_11)->(((eq hoare_1708887482_state) (F_11 ((insert528405184_state X_16) bot_bo19817387tate_o))) X_16)))
% FOF formula (forall (A_36:((hoare_2091234717iple_a->Prop)->Prop)) (F_10:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_9:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_10) F_9)->((finite1829014797le_a_o A_36)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_36) bot_bo1957696069_a_o_o))->((forall (X:(hoare_2091234717iple_a->Prop)) (Y_7:(hoare_2091234717iple_a->Prop)), ((member99268621le_a_o ((F_10 X) Y_7)) ((insert102003750le_a_o X) ((insert102003750le_a_o Y_7) bot_bo1957696069_a_o_o))))->((member99268621le_a_o (F_9 A_36)) A_36)))))) of role axiom named fact_769_folding__one_Oclosed
% A new axiom: (forall (A_36:((hoare_2091234717iple_a->Prop)->Prop)) (F_10:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_9:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_10) F_9)->((finite1829014797le_a_o A_36)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_36) bot_bo1957696069_a_o_o))->((forall (X:(hoare_2091234717iple_a->Prop)) (Y_7:(hoare_2091234717iple_a->Prop)), ((member99268621le_a_o ((F_10 X) Y_7)) ((insert102003750le_a_o X) ((insert102003750le_a_o Y_7) bot_bo1957696069_a_o_o))))->((member99268621le_a_o (F_9 A_36)) A_36))))))
% FOF formula (forall (A_36:(hoare_2091234717iple_a->Prop)) (F_10:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_9:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_10) F_9)->((finite232261744iple_a A_36)->((not (((eq (hoare_2091234717iple_a->Prop)) A_36) bot_bo1791335050le_a_o))->((forall (X:hoare_2091234717iple_a) (Y_7:hoare_2091234717iple_a), ((member290856304iple_a ((F_10 X) Y_7)) ((insert1597628439iple_a X) ((insert1597628439iple_a Y_7) bot_bo1791335050le_a_o))))->((member290856304iple_a (F_9 A_36)) A_36)))))) of role axiom named fact_770_folding__one_Oclosed
% A new axiom: (forall (A_36:(hoare_2091234717iple_a->Prop)) (F_10:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_9:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_10) F_9)->((finite232261744iple_a A_36)->((not (((eq (hoare_2091234717iple_a->Prop)) A_36) bot_bo1791335050le_a_o))->((forall (X:hoare_2091234717iple_a) (Y_7:hoare_2091234717iple_a), ((member290856304iple_a ((F_10 X) Y_7)) ((insert1597628439iple_a X) ((insert1597628439iple_a Y_7) bot_bo1791335050le_a_o))))->((member290856304iple_a (F_9 A_36)) A_36))))))
% FOF formula (forall (A_36:(hoare_1708887482_state->Prop)) (F_10:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_9:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_10) F_9)->((finite1625599783_state A_36)->((not (((eq (hoare_1708887482_state->Prop)) A_36) bot_bo19817387tate_o))->((forall (X:hoare_1708887482_state) (Y_7:hoare_1708887482_state), ((member451959335_state ((F_10 X) Y_7)) ((insert528405184_state X) ((insert528405184_state Y_7) bot_bo19817387tate_o))))->((member451959335_state (F_9 A_36)) A_36)))))) of role axiom named fact_771_folding__one_Oclosed
% A new axiom: (forall (A_36:(hoare_1708887482_state->Prop)) (F_10:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_9:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_10) F_9)->((finite1625599783_state A_36)->((not (((eq (hoare_1708887482_state->Prop)) A_36) bot_bo19817387tate_o))->((forall (X:hoare_1708887482_state) (Y_7:hoare_1708887482_state), ((member451959335_state ((F_10 X) Y_7)) ((insert528405184_state X) ((insert528405184_state Y_7) bot_bo19817387tate_o))))->((member451959335_state (F_9 A_36)) A_36))))))
% FOF formula (forall (A_36:(nat->Prop)) (F_10:(nat->(nat->nat))) (F_9:((nat->Prop)->nat)), (((finite988810631ne_nat F_10) F_9)->((finite_finite_nat A_36)->((not (((eq (nat->Prop)) A_36) bot_bot_nat_o))->((forall (X:nat) (Y_7:nat), ((member_nat ((F_10 X) Y_7)) ((insert_nat X) ((insert_nat Y_7) bot_bot_nat_o))))->((member_nat (F_9 A_36)) A_36)))))) of role axiom named fact_772_folding__one_Oclosed
% A new axiom: (forall (A_36:(nat->Prop)) (F_10:(nat->(nat->nat))) (F_9:((nat->Prop)->nat)), (((finite988810631ne_nat F_10) F_9)->((finite_finite_nat A_36)->((not (((eq (nat->Prop)) A_36) bot_bot_nat_o))->((forall (X:nat) (Y_7:nat), ((member_nat ((F_10 X) Y_7)) ((insert_nat X) ((insert_nat Y_7) bot_bot_nat_o))))->((member_nat (F_9 A_36)) A_36))))))
% FOF formula (forall (A_36:(pname->Prop)) (F_10:(pname->(pname->pname))) (F_9:((pname->Prop)->pname)), (((finite1282449217_pname F_10) F_9)->((finite_finite_pname A_36)->((not (((eq (pname->Prop)) A_36) bot_bot_pname_o))->((forall (X:pname) (Y_7:pname), ((member_pname ((F_10 X) Y_7)) ((insert_pname X) ((insert_pname Y_7) bot_bot_pname_o))))->((member_pname (F_9 A_36)) A_36)))))) of role axiom named fact_773_folding__one_Oclosed
% A new axiom: (forall (A_36:(pname->Prop)) (F_10:(pname->(pname->pname))) (F_9:((pname->Prop)->pname)), (((finite1282449217_pname F_10) F_9)->((finite_finite_pname A_36)->((not (((eq (pname->Prop)) A_36) bot_bot_pname_o))->((forall (X:pname) (Y_7:pname), ((member_pname ((F_10 X) Y_7)) ((insert_pname X) ((insert_pname Y_7) bot_bot_pname_o))))->((member_pname (F_9 A_36)) A_36))))))
% FOF formula (forall (X_15:nat) (A_35:(nat->Prop)), (((member_nat X_15) A_35)->((forall (B_26:(nat->Prop)), ((((eq (nat->Prop)) A_35) ((insert_nat X_15) B_26))->((member_nat X_15) B_26)))->False))) of role axiom named fact_774_Set_Oset__insert
% A new axiom: (forall (X_15:nat) (A_35:(nat->Prop)), (((member_nat X_15) A_35)->((forall (B_26:(nat->Prop)), ((((eq (nat->Prop)) A_35) ((insert_nat X_15) B_26))->((member_nat X_15) B_26)))->False)))
% FOF formula (forall (X_15:(hoare_2091234717iple_a->Prop)) (A_35:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o X_15) A_35)->((forall (B_26:((hoare_2091234717iple_a->Prop)->Prop)), ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_35) ((insert102003750le_a_o X_15) B_26))->((member99268621le_a_o X_15) B_26)))->False))) of role axiom named fact_775_Set_Oset__insert
% A new axiom: (forall (X_15:(hoare_2091234717iple_a->Prop)) (A_35:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o X_15) A_35)->((forall (B_26:((hoare_2091234717iple_a->Prop)->Prop)), ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_35) ((insert102003750le_a_o X_15) B_26))->((member99268621le_a_o X_15) B_26)))->False)))
% FOF formula (forall (X_15:hoare_2091234717iple_a) (A_35:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a X_15) A_35)->((forall (B_26:(hoare_2091234717iple_a->Prop)), ((((eq (hoare_2091234717iple_a->Prop)) A_35) ((insert1597628439iple_a X_15) B_26))->((member290856304iple_a X_15) B_26)))->False))) of role axiom named fact_776_Set_Oset__insert
% A new axiom: (forall (X_15:hoare_2091234717iple_a) (A_35:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a X_15) A_35)->((forall (B_26:(hoare_2091234717iple_a->Prop)), ((((eq (hoare_2091234717iple_a->Prop)) A_35) ((insert1597628439iple_a X_15) B_26))->((member290856304iple_a X_15) B_26)))->False)))
% FOF formula (forall (X_15:hoare_1708887482_state) (A_35:(hoare_1708887482_state->Prop)), (((member451959335_state X_15) A_35)->((forall (B_26:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_35) ((insert528405184_state X_15) B_26))->((member451959335_state X_15) B_26)))->False))) of role axiom named fact_777_Set_Oset__insert
% A new axiom: (forall (X_15:hoare_1708887482_state) (A_35:(hoare_1708887482_state->Prop)), (((member451959335_state X_15) A_35)->((forall (B_26:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_35) ((insert528405184_state X_15) B_26))->((member451959335_state X_15) B_26)))->False)))
% FOF formula (forall (X_15:pname) (A_35:(pname->Prop)), (((member_pname X_15) A_35)->((forall (B_26:(pname->Prop)), ((((eq (pname->Prop)) A_35) ((insert_pname X_15) B_26))->((member_pname X_15) B_26)))->False))) of role axiom named fact_778_Set_Oset__insert
% A new axiom: (forall (X_15:pname) (A_35:(pname->Prop)), (((member_pname X_15) A_35)->((forall (B_26:(pname->Prop)), ((((eq (pname->Prop)) A_35) ((insert_pname X_15) B_26))->((member_pname X_15) B_26)))->False)))
% FOF formula (forall (A_34:(nat->Prop)), ((forall (Y_7:nat), (((member_nat Y_7) A_34)->False))->(((eq (nat->Prop)) A_34) bot_bot_nat_o))) of role axiom named fact_779_equals0I
% A new axiom: (forall (A_34:(nat->Prop)), ((forall (Y_7:nat), (((member_nat Y_7) A_34)->False))->(((eq (nat->Prop)) A_34) bot_bot_nat_o)))
% FOF formula (forall (A_34:((hoare_2091234717iple_a->Prop)->Prop)), ((forall (Y_7:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o Y_7) A_34)->False))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_34) bot_bo1957696069_a_o_o))) of role axiom named fact_780_equals0I
% A new axiom: (forall (A_34:((hoare_2091234717iple_a->Prop)->Prop)), ((forall (Y_7:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o Y_7) A_34)->False))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_34) bot_bo1957696069_a_o_o)))
% FOF formula (forall (A_34:(hoare_2091234717iple_a->Prop)), ((forall (Y_7:hoare_2091234717iple_a), (((member290856304iple_a Y_7) A_34)->False))->(((eq (hoare_2091234717iple_a->Prop)) A_34) bot_bo1791335050le_a_o))) of role axiom named fact_781_equals0I
% A new axiom: (forall (A_34:(hoare_2091234717iple_a->Prop)), ((forall (Y_7:hoare_2091234717iple_a), (((member290856304iple_a Y_7) A_34)->False))->(((eq (hoare_2091234717iple_a->Prop)) A_34) bot_bo1791335050le_a_o)))
% FOF formula (forall (A_34:(hoare_1708887482_state->Prop)), ((forall (Y_7:hoare_1708887482_state), (((member451959335_state Y_7) A_34)->False))->(((eq (hoare_1708887482_state->Prop)) A_34) bot_bo19817387tate_o))) of role axiom named fact_782_equals0I
% A new axiom: (forall (A_34:(hoare_1708887482_state->Prop)), ((forall (Y_7:hoare_1708887482_state), (((member451959335_state Y_7) A_34)->False))->(((eq (hoare_1708887482_state->Prop)) A_34) bot_bo19817387tate_o)))
% FOF formula (forall (A_34:(pname->Prop)), ((forall (Y_7:pname), (((member_pname Y_7) A_34)->False))->(((eq (pname->Prop)) A_34) bot_bot_pname_o))) of role axiom named fact_783_equals0I
% A new axiom: (forall (A_34:(pname->Prop)), ((forall (Y_7:pname), (((member_pname Y_7) A_34)->False))->(((eq (pname->Prop)) A_34) bot_bot_pname_o)))
% FOF formula (forall (B_25:((nat->Prop)->Prop)) (A_33:((nat->Prop)->Prop)), ((finite_finite_nat_o A_33)->((not (((eq ((nat->Prop)->Prop)) A_33) bot_bot_nat_o_o))->((finite_finite_nat_o B_25)->((not (((eq ((nat->Prop)->Prop)) B_25) bot_bot_nat_o_o))->(((eq (nat->Prop)) (big_la1658356148_nat_o ((semila72246288at_o_o A_33) B_25))) ((semila848761471_nat_o (big_la1658356148_nat_o A_33)) (big_la1658356148_nat_o B_25)))))))) of role axiom named fact_784_Sup__fin_Ounion__idem
% A new axiom: (forall (B_25:((nat->Prop)->Prop)) (A_33:((nat->Prop)->Prop)), ((finite_finite_nat_o A_33)->((not (((eq ((nat->Prop)->Prop)) A_33) bot_bot_nat_o_o))->((finite_finite_nat_o B_25)->((not (((eq ((nat->Prop)->Prop)) B_25) bot_bot_nat_o_o))->(((eq (nat->Prop)) (big_la1658356148_nat_o ((semila72246288at_o_o A_33) B_25))) ((semila848761471_nat_o (big_la1658356148_nat_o A_33)) (big_la1658356148_nat_o B_25))))))))
% FOF formula (forall (B_25:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)) (A_33:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)), ((finite886417794_a_o_o A_33)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) A_33) bot_bo690906872_o_o_o))->((finite886417794_a_o_o B_25)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) B_25) bot_bo690906872_o_o_o))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (big_la1994307886_a_o_o ((semila484278426_o_o_o A_33) B_25))) ((semila2050116131_a_o_o (big_la1994307886_a_o_o A_33)) (big_la1994307886_a_o_o B_25)))))))) of role axiom named fact_785_Sup__fin_Ounion__idem
% A new axiom: (forall (B_25:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)) (A_33:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)), ((finite886417794_a_o_o A_33)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) A_33) bot_bo690906872_o_o_o))->((finite886417794_a_o_o B_25)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) B_25) bot_bo690906872_o_o_o))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (big_la1994307886_a_o_o ((semila484278426_o_o_o A_33) B_25))) ((semila2050116131_a_o_o (big_la1994307886_a_o_o A_33)) (big_la1994307886_a_o_o B_25))))))))
% FOF formula (forall (B_25:((hoare_1708887482_state->Prop)->Prop)) (A_33:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_33)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_33) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_25)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_25) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (big_la1088302868tate_o ((semila1853742644te_o_o A_33) B_25))) ((semila1122118281tate_o (big_la1088302868tate_o A_33)) (big_la1088302868tate_o B_25)))))))) of role axiom named fact_786_Sup__fin_Ounion__idem
% A new axiom: (forall (B_25:((hoare_1708887482_state->Prop)->Prop)) (A_33:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_33)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_33) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_25)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_25) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (big_la1088302868tate_o ((semila1853742644te_o_o A_33) B_25))) ((semila1122118281tate_o (big_la1088302868tate_o A_33)) (big_la1088302868tate_o B_25))))))))
% FOF formula (forall (B_25:((pname->Prop)->Prop)) (A_33:((pname->Prop)->Prop)), ((finite297249702name_o A_33)->((not (((eq ((pname->Prop)->Prop)) A_33) bot_bot_pname_o_o))->((finite297249702name_o B_25)->((not (((eq ((pname->Prop)->Prop)) B_25) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((semila181081674me_o_o A_33) B_25))) ((semila1780557381name_o (big_la1286884090name_o A_33)) (big_la1286884090name_o B_25)))))))) of role axiom named fact_787_Sup__fin_Ounion__idem
% A new axiom: (forall (B_25:((pname->Prop)->Prop)) (A_33:((pname->Prop)->Prop)), ((finite297249702name_o A_33)->((not (((eq ((pname->Prop)->Prop)) A_33) bot_bot_pname_o_o))->((finite297249702name_o B_25)->((not (((eq ((pname->Prop)->Prop)) B_25) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((semila181081674me_o_o A_33) B_25))) ((semila1780557381name_o (big_la1286884090name_o A_33)) (big_la1286884090name_o B_25))))))))
% FOF formula (forall (B_25:(Prop->Prop)) (A_33:(Prop->Prop)), ((finite_finite_o A_33)->((not (((eq (Prop->Prop)) A_33) bot_bot_o_o))->((finite_finite_o B_25)->((not (((eq (Prop->Prop)) B_25) bot_bot_o_o))->((iff (big_la727467310_fin_o ((semila2062604954up_o_o A_33) B_25))) ((semila10642723_sup_o (big_la727467310_fin_o A_33)) (big_la727467310_fin_o B_25)))))))) of role axiom named fact_788_Sup__fin_Ounion__idem
% A new axiom: (forall (B_25:(Prop->Prop)) (A_33:(Prop->Prop)), ((finite_finite_o A_33)->((not (((eq (Prop->Prop)) A_33) bot_bot_o_o))->((finite_finite_o B_25)->((not (((eq (Prop->Prop)) B_25) bot_bot_o_o))->((iff (big_la727467310_fin_o ((semila2062604954up_o_o A_33) B_25))) ((semila10642723_sup_o (big_la727467310_fin_o A_33)) (big_la727467310_fin_o B_25))))))))
% FOF formula (forall (B_25:((hoare_2091234717iple_a->Prop)->Prop)) (A_33:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_33)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_33) bot_bo1957696069_a_o_o))->((finite1829014797le_a_o B_25)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_25) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (big_la735727201le_a_o ((semila2050116131_a_o_o A_33) B_25))) ((semila1052848428le_a_o (big_la735727201le_a_o A_33)) (big_la735727201le_a_o B_25)))))))) of role axiom named fact_789_Sup__fin_Ounion__idem
% A new axiom: (forall (B_25:((hoare_2091234717iple_a->Prop)->Prop)) (A_33:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_33)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_33) bot_bo1957696069_a_o_o))->((finite1829014797le_a_o B_25)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_25) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (big_la735727201le_a_o ((semila2050116131_a_o_o A_33) B_25))) ((semila1052848428le_a_o (big_la735727201le_a_o A_33)) (big_la735727201le_a_o B_25))))))))
% FOF formula (forall (B_25:(nat->Prop)) (A_33:(nat->Prop)), ((finite_finite_nat A_33)->((not (((eq (nat->Prop)) A_33) bot_bot_nat_o))->((finite_finite_nat B_25)->((not (((eq (nat->Prop)) B_25) bot_bot_nat_o))->(((eq nat) (big_la43341705in_nat ((semila848761471_nat_o A_33) B_25))) ((semila972727038up_nat (big_la43341705in_nat A_33)) (big_la43341705in_nat B_25)))))))) of role axiom named fact_790_Sup__fin_Ounion__idem
% A new axiom: (forall (B_25:(nat->Prop)) (A_33:(nat->Prop)), ((finite_finite_nat A_33)->((not (((eq (nat->Prop)) A_33) bot_bot_nat_o))->((finite_finite_nat B_25)->((not (((eq (nat->Prop)) B_25) bot_bot_nat_o))->(((eq nat) (big_la43341705in_nat ((semila848761471_nat_o A_33) B_25))) ((semila972727038up_nat (big_la43341705in_nat A_33)) (big_la43341705in_nat B_25))))))))
% FOF formula (forall (X_14:(nat->Prop)) (A_32:((nat->Prop)->Prop)), ((finite_finite_nat_o A_32)->((((member_nat_o X_14) A_32)->False)->((not (((eq ((nat->Prop)->Prop)) A_32) bot_bot_nat_o_o))->(((eq (nat->Prop)) (big_la1658356148_nat_o ((insert_nat_o X_14) A_32))) ((semila848761471_nat_o X_14) (big_la1658356148_nat_o A_32))))))) of role axiom named fact_791_Sup__fin_Oinsert
% A new axiom: (forall (X_14:(nat->Prop)) (A_32:((nat->Prop)->Prop)), ((finite_finite_nat_o A_32)->((((member_nat_o X_14) A_32)->False)->((not (((eq ((nat->Prop)->Prop)) A_32) bot_bot_nat_o_o))->(((eq (nat->Prop)) (big_la1658356148_nat_o ((insert_nat_o X_14) A_32))) ((semila848761471_nat_o X_14) (big_la1658356148_nat_o A_32)))))))
% FOF formula (forall (X_14:((hoare_2091234717iple_a->Prop)->Prop)) (A_32:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)), ((finite886417794_a_o_o A_32)->((((member1297825410_a_o_o X_14) A_32)->False)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) A_32) bot_bo690906872_o_o_o))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (big_la1994307886_a_o_o ((insert987231145_a_o_o X_14) A_32))) ((semila2050116131_a_o_o X_14) (big_la1994307886_a_o_o A_32))))))) of role axiom named fact_792_Sup__fin_Oinsert
% A new axiom: (forall (X_14:((hoare_2091234717iple_a->Prop)->Prop)) (A_32:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)), ((finite886417794_a_o_o A_32)->((((member1297825410_a_o_o X_14) A_32)->False)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) A_32) bot_bo690906872_o_o_o))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (big_la1994307886_a_o_o ((insert987231145_a_o_o X_14) A_32))) ((semila2050116131_a_o_o X_14) (big_la1994307886_a_o_o A_32)))))))
% FOF formula (forall (X_14:(hoare_1708887482_state->Prop)) (A_32:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_32)->((((member814030440tate_o X_14) A_32)->False)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_32) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (big_la1088302868tate_o ((insert949073679tate_o X_14) A_32))) ((semila1122118281tate_o X_14) (big_la1088302868tate_o A_32))))))) of role axiom named fact_793_Sup__fin_Oinsert
% A new axiom: (forall (X_14:(hoare_1708887482_state->Prop)) (A_32:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_32)->((((member814030440tate_o X_14) A_32)->False)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_32) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (big_la1088302868tate_o ((insert949073679tate_o X_14) A_32))) ((semila1122118281tate_o X_14) (big_la1088302868tate_o A_32)))))))
% FOF formula (forall (X_14:(pname->Prop)) (A_32:((pname->Prop)->Prop)), ((finite297249702name_o A_32)->((((member_pname_o X_14) A_32)->False)->((not (((eq ((pname->Prop)->Prop)) A_32) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_14) A_32))) ((semila1780557381name_o X_14) (big_la1286884090name_o A_32))))))) of role axiom named fact_794_Sup__fin_Oinsert
% A new axiom: (forall (X_14:(pname->Prop)) (A_32:((pname->Prop)->Prop)), ((finite297249702name_o A_32)->((((member_pname_o X_14) A_32)->False)->((not (((eq ((pname->Prop)->Prop)) A_32) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_14) A_32))) ((semila1780557381name_o X_14) (big_la1286884090name_o A_32)))))))
% FOF formula (forall (X_14:Prop) (A_32:(Prop->Prop)), ((finite_finite_o A_32)->((((member_o X_14) A_32)->False)->((not (((eq (Prop->Prop)) A_32) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_14) A_32))) ((semila10642723_sup_o X_14) (big_la727467310_fin_o A_32))))))) of role axiom named fact_795_Sup__fin_Oinsert
% A new axiom: (forall (X_14:Prop) (A_32:(Prop->Prop)), ((finite_finite_o A_32)->((((member_o X_14) A_32)->False)->((not (((eq (Prop->Prop)) A_32) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_14) A_32))) ((semila10642723_sup_o X_14) (big_la727467310_fin_o A_32)))))))
% FOF formula (forall (X_14:(hoare_2091234717iple_a->Prop)) (A_32:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_32)->((((member99268621le_a_o X_14) A_32)->False)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_32) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (big_la735727201le_a_o ((insert102003750le_a_o X_14) A_32))) ((semila1052848428le_a_o X_14) (big_la735727201le_a_o A_32))))))) of role axiom named fact_796_Sup__fin_Oinsert
% A new axiom: (forall (X_14:(hoare_2091234717iple_a->Prop)) (A_32:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_32)->((((member99268621le_a_o X_14) A_32)->False)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_32) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (big_la735727201le_a_o ((insert102003750le_a_o X_14) A_32))) ((semila1052848428le_a_o X_14) (big_la735727201le_a_o A_32)))))))
% FOF formula (forall (X_14:nat) (A_32:(nat->Prop)), ((finite_finite_nat A_32)->((((member_nat X_14) A_32)->False)->((not (((eq (nat->Prop)) A_32) bot_bot_nat_o))->(((eq nat) (big_la43341705in_nat ((insert_nat X_14) A_32))) ((semila972727038up_nat X_14) (big_la43341705in_nat A_32))))))) of role axiom named fact_797_Sup__fin_Oinsert
% A new axiom: (forall (X_14:nat) (A_32:(nat->Prop)), ((finite_finite_nat A_32)->((((member_nat X_14) A_32)->False)->((not (((eq (nat->Prop)) A_32) bot_bot_nat_o))->(((eq nat) (big_la43341705in_nat ((insert_nat X_14) A_32))) ((semila972727038up_nat X_14) (big_la43341705in_nat A_32)))))))
% FOF formula (forall (X_13:(nat->Prop)) (A_31:((nat->Prop)->Prop)), ((finite_finite_nat_o A_31)->((not (((eq ((nat->Prop)->Prop)) A_31) bot_bot_nat_o_o))->(((eq (nat->Prop)) (big_la1658356148_nat_o ((insert_nat_o X_13) A_31))) ((semila848761471_nat_o X_13) (big_la1658356148_nat_o A_31)))))) of role axiom named fact_798_Sup__fin_Oinsert__idem
% A new axiom: (forall (X_13:(nat->Prop)) (A_31:((nat->Prop)->Prop)), ((finite_finite_nat_o A_31)->((not (((eq ((nat->Prop)->Prop)) A_31) bot_bot_nat_o_o))->(((eq (nat->Prop)) (big_la1658356148_nat_o ((insert_nat_o X_13) A_31))) ((semila848761471_nat_o X_13) (big_la1658356148_nat_o A_31))))))
% FOF formula (forall (X_13:((hoare_2091234717iple_a->Prop)->Prop)) (A_31:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)), ((finite886417794_a_o_o A_31)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) A_31) bot_bo690906872_o_o_o))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (big_la1994307886_a_o_o ((insert987231145_a_o_o X_13) A_31))) ((semila2050116131_a_o_o X_13) (big_la1994307886_a_o_o A_31)))))) of role axiom named fact_799_Sup__fin_Oinsert__idem
% A new axiom: (forall (X_13:((hoare_2091234717iple_a->Prop)->Prop)) (A_31:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)), ((finite886417794_a_o_o A_31)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) A_31) bot_bo690906872_o_o_o))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (big_la1994307886_a_o_o ((insert987231145_a_o_o X_13) A_31))) ((semila2050116131_a_o_o X_13) (big_la1994307886_a_o_o A_31))))))
% FOF formula (forall (X_13:(hoare_1708887482_state->Prop)) (A_31:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_31)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_31) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (big_la1088302868tate_o ((insert949073679tate_o X_13) A_31))) ((semila1122118281tate_o X_13) (big_la1088302868tate_o A_31)))))) of role axiom named fact_800_Sup__fin_Oinsert__idem
% A new axiom: (forall (X_13:(hoare_1708887482_state->Prop)) (A_31:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_31)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_31) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (big_la1088302868tate_o ((insert949073679tate_o X_13) A_31))) ((semila1122118281tate_o X_13) (big_la1088302868tate_o A_31))))))
% FOF formula (forall (X_13:(pname->Prop)) (A_31:((pname->Prop)->Prop)), ((finite297249702name_o A_31)->((not (((eq ((pname->Prop)->Prop)) A_31) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_13) A_31))) ((semila1780557381name_o X_13) (big_la1286884090name_o A_31)))))) of role axiom named fact_801_Sup__fin_Oinsert__idem
% A new axiom: (forall (X_13:(pname->Prop)) (A_31:((pname->Prop)->Prop)), ((finite297249702name_o A_31)->((not (((eq ((pname->Prop)->Prop)) A_31) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_13) A_31))) ((semila1780557381name_o X_13) (big_la1286884090name_o A_31))))))
% FOF formula (forall (X_13:Prop) (A_31:(Prop->Prop)), ((finite_finite_o A_31)->((not (((eq (Prop->Prop)) A_31) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_13) A_31))) ((semila10642723_sup_o X_13) (big_la727467310_fin_o A_31)))))) of role axiom named fact_802_Sup__fin_Oinsert__idem
% A new axiom: (forall (X_13:Prop) (A_31:(Prop->Prop)), ((finite_finite_o A_31)->((not (((eq (Prop->Prop)) A_31) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_13) A_31))) ((semila10642723_sup_o X_13) (big_la727467310_fin_o A_31))))))
% FOF formula (forall (X_13:(hoare_2091234717iple_a->Prop)) (A_31:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_31)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_31) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (big_la735727201le_a_o ((insert102003750le_a_o X_13) A_31))) ((semila1052848428le_a_o X_13) (big_la735727201le_a_o A_31)))))) of role axiom named fact_803_Sup__fin_Oinsert__idem
% A new axiom: (forall (X_13:(hoare_2091234717iple_a->Prop)) (A_31:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_31)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_31) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (big_la735727201le_a_o ((insert102003750le_a_o X_13) A_31))) ((semila1052848428le_a_o X_13) (big_la735727201le_a_o A_31))))))
% FOF formula (forall (X_13:nat) (A_31:(nat->Prop)), ((finite_finite_nat A_31)->((not (((eq (nat->Prop)) A_31) bot_bot_nat_o))->(((eq nat) (big_la43341705in_nat ((insert_nat X_13) A_31))) ((semila972727038up_nat X_13) (big_la43341705in_nat A_31)))))) of role axiom named fact_804_Sup__fin_Oinsert__idem
% A new axiom: (forall (X_13:nat) (A_31:(nat->Prop)), ((finite_finite_nat A_31)->((not (((eq (nat->Prop)) A_31) bot_bot_nat_o))->(((eq nat) (big_la43341705in_nat ((insert_nat X_13) A_31))) ((semila972727038up_nat X_13) (big_la43341705in_nat A_31))))))
% FOF formula (forall (B_24:((hoare_2091234717iple_a->Prop)->Prop)) (A_30:((hoare_2091234717iple_a->Prop)->Prop)) (F_8:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_7:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_8) F_7)->((finite1829014797le_a_o A_30)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_30) bot_bo1957696069_a_o_o))->((finite1829014797le_a_o B_24)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_24) bot_bo1957696069_a_o_o))->((((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila1672913213_a_o_o A_30) B_24)) bot_bo1957696069_a_o_o)->(((eq (hoare_2091234717iple_a->Prop)) (F_7 ((semila2050116131_a_o_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24)))))))))) of role axiom named fact_805_folding__one_Ounion__disjoint
% A new axiom: (forall (B_24:((hoare_2091234717iple_a->Prop)->Prop)) (A_30:((hoare_2091234717iple_a->Prop)->Prop)) (F_8:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_7:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_8) F_7)->((finite1829014797le_a_o A_30)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_30) bot_bo1957696069_a_o_o))->((finite1829014797le_a_o B_24)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_24) bot_bo1957696069_a_o_o))->((((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila1672913213_a_o_o A_30) B_24)) bot_bo1957696069_a_o_o)->(((eq (hoare_2091234717iple_a->Prop)) (F_7 ((semila2050116131_a_o_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24))))))))))
% FOF formula (forall (B_24:(pname->Prop)) (A_30:(pname->Prop)) (F_8:(pname->(pname->pname))) (F_7:((pname->Prop)->pname)), (((finite1282449217_pname F_8) F_7)->((finite_finite_pname A_30)->((not (((eq (pname->Prop)) A_30) bot_bot_pname_o))->((finite_finite_pname B_24)->((not (((eq (pname->Prop)) B_24) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_30) B_24)) bot_bot_pname_o)->(((eq pname) (F_7 ((semila1780557381name_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24)))))))))) of role axiom named fact_806_folding__one_Ounion__disjoint
% A new axiom: (forall (B_24:(pname->Prop)) (A_30:(pname->Prop)) (F_8:(pname->(pname->pname))) (F_7:((pname->Prop)->pname)), (((finite1282449217_pname F_8) F_7)->((finite_finite_pname A_30)->((not (((eq (pname->Prop)) A_30) bot_bot_pname_o))->((finite_finite_pname B_24)->((not (((eq (pname->Prop)) B_24) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_30) B_24)) bot_bot_pname_o)->(((eq pname) (F_7 ((semila1780557381name_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24))))))))))
% FOF formula (forall (B_24:(hoare_1708887482_state->Prop)) (A_30:(hoare_1708887482_state->Prop)) (F_8:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_7:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_8) F_7)->((finite1625599783_state A_30)->((not (((eq (hoare_1708887482_state->Prop)) A_30) bot_bo19817387tate_o))->((finite1625599783_state B_24)->((not (((eq (hoare_1708887482_state->Prop)) B_24) bot_bo19817387tate_o))->((((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_30) B_24)) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_7 ((semila1122118281tate_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24)))))))))) of role axiom named fact_807_folding__one_Ounion__disjoint
% A new axiom: (forall (B_24:(hoare_1708887482_state->Prop)) (A_30:(hoare_1708887482_state->Prop)) (F_8:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_7:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_8) F_7)->((finite1625599783_state A_30)->((not (((eq (hoare_1708887482_state->Prop)) A_30) bot_bo19817387tate_o))->((finite1625599783_state B_24)->((not (((eq (hoare_1708887482_state->Prop)) B_24) bot_bo19817387tate_o))->((((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_30) B_24)) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_7 ((semila1122118281tate_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24))))))))))
% FOF formula (forall (B_24:(hoare_2091234717iple_a->Prop)) (A_30:(hoare_2091234717iple_a->Prop)) (F_8:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_7:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_8) F_7)->((finite232261744iple_a A_30)->((not (((eq (hoare_2091234717iple_a->Prop)) A_30) bot_bo1791335050le_a_o))->((finite232261744iple_a B_24)->((not (((eq (hoare_2091234717iple_a->Prop)) B_24) bot_bo1791335050le_a_o))->((((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_30) B_24)) bot_bo1791335050le_a_o)->(((eq hoare_2091234717iple_a) (F_7 ((semila1052848428le_a_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24)))))))))) of role axiom named fact_808_folding__one_Ounion__disjoint
% A new axiom: (forall (B_24:(hoare_2091234717iple_a->Prop)) (A_30:(hoare_2091234717iple_a->Prop)) (F_8:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_7:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_8) F_7)->((finite232261744iple_a A_30)->((not (((eq (hoare_2091234717iple_a->Prop)) A_30) bot_bo1791335050le_a_o))->((finite232261744iple_a B_24)->((not (((eq (hoare_2091234717iple_a->Prop)) B_24) bot_bo1791335050le_a_o))->((((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_30) B_24)) bot_bo1791335050le_a_o)->(((eq hoare_2091234717iple_a) (F_7 ((semila1052848428le_a_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24))))))))))
% FOF formula (forall (B_24:(nat->Prop)) (A_30:(nat->Prop)) (F_8:(nat->(nat->nat))) (F_7:((nat->Prop)->nat)), (((finite988810631ne_nat F_8) F_7)->((finite_finite_nat A_30)->((not (((eq (nat->Prop)) A_30) bot_bot_nat_o))->((finite_finite_nat B_24)->((not (((eq (nat->Prop)) B_24) bot_bot_nat_o))->((((eq (nat->Prop)) ((semila1947288293_nat_o A_30) B_24)) bot_bot_nat_o)->(((eq nat) (F_7 ((semila848761471_nat_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24)))))))))) of role axiom named fact_809_folding__one_Ounion__disjoint
% A new axiom: (forall (B_24:(nat->Prop)) (A_30:(nat->Prop)) (F_8:(nat->(nat->nat))) (F_7:((nat->Prop)->nat)), (((finite988810631ne_nat F_8) F_7)->((finite_finite_nat A_30)->((not (((eq (nat->Prop)) A_30) bot_bot_nat_o))->((finite_finite_nat B_24)->((not (((eq (nat->Prop)) B_24) bot_bot_nat_o))->((((eq (nat->Prop)) ((semila1947288293_nat_o A_30) B_24)) bot_bot_nat_o)->(((eq nat) (F_7 ((semila848761471_nat_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24))))))))))
% FOF formula (forall (B_23:((hoare_2091234717iple_a->Prop)->Prop)) (A_29:((hoare_2091234717iple_a->Prop)->Prop)) (F_6:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_5:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_6) F_5)->((finite1829014797le_a_o A_29)->((finite1829014797le_a_o B_23)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila1672913213_a_o_o A_29) B_23)) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) ((F_6 (F_5 ((semila2050116131_a_o_o A_29) B_23))) (F_5 ((semila1672913213_a_o_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23)))))))) of role axiom named fact_810_folding__one_Ounion__inter
% A new axiom: (forall (B_23:((hoare_2091234717iple_a->Prop)->Prop)) (A_29:((hoare_2091234717iple_a->Prop)->Prop)) (F_6:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_5:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_6) F_5)->((finite1829014797le_a_o A_29)->((finite1829014797le_a_o B_23)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila1672913213_a_o_o A_29) B_23)) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) ((F_6 (F_5 ((semila2050116131_a_o_o A_29) B_23))) (F_5 ((semila1672913213_a_o_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23))))))))
% FOF formula (forall (B_23:(pname->Prop)) (A_29:(pname->Prop)) (F_6:(pname->(pname->pname))) (F_5:((pname->Prop)->pname)), (((finite1282449217_pname F_6) F_5)->((finite_finite_pname A_29)->((finite_finite_pname B_23)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_29) B_23)) bot_bot_pname_o))->(((eq pname) ((F_6 (F_5 ((semila1780557381name_o A_29) B_23))) (F_5 ((semila1673364395name_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23)))))))) of role axiom named fact_811_folding__one_Ounion__inter
% A new axiom: (forall (B_23:(pname->Prop)) (A_29:(pname->Prop)) (F_6:(pname->(pname->pname))) (F_5:((pname->Prop)->pname)), (((finite1282449217_pname F_6) F_5)->((finite_finite_pname A_29)->((finite_finite_pname B_23)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_29) B_23)) bot_bot_pname_o))->(((eq pname) ((F_6 (F_5 ((semila1780557381name_o A_29) B_23))) (F_5 ((semila1673364395name_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23))))))))
% FOF formula (forall (B_23:(hoare_1708887482_state->Prop)) (A_29:(hoare_1708887482_state->Prop)) (F_6:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_5:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_6) F_5)->((finite1625599783_state A_29)->((finite1625599783_state B_23)->((not (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_29) B_23)) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) ((F_6 (F_5 ((semila1122118281tate_o A_29) B_23))) (F_5 ((semila129691299tate_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23)))))))) of role axiom named fact_812_folding__one_Ounion__inter
% A new axiom: (forall (B_23:(hoare_1708887482_state->Prop)) (A_29:(hoare_1708887482_state->Prop)) (F_6:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_5:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_6) F_5)->((finite1625599783_state A_29)->((finite1625599783_state B_23)->((not (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_29) B_23)) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) ((F_6 (F_5 ((semila1122118281tate_o A_29) B_23))) (F_5 ((semila129691299tate_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23))))))))
% FOF formula (forall (B_23:(hoare_2091234717iple_a->Prop)) (A_29:(hoare_2091234717iple_a->Prop)) (F_6:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_5:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_6) F_5)->((finite232261744iple_a A_29)->((finite232261744iple_a B_23)->((not (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_29) B_23)) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) ((F_6 (F_5 ((semila1052848428le_a_o A_29) B_23))) (F_5 ((semila2006181266le_a_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23)))))))) of role axiom named fact_813_folding__one_Ounion__inter
% A new axiom: (forall (B_23:(hoare_2091234717iple_a->Prop)) (A_29:(hoare_2091234717iple_a->Prop)) (F_6:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_5:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_6) F_5)->((finite232261744iple_a A_29)->((finite232261744iple_a B_23)->((not (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_29) B_23)) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) ((F_6 (F_5 ((semila1052848428le_a_o A_29) B_23))) (F_5 ((semila2006181266le_a_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23))))))))
% FOF formula (forall (B_23:(nat->Prop)) (A_29:(nat->Prop)) (F_6:(nat->(nat->nat))) (F_5:((nat->Prop)->nat)), (((finite988810631ne_nat F_6) F_5)->((finite_finite_nat A_29)->((finite_finite_nat B_23)->((not (((eq (nat->Prop)) ((semila1947288293_nat_o A_29) B_23)) bot_bot_nat_o))->(((eq nat) ((F_6 (F_5 ((semila848761471_nat_o A_29) B_23))) (F_5 ((semila1947288293_nat_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23)))))))) of role axiom named fact_814_folding__one_Ounion__inter
% A new axiom: (forall (B_23:(nat->Prop)) (A_29:(nat->Prop)) (F_6:(nat->(nat->nat))) (F_5:((nat->Prop)->nat)), (((finite988810631ne_nat F_6) F_5)->((finite_finite_nat A_29)->((finite_finite_nat B_23)->((not (((eq (nat->Prop)) ((semila1947288293_nat_o A_29) B_23)) bot_bot_nat_o))->(((eq nat) ((F_6 (F_5 ((semila848761471_nat_o A_29) B_23))) (F_5 ((semila1947288293_nat_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23))))))))
% FOF formula (forall (X_12:(hoare_2091234717iple_a->Prop)) (A_28:((hoare_2091234717iple_a->Prop)->Prop)) (F_4:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_3:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_4) F_3)->((finite1829014797le_a_o A_28)->((and ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_28) ((insert102003750le_a_o X_12) bot_bo1957696069_a_o_o))) bot_bo1957696069_a_o_o)->(((eq (hoare_2091234717iple_a->Prop)) (F_3 ((insert102003750le_a_o X_12) A_28))) X_12))) ((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_28) ((insert102003750le_a_o X_12) bot_bo1957696069_a_o_o))) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_3 ((insert102003750le_a_o X_12) A_28))) ((F_4 X_12) (F_3 ((minus_1746272704_a_o_o A_28) ((insert102003750le_a_o X_12) bot_bo1957696069_a_o_o)))))))))) of role axiom named fact_815_folding__one_Oinsert__remove
% A new axiom: (forall (X_12:(hoare_2091234717iple_a->Prop)) (A_28:((hoare_2091234717iple_a->Prop)->Prop)) (F_4:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_3:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_4) F_3)->((finite1829014797le_a_o A_28)->((and ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_28) ((insert102003750le_a_o X_12) bot_bo1957696069_a_o_o))) bot_bo1957696069_a_o_o)->(((eq (hoare_2091234717iple_a->Prop)) (F_3 ((insert102003750le_a_o X_12) A_28))) X_12))) ((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_28) ((insert102003750le_a_o X_12) bot_bo1957696069_a_o_o))) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_3 ((insert102003750le_a_o X_12) A_28))) ((F_4 X_12) (F_3 ((minus_1746272704_a_o_o A_28) ((insert102003750le_a_o X_12) bot_bo1957696069_a_o_o))))))))))
% FOF formula (forall (X_12:pname) (A_28:(pname->Prop)) (F_4:(pname->(pname->pname))) (F_3:((pname->Prop)->pname)), (((finite1282449217_pname F_4) F_3)->((finite_finite_pname A_28)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_3 ((insert_pname X_12) A_28))) X_12))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_3 ((insert_pname X_12) A_28))) ((F_4 X_12) (F_3 ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o)))))))))) of role axiom named fact_816_folding__one_Oinsert__remove
% A new axiom: (forall (X_12:pname) (A_28:(pname->Prop)) (F_4:(pname->(pname->pname))) (F_3:((pname->Prop)->pname)), (((finite1282449217_pname F_4) F_3)->((finite_finite_pname A_28)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_3 ((insert_pname X_12) A_28))) X_12))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_3 ((insert_pname X_12) A_28))) ((F_4 X_12) (F_3 ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))))))))))
% FOF formula (forall (X_12:hoare_2091234717iple_a) (A_28:(hoare_2091234717iple_a->Prop)) (F_4:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_3:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_4) F_3)->((finite232261744iple_a A_28)->((and ((((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_28) ((insert1597628439iple_a X_12) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o)->(((eq hoare_2091234717iple_a) (F_3 ((insert1597628439iple_a X_12) A_28))) X_12))) ((not (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_28) ((insert1597628439iple_a X_12) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_3 ((insert1597628439iple_a X_12) A_28))) ((F_4 X_12) (F_3 ((minus_836160335le_a_o A_28) ((insert1597628439iple_a X_12) bot_bo1791335050le_a_o)))))))))) of role axiom named fact_817_folding__one_Oinsert__remove
% A new axiom: (forall (X_12:hoare_2091234717iple_a) (A_28:(hoare_2091234717iple_a->Prop)) (F_4:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_3:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_4) F_3)->((finite232261744iple_a A_28)->((and ((((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_28) ((insert1597628439iple_a X_12) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o)->(((eq hoare_2091234717iple_a) (F_3 ((insert1597628439iple_a X_12) A_28))) X_12))) ((not (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_28) ((insert1597628439iple_a X_12) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_3 ((insert1597628439iple_a X_12) A_28))) ((F_4 X_12) (F_3 ((minus_836160335le_a_o A_28) ((insert1597628439iple_a X_12) bot_bo1791335050le_a_o))))))))))
% FOF formula (forall (X_12:hoare_1708887482_state) (A_28:(hoare_1708887482_state->Prop)) (F_4:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_3:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_4) F_3)->((finite1625599783_state A_28)->((and ((((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_28) ((insert528405184_state X_12) bot_bo19817387tate_o))) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_3 ((insert528405184_state X_12) A_28))) X_12))) ((not (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_28) ((insert528405184_state X_12) bot_bo19817387tate_o))) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_3 ((insert528405184_state X_12) A_28))) ((F_4 X_12) (F_3 ((minus_2056855718tate_o A_28) ((insert528405184_state X_12) bot_bo19817387tate_o)))))))))) of role axiom named fact_818_folding__one_Oinsert__remove
% A new axiom: (forall (X_12:hoare_1708887482_state) (A_28:(hoare_1708887482_state->Prop)) (F_4:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_3:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_4) F_3)->((finite1625599783_state A_28)->((and ((((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_28) ((insert528405184_state X_12) bot_bo19817387tate_o))) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_3 ((insert528405184_state X_12) A_28))) X_12))) ((not (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_28) ((insert528405184_state X_12) bot_bo19817387tate_o))) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_3 ((insert528405184_state X_12) A_28))) ((F_4 X_12) (F_3 ((minus_2056855718tate_o A_28) ((insert528405184_state X_12) bot_bo19817387tate_o))))))))))
% FOF formula (forall (X_12:nat) (A_28:(nat->Prop)) (F_4:(nat->(nat->nat))) (F_3:((nat->Prop)->nat)), (((finite988810631ne_nat F_4) F_3)->((finite_finite_nat A_28)->((and ((((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o)->(((eq nat) (F_3 ((insert_nat X_12) A_28))) X_12))) ((not (((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o))->(((eq nat) (F_3 ((insert_nat X_12) A_28))) ((F_4 X_12) (F_3 ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o)))))))))) of role axiom named fact_819_folding__one_Oinsert__remove
% A new axiom: (forall (X_12:nat) (A_28:(nat->Prop)) (F_4:(nat->(nat->nat))) (F_3:((nat->Prop)->nat)), (((finite988810631ne_nat F_4) F_3)->((finite_finite_nat A_28)->((and ((((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o)->(((eq nat) (F_3 ((insert_nat X_12) A_28))) X_12))) ((not (((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o))->(((eq nat) (F_3 ((insert_nat X_12) A_28))) ((F_4 X_12) (F_3 ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))))))))))
% FOF formula (forall (B_22:(nat->Prop)) (A_27:(nat->Prop)) (X_11:nat), ((A_27 X_11)->((B_22 X_11)->(((semila1947288293_nat_o A_27) B_22) X_11)))) of role axiom named fact_820_inf1I
% A new axiom: (forall (B_22:(nat->Prop)) (A_27:(nat->Prop)) (X_11:nat), ((A_27 X_11)->((B_22 X_11)->(((semila1947288293_nat_o A_27) B_22) X_11))))
% FOF formula (forall (B_22:(hoare_2091234717iple_a->Prop)) (A_27:(hoare_2091234717iple_a->Prop)) (X_11:hoare_2091234717iple_a), ((A_27 X_11)->((B_22 X_11)->(((semila2006181266le_a_o A_27) B_22) X_11)))) of role axiom named fact_821_inf1I
% A new axiom: (forall (B_22:(hoare_2091234717iple_a->Prop)) (A_27:(hoare_2091234717iple_a->Prop)) (X_11:hoare_2091234717iple_a), ((A_27 X_11)->((B_22 X_11)->(((semila2006181266le_a_o A_27) B_22) X_11))))
% FOF formula (forall (B_22:(pname->Prop)) (A_27:(pname->Prop)) (X_11:pname), ((A_27 X_11)->((B_22 X_11)->(((semila1673364395name_o A_27) B_22) X_11)))) of role axiom named fact_822_inf1I
% A new axiom: (forall (B_22:(pname->Prop)) (A_27:(pname->Prop)) (X_11:pname), ((A_27 X_11)->((B_22 X_11)->(((semila1673364395name_o A_27) B_22) X_11))))
% FOF formula (forall (B_21:(nat->Prop)) (C_11:nat) (A_26:(nat->Prop)), (((member_nat C_11) A_26)->(((member_nat C_11) B_21)->((member_nat C_11) ((semila1947288293_nat_o A_26) B_21))))) of role axiom named fact_823_IntI
% A new axiom: (forall (B_21:(nat->Prop)) (C_11:nat) (A_26:(nat->Prop)), (((member_nat C_11) A_26)->(((member_nat C_11) B_21)->((member_nat C_11) ((semila1947288293_nat_o A_26) B_21)))))
% FOF formula (forall (B_21:((hoare_2091234717iple_a->Prop)->Prop)) (C_11:(hoare_2091234717iple_a->Prop)) (A_26:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_11) A_26)->(((member99268621le_a_o C_11) B_21)->((member99268621le_a_o C_11) ((semila1672913213_a_o_o A_26) B_21))))) of role axiom named fact_824_IntI
% A new axiom: (forall (B_21:((hoare_2091234717iple_a->Prop)->Prop)) (C_11:(hoare_2091234717iple_a->Prop)) (A_26:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_11) A_26)->(((member99268621le_a_o C_11) B_21)->((member99268621le_a_o C_11) ((semila1672913213_a_o_o A_26) B_21)))))
% FOF formula (forall (B_21:(hoare_2091234717iple_a->Prop)) (C_11:hoare_2091234717iple_a) (A_26:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_11) A_26)->(((member290856304iple_a C_11) B_21)->((member290856304iple_a C_11) ((semila2006181266le_a_o A_26) B_21))))) of role axiom named fact_825_IntI
% A new axiom: (forall (B_21:(hoare_2091234717iple_a->Prop)) (C_11:hoare_2091234717iple_a) (A_26:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_11) A_26)->(((member290856304iple_a C_11) B_21)->((member290856304iple_a C_11) ((semila2006181266le_a_o A_26) B_21)))))
% FOF formula (forall (B_21:(pname->Prop)) (C_11:pname) (A_26:(pname->Prop)), (((member_pname C_11) A_26)->(((member_pname C_11) B_21)->((member_pname C_11) ((semila1673364395name_o A_26) B_21))))) of role axiom named fact_826_IntI
% A new axiom: (forall (B_21:(pname->Prop)) (C_11:pname) (A_26:(pname->Prop)), (((member_pname C_11) A_26)->(((member_pname C_11) B_21)->((member_pname C_11) ((semila1673364395name_o A_26) B_21)))))
% FOF formula (forall (C_10:nat) (A_25:(nat->Prop)) (B_20:(nat->Prop)), (((member_nat C_10) ((semila1947288293_nat_o A_25) B_20))->((((member_nat C_10) A_25)->(((member_nat C_10) B_20)->False))->False))) of role axiom named fact_827_IntE
% A new axiom: (forall (C_10:nat) (A_25:(nat->Prop)) (B_20:(nat->Prop)), (((member_nat C_10) ((semila1947288293_nat_o A_25) B_20))->((((member_nat C_10) A_25)->(((member_nat C_10) B_20)->False))->False)))
% FOF formula (forall (C_10:(hoare_2091234717iple_a->Prop)) (A_25:((hoare_2091234717iple_a->Prop)->Prop)) (B_20:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_10) ((semila1672913213_a_o_o A_25) B_20))->((((member99268621le_a_o C_10) A_25)->(((member99268621le_a_o C_10) B_20)->False))->False))) of role axiom named fact_828_IntE
% A new axiom: (forall (C_10:(hoare_2091234717iple_a->Prop)) (A_25:((hoare_2091234717iple_a->Prop)->Prop)) (B_20:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_10) ((semila1672913213_a_o_o A_25) B_20))->((((member99268621le_a_o C_10) A_25)->(((member99268621le_a_o C_10) B_20)->False))->False)))
% FOF formula (forall (C_10:hoare_2091234717iple_a) (A_25:(hoare_2091234717iple_a->Prop)) (B_20:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_10) ((semila2006181266le_a_o A_25) B_20))->((((member290856304iple_a C_10) A_25)->(((member290856304iple_a C_10) B_20)->False))->False))) of role axiom named fact_829_IntE
% A new axiom: (forall (C_10:hoare_2091234717iple_a) (A_25:(hoare_2091234717iple_a->Prop)) (B_20:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_10) ((semila2006181266le_a_o A_25) B_20))->((((member290856304iple_a C_10) A_25)->(((member290856304iple_a C_10) B_20)->False))->False)))
% FOF formula (forall (C_10:pname) (A_25:(pname->Prop)) (B_20:(pname->Prop)), (((member_pname C_10) ((semila1673364395name_o A_25) B_20))->((((member_pname C_10) A_25)->(((member_pname C_10) B_20)->False))->False))) of role axiom named fact_830_IntE
% A new axiom: (forall (C_10:pname) (A_25:(pname->Prop)) (B_20:(pname->Prop)), (((member_pname C_10) ((semila1673364395name_o A_25) B_20))->((((member_pname C_10) A_25)->(((member_pname C_10) B_20)->False))->False)))
% FOF formula (forall (A_24:(nat->Prop)) (B_19:(nat->Prop)) (X_10:nat), ((((semila1947288293_nat_o A_24) B_19) X_10)->(((A_24 X_10)->((B_19 X_10)->False))->False))) of role axiom named fact_831_inf1E
% A new axiom: (forall (A_24:(nat->Prop)) (B_19:(nat->Prop)) (X_10:nat), ((((semila1947288293_nat_o A_24) B_19) X_10)->(((A_24 X_10)->((B_19 X_10)->False))->False)))
% FOF formula (forall (A_24:(hoare_2091234717iple_a->Prop)) (B_19:(hoare_2091234717iple_a->Prop)) (X_10:hoare_2091234717iple_a), ((((semila2006181266le_a_o A_24) B_19) X_10)->(((A_24 X_10)->((B_19 X_10)->False))->False))) of role axiom named fact_832_inf1E
% A new axiom: (forall (A_24:(hoare_2091234717iple_a->Prop)) (B_19:(hoare_2091234717iple_a->Prop)) (X_10:hoare_2091234717iple_a), ((((semila2006181266le_a_o A_24) B_19) X_10)->(((A_24 X_10)->((B_19 X_10)->False))->False)))
% FOF formula (forall (A_24:(pname->Prop)) (B_19:(pname->Prop)) (X_10:pname), ((((semila1673364395name_o A_24) B_19) X_10)->(((A_24 X_10)->((B_19 X_10)->False))->False))) of role axiom named fact_833_inf1E
% A new axiom: (forall (A_24:(pname->Prop)) (B_19:(pname->Prop)) (X_10:pname), ((((semila1673364395name_o A_24) B_19) X_10)->(((A_24 X_10)->((B_19 X_10)->False))->False)))
% FOF formula (forall (B_18:(nat->Prop)) (C_9:nat) (A_23:(nat->Prop)), (((member_nat C_9) A_23)->((((member_nat C_9) B_18)->False)->((member_nat C_9) ((minus_minus_nat_o A_23) B_18))))) of role axiom named fact_834_DiffI
% A new axiom: (forall (B_18:(nat->Prop)) (C_9:nat) (A_23:(nat->Prop)), (((member_nat C_9) A_23)->((((member_nat C_9) B_18)->False)->((member_nat C_9) ((minus_minus_nat_o A_23) B_18)))))
% FOF formula (forall (B_18:((hoare_2091234717iple_a->Prop)->Prop)) (C_9:(hoare_2091234717iple_a->Prop)) (A_23:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_9) A_23)->((((member99268621le_a_o C_9) B_18)->False)->((member99268621le_a_o C_9) ((minus_1746272704_a_o_o A_23) B_18))))) of role axiom named fact_835_DiffI
% A new axiom: (forall (B_18:((hoare_2091234717iple_a->Prop)->Prop)) (C_9:(hoare_2091234717iple_a->Prop)) (A_23:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_9) A_23)->((((member99268621le_a_o C_9) B_18)->False)->((member99268621le_a_o C_9) ((minus_1746272704_a_o_o A_23) B_18)))))
% FOF formula (forall (B_18:(hoare_2091234717iple_a->Prop)) (C_9:hoare_2091234717iple_a) (A_23:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_9) A_23)->((((member290856304iple_a C_9) B_18)->False)->((member290856304iple_a C_9) ((minus_836160335le_a_o A_23) B_18))))) of role axiom named fact_836_DiffI
% A new axiom: (forall (B_18:(hoare_2091234717iple_a->Prop)) (C_9:hoare_2091234717iple_a) (A_23:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_9) A_23)->((((member290856304iple_a C_9) B_18)->False)->((member290856304iple_a C_9) ((minus_836160335le_a_o A_23) B_18)))))
% FOF formula (forall (B_18:(pname->Prop)) (C_9:pname) (A_23:(pname->Prop)), (((member_pname C_9) A_23)->((((member_pname C_9) B_18)->False)->((member_pname C_9) ((minus_minus_pname_o A_23) B_18))))) of role axiom named fact_837_DiffI
% A new axiom: (forall (B_18:(pname->Prop)) (C_9:pname) (A_23:(pname->Prop)), (((member_pname C_9) A_23)->((((member_pname C_9) B_18)->False)->((member_pname C_9) ((minus_minus_pname_o A_23) B_18)))))
% FOF formula (forall (C_8:nat) (A_22:(nat->Prop)) (B_17:(nat->Prop)), (((member_nat C_8) ((minus_minus_nat_o A_22) B_17))->((((member_nat C_8) A_22)->((member_nat C_8) B_17))->False))) of role axiom named fact_838_DiffE
% A new axiom: (forall (C_8:nat) (A_22:(nat->Prop)) (B_17:(nat->Prop)), (((member_nat C_8) ((minus_minus_nat_o A_22) B_17))->((((member_nat C_8) A_22)->((member_nat C_8) B_17))->False)))
% FOF formula (forall (C_8:(hoare_2091234717iple_a->Prop)) (A_22:((hoare_2091234717iple_a->Prop)->Prop)) (B_17:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_8) ((minus_1746272704_a_o_o A_22) B_17))->((((member99268621le_a_o C_8) A_22)->((member99268621le_a_o C_8) B_17))->False))) of role axiom named fact_839_DiffE
% A new axiom: (forall (C_8:(hoare_2091234717iple_a->Prop)) (A_22:((hoare_2091234717iple_a->Prop)->Prop)) (B_17:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_8) ((minus_1746272704_a_o_o A_22) B_17))->((((member99268621le_a_o C_8) A_22)->((member99268621le_a_o C_8) B_17))->False)))
% FOF formula (forall (C_8:hoare_2091234717iple_a) (A_22:(hoare_2091234717iple_a->Prop)) (B_17:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_8) ((minus_836160335le_a_o A_22) B_17))->((((member290856304iple_a C_8) A_22)->((member290856304iple_a C_8) B_17))->False))) of role axiom named fact_840_DiffE
% A new axiom: (forall (C_8:hoare_2091234717iple_a) (A_22:(hoare_2091234717iple_a->Prop)) (B_17:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_8) ((minus_836160335le_a_o A_22) B_17))->((((member290856304iple_a C_8) A_22)->((member290856304iple_a C_8) B_17))->False)))
% FOF formula (forall (C_8:pname) (A_22:(pname->Prop)) (B_17:(pname->Prop)), (((member_pname C_8) ((minus_minus_pname_o A_22) B_17))->((((member_pname C_8) A_22)->((member_pname C_8) B_17))->False))) of role axiom named fact_841_DiffE
% A new axiom: (forall (C_8:pname) (A_22:(pname->Prop)) (B_17:(pname->Prop)), (((member_pname C_8) ((minus_minus_pname_o A_22) B_17))->((((member_pname C_8) A_22)->((member_pname C_8) B_17))->False)))
% FOF formula (forall (G_1:(hoare_2091234717iple_a->Prop)) (F_2:(hoare_2091234717iple_a->Prop)), (((or (finite232261744iple_a F_2)) (finite232261744iple_a G_1))->(finite232261744iple_a ((semila2006181266le_a_o F_2) G_1)))) of role axiom named fact_842_finite__Int
% A new axiom: (forall (G_1:(hoare_2091234717iple_a->Prop)) (F_2:(hoare_2091234717iple_a->Prop)), (((or (finite232261744iple_a F_2)) (finite232261744iple_a G_1))->(finite232261744iple_a ((semila2006181266le_a_o F_2) G_1))))
% FOF formula (forall (G_1:((hoare_2091234717iple_a->Prop)->Prop)) (F_2:((hoare_2091234717iple_a->Prop)->Prop)), (((or (finite1829014797le_a_o F_2)) (finite1829014797le_a_o G_1))->(finite1829014797le_a_o ((semila1672913213_a_o_o F_2) G_1)))) of role axiom named fact_843_finite__Int
% A new axiom: (forall (G_1:((hoare_2091234717iple_a->Prop)->Prop)) (F_2:((hoare_2091234717iple_a->Prop)->Prop)), (((or (finite1829014797le_a_o F_2)) (finite1829014797le_a_o G_1))->(finite1829014797le_a_o ((semila1672913213_a_o_o F_2) G_1))))
% FOF formula (forall (G_1:(pname->Prop)) (F_2:(pname->Prop)), (((or (finite_finite_pname F_2)) (finite_finite_pname G_1))->(finite_finite_pname ((semila1673364395name_o F_2) G_1)))) of role axiom named fact_844_finite__Int
% A new axiom: (forall (G_1:(pname->Prop)) (F_2:(pname->Prop)), (((or (finite_finite_pname F_2)) (finite_finite_pname G_1))->(finite_finite_pname ((semila1673364395name_o F_2) G_1))))
% FOF formula (forall (G_1:(nat->Prop)) (F_2:(nat->Prop)), (((or (finite_finite_nat F_2)) (finite_finite_nat G_1))->(finite_finite_nat ((semila1947288293_nat_o F_2) G_1)))) of role axiom named fact_845_finite__Int
% A new axiom: (forall (G_1:(nat->Prop)) (F_2:(nat->Prop)), (((or (finite_finite_nat F_2)) (finite_finite_nat G_1))->(finite_finite_nat ((semila1947288293_nat_o F_2) G_1))))
% FOF formula (forall (B_16:(hoare_2091234717iple_a->Prop)) (A_21:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a A_21)->(finite232261744iple_a ((minus_836160335le_a_o A_21) B_16)))) of role axiom named fact_846_finite__Diff
% A new axiom: (forall (B_16:(hoare_2091234717iple_a->Prop)) (A_21:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a A_21)->(finite232261744iple_a ((minus_836160335le_a_o A_21) B_16))))
% FOF formula (forall (B_16:((hoare_2091234717iple_a->Prop)->Prop)) (A_21:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_21)->(finite1829014797le_a_o ((minus_1746272704_a_o_o A_21) B_16)))) of role axiom named fact_847_finite__Diff
% A new axiom: (forall (B_16:((hoare_2091234717iple_a->Prop)->Prop)) (A_21:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_21)->(finite1829014797le_a_o ((minus_1746272704_a_o_o A_21) B_16))))
% FOF formula (forall (B_16:(pname->Prop)) (A_21:(pname->Prop)), ((finite_finite_pname A_21)->(finite_finite_pname ((minus_minus_pname_o A_21) B_16)))) of role axiom named fact_848_finite__Diff
% A new axiom: (forall (B_16:(pname->Prop)) (A_21:(pname->Prop)), ((finite_finite_pname A_21)->(finite_finite_pname ((minus_minus_pname_o A_21) B_16))))
% FOF formula (forall (B_16:(nat->Prop)) (A_21:(nat->Prop)), ((finite_finite_nat A_21)->(finite_finite_nat ((minus_minus_nat_o A_21) B_16)))) of role axiom named fact_849_finite__Diff
% A new axiom: (forall (B_16:(nat->Prop)) (A_21:(nat->Prop)), ((finite_finite_nat A_21)->(finite_finite_nat ((minus_minus_nat_o A_21) B_16))))
% FOF formula (forall (A_20:(hoare_2091234717iple_a->Prop)) (A_19:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_19)->(((member99268621le_a_o A_20) A_19)->(((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_20) (big_la735727201le_a_o A_19))) A_20)))) of role axiom named fact_850_inf__Sup__absorb
% A new axiom: (forall (A_20:(hoare_2091234717iple_a->Prop)) (A_19:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_19)->(((member99268621le_a_o A_20) A_19)->(((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_20) (big_la735727201le_a_o A_19))) A_20))))
% FOF formula (forall (A_20:(nat->Prop)) (A_19:((nat->Prop)->Prop)), ((finite_finite_nat_o A_19)->(((member_nat_o A_20) A_19)->(((eq (nat->Prop)) ((semila1947288293_nat_o A_20) (big_la1658356148_nat_o A_19))) A_20)))) of role axiom named fact_851_inf__Sup__absorb
% A new axiom: (forall (A_20:(nat->Prop)) (A_19:((nat->Prop)->Prop)), ((finite_finite_nat_o A_19)->(((member_nat_o A_20) A_19)->(((eq (nat->Prop)) ((semila1947288293_nat_o A_20) (big_la1658356148_nat_o A_19))) A_20))))
% FOF formula (forall (A_20:(pname->Prop)) (A_19:((pname->Prop)->Prop)), ((finite297249702name_o A_19)->(((member_pname_o A_20) A_19)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) (big_la1286884090name_o A_19))) A_20)))) of role axiom named fact_852_inf__Sup__absorb
% A new axiom: (forall (A_20:(pname->Prop)) (A_19:((pname->Prop)->Prop)), ((finite297249702name_o A_19)->(((member_pname_o A_20) A_19)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) (big_la1286884090name_o A_19))) A_20))))
% FOF formula (forall (A_20:nat) (A_19:(nat->Prop)), ((finite_finite_nat A_19)->(((member_nat A_20) A_19)->(((eq nat) ((semila80283416nf_nat A_20) (big_la43341705in_nat A_19))) A_20)))) of role axiom named fact_853_inf__Sup__absorb
% A new axiom: (forall (A_20:nat) (A_19:(nat->Prop)), ((finite_finite_nat A_19)->(((member_nat A_20) A_19)->(((eq nat) ((semila80283416nf_nat A_20) (big_la43341705in_nat A_19))) A_20))))
% FOF formula (forall (A_18:(nat->Prop)) (B_15:(nat->Prop)) (C_7:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_18) ((semila1947288293_nat_o B_15) C_7))) ((semila848761471_nat_o ((minus_minus_nat_o A_18) B_15)) ((minus_minus_nat_o A_18) C_7)))) of role axiom named fact_854_Diff__Int
% A new axiom: (forall (A_18:(nat->Prop)) (B_15:(nat->Prop)) (C_7:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_18) ((semila1947288293_nat_o B_15) C_7))) ((semila848761471_nat_o ((minus_minus_nat_o A_18) B_15)) ((minus_minus_nat_o A_18) C_7))))
% FOF formula (forall (A_18:(pname->Prop)) (B_15:(pname->Prop)) (C_7:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_18) ((semila1673364395name_o B_15) C_7))) ((semila1780557381name_o ((minus_minus_pname_o A_18) B_15)) ((minus_minus_pname_o A_18) C_7)))) of role axiom named fact_855_Diff__Int
% A new axiom: (forall (A_18:(pname->Prop)) (B_15:(pname->Prop)) (C_7:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_18) ((semila1673364395name_o B_15) C_7))) ((semila1780557381name_o ((minus_minus_pname_o A_18) B_15)) ((minus_minus_pname_o A_18) C_7))))
% FOF formula (forall (A_18:((hoare_2091234717iple_a->Prop)->Prop)) (B_15:((hoare_2091234717iple_a->Prop)->Prop)) (C_7:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_18) ((semila1672913213_a_o_o B_15) C_7))) ((semila2050116131_a_o_o ((minus_1746272704_a_o_o A_18) B_15)) ((minus_1746272704_a_o_o A_18) C_7)))) of role axiom named fact_856_Diff__Int
% A new axiom: (forall (A_18:((hoare_2091234717iple_a->Prop)->Prop)) (B_15:((hoare_2091234717iple_a->Prop)->Prop)) (C_7:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_18) ((semila1672913213_a_o_o B_15) C_7))) ((semila2050116131_a_o_o ((minus_1746272704_a_o_o A_18) B_15)) ((minus_1746272704_a_o_o A_18) C_7))))
% FOF formula (forall (A_18:(hoare_1708887482_state->Prop)) (B_15:(hoare_1708887482_state->Prop)) (C_7:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_18) ((semila129691299tate_o B_15) C_7))) ((semila1122118281tate_o ((minus_2056855718tate_o A_18) B_15)) ((minus_2056855718tate_o A_18) C_7)))) of role axiom named fact_857_Diff__Int
% A new axiom: (forall (A_18:(hoare_1708887482_state->Prop)) (B_15:(hoare_1708887482_state->Prop)) (C_7:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_18) ((semila129691299tate_o B_15) C_7))) ((semila1122118281tate_o ((minus_2056855718tate_o A_18) B_15)) ((minus_2056855718tate_o A_18) C_7))))
% FOF formula (forall (A_18:(hoare_2091234717iple_a->Prop)) (B_15:(hoare_2091234717iple_a->Prop)) (C_7:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_18) ((semila2006181266le_a_o B_15) C_7))) ((semila1052848428le_a_o ((minus_836160335le_a_o A_18) B_15)) ((minus_836160335le_a_o A_18) C_7)))) of role axiom named fact_858_Diff__Int
% A new axiom: (forall (A_18:(hoare_2091234717iple_a->Prop)) (B_15:(hoare_2091234717iple_a->Prop)) (C_7:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_18) ((semila2006181266le_a_o B_15) C_7))) ((semila1052848428le_a_o ((minus_836160335le_a_o A_18) B_15)) ((minus_836160335le_a_o A_18) C_7))))
% FOF formula (forall (A_17:(nat->Prop)) (B_14:(nat->Prop)) (C_6:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_17) ((semila848761471_nat_o B_14) C_6))) ((semila1947288293_nat_o ((minus_minus_nat_o A_17) B_14)) ((minus_minus_nat_o A_17) C_6)))) of role axiom named fact_859_Diff__Un
% A new axiom: (forall (A_17:(nat->Prop)) (B_14:(nat->Prop)) (C_6:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_17) ((semila848761471_nat_o B_14) C_6))) ((semila1947288293_nat_o ((minus_minus_nat_o A_17) B_14)) ((minus_minus_nat_o A_17) C_6))))
% FOF formula (forall (A_17:(pname->Prop)) (B_14:(pname->Prop)) (C_6:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_17) ((semila1780557381name_o B_14) C_6))) ((semila1673364395name_o ((minus_minus_pname_o A_17) B_14)) ((minus_minus_pname_o A_17) C_6)))) of role axiom named fact_860_Diff__Un
% A new axiom: (forall (A_17:(pname->Prop)) (B_14:(pname->Prop)) (C_6:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_17) ((semila1780557381name_o B_14) C_6))) ((semila1673364395name_o ((minus_minus_pname_o A_17) B_14)) ((minus_minus_pname_o A_17) C_6))))
% FOF formula (forall (A_17:((hoare_2091234717iple_a->Prop)->Prop)) (B_14:((hoare_2091234717iple_a->Prop)->Prop)) (C_6:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_17) ((semila2050116131_a_o_o B_14) C_6))) ((semila1672913213_a_o_o ((minus_1746272704_a_o_o A_17) B_14)) ((minus_1746272704_a_o_o A_17) C_6)))) of role axiom named fact_861_Diff__Un
% A new axiom: (forall (A_17:((hoare_2091234717iple_a->Prop)->Prop)) (B_14:((hoare_2091234717iple_a->Prop)->Prop)) (C_6:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_17) ((semila2050116131_a_o_o B_14) C_6))) ((semila1672913213_a_o_o ((minus_1746272704_a_o_o A_17) B_14)) ((minus_1746272704_a_o_o A_17) C_6))))
% FOF formula (forall (A_17:(hoare_1708887482_state->Prop)) (B_14:(hoare_1708887482_state->Prop)) (C_6:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_17) ((semila1122118281tate_o B_14) C_6))) ((semila129691299tate_o ((minus_2056855718tate_o A_17) B_14)) ((minus_2056855718tate_o A_17) C_6)))) of role axiom named fact_862_Diff__Un
% A new axiom: (forall (A_17:(hoare_1708887482_state->Prop)) (B_14:(hoare_1708887482_state->Prop)) (C_6:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_17) ((semila1122118281tate_o B_14) C_6))) ((semila129691299tate_o ((minus_2056855718tate_o A_17) B_14)) ((minus_2056855718tate_o A_17) C_6))))
% FOF formula (forall (A_17:(hoare_2091234717iple_a->Prop)) (B_14:(hoare_2091234717iple_a->Prop)) (C_6:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_17) ((semila1052848428le_a_o B_14) C_6))) ((semila2006181266le_a_o ((minus_836160335le_a_o A_17) B_14)) ((minus_836160335le_a_o A_17) C_6)))) of role axiom named fact_863_Diff__Un
% A new axiom: (forall (A_17:(hoare_2091234717iple_a->Prop)) (B_14:(hoare_2091234717iple_a->Prop)) (C_6:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_17) ((semila1052848428le_a_o B_14) C_6))) ((semila2006181266le_a_o ((minus_836160335le_a_o A_17) B_14)) ((minus_836160335le_a_o A_17) C_6))))
% FOF formula (forall (A_16:(nat->Prop)) (B_13:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((minus_minus_nat_o A_16) B_13)) ((semila1947288293_nat_o A_16) B_13))) A_16)) of role axiom named fact_864_Un__Diff__Int
% A new axiom: (forall (A_16:(nat->Prop)) (B_13:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((minus_minus_nat_o A_16) B_13)) ((semila1947288293_nat_o A_16) B_13))) A_16))
% FOF formula (forall (A_16:(pname->Prop)) (B_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o A_16) B_13)) ((semila1673364395name_o A_16) B_13))) A_16)) of role axiom named fact_865_Un__Diff__Int
% A new axiom: (forall (A_16:(pname->Prop)) (B_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o A_16) B_13)) ((semila1673364395name_o A_16) B_13))) A_16))
% FOF formula (forall (A_16:((hoare_2091234717iple_a->Prop)->Prop)) (B_13:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((minus_1746272704_a_o_o A_16) B_13)) ((semila1672913213_a_o_o A_16) B_13))) A_16)) of role axiom named fact_866_Un__Diff__Int
% A new axiom: (forall (A_16:((hoare_2091234717iple_a->Prop)->Prop)) (B_13:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((minus_1746272704_a_o_o A_16) B_13)) ((semila1672913213_a_o_o A_16) B_13))) A_16))
% FOF formula (forall (A_16:(hoare_1708887482_state->Prop)) (B_13:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((minus_2056855718tate_o A_16) B_13)) ((semila129691299tate_o A_16) B_13))) A_16)) of role axiom named fact_867_Un__Diff__Int
% A new axiom: (forall (A_16:(hoare_1708887482_state->Prop)) (B_13:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((minus_2056855718tate_o A_16) B_13)) ((semila129691299tate_o A_16) B_13))) A_16))
% FOF formula (forall (A_16:(hoare_2091234717iple_a->Prop)) (B_13:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((minus_836160335le_a_o A_16) B_13)) ((semila2006181266le_a_o A_16) B_13))) A_16)) of role axiom named fact_868_Un__Diff__Int
% A new axiom: (forall (A_16:(hoare_2091234717iple_a->Prop)) (B_13:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((minus_836160335le_a_o A_16) B_13)) ((semila2006181266le_a_o A_16) B_13))) A_16))
% FOF formula (forall (P_2:(pname->Prop)) (Q:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (P_2 X)) (Q X))))) ((semila1673364395name_o (collect_pname P_2)) (collect_pname Q)))) of role axiom named fact_869_Collect__conj__eq
% A new axiom: (forall (P_2:(pname->Prop)) (Q:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (P_2 X)) (Q X))))) ((semila1673364395name_o (collect_pname P_2)) (collect_pname Q))))
% FOF formula (forall (P_2:(hoare_2091234717iple_a->Prop)) (Q:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (P_2 X)) (Q X))))) ((semila2006181266le_a_o (collec992574898iple_a P_2)) (collec992574898iple_a Q)))) of role axiom named fact_870_Collect__conj__eq
% A new axiom: (forall (P_2:(hoare_2091234717iple_a->Prop)) (Q:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (P_2 X)) (Q X))))) ((semila2006181266le_a_o (collec992574898iple_a P_2)) (collec992574898iple_a Q))))
% FOF formula (forall (P_2:(nat->Prop)) (Q:(nat->Prop)), (((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (P_2 X)) (Q X))))) ((semila1947288293_nat_o (collect_nat P_2)) (collect_nat Q)))) of role axiom named fact_871_Collect__conj__eq
% A new axiom: (forall (P_2:(nat->Prop)) (Q:(nat->Prop)), (((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (P_2 X)) (Q X))))) ((semila1947288293_nat_o (collect_nat P_2)) (collect_nat Q))))
% FOF formula (forall (X_9:(hoare_2091234717iple_a->Prop)) (A_15:((hoare_2091234717iple_a->Prop)->Prop)) (P_1:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o X_9) ((semila1672913213_a_o_o A_15) (collec1008234059le_a_o P_1)))) ((and ((member99268621le_a_o X_9) A_15)) (P_1 X_9)))) of role axiom named fact_872_Int__Collect
% A new axiom: (forall (X_9:(hoare_2091234717iple_a->Prop)) (A_15:((hoare_2091234717iple_a->Prop)->Prop)) (P_1:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o X_9) ((semila1672913213_a_o_o A_15) (collec1008234059le_a_o P_1)))) ((and ((member99268621le_a_o X_9) A_15)) (P_1 X_9))))
% FOF formula (forall (X_9:nat) (A_15:(nat->Prop)) (P_1:(nat->Prop)), ((iff ((member_nat X_9) ((semila1947288293_nat_o A_15) (collect_nat P_1)))) ((and ((member_nat X_9) A_15)) (P_1 X_9)))) of role axiom named fact_873_Int__Collect
% A new axiom: (forall (X_9:nat) (A_15:(nat->Prop)) (P_1:(nat->Prop)), ((iff ((member_nat X_9) ((semila1947288293_nat_o A_15) (collect_nat P_1)))) ((and ((member_nat X_9) A_15)) (P_1 X_9))))
% FOF formula (forall (X_9:hoare_2091234717iple_a) (A_15:(hoare_2091234717iple_a->Prop)) (P_1:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a X_9) ((semila2006181266le_a_o A_15) (collec992574898iple_a P_1)))) ((and ((member290856304iple_a X_9) A_15)) (P_1 X_9)))) of role axiom named fact_874_Int__Collect
% A new axiom: (forall (X_9:hoare_2091234717iple_a) (A_15:(hoare_2091234717iple_a->Prop)) (P_1:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a X_9) ((semila2006181266le_a_o A_15) (collec992574898iple_a P_1)))) ((and ((member290856304iple_a X_9) A_15)) (P_1 X_9))))
% FOF formula (forall (X_9:pname) (A_15:(pname->Prop)) (P_1:(pname->Prop)), ((iff ((member_pname X_9) ((semila1673364395name_o A_15) (collect_pname P_1)))) ((and ((member_pname X_9) A_15)) (P_1 X_9)))) of role axiom named fact_875_Int__Collect
% A new axiom: (forall (X_9:pname) (A_15:(pname->Prop)) (P_1:(pname->Prop)), ((iff ((member_pname X_9) ((semila1673364395name_o A_15) (collect_pname P_1)))) ((and ((member_pname X_9) A_15)) (P_1 X_9))))
% FOF formula (forall (R:((hoare_2091234717iple_a->Prop)->Prop)) (S_1:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), ((iff (((semila1672913213_a_o_o (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) R))) (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) S_1))) X)) ((member99268621le_a_o X) ((semila1672913213_a_o_o R) S_1)))) of role axiom named fact_876_inf__Int__eq
% A new axiom: (forall (R:((hoare_2091234717iple_a->Prop)->Prop)) (S_1:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), ((iff (((semila1672913213_a_o_o (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) R))) (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) S_1))) X)) ((member99268621le_a_o X) ((semila1672913213_a_o_o R) S_1))))
% FOF formula (forall (R:(nat->Prop)) (S_1:(nat->Prop)) (X:nat), ((iff (((semila1947288293_nat_o (fun (Y_7:nat)=> ((member_nat Y_7) R))) (fun (Y_7:nat)=> ((member_nat Y_7) S_1))) X)) ((member_nat X) ((semila1947288293_nat_o R) S_1)))) of role axiom named fact_877_inf__Int__eq
% A new axiom: (forall (R:(nat->Prop)) (S_1:(nat->Prop)) (X:nat), ((iff (((semila1947288293_nat_o (fun (Y_7:nat)=> ((member_nat Y_7) R))) (fun (Y_7:nat)=> ((member_nat Y_7) S_1))) X)) ((member_nat X) ((semila1947288293_nat_o R) S_1))))
% FOF formula (forall (R:(hoare_2091234717iple_a->Prop)) (S_1:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila2006181266le_a_o (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) R))) (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) S_1))) X)) ((member290856304iple_a X) ((semila2006181266le_a_o R) S_1)))) of role axiom named fact_878_inf__Int__eq
% A new axiom: (forall (R:(hoare_2091234717iple_a->Prop)) (S_1:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila2006181266le_a_o (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) R))) (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) S_1))) X)) ((member290856304iple_a X) ((semila2006181266le_a_o R) S_1))))
% FOF formula (forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X:pname), ((iff (((semila1673364395name_o (fun (Y_7:pname)=> ((member_pname Y_7) R))) (fun (Y_7:pname)=> ((member_pname Y_7) S_1))) X)) ((member_pname X) ((semila1673364395name_o R) S_1)))) of role axiom named fact_879_inf__Int__eq
% A new axiom: (forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X:pname), ((iff (((semila1673364395name_o (fun (Y_7:pname)=> ((member_pname Y_7) R))) (fun (Y_7:pname)=> ((member_pname Y_7) S_1))) X)) ((member_pname X) ((semila1673364395name_o R) S_1))))
% FOF formula (forall (A_14:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_14) A_14)) A_14)) of role axiom named fact_880_Int__absorb
% A new axiom: (forall (A_14:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_14) A_14)) A_14))
% FOF formula (forall (A_14:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_14) A_14)) A_14)) of role axiom named fact_881_Int__absorb
% A new axiom: (forall (A_14:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_14) A_14)) A_14))
% FOF formula (forall (A_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_14) A_14)) A_14)) of role axiom named fact_882_Int__absorb
% A new axiom: (forall (A_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_14) A_14)) A_14))
% FOF formula (forall (A_13:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_13) A_13)) A_13)) of role axiom named fact_883_inf_Oidem
% A new axiom: (forall (A_13:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_13) A_13)) A_13))
% FOF formula (forall (A_13:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_13) A_13)) A_13)) of role axiom named fact_884_inf_Oidem
% A new axiom: (forall (A_13:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_13) A_13)) A_13))
% FOF formula (forall (A_13:nat), (((eq nat) ((semila80283416nf_nat A_13) A_13)) A_13)) of role axiom named fact_885_inf_Oidem
% A new axiom: (forall (A_13:nat), (((eq nat) ((semila80283416nf_nat A_13) A_13)) A_13))
% FOF formula (forall (A_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_13) A_13)) A_13)) of role axiom named fact_886_inf_Oidem
% A new axiom: (forall (A_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_13) A_13)) A_13))
% FOF formula (forall (X_8:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_8) X_8)) X_8)) of role axiom named fact_887_inf__idem
% A new axiom: (forall (X_8:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_8) X_8)) X_8))
% FOF formula (forall (X_8:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_8) X_8)) X_8)) of role axiom named fact_888_inf__idem
% A new axiom: (forall (X_8:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_8) X_8)) X_8))
% FOF formula (forall (X_8:nat), (((eq nat) ((semila80283416nf_nat X_8) X_8)) X_8)) of role axiom named fact_889_inf__idem
% A new axiom: (forall (X_8:nat), (((eq nat) ((semila80283416nf_nat X_8) X_8)) X_8))
% FOF formula (forall (X_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_8) X_8)) X_8)) of role axiom named fact_890_inf__idem
% A new axiom: (forall (X_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_8) X_8)) X_8))
% FOF formula (forall (A_12:(hoare_2091234717iple_a->Prop)) (B_12:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((minus_836160335le_a_o A_12) B_12) X)) ((minus_minus_o (A_12 X)) (B_12 X)))) of role axiom named fact_891_fun__diff__def
% A new axiom: (forall (A_12:(hoare_2091234717iple_a->Prop)) (B_12:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((minus_836160335le_a_o A_12) B_12) X)) ((minus_minus_o (A_12 X)) (B_12 X))))
% FOF formula (forall (A_12:(pname->Prop)) (B_12:(pname->Prop)) (X:pname), ((iff (((minus_minus_pname_o A_12) B_12) X)) ((minus_minus_o (A_12 X)) (B_12 X)))) of role axiom named fact_892_fun__diff__def
% A new axiom: (forall (A_12:(pname->Prop)) (B_12:(pname->Prop)) (X:pname), ((iff (((minus_minus_pname_o A_12) B_12) X)) ((minus_minus_o (A_12 X)) (B_12 X))))
% FOF formula (forall (A_12:(nat->Prop)) (B_12:(nat->Prop)) (X:nat), ((iff (((minus_minus_nat_o A_12) B_12) X)) ((minus_minus_o (A_12 X)) (B_12 X)))) of role axiom named fact_893_fun__diff__def
% A new axiom: (forall (A_12:(nat->Prop)) (B_12:(nat->Prop)) (X:nat), ((iff (((minus_minus_nat_o A_12) B_12) X)) ((minus_minus_o (A_12 X)) (B_12 X))))
% FOF formula (forall (F_1:(nat->Prop)) (G:(nat->Prop)) (X:nat), ((iff (((semila1947288293_nat_o F_1) G) X)) ((semila854092349_inf_o (F_1 X)) (G X)))) of role axiom named fact_894_inf__fun__def
% A new axiom: (forall (F_1:(nat->Prop)) (G:(nat->Prop)) (X:nat), ((iff (((semila1947288293_nat_o F_1) G) X)) ((semila854092349_inf_o (F_1 X)) (G X))))
% FOF formula (forall (F_1:(hoare_2091234717iple_a->Prop)) (G:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila2006181266le_a_o F_1) G) X)) ((semila854092349_inf_o (F_1 X)) (G X)))) of role axiom named fact_895_inf__fun__def
% A new axiom: (forall (F_1:(hoare_2091234717iple_a->Prop)) (G:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila2006181266le_a_o F_1) G) X)) ((semila854092349_inf_o (F_1 X)) (G X))))
% FOF formula (forall (F_1:(pname->Prop)) (G:(pname->Prop)) (X:pname), ((iff (((semila1673364395name_o F_1) G) X)) ((semila854092349_inf_o (F_1 X)) (G X)))) of role axiom named fact_896_inf__fun__def
% A new axiom: (forall (F_1:(pname->Prop)) (G:(pname->Prop)) (X:pname), ((iff (((semila1673364395name_o F_1) G) X)) ((semila854092349_inf_o (F_1 X)) (G X))))
% FOF formula (forall (A_11:((hoare_2091234717iple_a->Prop)->Prop)) (B_11:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_11) B_11)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_11)) (not ((member99268621le_a_o X) B_11))))))) of role axiom named fact_897_set__diff__eq
% A new axiom: (forall (A_11:((hoare_2091234717iple_a->Prop)->Prop)) (B_11:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_11) B_11)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_11)) (not ((member99268621le_a_o X) B_11)))))))
% FOF formula (forall (A_11:(nat->Prop)) (B_11:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_11) B_11)) (collect_nat (fun (X:nat)=> ((and ((member_nat X) A_11)) (not ((member_nat X) B_11))))))) of role axiom named fact_898_set__diff__eq
% A new axiom: (forall (A_11:(nat->Prop)) (B_11:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_11) B_11)) (collect_nat (fun (X:nat)=> ((and ((member_nat X) A_11)) (not ((member_nat X) B_11)))))))
% FOF formula (forall (A_11:(hoare_2091234717iple_a->Prop)) (B_11:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_11) B_11)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_11)) (not ((member290856304iple_a X) B_11))))))) of role axiom named fact_899_set__diff__eq
% A new axiom: (forall (A_11:(hoare_2091234717iple_a->Prop)) (B_11:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_11) B_11)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_11)) (not ((member290856304iple_a X) B_11)))))))
% FOF formula (forall (A_11:(pname->Prop)) (B_11:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_11) B_11)) (collect_pname (fun (X:pname)=> ((and ((member_pname X) A_11)) (not ((member_pname X) B_11))))))) of role axiom named fact_900_set__diff__eq
% A new axiom: (forall (A_11:(pname->Prop)) (B_11:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_11) B_11)) (collect_pname (fun (X:pname)=> ((and ((member_pname X) A_11)) (not ((member_pname X) B_11)))))))
% FOF formula (forall (A_10:((hoare_2091234717iple_a->Prop)->Prop)) (B_10:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila1672913213_a_o_o A_10) B_10)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_10)) ((member99268621le_a_o X) B_10)))))) of role axiom named fact_901_Int__def
% A new axiom: (forall (A_10:((hoare_2091234717iple_a->Prop)->Prop)) (B_10:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila1672913213_a_o_o A_10) B_10)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_10)) ((member99268621le_a_o X) B_10))))))
% FOF formula (forall (A_10:(nat->Prop)) (B_10:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_10) B_10)) (collect_nat (fun (X:nat)=> ((and ((member_nat X) A_10)) ((member_nat X) B_10)))))) of role axiom named fact_902_Int__def
% A new axiom: (forall (A_10:(nat->Prop)) (B_10:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_10) B_10)) (collect_nat (fun (X:nat)=> ((and ((member_nat X) A_10)) ((member_nat X) B_10))))))
% FOF formula (forall (A_10:(hoare_2091234717iple_a->Prop)) (B_10:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_10) B_10)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_10)) ((member290856304iple_a X) B_10)))))) of role axiom named fact_903_Int__def
% A new axiom: (forall (A_10:(hoare_2091234717iple_a->Prop)) (B_10:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_10) B_10)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_10)) ((member290856304iple_a X) B_10))))))
% FOF formula (forall (A_10:(pname->Prop)) (B_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_10) B_10)) (collect_pname (fun (X:pname)=> ((and ((member_pname X) A_10)) ((member_pname X) B_10)))))) of role axiom named fact_904_Int__def
% A new axiom: (forall (A_10:(pname->Prop)) (B_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_10) B_10)) (collect_pname (fun (X:pname)=> ((and ((member_pname X) A_10)) ((member_pname X) B_10))))))
% FOF formula (forall (A_9:(nat->Prop)) (B_9:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_9) B_9)) ((semila1947288293_nat_o B_9) A_9))) of role axiom named fact_905_Int__commute
% A new axiom: (forall (A_9:(nat->Prop)) (B_9:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_9) B_9)) ((semila1947288293_nat_o B_9) A_9)))
% FOF formula (forall (A_9:(hoare_2091234717iple_a->Prop)) (B_9:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_9) B_9)) ((semila2006181266le_a_o B_9) A_9))) of role axiom named fact_906_Int__commute
% A new axiom: (forall (A_9:(hoare_2091234717iple_a->Prop)) (B_9:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_9) B_9)) ((semila2006181266le_a_o B_9) A_9)))
% FOF formula (forall (A_9:(pname->Prop)) (B_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_9) B_9)) ((semila1673364395name_o B_9) A_9))) of role axiom named fact_907_Int__commute
% A new axiom: (forall (A_9:(pname->Prop)) (B_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_9) B_9)) ((semila1673364395name_o B_9) A_9)))
% FOF formula (forall (A_8:(nat->Prop)) (B_8:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_8) B_8)) ((semila1947288293_nat_o B_8) A_8))) of role axiom named fact_908_inf_Ocommute
% A new axiom: (forall (A_8:(nat->Prop)) (B_8:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_8) B_8)) ((semila1947288293_nat_o B_8) A_8)))
% FOF formula (forall (A_8:(hoare_2091234717iple_a->Prop)) (B_8:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_8) B_8)) ((semila2006181266le_a_o B_8) A_8))) of role axiom named fact_909_inf_Ocommute
% A new axiom: (forall (A_8:(hoare_2091234717iple_a->Prop)) (B_8:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_8) B_8)) ((semila2006181266le_a_o B_8) A_8)))
% FOF formula (forall (A_8:nat) (B_8:nat), (((eq nat) ((semila80283416nf_nat A_8) B_8)) ((semila80283416nf_nat B_8) A_8))) of role axiom named fact_910_inf_Ocommute
% A new axiom: (forall (A_8:nat) (B_8:nat), (((eq nat) ((semila80283416nf_nat A_8) B_8)) ((semila80283416nf_nat B_8) A_8)))
% FOF formula (forall (A_8:(pname->Prop)) (B_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_8) B_8)) ((semila1673364395name_o B_8) A_8))) of role axiom named fact_911_inf_Ocommute
% A new axiom: (forall (A_8:(pname->Prop)) (B_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_8) B_8)) ((semila1673364395name_o B_8) A_8)))
% FOF formula (forall (X_7:(nat->Prop)) (Y_6:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_7) Y_6)) ((semila1947288293_nat_o Y_6) X_7))) of role axiom named fact_912_inf__sup__aci_I1_J
% A new axiom: (forall (X_7:(nat->Prop)) (Y_6:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_7) Y_6)) ((semila1947288293_nat_o Y_6) X_7)))
% FOF formula (forall (X_7:(hoare_2091234717iple_a->Prop)) (Y_6:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_7) Y_6)) ((semila2006181266le_a_o Y_6) X_7))) of role axiom named fact_913_inf__sup__aci_I1_J
% A new axiom: (forall (X_7:(hoare_2091234717iple_a->Prop)) (Y_6:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_7) Y_6)) ((semila2006181266le_a_o Y_6) X_7)))
% FOF formula (forall (X_7:nat) (Y_6:nat), (((eq nat) ((semila80283416nf_nat X_7) Y_6)) ((semila80283416nf_nat Y_6) X_7))) of role axiom named fact_914_inf__sup__aci_I1_J
% A new axiom: (forall (X_7:nat) (Y_6:nat), (((eq nat) ((semila80283416nf_nat X_7) Y_6)) ((semila80283416nf_nat Y_6) X_7)))
% FOF formula (forall (X_7:(pname->Prop)) (Y_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_7) Y_6)) ((semila1673364395name_o Y_6) X_7))) of role axiom named fact_915_inf__sup__aci_I1_J
% A new axiom: (forall (X_7:(pname->Prop)) (Y_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_7) Y_6)) ((semila1673364395name_o Y_6) X_7)))
% FOF formula (forall (X_6:(nat->Prop)) (Y_5:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_6) Y_5)) ((semila1947288293_nat_o Y_5) X_6))) of role axiom named fact_916_inf__commute
% A new axiom: (forall (X_6:(nat->Prop)) (Y_5:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_6) Y_5)) ((semila1947288293_nat_o Y_5) X_6)))
% FOF formula (forall (X_6:(hoare_2091234717iple_a->Prop)) (Y_5:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_6) Y_5)) ((semila2006181266le_a_o Y_5) X_6))) of role axiom named fact_917_inf__commute
% A new axiom: (forall (X_6:(hoare_2091234717iple_a->Prop)) (Y_5:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_6) Y_5)) ((semila2006181266le_a_o Y_5) X_6)))
% FOF formula (forall (X_6:nat) (Y_5:nat), (((eq nat) ((semila80283416nf_nat X_6) Y_5)) ((semila80283416nf_nat Y_5) X_6))) of role axiom named fact_918_inf__commute
% A new axiom: (forall (X_6:nat) (Y_5:nat), (((eq nat) ((semila80283416nf_nat X_6) Y_5)) ((semila80283416nf_nat Y_5) X_6)))
% FOF formula (forall (X_6:(pname->Prop)) (Y_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_6) Y_5)) ((semila1673364395name_o Y_5) X_6))) of role axiom named fact_919_inf__commute
% A new axiom: (forall (X_6:(pname->Prop)) (Y_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_6) Y_5)) ((semila1673364395name_o Y_5) X_6)))
% FOF formula (forall (A_7:(nat->Prop)) (B_7:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_7) ((semila1947288293_nat_o A_7) B_7))) ((semila1947288293_nat_o A_7) B_7))) of role axiom named fact_920_Int__left__absorb
% A new axiom: (forall (A_7:(nat->Prop)) (B_7:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_7) ((semila1947288293_nat_o A_7) B_7))) ((semila1947288293_nat_o A_7) B_7)))
% FOF formula (forall (A_7:(hoare_2091234717iple_a->Prop)) (B_7:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_7) ((semila2006181266le_a_o A_7) B_7))) ((semila2006181266le_a_o A_7) B_7))) of role axiom named fact_921_Int__left__absorb
% A new axiom: (forall (A_7:(hoare_2091234717iple_a->Prop)) (B_7:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_7) ((semila2006181266le_a_o A_7) B_7))) ((semila2006181266le_a_o A_7) B_7)))
% FOF formula (forall (A_7:(pname->Prop)) (B_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_7) ((semila1673364395name_o A_7) B_7))) ((semila1673364395name_o A_7) B_7))) of role axiom named fact_922_Int__left__absorb
% A new axiom: (forall (A_7:(pname->Prop)) (B_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_7) ((semila1673364395name_o A_7) B_7))) ((semila1673364395name_o A_7) B_7)))
% FOF formula (forall (A_6:(nat->Prop)) (B_6:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_6) ((semila1947288293_nat_o A_6) B_6))) ((semila1947288293_nat_o A_6) B_6))) of role axiom named fact_923_inf_Oleft__idem
% A new axiom: (forall (A_6:(nat->Prop)) (B_6:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_6) ((semila1947288293_nat_o A_6) B_6))) ((semila1947288293_nat_o A_6) B_6)))
% FOF formula (forall (A_6:(hoare_2091234717iple_a->Prop)) (B_6:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_6) ((semila2006181266le_a_o A_6) B_6))) ((semila2006181266le_a_o A_6) B_6))) of role axiom named fact_924_inf_Oleft__idem
% A new axiom: (forall (A_6:(hoare_2091234717iple_a->Prop)) (B_6:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_6) ((semila2006181266le_a_o A_6) B_6))) ((semila2006181266le_a_o A_6) B_6)))
% FOF formula (forall (A_6:nat) (B_6:nat), (((eq nat) ((semila80283416nf_nat A_6) ((semila80283416nf_nat A_6) B_6))) ((semila80283416nf_nat A_6) B_6))) of role axiom named fact_925_inf_Oleft__idem
% A new axiom: (forall (A_6:nat) (B_6:nat), (((eq nat) ((semila80283416nf_nat A_6) ((semila80283416nf_nat A_6) B_6))) ((semila80283416nf_nat A_6) B_6)))
% FOF formula (forall (A_6:(pname->Prop)) (B_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_6) ((semila1673364395name_o A_6) B_6))) ((semila1673364395name_o A_6) B_6))) of role axiom named fact_926_inf_Oleft__idem
% A new axiom: (forall (A_6:(pname->Prop)) (B_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_6) ((semila1673364395name_o A_6) B_6))) ((semila1673364395name_o A_6) B_6)))
% FOF formula (forall (X_5:(nat->Prop)) (Y_4:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_5) ((semila1947288293_nat_o X_5) Y_4))) ((semila1947288293_nat_o X_5) Y_4))) of role axiom named fact_927_inf__sup__aci_I4_J
% A new axiom: (forall (X_5:(nat->Prop)) (Y_4:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_5) ((semila1947288293_nat_o X_5) Y_4))) ((semila1947288293_nat_o X_5) Y_4)))
% FOF formula (forall (X_5:(hoare_2091234717iple_a->Prop)) (Y_4:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_5) ((semila2006181266le_a_o X_5) Y_4))) ((semila2006181266le_a_o X_5) Y_4))) of role axiom named fact_928_inf__sup__aci_I4_J
% A new axiom: (forall (X_5:(hoare_2091234717iple_a->Prop)) (Y_4:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_5) ((semila2006181266le_a_o X_5) Y_4))) ((semila2006181266le_a_o X_5) Y_4)))
% FOF formula (forall (X_5:nat) (Y_4:nat), (((eq nat) ((semila80283416nf_nat X_5) ((semila80283416nf_nat X_5) Y_4))) ((semila80283416nf_nat X_5) Y_4))) of role axiom named fact_929_inf__sup__aci_I4_J
% A new axiom: (forall (X_5:nat) (Y_4:nat), (((eq nat) ((semila80283416nf_nat X_5) ((semila80283416nf_nat X_5) Y_4))) ((semila80283416nf_nat X_5) Y_4)))
% FOF formula (forall (X_5:(pname->Prop)) (Y_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_5) ((semila1673364395name_o X_5) Y_4))) ((semila1673364395name_o X_5) Y_4))) of role axiom named fact_930_inf__sup__aci_I4_J
% A new axiom: (forall (X_5:(pname->Prop)) (Y_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_5) ((semila1673364395name_o X_5) Y_4))) ((semila1673364395name_o X_5) Y_4)))
% FOF formula (forall (X_4:(nat->Prop)) (Y_3:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_4) ((semila1947288293_nat_o X_4) Y_3))) ((semila1947288293_nat_o X_4) Y_3))) of role axiom named fact_931_inf__left__idem
% A new axiom: (forall (X_4:(nat->Prop)) (Y_3:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_4) ((semila1947288293_nat_o X_4) Y_3))) ((semila1947288293_nat_o X_4) Y_3)))
% FOF formula (forall (X_4:(hoare_2091234717iple_a->Prop)) (Y_3:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_4) ((semila2006181266le_a_o X_4) Y_3))) ((semila2006181266le_a_o X_4) Y_3))) of role axiom named fact_932_inf__left__idem
% A new axiom: (forall (X_4:(hoare_2091234717iple_a->Prop)) (Y_3:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_4) ((semila2006181266le_a_o X_4) Y_3))) ((semila2006181266le_a_o X_4) Y_3)))
% FOF formula (forall (X_4:nat) (Y_3:nat), (((eq nat) ((semila80283416nf_nat X_4) ((semila80283416nf_nat X_4) Y_3))) ((semila80283416nf_nat X_4) Y_3))) of role axiom named fact_933_inf__left__idem
% A new axiom: (forall (X_4:nat) (Y_3:nat), (((eq nat) ((semila80283416nf_nat X_4) ((semila80283416nf_nat X_4) Y_3))) ((semila80283416nf_nat X_4) Y_3)))
% FOF formula (forall (X_4:(pname->Prop)) (Y_3:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_4) ((semila1673364395name_o X_4) Y_3))) ((semila1673364395name_o X_4) Y_3))) of role axiom named fact_934_inf__left__idem
% A new axiom: (forall (X_4:(pname->Prop)) (Y_3:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_4) ((semila1673364395name_o X_4) Y_3))) ((semila1673364395name_o X_4) Y_3)))
% FOF formula (forall (A_5:(nat->Prop)) (B_5:(nat->Prop)) (C_5:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_5) ((semila1947288293_nat_o B_5) C_5))) ((semila1947288293_nat_o B_5) ((semila1947288293_nat_o A_5) C_5)))) of role axiom named fact_935_Int__left__commute
% A new axiom: (forall (A_5:(nat->Prop)) (B_5:(nat->Prop)) (C_5:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_5) ((semila1947288293_nat_o B_5) C_5))) ((semila1947288293_nat_o B_5) ((semila1947288293_nat_o A_5) C_5))))
% FOF formula (forall (A_5:(hoare_2091234717iple_a->Prop)) (B_5:(hoare_2091234717iple_a->Prop)) (C_5:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_5) ((semila2006181266le_a_o B_5) C_5))) ((semila2006181266le_a_o B_5) ((semila2006181266le_a_o A_5) C_5)))) of role axiom named fact_936_Int__left__commute
% A new axiom: (forall (A_5:(hoare_2091234717iple_a->Prop)) (B_5:(hoare_2091234717iple_a->Prop)) (C_5:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_5) ((semila2006181266le_a_o B_5) C_5))) ((semila2006181266le_a_o B_5) ((semila2006181266le_a_o A_5) C_5))))
% FOF formula (forall (A_5:(pname->Prop)) (B_5:(pname->Prop)) (C_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_5) ((semila1673364395name_o B_5) C_5))) ((semila1673364395name_o B_5) ((semila1673364395name_o A_5) C_5)))) of role axiom named fact_937_Int__left__commute
% A new axiom: (forall (A_5:(pname->Prop)) (B_5:(pname->Prop)) (C_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_5) ((semila1673364395name_o B_5) C_5))) ((semila1673364395name_o B_5) ((semila1673364395name_o A_5) C_5))))
% FOF formula (forall (B_4:(nat->Prop)) (A_4:(nat->Prop)) (C_4:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o B_4) ((semila1947288293_nat_o A_4) C_4))) ((semila1947288293_nat_o A_4) ((semila1947288293_nat_o B_4) C_4)))) of role axiom named fact_938_inf_Oleft__commute
% A new axiom: (forall (B_4:(nat->Prop)) (A_4:(nat->Prop)) (C_4:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o B_4) ((semila1947288293_nat_o A_4) C_4))) ((semila1947288293_nat_o A_4) ((semila1947288293_nat_o B_4) C_4))))
% FOF formula (forall (B_4:(hoare_2091234717iple_a->Prop)) (A_4:(hoare_2091234717iple_a->Prop)) (C_4:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o B_4) ((semila2006181266le_a_o A_4) C_4))) ((semila2006181266le_a_o A_4) ((semila2006181266le_a_o B_4) C_4)))) of role axiom named fact_939_inf_Oleft__commute
% A new axiom: (forall (B_4:(hoare_2091234717iple_a->Prop)) (A_4:(hoare_2091234717iple_a->Prop)) (C_4:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o B_4) ((semila2006181266le_a_o A_4) C_4))) ((semila2006181266le_a_o A_4) ((semila2006181266le_a_o B_4) C_4))))
% FOF formula (forall (B_4:nat) (A_4:nat) (C_4:nat), (((eq nat) ((semila80283416nf_nat B_4) ((semila80283416nf_nat A_4) C_4))) ((semila80283416nf_nat A_4) ((semila80283416nf_nat B_4) C_4)))) of role axiom named fact_940_inf_Oleft__commute
% A new axiom: (forall (B_4:nat) (A_4:nat) (C_4:nat), (((eq nat) ((semila80283416nf_nat B_4) ((semila80283416nf_nat A_4) C_4))) ((semila80283416nf_nat A_4) ((semila80283416nf_nat B_4) C_4))))
% FOF formula (forall (B_4:(pname->Prop)) (A_4:(pname->Prop)) (C_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o B_4) ((semila1673364395name_o A_4) C_4))) ((semila1673364395name_o A_4) ((semila1673364395name_o B_4) C_4)))) of role axiom named fact_941_inf_Oleft__commute
% A new axiom: (forall (B_4:(pname->Prop)) (A_4:(pname->Prop)) (C_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o B_4) ((semila1673364395name_o A_4) C_4))) ((semila1673364395name_o A_4) ((semila1673364395name_o B_4) C_4))))
% FOF formula (forall (X_3:(nat->Prop)) (Y_2:(nat->Prop)) (Z_2:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_3) ((semila1947288293_nat_o Y_2) Z_2))) ((semila1947288293_nat_o Y_2) ((semila1947288293_nat_o X_3) Z_2)))) of role axiom named fact_942_inf__sup__aci_I3_J
% A new axiom: (forall (X_3:(nat->Prop)) (Y_2:(nat->Prop)) (Z_2:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_3) ((semila1947288293_nat_o Y_2) Z_2))) ((semila1947288293_nat_o Y_2) ((semila1947288293_nat_o X_3) Z_2))))
% FOF formula (forall (X_3:(hoare_2091234717iple_a->Prop)) (Y_2:(hoare_2091234717iple_a->Prop)) (Z_2:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_3) ((semila2006181266le_a_o Y_2) Z_2))) ((semila2006181266le_a_o Y_2) ((semila2006181266le_a_o X_3) Z_2)))) of role axiom named fact_943_inf__sup__aci_I3_J
% A new axiom: (forall (X_3:(hoare_2091234717iple_a->Prop)) (Y_2:(hoare_2091234717iple_a->Prop)) (Z_2:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_3) ((semila2006181266le_a_o Y_2) Z_2))) ((semila2006181266le_a_o Y_2) ((semila2006181266le_a_o X_3) Z_2))))
% FOF formula (forall (X_3:nat) (Y_2:nat) (Z_2:nat), (((eq nat) ((semila80283416nf_nat X_3) ((semila80283416nf_nat Y_2) Z_2))) ((semila80283416nf_nat Y_2) ((semila80283416nf_nat X_3) Z_2)))) of role axiom named fact_944_inf__sup__aci_I3_J
% A new axiom: (forall (X_3:nat) (Y_2:nat) (Z_2:nat), (((eq nat) ((semila80283416nf_nat X_3) ((semila80283416nf_nat Y_2) Z_2))) ((semila80283416nf_nat Y_2) ((semila80283416nf_nat X_3) Z_2))))
% FOF formula (forall (X_3:(pname->Prop)) (Y_2:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_3) ((semila1673364395name_o Y_2) Z_2))) ((semila1673364395name_o Y_2) ((semila1673364395name_o X_3) Z_2)))) of role axiom named fact_945_inf__sup__aci_I3_J
% A new axiom: (forall (X_3:(pname->Prop)) (Y_2:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_3) ((semila1673364395name_o Y_2) Z_2))) ((semila1673364395name_o Y_2) ((semila1673364395name_o X_3) Z_2))))
% FOF formula (forall (X_2:(nat->Prop)) (Y_1:(nat->Prop)) (Z_1:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_2) ((semila1947288293_nat_o Y_1) Z_1))) ((semila1947288293_nat_o Y_1) ((semila1947288293_nat_o X_2) Z_1)))) of role axiom named fact_946_inf__left__commute
% A new axiom: (forall (X_2:(nat->Prop)) (Y_1:(nat->Prop)) (Z_1:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_2) ((semila1947288293_nat_o Y_1) Z_1))) ((semila1947288293_nat_o Y_1) ((semila1947288293_nat_o X_2) Z_1))))
% FOF formula (forall (X_2:(hoare_2091234717iple_a->Prop)) (Y_1:(hoare_2091234717iple_a->Prop)) (Z_1:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_2) ((semila2006181266le_a_o Y_1) Z_1))) ((semila2006181266le_a_o Y_1) ((semila2006181266le_a_o X_2) Z_1)))) of role axiom named fact_947_inf__left__commute
% A new axiom: (forall (X_2:(hoare_2091234717iple_a->Prop)) (Y_1:(hoare_2091234717iple_a->Prop)) (Z_1:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_2) ((semila2006181266le_a_o Y_1) Z_1))) ((semila2006181266le_a_o Y_1) ((semila2006181266le_a_o X_2) Z_1))))
% FOF formula (forall (X_2:nat) (Y_1:nat) (Z_1:nat), (((eq nat) ((semila80283416nf_nat X_2) ((semila80283416nf_nat Y_1) Z_1))) ((semila80283416nf_nat Y_1) ((semila80283416nf_nat X_2) Z_1)))) of role axiom named fact_948_inf__left__commute
% A new axiom: (forall (X_2:nat) (Y_1:nat) (Z_1:nat), (((eq nat) ((semila80283416nf_nat X_2) ((semila80283416nf_nat Y_1) Z_1))) ((semila80283416nf_nat Y_1) ((semila80283416nf_nat X_2) Z_1))))
% FOF formula (forall (X_2:(pname->Prop)) (Y_1:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_2) ((semila1673364395name_o Y_1) Z_1))) ((semila1673364395name_o Y_1) ((semila1673364395name_o X_2) Z_1)))) of role axiom named fact_949_inf__left__commute
% A new axiom: (forall (X_2:(pname->Prop)) (Y_1:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_2) ((semila1673364395name_o Y_1) Z_1))) ((semila1673364395name_o Y_1) ((semila1673364395name_o X_2) Z_1))))
% FOF formula (forall (C_3:(hoare_2091234717iple_a->Prop)) (A_3:((hoare_2091234717iple_a->Prop)->Prop)) (B_3:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o C_3) ((minus_1746272704_a_o_o A_3) B_3))) ((and ((member99268621le_a_o C_3) A_3)) (((member99268621le_a_o C_3) B_3)->False)))) of role axiom named fact_950_Diff__iff
% A new axiom: (forall (C_3:(hoare_2091234717iple_a->Prop)) (A_3:((hoare_2091234717iple_a->Prop)->Prop)) (B_3:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o C_3) ((minus_1746272704_a_o_o A_3) B_3))) ((and ((member99268621le_a_o C_3) A_3)) (((member99268621le_a_o C_3) B_3)->False))))
% FOF formula (forall (C_3:nat) (A_3:(nat->Prop)) (B_3:(nat->Prop)), ((iff ((member_nat C_3) ((minus_minus_nat_o A_3) B_3))) ((and ((member_nat C_3) A_3)) (((member_nat C_3) B_3)->False)))) of role axiom named fact_951_Diff__iff
% A new axiom: (forall (C_3:nat) (A_3:(nat->Prop)) (B_3:(nat->Prop)), ((iff ((member_nat C_3) ((minus_minus_nat_o A_3) B_3))) ((and ((member_nat C_3) A_3)) (((member_nat C_3) B_3)->False))))
% FOF formula (forall (C_3:hoare_2091234717iple_a) (A_3:(hoare_2091234717iple_a->Prop)) (B_3:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a C_3) ((minus_836160335le_a_o A_3) B_3))) ((and ((member290856304iple_a C_3) A_3)) (((member290856304iple_a C_3) B_3)->False)))) of role axiom named fact_952_Diff__iff
% A new axiom: (forall (C_3:hoare_2091234717iple_a) (A_3:(hoare_2091234717iple_a->Prop)) (B_3:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a C_3) ((minus_836160335le_a_o A_3) B_3))) ((and ((member290856304iple_a C_3) A_3)) (((member290856304iple_a C_3) B_3)->False))))
% FOF formula (forall (C_3:pname) (A_3:(pname->Prop)) (B_3:(pname->Prop)), ((iff ((member_pname C_3) ((minus_minus_pname_o A_3) B_3))) ((and ((member_pname C_3) A_3)) (((member_pname C_3) B_3)->False)))) of role axiom named fact_953_Diff__iff
% A new axiom: (forall (C_3:pname) (A_3:(pname->Prop)) (B_3:(pname->Prop)), ((iff ((member_pname C_3) ((minus_minus_pname_o A_3) B_3))) ((and ((member_pname C_3) A_3)) (((member_pname C_3) B_3)->False))))
% FOF formula (forall (C_2:(hoare_2091234717iple_a->Prop)) (A_2:((hoare_2091234717iple_a->Prop)->Prop)) (B_2:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o C_2) ((semila1672913213_a_o_o A_2) B_2))) ((and ((member99268621le_a_o C_2) A_2)) ((member99268621le_a_o C_2) B_2)))) of role axiom named fact_954_Int__iff
% A new axiom: (forall (C_2:(hoare_2091234717iple_a->Prop)) (A_2:((hoare_2091234717iple_a->Prop)->Prop)) (B_2:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o C_2) ((semila1672913213_a_o_o A_2) B_2))) ((and ((member99268621le_a_o C_2) A_2)) ((member99268621le_a_o C_2) B_2))))
% FOF formula (forall (C_2:nat) (A_2:(nat->Prop)) (B_2:(nat->Prop)), ((iff ((member_nat C_2) ((semila1947288293_nat_o A_2) B_2))) ((and ((member_nat C_2) A_2)) ((member_nat C_2) B_2)))) of role axiom named fact_955_Int__iff
% A new axiom: (forall (C_2:nat) (A_2:(nat->Prop)) (B_2:(nat->Prop)), ((iff ((member_nat C_2) ((semila1947288293_nat_o A_2) B_2))) ((and ((member_nat C_2) A_2)) ((member_nat C_2) B_2))))
% FOF formula (forall (C_2:hoare_2091234717iple_a) (A_2:(hoare_2091234717iple_a->Prop)) (B_2:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a C_2) ((semila2006181266le_a_o A_2) B_2))) ((and ((member290856304iple_a C_2) A_2)) ((member290856304iple_a C_2) B_2)))) of role axiom named fact_956_Int__iff
% A new axiom: (forall (C_2:hoare_2091234717iple_a) (A_2:(hoare_2091234717iple_a->Prop)) (B_2:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a C_2) ((semila2006181266le_a_o A_2) B_2))) ((and ((member290856304iple_a C_2) A_2)) ((member290856304iple_a C_2) B_2))))
% FOF formula (forall (C_2:pname) (A_2:(pname->Prop)) (B_2:(pname->Prop)), ((iff ((member_pname C_2) ((semila1673364395name_o A_2) B_2))) ((and ((member_pname C_2) A_2)) ((member_pname C_2) B_2)))) of role axiom named fact_957_Int__iff
% A new axiom: (forall (C_2:pname) (A_2:(pname->Prop)) (B_2:(pname->Prop)), ((iff ((member_pname C_2) ((semila1673364395name_o A_2) B_2))) ((and ((member_pname C_2) A_2)) ((member_pname C_2) B_2))))
% FOF formula (forall (C_1:(hoare_2091234717iple_a->Prop)) (A_1:(hoare_2091234717iple_a->Prop)) (B_1:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o C_1) ((minus_836160335le_a_o A_1) B_1))) ((minus_836160335le_a_o ((semila2006181266le_a_o C_1) A_1)) ((semila2006181266le_a_o C_1) B_1)))) of role axiom named fact_958_Diff__Int__distrib
% A new axiom: (forall (C_1:(hoare_2091234717iple_a->Prop)) (A_1:(hoare_2091234717iple_a->Prop)) (B_1:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o C_1) ((minus_836160335le_a_o A_1) B_1))) ((minus_836160335le_a_o ((semila2006181266le_a_o C_1) A_1)) ((semila2006181266le_a_o C_1) B_1))))
% FOF formula (forall (C_1:(pname->Prop)) (A_1:(pname->Prop)) (B_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o C_1) ((minus_minus_pname_o A_1) B_1))) ((minus_minus_pname_o ((semila1673364395name_o C_1) A_1)) ((semila1673364395name_o C_1) B_1)))) of role axiom named fact_959_Diff__Int__distrib
% A new axiom: (forall (C_1:(pname->Prop)) (A_1:(pname->Prop)) (B_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o C_1) ((minus_minus_pname_o A_1) B_1))) ((minus_minus_pname_o ((semila1673364395name_o C_1) A_1)) ((semila1673364395name_o C_1) B_1))))
% FOF formula (forall (C_1:(nat->Prop)) (A_1:(nat->Prop)) (B_1:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o C_1) ((minus_minus_nat_o A_1) B_1))) ((minus_minus_nat_o ((semila1947288293_nat_o C_1) A_1)) ((semila1947288293_nat_o C_1) B_1)))) of role axiom named fact_960_Diff__Int__distrib
% A new axiom: (forall (C_1:(nat->Prop)) (A_1:(nat->Prop)) (B_1:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o C_1) ((minus_minus_nat_o A_1) B_1))) ((minus_minus_nat_o ((semila1947288293_nat_o C_1) A_1)) ((semila1947288293_nat_o C_1) B_1))))
% FOF formula (forall (N_1:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N_1)) zero_zero_nat)) of role axiom named fact_961_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_962_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_963_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_964_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 (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_965_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_1:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M)) N_1)) (suc K_1))) ((minus_minus_nat ((minus_minus_nat M) N_1)) K_1))) of role axiom named fact_966_Suc__diff__diff
% A new axiom: (forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M)) N_1)) (suc K_1))) ((minus_minus_nat ((minus_minus_nat M) N_1)) K_1)))
% FOF formula (forall (I_1:nat) (J_1:nat) (K_1:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K_1)) ((minus_minus_nat ((minus_minus_nat I_1) K_1)) J_1))) of role axiom named fact_967_diff__commute
% A new axiom: (forall (I_1:nat) (J_1:nat) (K_1:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K_1)) ((minus_minus_nat ((minus_minus_nat I_1) K_1)) J_1)))
% FOF formula (forall (I_1:nat) (P:(nat->Prop)) (K_1:nat), ((P K_1)->((forall (N:nat), ((P (suc N))->(P N)))->(P ((minus_minus_nat K_1) I_1))))) of role axiom named fact_968_zero__induct__lemma
% A new axiom: (forall (I_1:nat) (P:(nat->Prop)) (K_1:nat), ((P K_1)->((forall (N:nat), ((P (suc N))->(P N)))->(P ((minus_minus_nat K_1) I_1)))))
% 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:nat)=> K)) ((minus_minus_nat M) N_1)))) of role axiom named fact_969_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:nat)=> K)) ((minus_minus_nat M) N_1))))
% FOF formula (((eq nat) one_one_nat) (suc zero_zero_nat)) of role axiom named fact_970_One__nat__def
% A new axiom: (((eq nat) one_one_nat) (suc zero_zero_nat))
% FOF formula (forall (N_1:nat), (((eq nat) ((minus_minus_nat (suc N_1)) one_one_nat)) N_1)) of role axiom named fact_971_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_972_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 (forall (N_1:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N_1)) N_1)) of role axiom named fact_973_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_974_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_975_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_976_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 (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_977_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), (((eq nat) ((plus_plus_nat (suc M)) N_1)) (suc ((plus_plus_nat M) N_1)))) of role axiom named fact_978_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 (suc M)) N_1)) ((plus_plus_nat M) (suc N_1)))) of role axiom named fact_979_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 M) N_1)) ((plus_plus_nat N_1) M))) of role axiom named fact_980_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_981_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_1:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N_1)) K_1)) ((plus_plus_nat M) ((plus_plus_nat N_1) K_1)))) of role axiom named fact_982_nat__add__assoc
% A new axiom: (forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N_1)) K_1)) ((plus_plus_nat M) ((plus_plus_nat N_1) K_1))))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) (((eq nat) M) N_1))) of role axiom named fact_983_nat__add__left__cancel
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) (((eq nat) M) N_1)))
% FOF formula (forall (M:nat) (K_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) K_1)) ((plus_plus_nat N_1) K_1))) (((eq nat) M) N_1))) of role axiom named fact_984_nat__add__right__cancel
% A new axiom: (forall (M:nat) (K_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) K_1)) ((plus_plus_nat N_1) K_1))) (((eq nat) M) N_1)))
% 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_985_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 ((plus_plus_nat N_1) M)) N_1)) M)) of role axiom named fact_986_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 (I_1:nat) (J_1:nat) (K_1:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K_1)) ((minus_minus_nat I_1) ((plus_plus_nat J_1) K_1)))) of role axiom named fact_987_diff__diff__left
% A new axiom: (forall (I_1:nat) (J_1:nat) (K_1:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K_1)) ((minus_minus_nat I_1) ((plus_plus_nat J_1) K_1))))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) ((minus_minus_nat M) N_1))) of role axiom named fact_988_diff__cancel
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) ((minus_minus_nat M) N_1)))
% FOF formula (forall (M:nat) (K_1:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K_1)) ((plus_plus_nat N_1) K_1))) ((minus_minus_nat M) N_1))) of role axiom named fact_989_diff__cancel2
% A new axiom: (forall (M:nat) (K_1:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K_1)) ((plus_plus_nat N_1) K_1))) ((minus_minus_nat M) N_1)))
% 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_990_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 (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_991_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 (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_992_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 (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat N_1) one_one_nat))) of role axiom named fact_993_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_994_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 (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_995_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_1:com) (Com2_1:com), (((eq nat) (com_size ((semi Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (com_size Com1_1)) (com_size Com2_1))) (suc zero_zero_nat)))) of role axiom named fact_996_com_Osize_I4_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com), (((eq nat) (com_size ((semi Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (com_size Com1_1)) (com_size Com2_1))) (suc zero_zero_nat))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_1:com), (((eq nat) (com_size ((while Fun_1) Com_1))) ((plus_plus_nat (com_size Com_1)) (suc zero_zero_nat)))) of role axiom named fact_997_com_Osize_I6_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_1:com), (((eq nat) (com_size ((while Fun_1) Com_1))) ((plus_plus_nat (com_size Com_1)) (suc zero_zero_nat))))
% FOF formula (forall (Pname_1:pname), (((eq nat) (com_size (body Pname_1))) zero_zero_nat)) of role axiom named fact_998_com_Osize_I7_J
% A new axiom: (forall (Pname_1:pname), (((eq nat) (com_size (body Pname_1))) zero_zero_nat))
% FOF formula (((eq nat) (com_size skip)) zero_zero_nat) of role axiom named fact_999_com_Osize_I1_J
% A new axiom: (((eq nat) (com_size skip)) zero_zero_nat)
% FOF formula (forall (Com1_1:com) (Com2_1:com), (((eq nat) (size_size_com ((semi Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1_1)) (size_size_com Com2_1))) (suc zero_zero_nat)))) of role axiom named fact_1000_com_Osize_I12_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com), (((eq nat) (size_size_com ((semi Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1_1)) (size_size_com Com2_1))) (suc zero_zero_nat))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com_1:com), (((eq nat) (size_size_com ((while Fun_1) Com_1))) ((plus_plus_nat (size_size_com Com_1)) (suc zero_zero_nat)))) of role axiom named fact_1001_com_Osize_I14_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com_1:com), (((eq nat) (size_size_com ((while Fun_1) Com_1))) ((plus_plus_nat (size_size_com Com_1)) (suc zero_zero_nat))))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), (((eq nat) ((times_times_nat K_1) ((plus_plus_nat M) N_1))) ((plus_plus_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1)))) of role axiom named fact_1002_add__mult__distrib2
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), (((eq nat) ((times_times_nat K_1) ((plus_plus_nat M) N_1))) ((plus_plus_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))))
% FOF formula (forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N_1)) K_1)) ((plus_plus_nat ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1)))) of role axiom named fact_1003_add__mult__distrib
% A new axiom: (forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N_1)) K_1)) ((plus_plus_nat ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) N_1)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N_1) one_one_nat)))) of role axiom named fact_1004_nat__mult__eq__1__iff
% A new axiom: (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) N_1)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N_1) one_one_nat))))
% FOF formula (forall (N_1:nat), (((eq nat) ((times_times_nat N_1) one_one_nat)) N_1)) of role axiom named fact_1005_nat__mult__1__right
% A new axiom: (forall (N_1:nat), (((eq nat) ((times_times_nat N_1) one_one_nat)) N_1))
% FOF formula (forall (M:nat) (N_1:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M) N_1))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N_1) one_one_nat)))) of role axiom named fact_1006_nat__1__eq__mult__iff
% A new axiom: (forall (M:nat) (N_1:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M) N_1))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N_1) one_one_nat))))
% FOF formula (forall (N_1:nat), (((eq nat) ((times_times_nat one_one_nat) N_1)) N_1)) of role axiom named fact_1007_nat__mult__1
% A new axiom: (forall (N_1:nat), (((eq nat) ((times_times_nat one_one_nat) N_1)) N_1))
% FOF formula (forall (N_1:nat), (((eq nat) ((times_times_nat zero_zero_nat) N_1)) zero_zero_nat)) of role axiom named fact_1008_mult__0
% A new axiom: (forall (N_1:nat), (((eq nat) ((times_times_nat zero_zero_nat) N_1)) zero_zero_nat))
% FOF formula (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_1009_mult__0__right
% A new axiom: (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat))
% FOF formula (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) N_1)) zero_zero_nat)) ((or (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat)))) of role axiom named fact_1010_mult__is__0
% A new axiom: (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) N_1)) zero_zero_nat)) ((or (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat))))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((or (((eq nat) M) N_1)) (((eq nat) K_1) zero_zero_nat)))) of role axiom named fact_1011_mult__cancel1
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((or (((eq nat) M) N_1)) (((eq nat) K_1) zero_zero_nat))))
% FOF formula (forall (M:nat) (K_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1))) ((or (((eq nat) M) N_1)) (((eq nat) K_1) zero_zero_nat)))) of role axiom named fact_1012_mult__cancel2
% A new axiom: (forall (M:nat) (K_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1))) ((or (((eq nat) M) N_1)) (((eq nat) K_1) zero_zero_nat))))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat (suc K_1)) M)) ((times_times_nat (suc K_1)) N_1))) (((eq nat) M) N_1))) of role axiom named fact_1013_Suc__mult__cancel1
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat (suc K_1)) M)) ((times_times_nat (suc K_1)) N_1))) (((eq nat) M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((times_times_nat ((minus_minus_nat M) N_1)) K_1)) ((minus_minus_nat ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1)))) of role axiom named fact_1014_diff__mult__distrib
% A new axiom: (forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((times_times_nat ((minus_minus_nat M) N_1)) K_1)) ((minus_minus_nat ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1))))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), (((eq nat) ((times_times_nat K_1) ((minus_minus_nat M) N_1))) ((minus_minus_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1)))) of role axiom named fact_1015_diff__mult__distrib2
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), (((eq nat) ((times_times_nat K_1) ((minus_minus_nat M) N_1))) ((minus_minus_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) N_1)) (suc zero_zero_nat))) ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N_1) (suc zero_zero_nat))))) of role axiom named fact_1016_mult__eq__1__iff
% A new axiom: (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) N_1)) (suc zero_zero_nat))) ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N_1) (suc zero_zero_nat)))))
% FOF formula (forall (M:nat) (N_1:nat), (((eq nat) ((times_times_nat (suc M)) N_1)) ((plus_plus_nat N_1) ((times_times_nat M) N_1)))) of role axiom named fact_1017_mult__Suc
% A new axiom: (forall (M:nat) (N_1:nat), (((eq nat) ((times_times_nat (suc M)) N_1)) ((plus_plus_nat N_1) ((times_times_nat M) N_1))))
% FOF formula (forall (M:nat) (N_1:nat), (((eq nat) ((times_times_nat M) (suc N_1))) ((plus_plus_nat M) ((times_times_nat M) N_1)))) of role axiom named fact_1018_mult__Suc__right
% A new axiom: (forall (M:nat) (N_1:nat), (((eq nat) ((times_times_nat M) (suc N_1))) ((plus_plus_nat M) ((times_times_nat M) N_1))))
% FOF formula (forall (M:nat) (N_1:nat), ((((eq nat) M) ((times_times_nat M) N_1))->((or (((eq nat) N_1) one_one_nat)) (((eq nat) M) zero_zero_nat)))) of role axiom named fact_1019_mult__eq__self__implies__10
% A new axiom: (forall (M:nat) (N_1:nat), ((((eq nat) M) ((times_times_nat M) N_1))->((or (((eq nat) N_1) one_one_nat)) (((eq nat) M) zero_zero_nat))))
% FOF formula (forall (Pname_1:pname), (((eq nat) (size_size_com (body Pname_1))) zero_zero_nat)) of role axiom named fact_1020_com_Osize_I15_J
% A new axiom: (forall (Pname_1:pname), (((eq nat) (size_size_com (body Pname_1))) zero_zero_nat))
% FOF formula (((eq nat) (size_size_com skip)) zero_zero_nat) of role axiom named fact_1021_com_Osize_I9_J
% A new axiom: (((eq nat) (size_size_com skip)) zero_zero_nat)
% FOF formula (forall (N_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((times_times_nat M) N_1)) zero_zero_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((times_times_nat M) N_1)) ((plus_plus_nat N_1) ((times_times_nat ((minus_minus_nat M) one_one_nat)) N_1)))))) of role axiom named fact_1022_mult__eq__if
% A new axiom: (forall (N_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((times_times_nat M) N_1)) zero_zero_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((times_times_nat M) N_1)) ((plus_plus_nat N_1) ((times_times_nat ((minus_minus_nat M) one_one_nat)) N_1))))))
% FOF formula (forall (M:nat) (N_1:nat), (((eq nat) ((times_times_nat M) N_1)) ((times_times_nat N_1) M))) of role axiom named fact_1023_nat__mult__commute
% A new axiom: (forall (M:nat) (N_1:nat), (((eq nat) ((times_times_nat M) N_1)) ((times_times_nat N_1) M)))
% FOF formula (forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((times_times_nat ((times_times_nat M) N_1)) K_1)) ((times_times_nat M) ((times_times_nat N_1) K_1)))) of role axiom named fact_1024_nat__mult__assoc
% A new axiom: (forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((times_times_nat ((times_times_nat M) N_1)) K_1)) ((times_times_nat M) ((times_times_nat N_1) K_1))))
% FOF formula (forall (I_1:nat) (U:nat) (J_1:nat) (K_1:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J_1) U)) K_1))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J_1)) U)) K_1))) of role axiom named fact_1025_left__add__mult__distrib
% A new axiom: (forall (I_1:nat) (U:nat) (J_1:nat) (K_1:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J_1) U)) K_1))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J_1)) U)) K_1)))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((or (((eq nat) K_1) zero_zero_nat)) (((eq nat) M) N_1)))) of role axiom named fact_1026_nat__mult__eq__cancel__disj
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((or (((eq nat) K_1) zero_zero_nat)) (((eq nat) M) N_1))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (((eq nat) (size_size_com (((cond Fun_1) Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1_1)) (size_size_com Com2_1))) (suc zero_zero_nat)))) of role axiom named fact_1027_com_Osize_I13_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (((eq nat) (size_size_com (((cond Fun_1) Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1_1)) (size_size_com Com2_1))) (suc zero_zero_nat))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (((eq nat) (com_size (((cond Fun_1) Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (com_size Com1_1)) (com_size Com2_1))) (suc zero_zero_nat)))) of role axiom named fact_1028_com_Osize_I5_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (((eq nat) (com_size (((cond Fun_1) Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (com_size Com1_1)) (com_size Com2_1))) (suc zero_zero_nat))))
% FOF formula (forall (K_1:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat N) K_1))))) of role axiom named fact_1029_finite__Collect__le__nat
% A new axiom: (forall (K_1:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat N) K_1)))))
% FOF formula (forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1)) of role axiom named fact_1030_le0
% A new axiom: (forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1))
% 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_1031_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 (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_1032_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 (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_1033_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 (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_1034_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 (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_1035_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 (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_1036_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 (Pname:pname) (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (not (((eq com) (body Pname)) (((cond Fun_1) Com1_1) Com2_1)))) of role axiom named fact_1037_com_Osimps_I55_J
% A new axiom: (forall (Pname:pname) (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (not (((eq com) (body Pname)) (((cond Fun_1) Com1_1) Com2_1))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com) (Pname:pname), (not (((eq com) (((cond Fun_1) Com1_1) Com2_1)) (body Pname)))) of role axiom named fact_1038_com_Osimps_I54_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com) (Pname:pname), (not (((eq com) (((cond Fun_1) Com1_1) Com2_1)) (body Pname))))
% FOF formula (forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com1:com) (Com2:com), ((iff (((eq com) (((cond Fun_1) Com1_1) Com2_1)) (((cond Fun) Com1) Com2))) ((and ((and (((eq (state->Prop)) Fun_1) Fun)) (((eq com) Com1_1) Com1))) (((eq com) Com2_1) Com2)))) of role axiom named fact_1039_com_Osimps_I4_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com1:com) (Com2:com), ((iff (((eq com) (((cond Fun_1) Com1_1) Com2_1)) (((cond Fun) Com1) Com2))) ((and ((and (((eq (state->Prop)) Fun_1) Fun)) (((eq com) Com1_1) Com1))) (((eq com) Com2_1) Com2))))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->(((ord_less_eq_nat N_1) M)->(((eq nat) M) N_1)))) of role axiom named fact_1040_le__antisym
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->(((ord_less_eq_nat N_1) M)->(((eq nat) M) N_1))))
% FOF formula (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat J_1) K_1)->((ord_less_eq_nat I_1) K_1)))) of role axiom named fact_1041_le__trans
% A new axiom: (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat J_1) K_1)->((ord_less_eq_nat I_1) K_1))))
% FOF formula (forall (M:nat) (N_1:nat), ((((eq nat) M) N_1)->((ord_less_eq_nat M) N_1))) of role axiom named fact_1042_eq__imp__le
% A new axiom: (forall (M:nat) (N_1:nat), ((((eq nat) M) N_1)->((ord_less_eq_nat M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), ((or ((ord_less_eq_nat M) N_1)) ((ord_less_eq_nat N_1) M))) of role axiom named fact_1043_nat__le__linear
% A new axiom: (forall (M:nat) (N_1:nat), ((or ((ord_less_eq_nat M) N_1)) ((ord_less_eq_nat N_1) M)))
% FOF formula (forall (N_1:nat), ((ord_less_eq_nat N_1) N_1)) of role axiom named fact_1044_le__refl
% A new axiom: (forall (N_1:nat), ((ord_less_eq_nat N_1) N_1))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_eq_nat (suc M)) N_1)->((ord_less_eq_nat M) N_1))) of role axiom named fact_1045_Suc__leD
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_eq_nat (suc M)) N_1)->((ord_less_eq_nat M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) (suc N_1))->((((ord_less_eq_nat M) N_1)->False)->(((eq nat) M) (suc N_1))))) of role axiom named fact_1046_le__SucE
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) (suc N_1))->((((ord_less_eq_nat M) N_1)->False)->(((eq nat) M) (suc N_1)))))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_eq_nat M) (suc N_1)))) of role axiom named fact_1047_le__SucI
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_eq_nat M) (suc N_1))))
% FOF formula (forall (N_1:nat) (M:nat), ((iff ((ord_less_eq_nat (suc N_1)) (suc M))) ((ord_less_eq_nat N_1) M))) of role axiom named fact_1048_Suc__le__mono
% A new axiom: (forall (N_1:nat) (M:nat), ((iff ((ord_less_eq_nat (suc N_1)) (suc M))) ((ord_less_eq_nat N_1) M)))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat M) (suc N_1))) ((or ((ord_less_eq_nat M) N_1)) (((eq nat) M) (suc N_1))))) of role axiom named fact_1049_le__Suc__eq
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat M) (suc N_1))) ((or ((ord_less_eq_nat M) N_1)) (((eq nat) M) (suc N_1)))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff (((ord_less_eq_nat M) N_1)->False)) ((ord_less_eq_nat (suc N_1)) M))) of role axiom named fact_1050_not__less__eq__eq
% A new axiom: (forall (M:nat) (N_1:nat), ((iff (((ord_less_eq_nat M) N_1)->False)) ((ord_less_eq_nat (suc N_1)) M)))
% FOF formula (forall (N_1:nat), (((ord_less_eq_nat (suc N_1)) N_1)->False)) of role axiom named fact_1051_Suc__n__not__le__n
% A new axiom: (forall (N_1:nat), (((ord_less_eq_nat (suc N_1)) N_1)->False))
% FOF formula (forall (N_1:nat), ((iff ((ord_less_eq_nat N_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat))) of role axiom named fact_1052_le__0__eq
% A new axiom: (forall (N_1:nat), ((iff ((ord_less_eq_nat N_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat)))
% FOF formula (forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1)) of role axiom named fact_1053_less__eq__nat_Osimps_I1_J
% A new axiom: (forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1))
% FOF formula (forall (M:nat) (C:com) (S:state) (N_1:nat) (T:state), (((((evaln C) S) N_1) T)->(((ord_less_eq_nat N_1) M)->((((evaln C) S) M) T)))) of role axiom named fact_1054_evaln__nonstrict
% A new axiom: (forall (M:nat) (C:com) (S:state) (N_1:nat) (T:state), (((((evaln C) S) N_1) T)->(((ord_less_eq_nat N_1) M)->((((evaln C) S) M) T))))
% FOF formula (forall (M:nat) (N_1:nat), ((ord_less_eq_nat ((minus_minus_nat M) N_1)) M)) of role axiom named fact_1055_diff__le__self
% A new axiom: (forall (M:nat) (N_1:nat), ((ord_less_eq_nat ((minus_minus_nat M) N_1)) M))
% FOF formula (forall (L:nat) (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_eq_nat ((minus_minus_nat L) N_1)) ((minus_minus_nat L) M)))) of role axiom named fact_1056_diff__le__mono2
% A new axiom: (forall (L:nat) (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_eq_nat ((minus_minus_nat L) N_1)) ((minus_minus_nat L) M))))
% FOF formula (forall (L:nat) (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_eq_nat ((minus_minus_nat M) L)) ((minus_minus_nat N_1) L)))) of role axiom named fact_1057_diff__le__mono
% A new axiom: (forall (L:nat) (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_eq_nat ((minus_minus_nat M) L)) ((minus_minus_nat N_1) L))))
% FOF formula (forall (I_1:nat) (N_1:nat), (((ord_less_eq_nat I_1) N_1)->(((eq nat) ((minus_minus_nat N_1) ((minus_minus_nat N_1) I_1))) I_1))) of role axiom named fact_1058_diff__diff__cancel
% A new axiom: (forall (I_1:nat) (N_1:nat), (((ord_less_eq_nat I_1) N_1)->(((eq nat) ((minus_minus_nat N_1) ((minus_minus_nat N_1) I_1))) I_1)))
% FOF formula (forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->((iff (((eq nat) ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) (((eq nat) M) N_1))))) of role axiom named fact_1059_eq__diff__iff
% A new axiom: (forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->((iff (((eq nat) ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) (((eq nat) M) N_1)))))
% FOF formula (forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) ((minus_minus_nat M) N_1))))) of role axiom named fact_1060_Nat_Odiff__diff__eq
% A new axiom: (forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) ((minus_minus_nat M) N_1)))))
% FOF formula (forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->((iff ((ord_less_eq_nat ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) ((ord_less_eq_nat M) N_1))))) of role axiom named fact_1061_le__diff__iff
% A new axiom: (forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->((iff ((ord_less_eq_nat ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) ((ord_less_eq_nat M) N_1)))))
% FOF formula (forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M) K_1)) N_1)->((((ord_less_eq_nat M) N_1)->(((ord_less_eq_nat K_1) N_1)->False))->False))) of role axiom named fact_1062_add__leE
% A new axiom: (forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M) K_1)) N_1)->((((ord_less_eq_nat M) N_1)->(((ord_less_eq_nat K_1) N_1)->False))->False)))
% FOF formula (forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M) K_1)) N_1)->((ord_less_eq_nat M) N_1))) of role axiom named fact_1063_add__leD1
% A new axiom: (forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M) K_1)) N_1)->((ord_less_eq_nat M) N_1)))
% FOF formula (forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M) K_1)) N_1)->((ord_less_eq_nat K_1) N_1))) of role axiom named fact_1064_add__leD2
% A new axiom: (forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M) K_1)) N_1)->((ord_less_eq_nat K_1) N_1)))
% FOF formula (forall (K_1:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K_1) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) L))))) of role axiom named fact_1065_add__le__mono
% A new axiom: (forall (K_1:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K_1) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) L)))))
% FOF formula (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) K_1)))) of role axiom named fact_1066_add__le__mono1
% A new axiom: (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) K_1))))
% FOF formula (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J_1)))) of role axiom named fact_1067_trans__le__add2
% A new axiom: (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J_1))))
% FOF formula (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat J_1) M)))) of role axiom named fact_1068_trans__le__add1
% A new axiom: (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat J_1) M))))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) ((ord_less_eq_nat M) N_1))) of role axiom named fact_1069_nat__add__left__cancel__le
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) ((ord_less_eq_nat M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat M) N_1)) ((ex nat) (fun (K:nat)=> (((eq nat) N_1) ((plus_plus_nat M) K)))))) of role axiom named fact_1070_le__iff__add
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat M) N_1)) ((ex nat) (fun (K:nat)=> (((eq nat) N_1) ((plus_plus_nat M) K))))))
% FOF formula (forall (N_1:nat) (M:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat N_1) M))) of role axiom named fact_1071_le__add1
% A new axiom: (forall (N_1:nat) (M:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat N_1) M)))
% FOF formula (forall (N_1:nat) (M:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat M) N_1))) of role axiom named fact_1072_le__add2
% A new axiom: (forall (N_1:nat) (M:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat M) N_1)))
% FOF formula (forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_eq_nat _TPTP_I) N_1))))) (suc N_1))) of role axiom named fact_1073_card__Collect__le__nat
% A new axiom: (forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_eq_nat _TPTP_I) N_1))))) (suc N_1)))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M)) N_1)) (((nat_case_o False) (ord_less_eq_nat M)) N_1))) of role axiom named fact_1074_less__eq__nat_Osimps_I2_J
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M)) N_1)) (((nat_case_o False) (ord_less_eq_nat M)) N_1)))
% FOF formula (forall (K_1:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K_1) L)->((ord_less_eq_nat ((times_times_nat I_1) K_1)) ((times_times_nat J_1) L))))) of role axiom named fact_1075_mult__le__mono
% A new axiom: (forall (K_1:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K_1) L)->((ord_less_eq_nat ((times_times_nat I_1) K_1)) ((times_times_nat J_1) L)))))
% FOF formula (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat K_1) I_1)) ((times_times_nat K_1) J_1)))) of role axiom named fact_1076_mult__le__mono2
% A new axiom: (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat K_1) I_1)) ((times_times_nat K_1) J_1))))
% FOF formula (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat I_1) K_1)) ((times_times_nat J_1) K_1)))) of role axiom named fact_1077_mult__le__mono1
% A new axiom: (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat I_1) K_1)) ((times_times_nat J_1) K_1))))
% FOF formula (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M)))) of role axiom named fact_1078_le__cube
% A new axiom: (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M))))
% FOF formula (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M))) of role axiom named fact_1079_le__square
% A new axiom: (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M)))
% FOF formula (forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com:com), (not (((eq com) (((cond Fun_1) Com1_1) Com2_1)) ((while Fun) Com)))) of role axiom named fact_1080_com_Osimps_I52_J
% A new axiom: (forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com:com), (not (((eq com) (((cond Fun_1) Com1_1) Com2_1)) ((while Fun) Com))))
% FOF formula (forall (Fun:(state->Prop)) (Com:com) (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (not (((eq com) ((while Fun) Com)) (((cond Fun_1) Com1_1) Com2_1)))) of role axiom named fact_1081_com_Osimps_I53_J
% A new axiom: (forall (Fun:(state->Prop)) (Com:com) (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (not (((eq com) ((while Fun) Com)) (((cond Fun_1) Com1_1) Com2_1))))
% FOF formula (forall (Fun:(state->Prop)) (Com1:com) (Com2:com) (Com1_1:com) (Com2_1:com), (not (((eq com) (((cond Fun) Com1) Com2)) ((semi Com1_1) Com2_1)))) of role axiom named fact_1082_com_Osimps_I45_J
% A new axiom: (forall (Fun:(state->Prop)) (Com1:com) (Com2:com) (Com1_1:com) (Com2_1:com), (not (((eq com) (((cond Fun) Com1) Com2)) ((semi Com1_1) Com2_1))))
% FOF formula (forall (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com1:com) (Com2:com), (not (((eq com) ((semi Com1_1) Com2_1)) (((cond Fun) Com1) Com2)))) of role axiom named fact_1083_com_Osimps_I44_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com1:com) (Com2:com), (not (((eq com) ((semi Com1_1) Com2_1)) (((cond Fun) Com1) Com2))))
% FOF formula (forall (Fun:(state->Prop)) (Com1:com) (Com2:com), (not (((eq com) (((cond Fun) Com1) Com2)) skip))) of role axiom named fact_1084_com_Osimps_I15_J
% A new axiom: (forall (Fun:(state->Prop)) (Com1:com) (Com2:com), (not (((eq com) (((cond Fun) Com1) Com2)) skip)))
% FOF formula (forall (Fun:(state->Prop)) (Com1:com) (Com2:com), (not (((eq com) skip) (((cond Fun) Com1) Com2)))) of role axiom named fact_1085_com_Osimps_I14_J
% A new axiom: (forall (Fun:(state->Prop)) (Com1:com) (Com2:com), (not (((eq com) skip) (((cond Fun) Com1) Com2))))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->(((eq nat) ((minus_minus_nat M) N_1)) zero_zero_nat))) of role axiom named fact_1086_diff__is__0__eq_H
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->(((eq nat) ((minus_minus_nat M) N_1)) zero_zero_nat)))
% FOF formula (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((minus_minus_nat M) N_1)) zero_zero_nat)) ((ord_less_eq_nat M) N_1))) of role axiom named fact_1087_diff__is__0__eq
% A new axiom: (forall (M:nat) (N_1:nat), ((iff (((eq nat) ((minus_minus_nat M) N_1)) zero_zero_nat)) ((ord_less_eq_nat M) N_1)))
% FOF formula (forall (N_1:nat) (M:nat), (((ord_less_eq_nat N_1) M)->(((eq nat) ((minus_minus_nat (suc M)) N_1)) (suc ((minus_minus_nat M) N_1))))) of role axiom named fact_1088_Suc__diff__le
% A new axiom: (forall (N_1:nat) (M:nat), (((ord_less_eq_nat N_1) M)->(((eq nat) ((minus_minus_nat (suc M)) N_1)) (suc ((minus_minus_nat M) N_1)))))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat (suc K_1)) M)) ((times_times_nat (suc K_1)) N_1))) ((ord_less_eq_nat M) N_1))) of role axiom named fact_1089_Suc__mult__le__cancel1
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat (suc K_1)) M)) ((times_times_nat (suc K_1)) N_1))) ((ord_less_eq_nat M) N_1)))
% FOF formula (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J_1) K_1))) ((minus_minus_nat ((plus_plus_nat I_1) K_1)) J_1)))) of role axiom named fact_1090_diff__diff__right
% A new axiom: (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J_1) K_1))) ((minus_minus_nat ((plus_plus_nat I_1) K_1)) J_1))))
% FOF formula (forall (J_1:nat) (K_1:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J_1) K_1)) I_1)) ((ord_less_eq_nat J_1) ((plus_plus_nat I_1) K_1)))) of role axiom named fact_1091_le__diff__conv
% A new axiom: (forall (J_1:nat) (K_1:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J_1) K_1)) I_1)) ((ord_less_eq_nat J_1) ((plus_plus_nat I_1) K_1))))
% FOF formula (forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat K_1) N_1)->((ord_less_eq_nat M) ((minus_minus_nat ((plus_plus_nat N_1) M)) K_1)))) of role axiom named fact_1092_le__add__diff
% A new axiom: (forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat K_1) N_1)->((ord_less_eq_nat M) ((minus_minus_nat ((plus_plus_nat N_1) M)) K_1))))
% FOF formula (forall (N_1:nat) (M:nat), (((ord_less_eq_nat N_1) M)->(((eq nat) ((plus_plus_nat N_1) ((minus_minus_nat M) N_1))) M))) of role axiom named fact_1093_le__add__diff__inverse
% A new axiom: (forall (N_1:nat) (M:nat), (((ord_less_eq_nat N_1) M)->(((eq nat) ((plus_plus_nat N_1) ((minus_minus_nat M) N_1))) M)))
% FOF formula (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K_1))) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K_1)))) of role axiom named fact_1094_add__diff__assoc
% A new axiom: (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K_1))) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K_1))))
% FOF formula (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J_1) K_1))) ((ord_less_eq_nat ((plus_plus_nat I_1) K_1)) J_1)))) of role axiom named fact_1095_le__diff__conv2
% A new axiom: (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J_1) K_1))) ((ord_less_eq_nat ((plus_plus_nat I_1) K_1)) J_1))))
% FOF formula (forall (N_1:nat) (M:nat), (((ord_less_eq_nat N_1) M)->(((eq nat) ((plus_plus_nat ((minus_minus_nat M) N_1)) N_1)) M))) of role axiom named fact_1096_le__add__diff__inverse2
% A new axiom: (forall (N_1:nat) (M:nat), (((ord_less_eq_nat N_1) M)->(((eq nat) ((plus_plus_nat ((minus_minus_nat M) N_1)) N_1)) M)))
% FOF formula (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((minus_minus_nat J_1) I_1)) K_1)) (((eq nat) J_1) ((plus_plus_nat K_1) I_1))))) of role axiom named fact_1097_le__imp__diff__is__add
% A new axiom: (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((minus_minus_nat J_1) I_1)) K_1)) (((eq nat) J_1) ((plus_plus_nat K_1) I_1)))))
% FOF formula (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K_1)) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K_1))))) of role axiom named fact_1098_diff__add__assoc
% A new axiom: (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K_1)) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K_1)))))
% FOF formula (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J_1) K_1)) I_1)) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K_1)))) of role axiom named fact_1099_add__diff__assoc2
% A new axiom: (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J_1) K_1)) I_1)) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K_1))))
% FOF formula (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K_1)) ((plus_plus_nat ((minus_minus_nat J_1) K_1)) I_1)))) of role axiom named fact_1100_diff__add__assoc2
% A new axiom: (forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K_1)) ((plus_plus_nat ((minus_minus_nat J_1) K_1)) I_1))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc zero_zero_nat)) ((times_times_nat M) N_1))) ((and ((ord_less_eq_nat (suc zero_zero_nat)) M)) ((ord_less_eq_nat (suc zero_zero_nat)) N_1)))) of role axiom named fact_1101_one__le__mult__iff
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc zero_zero_nat)) ((times_times_nat M) N_1))) ((and ((ord_less_eq_nat (suc zero_zero_nat)) M)) ((ord_less_eq_nat (suc zero_zero_nat)) N_1))))
% FOF formula (forall (M:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat (suc ((minus_minus_nat J_1) K_1))) M)) ((minus_minus_nat (suc J_1)) ((plus_plus_nat K_1) M))))) of role axiom named fact_1102_diff__Suc__diff__eq2
% A new axiom: (forall (M:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat (suc ((minus_minus_nat J_1) K_1))) M)) ((minus_minus_nat (suc J_1)) ((plus_plus_nat K_1) M)))))
% FOF formula (forall (M:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat M) (suc ((minus_minus_nat J_1) K_1)))) ((minus_minus_nat ((plus_plus_nat M) K_1)) (suc J_1))))) of role axiom named fact_1103_diff__Suc__diff__eq1
% A new axiom: (forall (M:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat M) (suc ((minus_minus_nat J_1) K_1)))) ((minus_minus_nat ((plus_plus_nat M) K_1)) (suc J_1)))))
% FOF formula (forall (U:nat) (M:nat) (N_1:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N_1)))) of role axiom named fact_1104_nat__le__add__iff1
% A new axiom: (forall (U:nat) (M:nat) (N_1:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N_1))))
% FOF formula (forall (U:nat) (M:nat) (N_1:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N_1)))) of role axiom named fact_1105_nat__diff__add__eq1
% A new axiom: (forall (U:nat) (M:nat) (N_1:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N_1))))
% FOF formula (forall (U:nat) (M:nat) (N_1:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N_1)))) of role axiom named fact_1106_nat__eq__add__iff1
% A new axiom: (forall (U:nat) (M:nat) (N_1:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N_1))))
% FOF formula (forall (U:nat) (M:nat) (N_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N_1))))) of role axiom named fact_1107_nat__le__add__iff2
% A new axiom: (forall (U:nat) (M:nat) (N_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N_1)))))
% FOF formula (forall (U:nat) (M:nat) (N_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N_1))))) of role axiom named fact_1108_nat__diff__add__eq2
% A new axiom: (forall (U:nat) (M:nat) (N_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N_1)))))
% FOF formula (forall (U:nat) (M:nat) (N_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N_1))))) of role axiom named fact_1109_nat__eq__add__iff2
% A new axiom: (forall (U:nat) (M:nat) (N_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N_1)))))
% FOF formula (forall (N_1:nat) (M_2:nat), (((ord_less_eq_nat (suc N_1)) M_2)->((ex nat) (fun (M_1:nat)=> (((eq nat) M_2) (suc M_1)))))) of role axiom named fact_1110_Suc__le__D
% A new axiom: (forall (N_1:nat) (M_2:nat), (((ord_less_eq_nat (suc N_1)) M_2)->((ex nat) (fun (M_1:nat)=> (((eq nat) M_2) (suc M_1))))))
% FOF formula (forall (P:(nat->Prop)) (N_1:nat) (M_2:nat), (((ord_less_eq_nat (suc N_1)) M_2)->((forall (M_1:nat), (((ord_less_eq_nat N_1) M_1)->(P (suc M_1))))->(P M_2)))) of role axiom named fact_1111_Suc__le__D__lemma
% A new axiom: (forall (P:(nat->Prop)) (N_1:nat) (M_2:nat), (((ord_less_eq_nat (suc N_1)) M_2)->((forall (M_1:nat), (((ord_less_eq_nat N_1) M_1)->(P (suc M_1))))->(P M_2))))
% FOF formula (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X:nat), (((member_nat X) N_2)->((ord_less_eq_nat X) M_1))))))) of role axiom named fact_1112_finite__nat__set__iff__bounded__le
% A new axiom: (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X:nat), (((member_nat X) N_2)->((ord_less_eq_nat X) M_1)))))))
% FOF formula (forall (U:nat) (F:(nat->nat)), ((forall (N:nat), ((ord_less_eq_nat N) (F N)))->(finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat (F N)) U)))))) of role axiom named fact_1113_finite__less__ub
% A new axiom: (forall (U:nat) (F:(nat->nat)), ((forall (N:nat), ((ord_less_eq_nat N) (F N)))->(finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat (F N)) U))))))
% FOF formula (forall (Z:nat) (X_1:nat) (Y:nat), (((ord_less_eq_nat X_1) Y)->((ord_less_eq_nat X_1) ((plus_plus_nat Y) Z)))) of role axiom named fact_1114_termination__basic__simps_I3_J
% A new axiom: (forall (Z:nat) (X_1:nat) (Y:nat), (((ord_less_eq_nat X_1) Y)->((ord_less_eq_nat X_1) ((plus_plus_nat Y) Z))))
% FOF formula (forall (Y:nat) (X_1:nat) (Z:nat), (((ord_less_eq_nat X_1) Z)->((ord_less_eq_nat X_1) ((plus_plus_nat Y) Z)))) of role axiom named fact_1115_termination__basic__simps_I4_J
% A new axiom: (forall (Y:nat) (X_1:nat) (Z:nat), (((ord_less_eq_nat X_1) Z)->((ord_less_eq_nat X_1) ((plus_plus_nat Y) Z))))
% FOF formula (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)) of role axiom named fact_1116_less__zeroE
% A new axiom: (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False))
% FOF formula (forall (N_1:nat), ((ord_less_nat N_1) (suc N_1))) of role axiom named fact_1117_lessI
% A new axiom: (forall (N_1:nat), ((ord_less_nat N_1) (suc N_1)))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_nat (suc M)) (suc N_1)))) of role axiom named fact_1118_Suc__mono
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_nat (suc M)) (suc N_1))))
% FOF formula (forall (K_1:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_nat N) K_1))))) of role axiom named fact_1119_finite__Collect__less__nat
% A new axiom: (forall (K_1:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_nat N) K_1)))))
% FOF formula (forall (N_1:nat), ((ord_less_nat zero_zero_nat) (suc N_1))) of role axiom named fact_1120_zero__less__Suc
% A new axiom: (forall (N_1:nat), ((ord_less_nat zero_zero_nat) (suc N_1)))
% FOF formula (forall (P:(nat->Prop)) (I_1:nat), (finite_finite_nat (collect_nat (fun (K:nat)=> ((and (P K)) ((ord_less_nat K) I_1)))))) of role axiom named fact_1121_finite__M__bounded__by__nat
% A new axiom: (forall (P:(nat->Prop)) (I_1:nat), (finite_finite_nat (collect_nat (fun (K:nat)=> ((and (P K)) ((ord_less_nat K) I_1))))))
% FOF formula (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X:nat), (((member_nat X) N_2)->((ord_less_nat X) M_1))))))) of role axiom named fact_1122_finite__nat__set__iff__bounded
% A new axiom: (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X:nat), (((member_nat X) N_2)->((ord_less_nat X) M_1)))))))
% FOF formula (forall (M:nat) (N_1:nat), (((or ((ord_less_nat M) N_1)) (((eq nat) M) N_1))->((ord_less_eq_nat M) N_1))) of role axiom named fact_1123_less__or__eq__imp__le
% A new axiom: (forall (M:nat) (N_1:nat), (((or ((ord_less_nat M) N_1)) (((eq nat) M) N_1))->((ord_less_eq_nat M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((not (((eq nat) M) N_1))->((ord_less_nat M) N_1)))) of role axiom named fact_1124_le__neq__implies__less
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((not (((eq nat) M) N_1))->((ord_less_nat M) N_1))))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_eq_nat M) N_1))) of role axiom named fact_1125_less__imp__le__nat
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_eq_nat M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat M) N_1)) ((or ((ord_less_nat M) N_1)) (((eq nat) M) N_1)))) of role axiom named fact_1126_le__eq__less__or__eq
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat M) N_1)) ((or ((ord_less_nat M) N_1)) (((eq nat) M) N_1))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) N_1)) ((and ((ord_less_eq_nat M) N_1)) (not (((eq nat) M) N_1))))) of role axiom named fact_1127_nat__less__le
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) N_1)) ((and ((ord_less_eq_nat M) N_1)) (not (((eq nat) M) N_1)))))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_eq_nat (suc M)) N_1)->((ord_less_nat M) N_1))) of role axiom named fact_1128_Suc__le__lessD
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_eq_nat (suc M)) N_1)->((ord_less_nat M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((iff ((ord_less_nat N_1) (suc M))) (((eq nat) N_1) M)))) of role axiom named fact_1129_le__less__Suc__eq
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((iff ((ord_less_nat N_1) (suc M))) (((eq nat) N_1) M))))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_eq_nat (suc M)) N_1))) of role axiom named fact_1130_Suc__leI
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_eq_nat (suc M)) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_nat M) (suc N_1)))) of role axiom named fact_1131_le__imp__less__Suc
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_nat M) (suc N_1))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M)) N_1)) ((ord_less_nat M) N_1))) of role axiom named fact_1132_Suc__le__eq
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M)) N_1)) ((ord_less_nat M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) (suc N_1))) ((ord_less_eq_nat M) N_1))) of role axiom named fact_1133_less__Suc__eq__le
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) (suc N_1))) ((ord_less_eq_nat M) N_1)))
% FOF formula (forall (N_1:nat) (M:nat), ((iff ((ord_less_nat N_1) M)) ((ord_less_eq_nat (suc N_1)) M))) of role axiom named fact_1134_less__eq__Suc__le
% A new axiom: (forall (N_1:nat) (M:nat), ((iff ((ord_less_nat N_1) M)) ((ord_less_eq_nat (suc N_1)) M)))
% FOF formula (forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->((iff ((ord_less_nat ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) ((ord_less_nat M) N_1))))) of role axiom named fact_1135_less__diff__iff
% A new axiom: (forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->((iff ((ord_less_nat ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) ((ord_less_nat M) N_1)))))
% FOF formula (forall (C:nat) (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat C) A)->((ord_less_nat ((minus_minus_nat A) C)) ((minus_minus_nat B) C))))) of role axiom named fact_1136_diff__less__mono
% A new axiom: (forall (C:nat) (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat C) A)->((ord_less_nat ((minus_minus_nat A) C)) ((minus_minus_nat B) C)))))
% FOF formula (forall (I_1:nat) (J_1:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) I_1)->False)) of role axiom named fact_1137_not__add__less1
% A new axiom: (forall (I_1:nat) (J_1:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) I_1)->False))
% FOF formula (forall (J_1:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J_1) I_1)) I_1)->False)) of role axiom named fact_1138_not__add__less2
% A new axiom: (forall (J_1:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J_1) I_1)) I_1)->False))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_nat ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) ((ord_less_nat M) N_1))) of role axiom named fact_1139_nat__add__left__cancel__less
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_nat ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) ((ord_less_nat M) N_1)))
% FOF formula (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat J_1) M)))) of role axiom named fact_1140_trans__less__add1
% A new axiom: (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat J_1) M))))
% FOF formula (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat M) J_1)))) of role axiom named fact_1141_trans__less__add2
% A new axiom: (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat M) J_1))))
% FOF formula (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) K_1)))) of role axiom named fact_1142_add__less__mono1
% A new axiom: (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) K_1))))
% FOF formula (forall (K_1:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat K_1) L)->((ord_less_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) L))))) of role axiom named fact_1143_add__less__mono
% A new axiom: (forall (K_1:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat K_1) L)->((ord_less_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) L)))))
% FOF formula (forall (M:nat) (N_1:nat) (K_1:nat) (L:nat), (((ord_less_nat K_1) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K_1) N_1))->((ord_less_nat M) N_1)))) of role axiom named fact_1144_less__add__eq__less
% A new axiom: (forall (M:nat) (N_1:nat) (K_1:nat) (L:nat), (((ord_less_nat K_1) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K_1) N_1))->((ord_less_nat M) N_1))))
% FOF formula (forall (I_1:nat) (J_1:nat) (K_1:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) K_1)->((ord_less_nat I_1) K_1))) of role axiom named fact_1145_add__lessD1
% A new axiom: (forall (I_1:nat) (J_1:nat) (K_1:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) K_1)->((ord_less_nat I_1) K_1)))
% FOF formula (forall (L:nat) (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->(((ord_less_nat M) L)->((ord_less_nat ((minus_minus_nat L) N_1)) ((minus_minus_nat L) M))))) of role axiom named fact_1146_diff__less__mono2
% A new axiom: (forall (L:nat) (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->(((ord_less_nat M) L)->((ord_less_nat ((minus_minus_nat L) N_1)) ((minus_minus_nat L) M)))))
% FOF formula (forall (N_1:nat) (J_1:nat) (K_1:nat), (((ord_less_nat J_1) K_1)->((ord_less_nat ((minus_minus_nat J_1) N_1)) K_1))) of role axiom named fact_1147_less__imp__diff__less
% A new axiom: (forall (N_1:nat) (J_1:nat) (K_1:nat), (((ord_less_nat J_1) K_1)->((ord_less_nat ((minus_minus_nat J_1) N_1)) K_1)))
% FOF formula (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)) of role axiom named fact_1148_not__less0
% A new axiom: (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False))
% FOF formula (forall (N_1:nat), ((iff (not (((eq nat) N_1) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N_1))) of role axiom named fact_1149_neq0__conv
% A new axiom: (forall (N_1:nat), ((iff (not (((eq nat) N_1) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N_1)))
% FOF formula (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)) of role axiom named fact_1150_less__nat__zero__code
% A new axiom: (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->(not (((eq nat) N_1) zero_zero_nat)))) of role axiom named fact_1151_gr__implies__not0
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->(not (((eq nat) N_1) zero_zero_nat))))
% FOF formula (forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ord_less_nat zero_zero_nat) N_1))) of role axiom named fact_1152_gr0I
% A new axiom: (forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ord_less_nat zero_zero_nat) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), ((iff (((ord_less_nat M) N_1)->False)) ((ord_less_nat N_1) (suc M)))) of role axiom named fact_1153_not__less__eq
% A new axiom: (forall (M:nat) (N_1:nat), ((iff (((ord_less_nat M) N_1)->False)) ((ord_less_nat N_1) (suc M))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) (suc N_1))) ((or ((ord_less_nat M) N_1)) (((eq nat) M) N_1)))) of role axiom named fact_1154_less__Suc__eq
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) (suc N_1))) ((or ((ord_less_nat M) N_1)) (((eq nat) M) N_1))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat (suc M)) (suc N_1))) ((ord_less_nat M) N_1))) of role axiom named fact_1155_Suc__less__eq
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat (suc M)) (suc N_1))) ((ord_less_nat M) N_1)))
% FOF formula (forall (N_1:nat) (M:nat), ((((ord_less_nat N_1) M)->False)->((iff ((ord_less_nat N_1) (suc M))) (((eq nat) N_1) M)))) of role axiom named fact_1156_not__less__less__Suc__eq
% A new axiom: (forall (N_1:nat) (M:nat), ((((ord_less_nat N_1) M)->False)->((iff ((ord_less_nat N_1) (suc M))) (((eq nat) N_1) M))))
% FOF formula (forall (N_1:nat) (M:nat), ((((ord_less_nat N_1) M)->False)->(((ord_less_nat N_1) (suc M))->(((eq nat) M) N_1)))) of role axiom named fact_1157_less__antisym
% A new axiom: (forall (N_1:nat) (M:nat), ((((ord_less_nat N_1) M)->False)->(((ord_less_nat N_1) (suc M))->(((eq nat) M) N_1))))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_nat M) (suc N_1)))) of role axiom named fact_1158_less__SucI
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_nat M) (suc N_1))))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((not (((eq nat) (suc M)) N_1))->((ord_less_nat (suc M)) N_1)))) of role axiom named fact_1159_Suc__lessI
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((not (((eq nat) (suc M)) N_1))->((ord_less_nat (suc M)) N_1))))
% FOF formula (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat J_1) K_1)->((ord_less_nat (suc I_1)) K_1)))) of role axiom named fact_1160_less__trans__Suc
% A new axiom: (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat J_1) K_1)->((ord_less_nat (suc I_1)) K_1))))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_nat M) (suc N_1))->((((ord_less_nat M) N_1)->False)->(((eq nat) M) N_1)))) of role axiom named fact_1161_less__SucE
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_nat M) (suc N_1))->((((ord_less_nat M) N_1)->False)->(((eq nat) M) N_1))))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_nat (suc M)) N_1)->((ord_less_nat M) N_1))) of role axiom named fact_1162_Suc__lessD
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_nat (suc M)) N_1)->((ord_less_nat M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_nat (suc M)) (suc N_1))->((ord_less_nat M) N_1))) of role axiom named fact_1163_Suc__less__SucD
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_nat (suc M)) (suc N_1))->((ord_less_nat M) N_1)))
% FOF formula (forall (N_1:nat), (((ord_less_nat N_1) N_1)->False)) of role axiom named fact_1164_less__not__refl
% A new axiom: (forall (N_1:nat), (((ord_less_nat N_1) N_1)->False))
% FOF formula (forall (M:nat) (N_1:nat), ((iff (not (((eq nat) M) N_1))) ((or ((ord_less_nat M) N_1)) ((ord_less_nat N_1) M)))) of role axiom named fact_1165_nat__neq__iff
% A new axiom: (forall (M:nat) (N_1:nat), ((iff (not (((eq nat) M) N_1))) ((or ((ord_less_nat M) N_1)) ((ord_less_nat N_1) M))))
% FOF formula (forall (X_1:nat) (Y:nat), ((not (((eq nat) X_1) Y))->((((ord_less_nat X_1) Y)->False)->((ord_less_nat Y) X_1)))) of role axiom named fact_1166_linorder__neqE__nat
% A new axiom: (forall (X_1:nat) (Y:nat), ((not (((eq nat) X_1) Y))->((((ord_less_nat X_1) Y)->False)->((ord_less_nat Y) X_1))))
% FOF formula (forall (N_1:nat), (((ord_less_nat N_1) N_1)->False)) of role axiom named fact_1167_less__irrefl__nat
% A new axiom: (forall (N_1:nat), (((ord_less_nat N_1) N_1)->False))
% FOF formula (forall (N_1:nat) (M:nat), (((ord_less_nat N_1) M)->(not (((eq nat) M) N_1)))) of role axiom named fact_1168_less__not__refl2
% A new axiom: (forall (N_1:nat) (M:nat), (((ord_less_nat N_1) M)->(not (((eq nat) M) N_1))))
% FOF formula (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) of role axiom named fact_1169_less__not__refl3
% A new axiom: (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T))))
% FOF formula (forall (P:(nat->(nat->Prop))) (M:nat) (N_1:nat), ((((ord_less_nat M) N_1)->((P N_1) M))->(((((eq nat) M) N_1)->((P N_1) M))->((((ord_less_nat N_1) M)->((P N_1) M))->((P N_1) M))))) of role axiom named fact_1170_nat__less__cases
% A new axiom: (forall (P:(nat->(nat->Prop))) (M:nat) (N_1:nat), ((((ord_less_nat M) N_1)->((P N_1) M))->(((((eq nat) M) N_1)->((P N_1) M))->((((ord_less_nat N_1) M)->((P N_1) M))->((P N_1) M)))))
% FOF formula (forall (I_1:nat) (J_1:nat) (K_1:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J_1) K_1))) ((ord_less_nat ((plus_plus_nat I_1) K_1)) J_1))) of role axiom named fact_1171_less__diff__conv
% A new axiom: (forall (I_1:nat) (J_1:nat) (K_1:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J_1) K_1))) ((ord_less_nat ((plus_plus_nat I_1) K_1)) J_1)))
% FOF formula (forall (M:nat) (N_1:nat), ((((ord_less_nat M) N_1)->False)->(((eq nat) ((plus_plus_nat N_1) ((minus_minus_nat M) N_1))) M))) of role axiom named fact_1172_add__diff__inverse
% A new axiom: (forall (M:nat) (N_1:nat), ((((ord_less_nat M) N_1)->False)->(((eq nat) ((plus_plus_nat N_1) ((minus_minus_nat M) N_1))) M)))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat (suc K_1)) M)) ((times_times_nat (suc K_1)) N_1))) ((ord_less_nat M) N_1))) of role axiom named fact_1173_Suc__mult__less__cancel1
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat (suc K_1)) M)) ((times_times_nat (suc K_1)) N_1))) ((ord_less_nat M) N_1)))
% FOF formula (forall (M:nat) (N_1:nat), ((ord_less_nat ((minus_minus_nat M) N_1)) (suc M))) of role axiom named fact_1174_diff__less__Suc
% A new axiom: (forall (M:nat) (N_1:nat), ((ord_less_nat ((minus_minus_nat M) N_1)) (suc M)))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M) N_1))) ((and ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N_1)))) of role axiom named fact_1175_nat__0__less__mult__iff
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M) N_1))) ((and ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N_1))))
% FOF formula (forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((and ((ord_less_nat zero_zero_nat) K_1)) ((ord_less_nat M) N_1)))) of role axiom named fact_1176_mult__less__cancel1
% A new axiom: (forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((and ((ord_less_nat zero_zero_nat) K_1)) ((ord_less_nat M) N_1))))
% FOF formula (forall (M:nat) (K_1:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1))) ((and ((ord_less_nat zero_zero_nat) K_1)) ((ord_less_nat M) N_1)))) of role axiom named fact_1177_mult__less__cancel2
% A new axiom: (forall (M:nat) (K_1:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1))) ((and ((ord_less_nat zero_zero_nat) K_1)) ((ord_less_nat M) N_1))))
% FOF formula (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K_1)->((ord_less_nat ((times_times_nat I_1) K_1)) ((times_times_nat J_1) K_1))))) of role axiom named fact_1178_mult__less__mono1
% A new axiom: (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K_1)->((ord_less_nat ((times_times_nat I_1) K_1)) ((times_times_nat J_1) K_1)))))
% FOF formula (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K_1)->((ord_less_nat ((times_times_nat K_1) I_1)) ((times_times_nat K_1) J_1))))) of role axiom named fact_1179_mult__less__mono2
% A new axiom: (forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K_1)->((ord_less_nat ((times_times_nat K_1) I_1)) ((times_times_nat K_1) J_1)))))
% FOF formula (forall (M:nat) (N_1:nat) (K_1:nat), (((ord_less_nat zero_zero_nat) K_1)->((iff (((eq nat) ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) (((eq nat) M) N_1)))) of role axiom named fact_1180_nat__mult__eq__cancel1
% A new axiom: (forall (M:nat) (N_1:nat) (K_1:nat), (((ord_less_nat zero_zero_nat) K_1)->((iff (((eq nat) ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) (((eq nat) M) N_1))))
% FOF formula (forall (M:nat) (N_1:nat) (K_1:nat), (((ord_less_nat zero_zero_nat) K_1)->((iff ((ord_less_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((ord_less_nat M) N_1)))) of role axiom named fact_1181_nat__mult__less__cancel1
% A new axiom: (forall (M:nat) (N_1:nat) (K_1:nat), (((ord_less_nat zero_zero_nat) K_1)->((iff ((ord_less_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((ord_less_nat M) N_1))))
% FOF formula (forall (M:nat) (N_1:nat), (((ord_less_nat zero_zero_nat) N_1)->(((ord_less_nat zero_zero_nat) M)->((ord_less_nat ((minus_minus_nat M) N_1)) M)))) of role axiom named fact_1182_diff__less
% A new axiom: (forall (M:nat) (N_1:nat), (((ord_less_nat zero_zero_nat) N_1)->(((ord_less_nat zero_zero_nat) M)->((ord_less_nat ((minus_minus_nat M) N_1)) M))))
% FOF formula (forall (N_1:nat) (M:nat), ((iff ((ord_less_nat zero_zero_nat) ((minus_minus_nat N_1) M))) ((ord_less_nat M) N_1))) of role axiom named fact_1183_zero__less__diff
% A new axiom: (forall (N_1:nat) (M:nat), ((iff ((ord_less_nat zero_zero_nat) ((minus_minus_nat N_1) M))) ((ord_less_nat M) N_1)))
% FOF formula (forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat I_1) M)))) of role axiom named fact_1184_less__add__Suc1
% A new axiom: (forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat I_1) M))))
% FOF formula (forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat M) I_1)))) of role axiom named fact_1185_less__add__Suc2
% A new axiom: (forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat M) I_1))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) N_1)) ((ex nat) (fun (K:nat)=> (((eq nat) N_1) (suc ((plus_plus_nat M) K))))))) of role axiom named fact_1186_less__iff__Suc__add
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) N_1)) ((ex nat) (fun (K:nat)=> (((eq nat) N_1) (suc ((plus_plus_nat M) K)))))))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N_1))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N_1)))) of role axiom named fact_1187_add__gr__0
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N_1))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N_1))))
% FOF formula (forall (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) N_1)) ((ex nat) (fun (M_1:nat)=> (((eq nat) N_1) (suc M_1)))))) of role axiom named fact_1188_gr0__conv__Suc
% A new axiom: (forall (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) N_1)) ((ex nat) (fun (M_1:nat)=> (((eq nat) N_1) (suc M_1))))))
% FOF formula (forall (N_1:nat), ((iff ((ord_less_nat N_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) of role axiom named fact_1189_less__Suc0
% A new axiom: (forall (N_1:nat), ((iff ((ord_less_nat N_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat)))
% FOF formula (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) (suc N_1))) ((or (((eq nat) M) zero_zero_nat)) ((ex nat) (fun (J:nat)=> ((and (((eq nat) M) (suc J))) ((ord_less_nat J) N_1))))))) of role axiom named fact_1190_less__Suc__eq__0__disj
% A new axiom: (forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) (suc N_1))) ((or (((eq nat) M) zero_zero_nat)) ((ex nat) (fun (J:nat)=> ((and (((eq nat) M) (suc J))) ((ord_less_nat J) N_1)))))))
% FOF formula (forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_nat _TPTP_I) N_1))))) N_1)) of role axiom named fact_1191_card__Collect__less__nat
% A new axiom: (forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_nat _TPTP_I) N_1))))) N_1))
% FOF formula (forall (X:nat), (((eq (nat->Prop)) (ord_less_nat X)) (ord_less_eq_nat (suc X)))) of role axiom named fact_1192_less__eq__Suc__le__raw
% A new axiom: (forall (X:nat), (((eq (nat->Prop)) (ord_less_nat X)) (ord_less_eq_nat (suc X))))
% FOF formula (forall (Z:nat) (X_1:nat) (Y:nat), (((ord_less_nat X_1) Y)->((ord_less_nat X_1) ((plus_plus_nat Y) Z)))) of role axiom named fact_1193_termination__basic__simps_I1_J
% A new axiom: (forall (Z:nat) (X_1:nat) (Y:nat), (((ord_less_nat X_1) Y)->((ord_less_nat X_1) ((plus_plus_nat Y) Z))))
% FOF formula (forall (Y:nat) (X_1:nat) (Z:nat), (((ord_less_nat X_1) Z)->((ord_less_nat X_1) ((plus_plus_nat Y) Z)))) of role axiom named fact_1194_termination__basic__simps_I2_J
% A new axiom: (forall (Y:nat) (X_1:nat) (Z:nat), (((ord_less_nat X_1) Z)->((ord_less_nat X_1) ((plus_plus_nat Y) Z))))
% FOF formula (forall (X_1:nat) (Y:nat), (((ord_less_nat X_1) Y)->((ord_less_eq_nat X_1) Y))) of role axiom named fact_1195_termination__basic__simps_I5_J
% A new axiom: (forall (X_1:nat) (Y:nat), (((ord_less_nat X_1) Y)->((ord_less_eq_nat X_1) Y)))
% FOF formula (forall (X_1:nat) (Y:nat), ((or (((fequal_nat X_1) Y)->False)) (((eq nat) X_1) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Nat__Onat_T
% A new axiom: (forall (X_1:nat) (Y:nat), ((or (((fequal_nat X_1) Y)->False)) (((eq nat) X_1) Y)))
% FOF formula (forall (X_1:nat) (Y:nat), ((or (not (((eq nat) X_1) Y))) ((fequal_nat X_1) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Nat__Onat_T
% A new axiom: (forall (X_1:nat) (Y:nat), ((or (not (((eq nat) X_1) Y))) ((fequal_nat X_1) Y)))
% 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_2091234717iple_a) (Y:hoare_2091234717iple_a), ((or (((fequal1604381340iple_a X_1) Y)->False)) (((eq hoare_2091234717iple_a) X_1) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_
% A new axiom: (forall (X_1:hoare_2091234717iple_a) (Y:hoare_2091234717iple_a), ((or (((fequal1604381340iple_a X_1) Y)->False)) (((eq hoare_2091234717iple_a) X_1) Y)))
% FOF formula (forall (X_1:hoare_2091234717iple_a) (Y:hoare_2091234717iple_a), ((or (not (((eq hoare_2091234717iple_a) X_1) Y))) ((fequal1604381340iple_a X_1) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_
% A new axiom: (forall (X_1:hoare_2091234717iple_a) (Y:hoare_2091234717iple_a), ((or (not (((eq hoare_2091234717iple_a) X_1) Y))) ((fequal1604381340iple_a X_1) Y)))
% FOF formula (forall (X_1:hoare_1708887482_state) (Y:hoare_1708887482_state), ((or (((fequal224822779_state X_1) Y)->False)) (((eq hoare_1708887482_state) X_1) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com
% A new axiom: (forall (X_1:hoare_1708887482_state) (Y:hoare_1708887482_state), ((or (((fequal224822779_state X_1) Y)->False)) (((eq hoare_1708887482_state) X_1) Y)))
% FOF formula (forall (X_1:hoare_1708887482_state) (Y:hoare_1708887482_state), ((or (not (((eq hoare_1708887482_state) X_1) Y))) ((fequal224822779_state X_1) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com
% A new axiom: (forall (X_1:hoare_1708887482_state) (Y:hoare_1708887482_state), ((or (not (((eq hoare_1708887482_state) X_1) Y))) ((fequal224822779_state X_1) Y)))
% FOF formula (forall (X_1:(hoare_2091234717iple_a->Prop)) (Y:(hoare_2091234717iple_a->Prop)), ((or (((fequal845167073le_a_o X_1) Y)->False)) (((eq (hoare_2091234717iple_a->Prop)) X_1) Y))) of role axiom named help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It
% A new axiom: (forall (X_1:(hoare_2091234717iple_a->Prop)) (Y:(hoare_2091234717iple_a->Prop)), ((or (((fequal845167073le_a_o X_1) Y)->False)) (((eq (hoare_2091234717iple_a->Prop)) X_1) Y)))
% FOF formula (forall (X_1:(hoare_2091234717iple_a->Prop)) (Y:(hoare_2091234717iple_a->Prop)), ((or (not (((eq (hoare_2091234717iple_a->Prop)) X_1) Y))) ((fequal845167073le_a_o X_1) Y))) of role axiom named help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It
% A new axiom: (forall (X_1:(hoare_2091234717iple_a->Prop)) (Y:(hoare_2091234717iple_a->Prop)), ((or (not (((eq (hoare_2091234717iple_a->Prop)) X_1) Y))) ((fequal845167073le_a_o X_1) Y)))
% FOF formula (forall (N:nat), ((forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) ((semila1052848428le_a_o g) ((image_231808478iple_a (fun (Pn:pname)=> (((hoare_657976383iple_a (p Pn)) (body Pn)) (q Pn)))) procs)))->((hoare_1421888935alid_a N) X)))->(forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) ((image_231808478iple_a (fun (Pn:pname)=> (((hoare_657976383iple_a (p Pn)) (the_com (body_1 Pn))) (q Pn)))) procs))->((hoare_1421888935alid_a N) X))))) of role hypothesis named conj_0
% A new axiom: (forall (N:nat), ((forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) ((semila1052848428le_a_o g) ((image_231808478iple_a (fun (Pn:pname)=> (((hoare_657976383iple_a (p Pn)) (body Pn)) (q Pn)))) procs)))->((hoare_1421888935alid_a N) X)))->(forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) ((image_231808478iple_a (fun (Pn:pname)=> (((hoare_657976383iple_a (p Pn)) (the_com (body_1 Pn))) (q Pn)))) procs))->((hoare_1421888935alid_a N) X)))))
% FOF formula ((forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) g)->((hoare_1421888935alid_a n) X)))->(forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) ((image_231808478iple_a (fun (Pn:pname)=> (((hoare_657976383iple_a (p Pn)) (body Pn)) (q Pn)))) procs))->((hoare_1421888935alid_a n) X)))) of role conjecture named conj_1
% Conjecture to prove = ((forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) g)->((hoare_1421888935alid_a n) X)))->(forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) ((image_231808478iple_a (fun (Pn:pname)=> (((hoare_657976383iple_a (p Pn)) (body Pn)) (q Pn)))) procs))->((hoare_1421888935alid_a n) X)))):Prop
% Parameter x_a_DUMMY:x_a.
% Parameter pname_DUMMY:pname.
% Parameter state_DUMMY:state.
% Parameter hoare_2091234717iple_a_DUMMY:hoare_2091234717iple_a.
% Parameter hoare_1708887482_state_DUMMY:hoare_1708887482_state.
% Parameter option_com_DUMMY:option_com.
% We need to prove ['((forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) g)->((hoare_1421888935alid_a n) X)))->(forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) ((image_231808478iple_a (fun (Pn:pname)=> (((hoare_657976383iple_a (p Pn)) (body Pn)) (q Pn)))) procs))->((hoare_1421888935alid_a n) X))))']
% Parameter x_a:Type.
% Parameter com:Type.
% Parameter pname:Type.
% Parameter state:Type.
% Parameter hoare_2091234717iple_a:Type.
% Parameter hoare_1708887482_state:Type.
% Parameter nat:Type.
% Parameter option_com:Type.
% Parameter big_co1924420859_pname:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((hoare_2091234717iple_a->Prop)->(((pname->(hoare_2091234717iple_a->Prop))->((pname->Prop)->(hoare_2091234717iple_a->Prop)))->Prop))).
% Parameter big_la1994307886_a_o_o:((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop)).
% Parameter big_la1286884090name_o:(((pname->Prop)->Prop)->(pname->Prop)).
% Parameter big_la735727201le_a_o:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop)).
% Parameter big_la1088302868tate_o:(((hoare_1708887482_state->Prop)->Prop)->(hoare_1708887482_state->Prop)).
% Parameter big_la1658356148_nat_o:(((nat->Prop)->Prop)->(nat->Prop)).
% Parameter big_la727467310_fin_o:((Prop->Prop)->Prop).
% Parameter big_la43341705in_nat:((nat->Prop)->nat).
% 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 finite_card_nat:((nat->Prop)->nat).
% Parameter finite886417794_a_o_o:((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->Prop).
% Parameter finite297249702name_o:(((pname->Prop)->Prop)->Prop).
% Parameter finite1829014797le_a_o:(((hoare_2091234717iple_a->Prop)->Prop)->Prop).
% Parameter finite1329924456tate_o:(((hoare_1708887482_state->Prop)->Prop)->Prop).
% Parameter finite_finite_nat_o:(((nat->Prop)->Prop)->Prop).
% Parameter finite_finite_o:((Prop->Prop)->Prop).
% Parameter finite_finite_pname:((pname->Prop)->Prop).
% Parameter finite232261744iple_a:((hoare_2091234717iple_a->Prop)->Prop).
% Parameter finite1625599783_state:((hoare_1708887482_state->Prop)->Prop).
% Parameter finite_finite_nat:((nat->Prop)->Prop).
% Parameter finite2009943022_o_nat:((((hoare_2091234717iple_a->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop)))->((nat->((hoare_2091234717iple_a->Prop)->Prop))->(((hoare_2091234717iple_a->Prop)->Prop)->((nat->Prop)->((hoare_2091234717iple_a->Prop)->Prop))))).
% Parameter finite1427591632_o_nat:(((pname->Prop)->((pname->Prop)->(pname->Prop)))->((nat->(pname->Prop))->((pname->Prop)->((nat->Prop)->(pname->Prop))))).
% Parameter finite903029825le_a_o:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->(((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))->((hoare_2091234717iple_a->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))))).
% Parameter finite1290357347_pname:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((pname->(hoare_2091234717iple_a->Prop))->((hoare_2091234717iple_a->Prop)->((pname->Prop)->(hoare_2091234717iple_a->Prop))))).
% Parameter finite1481787452iple_a:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((hoare_2091234717iple_a->(hoare_2091234717iple_a->Prop))->((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))))).
% Parameter finite2100865449_o_nat:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((nat->(hoare_2091234717iple_a->Prop))->((hoare_2091234717iple_a->Prop)->((nat->Prop)->(hoare_2091234717iple_a->Prop))))).
% Parameter finite2139561282_pname:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((pname->(hoare_1708887482_state->Prop))->((hoare_1708887482_state->Prop)->((pname->Prop)->(hoare_1708887482_state->Prop))))).
% Parameter finite1400355848_o_nat:(((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)))->((nat->(hoare_1708887482_state->Prop))->((hoare_1708887482_state->Prop)->((nat->Prop)->(hoare_1708887482_state->Prop))))).
% Parameter finite141655318_o_nat:(((nat->Prop)->((nat->Prop)->(nat->Prop)))->((nat->(nat->Prop))->((nat->Prop)->((nat->Prop)->(nat->Prop))))).
% Parameter finite14499299le_a_o:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))->Prop)).
% Parameter finite1282449217_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)).
% Parameter finite247037978iple_a:((hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))->(((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)->Prop)).
% Parameter finite1615457021_state:((hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))->(((hoare_1708887482_state->Prop)->hoare_1708887482_state)->Prop)).
% Parameter finite988810631ne_nat:((nat->(nat->nat))->(((nat->Prop)->nat)->Prop)).
% Parameter finite574580006le_a_o:(((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))->((((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))->Prop)).
% Parameter finite89670078_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)).
% Parameter finite1674555159iple_a:((hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))->(((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)->Prop)).
% Parameter finite1347568576_state:((hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))->(((hoare_1708887482_state->Prop)->hoare_1708887482_state)->Prop)).
% Parameter finite795500164em_nat:((nat->(nat->nat))->(((nat->Prop)->nat)->Prop)).
% Parameter minus_1746272704_a_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop))).
% Parameter minus_minus_pname_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter minus_836160335le_a_o:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))).
% Parameter minus_2056855718tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))).
% Parameter minus_minus_nat_o:((nat->Prop)->((nat->Prop)->(nat->Prop))).
% Parameter minus_minus_o:(Prop->(Prop->Prop)).
% Parameter minus_minus_nat:(nat->(nat->nat)).
% Parameter one_one_nat:nat.
% Parameter plus_plus_nat:(nat->(nat->nat)).
% Parameter times_times_nat:(nat->(nat->nat)).
% Parameter zero_zero_nat:nat.
% Parameter the_Ho2077879471le_a_o:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop)).
% Parameter the_pname:((pname->Prop)->pname).
% Parameter the_Ho1471183438iple_a:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a).
% Parameter the_Ho851197897_state:((hoare_1708887482_state->Prop)->hoare_1708887482_state).
% Parameter the_nat:((nat->Prop)->nat).
% Parameter hoare_Mirabelle_MGT:(com->hoare_1708887482_state).
% Parameter hoare_1467856363rivs_a:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->Prop)).
% Parameter hoare_90032982_state:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop)).
% Parameter hoare_1805689709lids_a:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->Prop)).
% Parameter hoare_496444244_state:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->Prop)).
% Parameter hoare_657976383iple_a:((x_a->(state->Prop))->(com->((x_a->(state->Prop))->hoare_2091234717iple_a))).
% Parameter hoare_858012674_state:((state->(state->Prop))->(com->((state->(state->Prop))->hoare_1708887482_state))).
% Parameter hoare_1169027232size_a:((x_a->nat)->(hoare_2091234717iple_a->nat)).
% Parameter hoare_518771297_state:((state->nat)->(hoare_1708887482_state->nat)).
% Parameter hoare_1421888935alid_a:(nat->(hoare_2091234717iple_a->Prop)).
% Parameter hoare_23738522_state:(nat->(hoare_1708887482_state->Prop)).
% Parameter semila1672913213_a_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop))).
% Parameter semila1673364395name_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter semila2006181266le_a_o:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))).
% Parameter semila129691299tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))).
% Parameter semila1947288293_nat_o:((nat->Prop)->((nat->Prop)->(nat->Prop))).
% Parameter semila854092349_inf_o:(Prop->(Prop->Prop)).
% Parameter semila80283416nf_nat:(nat->(nat->nat)).
% Parameter semila484278426_o_o_o:((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->Prop))).
% Parameter semila181081674me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter semila2050116131_a_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop))).
% Parameter semila1853742644te_o_o:(((hoare_1708887482_state->Prop)->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop))).
% Parameter semila72246288at_o_o:(((nat->Prop)->Prop)->(((nat->Prop)->Prop)->((nat->Prop)->Prop))).
% Parameter semila2062604954up_o_o:((Prop->Prop)->((Prop->Prop)->(Prop->Prop))).
% Parameter semila1780557381name_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter semila1052848428le_a_o:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))).
% Parameter semila1122118281tate_o:((hoare_1708887482_state->Prop)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))).
% Parameter semila848761471_nat_o:((nat->Prop)->((nat->Prop)->(nat->Prop))).
% Parameter semila10642723_sup_o:(Prop->(Prop->Prop)).
% Parameter semila972727038up_nat:(nat->(nat->nat)).
% Parameter suc:(nat->nat).
% Parameter nat_case_o:(Prop->((nat->Prop)->(nat->Prop))).
% Parameter nat_case_nat:(nat->((nat->nat)->(nat->nat))).
% Parameter size_size_com:(com->nat).
% Parameter size_s1040486067iple_a:(hoare_2091234717iple_a->nat).
% Parameter size_s1186992420_state:(hoare_1708887482_state->nat).
% Parameter evalc:(com->(state->(state->Prop))).
% Parameter evaln:(com->(state->(nat->(state->Prop)))).
% Parameter the_com:(option_com->com).
% Parameter bot_bo690906872_o_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->Prop).
% Parameter bot_bot_pname_o_o:((pname->Prop)->Prop).
% Parameter bot_bo1957696069_a_o_o:((hoare_2091234717iple_a->Prop)->Prop).
% Parameter bot_bo1678742418te_o_o:((hoare_1708887482_state->Prop)->Prop).
% Parameter bot_bot_nat_o_o:((nat->Prop)->Prop).
% Parameter bot_bot_o_o:(Prop->Prop).
% Parameter bot_bot_pname_o:(pname->Prop).
% Parameter bot_bo1791335050le_a_o:(hoare_2091234717iple_a->Prop).
% Parameter bot_bo19817387tate_o:(hoare_1708887482_state->Prop).
% Parameter bot_bot_nat_o:(nat->Prop).
% Parameter bot_bot_o:Prop.
% Parameter bot_bot_nat:nat.
% Parameter ord_less_nat:(nat->(nat->Prop)).
% Parameter ord_less_eq_nat:(nat->(nat->Prop)).
% Parameter collec1008234059le_a_o:(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop)).
% Parameter collect_pname:((pname->Prop)->(pname->Prop)).
% Parameter collec992574898iple_a:((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)).
% Parameter collec1568722789_state:((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop)).
% Parameter collect_nat:((nat->Prop)->(nat->Prop)).
% Parameter image_784579955le_a_o:(((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop))).
% Parameter image_1908519857_pname:(((hoare_2091234717iple_a->Prop)->pname)->(((hoare_2091234717iple_a->Prop)->Prop)->(pname->Prop))).
% Parameter image_136408202iple_a:(((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)->(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))).
% Parameter image_1501246093_state:(((hoare_2091234717iple_a->Prop)->hoare_1708887482_state)->(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_1708887482_state->Prop))).
% Parameter image_75520503_o_nat:(((hoare_2091234717iple_a->Prop)->nat)->(((hoare_2091234717iple_a->Prop)->Prop)->(nat->Prop))).
% Parameter image_742317343le_a_o:((pname->(hoare_2091234717iple_a->Prop))->((pname->Prop)->((hoare_2091234717iple_a->Prop)->Prop))).
% Parameter image_pname_pname:((pname->pname)->((pname->Prop)->(pname->Prop))).
% Parameter image_231808478iple_a:((pname->hoare_2091234717iple_a)->((pname->Prop)->(hoare_2091234717iple_a->Prop))).
% Parameter image_1116629049_state:((pname->hoare_1708887482_state)->((pname->Prop)->(hoare_1708887482_state->Prop))).
% Parameter image_pname_nat:((pname->nat)->((pname->Prop)->(nat->Prop))).
% Parameter image_1642350072le_a_o:((hoare_2091234717iple_a->(hoare_2091234717iple_a->Prop))->((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->Prop))).
% Parameter image_924789612_pname:((hoare_2091234717iple_a->pname)->((hoare_2091234717iple_a->Prop)->(pname->Prop))).
% Parameter image_1661191109iple_a:((hoare_2091234717iple_a->hoare_2091234717iple_a)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))).
% Parameter image_1884482962_state:((hoare_2091234717iple_a->hoare_1708887482_state)->((hoare_2091234717iple_a->Prop)->(hoare_1708887482_state->Prop))).
% Parameter image_1773322034_a_nat:((hoare_2091234717iple_a->nat)->((hoare_2091234717iple_a->Prop)->(nat->Prop))).
% Parameter image_293283184iple_a:((hoare_1708887482_state->hoare_2091234717iple_a)->((hoare_1708887482_state->Prop)->(hoare_2091234717iple_a->Prop))).
% Parameter image_757158439_state:((hoare_1708887482_state->hoare_1708887482_state)->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))).
% Parameter image_1995609573le_a_o:((nat->(hoare_2091234717iple_a->Prop))->((nat->Prop)->((hoare_2091234717iple_a->Prop)->Prop))).
% Parameter image_nat_pname:((nat->pname)->((nat->Prop)->(pname->Prop))).
% Parameter image_359186840iple_a:((nat->hoare_2091234717iple_a)->((nat->Prop)->(hoare_2091234717iple_a->Prop))).
% Parameter image_514827263_state:((nat->hoare_1708887482_state)->((nat->Prop)->(hoare_1708887482_state->Prop))).
% Parameter image_nat_nat:((nat->nat)->((nat->Prop)->(nat->Prop))).
% Parameter insert987231145_a_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->Prop))).
% Parameter insert_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))).
% Parameter insert102003750le_a_o:((hoare_2091234717iple_a->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->((hoare_2091234717iple_a->Prop)->Prop))).
% Parameter insert949073679tate_o:((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->((hoare_1708887482_state->Prop)->Prop))).
% Parameter insert_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->((nat->Prop)->Prop))).
% Parameter insert_o:(Prop->((Prop->Prop)->(Prop->Prop))).
% Parameter insert_pname:(pname->((pname->Prop)->(pname->Prop))).
% Parameter insert1597628439iple_a:(hoare_2091234717iple_a->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))).
% Parameter insert528405184_state:(hoare_1708887482_state->((hoare_1708887482_state->Prop)->(hoare_1708887482_state->Prop))).
% Parameter insert_nat:(nat->((nat->Prop)->(nat->Prop))).
% Parameter the_el1618277441le_a_o:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop)).
% Parameter the_elem_pname:((pname->Prop)->pname).
% Parameter the_el13400124iple_a:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a).
% Parameter the_el864710747_state:((hoare_1708887482_state->Prop)->hoare_1708887482_state).
% Parameter the_elem_nat:((nat->Prop)->nat).
% Parameter fequal845167073le_a_o:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->Prop)).
% Parameter fequal_pname:(pname->(pname->Prop)).
% Parameter fequal_state:(state->(state->Prop)).
% Parameter fequal1604381340iple_a:(hoare_2091234717iple_a->(hoare_2091234717iple_a->Prop)).
% Parameter fequal224822779_state:(hoare_1708887482_state->(hoare_1708887482_state->Prop)).
% Parameter fequal_nat:(nat->(nat->Prop)).
% Parameter member1297825410_a_o_o:(((hoare_2091234717iple_a->Prop)->Prop)->((((hoare_2091234717iple_a->Prop)->Prop)->Prop)->Prop)).
% Parameter member_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->Prop)).
% Parameter member99268621le_a_o:((hoare_2091234717iple_a->Prop)->(((hoare_2091234717iple_a->Prop)->Prop)->Prop)).
% Parameter member814030440tate_o:((hoare_1708887482_state->Prop)->(((hoare_1708887482_state->Prop)->Prop)->Prop)).
% Parameter member_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->Prop)).
% Parameter member_o:(Prop->((Prop->Prop)->Prop)).
% Parameter member_pname:(pname->((pname->Prop)->Prop)).
% Parameter member290856304iple_a:(hoare_2091234717iple_a->((hoare_2091234717iple_a->Prop)->Prop)).
% Parameter member451959335_state:(hoare_1708887482_state->((hoare_1708887482_state->Prop)->Prop)).
% Parameter member_nat:(nat->((nat->Prop)->Prop)).
% Parameter g:(hoare_2091234717iple_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_1:com) (Fun2_4:(x_a->(state->Prop))) (Fun1_3:(x_a->(state->Prop))) (Com:com) (Fun2_3:(x_a->(state->Prop))), ((iff (((eq hoare_2091234717iple_a) (((hoare_657976383iple_a Fun1_4) Com_1) Fun2_4)) (((hoare_657976383iple_a Fun1_3) Com) Fun2_3))) ((and ((and (((eq (x_a->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com_1) Com))) (((eq (x_a->(state->Prop))) Fun2_4) Fun2_3)))).
% Axiom fact_1_triple_Oinject:(forall (Fun1_4:(state->(state->Prop))) (Com_1:com) (Fun2_4:(state->(state->Prop))) (Fun1_3:(state->(state->Prop))) (Com:com) (Fun2_3:(state->(state->Prop))), ((iff (((eq hoare_1708887482_state) (((hoare_858012674_state Fun1_4) Com_1) Fun2_4)) (((hoare_858012674_state Fun1_3) Com) Fun2_3))) ((and ((and (((eq (state->(state->Prop))) Fun1_4) Fun1_3)) (((eq com) Com_1) Com))) (((eq (state->(state->Prop))) Fun2_4) Fun2_3)))).
% Axiom fact_2_hoare__valids__def:(forall (G_28:(hoare_1708887482_state->Prop)) (Ts_4:(hoare_1708887482_state->Prop)), ((iff ((hoare_496444244_state G_28) Ts_4)) (forall (N:nat), ((forall (X:hoare_1708887482_state), (((member451959335_state X) G_28)->((hoare_23738522_state N) X)))->(forall (X:hoare_1708887482_state), (((member451959335_state X) Ts_4)->((hoare_23738522_state N) X))))))).
% Axiom fact_3_hoare__valids__def:(forall (G_28:(hoare_2091234717iple_a->Prop)) (Ts_4:(hoare_2091234717iple_a->Prop)), ((iff ((hoare_1805689709lids_a G_28) Ts_4)) (forall (N:nat), ((forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) G_28)->((hoare_1421888935alid_a N) X)))->(forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) Ts_4)->((hoare_1421888935alid_a N) X))))))).
% Axiom fact_4_hoare__derivs_OBody:(forall (G_27:(hoare_1708887482_state->Prop)) (P_36:(pname->(state->(state->Prop)))) (Q_20:(pname->(state->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_27) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1))) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_36 P_9)) (the_com (body_1 P_9))) (Q_20 P_9)))) Procs_1))->((hoare_90032982_state G_27) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1)))).
% Axiom fact_5_hoare__derivs_OBody:(forall (G_27:(hoare_2091234717iple_a->Prop)) (P_36:(pname->(x_a->(state->Prop)))) (Q_20:(pname->(x_a->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_1467856363rivs_a ((semila1052848428le_a_o G_27) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1))) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_36 P_9)) (the_com (body_1 P_9))) (Q_20 P_9)))) Procs_1))->((hoare_1467856363rivs_a G_27) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_36 P_9)) (body P_9)) (Q_20 P_9)))) Procs_1)))).
% Axiom fact_6_UnE:(forall (C_34:nat) (A_129:(nat->Prop)) (B_71:(nat->Prop)), (((member_nat C_34) ((semila848761471_nat_o A_129) B_71))->((((member_nat C_34) A_129)->False)->((member_nat C_34) B_71)))).
% Axiom fact_7_UnE:(forall (C_34:(hoare_2091234717iple_a->Prop)) (A_129:((hoare_2091234717iple_a->Prop)->Prop)) (B_71:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_34) ((semila2050116131_a_o_o A_129) B_71))->((((member99268621le_a_o C_34) A_129)->False)->((member99268621le_a_o C_34) B_71)))).
% Axiom fact_8_UnE:(forall (C_34:hoare_1708887482_state) (A_129:(hoare_1708887482_state->Prop)) (B_71:(hoare_1708887482_state->Prop)), (((member451959335_state C_34) ((semila1122118281tate_o A_129) B_71))->((((member451959335_state C_34) A_129)->False)->((member451959335_state C_34) B_71)))).
% Axiom fact_9_UnE:(forall (C_34:hoare_2091234717iple_a) (A_129:(hoare_2091234717iple_a->Prop)) (B_71:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_34) ((semila1052848428le_a_o A_129) B_71))->((((member290856304iple_a C_34) A_129)->False)->((member290856304iple_a C_34) B_71)))).
% Axiom fact_10_UnE:(forall (C_34:pname) (A_129:(pname->Prop)) (B_71:(pname->Prop)), (((member_pname C_34) ((semila1780557381name_o A_129) B_71))->((((member_pname C_34) A_129)->False)->((member_pname C_34) B_71)))).
% Axiom fact_11_sup1E:(forall (A_128:(nat->Prop)) (B_70:(nat->Prop)) (X_51:nat), ((((semila848761471_nat_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51)))).
% Axiom fact_12_sup1E:(forall (A_128:((hoare_2091234717iple_a->Prop)->Prop)) (B_70:((hoare_2091234717iple_a->Prop)->Prop)) (X_51:(hoare_2091234717iple_a->Prop)), ((((semila2050116131_a_o_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51)))).
% Axiom fact_13_sup1E:(forall (A_128:(hoare_1708887482_state->Prop)) (B_70:(hoare_1708887482_state->Prop)) (X_51:hoare_1708887482_state), ((((semila1122118281tate_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51)))).
% Axiom fact_14_sup1E:(forall (A_128:(pname->Prop)) (B_70:(pname->Prop)) (X_51:pname), ((((semila1780557381name_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51)))).
% Axiom fact_15_sup1E:(forall (A_128:(hoare_2091234717iple_a->Prop)) (B_70:(hoare_2091234717iple_a->Prop)) (X_51:hoare_2091234717iple_a), ((((semila1052848428le_a_o A_128) B_70) X_51)->(((A_128 X_51)->False)->(B_70 X_51)))).
% Axiom fact_16_sup1CI:(forall (A_127:(nat->Prop)) (B_69:(nat->Prop)) (X_50:nat), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila848761471_nat_o A_127) B_69) X_50))).
% Axiom fact_17_sup1CI:(forall (A_127:((hoare_2091234717iple_a->Prop)->Prop)) (B_69:((hoare_2091234717iple_a->Prop)->Prop)) (X_50:(hoare_2091234717iple_a->Prop)), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila2050116131_a_o_o A_127) B_69) X_50))).
% Axiom fact_18_sup1CI:(forall (A_127:(hoare_1708887482_state->Prop)) (B_69:(hoare_1708887482_state->Prop)) (X_50:hoare_1708887482_state), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila1122118281tate_o A_127) B_69) X_50))).
% Axiom fact_19_sup1CI:(forall (A_127:(pname->Prop)) (B_69:(pname->Prop)) (X_50:pname), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila1780557381name_o A_127) B_69) X_50))).
% Axiom fact_20_sup1CI:(forall (A_127:(hoare_2091234717iple_a->Prop)) (B_69:(hoare_2091234717iple_a->Prop)) (X_50:hoare_2091234717iple_a), ((((B_69 X_50)->False)->(A_127 X_50))->(((semila1052848428le_a_o A_127) B_69) X_50))).
% Axiom fact_21_UnCI:(forall (A_126:(nat->Prop)) (C_33:nat) (B_68:(nat->Prop)), (((((member_nat C_33) B_68)->False)->((member_nat C_33) A_126))->((member_nat C_33) ((semila848761471_nat_o A_126) B_68)))).
% Axiom fact_22_UnCI:(forall (A_126:((hoare_2091234717iple_a->Prop)->Prop)) (C_33:(hoare_2091234717iple_a->Prop)) (B_68:((hoare_2091234717iple_a->Prop)->Prop)), (((((member99268621le_a_o C_33) B_68)->False)->((member99268621le_a_o C_33) A_126))->((member99268621le_a_o C_33) ((semila2050116131_a_o_o A_126) B_68)))).
% Axiom fact_23_UnCI:(forall (A_126:(hoare_1708887482_state->Prop)) (C_33:hoare_1708887482_state) (B_68:(hoare_1708887482_state->Prop)), (((((member451959335_state C_33) B_68)->False)->((member451959335_state C_33) A_126))->((member451959335_state C_33) ((semila1122118281tate_o A_126) B_68)))).
% Axiom fact_24_UnCI:(forall (A_126:(hoare_2091234717iple_a->Prop)) (C_33:hoare_2091234717iple_a) (B_68:(hoare_2091234717iple_a->Prop)), (((((member290856304iple_a C_33) B_68)->False)->((member290856304iple_a C_33) A_126))->((member290856304iple_a C_33) ((semila1052848428le_a_o A_126) B_68)))).
% Axiom fact_25_UnCI:(forall (A_126:(pname->Prop)) (C_33:pname) (B_68:(pname->Prop)), (((((member_pname C_33) B_68)->False)->((member_pname C_33) A_126))->((member_pname C_33) ((semila1780557381name_o A_126) B_68)))).
% Axiom fact_26_image__eqI:(forall (A_125:(nat->Prop)) (B_67:nat) (F_50:(nat->nat)) (X_49:nat), ((((eq nat) B_67) (F_50 X_49))->(((member_nat X_49) A_125)->((member_nat B_67) ((image_nat_nat F_50) A_125))))).
% Axiom fact_27_image__eqI:(forall (A_125:(pname->Prop)) (B_67:hoare_1708887482_state) (F_50:(pname->hoare_1708887482_state)) (X_49:pname), ((((eq hoare_1708887482_state) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member451959335_state B_67) ((image_1116629049_state F_50) A_125))))).
% Axiom fact_28_image__eqI:(forall (A_125:(pname->Prop)) (B_67:nat) (F_50:(pname->nat)) (X_49:pname), ((((eq nat) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member_nat B_67) ((image_pname_nat F_50) A_125))))).
% Axiom fact_29_image__eqI:(forall (A_125:(pname->Prop)) (B_67:(hoare_2091234717iple_a->Prop)) (F_50:(pname->(hoare_2091234717iple_a->Prop))) (X_49:pname), ((((eq (hoare_2091234717iple_a->Prop)) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member99268621le_a_o B_67) ((image_742317343le_a_o F_50) A_125))))).
% Axiom fact_30_image__eqI:(forall (A_125:(nat->Prop)) (B_67:pname) (F_50:(nat->pname)) (X_49:nat), ((((eq pname) B_67) (F_50 X_49))->(((member_nat X_49) A_125)->((member_pname B_67) ((image_nat_pname F_50) A_125))))).
% Axiom fact_31_image__eqI:(forall (A_125:((hoare_2091234717iple_a->Prop)->Prop)) (B_67:pname) (F_50:((hoare_2091234717iple_a->Prop)->pname)) (X_49:(hoare_2091234717iple_a->Prop)), ((((eq pname) B_67) (F_50 X_49))->(((member99268621le_a_o X_49) A_125)->((member_pname B_67) ((image_1908519857_pname F_50) A_125))))).
% Axiom fact_32_image__eqI:(forall (A_125:(hoare_2091234717iple_a->Prop)) (B_67:pname) (F_50:(hoare_2091234717iple_a->pname)) (X_49:hoare_2091234717iple_a), ((((eq pname) B_67) (F_50 X_49))->(((member290856304iple_a X_49) A_125)->((member_pname B_67) ((image_924789612_pname F_50) A_125))))).
% Axiom fact_33_image__eqI:(forall (A_125:(pname->Prop)) (B_67:hoare_2091234717iple_a) (F_50:(pname->hoare_2091234717iple_a)) (X_49:pname), ((((eq hoare_2091234717iple_a) B_67) (F_50 X_49))->(((member_pname X_49) A_125)->((member290856304iple_a B_67) ((image_231808478iple_a F_50) A_125))))).
% Axiom fact_34_image__Un:(forall (F_49:(nat->nat)) (A_124:(nat->Prop)) (B_66:(nat->Prop)), (((eq (nat->Prop)) ((image_nat_nat F_49) ((semila848761471_nat_o A_124) B_66))) ((semila848761471_nat_o ((image_nat_nat F_49) A_124)) ((image_nat_nat F_49) B_66)))).
% Axiom fact_35_image__Un:(forall (F_49:(pname->hoare_1708887482_state)) (A_124:(pname->Prop)) (B_66:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_49) ((semila1780557381name_o A_124) B_66))) ((semila1122118281tate_o ((image_1116629049_state F_49) A_124)) ((image_1116629049_state F_49) B_66)))).
% Axiom fact_36_image__Un:(forall (F_49:(hoare_2091234717iple_a->nat)) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq (nat->Prop)) ((image_1773322034_a_nat F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila848761471_nat_o ((image_1773322034_a_nat F_49) A_124)) ((image_1773322034_a_nat F_49) B_66)))).
% Axiom fact_37_image__Un:(forall (F_49:(hoare_2091234717iple_a->(hoare_2091234717iple_a->Prop))) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((image_1642350072le_a_o F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila2050116131_a_o_o ((image_1642350072le_a_o F_49) A_124)) ((image_1642350072le_a_o F_49) B_66)))).
% Axiom fact_38_image__Un:(forall (F_49:(hoare_2091234717iple_a->hoare_1708887482_state)) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1884482962_state F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila1122118281tate_o ((image_1884482962_state F_49) A_124)) ((image_1884482962_state F_49) B_66)))).
% Axiom fact_39_image__Un:(forall (F_49:(hoare_2091234717iple_a->pname)) (A_124:(hoare_2091234717iple_a->Prop)) (B_66:(hoare_2091234717iple_a->Prop)), (((eq (pname->Prop)) ((image_924789612_pname F_49) ((semila1052848428le_a_o A_124) B_66))) ((semila1780557381name_o ((image_924789612_pname F_49) A_124)) ((image_924789612_pname F_49) B_66)))).
% Axiom fact_40_image__Un:(forall (F_49:(nat->hoare_2091234717iple_a)) (A_124:(nat->Prop)) (B_66:(nat->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_359186840iple_a F_49) ((semila848761471_nat_o A_124) B_66))) ((semila1052848428le_a_o ((image_359186840iple_a F_49) A_124)) ((image_359186840iple_a F_49) B_66)))).
% Axiom fact_41_image__Un:(forall (F_49:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)) (A_124:((hoare_2091234717iple_a->Prop)->Prop)) (B_66:((hoare_2091234717iple_a->Prop)->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_136408202iple_a F_49) ((semila2050116131_a_o_o A_124) B_66))) ((semila1052848428le_a_o ((image_136408202iple_a F_49) A_124)) ((image_136408202iple_a F_49) B_66)))).
% Axiom fact_42_image__Un:(forall (F_49:(hoare_1708887482_state->hoare_2091234717iple_a)) (A_124:(hoare_1708887482_state->Prop)) (B_66:(hoare_1708887482_state->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_293283184iple_a F_49) ((semila1122118281tate_o A_124) B_66))) ((semila1052848428le_a_o ((image_293283184iple_a F_49) A_124)) ((image_293283184iple_a F_49) B_66)))).
% Axiom fact_43_image__Un:(forall (F_49:(pname->hoare_2091234717iple_a)) (A_124:(pname->Prop)) (B_66:(pname->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_49) ((semila1780557381name_o A_124) B_66))) ((semila1052848428le_a_o ((image_231808478iple_a F_49) A_124)) ((image_231808478iple_a F_49) B_66)))).
% Axiom fact_44_sup__fun__def:(forall (F_48:(nat->Prop)) (G_26:(nat->Prop)) (X:nat), ((iff (((semila848761471_nat_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X)))).
% Axiom fact_45_sup__fun__def:(forall (F_48:((hoare_2091234717iple_a->Prop)->Prop)) (G_26:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), ((iff (((semila2050116131_a_o_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X)))).
% Axiom fact_46_sup__fun__def:(forall (F_48:(hoare_1708887482_state->Prop)) (G_26:(hoare_1708887482_state->Prop)) (X:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X)))).
% Axiom fact_47_sup__fun__def:(forall (F_48:(pname->Prop)) (G_26:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X)))).
% Axiom fact_48_sup__fun__def:(forall (F_48:(hoare_2091234717iple_a->Prop)) (G_26:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila1052848428le_a_o F_48) G_26) X)) ((semila10642723_sup_o (F_48 X)) (G_26 X)))).
% Axiom fact_49_sup__apply:(forall (F_47:(nat->Prop)) (G_25:(nat->Prop)) (X_48:nat), ((iff (((semila848761471_nat_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48)))).
% Axiom fact_50_sup__apply:(forall (F_47:((hoare_2091234717iple_a->Prop)->Prop)) (G_25:((hoare_2091234717iple_a->Prop)->Prop)) (X_48:(hoare_2091234717iple_a->Prop)), ((iff (((semila2050116131_a_o_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48)))).
% Axiom fact_51_sup__apply:(forall (F_47:(hoare_1708887482_state->Prop)) (G_25:(hoare_1708887482_state->Prop)) (X_48:hoare_1708887482_state), ((iff (((semila1122118281tate_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48)))).
% Axiom fact_52_sup__apply:(forall (F_47:(pname->Prop)) (G_25:(pname->Prop)) (X_48:pname), ((iff (((semila1780557381name_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48)))).
% Axiom fact_53_sup__apply:(forall (F_47:(hoare_2091234717iple_a->Prop)) (G_25:(hoare_2091234717iple_a->Prop)) (X_48:hoare_2091234717iple_a), ((iff (((semila1052848428le_a_o F_47) G_25) X_48)) ((semila10642723_sup_o (F_47 X_48)) (G_25 X_48)))).
% Axiom fact_54_cut:(forall (G_24:(hoare_2091234717iple_a->Prop)) (G_23:(hoare_2091234717iple_a->Prop)) (Ts_3:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a G_23) Ts_3)->(((hoare_1467856363rivs_a G_24) G_23)->((hoare_1467856363rivs_a G_24) Ts_3)))).
% Axiom fact_55_cut:(forall (G_24:(hoare_1708887482_state->Prop)) (G_23:(hoare_1708887482_state->Prop)) (Ts_3:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_23) Ts_3)->(((hoare_90032982_state G_24) G_23)->((hoare_90032982_state G_24) Ts_3)))).
% Axiom fact_56_sup__assoc:(forall (X_47:(nat->Prop)) (Y_20:(nat->Prop)) (Z_11:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o X_47) Y_20)) Z_11)) ((semila848761471_nat_o X_47) ((semila848761471_nat_o Y_20) Z_11)))).
% Axiom fact_57_sup__assoc:(forall (X_47:nat) (Y_20:nat) (Z_11:nat), (((eq nat) ((semila972727038up_nat ((semila972727038up_nat X_47) Y_20)) Z_11)) ((semila972727038up_nat X_47) ((semila972727038up_nat Y_20) Z_11)))).
% Axiom fact_58_sup__assoc:(forall (X_47:((hoare_2091234717iple_a->Prop)->Prop)) (Y_20:((hoare_2091234717iple_a->Prop)->Prop)) (Z_11:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o X_47) Y_20)) Z_11)) ((semila2050116131_a_o_o X_47) ((semila2050116131_a_o_o Y_20) Z_11)))).
% Axiom fact_59_sup__assoc:(forall (X_47:(hoare_1708887482_state->Prop)) (Y_20:(hoare_1708887482_state->Prop)) (Z_11:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_47) Y_20)) Z_11)) ((semila1122118281tate_o X_47) ((semila1122118281tate_o Y_20) Z_11)))).
% Axiom fact_60_sup__assoc:(forall (X_47:(pname->Prop)) (Y_20:(pname->Prop)) (Z_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_47) Y_20)) Z_11)) ((semila1780557381name_o X_47) ((semila1780557381name_o Y_20) Z_11)))).
% Axiom fact_61_sup__assoc:(forall (X_47:Prop) (Y_20:Prop) (Z_11:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_47) Y_20)) Z_11)) ((semila10642723_sup_o X_47) ((semila10642723_sup_o Y_20) Z_11)))).
% Axiom fact_62_sup__assoc:(forall (X_47:(hoare_2091234717iple_a->Prop)) (Y_20:(hoare_2091234717iple_a->Prop)) (Z_11:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o X_47) Y_20)) Z_11)) ((semila1052848428le_a_o X_47) ((semila1052848428le_a_o Y_20) Z_11)))).
% Axiom fact_63_inf__sup__aci_I6_J:(forall (X_46:(nat->Prop)) (Y_19:(nat->Prop)) (Z_10:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o X_46) Y_19)) Z_10)) ((semila848761471_nat_o X_46) ((semila848761471_nat_o Y_19) Z_10)))).
% Axiom fact_64_inf__sup__aci_I6_J:(forall (X_46:nat) (Y_19:nat) (Z_10:nat), (((eq nat) ((semila972727038up_nat ((semila972727038up_nat X_46) Y_19)) Z_10)) ((semila972727038up_nat X_46) ((semila972727038up_nat Y_19) Z_10)))).
% Axiom fact_65_inf__sup__aci_I6_J:(forall (X_46:((hoare_2091234717iple_a->Prop)->Prop)) (Y_19:((hoare_2091234717iple_a->Prop)->Prop)) (Z_10:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o X_46) Y_19)) Z_10)) ((semila2050116131_a_o_o X_46) ((semila2050116131_a_o_o Y_19) Z_10)))).
% Axiom fact_66_inf__sup__aci_I6_J:(forall (X_46:(hoare_1708887482_state->Prop)) (Y_19:(hoare_1708887482_state->Prop)) (Z_10:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o X_46) Y_19)) Z_10)) ((semila1122118281tate_o X_46) ((semila1122118281tate_o Y_19) Z_10)))).
% Axiom fact_67_inf__sup__aci_I6_J:(forall (X_46:(pname->Prop)) (Y_19:(pname->Prop)) (Z_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_46) Y_19)) Z_10)) ((semila1780557381name_o X_46) ((semila1780557381name_o Y_19) Z_10)))).
% Axiom fact_68_inf__sup__aci_I6_J:(forall (X_46:Prop) (Y_19:Prop) (Z_10:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_46) Y_19)) Z_10)) ((semila10642723_sup_o X_46) ((semila10642723_sup_o Y_19) Z_10)))).
% Axiom fact_69_inf__sup__aci_I6_J:(forall (X_46:(hoare_2091234717iple_a->Prop)) (Y_19:(hoare_2091234717iple_a->Prop)) (Z_10:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o X_46) Y_19)) Z_10)) ((semila1052848428le_a_o X_46) ((semila1052848428le_a_o Y_19) Z_10)))).
% Axiom fact_70_sup_Oassoc:(forall (A_123:(nat->Prop)) (B_65:(nat->Prop)) (C_32:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o A_123) B_65)) C_32)) ((semila848761471_nat_o A_123) ((semila848761471_nat_o B_65) C_32)))).
% Axiom fact_71_sup_Oassoc:(forall (A_123:nat) (B_65:nat) (C_32:nat), (((eq nat) ((semila972727038up_nat ((semila972727038up_nat A_123) B_65)) C_32)) ((semila972727038up_nat A_123) ((semila972727038up_nat B_65) C_32)))).
% Axiom fact_72_sup_Oassoc:(forall (A_123:((hoare_2091234717iple_a->Prop)->Prop)) (B_65:((hoare_2091234717iple_a->Prop)->Prop)) (C_32:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o A_123) B_65)) C_32)) ((semila2050116131_a_o_o A_123) ((semila2050116131_a_o_o B_65) C_32)))).
% Axiom fact_73_sup_Oassoc:(forall (A_123:(hoare_1708887482_state->Prop)) (B_65:(hoare_1708887482_state->Prop)) (C_32:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_123) B_65)) C_32)) ((semila1122118281tate_o A_123) ((semila1122118281tate_o B_65) C_32)))).
% Axiom fact_74_sup_Oassoc:(forall (A_123:(pname->Prop)) (B_65:(pname->Prop)) (C_32:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_123) B_65)) C_32)) ((semila1780557381name_o A_123) ((semila1780557381name_o B_65) C_32)))).
% Axiom fact_75_sup_Oassoc:(forall (A_123:Prop) (B_65:Prop) (C_32:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_123) B_65)) C_32)) ((semila10642723_sup_o A_123) ((semila10642723_sup_o B_65) C_32)))).
% Axiom fact_76_sup_Oassoc:(forall (A_123:(hoare_2091234717iple_a->Prop)) (B_65:(hoare_2091234717iple_a->Prop)) (C_32:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o A_123) B_65)) C_32)) ((semila1052848428le_a_o A_123) ((semila1052848428le_a_o B_65) C_32)))).
% Axiom fact_77_sup__left__commute:(forall (X_45:(nat->Prop)) (Y_18:(nat->Prop)) (Z_9:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_45) ((semila848761471_nat_o Y_18) Z_9))) ((semila848761471_nat_o Y_18) ((semila848761471_nat_o X_45) Z_9)))).
% Axiom fact_78_sup__left__commute:(forall (X_45:nat) (Y_18:nat) (Z_9:nat), (((eq nat) ((semila972727038up_nat X_45) ((semila972727038up_nat Y_18) Z_9))) ((semila972727038up_nat Y_18) ((semila972727038up_nat X_45) Z_9)))).
% Axiom fact_79_sup__left__commute:(forall (X_45:((hoare_2091234717iple_a->Prop)->Prop)) (Y_18:((hoare_2091234717iple_a->Prop)->Prop)) (Z_9:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_45) ((semila2050116131_a_o_o Y_18) Z_9))) ((semila2050116131_a_o_o Y_18) ((semila2050116131_a_o_o X_45) Z_9)))).
% Axiom fact_80_sup__left__commute:(forall (X_45:(hoare_1708887482_state->Prop)) (Y_18:(hoare_1708887482_state->Prop)) (Z_9:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_45) ((semila1122118281tate_o Y_18) Z_9))) ((semila1122118281tate_o Y_18) ((semila1122118281tate_o X_45) Z_9)))).
% Axiom fact_81_sup__left__commute:(forall (X_45:(pname->Prop)) (Y_18:(pname->Prop)) (Z_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_45) ((semila1780557381name_o Y_18) Z_9))) ((semila1780557381name_o Y_18) ((semila1780557381name_o X_45) Z_9)))).
% Axiom fact_82_sup__left__commute:(forall (X_45:Prop) (Y_18:Prop) (Z_9:Prop), ((iff ((semila10642723_sup_o X_45) ((semila10642723_sup_o Y_18) Z_9))) ((semila10642723_sup_o Y_18) ((semila10642723_sup_o X_45) Z_9)))).
% Axiom fact_83_sup__left__commute:(forall (X_45:(hoare_2091234717iple_a->Prop)) (Y_18:(hoare_2091234717iple_a->Prop)) (Z_9:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_45) ((semila1052848428le_a_o Y_18) Z_9))) ((semila1052848428le_a_o Y_18) ((semila1052848428le_a_o X_45) Z_9)))).
% Axiom fact_84_inf__sup__aci_I7_J:(forall (X_44:(nat->Prop)) (Y_17:(nat->Prop)) (Z_8:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_44) ((semila848761471_nat_o Y_17) Z_8))) ((semila848761471_nat_o Y_17) ((semila848761471_nat_o X_44) Z_8)))).
% Axiom fact_85_inf__sup__aci_I7_J:(forall (X_44:nat) (Y_17:nat) (Z_8:nat), (((eq nat) ((semila972727038up_nat X_44) ((semila972727038up_nat Y_17) Z_8))) ((semila972727038up_nat Y_17) ((semila972727038up_nat X_44) Z_8)))).
% Axiom fact_86_inf__sup__aci_I7_J:(forall (X_44:((hoare_2091234717iple_a->Prop)->Prop)) (Y_17:((hoare_2091234717iple_a->Prop)->Prop)) (Z_8:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_44) ((semila2050116131_a_o_o Y_17) Z_8))) ((semila2050116131_a_o_o Y_17) ((semila2050116131_a_o_o X_44) Z_8)))).
% Axiom fact_87_inf__sup__aci_I7_J:(forall (X_44:(hoare_1708887482_state->Prop)) (Y_17:(hoare_1708887482_state->Prop)) (Z_8:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_44) ((semila1122118281tate_o Y_17) Z_8))) ((semila1122118281tate_o Y_17) ((semila1122118281tate_o X_44) Z_8)))).
% Axiom fact_88_inf__sup__aci_I7_J:(forall (X_44:(pname->Prop)) (Y_17:(pname->Prop)) (Z_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_44) ((semila1780557381name_o Y_17) Z_8))) ((semila1780557381name_o Y_17) ((semila1780557381name_o X_44) Z_8)))).
% Axiom fact_89_inf__sup__aci_I7_J:(forall (X_44:Prop) (Y_17:Prop) (Z_8:Prop), ((iff ((semila10642723_sup_o X_44) ((semila10642723_sup_o Y_17) Z_8))) ((semila10642723_sup_o Y_17) ((semila10642723_sup_o X_44) Z_8)))).
% Axiom fact_90_inf__sup__aci_I7_J:(forall (X_44:(hoare_2091234717iple_a->Prop)) (Y_17:(hoare_2091234717iple_a->Prop)) (Z_8:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_44) ((semila1052848428le_a_o Y_17) Z_8))) ((semila1052848428le_a_o Y_17) ((semila1052848428le_a_o X_44) Z_8)))).
% Axiom fact_91_sup_Oleft__commute:(forall (B_64:(nat->Prop)) (A_122:(nat->Prop)) (C_31:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o B_64) ((semila848761471_nat_o A_122) C_31))) ((semila848761471_nat_o A_122) ((semila848761471_nat_o B_64) C_31)))).
% Axiom fact_92_sup_Oleft__commute:(forall (B_64:nat) (A_122:nat) (C_31:nat), (((eq nat) ((semila972727038up_nat B_64) ((semila972727038up_nat A_122) C_31))) ((semila972727038up_nat A_122) ((semila972727038up_nat B_64) C_31)))).
% Axiom fact_93_sup_Oleft__commute:(forall (B_64:((hoare_2091234717iple_a->Prop)->Prop)) (A_122:((hoare_2091234717iple_a->Prop)->Prop)) (C_31:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o B_64) ((semila2050116131_a_o_o A_122) C_31))) ((semila2050116131_a_o_o A_122) ((semila2050116131_a_o_o B_64) C_31)))).
% Axiom fact_94_sup_Oleft__commute:(forall (B_64:(hoare_1708887482_state->Prop)) (A_122:(hoare_1708887482_state->Prop)) (C_31:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o B_64) ((semila1122118281tate_o A_122) C_31))) ((semila1122118281tate_o A_122) ((semila1122118281tate_o B_64) C_31)))).
% Axiom fact_95_sup_Oleft__commute:(forall (B_64:(pname->Prop)) (A_122:(pname->Prop)) (C_31:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_64) ((semila1780557381name_o A_122) C_31))) ((semila1780557381name_o A_122) ((semila1780557381name_o B_64) C_31)))).
% Axiom fact_96_sup_Oleft__commute:(forall (B_64:Prop) (A_122:Prop) (C_31:Prop), ((iff ((semila10642723_sup_o B_64) ((semila10642723_sup_o A_122) C_31))) ((semila10642723_sup_o A_122) ((semila10642723_sup_o B_64) C_31)))).
% Axiom fact_97_sup_Oleft__commute:(forall (B_64:(hoare_2091234717iple_a->Prop)) (A_122:(hoare_2091234717iple_a->Prop)) (C_31:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o B_64) ((semila1052848428le_a_o A_122) C_31))) ((semila1052848428le_a_o A_122) ((semila1052848428le_a_o B_64) C_31)))).
% Axiom fact_98_sup__left__idem:(forall (X_43:(nat->Prop)) (Y_16:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_43) ((semila848761471_nat_o X_43) Y_16))) ((semila848761471_nat_o X_43) Y_16))).
% Axiom fact_99_sup__left__idem:(forall (X_43:nat) (Y_16:nat), (((eq nat) ((semila972727038up_nat X_43) ((semila972727038up_nat X_43) Y_16))) ((semila972727038up_nat X_43) Y_16))).
% Axiom fact_100_sup__left__idem:(forall (X_43:((hoare_2091234717iple_a->Prop)->Prop)) (Y_16:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_43) ((semila2050116131_a_o_o X_43) Y_16))) ((semila2050116131_a_o_o X_43) Y_16))).
% Axiom fact_101_sup__left__idem:(forall (X_43:(hoare_1708887482_state->Prop)) (Y_16:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_43) ((semila1122118281tate_o X_43) Y_16))) ((semila1122118281tate_o X_43) Y_16))).
% Axiom fact_102_sup__left__idem:(forall (X_43:(pname->Prop)) (Y_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_43) ((semila1780557381name_o X_43) Y_16))) ((semila1780557381name_o X_43) Y_16))).
% Axiom fact_103_sup__left__idem:(forall (X_43:Prop) (Y_16:Prop), ((iff ((semila10642723_sup_o X_43) ((semila10642723_sup_o X_43) Y_16))) ((semila10642723_sup_o X_43) Y_16))).
% Axiom fact_104_sup__left__idem:(forall (X_43:(hoare_2091234717iple_a->Prop)) (Y_16:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_43) ((semila1052848428le_a_o X_43) Y_16))) ((semila1052848428le_a_o X_43) Y_16))).
% Axiom fact_105_inf__sup__aci_I8_J:(forall (X_42:(nat->Prop)) (Y_15:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_42) ((semila848761471_nat_o X_42) Y_15))) ((semila848761471_nat_o X_42) Y_15))).
% Axiom fact_106_inf__sup__aci_I8_J:(forall (X_42:nat) (Y_15:nat), (((eq nat) ((semila972727038up_nat X_42) ((semila972727038up_nat X_42) Y_15))) ((semila972727038up_nat X_42) Y_15))).
% Axiom fact_107_inf__sup__aci_I8_J:(forall (X_42:((hoare_2091234717iple_a->Prop)->Prop)) (Y_15:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_42) ((semila2050116131_a_o_o X_42) Y_15))) ((semila2050116131_a_o_o X_42) Y_15))).
% Axiom fact_108_inf__sup__aci_I8_J:(forall (X_42:(hoare_1708887482_state->Prop)) (Y_15:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_42) ((semila1122118281tate_o X_42) Y_15))) ((semila1122118281tate_o X_42) Y_15))).
% Axiom fact_109_inf__sup__aci_I8_J:(forall (X_42:(pname->Prop)) (Y_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_42) ((semila1780557381name_o X_42) Y_15))) ((semila1780557381name_o X_42) Y_15))).
% Axiom fact_110_inf__sup__aci_I8_J:(forall (X_42:Prop) (Y_15:Prop), ((iff ((semila10642723_sup_o X_42) ((semila10642723_sup_o X_42) Y_15))) ((semila10642723_sup_o X_42) Y_15))).
% Axiom fact_111_inf__sup__aci_I8_J:(forall (X_42:(hoare_2091234717iple_a->Prop)) (Y_15:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_42) ((semila1052848428le_a_o X_42) Y_15))) ((semila1052848428le_a_o X_42) Y_15))).
% Axiom fact_112_sup_Oleft__idem:(forall (A_121:(nat->Prop)) (B_63:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_121) ((semila848761471_nat_o A_121) B_63))) ((semila848761471_nat_o A_121) B_63))).
% Axiom fact_113_sup_Oleft__idem:(forall (A_121:nat) (B_63:nat), (((eq nat) ((semila972727038up_nat A_121) ((semila972727038up_nat A_121) B_63))) ((semila972727038up_nat A_121) B_63))).
% Axiom fact_114_sup_Oleft__idem:(forall (A_121:((hoare_2091234717iple_a->Prop)->Prop)) (B_63:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_121) ((semila2050116131_a_o_o A_121) B_63))) ((semila2050116131_a_o_o A_121) B_63))).
% Axiom fact_115_sup_Oleft__idem:(forall (A_121:(hoare_1708887482_state->Prop)) (B_63:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_121) ((semila1122118281tate_o A_121) B_63))) ((semila1122118281tate_o A_121) B_63))).
% Axiom fact_116_sup_Oleft__idem:(forall (A_121:(pname->Prop)) (B_63:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_121) ((semila1780557381name_o A_121) B_63))) ((semila1780557381name_o A_121) B_63))).
% Axiom fact_117_sup_Oleft__idem:(forall (A_121:Prop) (B_63:Prop), ((iff ((semila10642723_sup_o A_121) ((semila10642723_sup_o A_121) B_63))) ((semila10642723_sup_o A_121) B_63))).
% Axiom fact_118_sup_Oleft__idem:(forall (A_121:(hoare_2091234717iple_a->Prop)) (B_63:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_121) ((semila1052848428le_a_o A_121) B_63))) ((semila1052848428le_a_o A_121) B_63))).
% Axiom fact_119_sup__commute:(forall (X_41:(nat->Prop)) (Y_14:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_41) Y_14)) ((semila848761471_nat_o Y_14) X_41))).
% Axiom fact_120_sup__commute:(forall (X_41:nat) (Y_14:nat), (((eq nat) ((semila972727038up_nat X_41) Y_14)) ((semila972727038up_nat Y_14) X_41))).
% Axiom fact_121_sup__commute:(forall (X_41:((hoare_2091234717iple_a->Prop)->Prop)) (Y_14:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_41) Y_14)) ((semila2050116131_a_o_o Y_14) X_41))).
% Axiom fact_122_sup__commute:(forall (X_41:(hoare_1708887482_state->Prop)) (Y_14:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_41) Y_14)) ((semila1122118281tate_o Y_14) X_41))).
% Axiom fact_123_sup__commute:(forall (X_41:(pname->Prop)) (Y_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_41) Y_14)) ((semila1780557381name_o Y_14) X_41))).
% Axiom fact_124_sup__commute:(forall (X_41:Prop) (Y_14:Prop), ((iff ((semila10642723_sup_o X_41) Y_14)) ((semila10642723_sup_o Y_14) X_41))).
% Axiom fact_125_sup__commute:(forall (X_41:(hoare_2091234717iple_a->Prop)) (Y_14:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_41) Y_14)) ((semila1052848428le_a_o Y_14) X_41))).
% Axiom fact_126_inf__sup__aci_I5_J:(forall (X_40:(nat->Prop)) (Y_13:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_40) Y_13)) ((semila848761471_nat_o Y_13) X_40))).
% Axiom fact_127_inf__sup__aci_I5_J:(forall (X_40:nat) (Y_13:nat), (((eq nat) ((semila972727038up_nat X_40) Y_13)) ((semila972727038up_nat Y_13) X_40))).
% Axiom fact_128_inf__sup__aci_I5_J:(forall (X_40:((hoare_2091234717iple_a->Prop)->Prop)) (Y_13:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_40) Y_13)) ((semila2050116131_a_o_o Y_13) X_40))).
% Axiom fact_129_inf__sup__aci_I5_J:(forall (X_40:(hoare_1708887482_state->Prop)) (Y_13:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_40) Y_13)) ((semila1122118281tate_o Y_13) X_40))).
% Axiom fact_130_inf__sup__aci_I5_J:(forall (X_40:(pname->Prop)) (Y_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_40) Y_13)) ((semila1780557381name_o Y_13) X_40))).
% Axiom fact_131_inf__sup__aci_I5_J:(forall (X_40:Prop) (Y_13:Prop), ((iff ((semila10642723_sup_o X_40) Y_13)) ((semila10642723_sup_o Y_13) X_40))).
% Axiom fact_132_inf__sup__aci_I5_J:(forall (X_40:(hoare_2091234717iple_a->Prop)) (Y_13:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_40) Y_13)) ((semila1052848428le_a_o Y_13) X_40))).
% Axiom fact_133_sup_Ocommute:(forall (A_120:(nat->Prop)) (B_62:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_120) B_62)) ((semila848761471_nat_o B_62) A_120))).
% Axiom fact_134_sup_Ocommute:(forall (A_120:nat) (B_62:nat), (((eq nat) ((semila972727038up_nat A_120) B_62)) ((semila972727038up_nat B_62) A_120))).
% Axiom fact_135_sup_Ocommute:(forall (A_120:((hoare_2091234717iple_a->Prop)->Prop)) (B_62:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_120) B_62)) ((semila2050116131_a_o_o B_62) A_120))).
% Axiom fact_136_sup_Ocommute:(forall (A_120:(hoare_1708887482_state->Prop)) (B_62:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_120) B_62)) ((semila1122118281tate_o B_62) A_120))).
% Axiom fact_137_sup_Ocommute:(forall (A_120:(pname->Prop)) (B_62:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_120) B_62)) ((semila1780557381name_o B_62) A_120))).
% Axiom fact_138_sup_Ocommute:(forall (A_120:Prop) (B_62:Prop), ((iff ((semila10642723_sup_o A_120) B_62)) ((semila10642723_sup_o B_62) A_120))).
% Axiom fact_139_sup_Ocommute:(forall (A_120:(hoare_2091234717iple_a->Prop)) (B_62:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_120) B_62)) ((semila1052848428le_a_o B_62) A_120))).
% Axiom fact_140_sup__idem:(forall (X_39:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_39) X_39)) X_39)).
% Axiom fact_141_sup__idem:(forall (X_39:nat), (((eq nat) ((semila972727038up_nat X_39) X_39)) X_39)).
% Axiom fact_142_sup__idem:(forall (X_39:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_39) X_39)) X_39)).
% Axiom fact_143_sup__idem:(forall (X_39:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_39) X_39)) X_39)).
% Axiom fact_144_sup__idem:(forall (X_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_39) X_39)) X_39)).
% Axiom fact_145_sup__idem:(forall (X_39:Prop), ((iff ((semila10642723_sup_o X_39) X_39)) X_39)).
% Axiom fact_146_sup__idem:(forall (X_39:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_39) X_39)) X_39)).
% Axiom fact_147_sup_Oidem:(forall (A_119:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_119) A_119)) A_119)).
% Axiom fact_148_sup_Oidem:(forall (A_119:nat), (((eq nat) ((semila972727038up_nat A_119) A_119)) A_119)).
% Axiom fact_149_sup_Oidem:(forall (A_119:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_119) A_119)) A_119)).
% Axiom fact_150_sup_Oidem:(forall (A_119:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_119) A_119)) A_119)).
% Axiom fact_151_sup_Oidem:(forall (A_119:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_119) A_119)) A_119)).
% Axiom fact_152_sup_Oidem:(forall (A_119:Prop), ((iff ((semila10642723_sup_o A_119) A_119)) A_119)).
% Axiom fact_153_sup_Oidem:(forall (A_119:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_119) A_119)) A_119)).
% Axiom fact_154_rev__image__eqI:(forall (B_61:nat) (F_46:(nat->nat)) (X_38:nat) (A_118:(nat->Prop)), (((member_nat X_38) A_118)->((((eq nat) B_61) (F_46 X_38))->((member_nat B_61) ((image_nat_nat F_46) A_118))))).
% Axiom fact_155_rev__image__eqI:(forall (B_61:hoare_1708887482_state) (F_46:(pname->hoare_1708887482_state)) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq hoare_1708887482_state) B_61) (F_46 X_38))->((member451959335_state B_61) ((image_1116629049_state F_46) A_118))))).
% Axiom fact_156_rev__image__eqI:(forall (B_61:nat) (F_46:(pname->nat)) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq nat) B_61) (F_46 X_38))->((member_nat B_61) ((image_pname_nat F_46) A_118))))).
% Axiom fact_157_rev__image__eqI:(forall (B_61:(hoare_2091234717iple_a->Prop)) (F_46:(pname->(hoare_2091234717iple_a->Prop))) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq (hoare_2091234717iple_a->Prop)) B_61) (F_46 X_38))->((member99268621le_a_o B_61) ((image_742317343le_a_o F_46) A_118))))).
% Axiom fact_158_rev__image__eqI:(forall (B_61:pname) (F_46:(nat->pname)) (X_38:nat) (A_118:(nat->Prop)), (((member_nat X_38) A_118)->((((eq pname) B_61) (F_46 X_38))->((member_pname B_61) ((image_nat_pname F_46) A_118))))).
% Axiom fact_159_rev__image__eqI:(forall (B_61:pname) (F_46:((hoare_2091234717iple_a->Prop)->pname)) (X_38:(hoare_2091234717iple_a->Prop)) (A_118:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o X_38) A_118)->((((eq pname) B_61) (F_46 X_38))->((member_pname B_61) ((image_1908519857_pname F_46) A_118))))).
% Axiom fact_160_rev__image__eqI:(forall (B_61:pname) (F_46:(hoare_2091234717iple_a->pname)) (X_38:hoare_2091234717iple_a) (A_118:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a X_38) A_118)->((((eq pname) B_61) (F_46 X_38))->((member_pname B_61) ((image_924789612_pname F_46) A_118))))).
% Axiom fact_161_rev__image__eqI:(forall (B_61:hoare_2091234717iple_a) (F_46:(pname->hoare_2091234717iple_a)) (X_38:pname) (A_118:(pname->Prop)), (((member_pname X_38) A_118)->((((eq hoare_2091234717iple_a) B_61) (F_46 X_38))->((member290856304iple_a B_61) ((image_231808478iple_a F_46) A_118))))).
% Axiom fact_162_imageI:(forall (F_45:(nat->nat)) (X_37:nat) (A_117:(nat->Prop)), (((member_nat X_37) A_117)->((member_nat (F_45 X_37)) ((image_nat_nat F_45) A_117)))).
% Axiom fact_163_imageI:(forall (F_45:(pname->hoare_1708887482_state)) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member451959335_state (F_45 X_37)) ((image_1116629049_state F_45) A_117)))).
% Axiom fact_164_imageI:(forall (F_45:(pname->nat)) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member_nat (F_45 X_37)) ((image_pname_nat F_45) A_117)))).
% Axiom fact_165_imageI:(forall (F_45:(pname->(hoare_2091234717iple_a->Prop))) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member99268621le_a_o (F_45 X_37)) ((image_742317343le_a_o F_45) A_117)))).
% Axiom fact_166_imageI:(forall (F_45:(nat->pname)) (X_37:nat) (A_117:(nat->Prop)), (((member_nat X_37) A_117)->((member_pname (F_45 X_37)) ((image_nat_pname F_45) A_117)))).
% Axiom fact_167_imageI:(forall (F_45:((hoare_2091234717iple_a->Prop)->pname)) (X_37:(hoare_2091234717iple_a->Prop)) (A_117:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o X_37) A_117)->((member_pname (F_45 X_37)) ((image_1908519857_pname F_45) A_117)))).
% Axiom fact_168_imageI:(forall (F_45:(hoare_2091234717iple_a->pname)) (X_37:hoare_2091234717iple_a) (A_117:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a X_37) A_117)->((member_pname (F_45 X_37)) ((image_924789612_pname F_45) A_117)))).
% Axiom fact_169_imageI:(forall (F_45:(pname->hoare_2091234717iple_a)) (X_37:pname) (A_117:(pname->Prop)), (((member_pname X_37) A_117)->((member290856304iple_a (F_45 X_37)) ((image_231808478iple_a F_45) A_117)))).
% Axiom fact_170_image__iff:(forall (Z_7:nat) (F_44:(nat->nat)) (A_116:(nat->Prop)), ((iff ((member_nat Z_7) ((image_nat_nat F_44) A_116))) ((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_116)) (((eq nat) Z_7) (F_44 X))))))).
% Axiom fact_171_image__iff:(forall (Z_7:hoare_1708887482_state) (F_44:(pname->hoare_1708887482_state)) (A_116:(pname->Prop)), ((iff ((member451959335_state Z_7) ((image_1116629049_state F_44) A_116))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_116)) (((eq hoare_1708887482_state) Z_7) (F_44 X))))))).
% Axiom fact_172_image__iff:(forall (Z_7:hoare_2091234717iple_a) (F_44:(pname->hoare_2091234717iple_a)) (A_116:(pname->Prop)), ((iff ((member290856304iple_a Z_7) ((image_231808478iple_a F_44) A_116))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_116)) (((eq hoare_2091234717iple_a) Z_7) (F_44 X))))))).
% Axiom fact_173_UnI2:(forall (A_115:(nat->Prop)) (C_30:nat) (B_60:(nat->Prop)), (((member_nat C_30) B_60)->((member_nat C_30) ((semila848761471_nat_o A_115) B_60)))).
% Axiom fact_174_UnI2:(forall (A_115:((hoare_2091234717iple_a->Prop)->Prop)) (C_30:(hoare_2091234717iple_a->Prop)) (B_60:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_30) B_60)->((member99268621le_a_o C_30) ((semila2050116131_a_o_o A_115) B_60)))).
% Axiom fact_175_UnI2:(forall (A_115:(hoare_1708887482_state->Prop)) (C_30:hoare_1708887482_state) (B_60:(hoare_1708887482_state->Prop)), (((member451959335_state C_30) B_60)->((member451959335_state C_30) ((semila1122118281tate_o A_115) B_60)))).
% Axiom fact_176_UnI2:(forall (A_115:(hoare_2091234717iple_a->Prop)) (C_30:hoare_2091234717iple_a) (B_60:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_30) B_60)->((member290856304iple_a C_30) ((semila1052848428le_a_o A_115) B_60)))).
% Axiom fact_177_UnI2:(forall (A_115:(pname->Prop)) (C_30:pname) (B_60:(pname->Prop)), (((member_pname C_30) B_60)->((member_pname C_30) ((semila1780557381name_o A_115) B_60)))).
% Axiom fact_178_UnI1:(forall (B_59:(nat->Prop)) (C_29:nat) (A_114:(nat->Prop)), (((member_nat C_29) A_114)->((member_nat C_29) ((semila848761471_nat_o A_114) B_59)))).
% Axiom fact_179_UnI1:(forall (B_59:((hoare_2091234717iple_a->Prop)->Prop)) (C_29:(hoare_2091234717iple_a->Prop)) (A_114:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_29) A_114)->((member99268621le_a_o C_29) ((semila2050116131_a_o_o A_114) B_59)))).
% Axiom fact_180_UnI1:(forall (B_59:(hoare_1708887482_state->Prop)) (C_29:hoare_1708887482_state) (A_114:(hoare_1708887482_state->Prop)), (((member451959335_state C_29) A_114)->((member451959335_state C_29) ((semila1122118281tate_o A_114) B_59)))).
% Axiom fact_181_UnI1:(forall (B_59:(hoare_2091234717iple_a->Prop)) (C_29:hoare_2091234717iple_a) (A_114:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_29) A_114)->((member290856304iple_a C_29) ((semila1052848428le_a_o A_114) B_59)))).
% Axiom fact_182_UnI1:(forall (B_59:(pname->Prop)) (C_29:pname) (A_114:(pname->Prop)), (((member_pname C_29) A_114)->((member_pname C_29) ((semila1780557381name_o A_114) B_59)))).
% Axiom fact_183_sup1I2:(forall (A_113:(nat->Prop)) (B_58:(nat->Prop)) (X_36:nat), ((B_58 X_36)->(((semila848761471_nat_o A_113) B_58) X_36))).
% Axiom fact_184_sup1I2:(forall (A_113:((hoare_2091234717iple_a->Prop)->Prop)) (B_58:((hoare_2091234717iple_a->Prop)->Prop)) (X_36:(hoare_2091234717iple_a->Prop)), ((B_58 X_36)->(((semila2050116131_a_o_o A_113) B_58) X_36))).
% Axiom fact_185_sup1I2:(forall (A_113:(hoare_1708887482_state->Prop)) (B_58:(hoare_1708887482_state->Prop)) (X_36:hoare_1708887482_state), ((B_58 X_36)->(((semila1122118281tate_o A_113) B_58) X_36))).
% Axiom fact_186_sup1I2:(forall (A_113:(pname->Prop)) (B_58:(pname->Prop)) (X_36:pname), ((B_58 X_36)->(((semila1780557381name_o A_113) B_58) X_36))).
% Axiom fact_187_sup1I2:(forall (A_113:(hoare_2091234717iple_a->Prop)) (B_58:(hoare_2091234717iple_a->Prop)) (X_36:hoare_2091234717iple_a), ((B_58 X_36)->(((semila1052848428le_a_o A_113) B_58) X_36))).
% Axiom fact_188_sup1I1:(forall (B_57:(nat->Prop)) (A_112:(nat->Prop)) (X_35:nat), ((A_112 X_35)->(((semila848761471_nat_o A_112) B_57) X_35))).
% Axiom fact_189_sup1I1:(forall (B_57:((hoare_2091234717iple_a->Prop)->Prop)) (A_112:((hoare_2091234717iple_a->Prop)->Prop)) (X_35:(hoare_2091234717iple_a->Prop)), ((A_112 X_35)->(((semila2050116131_a_o_o A_112) B_57) X_35))).
% Axiom fact_190_sup1I1:(forall (B_57:(hoare_1708887482_state->Prop)) (A_112:(hoare_1708887482_state->Prop)) (X_35:hoare_1708887482_state), ((A_112 X_35)->(((semila1122118281tate_o A_112) B_57) X_35))).
% Axiom fact_191_sup1I1:(forall (B_57:(pname->Prop)) (A_112:(pname->Prop)) (X_35:pname), ((A_112 X_35)->(((semila1780557381name_o A_112) B_57) X_35))).
% Axiom fact_192_sup1I1:(forall (B_57:(hoare_2091234717iple_a->Prop)) (A_112:(hoare_2091234717iple_a->Prop)) (X_35:hoare_2091234717iple_a), ((A_112 X_35)->(((semila1052848428le_a_o A_112) B_57) X_35))).
% Axiom fact_193_ball__Un:(forall (P_35:(nat->Prop)) (A_111:(nat->Prop)) (B_56:(nat->Prop)), ((iff (forall (X:nat), (((member_nat X) ((semila848761471_nat_o A_111) B_56))->(P_35 X)))) ((and (forall (X:nat), (((member_nat X) A_111)->(P_35 X)))) (forall (X:nat), (((member_nat X) B_56)->(P_35 X)))))).
% Axiom fact_194_ball__Un:(forall (P_35:((hoare_2091234717iple_a->Prop)->Prop)) (A_111:((hoare_2091234717iple_a->Prop)->Prop)) (B_56:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) ((semila2050116131_a_o_o A_111) B_56))->(P_35 X)))) ((and (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) A_111)->(P_35 X)))) (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) B_56)->(P_35 X)))))).
% Axiom fact_195_ball__Un:(forall (P_35:(hoare_1708887482_state->Prop)) (A_111:(hoare_1708887482_state->Prop)) (B_56:(hoare_1708887482_state->Prop)), ((iff (forall (X:hoare_1708887482_state), (((member451959335_state X) ((semila1122118281tate_o A_111) B_56))->(P_35 X)))) ((and (forall (X:hoare_1708887482_state), (((member451959335_state X) A_111)->(P_35 X)))) (forall (X:hoare_1708887482_state), (((member451959335_state X) B_56)->(P_35 X)))))).
% Axiom fact_196_ball__Un:(forall (P_35:(pname->Prop)) (A_111:(pname->Prop)) (B_56:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) ((semila1780557381name_o A_111) B_56))->(P_35 X)))) ((and (forall (X:pname), (((member_pname X) A_111)->(P_35 X)))) (forall (X:pname), (((member_pname X) B_56)->(P_35 X)))))).
% Axiom fact_197_ball__Un:(forall (P_35:(hoare_2091234717iple_a->Prop)) (A_111:(hoare_2091234717iple_a->Prop)) (B_56:(hoare_2091234717iple_a->Prop)), ((iff (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) ((semila1052848428le_a_o A_111) B_56))->(P_35 X)))) ((and (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) A_111)->(P_35 X)))) (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) B_56)->(P_35 X)))))).
% Axiom fact_198_bex__Un:(forall (P_34:(nat->Prop)) (A_110:(nat->Prop)) (B_55:(nat->Prop)), ((iff ((ex nat) (fun (X:nat)=> ((and ((member_nat X) ((semila848761471_nat_o A_110) B_55))) (P_34 X))))) ((or ((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_110)) (P_34 X))))) ((ex nat) (fun (X:nat)=> ((and ((member_nat X) B_55)) (P_34 X))))))).
% Axiom fact_199_bex__Un:(forall (P_34:((hoare_2091234717iple_a->Prop)->Prop)) (A_110:((hoare_2091234717iple_a->Prop)->Prop)) (B_55:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) ((semila2050116131_a_o_o A_110) B_55))) (P_34 X))))) ((or ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_110)) (P_34 X))))) ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) B_55)) (P_34 X))))))).
% Axiom fact_200_bex__Un:(forall (P_34:(hoare_1708887482_state->Prop)) (A_110:(hoare_1708887482_state->Prop)) (B_55:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((and ((member451959335_state X) ((semila1122118281tate_o A_110) B_55))) (P_34 X))))) ((or ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((and ((member451959335_state X) A_110)) (P_34 X))))) ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((and ((member451959335_state X) B_55)) (P_34 X))))))).
% Axiom fact_201_bex__Un:(forall (P_34:(pname->Prop)) (A_110:(pname->Prop)) (B_55:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((and ((member_pname X) ((semila1780557381name_o A_110) B_55))) (P_34 X))))) ((or ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_110)) (P_34 X))))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) B_55)) (P_34 X))))))).
% Axiom fact_202_bex__Un:(forall (P_34:(hoare_2091234717iple_a->Prop)) (A_110:(hoare_2091234717iple_a->Prop)) (B_55:(hoare_2091234717iple_a->Prop)), ((iff ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) ((semila1052848428le_a_o A_110) B_55))) (P_34 X))))) ((or ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_110)) (P_34 X))))) ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) B_55)) (P_34 X))))))).
% Axiom fact_203_Un__assoc:(forall (A_109:(nat->Prop)) (B_54:(nat->Prop)) (C_28:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((semila848761471_nat_o A_109) B_54)) C_28)) ((semila848761471_nat_o A_109) ((semila848761471_nat_o B_54) C_28)))).
% Axiom fact_204_Un__assoc:(forall (A_109:((hoare_2091234717iple_a->Prop)->Prop)) (B_54:((hoare_2091234717iple_a->Prop)->Prop)) (C_28:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((semila2050116131_a_o_o A_109) B_54)) C_28)) ((semila2050116131_a_o_o A_109) ((semila2050116131_a_o_o B_54) C_28)))).
% Axiom fact_205_Un__assoc:(forall (A_109:(hoare_1708887482_state->Prop)) (B_54:(hoare_1708887482_state->Prop)) (C_28:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((semila1122118281tate_o A_109) B_54)) C_28)) ((semila1122118281tate_o A_109) ((semila1122118281tate_o B_54) C_28)))).
% Axiom fact_206_Un__assoc:(forall (A_109:(pname->Prop)) (B_54:(pname->Prop)) (C_28:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_109) B_54)) C_28)) ((semila1780557381name_o A_109) ((semila1780557381name_o B_54) C_28)))).
% Axiom fact_207_Un__assoc:(forall (A_109:(hoare_2091234717iple_a->Prop)) (B_54:(hoare_2091234717iple_a->Prop)) (C_28:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((semila1052848428le_a_o A_109) B_54)) C_28)) ((semila1052848428le_a_o A_109) ((semila1052848428le_a_o B_54) C_28)))).
% Axiom fact_208_Un__iff:(forall (C_27:nat) (A_108:(nat->Prop)) (B_53:(nat->Prop)), ((iff ((member_nat C_27) ((semila848761471_nat_o A_108) B_53))) ((or ((member_nat C_27) A_108)) ((member_nat C_27) B_53)))).
% Axiom fact_209_Un__iff:(forall (C_27:(hoare_2091234717iple_a->Prop)) (A_108:((hoare_2091234717iple_a->Prop)->Prop)) (B_53:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o C_27) ((semila2050116131_a_o_o A_108) B_53))) ((or ((member99268621le_a_o C_27) A_108)) ((member99268621le_a_o C_27) B_53)))).
% Axiom fact_210_Un__iff:(forall (C_27:hoare_1708887482_state) (A_108:(hoare_1708887482_state->Prop)) (B_53:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state C_27) ((semila1122118281tate_o A_108) B_53))) ((or ((member451959335_state C_27) A_108)) ((member451959335_state C_27) B_53)))).
% Axiom fact_211_Un__iff:(forall (C_27:hoare_2091234717iple_a) (A_108:(hoare_2091234717iple_a->Prop)) (B_53:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a C_27) ((semila1052848428le_a_o A_108) B_53))) ((or ((member290856304iple_a C_27) A_108)) ((member290856304iple_a C_27) B_53)))).
% Axiom fact_212_Un__iff:(forall (C_27:pname) (A_108:(pname->Prop)) (B_53:(pname->Prop)), ((iff ((member_pname C_27) ((semila1780557381name_o A_108) B_53))) ((or ((member_pname C_27) A_108)) ((member_pname C_27) B_53)))).
% Axiom fact_213_Un__left__commute:(forall (A_107:(nat->Prop)) (B_52:(nat->Prop)) (C_26:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_107) ((semila848761471_nat_o B_52) C_26))) ((semila848761471_nat_o B_52) ((semila848761471_nat_o A_107) C_26)))).
% Axiom fact_214_Un__left__commute:(forall (A_107:((hoare_2091234717iple_a->Prop)->Prop)) (B_52:((hoare_2091234717iple_a->Prop)->Prop)) (C_26:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_107) ((semila2050116131_a_o_o B_52) C_26))) ((semila2050116131_a_o_o B_52) ((semila2050116131_a_o_o A_107) C_26)))).
% Axiom fact_215_Un__left__commute:(forall (A_107:(hoare_1708887482_state->Prop)) (B_52:(hoare_1708887482_state->Prop)) (C_26:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_107) ((semila1122118281tate_o B_52) C_26))) ((semila1122118281tate_o B_52) ((semila1122118281tate_o A_107) C_26)))).
% Axiom fact_216_Un__left__commute:(forall (A_107:(pname->Prop)) (B_52:(pname->Prop)) (C_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_107) ((semila1780557381name_o B_52) C_26))) ((semila1780557381name_o B_52) ((semila1780557381name_o A_107) C_26)))).
% Axiom fact_217_Un__left__commute:(forall (A_107:(hoare_2091234717iple_a->Prop)) (B_52:(hoare_2091234717iple_a->Prop)) (C_26:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_107) ((semila1052848428le_a_o B_52) C_26))) ((semila1052848428le_a_o B_52) ((semila1052848428le_a_o A_107) C_26)))).
% Axiom fact_218_Un__left__absorb:(forall (A_106:(nat->Prop)) (B_51:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_106) ((semila848761471_nat_o A_106) B_51))) ((semila848761471_nat_o A_106) B_51))).
% Axiom fact_219_Un__left__absorb:(forall (A_106:((hoare_2091234717iple_a->Prop)->Prop)) (B_51:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_106) ((semila2050116131_a_o_o A_106) B_51))) ((semila2050116131_a_o_o A_106) B_51))).
% Axiom fact_220_Un__left__absorb:(forall (A_106:(hoare_1708887482_state->Prop)) (B_51:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_106) ((semila1122118281tate_o A_106) B_51))) ((semila1122118281tate_o A_106) B_51))).
% Axiom fact_221_Un__left__absorb:(forall (A_106:(pname->Prop)) (B_51:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_106) ((semila1780557381name_o A_106) B_51))) ((semila1780557381name_o A_106) B_51))).
% Axiom fact_222_Un__left__absorb:(forall (A_106:(hoare_2091234717iple_a->Prop)) (B_51:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_106) ((semila1052848428le_a_o A_106) B_51))) ((semila1052848428le_a_o A_106) B_51))).
% Axiom fact_223_Un__commute:(forall (A_105:(nat->Prop)) (B_50:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_105) B_50)) ((semila848761471_nat_o B_50) A_105))).
% Axiom fact_224_Un__commute:(forall (A_105:((hoare_2091234717iple_a->Prop)->Prop)) (B_50:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_105) B_50)) ((semila2050116131_a_o_o B_50) A_105))).
% Axiom fact_225_Un__commute:(forall (A_105:(hoare_1708887482_state->Prop)) (B_50:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_105) B_50)) ((semila1122118281tate_o B_50) A_105))).
% Axiom fact_226_Un__commute:(forall (A_105:(pname->Prop)) (B_50:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_105) B_50)) ((semila1780557381name_o B_50) A_105))).
% Axiom fact_227_Un__commute:(forall (A_105:(hoare_2091234717iple_a->Prop)) (B_50:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_105) B_50)) ((semila1052848428le_a_o B_50) A_105))).
% Axiom fact_228_Un__def:(forall (A_104:((hoare_2091234717iple_a->Prop)->Prop)) (B_49:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_104) B_49)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or ((member99268621le_a_o X) A_104)) ((member99268621le_a_o X) B_49)))))).
% Axiom fact_229_Un__def:(forall (A_104:(hoare_1708887482_state->Prop)) (B_49:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_104) B_49)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((or ((member451959335_state X) A_104)) ((member451959335_state X) B_49)))))).
% Axiom fact_230_Un__def:(forall (A_104:(hoare_2091234717iple_a->Prop)) (B_49:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_104) B_49)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or ((member290856304iple_a X) A_104)) ((member290856304iple_a X) B_49)))))).
% Axiom fact_231_Un__def:(forall (A_104:(nat->Prop)) (B_49:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_104) B_49)) (collect_nat (fun (X:nat)=> ((or ((member_nat X) A_104)) ((member_nat X) B_49)))))).
% Axiom fact_232_Un__def:(forall (A_104:(pname->Prop)) (B_49:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_104) B_49)) (collect_pname (fun (X:pname)=> ((or ((member_pname X) A_104)) ((member_pname X) B_49)))))).
% Axiom fact_233_Un__absorb:(forall (A_103:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_103) A_103)) A_103)).
% Axiom fact_234_Un__absorb:(forall (A_103:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_103) A_103)) A_103)).
% Axiom fact_235_Un__absorb:(forall (A_103:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_103) A_103)) A_103)).
% Axiom fact_236_Un__absorb:(forall (A_103:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_103) A_103)) A_103)).
% Axiom fact_237_Un__absorb:(forall (A_103:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_103) A_103)) A_103)).
% Axiom fact_238_image__ident:(forall (Y_12:(nat->Prop)), (((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> X)) Y_12)) Y_12)).
% Axiom fact_239_image__image:(forall (F_43:(hoare_2091234717iple_a->hoare_1708887482_state)) (G_22:(pname->hoare_2091234717iple_a)) (A_102:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1884482962_state F_43) ((image_231808478iple_a G_22) A_102))) ((image_1116629049_state (fun (X:pname)=> (F_43 (G_22 X)))) A_102))).
% Axiom fact_240_image__image:(forall (F_43:(hoare_1708887482_state->hoare_2091234717iple_a)) (G_22:(pname->hoare_1708887482_state)) (A_102:(pname->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_293283184iple_a F_43) ((image_1116629049_state G_22) A_102))) ((image_231808478iple_a (fun (X:pname)=> (F_43 (G_22 X)))) A_102))).
% Axiom fact_241_sup__Un__eq:(forall (R_2:(nat->Prop)) (S_5:(nat->Prop)) (X:nat), ((iff (((semila848761471_nat_o (fun (Y_7:nat)=> ((member_nat Y_7) R_2))) (fun (Y_7:nat)=> ((member_nat Y_7) S_5))) X)) ((member_nat X) ((semila848761471_nat_o R_2) S_5)))).
% Axiom fact_242_sup__Un__eq:(forall (R_2:((hoare_2091234717iple_a->Prop)->Prop)) (S_5:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), ((iff (((semila2050116131_a_o_o (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) R_2))) (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) S_5))) X)) ((member99268621le_a_o X) ((semila2050116131_a_o_o R_2) S_5)))).
% Axiom fact_243_sup__Un__eq:(forall (R_2:(hoare_1708887482_state->Prop)) (S_5:(hoare_1708887482_state->Prop)) (X:hoare_1708887482_state), ((iff (((semila1122118281tate_o (fun (Y_7:hoare_1708887482_state)=> ((member451959335_state Y_7) R_2))) (fun (Y_7:hoare_1708887482_state)=> ((member451959335_state Y_7) S_5))) X)) ((member451959335_state X) ((semila1122118281tate_o R_2) S_5)))).
% Axiom fact_244_sup__Un__eq:(forall (R_2:(hoare_2091234717iple_a->Prop)) (S_5:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila1052848428le_a_o (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) R_2))) (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) S_5))) X)) ((member290856304iple_a X) ((semila1052848428le_a_o R_2) S_5)))).
% Axiom fact_245_sup__Un__eq:(forall (R_2:(pname->Prop)) (S_5:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o (fun (Y_7:pname)=> ((member_pname Y_7) R_2))) (fun (Y_7:pname)=> ((member_pname Y_7) S_5))) X)) ((member_pname X) ((semila1780557381name_o R_2) S_5)))).
% Axiom fact_246_Collect__disj__eq:(forall (P_33:(pname->Prop)) (Q_19:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((or (P_33 X)) (Q_19 X))))) ((semila1780557381name_o (collect_pname P_33)) (collect_pname Q_19)))).
% Axiom fact_247_Collect__disj__eq:(forall (P_33:((hoare_2091234717iple_a->Prop)->Prop)) (Q_19:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or (P_33 X)) (Q_19 X))))) ((semila2050116131_a_o_o (collec1008234059le_a_o P_33)) (collec1008234059le_a_o Q_19)))).
% Axiom fact_248_Collect__disj__eq:(forall (P_33:(hoare_1708887482_state->Prop)) (Q_19:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((or (P_33 X)) (Q_19 X))))) ((semila1122118281tate_o (collec1568722789_state P_33)) (collec1568722789_state Q_19)))).
% Axiom fact_249_Collect__disj__eq:(forall (P_33:(hoare_2091234717iple_a->Prop)) (Q_19:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or (P_33 X)) (Q_19 X))))) ((semila1052848428le_a_o (collec992574898iple_a P_33)) (collec992574898iple_a Q_19)))).
% Axiom fact_250_Collect__disj__eq:(forall (P_33:(nat->Prop)) (Q_19:(nat->Prop)), (((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((or (P_33 X)) (Q_19 X))))) ((semila848761471_nat_o (collect_nat P_33)) (collect_nat Q_19)))).
% Axiom fact_251_imageE:(forall (B_48:nat) (F_42:(nat->nat)) (A_101:(nat->Prop)), (((member_nat B_48) ((image_nat_nat F_42) A_101))->((forall (X:nat), ((((eq nat) B_48) (F_42 X))->(((member_nat X) A_101)->False)))->False))).
% Axiom fact_252_imageE:(forall (B_48:pname) (F_42:(nat->pname)) (A_101:(nat->Prop)), (((member_pname B_48) ((image_nat_pname F_42) A_101))->((forall (X:nat), ((((eq pname) B_48) (F_42 X))->(((member_nat X) A_101)->False)))->False))).
% Axiom fact_253_imageE:(forall (B_48:pname) (F_42:((hoare_2091234717iple_a->Prop)->pname)) (A_101:((hoare_2091234717iple_a->Prop)->Prop)), (((member_pname B_48) ((image_1908519857_pname F_42) A_101))->((forall (X:(hoare_2091234717iple_a->Prop)), ((((eq pname) B_48) (F_42 X))->(((member99268621le_a_o X) A_101)->False)))->False))).
% Axiom fact_254_imageE:(forall (B_48:pname) (F_42:(hoare_2091234717iple_a->pname)) (A_101:(hoare_2091234717iple_a->Prop)), (((member_pname B_48) ((image_924789612_pname F_42) A_101))->((forall (X:hoare_2091234717iple_a), ((((eq pname) B_48) (F_42 X))->(((member290856304iple_a X) A_101)->False)))->False))).
% Axiom fact_255_imageE:(forall (B_48:hoare_1708887482_state) (F_42:(pname->hoare_1708887482_state)) (A_101:(pname->Prop)), (((member451959335_state B_48) ((image_1116629049_state F_42) A_101))->((forall (X:pname), ((((eq hoare_1708887482_state) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False))).
% Axiom fact_256_imageE:(forall (B_48:nat) (F_42:(pname->nat)) (A_101:(pname->Prop)), (((member_nat B_48) ((image_pname_nat F_42) A_101))->((forall (X:pname), ((((eq nat) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False))).
% Axiom fact_257_imageE:(forall (B_48:(hoare_2091234717iple_a->Prop)) (F_42:(pname->(hoare_2091234717iple_a->Prop))) (A_101:(pname->Prop)), (((member99268621le_a_o B_48) ((image_742317343le_a_o F_42) A_101))->((forall (X:pname), ((((eq (hoare_2091234717iple_a->Prop)) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False))).
% Axiom fact_258_imageE:(forall (B_48:hoare_2091234717iple_a) (F_42:(pname->hoare_2091234717iple_a)) (A_101:(pname->Prop)), (((member290856304iple_a B_48) ((image_231808478iple_a F_42) A_101))->((forall (X:pname), ((((eq hoare_2091234717iple_a) B_48) (F_42 X))->(((member_pname X) A_101)->False)))->False))).
% Axiom fact_259_Body__triple__valid__Suc:(forall (N_8:nat) (P_32:(state->(state->Prop))) (Pn_6:pname) (Q_18:(state->(state->Prop))), ((iff ((hoare_23738522_state N_8) (((hoare_858012674_state P_32) (the_com (body_1 Pn_6))) Q_18))) ((hoare_23738522_state (suc N_8)) (((hoare_858012674_state P_32) (body Pn_6)) Q_18)))).
% Axiom fact_260_Body__triple__valid__Suc:(forall (N_8:nat) (P_32:(x_a->(state->Prop))) (Pn_6:pname) (Q_18:(x_a->(state->Prop))), ((iff ((hoare_1421888935alid_a N_8) (((hoare_657976383iple_a P_32) (the_com (body_1 Pn_6))) Q_18))) ((hoare_1421888935alid_a (suc N_8)) (((hoare_657976383iple_a P_32) (body Pn_6)) Q_18)))).
% Axiom fact_261_triple_Oexhaust:(forall (Y_11:hoare_2091234717iple_a), ((forall (Fun1_2:(x_a->(state->Prop))) (Com_4:com) (Fun2_2:(x_a->(state->Prop))), (not (((eq hoare_2091234717iple_a) Y_11) (((hoare_657976383iple_a Fun1_2) Com_4) Fun2_2))))->False)).
% Axiom fact_262_triple_Oexhaust:(forall (Y_11:hoare_1708887482_state), ((forall (Fun1_2:(state->(state->Prop))) (Com_4:com) (Fun2_2:(state->(state->Prop))), (not (((eq hoare_1708887482_state) Y_11) (((hoare_858012674_state Fun1_2) Com_4) Fun2_2))))->False)).
% Axiom fact_263_Body1:(forall (Pn_5:pname) (G_21:(hoare_1708887482_state->Prop)) (P_31:(pname->(state->(state->Prop)))) (Q_17:(pname->(state->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_90032982_state ((semila1122118281tate_o G_21) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_31 P_9)) (body P_9)) (Q_17 P_9)))) Procs))) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_31 P_9)) (the_com (body_1 P_9))) (Q_17 P_9)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_90032982_state G_21) ((insert528405184_state (((hoare_858012674_state (P_31 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo19817387tate_o))))).
% Axiom fact_264_Body1:(forall (Pn_5:pname) (G_21:(hoare_2091234717iple_a->Prop)) (P_31:(pname->(x_a->(state->Prop)))) (Q_17:(pname->(x_a->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_1467856363rivs_a ((semila1052848428le_a_o G_21) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_31 P_9)) (body P_9)) (Q_17 P_9)))) Procs))) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_31 P_9)) (the_com (body_1 P_9))) (Q_17 P_9)))) Procs))->(((member_pname Pn_5) Procs)->((hoare_1467856363rivs_a G_21) ((insert1597628439iple_a (((hoare_657976383iple_a (P_31 Pn_5)) (body Pn_5)) (Q_17 Pn_5))) bot_bo1791335050le_a_o))))).
% Axiom fact_265_image__cong:(forall (F_41:(nat->nat)) (G_20:(nat->nat)) (M_3:(nat->Prop)) (N_7:(nat->Prop)), ((((eq (nat->Prop)) M_3) N_7)->((forall (X:nat), (((member_nat X) N_7)->(((eq nat) (F_41 X)) (G_20 X))))->(((eq (nat->Prop)) ((image_nat_nat F_41) M_3)) ((image_nat_nat G_20) N_7))))).
% Axiom fact_266_image__cong:(forall (F_41:(pname->hoare_1708887482_state)) (G_20:(pname->hoare_1708887482_state)) (M_3:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_3) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_1708887482_state) (F_41 X)) (G_20 X))))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_41) M_3)) ((image_1116629049_state G_20) N_7))))).
% Axiom fact_267_image__cong:(forall (F_41:(pname->hoare_2091234717iple_a)) (G_20:(pname->hoare_2091234717iple_a)) (M_3:(pname->Prop)) (N_7:(pname->Prop)), ((((eq (pname->Prop)) M_3) N_7)->((forall (X:pname), (((member_pname X) N_7)->(((eq hoare_2091234717iple_a) (F_41 X)) (G_20 X))))->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_41) M_3)) ((image_231808478iple_a G_20) N_7))))).
% Axiom fact_268_Body__triple__valid__0:(forall (P_30:(state->(state->Prop))) (Pn_4:pname) (Q_16:(state->(state->Prop))), ((hoare_23738522_state zero_zero_nat) (((hoare_858012674_state P_30) (body Pn_4)) Q_16))).
% Axiom fact_269_Body__triple__valid__0:(forall (P_30:(x_a->(state->Prop))) (Pn_4:pname) (Q_16:(x_a->(state->Prop))), ((hoare_1421888935alid_a zero_zero_nat) (((hoare_657976383iple_a P_30) (body Pn_4)) Q_16))).
% Axiom fact_270_com_Osimps_I6_J:(forall (Pname_1:pname) (Pname:pname), ((iff (((eq com) (body Pname_1)) (body Pname))) (((eq pname) Pname_1) Pname))).
% Axiom fact_271_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_272_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_273_Sup__fin_Oidem:(forall (X_34:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_34) X_34)) X_34)).
% Axiom fact_274_Sup__fin_Oidem:(forall (X_34:nat), (((eq nat) ((semila972727038up_nat X_34) X_34)) X_34)).
% Axiom fact_275_Sup__fin_Oidem:(forall (X_34:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_34) X_34)) X_34)).
% Axiom fact_276_Sup__fin_Oidem:(forall (X_34:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_34) X_34)) X_34)).
% Axiom fact_277_Sup__fin_Oidem:(forall (X_34:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_34) X_34)) X_34)).
% Axiom fact_278_Sup__fin_Oidem:(forall (X_34:Prop), ((iff ((semila10642723_sup_o X_34) X_34)) X_34)).
% Axiom fact_279_Sup__fin_Oidem:(forall (X_34:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_34) X_34)) X_34)).
% Axiom fact_280_triples__valid__Suc:(forall (N_6:nat) (Ts_2:(hoare_1708887482_state->Prop)), ((forall (X:hoare_1708887482_state), (((member451959335_state X) Ts_2)->((hoare_23738522_state (suc N_6)) X)))->(forall (X:hoare_1708887482_state), (((member451959335_state X) Ts_2)->((hoare_23738522_state N_6) X))))).
% Axiom fact_281_triples__valid__Suc:(forall (N_6:nat) (Ts_2:(hoare_2091234717iple_a->Prop)), ((forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) Ts_2)->((hoare_1421888935alid_a (suc N_6)) X)))->(forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) Ts_2)->((hoare_1421888935alid_a N_6) X))))).
% Axiom fact_282_emptyE:(forall (A_100:nat), (((member_nat A_100) bot_bot_nat_o)->False)).
% Axiom fact_283_emptyE:(forall (A_100:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o A_100) bot_bo1957696069_a_o_o)->False)).
% Axiom fact_284_emptyE:(forall (A_100:hoare_2091234717iple_a), (((member290856304iple_a A_100) bot_bo1791335050le_a_o)->False)).
% Axiom fact_285_emptyE:(forall (A_100:hoare_1708887482_state), (((member451959335_state A_100) bot_bo19817387tate_o)->False)).
% Axiom fact_286_emptyE:(forall (A_100:pname), (((member_pname A_100) bot_bot_pname_o)->False)).
% Axiom fact_287_insertE:(forall (A_99:nat) (B_47:nat) (A_98:(nat->Prop)), (((member_nat A_99) ((insert_nat B_47) A_98))->((not (((eq nat) A_99) B_47))->((member_nat A_99) A_98)))).
% Axiom fact_288_insertE:(forall (A_99:(hoare_2091234717iple_a->Prop)) (B_47:(hoare_2091234717iple_a->Prop)) (A_98:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_99) ((insert102003750le_a_o B_47) A_98))->((not (((eq (hoare_2091234717iple_a->Prop)) A_99) B_47))->((member99268621le_a_o A_99) A_98)))).
% Axiom fact_289_insertE:(forall (A_99:hoare_2091234717iple_a) (B_47:hoare_2091234717iple_a) (A_98:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_99) ((insert1597628439iple_a B_47) A_98))->((not (((eq hoare_2091234717iple_a) A_99) B_47))->((member290856304iple_a A_99) A_98)))).
% Axiom fact_290_insertE:(forall (A_99:hoare_1708887482_state) (B_47:hoare_1708887482_state) (A_98:(hoare_1708887482_state->Prop)), (((member451959335_state A_99) ((insert528405184_state B_47) A_98))->((not (((eq hoare_1708887482_state) A_99) B_47))->((member451959335_state A_99) A_98)))).
% Axiom fact_291_insertE:(forall (A_99:pname) (B_47:pname) (A_98:(pname->Prop)), (((member_pname A_99) ((insert_pname B_47) A_98))->((not (((eq pname) A_99) B_47))->((member_pname A_99) A_98)))).
% Axiom fact_292_insertCI:(forall (B_46:nat) (A_97:nat) (B_45:(nat->Prop)), (((((member_nat A_97) B_45)->False)->(((eq nat) A_97) B_46))->((member_nat A_97) ((insert_nat B_46) B_45)))).
% Axiom fact_293_insertCI:(forall (B_46:(hoare_2091234717iple_a->Prop)) (A_97:(hoare_2091234717iple_a->Prop)) (B_45:((hoare_2091234717iple_a->Prop)->Prop)), (((((member99268621le_a_o A_97) B_45)->False)->(((eq (hoare_2091234717iple_a->Prop)) A_97) B_46))->((member99268621le_a_o A_97) ((insert102003750le_a_o B_46) B_45)))).
% Axiom fact_294_insertCI:(forall (B_46:hoare_2091234717iple_a) (A_97:hoare_2091234717iple_a) (B_45:(hoare_2091234717iple_a->Prop)), (((((member290856304iple_a A_97) B_45)->False)->(((eq hoare_2091234717iple_a) A_97) B_46))->((member290856304iple_a A_97) ((insert1597628439iple_a B_46) B_45)))).
% Axiom fact_295_insertCI:(forall (B_46:hoare_1708887482_state) (A_97:hoare_1708887482_state) (B_45:(hoare_1708887482_state->Prop)), (((((member451959335_state A_97) B_45)->False)->(((eq hoare_1708887482_state) A_97) B_46))->((member451959335_state A_97) ((insert528405184_state B_46) B_45)))).
% Axiom fact_296_insertCI:(forall (B_46:pname) (A_97:pname) (B_45:(pname->Prop)), (((((member_pname A_97) B_45)->False)->(((eq pname) A_97) B_46))->((member_pname A_97) ((insert_pname B_46) B_45)))).
% Axiom fact_297_empty__not__insert:(forall (A_96:nat) (A_95:(nat->Prop)), (not (((eq (nat->Prop)) bot_bot_nat_o) ((insert_nat A_96) A_95)))).
% Axiom fact_298_empty__not__insert:(forall (A_96:(hoare_2091234717iple_a->Prop)) (A_95:((hoare_2091234717iple_a->Prop)->Prop)), (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) bot_bo1957696069_a_o_o) ((insert102003750le_a_o A_96) A_95)))).
% Axiom fact_299_empty__not__insert:(forall (A_96:pname) (A_95:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_96) A_95)))).
% Axiom fact_300_empty__not__insert:(forall (A_96:hoare_2091234717iple_a) (A_95:(hoare_2091234717iple_a->Prop)), (not (((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) ((insert1597628439iple_a A_96) A_95)))).
% Axiom fact_301_empty__not__insert:(forall (A_96:hoare_1708887482_state) (A_95:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((insert528405184_state A_96) A_95)))).
% Axiom fact_302_insert__not__empty:(forall (A_94:nat) (A_93:(nat->Prop)), (not (((eq (nat->Prop)) ((insert_nat A_94) A_93)) bot_bot_nat_o))).
% Axiom fact_303_insert__not__empty:(forall (A_94:(hoare_2091234717iple_a->Prop)) (A_93:((hoare_2091234717iple_a->Prop)->Prop)), (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_94) A_93)) bot_bo1957696069_a_o_o))).
% Axiom fact_304_insert__not__empty:(forall (A_94:pname) (A_93:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_94) A_93)) bot_bot_pname_o))).
% Axiom fact_305_insert__not__empty:(forall (A_94:hoare_2091234717iple_a) (A_93:(hoare_2091234717iple_a->Prop)), (not (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_94) A_93)) bot_bo1791335050le_a_o))).
% Axiom fact_306_insert__not__empty:(forall (A_94:hoare_1708887482_state) (A_93:(hoare_1708887482_state->Prop)), (not (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_94) A_93)) bot_bo19817387tate_o))).
% Axiom fact_307_bot__empty__eq:(forall (X:nat), ((iff (bot_bot_nat_o X)) ((member_nat X) bot_bot_nat_o))).
% Axiom fact_308_bot__empty__eq:(forall (X:(hoare_2091234717iple_a->Prop)), ((iff (bot_bo1957696069_a_o_o X)) ((member99268621le_a_o X) bot_bo1957696069_a_o_o))).
% Axiom fact_309_bot__empty__eq:(forall (X:hoare_2091234717iple_a), ((iff (bot_bo1791335050le_a_o X)) ((member290856304iple_a X) bot_bo1791335050le_a_o))).
% Axiom fact_310_bot__empty__eq:(forall (X:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X)) ((member451959335_state X) bot_bo19817387tate_o))).
% Axiom fact_311_bot__empty__eq:(forall (X:pname), ((iff (bot_bot_pname_o X)) ((member_pname X) bot_bot_pname_o))).
% Axiom fact_312_empty__def:(((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X:pname)=> False))).
% Axiom fact_313_empty__def:(((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> False))).
% Axiom fact_314_empty__def:(((eq ((hoare_2091234717iple_a->Prop)->Prop)) bot_bo1957696069_a_o_o) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> False))).
% Axiom fact_315_empty__def:(((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state (fun (X:hoare_1708887482_state)=> False))).
% Axiom fact_316_empty__def:(((eq (nat->Prop)) bot_bot_nat_o) (collect_nat (fun (X:nat)=> False))).
% Axiom fact_317_insertI1:(forall (A_92:nat) (B_44:(nat->Prop)), ((member_nat A_92) ((insert_nat A_92) B_44))).
% Axiom fact_318_insertI1:(forall (A_92:(hoare_2091234717iple_a->Prop)) (B_44:((hoare_2091234717iple_a->Prop)->Prop)), ((member99268621le_a_o A_92) ((insert102003750le_a_o A_92) B_44))).
% Axiom fact_319_insertI1:(forall (A_92:hoare_2091234717iple_a) (B_44:(hoare_2091234717iple_a->Prop)), ((member290856304iple_a A_92) ((insert1597628439iple_a A_92) B_44))).
% Axiom fact_320_insertI1:(forall (A_92:hoare_1708887482_state) (B_44:(hoare_1708887482_state->Prop)), ((member451959335_state A_92) ((insert528405184_state A_92) B_44))).
% Axiom fact_321_insertI1:(forall (A_92:pname) (B_44:(pname->Prop)), ((member_pname A_92) ((insert_pname A_92) B_44))).
% Axiom fact_322_all__not__in__conv:(forall (A_91:(nat->Prop)), ((iff (forall (X:nat), (((member_nat X) A_91)->False))) (((eq (nat->Prop)) A_91) bot_bot_nat_o))).
% Axiom fact_323_all__not__in__conv:(forall (A_91:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (forall (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) A_91)->False))) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_91) bot_bo1957696069_a_o_o))).
% Axiom fact_324_all__not__in__conv:(forall (A_91:(hoare_2091234717iple_a->Prop)), ((iff (forall (X:hoare_2091234717iple_a), (((member290856304iple_a X) A_91)->False))) (((eq (hoare_2091234717iple_a->Prop)) A_91) bot_bo1791335050le_a_o))).
% Axiom fact_325_all__not__in__conv:(forall (A_91:(hoare_1708887482_state->Prop)), ((iff (forall (X:hoare_1708887482_state), (((member451959335_state X) A_91)->False))) (((eq (hoare_1708887482_state->Prop)) A_91) bot_bo19817387tate_o))).
% Axiom fact_326_all__not__in__conv:(forall (A_91:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) A_91)->False))) (((eq (pname->Prop)) A_91) bot_bot_pname_o))).
% Axiom fact_327_singleton__conv2:(forall (A_90:(hoare_2091234717iple_a->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fequal845167073le_a_o A_90))) ((insert102003750le_a_o A_90) bot_bo1957696069_a_o_o))).
% Axiom fact_328_singleton__conv2:(forall (A_90:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_90))) ((insert_pname A_90) bot_bot_pname_o))).
% Axiom fact_329_singleton__conv2:(forall (A_90:hoare_2091234717iple_a), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fequal1604381340iple_a A_90))) ((insert1597628439iple_a A_90) bot_bo1791335050le_a_o))).
% Axiom fact_330_singleton__conv2:(forall (A_90:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fequal224822779_state A_90))) ((insert528405184_state A_90) bot_bo19817387tate_o))).
% Axiom fact_331_singleton__conv2:(forall (A_90:nat), (((eq (nat->Prop)) (collect_nat (fequal_nat A_90))) ((insert_nat A_90) bot_bot_nat_o))).
% Axiom fact_332_ex__in__conv:(forall (A_89:(nat->Prop)), ((iff ((ex nat) (fun (X:nat)=> ((member_nat X) A_89)))) (not (((eq (nat->Prop)) A_89) bot_bot_nat_o)))).
% Axiom fact_333_ex__in__conv:(forall (A_89:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o X) A_89)))) (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_89) bot_bo1957696069_a_o_o)))).
% Axiom fact_334_ex__in__conv:(forall (A_89:(hoare_2091234717iple_a->Prop)), ((iff ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((member290856304iple_a X) A_89)))) (not (((eq (hoare_2091234717iple_a->Prop)) A_89) bot_bo1791335050le_a_o)))).
% Axiom fact_335_ex__in__conv:(forall (A_89:(hoare_1708887482_state->Prop)), ((iff ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((member451959335_state X) A_89)))) (not (((eq (hoare_1708887482_state->Prop)) A_89) bot_bo19817387tate_o)))).
% Axiom fact_336_ex__in__conv:(forall (A_89:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((member_pname X) A_89)))) (not (((eq (pname->Prop)) A_89) bot_bot_pname_o)))).
% Axiom fact_337_singleton__conv:(forall (A_88:(hoare_2091234717iple_a->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> (((eq (hoare_2091234717iple_a->Prop)) X) A_88)))) ((insert102003750le_a_o A_88) bot_bo1957696069_a_o_o))).
% Axiom fact_338_singleton__conv:(forall (A_88:pname), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> (((eq pname) X) A_88)))) ((insert_pname A_88) bot_bot_pname_o))).
% Axiom fact_339_singleton__conv:(forall (A_88:hoare_2091234717iple_a), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> (((eq hoare_2091234717iple_a) X) A_88)))) ((insert1597628439iple_a A_88) bot_bo1791335050le_a_o))).
% Axiom fact_340_singleton__conv:(forall (A_88:hoare_1708887482_state), (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X) A_88)))) ((insert528405184_state A_88) bot_bo19817387tate_o))).
% Axiom fact_341_singleton__conv:(forall (A_88:nat), (((eq (nat->Prop)) (collect_nat (fun (X:nat)=> (((eq nat) X) A_88)))) ((insert_nat A_88) bot_bot_nat_o))).
% Axiom fact_342_Collect__conv__if2:(forall (P_29:((hoare_2091234717iple_a->Prop)->Prop)) (A_87:(hoare_2091234717iple_a->Prop)), ((and ((P_29 A_87)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_87) X)) (P_29 X))))) ((insert102003750le_a_o A_87) bot_bo1957696069_a_o_o)))) (((P_29 A_87)->False)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_87) X)) (P_29 X))))) bot_bo1957696069_a_o_o)))).
% Axiom fact_343_Collect__conv__if2:(forall (P_29:(pname->Prop)) (A_87:pname), ((and ((P_29 A_87)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_87) X)) (P_29 X))))) ((insert_pname A_87) bot_bot_pname_o)))) (((P_29 A_87)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_87) X)) (P_29 X))))) bot_bot_pname_o)))).
% Axiom fact_344_Collect__conv__if2:(forall (P_29:(hoare_2091234717iple_a->Prop)) (A_87:hoare_2091234717iple_a), ((and ((P_29 A_87)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) A_87) X)) (P_29 X))))) ((insert1597628439iple_a A_87) bot_bo1791335050le_a_o)))) (((P_29 A_87)->False)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) A_87) X)) (P_29 X))))) bot_bo1791335050le_a_o)))).
% Axiom fact_345_Collect__conv__if2:(forall (P_29:(hoare_1708887482_state->Prop)) (A_87:hoare_1708887482_state), ((and ((P_29 A_87)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_87) X)) (P_29 X))))) ((insert528405184_state A_87) bot_bo19817387tate_o)))) (((P_29 A_87)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) A_87) X)) (P_29 X))))) bot_bo19817387tate_o)))).
% Axiom fact_346_Collect__conv__if2:(forall (P_29:(nat->Prop)) (A_87:nat), ((and ((P_29 A_87)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) A_87) X)) (P_29 X))))) ((insert_nat A_87) bot_bot_nat_o)))) (((P_29 A_87)->False)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) A_87) X)) (P_29 X))))) bot_bot_nat_o)))).
% Axiom fact_347_Collect__conv__if:(forall (P_28:((hoare_2091234717iple_a->Prop)->Prop)) (A_86:(hoare_2091234717iple_a->Prop)), ((and ((P_28 A_86)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) X) A_86)) (P_28 X))))) ((insert102003750le_a_o A_86) bot_bo1957696069_a_o_o)))) (((P_28 A_86)->False)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) X) A_86)) (P_28 X))))) bot_bo1957696069_a_o_o)))).
% Axiom fact_348_Collect__conv__if:(forall (P_28:(pname->Prop)) (A_86:pname), ((and ((P_28 A_86)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_86)) (P_28 X))))) ((insert_pname A_86) bot_bot_pname_o)))) (((P_28 A_86)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_86)) (P_28 X))))) bot_bot_pname_o)))).
% Axiom fact_349_Collect__conv__if:(forall (P_28:(hoare_2091234717iple_a->Prop)) (A_86:hoare_2091234717iple_a), ((and ((P_28 A_86)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) X) A_86)) (P_28 X))))) ((insert1597628439iple_a A_86) bot_bo1791335050le_a_o)))) (((P_28 A_86)->False)->(((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (((eq hoare_2091234717iple_a) X) A_86)) (P_28 X))))) bot_bo1791335050le_a_o)))).
% Axiom fact_350_Collect__conv__if:(forall (P_28:(hoare_1708887482_state->Prop)) (A_86:hoare_1708887482_state), ((and ((P_28 A_86)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X) A_86)) (P_28 X))))) ((insert528405184_state A_86) bot_bo19817387tate_o)))) (((P_28 A_86)->False)->(((eq (hoare_1708887482_state->Prop)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((and (((eq hoare_1708887482_state) X) A_86)) (P_28 X))))) bot_bo19817387tate_o)))).
% Axiom fact_351_Collect__conv__if:(forall (P_28:(nat->Prop)) (A_86:nat), ((and ((P_28 A_86)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) X) A_86)) (P_28 X))))) ((insert_nat A_86) bot_bot_nat_o)))) (((P_28 A_86)->False)->(((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (((eq nat) X) A_86)) (P_28 X))))) bot_bot_nat_o)))).
% Axiom fact_352_mem__def:(forall (X_33:nat) (A_85:(nat->Prop)), ((iff ((member_nat X_33) A_85)) (A_85 X_33))).
% Axiom fact_353_mem__def:(forall (X_33:(hoare_2091234717iple_a->Prop)) (A_85:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o X_33) A_85)) (A_85 X_33))).
% Axiom fact_354_mem__def:(forall (X_33:hoare_2091234717iple_a) (A_85:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a X_33) A_85)) (A_85 X_33))).
% Axiom fact_355_mem__def:(forall (X_33:pname) (A_85:(pname->Prop)), ((iff ((member_pname X_33) A_85)) (A_85 X_33))).
% Axiom fact_356_Collect__def:(forall (P_27:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_27)) P_27)).
% Axiom fact_357_Collect__def:(forall (P_27:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a P_27)) P_27)).
% Axiom fact_358_Collect__def:(forall (P_27:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_27)) P_27)).
% Axiom fact_359_empty__Collect__eq:(forall (P_26:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_26))) (forall (X:pname), ((P_26 X)->False)))).
% Axiom fact_360_empty__Collect__eq:(forall (P_26:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) (collec992574898iple_a P_26))) (forall (X:hoare_2091234717iple_a), ((P_26 X)->False)))).
% Axiom fact_361_empty__Collect__eq:(forall (P_26:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) bot_bo1957696069_a_o_o) (collec1008234059le_a_o P_26))) (forall (X:(hoare_2091234717iple_a->Prop)), ((P_26 X)->False)))).
% Axiom fact_362_empty__Collect__eq:(forall (P_26:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) (collec1568722789_state P_26))) (forall (X:hoare_1708887482_state), ((P_26 X)->False)))).
% Axiom fact_363_empty__Collect__eq:(forall (P_26:(nat->Prop)), ((iff (((eq (nat->Prop)) bot_bot_nat_o) (collect_nat P_26))) (forall (X:nat), ((P_26 X)->False)))).
% Axiom fact_364_empty__iff:(forall (C_25:nat), (((member_nat C_25) bot_bot_nat_o)->False)).
% Axiom fact_365_empty__iff:(forall (C_25:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o C_25) bot_bo1957696069_a_o_o)->False)).
% Axiom fact_366_empty__iff:(forall (C_25:hoare_2091234717iple_a), (((member290856304iple_a C_25) bot_bo1791335050le_a_o)->False)).
% Axiom fact_367_empty__iff:(forall (C_25:hoare_1708887482_state), (((member451959335_state C_25) bot_bo19817387tate_o)->False)).
% Axiom fact_368_empty__iff:(forall (C_25:pname), (((member_pname C_25) bot_bot_pname_o)->False)).
% Axiom fact_369_insert__compr:(forall (A_84:(hoare_2091234717iple_a->Prop)) (B_43:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_84) B_43)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or (((eq (hoare_2091234717iple_a->Prop)) X) A_84)) ((member99268621le_a_o X) B_43)))))).
% Axiom fact_370_insert__compr:(forall (A_84:hoare_2091234717iple_a) (B_43:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_84) B_43)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or (((eq hoare_2091234717iple_a) X) A_84)) ((member290856304iple_a X) B_43)))))).
% Axiom fact_371_insert__compr:(forall (A_84:hoare_1708887482_state) (B_43:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_84) B_43)) (collec1568722789_state (fun (X:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) X) A_84)) ((member451959335_state X) B_43)))))).
% Axiom fact_372_insert__compr:(forall (A_84:nat) (B_43:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_84) B_43)) (collect_nat (fun (X:nat)=> ((or (((eq nat) X) A_84)) ((member_nat X) B_43)))))).
% Axiom fact_373_insert__compr:(forall (A_84:pname) (B_43:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_84) B_43)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_84)) ((member_pname X) B_43)))))).
% Axiom fact_374_insert__Collect:(forall (A_83:(hoare_2091234717iple_a->Prop)) (P_25:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_83) (collec1008234059le_a_o P_25))) (collec1008234059le_a_o (fun (U_2:(hoare_2091234717iple_a->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_2091234717iple_a->Prop)) U_2) A_83))) (P_25 U_2)))))).
% Axiom fact_375_insert__Collect:(forall (A_83:pname) (P_25:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_83) (collect_pname P_25))) (collect_pname (fun (U_2:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_2) A_83))) (P_25 U_2)))))).
% Axiom fact_376_insert__Collect:(forall (A_83:hoare_2091234717iple_a) (P_25:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_83) (collec992574898iple_a P_25))) (collec992574898iple_a (fun (U_2:hoare_2091234717iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_2091234717iple_a) U_2) A_83))) (P_25 U_2)))))).
% Axiom fact_377_insert__Collect:(forall (A_83:hoare_1708887482_state) (P_25:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_83) (collec1568722789_state P_25))) (collec1568722789_state (fun (U_2:hoare_1708887482_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1708887482_state) U_2) A_83))) (P_25 U_2)))))).
% Axiom fact_378_insert__Collect:(forall (A_83:nat) (P_25:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_83) (collect_nat P_25))) (collect_nat (fun (U_2:nat)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq nat) U_2) A_83))) (P_25 U_2)))))).
% Axiom fact_379_singleton__iff:(forall (B_42:nat) (A_82:nat), ((iff ((member_nat B_42) ((insert_nat A_82) bot_bot_nat_o))) (((eq nat) B_42) A_82))).
% Axiom fact_380_singleton__iff:(forall (B_42:(hoare_2091234717iple_a->Prop)) (A_82:(hoare_2091234717iple_a->Prop)), ((iff ((member99268621le_a_o B_42) ((insert102003750le_a_o A_82) bot_bo1957696069_a_o_o))) (((eq (hoare_2091234717iple_a->Prop)) B_42) A_82))).
% Axiom fact_381_singleton__iff:(forall (B_42:hoare_2091234717iple_a) (A_82:hoare_2091234717iple_a), ((iff ((member290856304iple_a B_42) ((insert1597628439iple_a A_82) bot_bo1791335050le_a_o))) (((eq hoare_2091234717iple_a) B_42) A_82))).
% Axiom fact_382_singleton__iff:(forall (B_42:hoare_1708887482_state) (A_82:hoare_1708887482_state), ((iff ((member451959335_state B_42) ((insert528405184_state A_82) bot_bo19817387tate_o))) (((eq hoare_1708887482_state) B_42) A_82))).
% Axiom fact_383_singleton__iff:(forall (B_42:pname) (A_82:pname), ((iff ((member_pname B_42) ((insert_pname A_82) bot_bot_pname_o))) (((eq pname) B_42) A_82))).
% Axiom fact_384_insert__absorb2:(forall (X_32:nat) (A_81:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_32) ((insert_nat X_32) A_81))) ((insert_nat X_32) A_81))).
% Axiom fact_385_insert__absorb2:(forall (X_32:(hoare_2091234717iple_a->Prop)) (A_81:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X_32) ((insert102003750le_a_o X_32) A_81))) ((insert102003750le_a_o X_32) A_81))).
% Axiom fact_386_insert__absorb2:(forall (X_32:pname) (A_81:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_32) ((insert_pname X_32) A_81))) ((insert_pname X_32) A_81))).
% Axiom fact_387_insert__absorb2:(forall (X_32:hoare_2091234717iple_a) (A_81:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X_32) ((insert1597628439iple_a X_32) A_81))) ((insert1597628439iple_a X_32) A_81))).
% Axiom fact_388_insert__absorb2:(forall (X_32:hoare_1708887482_state) (A_81:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_32) ((insert528405184_state X_32) A_81))) ((insert528405184_state X_32) A_81))).
% Axiom fact_389_insert__commute:(forall (X_31:nat) (Y_10:nat) (A_80:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_31) ((insert_nat Y_10) A_80))) ((insert_nat Y_10) ((insert_nat X_31) A_80)))).
% Axiom fact_390_insert__commute:(forall (X_31:(hoare_2091234717iple_a->Prop)) (Y_10:(hoare_2091234717iple_a->Prop)) (A_80:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X_31) ((insert102003750le_a_o Y_10) A_80))) ((insert102003750le_a_o Y_10) ((insert102003750le_a_o X_31) A_80)))).
% Axiom fact_391_insert__commute:(forall (X_31:pname) (Y_10:pname) (A_80:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_31) ((insert_pname Y_10) A_80))) ((insert_pname Y_10) ((insert_pname X_31) A_80)))).
% Axiom fact_392_insert__commute:(forall (X_31:hoare_2091234717iple_a) (Y_10:hoare_2091234717iple_a) (A_80:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X_31) ((insert1597628439iple_a Y_10) A_80))) ((insert1597628439iple_a Y_10) ((insert1597628439iple_a X_31) A_80)))).
% Axiom fact_393_insert__commute:(forall (X_31:hoare_1708887482_state) (Y_10:hoare_1708887482_state) (A_80:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_31) ((insert528405184_state Y_10) A_80))) ((insert528405184_state Y_10) ((insert528405184_state X_31) A_80)))).
% Axiom fact_394_insert__iff:(forall (A_79:nat) (B_41:nat) (A_78:(nat->Prop)), ((iff ((member_nat A_79) ((insert_nat B_41) A_78))) ((or (((eq nat) A_79) B_41)) ((member_nat A_79) A_78)))).
% Axiom fact_395_insert__iff:(forall (A_79:(hoare_2091234717iple_a->Prop)) (B_41:(hoare_2091234717iple_a->Prop)) (A_78:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o A_79) ((insert102003750le_a_o B_41) A_78))) ((or (((eq (hoare_2091234717iple_a->Prop)) A_79) B_41)) ((member99268621le_a_o A_79) A_78)))).
% Axiom fact_396_insert__iff:(forall (A_79:hoare_2091234717iple_a) (B_41:hoare_2091234717iple_a) (A_78:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a A_79) ((insert1597628439iple_a B_41) A_78))) ((or (((eq hoare_2091234717iple_a) A_79) B_41)) ((member290856304iple_a A_79) A_78)))).
% Axiom fact_397_insert__iff:(forall (A_79:hoare_1708887482_state) (B_41:hoare_1708887482_state) (A_78:(hoare_1708887482_state->Prop)), ((iff ((member451959335_state A_79) ((insert528405184_state B_41) A_78))) ((or (((eq hoare_1708887482_state) A_79) B_41)) ((member451959335_state A_79) A_78)))).
% Axiom fact_398_insert__iff:(forall (A_79:pname) (B_41:pname) (A_78:(pname->Prop)), ((iff ((member_pname A_79) ((insert_pname B_41) A_78))) ((or (((eq pname) A_79) B_41)) ((member_pname A_79) A_78)))).
% Axiom fact_399_Collect__empty__eq:(forall (P_24:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_24)) bot_bot_pname_o)) (forall (X:pname), ((P_24 X)->False)))).
% Axiom fact_400_Collect__empty__eq:(forall (P_24:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a P_24)) bot_bo1791335050le_a_o)) (forall (X:hoare_2091234717iple_a), ((P_24 X)->False)))).
% Axiom fact_401_Collect__empty__eq:(forall (P_24:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) (collec1008234059le_a_o P_24)) bot_bo1957696069_a_o_o)) (forall (X:(hoare_2091234717iple_a->Prop)), ((P_24 X)->False)))).
% Axiom fact_402_Collect__empty__eq:(forall (P_24:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) (collec1568722789_state P_24)) bot_bo19817387tate_o)) (forall (X:hoare_1708887482_state), ((P_24 X)->False)))).
% Axiom fact_403_Collect__empty__eq:(forall (P_24:(nat->Prop)), ((iff (((eq (nat->Prop)) (collect_nat P_24)) bot_bot_nat_o)) (forall (X:nat), ((P_24 X)->False)))).
% Axiom fact_404_doubleton__eq__iff:(forall (A_77:nat) (B_40:nat) (C_24:nat) (D_1:nat), ((iff (((eq (nat->Prop)) ((insert_nat A_77) ((insert_nat B_40) bot_bot_nat_o))) ((insert_nat C_24) ((insert_nat D_1) bot_bot_nat_o)))) ((or ((and (((eq nat) A_77) C_24)) (((eq nat) B_40) D_1))) ((and (((eq nat) A_77) D_1)) (((eq nat) B_40) C_24))))).
% Axiom fact_405_doubleton__eq__iff:(forall (A_77:(hoare_2091234717iple_a->Prop)) (B_40:(hoare_2091234717iple_a->Prop)) (C_24:(hoare_2091234717iple_a->Prop)) (D_1:(hoare_2091234717iple_a->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_77) ((insert102003750le_a_o B_40) bot_bo1957696069_a_o_o))) ((insert102003750le_a_o C_24) ((insert102003750le_a_o D_1) bot_bo1957696069_a_o_o)))) ((or ((and (((eq (hoare_2091234717iple_a->Prop)) A_77) C_24)) (((eq (hoare_2091234717iple_a->Prop)) B_40) D_1))) ((and (((eq (hoare_2091234717iple_a->Prop)) A_77) D_1)) (((eq (hoare_2091234717iple_a->Prop)) B_40) C_24))))).
% Axiom fact_406_doubleton__eq__iff:(forall (A_77:pname) (B_40:pname) (C_24:pname) (D_1:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_77) ((insert_pname B_40) bot_bot_pname_o))) ((insert_pname C_24) ((insert_pname D_1) bot_bot_pname_o)))) ((or ((and (((eq pname) A_77) C_24)) (((eq pname) B_40) D_1))) ((and (((eq pname) A_77) D_1)) (((eq pname) B_40) C_24))))).
% Axiom fact_407_doubleton__eq__iff:(forall (A_77:hoare_2091234717iple_a) (B_40:hoare_2091234717iple_a) (C_24:hoare_2091234717iple_a) (D_1:hoare_2091234717iple_a), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_77) ((insert1597628439iple_a B_40) bot_bo1791335050le_a_o))) ((insert1597628439iple_a C_24) ((insert1597628439iple_a D_1) bot_bo1791335050le_a_o)))) ((or ((and (((eq hoare_2091234717iple_a) A_77) C_24)) (((eq hoare_2091234717iple_a) B_40) D_1))) ((and (((eq hoare_2091234717iple_a) A_77) D_1)) (((eq hoare_2091234717iple_a) B_40) C_24))))).
% Axiom fact_408_doubleton__eq__iff:(forall (A_77:hoare_1708887482_state) (B_40:hoare_1708887482_state) (C_24:hoare_1708887482_state) (D_1:hoare_1708887482_state), ((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_77) ((insert528405184_state B_40) bot_bo19817387tate_o))) ((insert528405184_state C_24) ((insert528405184_state D_1) bot_bo19817387tate_o)))) ((or ((and (((eq hoare_1708887482_state) A_77) C_24)) (((eq hoare_1708887482_state) B_40) D_1))) ((and (((eq hoare_1708887482_state) A_77) D_1)) (((eq hoare_1708887482_state) B_40) C_24))))).
% Axiom fact_409_insert__code:(forall (Y_9:nat) (A_76:(nat->Prop)) (X_30:nat), ((iff (((insert_nat Y_9) A_76) X_30)) ((or (((eq nat) Y_9) X_30)) (A_76 X_30)))).
% Axiom fact_410_insert__code:(forall (Y_9:(hoare_2091234717iple_a->Prop)) (A_76:((hoare_2091234717iple_a->Prop)->Prop)) (X_30:(hoare_2091234717iple_a->Prop)), ((iff (((insert102003750le_a_o Y_9) A_76) X_30)) ((or (((eq (hoare_2091234717iple_a->Prop)) Y_9) X_30)) (A_76 X_30)))).
% Axiom fact_411_insert__code:(forall (Y_9:pname) (A_76:(pname->Prop)) (X_30:pname), ((iff (((insert_pname Y_9) A_76) X_30)) ((or (((eq pname) Y_9) X_30)) (A_76 X_30)))).
% Axiom fact_412_insert__code:(forall (Y_9:hoare_2091234717iple_a) (A_76:(hoare_2091234717iple_a->Prop)) (X_30:hoare_2091234717iple_a), ((iff (((insert1597628439iple_a Y_9) A_76) X_30)) ((or (((eq hoare_2091234717iple_a) Y_9) X_30)) (A_76 X_30)))).
% Axiom fact_413_insert__code:(forall (Y_9:hoare_1708887482_state) (A_76:(hoare_1708887482_state->Prop)) (X_30:hoare_1708887482_state), ((iff (((insert528405184_state Y_9) A_76) X_30)) ((or (((eq hoare_1708887482_state) Y_9) X_30)) (A_76 X_30)))).
% Axiom fact_414_insert__ident:(forall (B_39:(nat->Prop)) (X_29:nat) (A_75:(nat->Prop)), ((((member_nat X_29) A_75)->False)->((((member_nat X_29) B_39)->False)->((iff (((eq (nat->Prop)) ((insert_nat X_29) A_75)) ((insert_nat X_29) B_39))) (((eq (nat->Prop)) A_75) B_39))))).
% Axiom fact_415_insert__ident:(forall (B_39:((hoare_2091234717iple_a->Prop)->Prop)) (X_29:(hoare_2091234717iple_a->Prop)) (A_75:((hoare_2091234717iple_a->Prop)->Prop)), ((((member99268621le_a_o X_29) A_75)->False)->((((member99268621le_a_o X_29) B_39)->False)->((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X_29) A_75)) ((insert102003750le_a_o X_29) B_39))) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_75) B_39))))).
% Axiom fact_416_insert__ident:(forall (B_39:(hoare_2091234717iple_a->Prop)) (X_29:hoare_2091234717iple_a) (A_75:(hoare_2091234717iple_a->Prop)), ((((member290856304iple_a X_29) A_75)->False)->((((member290856304iple_a X_29) B_39)->False)->((iff (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X_29) A_75)) ((insert1597628439iple_a X_29) B_39))) (((eq (hoare_2091234717iple_a->Prop)) A_75) B_39))))).
% Axiom fact_417_insert__ident:(forall (B_39:(hoare_1708887482_state->Prop)) (X_29:hoare_1708887482_state) (A_75:(hoare_1708887482_state->Prop)), ((((member451959335_state X_29) A_75)->False)->((((member451959335_state X_29) B_39)->False)->((iff (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X_29) A_75)) ((insert528405184_state X_29) B_39))) (((eq (hoare_1708887482_state->Prop)) A_75) B_39))))).
% Axiom fact_418_insert__ident:(forall (B_39:(pname->Prop)) (X_29:pname) (A_75:(pname->Prop)), ((((member_pname X_29) A_75)->False)->((((member_pname X_29) B_39)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_29) A_75)) ((insert_pname X_29) B_39))) (((eq (pname->Prop)) A_75) B_39))))).
% Axiom fact_419_equals0D:(forall (A_74:nat) (A_73:(nat->Prop)), ((((eq (nat->Prop)) A_73) bot_bot_nat_o)->(((member_nat A_74) A_73)->False))).
% Axiom fact_420_equals0D:(forall (A_74:(hoare_2091234717iple_a->Prop)) (A_73:((hoare_2091234717iple_a->Prop)->Prop)), ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_73) bot_bo1957696069_a_o_o)->(((member99268621le_a_o A_74) A_73)->False))).
% Axiom fact_421_equals0D:(forall (A_74:hoare_2091234717iple_a) (A_73:(hoare_2091234717iple_a->Prop)), ((((eq (hoare_2091234717iple_a->Prop)) A_73) bot_bo1791335050le_a_o)->(((member290856304iple_a A_74) A_73)->False))).
% Axiom fact_422_equals0D:(forall (A_74:hoare_1708887482_state) (A_73:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_73) bot_bo19817387tate_o)->(((member451959335_state A_74) A_73)->False))).
% Axiom fact_423_equals0D:(forall (A_74:pname) (A_73:(pname->Prop)), ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((member_pname A_74) A_73)->False))).
% Axiom fact_424_insertI2:(forall (B_38:nat) (A_72:nat) (B_37:(nat->Prop)), (((member_nat A_72) B_37)->((member_nat A_72) ((insert_nat B_38) B_37)))).
% Axiom fact_425_insertI2:(forall (B_38:(hoare_2091234717iple_a->Prop)) (A_72:(hoare_2091234717iple_a->Prop)) (B_37:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_72) B_37)->((member99268621le_a_o A_72) ((insert102003750le_a_o B_38) B_37)))).
% Axiom fact_426_insertI2:(forall (B_38:hoare_2091234717iple_a) (A_72:hoare_2091234717iple_a) (B_37:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_72) B_37)->((member290856304iple_a A_72) ((insert1597628439iple_a B_38) B_37)))).
% Axiom fact_427_insertI2:(forall (B_38:hoare_1708887482_state) (A_72:hoare_1708887482_state) (B_37:(hoare_1708887482_state->Prop)), (((member451959335_state A_72) B_37)->((member451959335_state A_72) ((insert528405184_state B_38) B_37)))).
% Axiom fact_428_insertI2:(forall (B_38:pname) (A_72:pname) (B_37:(pname->Prop)), (((member_pname A_72) B_37)->((member_pname A_72) ((insert_pname B_38) B_37)))).
% Axiom fact_429_insert__absorb:(forall (A_71:nat) (A_70:(nat->Prop)), (((member_nat A_71) A_70)->(((eq (nat->Prop)) ((insert_nat A_71) A_70)) A_70))).
% Axiom fact_430_insert__absorb:(forall (A_71:(hoare_2091234717iple_a->Prop)) (A_70:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_71) A_70)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_71) A_70)) A_70))).
% Axiom fact_431_insert__absorb:(forall (A_71:hoare_2091234717iple_a) (A_70:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_71) A_70)->(((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_71) A_70)) A_70))).
% Axiom fact_432_insert__absorb:(forall (A_71:hoare_1708887482_state) (A_70:(hoare_1708887482_state->Prop)), (((member451959335_state A_71) A_70)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_71) A_70)) A_70))).
% Axiom fact_433_insert__absorb:(forall (A_71:pname) (A_70:(pname->Prop)), (((member_pname A_71) A_70)->(((eq (pname->Prop)) ((insert_pname A_71) A_70)) A_70))).
% Axiom fact_434_singletonE:(forall (B_36:nat) (A_69:nat), (((member_nat B_36) ((insert_nat A_69) bot_bot_nat_o))->(((eq nat) B_36) A_69))).
% Axiom fact_435_singletonE:(forall (B_36:(hoare_2091234717iple_a->Prop)) (A_69:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o B_36) ((insert102003750le_a_o A_69) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) B_36) A_69))).
% Axiom fact_436_singletonE:(forall (B_36:hoare_2091234717iple_a) (A_69:hoare_2091234717iple_a), (((member290856304iple_a B_36) ((insert1597628439iple_a A_69) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) B_36) A_69))).
% Axiom fact_437_singletonE:(forall (B_36:hoare_1708887482_state) (A_69:hoare_1708887482_state), (((member451959335_state B_36) ((insert528405184_state A_69) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) B_36) A_69))).
% Axiom fact_438_singletonE:(forall (B_36:pname) (A_69:pname), (((member_pname B_36) ((insert_pname A_69) bot_bot_pname_o))->(((eq pname) B_36) A_69))).
% Axiom fact_439_singleton__inject:(forall (A_68:nat) (B_35:nat), ((((eq (nat->Prop)) ((insert_nat A_68) bot_bot_nat_o)) ((insert_nat B_35) bot_bot_nat_o))->(((eq nat) A_68) B_35))).
% Axiom fact_440_singleton__inject:(forall (A_68:(hoare_2091234717iple_a->Prop)) (B_35:(hoare_2091234717iple_a->Prop)), ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_68) bot_bo1957696069_a_o_o)) ((insert102003750le_a_o B_35) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) A_68) B_35))).
% Axiom fact_441_singleton__inject:(forall (A_68:pname) (B_35:pname), ((((eq (pname->Prop)) ((insert_pname A_68) bot_bot_pname_o)) ((insert_pname B_35) bot_bot_pname_o))->(((eq pname) A_68) B_35))).
% Axiom fact_442_singleton__inject:(forall (A_68:hoare_2091234717iple_a) (B_35:hoare_2091234717iple_a), ((((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_68) bot_bo1791335050le_a_o)) ((insert1597628439iple_a B_35) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) A_68) B_35))).
% Axiom fact_443_singleton__inject:(forall (A_68:hoare_1708887482_state) (B_35:hoare_1708887482_state), ((((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_68) bot_bo19817387tate_o)) ((insert528405184_state B_35) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) A_68) B_35))).
% Axiom fact_444_com__det:(forall (U:state) (C:com) (S:state) (T:state), ((((evalc C) S) T)->((((evalc C) S) U)->(((eq state) U) T)))).
% Axiom fact_445_insert__is__Un:(forall (A_67:nat) (A_66:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_67) A_66)) ((semila848761471_nat_o ((insert_nat A_67) bot_bot_nat_o)) A_66))).
% Axiom fact_446_insert__is__Un:(forall (A_67:(hoare_2091234717iple_a->Prop)) (A_66:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_67) A_66)) ((semila2050116131_a_o_o ((insert102003750le_a_o A_67) bot_bo1957696069_a_o_o)) A_66))).
% Axiom fact_447_insert__is__Un:(forall (A_67:pname) (A_66:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_67) A_66)) ((semila1780557381name_o ((insert_pname A_67) bot_bot_pname_o)) A_66))).
% Axiom fact_448_insert__is__Un:(forall (A_67:hoare_1708887482_state) (A_66:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_67) A_66)) ((semila1122118281tate_o ((insert528405184_state A_67) bot_bo19817387tate_o)) A_66))).
% Axiom fact_449_insert__is__Un:(forall (A_67:hoare_2091234717iple_a) (A_66:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_67) A_66)) ((semila1052848428le_a_o ((insert1597628439iple_a A_67) bot_bo1791335050le_a_o)) A_66))).
% Axiom fact_450_insert__compr__raw:(forall (X:(hoare_2091234717iple_a->Prop)) (Xa:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o X) Xa)) (collec1008234059le_a_o (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((or (((eq (hoare_2091234717iple_a->Prop)) Y_7) X)) ((member99268621le_a_o Y_7) Xa)))))).
% Axiom fact_451_insert__compr__raw:(forall (X:hoare_2091234717iple_a) (Xa:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a X) Xa)) (collec992574898iple_a (fun (Y_7:hoare_2091234717iple_a)=> ((or (((eq hoare_2091234717iple_a) Y_7) X)) ((member290856304iple_a Y_7) Xa)))))).
% Axiom fact_452_insert__compr__raw:(forall (X:hoare_1708887482_state) (Xa:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state X) Xa)) (collec1568722789_state (fun (Y_7:hoare_1708887482_state)=> ((or (((eq hoare_1708887482_state) Y_7) X)) ((member451959335_state Y_7) Xa)))))).
% Axiom fact_453_insert__compr__raw:(forall (X:nat) (Xa:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X) Xa)) (collect_nat (fun (Y_7:nat)=> ((or (((eq nat) Y_7) X)) ((member_nat Y_7) Xa)))))).
% Axiom fact_454_insert__compr__raw:(forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y_7:pname)=> ((or (((eq pname) Y_7) X)) ((member_pname Y_7) Xa)))))).
% Axiom fact_455_derivs__insertD:(forall (G_19:(hoare_2091234717iple_a->Prop)) (T_3:hoare_2091234717iple_a) (Ts_1:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a G_19) ((insert1597628439iple_a T_3) Ts_1))->((and ((hoare_1467856363rivs_a G_19) ((insert1597628439iple_a T_3) bot_bo1791335050le_a_o))) ((hoare_1467856363rivs_a G_19) Ts_1)))).
% Axiom fact_456_derivs__insertD:(forall (G_19:(hoare_1708887482_state->Prop)) (T_3:hoare_1708887482_state) (Ts_1:(hoare_1708887482_state->Prop)), (((hoare_90032982_state G_19) ((insert528405184_state T_3) Ts_1))->((and ((hoare_90032982_state G_19) ((insert528405184_state T_3) bot_bo19817387tate_o))) ((hoare_90032982_state G_19) Ts_1)))).
% Axiom fact_457_hoare__derivs_Oinsert:(forall (Ts:(hoare_2091234717iple_a->Prop)) (G_18:(hoare_2091234717iple_a->Prop)) (T_2:hoare_2091234717iple_a), (((hoare_1467856363rivs_a G_18) ((insert1597628439iple_a T_2) bot_bo1791335050le_a_o))->(((hoare_1467856363rivs_a G_18) Ts)->((hoare_1467856363rivs_a G_18) ((insert1597628439iple_a T_2) Ts))))).
% Axiom fact_458_hoare__derivs_Oinsert:(forall (Ts:(hoare_1708887482_state->Prop)) (G_18:(hoare_1708887482_state->Prop)) (T_2:hoare_1708887482_state), (((hoare_90032982_state G_18) ((insert528405184_state T_2) bot_bo19817387tate_o))->(((hoare_90032982_state G_18) Ts)->((hoare_90032982_state G_18) ((insert528405184_state T_2) Ts))))).
% Axiom fact_459_image__constant__conv:(forall (C_23:nat) (A_65:(nat->Prop)), ((and ((((eq (nat->Prop)) A_65) bot_bot_nat_o)->(((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> C_23)) A_65)) bot_bot_nat_o))) ((not (((eq (nat->Prop)) A_65) bot_bot_nat_o))->(((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> C_23)) A_65)) ((insert_nat C_23) bot_bot_nat_o))))).
% Axiom fact_460_image__constant__conv:(forall (C_23:hoare_1708887482_state) (A_65:(pname->Prop)), ((and ((((eq (pname->Prop)) A_65) bot_bot_pname_o)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X:pname)=> C_23)) A_65)) bot_bo19817387tate_o))) ((not (((eq (pname->Prop)) A_65) bot_bot_pname_o))->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X:pname)=> C_23)) A_65)) ((insert528405184_state C_23) bot_bo19817387tate_o))))).
% Axiom fact_461_image__constant__conv:(forall (C_23:hoare_2091234717iple_a) (A_65:(pname->Prop)), ((and ((((eq (pname->Prop)) A_65) bot_bot_pname_o)->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a (fun (X:pname)=> C_23)) A_65)) bot_bo1791335050le_a_o))) ((not (((eq (pname->Prop)) A_65) bot_bot_pname_o))->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a (fun (X:pname)=> C_23)) A_65)) ((insert1597628439iple_a C_23) bot_bo1791335050le_a_o))))).
% Axiom fact_462_image__constant:(forall (C_22:nat) (X_28:nat) (A_64:(nat->Prop)), (((member_nat X_28) A_64)->(((eq (nat->Prop)) ((image_nat_nat (fun (X:nat)=> C_22)) A_64)) ((insert_nat C_22) bot_bot_nat_o)))).
% Axiom fact_463_image__constant:(forall (C_22:hoare_1708887482_state) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state (fun (X:pname)=> C_22)) A_64)) ((insert528405184_state C_22) bot_bo19817387tate_o)))).
% Axiom fact_464_image__constant:(forall (C_22:nat) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (nat->Prop)) ((image_pname_nat (fun (X:pname)=> C_22)) A_64)) ((insert_nat C_22) bot_bot_nat_o)))).
% Axiom fact_465_image__constant:(forall (C_22:(hoare_2091234717iple_a->Prop)) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((image_742317343le_a_o (fun (X:pname)=> C_22)) A_64)) ((insert102003750le_a_o C_22) bot_bo1957696069_a_o_o)))).
% Axiom fact_466_image__constant:(forall (C_22:pname) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (pname->Prop)) ((image_pname_pname (fun (X:pname)=> C_22)) A_64)) ((insert_pname C_22) bot_bot_pname_o)))).
% Axiom fact_467_image__constant:(forall (C_22:hoare_2091234717iple_a) (X_28:pname) (A_64:(pname->Prop)), (((member_pname X_28) A_64)->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a (fun (X:pname)=> C_22)) A_64)) ((insert1597628439iple_a C_22) bot_bo1791335050le_a_o)))).
% Axiom fact_468_image__insert:(forall (F_40:(nat->nat)) (A_63:nat) (B_34:(nat->Prop)), (((eq (nat->Prop)) ((image_nat_nat F_40) ((insert_nat A_63) B_34))) ((insert_nat (F_40 A_63)) ((image_nat_nat F_40) B_34)))).
% Axiom fact_469_image__insert:(forall (F_40:(pname->hoare_1708887482_state)) (A_63:pname) (B_34:(pname->Prop)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_40) ((insert_pname A_63) B_34))) ((insert528405184_state (F_40 A_63)) ((image_1116629049_state F_40) B_34)))).
% Axiom fact_470_image__insert:(forall (F_40:(pname->hoare_2091234717iple_a)) (A_63:pname) (B_34:(pname->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_40) ((insert_pname A_63) B_34))) ((insert1597628439iple_a (F_40 A_63)) ((image_231808478iple_a F_40) B_34)))).
% Axiom fact_471_insert__image:(forall (F_39:(nat->nat)) (X_27:nat) (A_62:(nat->Prop)), (((member_nat X_27) A_62)->(((eq (nat->Prop)) ((insert_nat (F_39 X_27)) ((image_nat_nat F_39) A_62))) ((image_nat_nat F_39) A_62)))).
% Axiom fact_472_insert__image:(forall (F_39:(pname->hoare_1708887482_state)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (hoare_1708887482_state->Prop)) ((insert528405184_state (F_39 X_27)) ((image_1116629049_state F_39) A_62))) ((image_1116629049_state F_39) A_62)))).
% Axiom fact_473_insert__image:(forall (F_39:(pname->nat)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (nat->Prop)) ((insert_nat (F_39 X_27)) ((image_pname_nat F_39) A_62))) ((image_pname_nat F_39) A_62)))).
% Axiom fact_474_insert__image:(forall (F_39:(pname->(hoare_2091234717iple_a->Prop))) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o (F_39 X_27)) ((image_742317343le_a_o F_39) A_62))) ((image_742317343le_a_o F_39) A_62)))).
% Axiom fact_475_insert__image:(forall (F_39:(pname->pname)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (pname->Prop)) ((insert_pname (F_39 X_27)) ((image_pname_pname F_39) A_62))) ((image_pname_pname F_39) A_62)))).
% Axiom fact_476_insert__image:(forall (F_39:(pname->hoare_2091234717iple_a)) (X_27:pname) (A_62:(pname->Prop)), (((member_pname X_27) A_62)->(((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a (F_39 X_27)) ((image_231808478iple_a F_39) A_62))) ((image_231808478iple_a F_39) A_62)))).
% Axiom fact_477_Un__insert__right:(forall (A_61:(nat->Prop)) (A_60:nat) (B_33:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_61) ((insert_nat A_60) B_33))) ((insert_nat A_60) ((semila848761471_nat_o A_61) B_33)))).
% Axiom fact_478_Un__insert__right:(forall (A_61:((hoare_2091234717iple_a->Prop)->Prop)) (A_60:(hoare_2091234717iple_a->Prop)) (B_33:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_61) ((insert102003750le_a_o A_60) B_33))) ((insert102003750le_a_o A_60) ((semila2050116131_a_o_o A_61) B_33)))).
% Axiom fact_479_Un__insert__right:(forall (A_61:(pname->Prop)) (A_60:pname) (B_33:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_61) ((insert_pname A_60) B_33))) ((insert_pname A_60) ((semila1780557381name_o A_61) B_33)))).
% Axiom fact_480_Un__insert__right:(forall (A_61:(hoare_1708887482_state->Prop)) (A_60:hoare_1708887482_state) (B_33:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_61) ((insert528405184_state A_60) B_33))) ((insert528405184_state A_60) ((semila1122118281tate_o A_61) B_33)))).
% Axiom fact_481_Un__insert__right:(forall (A_61:(hoare_2091234717iple_a->Prop)) (A_60:hoare_2091234717iple_a) (B_33:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_61) ((insert1597628439iple_a A_60) B_33))) ((insert1597628439iple_a A_60) ((semila1052848428le_a_o A_61) B_33)))).
% Axiom fact_482_Un__insert__left:(forall (A_59:nat) (B_32:(nat->Prop)) (C_21:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((insert_nat A_59) B_32)) C_21)) ((insert_nat A_59) ((semila848761471_nat_o B_32) C_21)))).
% Axiom fact_483_Un__insert__left:(forall (A_59:(hoare_2091234717iple_a->Prop)) (B_32:((hoare_2091234717iple_a->Prop)->Prop)) (C_21:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((insert102003750le_a_o A_59) B_32)) C_21)) ((insert102003750le_a_o A_59) ((semila2050116131_a_o_o B_32) C_21)))).
% Axiom fact_484_Un__insert__left:(forall (A_59:pname) (B_32:(pname->Prop)) (C_21:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((insert_pname A_59) B_32)) C_21)) ((insert_pname A_59) ((semila1780557381name_o B_32) C_21)))).
% Axiom fact_485_Un__insert__left:(forall (A_59:hoare_1708887482_state) (B_32:(hoare_1708887482_state->Prop)) (C_21:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((insert528405184_state A_59) B_32)) C_21)) ((insert528405184_state A_59) ((semila1122118281tate_o B_32) C_21)))).
% Axiom fact_486_Un__insert__left:(forall (A_59:hoare_2091234717iple_a) (B_32:(hoare_2091234717iple_a->Prop)) (C_21:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((insert1597628439iple_a A_59) B_32)) C_21)) ((insert1597628439iple_a A_59) ((semila1052848428le_a_o B_32) C_21)))).
% Axiom fact_487_empty__is__image:(forall (F_38:(nat->nat)) (A_58:(nat->Prop)), ((iff (((eq (nat->Prop)) bot_bot_nat_o) ((image_nat_nat F_38) A_58))) (((eq (nat->Prop)) A_58) bot_bot_nat_o))).
% Axiom fact_488_empty__is__image:(forall (F_38:(pname->hoare_1708887482_state)) (A_58:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) bot_bo19817387tate_o) ((image_1116629049_state F_38) A_58))) (((eq (pname->Prop)) A_58) bot_bot_pname_o))).
% Axiom fact_489_empty__is__image:(forall (F_38:(pname->hoare_2091234717iple_a)) (A_58:(pname->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) bot_bo1791335050le_a_o) ((image_231808478iple_a F_38) A_58))) (((eq (pname->Prop)) A_58) bot_bot_pname_o))).
% Axiom fact_490_image__empty:(forall (F_37:(nat->nat)), (((eq (nat->Prop)) ((image_nat_nat F_37) bot_bot_nat_o)) bot_bot_nat_o)).
% Axiom fact_491_image__empty:(forall (F_37:(pname->hoare_1708887482_state)), (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_37) bot_bot_pname_o)) bot_bo19817387tate_o)).
% Axiom fact_492_image__empty:(forall (F_37:(pname->hoare_2091234717iple_a)), (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_37) bot_bot_pname_o)) bot_bo1791335050le_a_o)).
% Axiom fact_493_image__is__empty:(forall (F_36:(nat->nat)) (A_57:(nat->Prop)), ((iff (((eq (nat->Prop)) ((image_nat_nat F_36) A_57)) bot_bot_nat_o)) (((eq (nat->Prop)) A_57) bot_bot_nat_o))).
% Axiom fact_494_image__is__empty:(forall (F_36:(pname->hoare_1708887482_state)) (A_57:(pname->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_36) A_57)) bot_bo19817387tate_o)) (((eq (pname->Prop)) A_57) bot_bot_pname_o))).
% Axiom fact_495_image__is__empty:(forall (F_36:(pname->hoare_2091234717iple_a)) (A_57:(pname->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_36) A_57)) bot_bo1791335050le_a_o)) (((eq (pname->Prop)) A_57) bot_bot_pname_o))).
% Axiom fact_496_ball__empty:(forall (P_23:(nat->Prop)) (X:nat), (((member_nat X) bot_bot_nat_o)->(P_23 X))).
% Axiom fact_497_ball__empty:(forall (P_23:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), (((member290856304iple_a X) bot_bo1791335050le_a_o)->(P_23 X))).
% Axiom fact_498_ball__empty:(forall (P_23:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o X) bot_bo1957696069_a_o_o)->(P_23 X))).
% Axiom fact_499_ball__empty:(forall (P_23:(pname->Prop)) (X:pname), (((member_pname X) bot_bot_pname_o)->(P_23 X))).
% Axiom fact_500_ball__empty:(forall (P_23:(hoare_1708887482_state->Prop)) (X:hoare_1708887482_state), (((member451959335_state X) bot_bo19817387tate_o)->(P_23 X))).
% Axiom fact_501_Un__empty__left:(forall (B_31:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o bot_bot_nat_o) B_31)) B_31)).
% Axiom fact_502_Un__empty__left:(forall (B_31:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o bot_bo1957696069_a_o_o) B_31)) B_31)).
% Axiom fact_503_Un__empty__left:(forall (B_31:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) B_31)) B_31)).
% Axiom fact_504_Un__empty__left:(forall (B_31:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_o) B_31)) B_31)).
% Axiom fact_505_Un__empty__left:(forall (B_31:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o bot_bo1791335050le_a_o) B_31)) B_31)).
% Axiom fact_506_Un__empty__right:(forall (A_56:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o A_56) bot_bot_nat_o)) A_56)).
% Axiom fact_507_Un__empty__right:(forall (A_56:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_56) bot_bo1957696069_a_o_o)) A_56)).
% Axiom fact_508_Un__empty__right:(forall (A_56:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_56) bot_bot_pname_o)) A_56)).
% Axiom fact_509_Un__empty__right:(forall (A_56:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_56) bot_bo19817387tate_o)) A_56)).
% Axiom fact_510_Un__empty__right:(forall (A_56:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_56) bot_bo1791335050le_a_o)) A_56)).
% Axiom fact_511_Un__empty:(forall (A_55:(nat->Prop)) (B_30:(nat->Prop)), ((iff (((eq (nat->Prop)) ((semila848761471_nat_o A_55) B_30)) bot_bot_nat_o)) ((and (((eq (nat->Prop)) A_55) bot_bot_nat_o)) (((eq (nat->Prop)) B_30) bot_bot_nat_o)))).
% Axiom fact_512_Un__empty:(forall (A_55:((hoare_2091234717iple_a->Prop)->Prop)) (B_30:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o A_55) B_30)) bot_bo1957696069_a_o_o)) ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_55) bot_bo1957696069_a_o_o)) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_30) bot_bo1957696069_a_o_o)))).
% Axiom fact_513_Un__empty:(forall (A_55:(pname->Prop)) (B_30:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o A_55) B_30)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) A_55) bot_bot_pname_o)) (((eq (pname->Prop)) B_30) bot_bot_pname_o)))).
% Axiom fact_514_Un__empty:(forall (A_55:(hoare_1708887482_state->Prop)) (B_30:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o A_55) B_30)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) A_55) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) B_30) bot_bo19817387tate_o)))).
% Axiom fact_515_Un__empty:(forall (A_55:(hoare_2091234717iple_a->Prop)) (B_30:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o A_55) B_30)) bot_bo1791335050le_a_o)) ((and (((eq (hoare_2091234717iple_a->Prop)) A_55) bot_bo1791335050le_a_o)) (((eq (hoare_2091234717iple_a->Prop)) B_30) bot_bo1791335050le_a_o)))).
% Axiom fact_516_constant:(forall (G_17:(hoare_2091234717iple_a->Prop)) (P_22:(x_a->(state->Prop))) (C_20:com) (Q_15:(x_a->(state->Prop))) (C_19:Prop), ((C_19->((hoare_1467856363rivs_a G_17) ((insert1597628439iple_a (((hoare_657976383iple_a P_22) C_20) Q_15)) bot_bo1791335050le_a_o)))->((hoare_1467856363rivs_a G_17) ((insert1597628439iple_a (((hoare_657976383iple_a (fun (Z_5:x_a) (S_2:state)=> ((and ((P_22 Z_5) S_2)) C_19))) C_20) Q_15)) bot_bo1791335050le_a_o)))).
% Axiom fact_517_constant:(forall (G_17:(hoare_1708887482_state->Prop)) (P_22:(state->(state->Prop))) (C_20:com) (Q_15:(state->(state->Prop))) (C_19:Prop), ((C_19->((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state P_22) C_20) Q_15)) bot_bo19817387tate_o)))->((hoare_90032982_state G_17) ((insert528405184_state (((hoare_858012674_state (fun (Z_5:state) (S_2:state)=> ((and ((P_22 Z_5) S_2)) C_19))) C_20) Q_15)) bot_bo19817387tate_o)))).
% Axiom fact_518_empty:(forall (G_16:(hoare_2091234717iple_a->Prop)), ((hoare_1467856363rivs_a G_16) bot_bo1791335050le_a_o)).
% Axiom fact_519_empty:(forall (G_16:(hoare_1708887482_state->Prop)), ((hoare_90032982_state G_16) bot_bo19817387tate_o)).
% Axiom fact_520_sup__bot__left:(forall (X_26:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o bot_bot_nat_o) X_26)) X_26)).
% Axiom fact_521_sup__bot__left:(forall (X_26:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o bot_bo1957696069_a_o_o) X_26)) X_26)).
% Axiom fact_522_sup__bot__left:(forall (X_26:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o bot_bot_pname_o) X_26)) X_26)).
% Axiom fact_523_sup__bot__left:(forall (X_26:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o bot_bo19817387tate_o) X_26)) X_26)).
% Axiom fact_524_sup__bot__left:(forall (X_26:Prop), ((iff ((semila10642723_sup_o bot_bot_o) X_26)) X_26)).
% Axiom fact_525_sup__bot__left:(forall (X_26:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o bot_bo1791335050le_a_o) X_26)) X_26)).
% Axiom fact_526_sup__bot__right:(forall (X_25:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o X_25) bot_bot_nat_o)) X_25)).
% Axiom fact_527_sup__bot__right:(forall (X_25:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_25) bot_bo1957696069_a_o_o)) X_25)).
% Axiom fact_528_sup__bot__right:(forall (X_25:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_25) bot_bot_pname_o)) X_25)).
% Axiom fact_529_sup__bot__right:(forall (X_25:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_25) bot_bo19817387tate_o)) X_25)).
% Axiom fact_530_sup__bot__right:(forall (X_25:Prop), ((iff ((semila10642723_sup_o X_25) bot_bot_o)) X_25)).
% Axiom fact_531_sup__bot__right:(forall (X_25:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_25) bot_bo1791335050le_a_o)) X_25)).
% Axiom fact_532_sup__eq__bot__iff:(forall (X_24:(nat->Prop)) (Y_8:(nat->Prop)), ((iff (((eq (nat->Prop)) ((semila848761471_nat_o X_24) Y_8)) bot_bot_nat_o)) ((and (((eq (nat->Prop)) X_24) bot_bot_nat_o)) (((eq (nat->Prop)) Y_8) bot_bot_nat_o)))).
% Axiom fact_533_sup__eq__bot__iff:(forall (X_24:((hoare_2091234717iple_a->Prop)->Prop)) (Y_8:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o X_24) Y_8)) bot_bo1957696069_a_o_o)) ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) X_24) bot_bo1957696069_a_o_o)) (((eq ((hoare_2091234717iple_a->Prop)->Prop)) Y_8) bot_bo1957696069_a_o_o)))).
% Axiom fact_534_sup__eq__bot__iff:(forall (X_24:(pname->Prop)) (Y_8:(pname->Prop)), ((iff (((eq (pname->Prop)) ((semila1780557381name_o X_24) Y_8)) bot_bot_pname_o)) ((and (((eq (pname->Prop)) X_24) bot_bot_pname_o)) (((eq (pname->Prop)) Y_8) bot_bot_pname_o)))).
% Axiom fact_535_sup__eq__bot__iff:(forall (X_24:(hoare_1708887482_state->Prop)) (Y_8:(hoare_1708887482_state->Prop)), ((iff (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o X_24) Y_8)) bot_bo19817387tate_o)) ((and (((eq (hoare_1708887482_state->Prop)) X_24) bot_bo19817387tate_o)) (((eq (hoare_1708887482_state->Prop)) Y_8) bot_bo19817387tate_o)))).
% Axiom fact_536_sup__eq__bot__iff:(forall (X_24:Prop) (Y_8:Prop), ((iff ((iff ((semila10642723_sup_o X_24) Y_8)) bot_bot_o)) ((and ((iff X_24) bot_bot_o)) ((iff Y_8) bot_bot_o)))).
% Axiom fact_537_sup__eq__bot__iff:(forall (X_24:(hoare_2091234717iple_a->Prop)) (Y_8:(hoare_2091234717iple_a->Prop)), ((iff (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o X_24) Y_8)) bot_bo1791335050le_a_o)) ((and (((eq (hoare_2091234717iple_a->Prop)) X_24) bot_bo1791335050le_a_o)) (((eq (hoare_2091234717iple_a->Prop)) Y_8) bot_bo1791335050le_a_o)))).
% Axiom fact_538_triple__valid__Suc:(forall (N_5:nat) (T_1:hoare_1708887482_state), (((hoare_23738522_state (suc N_5)) T_1)->((hoare_23738522_state N_5) T_1))).
% Axiom fact_539_triple__valid__Suc:(forall (N_5:nat) (T_1:hoare_2091234717iple_a), (((hoare_1421888935alid_a (suc N_5)) T_1)->((hoare_1421888935alid_a N_5) T_1))).
% Axiom fact_540_insert__def:(forall (A_54:(hoare_2091234717iple_a->Prop)) (B_29:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((insert102003750le_a_o A_54) B_29)) ((semila2050116131_a_o_o (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> (((eq (hoare_2091234717iple_a->Prop)) X) A_54)))) B_29))).
% Axiom fact_541_insert__def:(forall (A_54:pname) (B_29:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_54) B_29)) ((semila1780557381name_o (collect_pname (fun (X:pname)=> (((eq pname) X) A_54)))) B_29))).
% Axiom fact_542_insert__def:(forall (A_54:hoare_1708887482_state) (B_29:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((insert528405184_state A_54) B_29)) ((semila1122118281tate_o (collec1568722789_state (fun (X:hoare_1708887482_state)=> (((eq hoare_1708887482_state) X) A_54)))) B_29))).
% Axiom fact_543_insert__def:(forall (A_54:hoare_2091234717iple_a) (B_29:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((insert1597628439iple_a A_54) B_29)) ((semila1052848428le_a_o (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> (((eq hoare_2091234717iple_a) X) A_54)))) B_29))).
% Axiom fact_544_insert__def:(forall (A_54:nat) (B_29:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_54) B_29)) ((semila848761471_nat_o (collect_nat (fun (X:nat)=> (((eq nat) X) A_54)))) B_29))).
% Axiom fact_545_weak__Body:(forall (G_15:(hoare_2091234717iple_a->Prop)) (P_21:(x_a->(state->Prop))) (Pn_3:pname) (Q_14:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_15) ((insert1597628439iple_a (((hoare_657976383iple_a P_21) (the_com (body_1 Pn_3))) Q_14)) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_15) ((insert1597628439iple_a (((hoare_657976383iple_a P_21) (body Pn_3)) Q_14)) bot_bo1791335050le_a_o)))).
% Axiom fact_546_weak__Body:(forall (G_15:(hoare_1708887482_state->Prop)) (P_21:(state->(state->Prop))) (Pn_3:pname) (Q_14:(state->(state->Prop))), (((hoare_90032982_state G_15) ((insert528405184_state (((hoare_858012674_state P_21) (the_com (body_1 Pn_3))) Q_14)) bot_bo19817387tate_o))->((hoare_90032982_state G_15) ((insert528405184_state (((hoare_858012674_state P_21) (body Pn_3)) Q_14)) bot_bo19817387tate_o)))).
% Axiom fact_547_BodyN:(forall (P_20:(x_a->(state->Prop))) (Pn_2:pname) (Q_13:(x_a->(state->Prop))) (G_14:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a ((insert1597628439iple_a (((hoare_657976383iple_a P_20) (body Pn_2)) Q_13)) G_14)) ((insert1597628439iple_a (((hoare_657976383iple_a P_20) (the_com (body_1 Pn_2))) Q_13)) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_14) ((insert1597628439iple_a (((hoare_657976383iple_a P_20) (body Pn_2)) Q_13)) bot_bo1791335050le_a_o)))).
% Axiom fact_548_BodyN:(forall (P_20:(state->(state->Prop))) (Pn_2:pname) (Q_13:(state->(state->Prop))) (G_14:(hoare_1708887482_state->Prop)), (((hoare_90032982_state ((insert528405184_state (((hoare_858012674_state P_20) (body Pn_2)) Q_13)) G_14)) ((insert528405184_state (((hoare_858012674_state P_20) (the_com (body_1 Pn_2))) Q_13)) bot_bo19817387tate_o))->((hoare_90032982_state G_14) ((insert528405184_state (((hoare_858012674_state P_20) (body Pn_2)) Q_13)) bot_bo19817387tate_o)))).
% Axiom fact_549_escape:(forall (G_13:(hoare_2091234717iple_a->Prop)) (C_18:com) (Q_12:(x_a->(state->Prop))) (P_19:(x_a->(state->Prop))), ((forall (Z_5:x_a) (S_2:state), (((P_19 Z_5) S_2)->((hoare_1467856363rivs_a G_13) ((insert1597628439iple_a (((hoare_657976383iple_a (fun (Za:x_a) (S_3:state)=> (((eq state) S_3) S_2))) C_18) (fun (Z_6:x_a)=> (Q_12 Z_5)))) bot_bo1791335050le_a_o))))->((hoare_1467856363rivs_a G_13) ((insert1597628439iple_a (((hoare_657976383iple_a P_19) C_18) Q_12)) bot_bo1791335050le_a_o)))).
% Axiom fact_550_escape:(forall (G_13:(hoare_1708887482_state->Prop)) (C_18:com) (Q_12:(state->(state->Prop))) (P_19:(state->(state->Prop))), ((forall (Z_5:state) (S_2:state), (((P_19 Z_5) S_2)->((hoare_90032982_state G_13) ((insert528405184_state (((hoare_858012674_state (fun (Za:state) (S_3:state)=> (((eq state) S_3) S_2))) C_18) (fun (Z_6:state)=> (Q_12 Z_5)))) bot_bo19817387tate_o))))->((hoare_90032982_state G_13) ((insert528405184_state (((hoare_858012674_state P_19) C_18) Q_12)) bot_bo19817387tate_o)))).
% Axiom fact_551_conseq1:(forall (P_18:(x_a->(state->Prop))) (G_12:(hoare_2091234717iple_a->Prop)) (P_17:(x_a->(state->Prop))) (C_17:com) (Q_11:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_12) ((insert1597628439iple_a (((hoare_657976383iple_a P_17) C_17) Q_11)) bot_bo1791335050le_a_o))->((forall (Z_5:x_a) (S_2:state), (((P_18 Z_5) S_2)->((P_17 Z_5) S_2)))->((hoare_1467856363rivs_a G_12) ((insert1597628439iple_a (((hoare_657976383iple_a P_18) C_17) Q_11)) bot_bo1791335050le_a_o))))).
% Axiom fact_552_conseq1:(forall (P_18:(state->(state->Prop))) (G_12:(hoare_1708887482_state->Prop)) (P_17:(state->(state->Prop))) (C_17:com) (Q_11:(state->(state->Prop))), (((hoare_90032982_state G_12) ((insert528405184_state (((hoare_858012674_state P_17) C_17) Q_11)) bot_bo19817387tate_o))->((forall (Z_5:state) (S_2:state), (((P_18 Z_5) S_2)->((P_17 Z_5) S_2)))->((hoare_90032982_state G_12) ((insert528405184_state (((hoare_858012674_state P_18) C_17) Q_11)) bot_bo19817387tate_o))))).
% Axiom fact_553_conseq2:(forall (Q_10:(x_a->(state->Prop))) (G_11:(hoare_2091234717iple_a->Prop)) (P_16:(x_a->(state->Prop))) (C_16:com) (Q_9:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_11) ((insert1597628439iple_a (((hoare_657976383iple_a P_16) C_16) Q_9)) bot_bo1791335050le_a_o))->((forall (Z_5:x_a) (S_2:state), (((Q_9 Z_5) S_2)->((Q_10 Z_5) S_2)))->((hoare_1467856363rivs_a G_11) ((insert1597628439iple_a (((hoare_657976383iple_a P_16) C_16) Q_10)) bot_bo1791335050le_a_o))))).
% Axiom fact_554_conseq2:(forall (Q_10:(state->(state->Prop))) (G_11:(hoare_1708887482_state->Prop)) (P_16:(state->(state->Prop))) (C_16:com) (Q_9:(state->(state->Prop))), (((hoare_90032982_state G_11) ((insert528405184_state (((hoare_858012674_state P_16) C_16) Q_9)) bot_bo19817387tate_o))->((forall (Z_5:state) (S_2:state), (((Q_9 Z_5) S_2)->((Q_10 Z_5) S_2)))->((hoare_90032982_state G_11) ((insert528405184_state (((hoare_858012674_state P_16) C_16) Q_10)) bot_bo19817387tate_o))))).
% Axiom fact_555_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_1169027232size_a Fa) (((hoare_657976383iple_a Fun1_1) Com_3) Fun2_1))) zero_zero_nat)).
% Axiom fact_556_triple_Osize_I1_J:(forall (Fa:(state->nat)) (Fun1_1:(state->(state->Prop))) (Com_3:com) (Fun2_1:(state->(state->Prop))), (((eq nat) ((hoare_518771297_state Fa) (((hoare_858012674_state Fun1_1) Com_3) Fun2_1))) zero_zero_nat)).
% Axiom fact_557_MGT__def:(forall (C:com), (((eq hoare_1708887482_state) (hoare_Mirabelle_MGT C)) (((hoare_858012674_state fequal_state) C) (evalc C)))).
% Axiom fact_558_triple_Osize_I2_J:(forall (Fun1:(x_a->(state->Prop))) (Com_2:com) (Fun2:(x_a->(state->Prop))), (((eq nat) (size_s1040486067iple_a (((hoare_657976383iple_a Fun1) Com_2) Fun2))) zero_zero_nat)).
% Axiom fact_559_triple_Osize_I2_J:(forall (Fun1:(state->(state->Prop))) (Com_2:com) (Fun2:(state->(state->Prop))), (((eq nat) (size_s1186992420_state (((hoare_858012674_state Fun1) Com_2) Fun2))) zero_zero_nat)).
% Axiom fact_560_conseq12:(forall (Q_8:(x_a->(state->Prop))) (P_15:(x_a->(state->Prop))) (G_10:(hoare_2091234717iple_a->Prop)) (P_14:(x_a->(state->Prop))) (C_15:com) (Q_7:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_10) ((insert1597628439iple_a (((hoare_657976383iple_a P_14) C_15) Q_7)) bot_bo1791335050le_a_o))->((forall (Z_5:x_a) (S_2:state), (((P_15 Z_5) S_2)->(forall (S_3:state), ((forall (Z_6:x_a), (((P_14 Z_6) S_2)->((Q_7 Z_6) S_3)))->((Q_8 Z_5) S_3)))))->((hoare_1467856363rivs_a G_10) ((insert1597628439iple_a (((hoare_657976383iple_a P_15) C_15) Q_8)) bot_bo1791335050le_a_o))))).
% Axiom fact_561_conseq12:(forall (Q_8:(state->(state->Prop))) (P_15:(state->(state->Prop))) (G_10:(hoare_1708887482_state->Prop)) (P_14:(state->(state->Prop))) (C_15:com) (Q_7:(state->(state->Prop))), (((hoare_90032982_state G_10) ((insert528405184_state (((hoare_858012674_state P_14) C_15) Q_7)) bot_bo19817387tate_o))->((forall (Z_5:state) (S_2:state), (((P_15 Z_5) S_2)->(forall (S_3:state), ((forall (Z_6:state), (((P_14 Z_6) S_2)->((Q_7 Z_6) S_3)))->((Q_8 Z_5) S_3)))))->((hoare_90032982_state G_10) ((insert528405184_state (((hoare_858012674_state P_15) C_15) Q_8)) bot_bo19817387tate_o))))).
% Axiom fact_562_the__elem__eq:(forall (X_23:nat), (((eq nat) (the_elem_nat ((insert_nat X_23) bot_bot_nat_o))) X_23)).
% Axiom fact_563_the__elem__eq:(forall (X_23:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (the_el1618277441le_a_o ((insert102003750le_a_o X_23) bot_bo1957696069_a_o_o))) X_23)).
% Axiom fact_564_the__elem__eq:(forall (X_23:pname), (((eq pname) (the_elem_pname ((insert_pname X_23) bot_bot_pname_o))) X_23)).
% Axiom fact_565_the__elem__eq:(forall (X_23:hoare_2091234717iple_a), (((eq hoare_2091234717iple_a) (the_el13400124iple_a ((insert1597628439iple_a X_23) bot_bo1791335050le_a_o))) X_23)).
% Axiom fact_566_the__elem__eq:(forall (X_23:hoare_1708887482_state), (((eq hoare_1708887482_state) (the_el864710747_state ((insert528405184_state X_23) bot_bo19817387tate_o))) X_23)).
% Axiom fact_567_Suc__neq__Zero:(forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))).
% Axiom fact_568_bot__nat__def:(((eq nat) bot_bot_nat) zero_zero_nat).
% Axiom fact_569_n__not__Suc__n:(forall (N_1:nat), (not (((eq nat) N_1) (suc N_1)))).
% Axiom fact_570_Suc__n__not__n:(forall (N_1:nat), (not (((eq nat) (suc N_1)) N_1))).
% Axiom fact_571_nat_Oinject:(forall (Nat_3:nat) (Nat_2:nat), ((iff (((eq nat) (suc Nat_3)) (suc Nat_2))) (((eq nat) Nat_3) Nat_2))).
% Axiom fact_572_Suc__inject:(forall (X_1:nat) (Y:nat), ((((eq nat) (suc X_1)) (suc Y))->(((eq nat) X_1) Y))).
% Axiom fact_573_Zero__not__Suc:(forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))).
% Axiom fact_574_nat_Osimps_I2_J:(forall (Nat_2:nat), (not (((eq nat) zero_zero_nat) (suc Nat_2)))).
% Axiom fact_575_Suc__not__Zero:(forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))).
% Axiom fact_576_nat_Osimps_I3_J:(forall (Nat_1:nat), (not (((eq nat) (suc Nat_1)) zero_zero_nat))).
% Axiom fact_577_Zero__neq__Suc:(forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))).
% Axiom fact_578_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_579_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_580_zero__induct:(forall (P:(nat->Prop)) (K_1:nat), ((P K_1)->((forall (N:nat), ((P (suc N))->(P N)))->(P zero_zero_nat)))).
% Axiom fact_581_nat_Oexhaust:(forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat:nat), (not (((eq nat) Y) (suc Nat))))->False))).
% Axiom fact_582_bot__fun__def:(forall (X:nat), ((iff (bot_bot_nat_o X)) bot_bot_o)).
% Axiom fact_583_bot__fun__def:(forall (X:hoare_2091234717iple_a), ((iff (bot_bo1791335050le_a_o X)) bot_bot_o)).
% Axiom fact_584_bot__fun__def:(forall (X:(hoare_2091234717iple_a->Prop)), ((iff (bot_bo1957696069_a_o_o X)) bot_bot_o)).
% Axiom fact_585_bot__fun__def:(forall (X:pname), ((iff (bot_bot_pname_o X)) bot_bot_o)).
% Axiom fact_586_bot__fun__def:(forall (X:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X)) bot_bot_o)).
% Axiom fact_587_bot__apply:(forall (X_22:nat), ((iff (bot_bot_nat_o X_22)) bot_bot_o)).
% Axiom fact_588_bot__apply:(forall (X_22:hoare_2091234717iple_a), ((iff (bot_bo1791335050le_a_o X_22)) bot_bot_o)).
% Axiom fact_589_bot__apply:(forall (X_22:(hoare_2091234717iple_a->Prop)), ((iff (bot_bo1957696069_a_o_o X_22)) bot_bot_o)).
% Axiom fact_590_bot__apply:(forall (X_22:pname), ((iff (bot_bot_pname_o X_22)) bot_bot_o)).
% Axiom fact_591_bot__apply:(forall (X_22:hoare_1708887482_state), ((iff (bot_bo19817387tate_o X_22)) bot_bot_o)).
% Axiom fact_592_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_593_hoare__derivs_OSkip:(forall (G_9:(hoare_2091234717iple_a->Prop)) (P_13:(x_a->(state->Prop))), ((hoare_1467856363rivs_a G_9) ((insert1597628439iple_a (((hoare_657976383iple_a P_13) skip) P_13)) bot_bo1791335050le_a_o))).
% Axiom fact_594_hoare__derivs_OSkip:(forall (G_9:(hoare_1708887482_state->Prop)) (P_13:(state->(state->Prop))), ((hoare_90032982_state G_9) ((insert528405184_state (((hoare_858012674_state P_13) skip) P_13)) bot_bo19817387tate_o))).
% Axiom fact_595_LoopF:(forall (G_8:(hoare_2091234717iple_a->Prop)) (P_12:(x_a->(state->Prop))) (B_28:(state->Prop)) (C_14:com), ((hoare_1467856363rivs_a G_8) ((insert1597628439iple_a (((hoare_657976383iple_a (fun (Z_5:x_a) (S_2:state)=> ((and ((P_12 Z_5) S_2)) (not (B_28 S_2))))) ((while B_28) C_14)) P_12)) bot_bo1791335050le_a_o))).
% Axiom fact_596_LoopF:(forall (G_8:(hoare_1708887482_state->Prop)) (P_12:(state->(state->Prop))) (B_28:(state->Prop)) (C_14:com), ((hoare_90032982_state G_8) ((insert528405184_state (((hoare_858012674_state (fun (Z_5:state) (S_2:state)=> ((and ((P_12 Z_5) S_2)) (not (B_28 S_2))))) ((while B_28) C_14)) P_12)) bot_bo19817387tate_o))).
% Axiom fact_597_evaln_OWhileFalse:(forall (C:com) (N_1:nat) (B:(state->Prop)) (S:state), (((B S)->False)->((((evaln ((while B) C)) S) N_1) S))).
% Axiom fact_598_evaln_OWhileTrue:(forall (S2:state) (C:com) (N_1:nat) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->(((((evaln C) S0) N_1) S1)->(((((evaln ((while B) C)) S1) N_1) S2)->((((evaln ((while B) C)) S0) N_1) S2))))).
% Axiom fact_599_evalc_OWhileTrue:(forall (S2:state) (C:com) (S1:state) (B:(state->Prop)) (S0:state), ((B S0)->((((evalc C) S0) S1)->((((evalc ((while B) C)) S1) S2)->(((evalc ((while B) C)) S0) S2))))).
% Axiom fact_600_evalc_OWhileFalse:(forall (C:com) (B:(state->Prop)) (S:state), (((B S)->False)->(((evalc ((while B) C)) S) S))).
% Axiom fact_601_evaln_OSkip:(forall (S:state) (N_1:nat), ((((evaln skip) S) N_1) S)).
% Axiom fact_602_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_603_evalc__elim__cases_I1_J:(forall (S:state) (T:state), ((((evalc skip) S) T)->(((eq state) T) S))).
% Axiom fact_604_evalc_OSkip:(forall (S:state), (((evalc skip) S) S)).
% Axiom fact_605_com_Osimps_I16_J:(forall (Fun:(state->Prop)) (Com:com), (not (((eq com) skip) ((while Fun) Com)))).
% Axiom fact_606_com_Osimps_I17_J:(forall (Fun:(state->Prop)) (Com:com), (not (((eq com) ((while Fun) Com)) skip))).
% Axiom fact_607_com_Osimps_I5_J:(forall (Fun_1:(state->Prop)) (Com_1:com) (Fun:(state->Prop)) (Com:com), ((iff (((eq com) ((while Fun_1) Com_1)) ((while Fun) Com))) ((and (((eq (state->Prop)) Fun_1) Fun)) (((eq com) Com_1) Com)))).
% Axiom fact_608_evaln__Suc:(forall (C:com) (S:state) (N_1:nat) (S_4:state), (((((evaln C) S) N_1) S_4)->((((evaln C) S) (suc N_1)) S_4))).
% Axiom fact_609_evaln__evalc:(forall (C:com) (S:state) (N_1:nat) (T:state), (((((evaln C) S) N_1) T)->(((evalc C) S) T))).
% Axiom fact_610_eval__eq:(forall (C:com) (S:state) (T:state), ((iff (((evalc C) S) T)) ((ex nat) (fun (N:nat)=> ((((evaln C) S) N) T))))).
% Axiom fact_611_com_Osimps_I59_J:(forall (Pname:pname) (Fun_1:(state->Prop)) (Com_1:com), (not (((eq com) (body Pname)) ((while Fun_1) Com_1)))).
% Axiom fact_612_com_Osimps_I58_J:(forall (Fun_1:(state->Prop)) (Com_1:com) (Pname:pname), (not (((eq com) ((while Fun_1) Com_1)) (body Pname)))).
% Axiom fact_613_com_Osimps_I18_J:(forall (Pname:pname), (not (((eq com) skip) (body Pname)))).
% Axiom fact_614_com_Osimps_I19_J:(forall (Pname:pname), (not (((eq com) (body Pname)) skip))).
% Axiom fact_615_triple__valid__def2:(forall (N_4:nat) (P_11:(state->(state->Prop))) (C_13:com) (Q_6:(state->(state->Prop))), ((iff ((hoare_23738522_state N_4) (((hoare_858012674_state P_11) C_13) Q_6))) (forall (Z_5:state) (S_2:state), (((P_11 Z_5) S_2)->(forall (S_3:state), (((((evaln C_13) S_2) N_4) S_3)->((Q_6 Z_5) S_3))))))).
% Axiom fact_616_triple__valid__def2:(forall (N_4:nat) (P_11:(x_a->(state->Prop))) (C_13:com) (Q_6:(x_a->(state->Prop))), ((iff ((hoare_1421888935alid_a N_4) (((hoare_657976383iple_a P_11) C_13) Q_6))) (forall (Z_5:x_a) (S_2:state), (((P_11 Z_5) S_2)->(forall (S_3:state), (((((evaln C_13) S_2) N_4) S_3)->((Q_6 Z_5) S_3))))))).
% Axiom fact_617_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_618_evalc__WHILE__case:(forall (B:(state->Prop)) (C:com) (S:state) (T:state), ((((evalc ((while B) C)) S) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), ((((evalc C) S) S1_1)->((((evalc ((while B) C)) S1_1) T)->False))))->False)))).
% Axiom fact_619_evaln__WHILE__case:(forall (B:(state->Prop)) (C:com) (S:state) (N_1:nat) (T:state), (((((evaln ((while B) C)) S) N_1) T)->(((((eq state) T) S)->(B S))->(((B S)->(forall (S1_1:state), (((((evaln C) S) N_1) S1_1)->(((((evaln ((while B) C)) S1_1) N_1) T)->False))))->False)))).
% Axiom fact_620_evalc__evaln:(forall (C:com) (S:state) (T:state), ((((evalc C) S) T)->((ex nat) (fun (N:nat)=> ((((evaln C) S) N) T))))).
% Axiom fact_621_Comp:(forall (D:com) (R_1:(x_a->(state->Prop))) (G_7:(hoare_2091234717iple_a->Prop)) (P_10:(x_a->(state->Prop))) (C_12:com) (Q_5:(x_a->(state->Prop))), (((hoare_1467856363rivs_a G_7) ((insert1597628439iple_a (((hoare_657976383iple_a P_10) C_12) Q_5)) bot_bo1791335050le_a_o))->(((hoare_1467856363rivs_a G_7) ((insert1597628439iple_a (((hoare_657976383iple_a Q_5) D) R_1)) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_7) ((insert1597628439iple_a (((hoare_657976383iple_a P_10) ((semi C_12) D)) R_1)) bot_bo1791335050le_a_o))))).
% Axiom fact_622_Comp:(forall (D:com) (R_1:(state->(state->Prop))) (G_7:(hoare_1708887482_state->Prop)) (P_10:(state->(state->Prop))) (C_12:com) (Q_5:(state->(state->Prop))), (((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state P_10) C_12) Q_5)) bot_bo19817387tate_o))->(((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state Q_5) D) R_1)) bot_bo19817387tate_o))->((hoare_90032982_state G_7) ((insert528405184_state (((hoare_858012674_state P_10) ((semi C_12) D)) R_1)) bot_bo19817387tate_o))))).
% Axiom fact_623_the__elem__def:(forall (X_21:(nat->Prop)), (((eq nat) (the_elem_nat X_21)) (the_nat (fun (X:nat)=> (((eq (nat->Prop)) X_21) ((insert_nat X) bot_bot_nat_o)))))).
% Axiom fact_624_the__elem__def:(forall (X_21:((hoare_2091234717iple_a->Prop)->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (the_el1618277441le_a_o X_21)) (the_Ho2077879471le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> (((eq ((hoare_2091234717iple_a->Prop)->Prop)) X_21) ((insert102003750le_a_o X) bot_bo1957696069_a_o_o)))))).
% Axiom fact_625_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_626_the__elem__def:(forall (X_21:(hoare_2091234717iple_a->Prop)), (((eq hoare_2091234717iple_a) (the_el13400124iple_a X_21)) (the_Ho1471183438iple_a (fun (X:hoare_2091234717iple_a)=> (((eq (hoare_2091234717iple_a->Prop)) X_21) ((insert1597628439iple_a X) bot_bo1791335050le_a_o)))))).
% Axiom fact_627_the__elem__def:(forall (X_21:(hoare_1708887482_state->Prop)), (((eq hoare_1708887482_state) (the_el864710747_state X_21)) (the_Ho851197897_state (fun (X:hoare_1708887482_state)=> (((eq (hoare_1708887482_state->Prop)) X_21) ((insert528405184_state X) bot_bo19817387tate_o)))))).
% Axiom fact_628_finite__pointwise:(forall (P_8:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (Q_4:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (C0_1:(hoare_2091234717iple_a->com)) (Q_3:(hoare_2091234717iple_a->(x_a->(state->Prop)))) (U_1:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a U_1)->((forall (P_9:hoare_2091234717iple_a), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_1661191109iple_a (fun (P_9:hoare_2091234717iple_a)=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_1661191109iple_a (fun (P_9:hoare_2091234717iple_a)=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))).
% Axiom fact_629_finite__pointwise:(forall (P_8:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (Q_4:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (C0_1:((hoare_2091234717iple_a->Prop)->com)) (Q_3:((hoare_2091234717iple_a->Prop)->(x_a->(state->Prop)))) (U_1:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o U_1)->((forall (P_9:(hoare_2091234717iple_a->Prop)), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_136408202iple_a (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_136408202iple_a (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))).
% Axiom fact_630_finite__pointwise:(forall (P_8:(pname->(state->(state->Prop)))) (Q_4:(pname->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:(pname->(state->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(state->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_9:pname), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_1116629049_state (fun (P_9:pname)=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))).
% Axiom fact_631_finite__pointwise:(forall (P_8:(hoare_2091234717iple_a->(state->(state->Prop)))) (Q_4:(hoare_2091234717iple_a->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:(hoare_2091234717iple_a->(state->(state->Prop)))) (C0_1:(hoare_2091234717iple_a->com)) (Q_3:(hoare_2091234717iple_a->(state->(state->Prop)))) (U_1:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a U_1)->((forall (P_9:hoare_2091234717iple_a), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_1884482962_state (fun (P_9:hoare_2091234717iple_a)=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_1884482962_state (fun (P_9:hoare_2091234717iple_a)=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))).
% Axiom fact_632_finite__pointwise:(forall (P_8:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (Q_4:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (C0_1:((hoare_2091234717iple_a->Prop)->com)) (Q_3:((hoare_2091234717iple_a->Prop)->(state->(state->Prop)))) (U_1:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o U_1)->((forall (P_9:(hoare_2091234717iple_a->Prop)), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_1501246093_state (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_1501246093_state (fun (P_9:(hoare_2091234717iple_a->Prop))=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))).
% Axiom fact_633_finite__pointwise:(forall (P_8:(nat->(x_a->(state->Prop)))) (Q_4:(nat->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:(nat->(x_a->(state->Prop)))) (C0_1:(nat->com)) (Q_3:(nat->(x_a->(state->Prop)))) (U_1:(nat->Prop)), ((finite_finite_nat U_1)->((forall (P_9:nat), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_359186840iple_a (fun (P_9:nat)=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_359186840iple_a (fun (P_9:nat)=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))).
% Axiom fact_634_finite__pointwise:(forall (P_8:(nat->(state->(state->Prop)))) (Q_4:(nat->(state->(state->Prop)))) (G_6:(hoare_1708887482_state->Prop)) (P_7:(nat->(state->(state->Prop)))) (C0_1:(nat->com)) (Q_3:(nat->(state->(state->Prop)))) (U_1:(nat->Prop)), ((finite_finite_nat U_1)->((forall (P_9:nat), (((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo19817387tate_o))->((hoare_90032982_state G_6) ((insert528405184_state (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo19817387tate_o))))->(((hoare_90032982_state G_6) ((image_514827263_state (fun (P_9:nat)=> (((hoare_858012674_state (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_90032982_state G_6) ((image_514827263_state (fun (P_9:nat)=> (((hoare_858012674_state (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))).
% Axiom fact_635_finite__pointwise:(forall (P_8:(pname->(x_a->(state->Prop)))) (Q_4:(pname->(x_a->(state->Prop)))) (G_6:(hoare_2091234717iple_a->Prop)) (P_7:(pname->(x_a->(state->Prop)))) (C0_1:(pname->com)) (Q_3:(pname->(x_a->(state->Prop)))) (U_1:(pname->Prop)), ((finite_finite_pname U_1)->((forall (P_9:pname), (((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9))) bot_bo1791335050le_a_o))->((hoare_1467856363rivs_a G_6) ((insert1597628439iple_a (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9))) bot_bo1791335050le_a_o))))->(((hoare_1467856363rivs_a G_6) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_7 P_9)) (C0_1 P_9)) (Q_3 P_9)))) U_1))->((hoare_1467856363rivs_a G_6) ((image_231808478iple_a (fun (P_9:pname)=> (((hoare_657976383iple_a (P_8 P_9)) (C0_1 P_9)) (Q_4 P_9)))) U_1)))))).
% Axiom fact_636_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_637_mk__disjoint__insert:(forall (A_53:nat) (A_52:(nat->Prop)), (((member_nat A_53) A_52)->((ex (nat->Prop)) (fun (B_26:(nat->Prop))=> ((and (((eq (nat->Prop)) A_52) ((insert_nat A_53) B_26))) (((member_nat A_53) B_26)->False)))))).
% Axiom fact_638_mk__disjoint__insert:(forall (A_53:(hoare_2091234717iple_a->Prop)) (A_52:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o A_53) A_52)->((ex ((hoare_2091234717iple_a->Prop)->Prop)) (fun (B_26:((hoare_2091234717iple_a->Prop)->Prop))=> ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_52) ((insert102003750le_a_o A_53) B_26))) (((member99268621le_a_o A_53) B_26)->False)))))).
% Axiom fact_639_mk__disjoint__insert:(forall (A_53:hoare_2091234717iple_a) (A_52:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a A_53) A_52)->((ex (hoare_2091234717iple_a->Prop)) (fun (B_26:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_52) ((insert1597628439iple_a A_53) B_26))) (((member290856304iple_a A_53) B_26)->False)))))).
% Axiom fact_640_mk__disjoint__insert:(forall (A_53:hoare_1708887482_state) (A_52:(hoare_1708887482_state->Prop)), (((member451959335_state A_53) A_52)->((ex (hoare_1708887482_state->Prop)) (fun (B_26:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_52) ((insert528405184_state A_53) B_26))) (((member451959335_state A_53) B_26)->False)))))).
% Axiom fact_641_mk__disjoint__insert:(forall (A_53:pname) (A_52:(pname->Prop)), (((member_pname A_53) A_52)->((ex (pname->Prop)) (fun (B_26:(pname->Prop))=> ((and (((eq (pname->Prop)) A_52) ((insert_pname A_53) B_26))) (((member_pname A_53) B_26)->False)))))).
% Axiom fact_642_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_643_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_644_com_Osimps_I3_J:(forall (Com1_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2)))).
% Axiom fact_645_com_Osimps_I48_J:(forall (Com1_1:com) (Com2_1:com) (Pname:pname), (not (((eq com) ((semi Com1_1) Com2_1)) (body Pname)))).
% Axiom fact_646_com_Osimps_I49_J:(forall (Pname:pname) (Com1_1:com) (Com2_1:com), (not (((eq com) (body Pname)) ((semi Com1_1) Com2_1)))).
% Axiom fact_647_com_Osimps_I47_J:(forall (Fun:(state->Prop)) (Com:com) (Com1_1:com) (Com2_1:com), (not (((eq com) ((while Fun) Com)) ((semi Com1_1) Com2_1)))).
% Axiom fact_648_com_Osimps_I46_J:(forall (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com:com), (not (((eq com) ((semi Com1_1) Com2_1)) ((while Fun) Com)))).
% Axiom fact_649_com_Osimps_I13_J:(forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip))).
% Axiom fact_650_com_Osimps_I12_J:(forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2)))).
% Axiom fact_651_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_652_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_653_finite__imageI:(forall (H_1:(pname->hoare_1708887482_state)) (F_35:(pname->Prop)), ((finite_finite_pname F_35)->(finite1625599783_state ((image_1116629049_state H_1) F_35)))).
% Axiom fact_654_finite__imageI:(forall (H_1:(nat->hoare_2091234717iple_a)) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite232261744iple_a ((image_359186840iple_a H_1) F_35)))).
% Axiom fact_655_finite__imageI:(forall (H_1:(nat->(hoare_2091234717iple_a->Prop))) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite1829014797le_a_o ((image_1995609573le_a_o H_1) F_35)))).
% Axiom fact_656_finite__imageI:(forall (H_1:(nat->pname)) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite_finite_pname ((image_nat_pname H_1) F_35)))).
% Axiom fact_657_finite__imageI:(forall (H_1:(nat->nat)) (F_35:(nat->Prop)), ((finite_finite_nat F_35)->(finite_finite_nat ((image_nat_nat H_1) F_35)))).
% Axiom fact_658_finite__imageI:(forall (H_1:(hoare_2091234717iple_a->nat)) (F_35:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_35)->(finite_finite_nat ((image_1773322034_a_nat H_1) F_35)))).
% Axiom fact_659_finite__imageI:(forall (H_1:((hoare_2091234717iple_a->Prop)->nat)) (F_35:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_35)->(finite_finite_nat ((image_75520503_o_nat H_1) F_35)))).
% Axiom fact_660_finite__imageI:(forall (H_1:(pname->nat)) (F_35:(pname->Prop)), ((finite_finite_pname F_35)->(finite_finite_nat ((image_pname_nat H_1) F_35)))).
% Axiom fact_661_finite__imageI:(forall (H_1:(pname->hoare_2091234717iple_a)) (F_35:(pname->Prop)), ((finite_finite_pname F_35)->(finite232261744iple_a ((image_231808478iple_a H_1) F_35)))).
% Axiom fact_662_finite_OinsertI:(forall (A_51:(hoare_2091234717iple_a->Prop)) (A_50:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_50)->(finite1829014797le_a_o ((insert102003750le_a_o A_51) A_50)))).
% Axiom fact_663_finite_OinsertI:(forall (A_51:pname) (A_50:(pname->Prop)), ((finite_finite_pname A_50)->(finite_finite_pname ((insert_pname A_51) A_50)))).
% Axiom fact_664_finite_OinsertI:(forall (A_51:hoare_2091234717iple_a) (A_50:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a A_50)->(finite232261744iple_a ((insert1597628439iple_a A_51) A_50)))).
% Axiom fact_665_finite_OinsertI:(forall (A_51:hoare_1708887482_state) (A_50:(hoare_1708887482_state->Prop)), ((finite1625599783_state A_50)->(finite1625599783_state ((insert528405184_state A_51) A_50)))).
% Axiom fact_666_finite_OinsertI:(forall (A_51:nat) (A_50:(nat->Prop)), ((finite_finite_nat A_50)->(finite_finite_nat ((insert_nat A_51) A_50)))).
% Axiom fact_667_finite_OemptyI:(finite232261744iple_a bot_bo1791335050le_a_o).
% Axiom fact_668_finite_OemptyI:(finite1829014797le_a_o bot_bo1957696069_a_o_o).
% Axiom fact_669_finite_OemptyI:(finite_finite_pname bot_bot_pname_o).
% Axiom fact_670_finite_OemptyI:(finite1625599783_state bot_bo19817387tate_o).
% Axiom fact_671_finite_OemptyI:(finite_finite_nat bot_bot_nat_o).
% Axiom fact_672_finite__Collect__conjI:(forall (Q_2:(pname->Prop)) (P_6:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_6))) (finite_finite_pname (collect_pname Q_2)))->(finite_finite_pname (collect_pname (fun (X:pname)=> ((and (P_6 X)) (Q_2 X))))))).
% Axiom fact_673_finite__Collect__conjI:(forall (Q_2:(hoare_2091234717iple_a->Prop)) (P_6:(hoare_2091234717iple_a->Prop)), (((or (finite232261744iple_a (collec992574898iple_a P_6))) (finite232261744iple_a (collec992574898iple_a Q_2)))->(finite232261744iple_a (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (P_6 X)) (Q_2 X))))))).
% Axiom fact_674_finite__Collect__conjI:(forall (Q_2:((hoare_2091234717iple_a->Prop)->Prop)) (P_6:((hoare_2091234717iple_a->Prop)->Prop)), (((or (finite1829014797le_a_o (collec1008234059le_a_o P_6))) (finite1829014797le_a_o (collec1008234059le_a_o Q_2)))->(finite1829014797le_a_o (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and (P_6 X)) (Q_2 X))))))).
% Axiom fact_675_finite__Collect__conjI:(forall (Q_2:(nat->Prop)) (P_6:(nat->Prop)), (((or (finite_finite_nat (collect_nat P_6))) (finite_finite_nat (collect_nat Q_2)))->(finite_finite_nat (collect_nat (fun (X:nat)=> ((and (P_6 X)) (Q_2 X))))))).
% Axiom fact_676_finite__Un:(forall (F_34:((hoare_2091234717iple_a->Prop)->Prop)) (G_5:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o ((semila2050116131_a_o_o F_34) G_5))) ((and (finite1829014797le_a_o F_34)) (finite1829014797le_a_o G_5)))).
% Axiom fact_677_finite__Un:(forall (F_34:(pname->Prop)) (G_5:(pname->Prop)), ((iff (finite_finite_pname ((semila1780557381name_o F_34) G_5))) ((and (finite_finite_pname F_34)) (finite_finite_pname G_5)))).
% Axiom fact_678_finite__Un:(forall (F_34:(hoare_1708887482_state->Prop)) (G_5:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((semila1122118281tate_o F_34) G_5))) ((and (finite1625599783_state F_34)) (finite1625599783_state G_5)))).
% Axiom fact_679_finite__Un:(forall (F_34:(hoare_2091234717iple_a->Prop)) (G_5:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a ((semila1052848428le_a_o F_34) G_5))) ((and (finite232261744iple_a F_34)) (finite232261744iple_a G_5)))).
% Axiom fact_680_finite__Un:(forall (F_34:(nat->Prop)) (G_5:(nat->Prop)), ((iff (finite_finite_nat ((semila848761471_nat_o F_34) G_5))) ((and (finite_finite_nat F_34)) (finite_finite_nat G_5)))).
% Axiom fact_681_finite__UnI:(forall (G_4:((hoare_2091234717iple_a->Prop)->Prop)) (F_33:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_33)->((finite1829014797le_a_o G_4)->(finite1829014797le_a_o ((semila2050116131_a_o_o F_33) G_4))))).
% Axiom fact_682_finite__UnI:(forall (G_4:(pname->Prop)) (F_33:(pname->Prop)), ((finite_finite_pname F_33)->((finite_finite_pname G_4)->(finite_finite_pname ((semila1780557381name_o F_33) G_4))))).
% Axiom fact_683_finite__UnI:(forall (G_4:(hoare_1708887482_state->Prop)) (F_33:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_33)->((finite1625599783_state G_4)->(finite1625599783_state ((semila1122118281tate_o F_33) G_4))))).
% Axiom fact_684_finite__UnI:(forall (G_4:(hoare_2091234717iple_a->Prop)) (F_33:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_33)->((finite232261744iple_a G_4)->(finite232261744iple_a ((semila1052848428le_a_o F_33) G_4))))).
% Axiom fact_685_finite__UnI:(forall (G_4:(nat->Prop)) (F_33:(nat->Prop)), ((finite_finite_nat F_33)->((finite_finite_nat G_4)->(finite_finite_nat ((semila848761471_nat_o F_33) G_4))))).
% Axiom fact_686_finite__Collect__disjI:(forall (P_5:(pname->Prop)) (Q_1:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X:pname)=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite_finite_pname (collect_pname P_5))) (finite_finite_pname (collect_pname Q_1))))).
% Axiom fact_687_finite__Collect__disjI:(forall (P_5:(hoare_2091234717iple_a->Prop)) (Q_1:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite232261744iple_a (collec992574898iple_a P_5))) (finite232261744iple_a (collec992574898iple_a Q_1))))).
% Axiom fact_688_finite__Collect__disjI:(forall (P_5:((hoare_2091234717iple_a->Prop)->Prop)) (Q_1:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite1829014797le_a_o (collec1008234059le_a_o P_5))) (finite1829014797le_a_o (collec1008234059le_a_o Q_1))))).
% Axiom fact_689_finite__Collect__disjI:(forall (P_5:(nat->Prop)) (Q_1:(nat->Prop)), ((iff (finite_finite_nat (collect_nat (fun (X:nat)=> ((or (P_5 X)) (Q_1 X)))))) ((and (finite_finite_nat (collect_nat P_5))) (finite_finite_nat (collect_nat Q_1))))).
% Axiom fact_690_finite__insert:(forall (A_49:(hoare_2091234717iple_a->Prop)) (A_48:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o ((insert102003750le_a_o A_49) A_48))) (finite1829014797le_a_o A_48))).
% Axiom fact_691_finite__insert:(forall (A_49:pname) (A_48:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_49) A_48))) (finite_finite_pname A_48))).
% Axiom fact_692_finite__insert:(forall (A_49:hoare_2091234717iple_a) (A_48:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a ((insert1597628439iple_a A_49) A_48))) (finite232261744iple_a A_48))).
% Axiom fact_693_finite__insert:(forall (A_49:hoare_1708887482_state) (A_48:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state ((insert528405184_state A_49) A_48))) (finite1625599783_state A_48))).
% Axiom fact_694_finite__insert:(forall (A_49:nat) (A_48:(nat->Prop)), ((iff (finite_finite_nat ((insert_nat A_49) A_48))) (finite_finite_nat A_48))).
% Axiom fact_695_finite__induct:(forall (P_4:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)) (F_32:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_32)->((P_4 bot_bo1957696069_a_o_o)->((forall (X:(hoare_2091234717iple_a->Prop)) (F_25:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_25)->((((member99268621le_a_o X) F_25)->False)->((P_4 F_25)->(P_4 ((insert102003750le_a_o X) F_25))))))->(P_4 F_32))))).
% Axiom fact_696_finite__induct:(forall (P_4:((hoare_2091234717iple_a->Prop)->Prop)) (F_32:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_32)->((P_4 bot_bo1791335050le_a_o)->((forall (X:hoare_2091234717iple_a) (F_25:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_25)->((((member290856304iple_a X) F_25)->False)->((P_4 F_25)->(P_4 ((insert1597628439iple_a X) F_25))))))->(P_4 F_32))))).
% Axiom fact_697_finite__induct:(forall (P_4:((hoare_1708887482_state->Prop)->Prop)) (F_32:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_32)->((P_4 bot_bo19817387tate_o)->((forall (X:hoare_1708887482_state) (F_25:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_25)->((((member451959335_state X) F_25)->False)->((P_4 F_25)->(P_4 ((insert528405184_state X) F_25))))))->(P_4 F_32))))).
% Axiom fact_698_finite__induct:(forall (P_4:((nat->Prop)->Prop)) (F_32:(nat->Prop)), ((finite_finite_nat F_32)->((P_4 bot_bot_nat_o)->((forall (X:nat) (F_25:(nat->Prop)), ((finite_finite_nat F_25)->((((member_nat X) F_25)->False)->((P_4 F_25)->(P_4 ((insert_nat X) F_25))))))->(P_4 F_32))))).
% Axiom fact_699_finite__induct:(forall (P_4:((pname->Prop)->Prop)) (F_32:(pname->Prop)), ((finite_finite_pname F_32)->((P_4 bot_bot_pname_o)->((forall (X:pname) (F_25:(pname->Prop)), ((finite_finite_pname F_25)->((((member_pname X) F_25)->False)->((P_4 F_25)->(P_4 ((insert_pname X) F_25))))))->(P_4 F_32))))).
% Axiom fact_700_finite_Osimps:(forall (A_46:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (finite1829014797le_a_o A_46)) ((or (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_46) bot_bo1957696069_a_o_o)) ((ex ((hoare_2091234717iple_a->Prop)->Prop)) (fun (A_47:((hoare_2091234717iple_a->Prop)->Prop))=> ((ex (hoare_2091234717iple_a->Prop)) (fun (A_45:(hoare_2091234717iple_a->Prop))=> ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_46) ((insert102003750le_a_o A_45) A_47))) (finite1829014797le_a_o A_47))))))))).
% Axiom fact_701_finite_Osimps:(forall (A_46:(pname->Prop)), ((iff (finite_finite_pname A_46)) ((or (((eq (pname->Prop)) A_46) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_47:(pname->Prop))=> ((ex pname) (fun (A_45:pname)=> ((and (((eq (pname->Prop)) A_46) ((insert_pname A_45) A_47))) (finite_finite_pname A_47))))))))).
% Axiom fact_702_finite_Osimps:(forall (A_46:(hoare_2091234717iple_a->Prop)), ((iff (finite232261744iple_a A_46)) ((or (((eq (hoare_2091234717iple_a->Prop)) A_46) bot_bo1791335050le_a_o)) ((ex (hoare_2091234717iple_a->Prop)) (fun (A_47:(hoare_2091234717iple_a->Prop))=> ((ex hoare_2091234717iple_a) (fun (A_45:hoare_2091234717iple_a)=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_46) ((insert1597628439iple_a A_45) A_47))) (finite232261744iple_a A_47))))))))).
% Axiom fact_703_finite_Osimps:(forall (A_46:(hoare_1708887482_state->Prop)), ((iff (finite1625599783_state A_46)) ((or (((eq (hoare_1708887482_state->Prop)) A_46) bot_bo19817387tate_o)) ((ex (hoare_1708887482_state->Prop)) (fun (A_47:(hoare_1708887482_state->Prop))=> ((ex hoare_1708887482_state) (fun (A_45:hoare_1708887482_state)=> ((and (((eq (hoare_1708887482_state->Prop)) A_46) ((insert528405184_state A_45) A_47))) (finite1625599783_state A_47))))))))).
% Axiom fact_704_finite_Osimps:(forall (A_46:(nat->Prop)), ((iff (finite_finite_nat A_46)) ((or (((eq (nat->Prop)) A_46) bot_bot_nat_o)) ((ex (nat->Prop)) (fun (A_47:(nat->Prop))=> ((ex nat) (fun (A_45:nat)=> ((and (((eq (nat->Prop)) A_46) ((insert_nat A_45) A_47))) (finite_finite_nat A_47))))))))).
% Axiom fact_705_pigeonhole__infinite:(forall (F_31:((hoare_2091234717iple_a->Prop)->nat)) (A_44:((hoare_2091234717iple_a->Prop)->Prop)), (((finite1829014797le_a_o A_44)->False)->((finite_finite_nat ((image_75520503_o_nat F_31) A_44))->((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_44)) ((finite1829014797le_a_o (collec1008234059le_a_o (fun (A_45:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False))))))).
% Axiom fact_706_pigeonhole__infinite:(forall (F_31:(hoare_2091234717iple_a->nat)) (A_44:(hoare_2091234717iple_a->Prop)), (((finite232261744iple_a A_44)->False)->((finite_finite_nat ((image_1773322034_a_nat F_31) A_44))->((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_44)) ((finite232261744iple_a (collec992574898iple_a (fun (A_45:hoare_2091234717iple_a)=> ((and ((member290856304iple_a A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False))))))).
% Axiom fact_707_pigeonhole__infinite:(forall (F_31:(pname->nat)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite_finite_nat ((image_pname_nat F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False))))))).
% Axiom fact_708_pigeonhole__infinite:(forall (F_31:(nat->nat)) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite_finite_nat ((image_nat_nat F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq nat) (F_31 A_45)) (F_31 X))))))->False))))))).
% Axiom fact_709_pigeonhole__infinite:(forall (F_31:(nat->hoare_2091234717iple_a)) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite232261744iple_a ((image_359186840iple_a F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq hoare_2091234717iple_a) (F_31 A_45)) (F_31 X))))))->False))))))).
% Axiom fact_710_pigeonhole__infinite:(forall (F_31:(nat->(hoare_2091234717iple_a->Prop))) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite1829014797le_a_o ((image_1995609573le_a_o F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq (hoare_2091234717iple_a->Prop)) (F_31 A_45)) (F_31 X))))))->False))))))).
% Axiom fact_711_pigeonhole__infinite:(forall (F_31:(nat->pname)) (A_44:(nat->Prop)), (((finite_finite_nat A_44)->False)->((finite_finite_pname ((image_nat_pname F_31) A_44))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) A_44)) ((finite_finite_nat (collect_nat (fun (A_45:nat)=> ((and ((member_nat A_45) A_44)) (((eq pname) (F_31 A_45)) (F_31 X))))))->False))))))).
% Axiom fact_712_pigeonhole__infinite:(forall (F_31:(pname->hoare_1708887482_state)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite1625599783_state ((image_1116629049_state F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq hoare_1708887482_state) (F_31 A_45)) (F_31 X))))))->False))))))).
% Axiom fact_713_pigeonhole__infinite:(forall (F_31:(pname->(hoare_2091234717iple_a->Prop))) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite1829014797le_a_o ((image_742317343le_a_o F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq (hoare_2091234717iple_a->Prop)) (F_31 A_45)) (F_31 X))))))->False))))))).
% Axiom fact_714_pigeonhole__infinite:(forall (F_31:(pname->pname)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite_finite_pname ((image_pname_pname F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq pname) (F_31 A_45)) (F_31 X))))))->False))))))).
% Axiom fact_715_pigeonhole__infinite:(forall (F_31:(pname->hoare_2091234717iple_a)) (A_44:(pname->Prop)), (((finite_finite_pname A_44)->False)->((finite232261744iple_a ((image_231808478iple_a F_31) A_44))->((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_44)) ((finite_finite_pname (collect_pname (fun (A_45:pname)=> ((and ((member_pname A_45) A_44)) (((eq hoare_2091234717iple_a) (F_31 A_45)) (F_31 X))))))->False))))))).
% Axiom fact_716_nonempty__iff:(forall (A_43:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_43) bot_bot_nat_o))) ((ex nat) (fun (X:nat)=> ((ex (nat->Prop)) (fun (B_26:(nat->Prop))=> ((and (((eq (nat->Prop)) A_43) ((insert_nat X) B_26))) (((member_nat X) B_26)->False)))))))).
% Axiom fact_717_nonempty__iff:(forall (A_43:((hoare_2091234717iple_a->Prop)->Prop)), ((iff (not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_43) bot_bo1957696069_a_o_o))) ((ex (hoare_2091234717iple_a->Prop)) (fun (X:(hoare_2091234717iple_a->Prop))=> ((ex ((hoare_2091234717iple_a->Prop)->Prop)) (fun (B_26:((hoare_2091234717iple_a->Prop)->Prop))=> ((and (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_43) ((insert102003750le_a_o X) B_26))) (((member99268621le_a_o X) B_26)->False)))))))).
% Axiom fact_718_nonempty__iff:(forall (A_43:(hoare_2091234717iple_a->Prop)), ((iff (not (((eq (hoare_2091234717iple_a->Prop)) A_43) bot_bo1791335050le_a_o))) ((ex hoare_2091234717iple_a) (fun (X:hoare_2091234717iple_a)=> ((ex (hoare_2091234717iple_a->Prop)) (fun (B_26:(hoare_2091234717iple_a->Prop))=> ((and (((eq (hoare_2091234717iple_a->Prop)) A_43) ((insert1597628439iple_a X) B_26))) (((member290856304iple_a X) B_26)->False)))))))).
% Axiom fact_719_nonempty__iff:(forall (A_43:(hoare_1708887482_state->Prop)), ((iff (not (((eq (hoare_1708887482_state->Prop)) A_43) bot_bo19817387tate_o))) ((ex hoare_1708887482_state) (fun (X:hoare_1708887482_state)=> ((ex (hoare_1708887482_state->Prop)) (fun (B_26:(hoare_1708887482_state->Prop))=> ((and (((eq (hoare_1708887482_state->Prop)) A_43) ((insert528405184_state X) B_26))) (((member451959335_state X) B_26)->False)))))))).
% Axiom fact_720_nonempty__iff:(forall (A_43:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_43) bot_bot_pname_o))) ((ex pname) (fun (X:pname)=> ((ex (pname->Prop)) (fun (B_26:(pname->Prop))=> ((and (((eq (pname->Prop)) A_43) ((insert_pname X) B_26))) (((member_pname X) B_26)->False)))))))).
% Axiom fact_721_folding__one__idem_Ounion__idem:(forall (B_27:((hoare_2091234717iple_a->Prop)->Prop)) (A_42:((hoare_2091234717iple_a->Prop)->Prop)) (F_30:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_29:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_30) F_29)->((finite1829014797le_a_o A_42)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_42) bot_bo1957696069_a_o_o))->((finite1829014797le_a_o B_27)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_27) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_29 ((semila2050116131_a_o_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27))))))))).
% Axiom fact_722_folding__one__idem_Ounion__idem:(forall (B_27:(pname->Prop)) (A_42:(pname->Prop)) (F_30:(pname->(pname->pname))) (F_29:((pname->Prop)->pname)), (((finite89670078_pname F_30) F_29)->((finite_finite_pname A_42)->((not (((eq (pname->Prop)) A_42) bot_bot_pname_o))->((finite_finite_pname B_27)->((not (((eq (pname->Prop)) B_27) bot_bot_pname_o))->(((eq pname) (F_29 ((semila1780557381name_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27))))))))).
% Axiom fact_723_folding__one__idem_Ounion__idem:(forall (B_27:(hoare_1708887482_state->Prop)) (A_42:(hoare_1708887482_state->Prop)) (F_30:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_29:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_30) F_29)->((finite1625599783_state A_42)->((not (((eq (hoare_1708887482_state->Prop)) A_42) bot_bo19817387tate_o))->((finite1625599783_state B_27)->((not (((eq (hoare_1708887482_state->Prop)) B_27) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_29 ((semila1122118281tate_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27))))))))).
% Axiom fact_724_folding__one__idem_Ounion__idem:(forall (B_27:(hoare_2091234717iple_a->Prop)) (A_42:(hoare_2091234717iple_a->Prop)) (F_30:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_29:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_30) F_29)->((finite232261744iple_a A_42)->((not (((eq (hoare_2091234717iple_a->Prop)) A_42) bot_bo1791335050le_a_o))->((finite232261744iple_a B_27)->((not (((eq (hoare_2091234717iple_a->Prop)) B_27) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_29 ((semila1052848428le_a_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27))))))))).
% Axiom fact_725_folding__one__idem_Ounion__idem:(forall (B_27:(nat->Prop)) (A_42:(nat->Prop)) (F_30:(nat->(nat->nat))) (F_29:((nat->Prop)->nat)), (((finite795500164em_nat F_30) F_29)->((finite_finite_nat A_42)->((not (((eq (nat->Prop)) A_42) bot_bot_nat_o))->((finite_finite_nat B_27)->((not (((eq (nat->Prop)) B_27) bot_bot_nat_o))->(((eq nat) (F_29 ((semila848761471_nat_o A_42) B_27))) ((F_30 (F_29 A_42)) (F_29 B_27))))))))).
% Axiom fact_726_folding__one__idem_Oinsert__idem:(forall (X_20:(hoare_2091234717iple_a->Prop)) (A_41:((hoare_2091234717iple_a->Prop)->Prop)) (F_28:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_27:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_28) F_27)->((finite1829014797le_a_o A_41)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_41) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_27 ((insert102003750le_a_o X_20) A_41))) ((F_28 X_20) (F_27 A_41))))))).
% Axiom fact_727_folding__one__idem_Oinsert__idem:(forall (X_20:pname) (A_41:(pname->Prop)) (F_28:(pname->(pname->pname))) (F_27:((pname->Prop)->pname)), (((finite89670078_pname F_28) F_27)->((finite_finite_pname A_41)->((not (((eq (pname->Prop)) A_41) bot_bot_pname_o))->(((eq pname) (F_27 ((insert_pname X_20) A_41))) ((F_28 X_20) (F_27 A_41))))))).
% Axiom fact_728_folding__one__idem_Oinsert__idem:(forall (X_20:hoare_2091234717iple_a) (A_41:(hoare_2091234717iple_a->Prop)) (F_28:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_27:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_28) F_27)->((finite232261744iple_a A_41)->((not (((eq (hoare_2091234717iple_a->Prop)) A_41) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_27 ((insert1597628439iple_a X_20) A_41))) ((F_28 X_20) (F_27 A_41))))))).
% Axiom fact_729_folding__one__idem_Oinsert__idem:(forall (X_20:hoare_1708887482_state) (A_41:(hoare_1708887482_state->Prop)) (F_28:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_27:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_28) F_27)->((finite1625599783_state A_41)->((not (((eq (hoare_1708887482_state->Prop)) A_41) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_27 ((insert528405184_state X_20) A_41))) ((F_28 X_20) (F_27 A_41))))))).
% Axiom fact_730_folding__one__idem_Oinsert__idem:(forall (X_20:nat) (A_41:(nat->Prop)) (F_28:(nat->(nat->nat))) (F_27:((nat->Prop)->nat)), (((finite795500164em_nat F_28) F_27)->((finite_finite_nat A_41)->((not (((eq (nat->Prop)) A_41) bot_bot_nat_o))->(((eq nat) (F_27 ((insert_nat X_20) A_41))) ((F_28 X_20) (F_27 A_41))))))).
% Axiom fact_731_image__eq__fold__image:(forall (F_26:(pname->hoare_1708887482_state)) (A_40:(pname->Prop)), ((finite_finite_pname A_40)->(((eq (hoare_1708887482_state->Prop)) ((image_1116629049_state F_26) A_40)) ((((finite2139561282_pname semila1122118281tate_o) (fun (X:pname)=> ((insert528405184_state (F_26 X)) bot_bo19817387tate_o))) bot_bo19817387tate_o) A_40)))).
% Axiom fact_732_image__eq__fold__image:(forall (F_26:(hoare_2091234717iple_a->hoare_2091234717iple_a)) (A_40:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_1661191109iple_a F_26) A_40)) ((((finite1481787452iple_a semila1052848428le_a_o) (fun (X:hoare_2091234717iple_a)=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40)))).
% Axiom fact_733_image__eq__fold__image:(forall (F_26:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)) (A_40:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_136408202iple_a F_26) A_40)) ((((finite903029825le_a_o semila1052848428le_a_o) (fun (X:(hoare_2091234717iple_a->Prop))=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40)))).
% Axiom fact_734_image__eq__fold__image:(forall (F_26:(nat->nat)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (nat->Prop)) ((image_nat_nat F_26) A_40)) ((((finite141655318_o_nat semila848761471_nat_o) (fun (X:nat)=> ((insert_nat (F_26 X)) bot_bot_nat_o))) bot_bot_nat_o) A_40)))).
% Axiom fact_735_image__eq__fold__image:(forall (F_26:(nat->(hoare_2091234717iple_a->Prop))) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((image_1995609573le_a_o F_26) A_40)) ((((finite2009943022_o_nat semila2050116131_a_o_o) (fun (X:nat)=> ((insert102003750le_a_o (F_26 X)) bot_bo1957696069_a_o_o))) bot_bo1957696069_a_o_o) A_40)))).
% Axiom fact_736_image__eq__fold__image:(forall (F_26:(nat->pname)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (pname->Prop)) ((image_nat_pname F_26) A_40)) ((((finite1427591632_o_nat semila1780557381name_o) (fun (X:nat)=> ((insert_pname (F_26 X)) bot_bot_pname_o))) bot_bot_pname_o) A_40)))).
% Axiom fact_737_image__eq__fold__image:(forall (F_26:(nat->hoare_2091234717iple_a)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_359186840iple_a F_26) A_40)) ((((finite2100865449_o_nat semila1052848428le_a_o) (fun (X:nat)=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40)))).
% Axiom fact_738_image__eq__fold__image:(forall (F_26:(nat->hoare_1708887482_state)) (A_40:(nat->Prop)), ((finite_finite_nat A_40)->(((eq (hoare_1708887482_state->Prop)) ((image_514827263_state F_26) A_40)) ((((finite1400355848_o_nat semila1122118281tate_o) (fun (X:nat)=> ((insert528405184_state (F_26 X)) bot_bo19817387tate_o))) bot_bo19817387tate_o) A_40)))).
% Axiom fact_739_image__eq__fold__image:(forall (F_26:(pname->hoare_2091234717iple_a)) (A_40:(pname->Prop)), ((finite_finite_pname A_40)->(((eq (hoare_2091234717iple_a->Prop)) ((image_231808478iple_a F_26) A_40)) ((((finite1290357347_pname semila1052848428le_a_o) (fun (X:pname)=> ((insert1597628439iple_a (F_26 X)) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o) A_40)))).
% Axiom fact_740_finite__ne__induct:(forall (P_3:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)) (F_24:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_24)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) F_24) bot_bo1957696069_a_o_o))->((forall (X:(hoare_2091234717iple_a->Prop)), (P_3 ((insert102003750le_a_o X) bot_bo1957696069_a_o_o)))->((forall (X:(hoare_2091234717iple_a->Prop)) (F_25:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o F_25)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) F_25) bot_bo1957696069_a_o_o))->((((member99268621le_a_o X) F_25)->False)->((P_3 F_25)->(P_3 ((insert102003750le_a_o X) F_25)))))))->(P_3 F_24)))))).
% Axiom fact_741_finite__ne__induct:(forall (P_3:((hoare_2091234717iple_a->Prop)->Prop)) (F_24:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_24)->((not (((eq (hoare_2091234717iple_a->Prop)) F_24) bot_bo1791335050le_a_o))->((forall (X:hoare_2091234717iple_a), (P_3 ((insert1597628439iple_a X) bot_bo1791335050le_a_o)))->((forall (X:hoare_2091234717iple_a) (F_25:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a F_25)->((not (((eq (hoare_2091234717iple_a->Prop)) F_25) bot_bo1791335050le_a_o))->((((member290856304iple_a X) F_25)->False)->((P_3 F_25)->(P_3 ((insert1597628439iple_a X) F_25)))))))->(P_3 F_24)))))).
% Axiom fact_742_finite__ne__induct:(forall (P_3:((hoare_1708887482_state->Prop)->Prop)) (F_24:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_24)->((not (((eq (hoare_1708887482_state->Prop)) F_24) bot_bo19817387tate_o))->((forall (X:hoare_1708887482_state), (P_3 ((insert528405184_state X) bot_bo19817387tate_o)))->((forall (X:hoare_1708887482_state) (F_25:(hoare_1708887482_state->Prop)), ((finite1625599783_state F_25)->((not (((eq (hoare_1708887482_state->Prop)) F_25) bot_bo19817387tate_o))->((((member451959335_state X) F_25)->False)->((P_3 F_25)->(P_3 ((insert528405184_state X) F_25)))))))->(P_3 F_24)))))).
% Axiom fact_743_finite__ne__induct:(forall (P_3:((nat->Prop)->Prop)) (F_24:(nat->Prop)), ((finite_finite_nat F_24)->((not (((eq (nat->Prop)) F_24) bot_bot_nat_o))->((forall (X:nat), (P_3 ((insert_nat X) bot_bot_nat_o)))->((forall (X:nat) (F_25:(nat->Prop)), ((finite_finite_nat F_25)->((not (((eq (nat->Prop)) F_25) bot_bot_nat_o))->((((member_nat X) F_25)->False)->((P_3 F_25)->(P_3 ((insert_nat X) F_25)))))))->(P_3 F_24)))))).
% Axiom fact_744_finite__ne__induct:(forall (P_3:((pname->Prop)->Prop)) (F_24:(pname->Prop)), ((finite_finite_pname F_24)->((not (((eq (pname->Prop)) F_24) bot_bot_pname_o))->((forall (X:pname), (P_3 ((insert_pname X) bot_bot_pname_o)))->((forall (X:pname) (F_25:(pname->Prop)), ((finite_finite_pname F_25)->((not (((eq (pname->Prop)) F_25) bot_bot_pname_o))->((((member_pname X) F_25)->False)->((P_3 F_25)->(P_3 ((insert_pname X) F_25)))))))->(P_3 F_24)))))).
% Axiom fact_745_folding__one__idem_Oidem:(forall (X_19:nat) (F_23:(nat->(nat->nat))) (F_22:((nat->Prop)->nat)), (((finite795500164em_nat F_23) F_22)->(((eq nat) ((F_23 X_19) X_19)) X_19))).
% Axiom fact_746_folding__one__idem_Oidem:(forall (X_19:pname) (F_23:(pname->(pname->pname))) (F_22:((pname->Prop)->pname)), (((finite89670078_pname F_23) F_22)->(((eq pname) ((F_23 X_19) X_19)) X_19))).
% Axiom fact_747_folding__one__idem_Oidem:(forall (X_19:hoare_2091234717iple_a) (F_23:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_22:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_23) F_22)->(((eq hoare_2091234717iple_a) ((F_23 X_19) X_19)) X_19))).
% Axiom fact_748_fold__image__empty:(forall (F_21:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (G_3:(pname->(hoare_2091234717iple_a->Prop))) (Z_4:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((((finite1290357347_pname F_21) G_3) Z_4) bot_bot_pname_o)) Z_4)).
% Axiom fact_749_folding__one__idem_Oin__idem:(forall (X_18:(hoare_2091234717iple_a->Prop)) (A_39:((hoare_2091234717iple_a->Prop)->Prop)) (F_20:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_19:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_20) F_19)->((finite1829014797le_a_o A_39)->(((member99268621le_a_o X_18) A_39)->(((eq (hoare_2091234717iple_a->Prop)) ((F_20 X_18) (F_19 A_39))) (F_19 A_39)))))).
% Axiom fact_750_folding__one__idem_Oin__idem:(forall (X_18:hoare_2091234717iple_a) (A_39:(hoare_2091234717iple_a->Prop)) (F_20:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_19:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_20) F_19)->((finite232261744iple_a A_39)->(((member290856304iple_a X_18) A_39)->(((eq hoare_2091234717iple_a) ((F_20 X_18) (F_19 A_39))) (F_19 A_39)))))).
% Axiom fact_751_folding__one__idem_Oin__idem:(forall (X_18:nat) (A_39:(nat->Prop)) (F_20:(nat->(nat->nat))) (F_19:((nat->Prop)->nat)), (((finite795500164em_nat F_20) F_19)->((finite_finite_nat A_39)->(((member_nat X_18) A_39)->(((eq nat) ((F_20 X_18) (F_19 A_39))) (F_19 A_39)))))).
% Axiom fact_752_folding__one__idem_Oin__idem:(forall (X_18:pname) (A_39:(pname->Prop)) (F_20:(pname->(pname->pname))) (F_19:((pname->Prop)->pname)), (((finite89670078_pname F_20) F_19)->((finite_finite_pname A_39)->(((member_pname X_18) A_39)->(((eq pname) ((F_20 X_18) (F_19 A_39))) (F_19 A_39)))))).
% Axiom fact_753_folding__one__idem_Ohom__commute:(forall (N_3:(hoare_2091234717iple_a->Prop)) (H:(hoare_2091234717iple_a->hoare_2091234717iple_a)) (F_18:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_17:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite1674555159iple_a F_18) F_17)->((forall (X:hoare_2091234717iple_a) (Y_7:hoare_2091234717iple_a), (((eq hoare_2091234717iple_a) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite232261744iple_a N_3)->((not (((eq (hoare_2091234717iple_a->Prop)) N_3) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (H (F_17 N_3))) (F_17 ((image_1661191109iple_a H) N_3)))))))).
% Axiom fact_754_folding__one__idem_Ohom__commute:(forall (N_3:((hoare_2091234717iple_a->Prop)->Prop)) (H:((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop))) (F_18:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_17:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite574580006le_a_o F_18) F_17)->((forall (X:(hoare_2091234717iple_a->Prop)) (Y_7:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite1829014797le_a_o N_3)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) N_3) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (H (F_17 N_3))) (F_17 ((image_784579955le_a_o H) N_3)))))))).
% Axiom fact_755_folding__one__idem_Ohom__commute:(forall (N_3:(pname->Prop)) (H:(pname->pname)) (F_18:(pname->(pname->pname))) (F_17:((pname->Prop)->pname)), (((finite89670078_pname F_18) F_17)->((forall (X:pname) (Y_7:pname), (((eq pname) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite_finite_pname N_3)->((not (((eq (pname->Prop)) N_3) bot_bot_pname_o))->(((eq pname) (H (F_17 N_3))) (F_17 ((image_pname_pname H) N_3)))))))).
% Axiom fact_756_folding__one__idem_Ohom__commute:(forall (N_3:(hoare_1708887482_state->Prop)) (H:(hoare_1708887482_state->hoare_1708887482_state)) (F_18:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_17:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1347568576_state F_18) F_17)->((forall (X:hoare_1708887482_state) (Y_7:hoare_1708887482_state), (((eq hoare_1708887482_state) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite1625599783_state N_3)->((not (((eq (hoare_1708887482_state->Prop)) N_3) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (H (F_17 N_3))) (F_17 ((image_757158439_state H) N_3)))))))).
% Axiom fact_757_folding__one__idem_Ohom__commute:(forall (N_3:(nat->Prop)) (H:(nat->nat)) (F_18:(nat->(nat->nat))) (F_17:((nat->Prop)->nat)), (((finite795500164em_nat F_18) F_17)->((forall (X:nat) (Y_7:nat), (((eq nat) (H ((F_18 X) Y_7))) ((F_18 (H X)) (H Y_7))))->((finite_finite_nat N_3)->((not (((eq (nat->Prop)) N_3) bot_bot_nat_o))->(((eq nat) (H (F_17 N_3))) (F_17 ((image_nat_nat H) N_3)))))))).
% Axiom fact_758_comm__monoid__big_OF__eq:(forall (G_2:(pname->(hoare_2091234717iple_a->Prop))) (A_38:(pname->Prop)) (F_16:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (Z_3:(hoare_2091234717iple_a->Prop)) (F_15:((pname->(hoare_2091234717iple_a->Prop))->((pname->Prop)->(hoare_2091234717iple_a->Prop)))), ((((big_co1924420859_pname F_16) Z_3) F_15)->((and ((finite_finite_pname A_38)->(((eq (hoare_2091234717iple_a->Prop)) ((F_15 G_2) A_38)) ((((finite1290357347_pname F_16) G_2) Z_3) A_38)))) (((finite_finite_pname A_38)->False)->(((eq (hoare_2091234717iple_a->Prop)) ((F_15 G_2) A_38)) Z_3))))).
% Axiom fact_759_folding__one_Oinsert:(forall (X_17:(hoare_2091234717iple_a->Prop)) (A_37:((hoare_2091234717iple_a->Prop)->Prop)) (F_14:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_13:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_14) F_13)->((finite1829014797le_a_o A_37)->((((member99268621le_a_o X_17) A_37)->False)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_37) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_13 ((insert102003750le_a_o X_17) A_37))) ((F_14 X_17) (F_13 A_37)))))))).
% Axiom fact_760_folding__one_Oinsert:(forall (X_17:hoare_2091234717iple_a) (A_37:(hoare_2091234717iple_a->Prop)) (F_14:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_13:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_14) F_13)->((finite232261744iple_a A_37)->((((member290856304iple_a X_17) A_37)->False)->((not (((eq (hoare_2091234717iple_a->Prop)) A_37) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_13 ((insert1597628439iple_a X_17) A_37))) ((F_14 X_17) (F_13 A_37)))))))).
% Axiom fact_761_folding__one_Oinsert:(forall (X_17:hoare_1708887482_state) (A_37:(hoare_1708887482_state->Prop)) (F_14:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_13:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_14) F_13)->((finite1625599783_state A_37)->((((member451959335_state X_17) A_37)->False)->((not (((eq (hoare_1708887482_state->Prop)) A_37) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_13 ((insert528405184_state X_17) A_37))) ((F_14 X_17) (F_13 A_37)))))))).
% Axiom fact_762_folding__one_Oinsert:(forall (X_17:nat) (A_37:(nat->Prop)) (F_14:(nat->(nat->nat))) (F_13:((nat->Prop)->nat)), (((finite988810631ne_nat F_14) F_13)->((finite_finite_nat A_37)->((((member_nat X_17) A_37)->False)->((not (((eq (nat->Prop)) A_37) bot_bot_nat_o))->(((eq nat) (F_13 ((insert_nat X_17) A_37))) ((F_14 X_17) (F_13 A_37)))))))).
% Axiom fact_763_folding__one_Oinsert:(forall (X_17:pname) (A_37:(pname->Prop)) (F_14:(pname->(pname->pname))) (F_13:((pname->Prop)->pname)), (((finite1282449217_pname F_14) F_13)->((finite_finite_pname A_37)->((((member_pname X_17) A_37)->False)->((not (((eq (pname->Prop)) A_37) bot_bot_pname_o))->(((eq pname) (F_13 ((insert_pname X_17) A_37))) ((F_14 X_17) (F_13 A_37)))))))).
% Axiom fact_764_folding__one_Osingleton:(forall (X_16:nat) (F_12:(nat->(nat->nat))) (F_11:((nat->Prop)->nat)), (((finite988810631ne_nat F_12) F_11)->(((eq nat) (F_11 ((insert_nat X_16) bot_bot_nat_o))) X_16))).
% Axiom fact_765_folding__one_Osingleton:(forall (X_16:(hoare_2091234717iple_a->Prop)) (F_12:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_11:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_12) F_11)->(((eq (hoare_2091234717iple_a->Prop)) (F_11 ((insert102003750le_a_o X_16) bot_bo1957696069_a_o_o))) X_16))).
% Axiom fact_766_folding__one_Osingleton:(forall (X_16:pname) (F_12:(pname->(pname->pname))) (F_11:((pname->Prop)->pname)), (((finite1282449217_pname F_12) F_11)->(((eq pname) (F_11 ((insert_pname X_16) bot_bot_pname_o))) X_16))).
% Axiom fact_767_folding__one_Osingleton:(forall (X_16:hoare_2091234717iple_a) (F_12:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_11:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_12) F_11)->(((eq hoare_2091234717iple_a) (F_11 ((insert1597628439iple_a X_16) bot_bo1791335050le_a_o))) X_16))).
% Axiom fact_768_folding__one_Osingleton:(forall (X_16:hoare_1708887482_state) (F_12:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_11:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_12) F_11)->(((eq hoare_1708887482_state) (F_11 ((insert528405184_state X_16) bot_bo19817387tate_o))) X_16))).
% Axiom fact_769_folding__one_Oclosed:(forall (A_36:((hoare_2091234717iple_a->Prop)->Prop)) (F_10:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_9:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_10) F_9)->((finite1829014797le_a_o A_36)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_36) bot_bo1957696069_a_o_o))->((forall (X:(hoare_2091234717iple_a->Prop)) (Y_7:(hoare_2091234717iple_a->Prop)), ((member99268621le_a_o ((F_10 X) Y_7)) ((insert102003750le_a_o X) ((insert102003750le_a_o Y_7) bot_bo1957696069_a_o_o))))->((member99268621le_a_o (F_9 A_36)) A_36)))))).
% Axiom fact_770_folding__one_Oclosed:(forall (A_36:(hoare_2091234717iple_a->Prop)) (F_10:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_9:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_10) F_9)->((finite232261744iple_a A_36)->((not (((eq (hoare_2091234717iple_a->Prop)) A_36) bot_bo1791335050le_a_o))->((forall (X:hoare_2091234717iple_a) (Y_7:hoare_2091234717iple_a), ((member290856304iple_a ((F_10 X) Y_7)) ((insert1597628439iple_a X) ((insert1597628439iple_a Y_7) bot_bo1791335050le_a_o))))->((member290856304iple_a (F_9 A_36)) A_36)))))).
% Axiom fact_771_folding__one_Oclosed:(forall (A_36:(hoare_1708887482_state->Prop)) (F_10:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_9:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_10) F_9)->((finite1625599783_state A_36)->((not (((eq (hoare_1708887482_state->Prop)) A_36) bot_bo19817387tate_o))->((forall (X:hoare_1708887482_state) (Y_7:hoare_1708887482_state), ((member451959335_state ((F_10 X) Y_7)) ((insert528405184_state X) ((insert528405184_state Y_7) bot_bo19817387tate_o))))->((member451959335_state (F_9 A_36)) A_36)))))).
% Axiom fact_772_folding__one_Oclosed:(forall (A_36:(nat->Prop)) (F_10:(nat->(nat->nat))) (F_9:((nat->Prop)->nat)), (((finite988810631ne_nat F_10) F_9)->((finite_finite_nat A_36)->((not (((eq (nat->Prop)) A_36) bot_bot_nat_o))->((forall (X:nat) (Y_7:nat), ((member_nat ((F_10 X) Y_7)) ((insert_nat X) ((insert_nat Y_7) bot_bot_nat_o))))->((member_nat (F_9 A_36)) A_36)))))).
% Axiom fact_773_folding__one_Oclosed:(forall (A_36:(pname->Prop)) (F_10:(pname->(pname->pname))) (F_9:((pname->Prop)->pname)), (((finite1282449217_pname F_10) F_9)->((finite_finite_pname A_36)->((not (((eq (pname->Prop)) A_36) bot_bot_pname_o))->((forall (X:pname) (Y_7:pname), ((member_pname ((F_10 X) Y_7)) ((insert_pname X) ((insert_pname Y_7) bot_bot_pname_o))))->((member_pname (F_9 A_36)) A_36)))))).
% Axiom fact_774_Set_Oset__insert:(forall (X_15:nat) (A_35:(nat->Prop)), (((member_nat X_15) A_35)->((forall (B_26:(nat->Prop)), ((((eq (nat->Prop)) A_35) ((insert_nat X_15) B_26))->((member_nat X_15) B_26)))->False))).
% Axiom fact_775_Set_Oset__insert:(forall (X_15:(hoare_2091234717iple_a->Prop)) (A_35:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o X_15) A_35)->((forall (B_26:((hoare_2091234717iple_a->Prop)->Prop)), ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_35) ((insert102003750le_a_o X_15) B_26))->((member99268621le_a_o X_15) B_26)))->False))).
% Axiom fact_776_Set_Oset__insert:(forall (X_15:hoare_2091234717iple_a) (A_35:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a X_15) A_35)->((forall (B_26:(hoare_2091234717iple_a->Prop)), ((((eq (hoare_2091234717iple_a->Prop)) A_35) ((insert1597628439iple_a X_15) B_26))->((member290856304iple_a X_15) B_26)))->False))).
% Axiom fact_777_Set_Oset__insert:(forall (X_15:hoare_1708887482_state) (A_35:(hoare_1708887482_state->Prop)), (((member451959335_state X_15) A_35)->((forall (B_26:(hoare_1708887482_state->Prop)), ((((eq (hoare_1708887482_state->Prop)) A_35) ((insert528405184_state X_15) B_26))->((member451959335_state X_15) B_26)))->False))).
% Axiom fact_778_Set_Oset__insert:(forall (X_15:pname) (A_35:(pname->Prop)), (((member_pname X_15) A_35)->((forall (B_26:(pname->Prop)), ((((eq (pname->Prop)) A_35) ((insert_pname X_15) B_26))->((member_pname X_15) B_26)))->False))).
% Axiom fact_779_equals0I:(forall (A_34:(nat->Prop)), ((forall (Y_7:nat), (((member_nat Y_7) A_34)->False))->(((eq (nat->Prop)) A_34) bot_bot_nat_o))).
% Axiom fact_780_equals0I:(forall (A_34:((hoare_2091234717iple_a->Prop)->Prop)), ((forall (Y_7:(hoare_2091234717iple_a->Prop)), (((member99268621le_a_o Y_7) A_34)->False))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_34) bot_bo1957696069_a_o_o))).
% Axiom fact_781_equals0I:(forall (A_34:(hoare_2091234717iple_a->Prop)), ((forall (Y_7:hoare_2091234717iple_a), (((member290856304iple_a Y_7) A_34)->False))->(((eq (hoare_2091234717iple_a->Prop)) A_34) bot_bo1791335050le_a_o))).
% Axiom fact_782_equals0I:(forall (A_34:(hoare_1708887482_state->Prop)), ((forall (Y_7:hoare_1708887482_state), (((member451959335_state Y_7) A_34)->False))->(((eq (hoare_1708887482_state->Prop)) A_34) bot_bo19817387tate_o))).
% Axiom fact_783_equals0I:(forall (A_34:(pname->Prop)), ((forall (Y_7:pname), (((member_pname Y_7) A_34)->False))->(((eq (pname->Prop)) A_34) bot_bot_pname_o))).
% Axiom fact_784_Sup__fin_Ounion__idem:(forall (B_25:((nat->Prop)->Prop)) (A_33:((nat->Prop)->Prop)), ((finite_finite_nat_o A_33)->((not (((eq ((nat->Prop)->Prop)) A_33) bot_bot_nat_o_o))->((finite_finite_nat_o B_25)->((not (((eq ((nat->Prop)->Prop)) B_25) bot_bot_nat_o_o))->(((eq (nat->Prop)) (big_la1658356148_nat_o ((semila72246288at_o_o A_33) B_25))) ((semila848761471_nat_o (big_la1658356148_nat_o A_33)) (big_la1658356148_nat_o B_25)))))))).
% Axiom fact_785_Sup__fin_Ounion__idem:(forall (B_25:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)) (A_33:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)), ((finite886417794_a_o_o A_33)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) A_33) bot_bo690906872_o_o_o))->((finite886417794_a_o_o B_25)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) B_25) bot_bo690906872_o_o_o))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (big_la1994307886_a_o_o ((semila484278426_o_o_o A_33) B_25))) ((semila2050116131_a_o_o (big_la1994307886_a_o_o A_33)) (big_la1994307886_a_o_o B_25)))))))).
% Axiom fact_786_Sup__fin_Ounion__idem:(forall (B_25:((hoare_1708887482_state->Prop)->Prop)) (A_33:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_33)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_33) bot_bo1678742418te_o_o))->((finite1329924456tate_o B_25)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) B_25) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (big_la1088302868tate_o ((semila1853742644te_o_o A_33) B_25))) ((semila1122118281tate_o (big_la1088302868tate_o A_33)) (big_la1088302868tate_o B_25)))))))).
% Axiom fact_787_Sup__fin_Ounion__idem:(forall (B_25:((pname->Prop)->Prop)) (A_33:((pname->Prop)->Prop)), ((finite297249702name_o A_33)->((not (((eq ((pname->Prop)->Prop)) A_33) bot_bot_pname_o_o))->((finite297249702name_o B_25)->((not (((eq ((pname->Prop)->Prop)) B_25) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((semila181081674me_o_o A_33) B_25))) ((semila1780557381name_o (big_la1286884090name_o A_33)) (big_la1286884090name_o B_25)))))))).
% Axiom fact_788_Sup__fin_Ounion__idem:(forall (B_25:(Prop->Prop)) (A_33:(Prop->Prop)), ((finite_finite_o A_33)->((not (((eq (Prop->Prop)) A_33) bot_bot_o_o))->((finite_finite_o B_25)->((not (((eq (Prop->Prop)) B_25) bot_bot_o_o))->((iff (big_la727467310_fin_o ((semila2062604954up_o_o A_33) B_25))) ((semila10642723_sup_o (big_la727467310_fin_o A_33)) (big_la727467310_fin_o B_25)))))))).
% Axiom fact_789_Sup__fin_Ounion__idem:(forall (B_25:((hoare_2091234717iple_a->Prop)->Prop)) (A_33:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_33)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_33) bot_bo1957696069_a_o_o))->((finite1829014797le_a_o B_25)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_25) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (big_la735727201le_a_o ((semila2050116131_a_o_o A_33) B_25))) ((semila1052848428le_a_o (big_la735727201le_a_o A_33)) (big_la735727201le_a_o B_25)))))))).
% Axiom fact_790_Sup__fin_Ounion__idem:(forall (B_25:(nat->Prop)) (A_33:(nat->Prop)), ((finite_finite_nat A_33)->((not (((eq (nat->Prop)) A_33) bot_bot_nat_o))->((finite_finite_nat B_25)->((not (((eq (nat->Prop)) B_25) bot_bot_nat_o))->(((eq nat) (big_la43341705in_nat ((semila848761471_nat_o A_33) B_25))) ((semila972727038up_nat (big_la43341705in_nat A_33)) (big_la43341705in_nat B_25)))))))).
% Axiom fact_791_Sup__fin_Oinsert:(forall (X_14:(nat->Prop)) (A_32:((nat->Prop)->Prop)), ((finite_finite_nat_o A_32)->((((member_nat_o X_14) A_32)->False)->((not (((eq ((nat->Prop)->Prop)) A_32) bot_bot_nat_o_o))->(((eq (nat->Prop)) (big_la1658356148_nat_o ((insert_nat_o X_14) A_32))) ((semila848761471_nat_o X_14) (big_la1658356148_nat_o A_32))))))).
% Axiom fact_792_Sup__fin_Oinsert:(forall (X_14:((hoare_2091234717iple_a->Prop)->Prop)) (A_32:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)), ((finite886417794_a_o_o A_32)->((((member1297825410_a_o_o X_14) A_32)->False)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) A_32) bot_bo690906872_o_o_o))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (big_la1994307886_a_o_o ((insert987231145_a_o_o X_14) A_32))) ((semila2050116131_a_o_o X_14) (big_la1994307886_a_o_o A_32))))))).
% Axiom fact_793_Sup__fin_Oinsert:(forall (X_14:(hoare_1708887482_state->Prop)) (A_32:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_32)->((((member814030440tate_o X_14) A_32)->False)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_32) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (big_la1088302868tate_o ((insert949073679tate_o X_14) A_32))) ((semila1122118281tate_o X_14) (big_la1088302868tate_o A_32))))))).
% Axiom fact_794_Sup__fin_Oinsert:(forall (X_14:(pname->Prop)) (A_32:((pname->Prop)->Prop)), ((finite297249702name_o A_32)->((((member_pname_o X_14) A_32)->False)->((not (((eq ((pname->Prop)->Prop)) A_32) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_14) A_32))) ((semila1780557381name_o X_14) (big_la1286884090name_o A_32))))))).
% Axiom fact_795_Sup__fin_Oinsert:(forall (X_14:Prop) (A_32:(Prop->Prop)), ((finite_finite_o A_32)->((((member_o X_14) A_32)->False)->((not (((eq (Prop->Prop)) A_32) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_14) A_32))) ((semila10642723_sup_o X_14) (big_la727467310_fin_o A_32))))))).
% Axiom fact_796_Sup__fin_Oinsert:(forall (X_14:(hoare_2091234717iple_a->Prop)) (A_32:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_32)->((((member99268621le_a_o X_14) A_32)->False)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_32) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (big_la735727201le_a_o ((insert102003750le_a_o X_14) A_32))) ((semila1052848428le_a_o X_14) (big_la735727201le_a_o A_32))))))).
% Axiom fact_797_Sup__fin_Oinsert:(forall (X_14:nat) (A_32:(nat->Prop)), ((finite_finite_nat A_32)->((((member_nat X_14) A_32)->False)->((not (((eq (nat->Prop)) A_32) bot_bot_nat_o))->(((eq nat) (big_la43341705in_nat ((insert_nat X_14) A_32))) ((semila972727038up_nat X_14) (big_la43341705in_nat A_32))))))).
% Axiom fact_798_Sup__fin_Oinsert__idem:(forall (X_13:(nat->Prop)) (A_31:((nat->Prop)->Prop)), ((finite_finite_nat_o A_31)->((not (((eq ((nat->Prop)->Prop)) A_31) bot_bot_nat_o_o))->(((eq (nat->Prop)) (big_la1658356148_nat_o ((insert_nat_o X_13) A_31))) ((semila848761471_nat_o X_13) (big_la1658356148_nat_o A_31)))))).
% Axiom fact_799_Sup__fin_Oinsert__idem:(forall (X_13:((hoare_2091234717iple_a->Prop)->Prop)) (A_31:(((hoare_2091234717iple_a->Prop)->Prop)->Prop)), ((finite886417794_a_o_o A_31)->((not (((eq (((hoare_2091234717iple_a->Prop)->Prop)->Prop)) A_31) bot_bo690906872_o_o_o))->(((eq ((hoare_2091234717iple_a->Prop)->Prop)) (big_la1994307886_a_o_o ((insert987231145_a_o_o X_13) A_31))) ((semila2050116131_a_o_o X_13) (big_la1994307886_a_o_o A_31)))))).
% Axiom fact_800_Sup__fin_Oinsert__idem:(forall (X_13:(hoare_1708887482_state->Prop)) (A_31:((hoare_1708887482_state->Prop)->Prop)), ((finite1329924456tate_o A_31)->((not (((eq ((hoare_1708887482_state->Prop)->Prop)) A_31) bot_bo1678742418te_o_o))->(((eq (hoare_1708887482_state->Prop)) (big_la1088302868tate_o ((insert949073679tate_o X_13) A_31))) ((semila1122118281tate_o X_13) (big_la1088302868tate_o A_31)))))).
% Axiom fact_801_Sup__fin_Oinsert__idem:(forall (X_13:(pname->Prop)) (A_31:((pname->Prop)->Prop)), ((finite297249702name_o A_31)->((not (((eq ((pname->Prop)->Prop)) A_31) bot_bot_pname_o_o))->(((eq (pname->Prop)) (big_la1286884090name_o ((insert_pname_o X_13) A_31))) ((semila1780557381name_o X_13) (big_la1286884090name_o A_31)))))).
% Axiom fact_802_Sup__fin_Oinsert__idem:(forall (X_13:Prop) (A_31:(Prop->Prop)), ((finite_finite_o A_31)->((not (((eq (Prop->Prop)) A_31) bot_bot_o_o))->((iff (big_la727467310_fin_o ((insert_o X_13) A_31))) ((semila10642723_sup_o X_13) (big_la727467310_fin_o A_31)))))).
% Axiom fact_803_Sup__fin_Oinsert__idem:(forall (X_13:(hoare_2091234717iple_a->Prop)) (A_31:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_31)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_31) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (big_la735727201le_a_o ((insert102003750le_a_o X_13) A_31))) ((semila1052848428le_a_o X_13) (big_la735727201le_a_o A_31)))))).
% Axiom fact_804_Sup__fin_Oinsert__idem:(forall (X_13:nat) (A_31:(nat->Prop)), ((finite_finite_nat A_31)->((not (((eq (nat->Prop)) A_31) bot_bot_nat_o))->(((eq nat) (big_la43341705in_nat ((insert_nat X_13) A_31))) ((semila972727038up_nat X_13) (big_la43341705in_nat A_31)))))).
% Axiom fact_805_folding__one_Ounion__disjoint:(forall (B_24:((hoare_2091234717iple_a->Prop)->Prop)) (A_30:((hoare_2091234717iple_a->Prop)->Prop)) (F_8:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_7:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_8) F_7)->((finite1829014797le_a_o A_30)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) A_30) bot_bo1957696069_a_o_o))->((finite1829014797le_a_o B_24)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) B_24) bot_bo1957696069_a_o_o))->((((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila1672913213_a_o_o A_30) B_24)) bot_bo1957696069_a_o_o)->(((eq (hoare_2091234717iple_a->Prop)) (F_7 ((semila2050116131_a_o_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24)))))))))).
% Axiom fact_806_folding__one_Ounion__disjoint:(forall (B_24:(pname->Prop)) (A_30:(pname->Prop)) (F_8:(pname->(pname->pname))) (F_7:((pname->Prop)->pname)), (((finite1282449217_pname F_8) F_7)->((finite_finite_pname A_30)->((not (((eq (pname->Prop)) A_30) bot_bot_pname_o))->((finite_finite_pname B_24)->((not (((eq (pname->Prop)) B_24) bot_bot_pname_o))->((((eq (pname->Prop)) ((semila1673364395name_o A_30) B_24)) bot_bot_pname_o)->(((eq pname) (F_7 ((semila1780557381name_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24)))))))))).
% Axiom fact_807_folding__one_Ounion__disjoint:(forall (B_24:(hoare_1708887482_state->Prop)) (A_30:(hoare_1708887482_state->Prop)) (F_8:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_7:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_8) F_7)->((finite1625599783_state A_30)->((not (((eq (hoare_1708887482_state->Prop)) A_30) bot_bo19817387tate_o))->((finite1625599783_state B_24)->((not (((eq (hoare_1708887482_state->Prop)) B_24) bot_bo19817387tate_o))->((((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_30) B_24)) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_7 ((semila1122118281tate_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24)))))))))).
% Axiom fact_808_folding__one_Ounion__disjoint:(forall (B_24:(hoare_2091234717iple_a->Prop)) (A_30:(hoare_2091234717iple_a->Prop)) (F_8:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_7:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_8) F_7)->((finite232261744iple_a A_30)->((not (((eq (hoare_2091234717iple_a->Prop)) A_30) bot_bo1791335050le_a_o))->((finite232261744iple_a B_24)->((not (((eq (hoare_2091234717iple_a->Prop)) B_24) bot_bo1791335050le_a_o))->((((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_30) B_24)) bot_bo1791335050le_a_o)->(((eq hoare_2091234717iple_a) (F_7 ((semila1052848428le_a_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24)))))))))).
% Axiom fact_809_folding__one_Ounion__disjoint:(forall (B_24:(nat->Prop)) (A_30:(nat->Prop)) (F_8:(nat->(nat->nat))) (F_7:((nat->Prop)->nat)), (((finite988810631ne_nat F_8) F_7)->((finite_finite_nat A_30)->((not (((eq (nat->Prop)) A_30) bot_bot_nat_o))->((finite_finite_nat B_24)->((not (((eq (nat->Prop)) B_24) bot_bot_nat_o))->((((eq (nat->Prop)) ((semila1947288293_nat_o A_30) B_24)) bot_bot_nat_o)->(((eq nat) (F_7 ((semila848761471_nat_o A_30) B_24))) ((F_8 (F_7 A_30)) (F_7 B_24)))))))))).
% Axiom fact_810_folding__one_Ounion__inter:(forall (B_23:((hoare_2091234717iple_a->Prop)->Prop)) (A_29:((hoare_2091234717iple_a->Prop)->Prop)) (F_6:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_5:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_6) F_5)->((finite1829014797le_a_o A_29)->((finite1829014797le_a_o B_23)->((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila1672913213_a_o_o A_29) B_23)) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) ((F_6 (F_5 ((semila2050116131_a_o_o A_29) B_23))) (F_5 ((semila1672913213_a_o_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23)))))))).
% Axiom fact_811_folding__one_Ounion__inter:(forall (B_23:(pname->Prop)) (A_29:(pname->Prop)) (F_6:(pname->(pname->pname))) (F_5:((pname->Prop)->pname)), (((finite1282449217_pname F_6) F_5)->((finite_finite_pname A_29)->((finite_finite_pname B_23)->((not (((eq (pname->Prop)) ((semila1673364395name_o A_29) B_23)) bot_bot_pname_o))->(((eq pname) ((F_6 (F_5 ((semila1780557381name_o A_29) B_23))) (F_5 ((semila1673364395name_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23)))))))).
% Axiom fact_812_folding__one_Ounion__inter:(forall (B_23:(hoare_1708887482_state->Prop)) (A_29:(hoare_1708887482_state->Prop)) (F_6:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_5:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_6) F_5)->((finite1625599783_state A_29)->((finite1625599783_state B_23)->((not (((eq (hoare_1708887482_state->Prop)) ((semila129691299tate_o A_29) B_23)) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) ((F_6 (F_5 ((semila1122118281tate_o A_29) B_23))) (F_5 ((semila129691299tate_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23)))))))).
% Axiom fact_813_folding__one_Ounion__inter:(forall (B_23:(hoare_2091234717iple_a->Prop)) (A_29:(hoare_2091234717iple_a->Prop)) (F_6:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_5:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_6) F_5)->((finite232261744iple_a A_29)->((finite232261744iple_a B_23)->((not (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_29) B_23)) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) ((F_6 (F_5 ((semila1052848428le_a_o A_29) B_23))) (F_5 ((semila2006181266le_a_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23)))))))).
% Axiom fact_814_folding__one_Ounion__inter:(forall (B_23:(nat->Prop)) (A_29:(nat->Prop)) (F_6:(nat->(nat->nat))) (F_5:((nat->Prop)->nat)), (((finite988810631ne_nat F_6) F_5)->((finite_finite_nat A_29)->((finite_finite_nat B_23)->((not (((eq (nat->Prop)) ((semila1947288293_nat_o A_29) B_23)) bot_bot_nat_o))->(((eq nat) ((F_6 (F_5 ((semila848761471_nat_o A_29) B_23))) (F_5 ((semila1947288293_nat_o A_29) B_23)))) ((F_6 (F_5 A_29)) (F_5 B_23)))))))).
% Axiom fact_815_folding__one_Oinsert__remove:(forall (X_12:(hoare_2091234717iple_a->Prop)) (A_28:((hoare_2091234717iple_a->Prop)->Prop)) (F_4:((hoare_2091234717iple_a->Prop)->((hoare_2091234717iple_a->Prop)->(hoare_2091234717iple_a->Prop)))) (F_3:(((hoare_2091234717iple_a->Prop)->Prop)->(hoare_2091234717iple_a->Prop))), (((finite14499299le_a_o F_4) F_3)->((finite1829014797le_a_o A_28)->((and ((((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_28) ((insert102003750le_a_o X_12) bot_bo1957696069_a_o_o))) bot_bo1957696069_a_o_o)->(((eq (hoare_2091234717iple_a->Prop)) (F_3 ((insert102003750le_a_o X_12) A_28))) X_12))) ((not (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_28) ((insert102003750le_a_o X_12) bot_bo1957696069_a_o_o))) bot_bo1957696069_a_o_o))->(((eq (hoare_2091234717iple_a->Prop)) (F_3 ((insert102003750le_a_o X_12) A_28))) ((F_4 X_12) (F_3 ((minus_1746272704_a_o_o A_28) ((insert102003750le_a_o X_12) bot_bo1957696069_a_o_o)))))))))).
% Axiom fact_816_folding__one_Oinsert__remove:(forall (X_12:pname) (A_28:(pname->Prop)) (F_4:(pname->(pname->pname))) (F_3:((pname->Prop)->pname)), (((finite1282449217_pname F_4) F_3)->((finite_finite_pname A_28)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_3 ((insert_pname X_12) A_28))) X_12))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_3 ((insert_pname X_12) A_28))) ((F_4 X_12) (F_3 ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o)))))))))).
% Axiom fact_817_folding__one_Oinsert__remove:(forall (X_12:hoare_2091234717iple_a) (A_28:(hoare_2091234717iple_a->Prop)) (F_4:(hoare_2091234717iple_a->(hoare_2091234717iple_a->hoare_2091234717iple_a))) (F_3:((hoare_2091234717iple_a->Prop)->hoare_2091234717iple_a)), (((finite247037978iple_a F_4) F_3)->((finite232261744iple_a A_28)->((and ((((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_28) ((insert1597628439iple_a X_12) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o)->(((eq hoare_2091234717iple_a) (F_3 ((insert1597628439iple_a X_12) A_28))) X_12))) ((not (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_28) ((insert1597628439iple_a X_12) bot_bo1791335050le_a_o))) bot_bo1791335050le_a_o))->(((eq hoare_2091234717iple_a) (F_3 ((insert1597628439iple_a X_12) A_28))) ((F_4 X_12) (F_3 ((minus_836160335le_a_o A_28) ((insert1597628439iple_a X_12) bot_bo1791335050le_a_o)))))))))).
% Axiom fact_818_folding__one_Oinsert__remove:(forall (X_12:hoare_1708887482_state) (A_28:(hoare_1708887482_state->Prop)) (F_4:(hoare_1708887482_state->(hoare_1708887482_state->hoare_1708887482_state))) (F_3:((hoare_1708887482_state->Prop)->hoare_1708887482_state)), (((finite1615457021_state F_4) F_3)->((finite1625599783_state A_28)->((and ((((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_28) ((insert528405184_state X_12) bot_bo19817387tate_o))) bot_bo19817387tate_o)->(((eq hoare_1708887482_state) (F_3 ((insert528405184_state X_12) A_28))) X_12))) ((not (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_28) ((insert528405184_state X_12) bot_bo19817387tate_o))) bot_bo19817387tate_o))->(((eq hoare_1708887482_state) (F_3 ((insert528405184_state X_12) A_28))) ((F_4 X_12) (F_3 ((minus_2056855718tate_o A_28) ((insert528405184_state X_12) bot_bo19817387tate_o)))))))))).
% Axiom fact_819_folding__one_Oinsert__remove:(forall (X_12:nat) (A_28:(nat->Prop)) (F_4:(nat->(nat->nat))) (F_3:((nat->Prop)->nat)), (((finite988810631ne_nat F_4) F_3)->((finite_finite_nat A_28)->((and ((((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o)->(((eq nat) (F_3 ((insert_nat X_12) A_28))) X_12))) ((not (((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o))->(((eq nat) (F_3 ((insert_nat X_12) A_28))) ((F_4 X_12) (F_3 ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o)))))))))).
% Axiom fact_820_inf1I:(forall (B_22:(nat->Prop)) (A_27:(nat->Prop)) (X_11:nat), ((A_27 X_11)->((B_22 X_11)->(((semila1947288293_nat_o A_27) B_22) X_11)))).
% Axiom fact_821_inf1I:(forall (B_22:(hoare_2091234717iple_a->Prop)) (A_27:(hoare_2091234717iple_a->Prop)) (X_11:hoare_2091234717iple_a), ((A_27 X_11)->((B_22 X_11)->(((semila2006181266le_a_o A_27) B_22) X_11)))).
% Axiom fact_822_inf1I:(forall (B_22:(pname->Prop)) (A_27:(pname->Prop)) (X_11:pname), ((A_27 X_11)->((B_22 X_11)->(((semila1673364395name_o A_27) B_22) X_11)))).
% Axiom fact_823_IntI:(forall (B_21:(nat->Prop)) (C_11:nat) (A_26:(nat->Prop)), (((member_nat C_11) A_26)->(((member_nat C_11) B_21)->((member_nat C_11) ((semila1947288293_nat_o A_26) B_21))))).
% Axiom fact_824_IntI:(forall (B_21:((hoare_2091234717iple_a->Prop)->Prop)) (C_11:(hoare_2091234717iple_a->Prop)) (A_26:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_11) A_26)->(((member99268621le_a_o C_11) B_21)->((member99268621le_a_o C_11) ((semila1672913213_a_o_o A_26) B_21))))).
% Axiom fact_825_IntI:(forall (B_21:(hoare_2091234717iple_a->Prop)) (C_11:hoare_2091234717iple_a) (A_26:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_11) A_26)->(((member290856304iple_a C_11) B_21)->((member290856304iple_a C_11) ((semila2006181266le_a_o A_26) B_21))))).
% Axiom fact_826_IntI:(forall (B_21:(pname->Prop)) (C_11:pname) (A_26:(pname->Prop)), (((member_pname C_11) A_26)->(((member_pname C_11) B_21)->((member_pname C_11) ((semila1673364395name_o A_26) B_21))))).
% Axiom fact_827_IntE:(forall (C_10:nat) (A_25:(nat->Prop)) (B_20:(nat->Prop)), (((member_nat C_10) ((semila1947288293_nat_o A_25) B_20))->((((member_nat C_10) A_25)->(((member_nat C_10) B_20)->False))->False))).
% Axiom fact_828_IntE:(forall (C_10:(hoare_2091234717iple_a->Prop)) (A_25:((hoare_2091234717iple_a->Prop)->Prop)) (B_20:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_10) ((semila1672913213_a_o_o A_25) B_20))->((((member99268621le_a_o C_10) A_25)->(((member99268621le_a_o C_10) B_20)->False))->False))).
% Axiom fact_829_IntE:(forall (C_10:hoare_2091234717iple_a) (A_25:(hoare_2091234717iple_a->Prop)) (B_20:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_10) ((semila2006181266le_a_o A_25) B_20))->((((member290856304iple_a C_10) A_25)->(((member290856304iple_a C_10) B_20)->False))->False))).
% Axiom fact_830_IntE:(forall (C_10:pname) (A_25:(pname->Prop)) (B_20:(pname->Prop)), (((member_pname C_10) ((semila1673364395name_o A_25) B_20))->((((member_pname C_10) A_25)->(((member_pname C_10) B_20)->False))->False))).
% Axiom fact_831_inf1E:(forall (A_24:(nat->Prop)) (B_19:(nat->Prop)) (X_10:nat), ((((semila1947288293_nat_o A_24) B_19) X_10)->(((A_24 X_10)->((B_19 X_10)->False))->False))).
% Axiom fact_832_inf1E:(forall (A_24:(hoare_2091234717iple_a->Prop)) (B_19:(hoare_2091234717iple_a->Prop)) (X_10:hoare_2091234717iple_a), ((((semila2006181266le_a_o A_24) B_19) X_10)->(((A_24 X_10)->((B_19 X_10)->False))->False))).
% Axiom fact_833_inf1E:(forall (A_24:(pname->Prop)) (B_19:(pname->Prop)) (X_10:pname), ((((semila1673364395name_o A_24) B_19) X_10)->(((A_24 X_10)->((B_19 X_10)->False))->False))).
% Axiom fact_834_DiffI:(forall (B_18:(nat->Prop)) (C_9:nat) (A_23:(nat->Prop)), (((member_nat C_9) A_23)->((((member_nat C_9) B_18)->False)->((member_nat C_9) ((minus_minus_nat_o A_23) B_18))))).
% Axiom fact_835_DiffI:(forall (B_18:((hoare_2091234717iple_a->Prop)->Prop)) (C_9:(hoare_2091234717iple_a->Prop)) (A_23:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_9) A_23)->((((member99268621le_a_o C_9) B_18)->False)->((member99268621le_a_o C_9) ((minus_1746272704_a_o_o A_23) B_18))))).
% Axiom fact_836_DiffI:(forall (B_18:(hoare_2091234717iple_a->Prop)) (C_9:hoare_2091234717iple_a) (A_23:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_9) A_23)->((((member290856304iple_a C_9) B_18)->False)->((member290856304iple_a C_9) ((minus_836160335le_a_o A_23) B_18))))).
% Axiom fact_837_DiffI:(forall (B_18:(pname->Prop)) (C_9:pname) (A_23:(pname->Prop)), (((member_pname C_9) A_23)->((((member_pname C_9) B_18)->False)->((member_pname C_9) ((minus_minus_pname_o A_23) B_18))))).
% Axiom fact_838_DiffE:(forall (C_8:nat) (A_22:(nat->Prop)) (B_17:(nat->Prop)), (((member_nat C_8) ((minus_minus_nat_o A_22) B_17))->((((member_nat C_8) A_22)->((member_nat C_8) B_17))->False))).
% Axiom fact_839_DiffE:(forall (C_8:(hoare_2091234717iple_a->Prop)) (A_22:((hoare_2091234717iple_a->Prop)->Prop)) (B_17:((hoare_2091234717iple_a->Prop)->Prop)), (((member99268621le_a_o C_8) ((minus_1746272704_a_o_o A_22) B_17))->((((member99268621le_a_o C_8) A_22)->((member99268621le_a_o C_8) B_17))->False))).
% Axiom fact_840_DiffE:(forall (C_8:hoare_2091234717iple_a) (A_22:(hoare_2091234717iple_a->Prop)) (B_17:(hoare_2091234717iple_a->Prop)), (((member290856304iple_a C_8) ((minus_836160335le_a_o A_22) B_17))->((((member290856304iple_a C_8) A_22)->((member290856304iple_a C_8) B_17))->False))).
% Axiom fact_841_DiffE:(forall (C_8:pname) (A_22:(pname->Prop)) (B_17:(pname->Prop)), (((member_pname C_8) ((minus_minus_pname_o A_22) B_17))->((((member_pname C_8) A_22)->((member_pname C_8) B_17))->False))).
% Axiom fact_842_finite__Int:(forall (G_1:(hoare_2091234717iple_a->Prop)) (F_2:(hoare_2091234717iple_a->Prop)), (((or (finite232261744iple_a F_2)) (finite232261744iple_a G_1))->(finite232261744iple_a ((semila2006181266le_a_o F_2) G_1)))).
% Axiom fact_843_finite__Int:(forall (G_1:((hoare_2091234717iple_a->Prop)->Prop)) (F_2:((hoare_2091234717iple_a->Prop)->Prop)), (((or (finite1829014797le_a_o F_2)) (finite1829014797le_a_o G_1))->(finite1829014797le_a_o ((semila1672913213_a_o_o F_2) G_1)))).
% Axiom fact_844_finite__Int:(forall (G_1:(pname->Prop)) (F_2:(pname->Prop)), (((or (finite_finite_pname F_2)) (finite_finite_pname G_1))->(finite_finite_pname ((semila1673364395name_o F_2) G_1)))).
% Axiom fact_845_finite__Int:(forall (G_1:(nat->Prop)) (F_2:(nat->Prop)), (((or (finite_finite_nat F_2)) (finite_finite_nat G_1))->(finite_finite_nat ((semila1947288293_nat_o F_2) G_1)))).
% Axiom fact_846_finite__Diff:(forall (B_16:(hoare_2091234717iple_a->Prop)) (A_21:(hoare_2091234717iple_a->Prop)), ((finite232261744iple_a A_21)->(finite232261744iple_a ((minus_836160335le_a_o A_21) B_16)))).
% Axiom fact_847_finite__Diff:(forall (B_16:((hoare_2091234717iple_a->Prop)->Prop)) (A_21:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_21)->(finite1829014797le_a_o ((minus_1746272704_a_o_o A_21) B_16)))).
% Axiom fact_848_finite__Diff:(forall (B_16:(pname->Prop)) (A_21:(pname->Prop)), ((finite_finite_pname A_21)->(finite_finite_pname ((minus_minus_pname_o A_21) B_16)))).
% Axiom fact_849_finite__Diff:(forall (B_16:(nat->Prop)) (A_21:(nat->Prop)), ((finite_finite_nat A_21)->(finite_finite_nat ((minus_minus_nat_o A_21) B_16)))).
% Axiom fact_850_inf__Sup__absorb:(forall (A_20:(hoare_2091234717iple_a->Prop)) (A_19:((hoare_2091234717iple_a->Prop)->Prop)), ((finite1829014797le_a_o A_19)->(((member99268621le_a_o A_20) A_19)->(((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_20) (big_la735727201le_a_o A_19))) A_20)))).
% Axiom fact_851_inf__Sup__absorb:(forall (A_20:(nat->Prop)) (A_19:((nat->Prop)->Prop)), ((finite_finite_nat_o A_19)->(((member_nat_o A_20) A_19)->(((eq (nat->Prop)) ((semila1947288293_nat_o A_20) (big_la1658356148_nat_o A_19))) A_20)))).
% Axiom fact_852_inf__Sup__absorb:(forall (A_20:(pname->Prop)) (A_19:((pname->Prop)->Prop)), ((finite297249702name_o A_19)->(((member_pname_o A_20) A_19)->(((eq (pname->Prop)) ((semila1673364395name_o A_20) (big_la1286884090name_o A_19))) A_20)))).
% Axiom fact_853_inf__Sup__absorb:(forall (A_20:nat) (A_19:(nat->Prop)), ((finite_finite_nat A_19)->(((member_nat A_20) A_19)->(((eq nat) ((semila80283416nf_nat A_20) (big_la43341705in_nat A_19))) A_20)))).
% Axiom fact_854_Diff__Int:(forall (A_18:(nat->Prop)) (B_15:(nat->Prop)) (C_7:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_18) ((semila1947288293_nat_o B_15) C_7))) ((semila848761471_nat_o ((minus_minus_nat_o A_18) B_15)) ((minus_minus_nat_o A_18) C_7)))).
% Axiom fact_855_Diff__Int:(forall (A_18:(pname->Prop)) (B_15:(pname->Prop)) (C_7:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_18) ((semila1673364395name_o B_15) C_7))) ((semila1780557381name_o ((minus_minus_pname_o A_18) B_15)) ((minus_minus_pname_o A_18) C_7)))).
% Axiom fact_856_Diff__Int:(forall (A_18:((hoare_2091234717iple_a->Prop)->Prop)) (B_15:((hoare_2091234717iple_a->Prop)->Prop)) (C_7:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_18) ((semila1672913213_a_o_o B_15) C_7))) ((semila2050116131_a_o_o ((minus_1746272704_a_o_o A_18) B_15)) ((minus_1746272704_a_o_o A_18) C_7)))).
% Axiom fact_857_Diff__Int:(forall (A_18:(hoare_1708887482_state->Prop)) (B_15:(hoare_1708887482_state->Prop)) (C_7:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_18) ((semila129691299tate_o B_15) C_7))) ((semila1122118281tate_o ((minus_2056855718tate_o A_18) B_15)) ((minus_2056855718tate_o A_18) C_7)))).
% Axiom fact_858_Diff__Int:(forall (A_18:(hoare_2091234717iple_a->Prop)) (B_15:(hoare_2091234717iple_a->Prop)) (C_7:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_18) ((semila2006181266le_a_o B_15) C_7))) ((semila1052848428le_a_o ((minus_836160335le_a_o A_18) B_15)) ((minus_836160335le_a_o A_18) C_7)))).
% Axiom fact_859_Diff__Un:(forall (A_17:(nat->Prop)) (B_14:(nat->Prop)) (C_6:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_17) ((semila848761471_nat_o B_14) C_6))) ((semila1947288293_nat_o ((minus_minus_nat_o A_17) B_14)) ((minus_minus_nat_o A_17) C_6)))).
% Axiom fact_860_Diff__Un:(forall (A_17:(pname->Prop)) (B_14:(pname->Prop)) (C_6:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_17) ((semila1780557381name_o B_14) C_6))) ((semila1673364395name_o ((minus_minus_pname_o A_17) B_14)) ((minus_minus_pname_o A_17) C_6)))).
% Axiom fact_861_Diff__Un:(forall (A_17:((hoare_2091234717iple_a->Prop)->Prop)) (B_14:((hoare_2091234717iple_a->Prop)->Prop)) (C_6:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_17) ((semila2050116131_a_o_o B_14) C_6))) ((semila1672913213_a_o_o ((minus_1746272704_a_o_o A_17) B_14)) ((minus_1746272704_a_o_o A_17) C_6)))).
% Axiom fact_862_Diff__Un:(forall (A_17:(hoare_1708887482_state->Prop)) (B_14:(hoare_1708887482_state->Prop)) (C_6:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((minus_2056855718tate_o A_17) ((semila1122118281tate_o B_14) C_6))) ((semila129691299tate_o ((minus_2056855718tate_o A_17) B_14)) ((minus_2056855718tate_o A_17) C_6)))).
% Axiom fact_863_Diff__Un:(forall (A_17:(hoare_2091234717iple_a->Prop)) (B_14:(hoare_2091234717iple_a->Prop)) (C_6:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_17) ((semila1052848428le_a_o B_14) C_6))) ((semila2006181266le_a_o ((minus_836160335le_a_o A_17) B_14)) ((minus_836160335le_a_o A_17) C_6)))).
% Axiom fact_864_Un__Diff__Int:(forall (A_16:(nat->Prop)) (B_13:(nat->Prop)), (((eq (nat->Prop)) ((semila848761471_nat_o ((minus_minus_nat_o A_16) B_13)) ((semila1947288293_nat_o A_16) B_13))) A_16)).
% Axiom fact_865_Un__Diff__Int:(forall (A_16:(pname->Prop)) (B_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((minus_minus_pname_o A_16) B_13)) ((semila1673364395name_o A_16) B_13))) A_16)).
% Axiom fact_866_Un__Diff__Int:(forall (A_16:((hoare_2091234717iple_a->Prop)->Prop)) (B_13:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila2050116131_a_o_o ((minus_1746272704_a_o_o A_16) B_13)) ((semila1672913213_a_o_o A_16) B_13))) A_16)).
% Axiom fact_867_Un__Diff__Int:(forall (A_16:(hoare_1708887482_state->Prop)) (B_13:(hoare_1708887482_state->Prop)), (((eq (hoare_1708887482_state->Prop)) ((semila1122118281tate_o ((minus_2056855718tate_o A_16) B_13)) ((semila129691299tate_o A_16) B_13))) A_16)).
% Axiom fact_868_Un__Diff__Int:(forall (A_16:(hoare_2091234717iple_a->Prop)) (B_13:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila1052848428le_a_o ((minus_836160335le_a_o A_16) B_13)) ((semila2006181266le_a_o A_16) B_13))) A_16)).
% Axiom fact_869_Collect__conj__eq:(forall (P_2:(pname->Prop)) (Q:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (P_2 X)) (Q X))))) ((semila1673364395name_o (collect_pname P_2)) (collect_pname Q)))).
% Axiom fact_870_Collect__conj__eq:(forall (P_2:(hoare_2091234717iple_a->Prop)) (Q:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and (P_2 X)) (Q X))))) ((semila2006181266le_a_o (collec992574898iple_a P_2)) (collec992574898iple_a Q)))).
% Axiom fact_871_Collect__conj__eq:(forall (P_2:(nat->Prop)) (Q:(nat->Prop)), (((eq (nat->Prop)) (collect_nat (fun (X:nat)=> ((and (P_2 X)) (Q X))))) ((semila1947288293_nat_o (collect_nat P_2)) (collect_nat Q)))).
% Axiom fact_872_Int__Collect:(forall (X_9:(hoare_2091234717iple_a->Prop)) (A_15:((hoare_2091234717iple_a->Prop)->Prop)) (P_1:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o X_9) ((semila1672913213_a_o_o A_15) (collec1008234059le_a_o P_1)))) ((and ((member99268621le_a_o X_9) A_15)) (P_1 X_9)))).
% Axiom fact_873_Int__Collect:(forall (X_9:nat) (A_15:(nat->Prop)) (P_1:(nat->Prop)), ((iff ((member_nat X_9) ((semila1947288293_nat_o A_15) (collect_nat P_1)))) ((and ((member_nat X_9) A_15)) (P_1 X_9)))).
% Axiom fact_874_Int__Collect:(forall (X_9:hoare_2091234717iple_a) (A_15:(hoare_2091234717iple_a->Prop)) (P_1:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a X_9) ((semila2006181266le_a_o A_15) (collec992574898iple_a P_1)))) ((and ((member290856304iple_a X_9) A_15)) (P_1 X_9)))).
% Axiom fact_875_Int__Collect:(forall (X_9:pname) (A_15:(pname->Prop)) (P_1:(pname->Prop)), ((iff ((member_pname X_9) ((semila1673364395name_o A_15) (collect_pname P_1)))) ((and ((member_pname X_9) A_15)) (P_1 X_9)))).
% Axiom fact_876_inf__Int__eq:(forall (R:((hoare_2091234717iple_a->Prop)->Prop)) (S_1:((hoare_2091234717iple_a->Prop)->Prop)) (X:(hoare_2091234717iple_a->Prop)), ((iff (((semila1672913213_a_o_o (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) R))) (fun (Y_7:(hoare_2091234717iple_a->Prop))=> ((member99268621le_a_o Y_7) S_1))) X)) ((member99268621le_a_o X) ((semila1672913213_a_o_o R) S_1)))).
% Axiom fact_877_inf__Int__eq:(forall (R:(nat->Prop)) (S_1:(nat->Prop)) (X:nat), ((iff (((semila1947288293_nat_o (fun (Y_7:nat)=> ((member_nat Y_7) R))) (fun (Y_7:nat)=> ((member_nat Y_7) S_1))) X)) ((member_nat X) ((semila1947288293_nat_o R) S_1)))).
% Axiom fact_878_inf__Int__eq:(forall (R:(hoare_2091234717iple_a->Prop)) (S_1:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila2006181266le_a_o (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) R))) (fun (Y_7:hoare_2091234717iple_a)=> ((member290856304iple_a Y_7) S_1))) X)) ((member290856304iple_a X) ((semila2006181266le_a_o R) S_1)))).
% Axiom fact_879_inf__Int__eq:(forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X:pname), ((iff (((semila1673364395name_o (fun (Y_7:pname)=> ((member_pname Y_7) R))) (fun (Y_7:pname)=> ((member_pname Y_7) S_1))) X)) ((member_pname X) ((semila1673364395name_o R) S_1)))).
% Axiom fact_880_Int__absorb:(forall (A_14:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_14) A_14)) A_14)).
% Axiom fact_881_Int__absorb:(forall (A_14:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_14) A_14)) A_14)).
% Axiom fact_882_Int__absorb:(forall (A_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_14) A_14)) A_14)).
% Axiom fact_883_inf_Oidem:(forall (A_13:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_13) A_13)) A_13)).
% Axiom fact_884_inf_Oidem:(forall (A_13:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_13) A_13)) A_13)).
% Axiom fact_885_inf_Oidem:(forall (A_13:nat), (((eq nat) ((semila80283416nf_nat A_13) A_13)) A_13)).
% Axiom fact_886_inf_Oidem:(forall (A_13:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_13) A_13)) A_13)).
% Axiom fact_887_inf__idem:(forall (X_8:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_8) X_8)) X_8)).
% Axiom fact_888_inf__idem:(forall (X_8:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_8) X_8)) X_8)).
% Axiom fact_889_inf__idem:(forall (X_8:nat), (((eq nat) ((semila80283416nf_nat X_8) X_8)) X_8)).
% Axiom fact_890_inf__idem:(forall (X_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_8) X_8)) X_8)).
% Axiom fact_891_fun__diff__def:(forall (A_12:(hoare_2091234717iple_a->Prop)) (B_12:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((minus_836160335le_a_o A_12) B_12) X)) ((minus_minus_o (A_12 X)) (B_12 X)))).
% Axiom fact_892_fun__diff__def:(forall (A_12:(pname->Prop)) (B_12:(pname->Prop)) (X:pname), ((iff (((minus_minus_pname_o A_12) B_12) X)) ((minus_minus_o (A_12 X)) (B_12 X)))).
% Axiom fact_893_fun__diff__def:(forall (A_12:(nat->Prop)) (B_12:(nat->Prop)) (X:nat), ((iff (((minus_minus_nat_o A_12) B_12) X)) ((minus_minus_o (A_12 X)) (B_12 X)))).
% Axiom fact_894_inf__fun__def:(forall (F_1:(nat->Prop)) (G:(nat->Prop)) (X:nat), ((iff (((semila1947288293_nat_o F_1) G) X)) ((semila854092349_inf_o (F_1 X)) (G X)))).
% Axiom fact_895_inf__fun__def:(forall (F_1:(hoare_2091234717iple_a->Prop)) (G:(hoare_2091234717iple_a->Prop)) (X:hoare_2091234717iple_a), ((iff (((semila2006181266le_a_o F_1) G) X)) ((semila854092349_inf_o (F_1 X)) (G X)))).
% Axiom fact_896_inf__fun__def:(forall (F_1:(pname->Prop)) (G:(pname->Prop)) (X:pname), ((iff (((semila1673364395name_o F_1) G) X)) ((semila854092349_inf_o (F_1 X)) (G X)))).
% Axiom fact_897_set__diff__eq:(forall (A_11:((hoare_2091234717iple_a->Prop)->Prop)) (B_11:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((minus_1746272704_a_o_o A_11) B_11)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_11)) (not ((member99268621le_a_o X) B_11))))))).
% Axiom fact_898_set__diff__eq:(forall (A_11:(nat->Prop)) (B_11:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_11) B_11)) (collect_nat (fun (X:nat)=> ((and ((member_nat X) A_11)) (not ((member_nat X) B_11))))))).
% Axiom fact_899_set__diff__eq:(forall (A_11:(hoare_2091234717iple_a->Prop)) (B_11:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((minus_836160335le_a_o A_11) B_11)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_11)) (not ((member290856304iple_a X) B_11))))))).
% Axiom fact_900_set__diff__eq:(forall (A_11:(pname->Prop)) (B_11:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_11) B_11)) (collect_pname (fun (X:pname)=> ((and ((member_pname X) A_11)) (not ((member_pname X) B_11))))))).
% Axiom fact_901_Int__def:(forall (A_10:((hoare_2091234717iple_a->Prop)->Prop)) (B_10:((hoare_2091234717iple_a->Prop)->Prop)), (((eq ((hoare_2091234717iple_a->Prop)->Prop)) ((semila1672913213_a_o_o A_10) B_10)) (collec1008234059le_a_o (fun (X:(hoare_2091234717iple_a->Prop))=> ((and ((member99268621le_a_o X) A_10)) ((member99268621le_a_o X) B_10)))))).
% Axiom fact_902_Int__def:(forall (A_10:(nat->Prop)) (B_10:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_10) B_10)) (collect_nat (fun (X:nat)=> ((and ((member_nat X) A_10)) ((member_nat X) B_10)))))).
% Axiom fact_903_Int__def:(forall (A_10:(hoare_2091234717iple_a->Prop)) (B_10:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_10) B_10)) (collec992574898iple_a (fun (X:hoare_2091234717iple_a)=> ((and ((member290856304iple_a X) A_10)) ((member290856304iple_a X) B_10)))))).
% Axiom fact_904_Int__def:(forall (A_10:(pname->Prop)) (B_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_10) B_10)) (collect_pname (fun (X:pname)=> ((and ((member_pname X) A_10)) ((member_pname X) B_10)))))).
% Axiom fact_905_Int__commute:(forall (A_9:(nat->Prop)) (B_9:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_9) B_9)) ((semila1947288293_nat_o B_9) A_9))).
% Axiom fact_906_Int__commute:(forall (A_9:(hoare_2091234717iple_a->Prop)) (B_9:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_9) B_9)) ((semila2006181266le_a_o B_9) A_9))).
% Axiom fact_907_Int__commute:(forall (A_9:(pname->Prop)) (B_9:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_9) B_9)) ((semila1673364395name_o B_9) A_9))).
% Axiom fact_908_inf_Ocommute:(forall (A_8:(nat->Prop)) (B_8:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_8) B_8)) ((semila1947288293_nat_o B_8) A_8))).
% Axiom fact_909_inf_Ocommute:(forall (A_8:(hoare_2091234717iple_a->Prop)) (B_8:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_8) B_8)) ((semila2006181266le_a_o B_8) A_8))).
% Axiom fact_910_inf_Ocommute:(forall (A_8:nat) (B_8:nat), (((eq nat) ((semila80283416nf_nat A_8) B_8)) ((semila80283416nf_nat B_8) A_8))).
% Axiom fact_911_inf_Ocommute:(forall (A_8:(pname->Prop)) (B_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_8) B_8)) ((semila1673364395name_o B_8) A_8))).
% Axiom fact_912_inf__sup__aci_I1_J:(forall (X_7:(nat->Prop)) (Y_6:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_7) Y_6)) ((semila1947288293_nat_o Y_6) X_7))).
% Axiom fact_913_inf__sup__aci_I1_J:(forall (X_7:(hoare_2091234717iple_a->Prop)) (Y_6:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_7) Y_6)) ((semila2006181266le_a_o Y_6) X_7))).
% Axiom fact_914_inf__sup__aci_I1_J:(forall (X_7:nat) (Y_6:nat), (((eq nat) ((semila80283416nf_nat X_7) Y_6)) ((semila80283416nf_nat Y_6) X_7))).
% Axiom fact_915_inf__sup__aci_I1_J:(forall (X_7:(pname->Prop)) (Y_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_7) Y_6)) ((semila1673364395name_o Y_6) X_7))).
% Axiom fact_916_inf__commute:(forall (X_6:(nat->Prop)) (Y_5:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_6) Y_5)) ((semila1947288293_nat_o Y_5) X_6))).
% Axiom fact_917_inf__commute:(forall (X_6:(hoare_2091234717iple_a->Prop)) (Y_5:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_6) Y_5)) ((semila2006181266le_a_o Y_5) X_6))).
% Axiom fact_918_inf__commute:(forall (X_6:nat) (Y_5:nat), (((eq nat) ((semila80283416nf_nat X_6) Y_5)) ((semila80283416nf_nat Y_5) X_6))).
% Axiom fact_919_inf__commute:(forall (X_6:(pname->Prop)) (Y_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_6) Y_5)) ((semila1673364395name_o Y_5) X_6))).
% Axiom fact_920_Int__left__absorb:(forall (A_7:(nat->Prop)) (B_7:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_7) ((semila1947288293_nat_o A_7) B_7))) ((semila1947288293_nat_o A_7) B_7))).
% Axiom fact_921_Int__left__absorb:(forall (A_7:(hoare_2091234717iple_a->Prop)) (B_7:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_7) ((semila2006181266le_a_o A_7) B_7))) ((semila2006181266le_a_o A_7) B_7))).
% Axiom fact_922_Int__left__absorb:(forall (A_7:(pname->Prop)) (B_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_7) ((semila1673364395name_o A_7) B_7))) ((semila1673364395name_o A_7) B_7))).
% Axiom fact_923_inf_Oleft__idem:(forall (A_6:(nat->Prop)) (B_6:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_6) ((semila1947288293_nat_o A_6) B_6))) ((semila1947288293_nat_o A_6) B_6))).
% Axiom fact_924_inf_Oleft__idem:(forall (A_6:(hoare_2091234717iple_a->Prop)) (B_6:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_6) ((semila2006181266le_a_o A_6) B_6))) ((semila2006181266le_a_o A_6) B_6))).
% Axiom fact_925_inf_Oleft__idem:(forall (A_6:nat) (B_6:nat), (((eq nat) ((semila80283416nf_nat A_6) ((semila80283416nf_nat A_6) B_6))) ((semila80283416nf_nat A_6) B_6))).
% Axiom fact_926_inf_Oleft__idem:(forall (A_6:(pname->Prop)) (B_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_6) ((semila1673364395name_o A_6) B_6))) ((semila1673364395name_o A_6) B_6))).
% Axiom fact_927_inf__sup__aci_I4_J:(forall (X_5:(nat->Prop)) (Y_4:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_5) ((semila1947288293_nat_o X_5) Y_4))) ((semila1947288293_nat_o X_5) Y_4))).
% Axiom fact_928_inf__sup__aci_I4_J:(forall (X_5:(hoare_2091234717iple_a->Prop)) (Y_4:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_5) ((semila2006181266le_a_o X_5) Y_4))) ((semila2006181266le_a_o X_5) Y_4))).
% Axiom fact_929_inf__sup__aci_I4_J:(forall (X_5:nat) (Y_4:nat), (((eq nat) ((semila80283416nf_nat X_5) ((semila80283416nf_nat X_5) Y_4))) ((semila80283416nf_nat X_5) Y_4))).
% Axiom fact_930_inf__sup__aci_I4_J:(forall (X_5:(pname->Prop)) (Y_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_5) ((semila1673364395name_o X_5) Y_4))) ((semila1673364395name_o X_5) Y_4))).
% Axiom fact_931_inf__left__idem:(forall (X_4:(nat->Prop)) (Y_3:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_4) ((semila1947288293_nat_o X_4) Y_3))) ((semila1947288293_nat_o X_4) Y_3))).
% Axiom fact_932_inf__left__idem:(forall (X_4:(hoare_2091234717iple_a->Prop)) (Y_3:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_4) ((semila2006181266le_a_o X_4) Y_3))) ((semila2006181266le_a_o X_4) Y_3))).
% Axiom fact_933_inf__left__idem:(forall (X_4:nat) (Y_3:nat), (((eq nat) ((semila80283416nf_nat X_4) ((semila80283416nf_nat X_4) Y_3))) ((semila80283416nf_nat X_4) Y_3))).
% Axiom fact_934_inf__left__idem:(forall (X_4:(pname->Prop)) (Y_3:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_4) ((semila1673364395name_o X_4) Y_3))) ((semila1673364395name_o X_4) Y_3))).
% Axiom fact_935_Int__left__commute:(forall (A_5:(nat->Prop)) (B_5:(nat->Prop)) (C_5:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o A_5) ((semila1947288293_nat_o B_5) C_5))) ((semila1947288293_nat_o B_5) ((semila1947288293_nat_o A_5) C_5)))).
% Axiom fact_936_Int__left__commute:(forall (A_5:(hoare_2091234717iple_a->Prop)) (B_5:(hoare_2091234717iple_a->Prop)) (C_5:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o A_5) ((semila2006181266le_a_o B_5) C_5))) ((semila2006181266le_a_o B_5) ((semila2006181266le_a_o A_5) C_5)))).
% Axiom fact_937_Int__left__commute:(forall (A_5:(pname->Prop)) (B_5:(pname->Prop)) (C_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o A_5) ((semila1673364395name_o B_5) C_5))) ((semila1673364395name_o B_5) ((semila1673364395name_o A_5) C_5)))).
% Axiom fact_938_inf_Oleft__commute:(forall (B_4:(nat->Prop)) (A_4:(nat->Prop)) (C_4:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o B_4) ((semila1947288293_nat_o A_4) C_4))) ((semila1947288293_nat_o A_4) ((semila1947288293_nat_o B_4) C_4)))).
% Axiom fact_939_inf_Oleft__commute:(forall (B_4:(hoare_2091234717iple_a->Prop)) (A_4:(hoare_2091234717iple_a->Prop)) (C_4:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o B_4) ((semila2006181266le_a_o A_4) C_4))) ((semila2006181266le_a_o A_4) ((semila2006181266le_a_o B_4) C_4)))).
% Axiom fact_940_inf_Oleft__commute:(forall (B_4:nat) (A_4:nat) (C_4:nat), (((eq nat) ((semila80283416nf_nat B_4) ((semila80283416nf_nat A_4) C_4))) ((semila80283416nf_nat A_4) ((semila80283416nf_nat B_4) C_4)))).
% Axiom fact_941_inf_Oleft__commute:(forall (B_4:(pname->Prop)) (A_4:(pname->Prop)) (C_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o B_4) ((semila1673364395name_o A_4) C_4))) ((semila1673364395name_o A_4) ((semila1673364395name_o B_4) C_4)))).
% Axiom fact_942_inf__sup__aci_I3_J:(forall (X_3:(nat->Prop)) (Y_2:(nat->Prop)) (Z_2:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_3) ((semila1947288293_nat_o Y_2) Z_2))) ((semila1947288293_nat_o Y_2) ((semila1947288293_nat_o X_3) Z_2)))).
% Axiom fact_943_inf__sup__aci_I3_J:(forall (X_3:(hoare_2091234717iple_a->Prop)) (Y_2:(hoare_2091234717iple_a->Prop)) (Z_2:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_3) ((semila2006181266le_a_o Y_2) Z_2))) ((semila2006181266le_a_o Y_2) ((semila2006181266le_a_o X_3) Z_2)))).
% Axiom fact_944_inf__sup__aci_I3_J:(forall (X_3:nat) (Y_2:nat) (Z_2:nat), (((eq nat) ((semila80283416nf_nat X_3) ((semila80283416nf_nat Y_2) Z_2))) ((semila80283416nf_nat Y_2) ((semila80283416nf_nat X_3) Z_2)))).
% Axiom fact_945_inf__sup__aci_I3_J:(forall (X_3:(pname->Prop)) (Y_2:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_3) ((semila1673364395name_o Y_2) Z_2))) ((semila1673364395name_o Y_2) ((semila1673364395name_o X_3) Z_2)))).
% Axiom fact_946_inf__left__commute:(forall (X_2:(nat->Prop)) (Y_1:(nat->Prop)) (Z_1:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o X_2) ((semila1947288293_nat_o Y_1) Z_1))) ((semila1947288293_nat_o Y_1) ((semila1947288293_nat_o X_2) Z_1)))).
% Axiom fact_947_inf__left__commute:(forall (X_2:(hoare_2091234717iple_a->Prop)) (Y_1:(hoare_2091234717iple_a->Prop)) (Z_1:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o X_2) ((semila2006181266le_a_o Y_1) Z_1))) ((semila2006181266le_a_o Y_1) ((semila2006181266le_a_o X_2) Z_1)))).
% Axiom fact_948_inf__left__commute:(forall (X_2:nat) (Y_1:nat) (Z_1:nat), (((eq nat) ((semila80283416nf_nat X_2) ((semila80283416nf_nat Y_1) Z_1))) ((semila80283416nf_nat Y_1) ((semila80283416nf_nat X_2) Z_1)))).
% Axiom fact_949_inf__left__commute:(forall (X_2:(pname->Prop)) (Y_1:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o X_2) ((semila1673364395name_o Y_1) Z_1))) ((semila1673364395name_o Y_1) ((semila1673364395name_o X_2) Z_1)))).
% Axiom fact_950_Diff__iff:(forall (C_3:(hoare_2091234717iple_a->Prop)) (A_3:((hoare_2091234717iple_a->Prop)->Prop)) (B_3:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o C_3) ((minus_1746272704_a_o_o A_3) B_3))) ((and ((member99268621le_a_o C_3) A_3)) (((member99268621le_a_o C_3) B_3)->False)))).
% Axiom fact_951_Diff__iff:(forall (C_3:nat) (A_3:(nat->Prop)) (B_3:(nat->Prop)), ((iff ((member_nat C_3) ((minus_minus_nat_o A_3) B_3))) ((and ((member_nat C_3) A_3)) (((member_nat C_3) B_3)->False)))).
% Axiom fact_952_Diff__iff:(forall (C_3:hoare_2091234717iple_a) (A_3:(hoare_2091234717iple_a->Prop)) (B_3:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a C_3) ((minus_836160335le_a_o A_3) B_3))) ((and ((member290856304iple_a C_3) A_3)) (((member290856304iple_a C_3) B_3)->False)))).
% Axiom fact_953_Diff__iff:(forall (C_3:pname) (A_3:(pname->Prop)) (B_3:(pname->Prop)), ((iff ((member_pname C_3) ((minus_minus_pname_o A_3) B_3))) ((and ((member_pname C_3) A_3)) (((member_pname C_3) B_3)->False)))).
% Axiom fact_954_Int__iff:(forall (C_2:(hoare_2091234717iple_a->Prop)) (A_2:((hoare_2091234717iple_a->Prop)->Prop)) (B_2:((hoare_2091234717iple_a->Prop)->Prop)), ((iff ((member99268621le_a_o C_2) ((semila1672913213_a_o_o A_2) B_2))) ((and ((member99268621le_a_o C_2) A_2)) ((member99268621le_a_o C_2) B_2)))).
% Axiom fact_955_Int__iff:(forall (C_2:nat) (A_2:(nat->Prop)) (B_2:(nat->Prop)), ((iff ((member_nat C_2) ((semila1947288293_nat_o A_2) B_2))) ((and ((member_nat C_2) A_2)) ((member_nat C_2) B_2)))).
% Axiom fact_956_Int__iff:(forall (C_2:hoare_2091234717iple_a) (A_2:(hoare_2091234717iple_a->Prop)) (B_2:(hoare_2091234717iple_a->Prop)), ((iff ((member290856304iple_a C_2) ((semila2006181266le_a_o A_2) B_2))) ((and ((member290856304iple_a C_2) A_2)) ((member290856304iple_a C_2) B_2)))).
% Axiom fact_957_Int__iff:(forall (C_2:pname) (A_2:(pname->Prop)) (B_2:(pname->Prop)), ((iff ((member_pname C_2) ((semila1673364395name_o A_2) B_2))) ((and ((member_pname C_2) A_2)) ((member_pname C_2) B_2)))).
% Axiom fact_958_Diff__Int__distrib:(forall (C_1:(hoare_2091234717iple_a->Prop)) (A_1:(hoare_2091234717iple_a->Prop)) (B_1:(hoare_2091234717iple_a->Prop)), (((eq (hoare_2091234717iple_a->Prop)) ((semila2006181266le_a_o C_1) ((minus_836160335le_a_o A_1) B_1))) ((minus_836160335le_a_o ((semila2006181266le_a_o C_1) A_1)) ((semila2006181266le_a_o C_1) B_1)))).
% Axiom fact_959_Diff__Int__distrib:(forall (C_1:(pname->Prop)) (A_1:(pname->Prop)) (B_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1673364395name_o C_1) ((minus_minus_pname_o A_1) B_1))) ((minus_minus_pname_o ((semila1673364395name_o C_1) A_1)) ((semila1673364395name_o C_1) B_1)))).
% Axiom fact_960_Diff__Int__distrib:(forall (C_1:(nat->Prop)) (A_1:(nat->Prop)) (B_1:(nat->Prop)), (((eq (nat->Prop)) ((semila1947288293_nat_o C_1) ((minus_minus_nat_o A_1) B_1))) ((minus_minus_nat_o ((semila1947288293_nat_o C_1) A_1)) ((semila1947288293_nat_o C_1) B_1)))).
% Axiom fact_961_diff__0__eq__0:(forall (N_1:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N_1)) zero_zero_nat)).
% Axiom fact_962_minus__nat_Odiff__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)).
% Axiom fact_963_diff__self__eq__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)).
% Axiom fact_964_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_965_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_966_Suc__diff__diff:(forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M)) N_1)) (suc K_1))) ((minus_minus_nat ((minus_minus_nat M) N_1)) K_1))).
% Axiom fact_967_diff__commute:(forall (I_1:nat) (J_1:nat) (K_1:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K_1)) ((minus_minus_nat ((minus_minus_nat I_1) K_1)) J_1))).
% Axiom fact_968_zero__induct__lemma:(forall (I_1:nat) (P:(nat->Prop)) (K_1:nat), ((P K_1)->((forall (N:nat), ((P (suc N))->(P N)))->(P ((minus_minus_nat K_1) I_1))))).
% Axiom fact_969_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:nat)=> K)) ((minus_minus_nat M) N_1)))).
% Axiom fact_970_One__nat__def:(((eq nat) one_one_nat) (suc zero_zero_nat)).
% Axiom fact_971_diff__Suc__1:(forall (N_1:nat), (((eq nat) ((minus_minus_nat (suc N_1)) one_one_nat)) N_1)).
% Axiom fact_972_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_973_plus__nat_Oadd__0:(forall (N_1:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N_1)) N_1)).
% Axiom fact_974_Nat_Oadd__0__right:(forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)).
% Axiom fact_975_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_976_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_977_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_978_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_979_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_980_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_981_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_982_nat__add__assoc:(forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N_1)) K_1)) ((plus_plus_nat M) ((plus_plus_nat N_1) K_1)))).
% Axiom fact_983_nat__add__left__cancel:(forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) (((eq nat) M) N_1))).
% Axiom fact_984_nat__add__right__cancel:(forall (M:nat) (K_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M) K_1)) ((plus_plus_nat N_1) K_1))) (((eq nat) M) N_1))).
% Axiom fact_985_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_986_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_987_diff__diff__left:(forall (I_1:nat) (J_1:nat) (K_1:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K_1)) ((minus_minus_nat I_1) ((plus_plus_nat J_1) K_1)))).
% Axiom fact_988_diff__cancel:(forall (K_1:nat) (M:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) ((minus_minus_nat M) N_1))).
% Axiom fact_989_diff__cancel2:(forall (M:nat) (K_1:nat) (N_1:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K_1)) ((plus_plus_nat N_1) K_1))) ((minus_minus_nat M) N_1))).
% Axiom fact_990_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_991_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_992_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_993_Suc__eq__plus1:(forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat N_1) one_one_nat))).
% Axiom fact_994_Suc__eq__plus1__left:(forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat one_one_nat) N_1))).
% Axiom fact_995_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_996_com_Osize_I4_J:(forall (Com1_1:com) (Com2_1:com), (((eq nat) (com_size ((semi Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (com_size Com1_1)) (com_size Com2_1))) (suc zero_zero_nat)))).
% Axiom fact_997_com_Osize_I6_J:(forall (Fun_1:(state->Prop)) (Com_1:com), (((eq nat) (com_size ((while Fun_1) Com_1))) ((plus_plus_nat (com_size Com_1)) (suc zero_zero_nat)))).
% Axiom fact_998_com_Osize_I7_J:(forall (Pname_1:pname), (((eq nat) (com_size (body Pname_1))) zero_zero_nat)).
% Axiom fact_999_com_Osize_I1_J:(((eq nat) (com_size skip)) zero_zero_nat).
% Axiom fact_1000_com_Osize_I12_J:(forall (Com1_1:com) (Com2_1:com), (((eq nat) (size_size_com ((semi Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1_1)) (size_size_com Com2_1))) (suc zero_zero_nat)))).
% Axiom fact_1001_com_Osize_I14_J:(forall (Fun_1:(state->Prop)) (Com_1:com), (((eq nat) (size_size_com ((while Fun_1) Com_1))) ((plus_plus_nat (size_size_com Com_1)) (suc zero_zero_nat)))).
% Axiom fact_1002_add__mult__distrib2:(forall (K_1:nat) (M:nat) (N_1:nat), (((eq nat) ((times_times_nat K_1) ((plus_plus_nat M) N_1))) ((plus_plus_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1)))).
% Axiom fact_1003_add__mult__distrib:(forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N_1)) K_1)) ((plus_plus_nat ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1)))).
% Axiom fact_1004_nat__mult__eq__1__iff:(forall (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) N_1)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N_1) one_one_nat)))).
% Axiom fact_1005_nat__mult__1__right:(forall (N_1:nat), (((eq nat) ((times_times_nat N_1) one_one_nat)) N_1)).
% Axiom fact_1006_nat__1__eq__mult__iff:(forall (M:nat) (N_1:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M) N_1))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N_1) one_one_nat)))).
% Axiom fact_1007_nat__mult__1:(forall (N_1:nat), (((eq nat) ((times_times_nat one_one_nat) N_1)) N_1)).
% Axiom fact_1008_mult__0:(forall (N_1:nat), (((eq nat) ((times_times_nat zero_zero_nat) N_1)) zero_zero_nat)).
% Axiom fact_1009_mult__0__right:(forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)).
% Axiom fact_1010_mult__is__0:(forall (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) N_1)) zero_zero_nat)) ((or (((eq nat) M) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat)))).
% Axiom fact_1011_mult__cancel1:(forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((or (((eq nat) M) N_1)) (((eq nat) K_1) zero_zero_nat)))).
% Axiom fact_1012_mult__cancel2:(forall (M:nat) (K_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1))) ((or (((eq nat) M) N_1)) (((eq nat) K_1) zero_zero_nat)))).
% Axiom fact_1013_Suc__mult__cancel1:(forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat (suc K_1)) M)) ((times_times_nat (suc K_1)) N_1))) (((eq nat) M) N_1))).
% Axiom fact_1014_diff__mult__distrib:(forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((times_times_nat ((minus_minus_nat M) N_1)) K_1)) ((minus_minus_nat ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1)))).
% Axiom fact_1015_diff__mult__distrib2:(forall (K_1:nat) (M:nat) (N_1:nat), (((eq nat) ((times_times_nat K_1) ((minus_minus_nat M) N_1))) ((minus_minus_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1)))).
% Axiom fact_1016_mult__eq__1__iff:(forall (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M) N_1)) (suc zero_zero_nat))) ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N_1) (suc zero_zero_nat))))).
% Axiom fact_1017_mult__Suc:(forall (M:nat) (N_1:nat), (((eq nat) ((times_times_nat (suc M)) N_1)) ((plus_plus_nat N_1) ((times_times_nat M) N_1)))).
% Axiom fact_1018_mult__Suc__right:(forall (M:nat) (N_1:nat), (((eq nat) ((times_times_nat M) (suc N_1))) ((plus_plus_nat M) ((times_times_nat M) N_1)))).
% Axiom fact_1019_mult__eq__self__implies__10:(forall (M:nat) (N_1:nat), ((((eq nat) M) ((times_times_nat M) N_1))->((or (((eq nat) N_1) one_one_nat)) (((eq nat) M) zero_zero_nat)))).
% Axiom fact_1020_com_Osize_I15_J:(forall (Pname_1:pname), (((eq nat) (size_size_com (body Pname_1))) zero_zero_nat)).
% Axiom fact_1021_com_Osize_I9_J:(((eq nat) (size_size_com skip)) zero_zero_nat).
% Axiom fact_1022_mult__eq__if:(forall (N_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((times_times_nat M) N_1)) zero_zero_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((times_times_nat M) N_1)) ((plus_plus_nat N_1) ((times_times_nat ((minus_minus_nat M) one_one_nat)) N_1)))))).
% Axiom fact_1023_nat__mult__commute:(forall (M:nat) (N_1:nat), (((eq nat) ((times_times_nat M) N_1)) ((times_times_nat N_1) M))).
% Axiom fact_1024_nat__mult__assoc:(forall (M:nat) (N_1:nat) (K_1:nat), (((eq nat) ((times_times_nat ((times_times_nat M) N_1)) K_1)) ((times_times_nat M) ((times_times_nat N_1) K_1)))).
% Axiom fact_1025_left__add__mult__distrib:(forall (I_1:nat) (U:nat) (J_1:nat) (K_1:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J_1) U)) K_1))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J_1)) U)) K_1))).
% Axiom fact_1026_nat__mult__eq__cancel__disj:(forall (K_1:nat) (M:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((or (((eq nat) K_1) zero_zero_nat)) (((eq nat) M) N_1)))).
% Axiom fact_1027_com_Osize_I13_J:(forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (((eq nat) (size_size_com (((cond Fun_1) Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (size_size_com Com1_1)) (size_size_com Com2_1))) (suc zero_zero_nat)))).
% Axiom fact_1028_com_Osize_I5_J:(forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (((eq nat) (com_size (((cond Fun_1) Com1_1) Com2_1))) ((plus_plus_nat ((plus_plus_nat (com_size Com1_1)) (com_size Com2_1))) (suc zero_zero_nat)))).
% Axiom fact_1029_finite__Collect__le__nat:(forall (K_1:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat N) K_1))))).
% Axiom fact_1030_le0:(forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1)).
% Axiom fact_1031_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_1032_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_1033_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_1034_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 fact_1035_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_1036_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_1037_com_Osimps_I55_J:(forall (Pname:pname) (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (not (((eq com) (body Pname)) (((cond Fun_1) Com1_1) Com2_1)))).
% Axiom fact_1038_com_Osimps_I54_J:(forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com) (Pname:pname), (not (((eq com) (((cond Fun_1) Com1_1) Com2_1)) (body Pname)))).
% Axiom fact_1039_com_Osimps_I4_J:(forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com1:com) (Com2:com), ((iff (((eq com) (((cond Fun_1) Com1_1) Com2_1)) (((cond Fun) Com1) Com2))) ((and ((and (((eq (state->Prop)) Fun_1) Fun)) (((eq com) Com1_1) Com1))) (((eq com) Com2_1) Com2)))).
% Axiom fact_1040_le__antisym:(forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->(((ord_less_eq_nat N_1) M)->(((eq nat) M) N_1)))).
% Axiom fact_1041_le__trans:(forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat J_1) K_1)->((ord_less_eq_nat I_1) K_1)))).
% Axiom fact_1042_eq__imp__le:(forall (M:nat) (N_1:nat), ((((eq nat) M) N_1)->((ord_less_eq_nat M) N_1))).
% Axiom fact_1043_nat__le__linear:(forall (M:nat) (N_1:nat), ((or ((ord_less_eq_nat M) N_1)) ((ord_less_eq_nat N_1) M))).
% Axiom fact_1044_le__refl:(forall (N_1:nat), ((ord_less_eq_nat N_1) N_1)).
% Axiom fact_1045_Suc__leD:(forall (M:nat) (N_1:nat), (((ord_less_eq_nat (suc M)) N_1)->((ord_less_eq_nat M) N_1))).
% Axiom fact_1046_le__SucE:(forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) (suc N_1))->((((ord_less_eq_nat M) N_1)->False)->(((eq nat) M) (suc N_1))))).
% Axiom fact_1047_le__SucI:(forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_eq_nat M) (suc N_1)))).
% Axiom fact_1048_Suc__le__mono:(forall (N_1:nat) (M:nat), ((iff ((ord_less_eq_nat (suc N_1)) (suc M))) ((ord_less_eq_nat N_1) M))).
% Axiom fact_1049_le__Suc__eq:(forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat M) (suc N_1))) ((or ((ord_less_eq_nat M) N_1)) (((eq nat) M) (suc N_1))))).
% Axiom fact_1050_not__less__eq__eq:(forall (M:nat) (N_1:nat), ((iff (((ord_less_eq_nat M) N_1)->False)) ((ord_less_eq_nat (suc N_1)) M))).
% Axiom fact_1051_Suc__n__not__le__n:(forall (N_1:nat), (((ord_less_eq_nat (suc N_1)) N_1)->False)).
% Axiom fact_1052_le__0__eq:(forall (N_1:nat), ((iff ((ord_less_eq_nat N_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat))).
% Axiom fact_1053_less__eq__nat_Osimps_I1_J:(forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1)).
% Axiom fact_1054_evaln__nonstrict:(forall (M:nat) (C:com) (S:state) (N_1:nat) (T:state), (((((evaln C) S) N_1) T)->(((ord_less_eq_nat N_1) M)->((((evaln C) S) M) T)))).
% Axiom fact_1055_diff__le__self:(forall (M:nat) (N_1:nat), ((ord_less_eq_nat ((minus_minus_nat M) N_1)) M)).
% Axiom fact_1056_diff__le__mono2:(forall (L:nat) (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_eq_nat ((minus_minus_nat L) N_1)) ((minus_minus_nat L) M)))).
% Axiom fact_1057_diff__le__mono:(forall (L:nat) (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_eq_nat ((minus_minus_nat M) L)) ((minus_minus_nat N_1) L)))).
% Axiom fact_1058_diff__diff__cancel:(forall (I_1:nat) (N_1:nat), (((ord_less_eq_nat I_1) N_1)->(((eq nat) ((minus_minus_nat N_1) ((minus_minus_nat N_1) I_1))) I_1))).
% Axiom fact_1059_eq__diff__iff:(forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->((iff (((eq nat) ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) (((eq nat) M) N_1))))).
% Axiom fact_1060_Nat_Odiff__diff__eq:(forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) ((minus_minus_nat M) N_1))))).
% Axiom fact_1061_le__diff__iff:(forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->((iff ((ord_less_eq_nat ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) ((ord_less_eq_nat M) N_1))))).
% Axiom fact_1062_add__leE:(forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M) K_1)) N_1)->((((ord_less_eq_nat M) N_1)->(((ord_less_eq_nat K_1) N_1)->False))->False))).
% Axiom fact_1063_add__leD1:(forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M) K_1)) N_1)->((ord_less_eq_nat M) N_1))).
% Axiom fact_1064_add__leD2:(forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M) K_1)) N_1)->((ord_less_eq_nat K_1) N_1))).
% Axiom fact_1065_add__le__mono:(forall (K_1:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K_1) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) L))))).
% Axiom fact_1066_add__le__mono1:(forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) K_1)))).
% Axiom fact_1067_trans__le__add2:(forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J_1)))).
% Axiom fact_1068_trans__le__add1:(forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat J_1) M)))).
% Axiom fact_1069_nat__add__left__cancel__le:(forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) ((ord_less_eq_nat M) N_1))).
% Axiom fact_1070_le__iff__add:(forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat M) N_1)) ((ex nat) (fun (K:nat)=> (((eq nat) N_1) ((plus_plus_nat M) K)))))).
% Axiom fact_1071_le__add1:(forall (N_1:nat) (M:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat N_1) M))).
% Axiom fact_1072_le__add2:(forall (N_1:nat) (M:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat M) N_1))).
% Axiom fact_1073_card__Collect__le__nat:(forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_eq_nat _TPTP_I) N_1))))) (suc N_1))).
% Axiom fact_1074_less__eq__nat_Osimps_I2_J:(forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M)) N_1)) (((nat_case_o False) (ord_less_eq_nat M)) N_1))).
% Axiom fact_1075_mult__le__mono:(forall (K_1:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K_1) L)->((ord_less_eq_nat ((times_times_nat I_1) K_1)) ((times_times_nat J_1) L))))).
% Axiom fact_1076_mult__le__mono2:(forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat K_1) I_1)) ((times_times_nat K_1) J_1)))).
% Axiom fact_1077_mult__le__mono1:(forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat I_1) K_1)) ((times_times_nat J_1) K_1)))).
% Axiom fact_1078_le__cube:(forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M)))).
% Axiom fact_1079_le__square:(forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M))).
% Axiom fact_1080_com_Osimps_I52_J:(forall (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com:com), (not (((eq com) (((cond Fun_1) Com1_1) Com2_1)) ((while Fun) Com)))).
% Axiom fact_1081_com_Osimps_I53_J:(forall (Fun:(state->Prop)) (Com:com) (Fun_1:(state->Prop)) (Com1_1:com) (Com2_1:com), (not (((eq com) ((while Fun) Com)) (((cond Fun_1) Com1_1) Com2_1)))).
% Axiom fact_1082_com_Osimps_I45_J:(forall (Fun:(state->Prop)) (Com1:com) (Com2:com) (Com1_1:com) (Com2_1:com), (not (((eq com) (((cond Fun) Com1) Com2)) ((semi Com1_1) Com2_1)))).
% Axiom fact_1083_com_Osimps_I44_J:(forall (Com1_1:com) (Com2_1:com) (Fun:(state->Prop)) (Com1:com) (Com2:com), (not (((eq com) ((semi Com1_1) Com2_1)) (((cond Fun) Com1) Com2)))).
% Axiom fact_1084_com_Osimps_I15_J:(forall (Fun:(state->Prop)) (Com1:com) (Com2:com), (not (((eq com) (((cond Fun) Com1) Com2)) skip))).
% Axiom fact_1085_com_Osimps_I14_J:(forall (Fun:(state->Prop)) (Com1:com) (Com2:com), (not (((eq com) skip) (((cond Fun) Com1) Com2)))).
% Axiom fact_1086_diff__is__0__eq_H:(forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->(((eq nat) ((minus_minus_nat M) N_1)) zero_zero_nat))).
% Axiom fact_1087_diff__is__0__eq:(forall (M:nat) (N_1:nat), ((iff (((eq nat) ((minus_minus_nat M) N_1)) zero_zero_nat)) ((ord_less_eq_nat M) N_1))).
% Axiom fact_1088_Suc__diff__le:(forall (N_1:nat) (M:nat), (((ord_less_eq_nat N_1) M)->(((eq nat) ((minus_minus_nat (suc M)) N_1)) (suc ((minus_minus_nat M) N_1))))).
% Axiom fact_1089_Suc__mult__le__cancel1:(forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat (suc K_1)) M)) ((times_times_nat (suc K_1)) N_1))) ((ord_less_eq_nat M) N_1))).
% Axiom fact_1090_diff__diff__right:(forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J_1) K_1))) ((minus_minus_nat ((plus_plus_nat I_1) K_1)) J_1)))).
% Axiom fact_1091_le__diff__conv:(forall (J_1:nat) (K_1:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J_1) K_1)) I_1)) ((ord_less_eq_nat J_1) ((plus_plus_nat I_1) K_1)))).
% Axiom fact_1092_le__add__diff:(forall (M:nat) (K_1:nat) (N_1:nat), (((ord_less_eq_nat K_1) N_1)->((ord_less_eq_nat M) ((minus_minus_nat ((plus_plus_nat N_1) M)) K_1)))).
% Axiom fact_1093_le__add__diff__inverse:(forall (N_1:nat) (M:nat), (((ord_less_eq_nat N_1) M)->(((eq nat) ((plus_plus_nat N_1) ((minus_minus_nat M) N_1))) M))).
% Axiom fact_1094_add__diff__assoc:(forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K_1))) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K_1)))).
% Axiom fact_1095_le__diff__conv2:(forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J_1) K_1))) ((ord_less_eq_nat ((plus_plus_nat I_1) K_1)) J_1)))).
% Axiom fact_1096_le__add__diff__inverse2:(forall (N_1:nat) (M:nat), (((ord_less_eq_nat N_1) M)->(((eq nat) ((plus_plus_nat ((minus_minus_nat M) N_1)) N_1)) M))).
% Axiom fact_1097_le__imp__diff__is__add:(forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((minus_minus_nat J_1) I_1)) K_1)) (((eq nat) J_1) ((plus_plus_nat K_1) I_1))))).
% Axiom fact_1098_diff__add__assoc:(forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K_1)) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K_1))))).
% Axiom fact_1099_add__diff__assoc2:(forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J_1) K_1)) I_1)) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K_1)))).
% Axiom fact_1100_diff__add__assoc2:(forall (I_1:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K_1)) ((plus_plus_nat ((minus_minus_nat J_1) K_1)) I_1)))).
% Axiom fact_1101_one__le__mult__iff:(forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc zero_zero_nat)) ((times_times_nat M) N_1))) ((and ((ord_less_eq_nat (suc zero_zero_nat)) M)) ((ord_less_eq_nat (suc zero_zero_nat)) N_1)))).
% Axiom fact_1102_diff__Suc__diff__eq2:(forall (M:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat (suc ((minus_minus_nat J_1) K_1))) M)) ((minus_minus_nat (suc J_1)) ((plus_plus_nat K_1) M))))).
% Axiom fact_1103_diff__Suc__diff__eq1:(forall (M:nat) (K_1:nat) (J_1:nat), (((ord_less_eq_nat K_1) J_1)->(((eq nat) ((minus_minus_nat M) (suc ((minus_minus_nat J_1) K_1)))) ((minus_minus_nat ((plus_plus_nat M) K_1)) (suc J_1))))).
% Axiom fact_1104_nat__le__add__iff1:(forall (U:nat) (M:nat) (N_1:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N_1)))).
% Axiom fact_1105_nat__diff__add__eq1:(forall (U:nat) (M:nat) (N_1:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N_1)))).
% Axiom fact_1106_nat__eq__add__iff1:(forall (U:nat) (M:nat) (N_1:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N_1)))).
% Axiom fact_1107_nat__le__add__iff2:(forall (U:nat) (M:nat) (N_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N_1))))).
% Axiom fact_1108_nat__diff__add__eq2:(forall (U:nat) (M:nat) (N_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N_1))))).
% Axiom fact_1109_nat__eq__add__iff2:(forall (U:nat) (M:nat) (N_1:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N_1))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N_1))))).
% Axiom fact_1110_Suc__le__D:(forall (N_1:nat) (M_2:nat), (((ord_less_eq_nat (suc N_1)) M_2)->((ex nat) (fun (M_1:nat)=> (((eq nat) M_2) (suc M_1)))))).
% Axiom fact_1111_Suc__le__D__lemma:(forall (P:(nat->Prop)) (N_1:nat) (M_2:nat), (((ord_less_eq_nat (suc N_1)) M_2)->((forall (M_1:nat), (((ord_less_eq_nat N_1) M_1)->(P (suc M_1))))->(P M_2)))).
% Axiom fact_1112_finite__nat__set__iff__bounded__le:(forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X:nat), (((member_nat X) N_2)->((ord_less_eq_nat X) M_1))))))).
% Axiom fact_1113_finite__less__ub:(forall (U:nat) (F:(nat->nat)), ((forall (N:nat), ((ord_less_eq_nat N) (F N)))->(finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat (F N)) U)))))).
% Axiom fact_1114_termination__basic__simps_I3_J:(forall (Z:nat) (X_1:nat) (Y:nat), (((ord_less_eq_nat X_1) Y)->((ord_less_eq_nat X_1) ((plus_plus_nat Y) Z)))).
% Axiom fact_1115_termination__basic__simps_I4_J:(forall (Y:nat) (X_1:nat) (Z:nat), (((ord_less_eq_nat X_1) Z)->((ord_less_eq_nat X_1) ((plus_plus_nat Y) Z)))).
% Axiom fact_1116_less__zeroE:(forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)).
% Axiom fact_1117_lessI:(forall (N_1:nat), ((ord_less_nat N_1) (suc N_1))).
% Axiom fact_1118_Suc__mono:(forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_nat (suc M)) (suc N_1)))).
% Axiom fact_1119_finite__Collect__less__nat:(forall (K_1:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_nat N) K_1))))).
% Axiom fact_1120_zero__less__Suc:(forall (N_1:nat), ((ord_less_nat zero_zero_nat) (suc N_1))).
% Axiom fact_1121_finite__M__bounded__by__nat:(forall (P:(nat->Prop)) (I_1:nat), (finite_finite_nat (collect_nat (fun (K:nat)=> ((and (P K)) ((ord_less_nat K) I_1)))))).
% Axiom fact_1122_finite__nat__set__iff__bounded:(forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X:nat), (((member_nat X) N_2)->((ord_less_nat X) M_1))))))).
% Axiom fact_1123_less__or__eq__imp__le:(forall (M:nat) (N_1:nat), (((or ((ord_less_nat M) N_1)) (((eq nat) M) N_1))->((ord_less_eq_nat M) N_1))).
% Axiom fact_1124_le__neq__implies__less:(forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((not (((eq nat) M) N_1))->((ord_less_nat M) N_1)))).
% Axiom fact_1125_less__imp__le__nat:(forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_eq_nat M) N_1))).
% Axiom fact_1126_le__eq__less__or__eq:(forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat M) N_1)) ((or ((ord_less_nat M) N_1)) (((eq nat) M) N_1)))).
% Axiom fact_1127_nat__less__le:(forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) N_1)) ((and ((ord_less_eq_nat M) N_1)) (not (((eq nat) M) N_1))))).
% Axiom fact_1128_Suc__le__lessD:(forall (M:nat) (N_1:nat), (((ord_less_eq_nat (suc M)) N_1)->((ord_less_nat M) N_1))).
% Axiom fact_1129_le__less__Suc__eq:(forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((iff ((ord_less_nat N_1) (suc M))) (((eq nat) N_1) M)))).
% Axiom fact_1130_Suc__leI:(forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_eq_nat (suc M)) N_1))).
% Axiom fact_1131_le__imp__less__Suc:(forall (M:nat) (N_1:nat), (((ord_less_eq_nat M) N_1)->((ord_less_nat M) (suc N_1)))).
% Axiom fact_1132_Suc__le__eq:(forall (M:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M)) N_1)) ((ord_less_nat M) N_1))).
% Axiom fact_1133_less__Suc__eq__le:(forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) (suc N_1))) ((ord_less_eq_nat M) N_1))).
% Axiom fact_1134_less__eq__Suc__le:(forall (N_1:nat) (M:nat), ((iff ((ord_less_nat N_1) M)) ((ord_less_eq_nat (suc N_1)) M))).
% Axiom fact_1135_less__diff__iff:(forall (N_1:nat) (K_1:nat) (M:nat), (((ord_less_eq_nat K_1) M)->(((ord_less_eq_nat K_1) N_1)->((iff ((ord_less_nat ((minus_minus_nat M) K_1)) ((minus_minus_nat N_1) K_1))) ((ord_less_nat M) N_1))))).
% Axiom fact_1136_diff__less__mono:(forall (C:nat) (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat C) A)->((ord_less_nat ((minus_minus_nat A) C)) ((minus_minus_nat B) C))))).
% Axiom fact_1137_not__add__less1:(forall (I_1:nat) (J_1:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) I_1)->False)).
% Axiom fact_1138_not__add__less2:(forall (J_1:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J_1) I_1)) I_1)->False)).
% Axiom fact_1139_nat__add__left__cancel__less:(forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_nat ((plus_plus_nat K_1) M)) ((plus_plus_nat K_1) N_1))) ((ord_less_nat M) N_1))).
% Axiom fact_1140_trans__less__add1:(forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat J_1) M)))).
% Axiom fact_1141_trans__less__add2:(forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat M) J_1)))).
% Axiom fact_1142_add__less__mono1:(forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) K_1)))).
% Axiom fact_1143_add__less__mono:(forall (K_1:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat K_1) L)->((ord_less_nat ((plus_plus_nat I_1) K_1)) ((plus_plus_nat J_1) L))))).
% Axiom fact_1144_less__add__eq__less:(forall (M:nat) (N_1:nat) (K_1:nat) (L:nat), (((ord_less_nat K_1) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K_1) N_1))->((ord_less_nat M) N_1)))).
% Axiom fact_1145_add__lessD1:(forall (I_1:nat) (J_1:nat) (K_1:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) K_1)->((ord_less_nat I_1) K_1))).
% Axiom fact_1146_diff__less__mono2:(forall (L:nat) (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->(((ord_less_nat M) L)->((ord_less_nat ((minus_minus_nat L) N_1)) ((minus_minus_nat L) M))))).
% Axiom fact_1147_less__imp__diff__less:(forall (N_1:nat) (J_1:nat) (K_1:nat), (((ord_less_nat J_1) K_1)->((ord_less_nat ((minus_minus_nat J_1) N_1)) K_1))).
% Axiom fact_1148_not__less0:(forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)).
% Axiom fact_1149_neq0__conv:(forall (N_1:nat), ((iff (not (((eq nat) N_1) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N_1))).
% Axiom fact_1150_less__nat__zero__code:(forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)).
% Axiom fact_1151_gr__implies__not0:(forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->(not (((eq nat) N_1) zero_zero_nat)))).
% Axiom fact_1152_gr0I:(forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ord_less_nat zero_zero_nat) N_1))).
% Axiom fact_1153_not__less__eq:(forall (M:nat) (N_1:nat), ((iff (((ord_less_nat M) N_1)->False)) ((ord_less_nat N_1) (suc M)))).
% Axiom fact_1154_less__Suc__eq:(forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) (suc N_1))) ((or ((ord_less_nat M) N_1)) (((eq nat) M) N_1)))).
% Axiom fact_1155_Suc__less__eq:(forall (M:nat) (N_1:nat), ((iff ((ord_less_nat (suc M)) (suc N_1))) ((ord_less_nat M) N_1))).
% Axiom fact_1156_not__less__less__Suc__eq:(forall (N_1:nat) (M:nat), ((((ord_less_nat N_1) M)->False)->((iff ((ord_less_nat N_1) (suc M))) (((eq nat) N_1) M)))).
% Axiom fact_1157_less__antisym:(forall (N_1:nat) (M:nat), ((((ord_less_nat N_1) M)->False)->(((ord_less_nat N_1) (suc M))->(((eq nat) M) N_1)))).
% Axiom fact_1158_less__SucI:(forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_nat M) (suc N_1)))).
% Axiom fact_1159_Suc__lessI:(forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((not (((eq nat) (suc M)) N_1))->((ord_less_nat (suc M)) N_1)))).
% Axiom fact_1160_less__trans__Suc:(forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat J_1) K_1)->((ord_less_nat (suc I_1)) K_1)))).
% Axiom fact_1161_less__SucE:(forall (M:nat) (N_1:nat), (((ord_less_nat M) (suc N_1))->((((ord_less_nat M) N_1)->False)->(((eq nat) M) N_1)))).
% Axiom fact_1162_Suc__lessD:(forall (M:nat) (N_1:nat), (((ord_less_nat (suc M)) N_1)->((ord_less_nat M) N_1))).
% Axiom fact_1163_Suc__less__SucD:(forall (M:nat) (N_1:nat), (((ord_less_nat (suc M)) (suc N_1))->((ord_less_nat M) N_1))).
% Axiom fact_1164_less__not__refl:(forall (N_1:nat), (((ord_less_nat N_1) N_1)->False)).
% Axiom fact_1165_nat__neq__iff:(forall (M:nat) (N_1:nat), ((iff (not (((eq nat) M) N_1))) ((or ((ord_less_nat M) N_1)) ((ord_less_nat N_1) M)))).
% Axiom fact_1166_linorder__neqE__nat:(forall (X_1:nat) (Y:nat), ((not (((eq nat) X_1) Y))->((((ord_less_nat X_1) Y)->False)->((ord_less_nat Y) X_1)))).
% Axiom fact_1167_less__irrefl__nat:(forall (N_1:nat), (((ord_less_nat N_1) N_1)->False)).
% Axiom fact_1168_less__not__refl2:(forall (N_1:nat) (M:nat), (((ord_less_nat N_1) M)->(not (((eq nat) M) N_1)))).
% Axiom fact_1169_less__not__refl3:(forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))).
% Axiom fact_1170_nat__less__cases:(forall (P:(nat->(nat->Prop))) (M:nat) (N_1:nat), ((((ord_less_nat M) N_1)->((P N_1) M))->(((((eq nat) M) N_1)->((P N_1) M))->((((ord_less_nat N_1) M)->((P N_1) M))->((P N_1) M))))).
% Axiom fact_1171_less__diff__conv:(forall (I_1:nat) (J_1:nat) (K_1:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J_1) K_1))) ((ord_less_nat ((plus_plus_nat I_1) K_1)) J_1))).
% Axiom fact_1172_add__diff__inverse:(forall (M:nat) (N_1:nat), ((((ord_less_nat M) N_1)->False)->(((eq nat) ((plus_plus_nat N_1) ((minus_minus_nat M) N_1))) M))).
% Axiom fact_1173_Suc__mult__less__cancel1:(forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat (suc K_1)) M)) ((times_times_nat (suc K_1)) N_1))) ((ord_less_nat M) N_1))).
% Axiom fact_1174_diff__less__Suc:(forall (M:nat) (N_1:nat), ((ord_less_nat ((minus_minus_nat M) N_1)) (suc M))).
% Axiom fact_1175_nat__0__less__mult__iff:(forall (M:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M) N_1))) ((and ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N_1)))).
% Axiom fact_1176_mult__less__cancel1:(forall (K_1:nat) (M:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((and ((ord_less_nat zero_zero_nat) K_1)) ((ord_less_nat M) N_1)))).
% Axiom fact_1177_mult__less__cancel2:(forall (M:nat) (K_1:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat M) K_1)) ((times_times_nat N_1) K_1))) ((and ((ord_less_nat zero_zero_nat) K_1)) ((ord_less_nat M) N_1)))).
% Axiom fact_1178_mult__less__mono1:(forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K_1)->((ord_less_nat ((times_times_nat I_1) K_1)) ((times_times_nat J_1) K_1))))).
% Axiom fact_1179_mult__less__mono2:(forall (K_1:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K_1)->((ord_less_nat ((times_times_nat K_1) I_1)) ((times_times_nat K_1) J_1))))).
% Axiom fact_1180_nat__mult__eq__cancel1:(forall (M:nat) (N_1:nat) (K_1:nat), (((ord_less_nat zero_zero_nat) K_1)->((iff (((eq nat) ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) (((eq nat) M) N_1)))).
% Axiom fact_1181_nat__mult__less__cancel1:(forall (M:nat) (N_1:nat) (K_1:nat), (((ord_less_nat zero_zero_nat) K_1)->((iff ((ord_less_nat ((times_times_nat K_1) M)) ((times_times_nat K_1) N_1))) ((ord_less_nat M) N_1)))).
% Axiom fact_1182_diff__less:(forall (M:nat) (N_1:nat), (((ord_less_nat zero_zero_nat) N_1)->(((ord_less_nat zero_zero_nat) M)->((ord_less_nat ((minus_minus_nat M) N_1)) M)))).
% Axiom fact_1183_zero__less__diff:(forall (N_1:nat) (M:nat), ((iff ((ord_less_nat zero_zero_nat) ((minus_minus_nat N_1) M))) ((ord_less_nat M) N_1))).
% Axiom fact_1184_less__add__Suc1:(forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat I_1) M)))).
% Axiom fact_1185_less__add__Suc2:(forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat M) I_1)))).
% Axiom fact_1186_less__iff__Suc__add:(forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) N_1)) ((ex nat) (fun (K:nat)=> (((eq nat) N_1) (suc ((plus_plus_nat M) K))))))).
% Axiom fact_1187_add__gr__0:(forall (M:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N_1))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N_1)))).
% Axiom fact_1188_gr0__conv__Suc:(forall (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) N_1)) ((ex nat) (fun (M_1:nat)=> (((eq nat) N_1) (suc M_1)))))).
% Axiom fact_1189_less__Suc0:(forall (N_1:nat), ((iff ((ord_less_nat N_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))).
% Axiom fact_1190_less__Suc__eq__0__disj:(forall (M:nat) (N_1:nat), ((iff ((ord_less_nat M) (suc N_1))) ((or (((eq nat) M) zero_zero_nat)) ((ex nat) (fun (J:nat)=> ((and (((eq nat) M) (suc J))) ((ord_less_nat J) N_1))))))).
% Axiom fact_1191_card__Collect__less__nat:(forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_nat _TPTP_I) N_1))))) N_1)).
% Axiom fact_1192_less__eq__Suc__le__raw:(forall (X:nat), (((eq (nat->Prop)) (ord_less_nat X)) (ord_less_eq_nat (suc X)))).
% Axiom fact_1193_termination__basic__simps_I1_J:(forall (Z:nat) (X_1:nat) (Y:nat), (((ord_less_nat X_1) Y)->((ord_less_nat X_1) ((plus_plus_nat Y) Z)))).
% Axiom fact_1194_termination__basic__simps_I2_J:(forall (Y:nat) (X_1:nat) (Z:nat), (((ord_less_nat X_1) Z)->((ord_less_nat X_1) ((plus_plus_nat Y) Z)))).
% Axiom fact_1195_termination__basic__simps_I5_J:(forall (X_1:nat) (Y:nat), (((ord_less_nat X_1) Y)->((ord_less_eq_nat X_1) Y))).
% Axiom help_fequal_1_1_fequal_000tc__Nat__Onat_T:(forall (X_1:nat) (Y:nat), ((or (((fequal_nat X_1) Y)->False)) (((eq nat) X_1) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Nat__Onat_T:(forall (X_1:nat) (Y:nat), ((or (not (((eq nat) X_1) Y))) ((fequal_nat X_1) Y))).
% 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_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_:(forall (X_1:hoare_2091234717iple_a) (Y:hoare_2091234717iple_a), ((or (((fequal1604381340iple_a X_1) Y)->False)) (((eq hoare_2091234717iple_a) X_1) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_:(forall (X_1:hoare_2091234717iple_a) (Y:hoare_2091234717iple_a), ((or (not (((eq hoare_2091234717iple_a) X_1) Y))) ((fequal1604381340iple_a X_1) Y))).
% Axiom help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com:(forall (X_1:hoare_1708887482_state) (Y:hoare_1708887482_state), ((or (((fequal224822779_state X_1) Y)->False)) (((eq hoare_1708887482_state) X_1) Y))
% EOF
%------------------------------------------------------------------------------