%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SWW471^1 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n096.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 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SWW471^1 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n096.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 09:14:26 CDT 2014
% % CPUTime  : 300.10 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x2bc7a70>, <kernel.Type object at 0x2bc77e8>) of role type named ty_ty_t__a
% Using role type
% Declaring x_a:Type
% FOF formula (<kernel.Constant object at 0x2972a28>, <kernel.Type object at 0x2bc7638>) of role type named ty_ty_tc__Com__Ocom
% Using role type
% Declaring com:Type
% FOF formula (<kernel.Constant object at 0x2bc7488>, <kernel.Type object at 0x2bc76c8>) of role type named ty_ty_tc__Com__Opname
% Using role type
% Declaring pname:Type
% FOF formula (<kernel.Constant object at 0x2bc77e8>, <kernel.Type object at 0x2bc7b90>) of role type named ty_ty_tc__Com__Ostate
% Using role type
% Declaring state:Type
% FOF formula (<kernel.Constant object at 0x2bc7638>, <kernel.Type object at 0x2bc7440>) of role type named ty_ty_tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J
% Using role type
% Declaring hoare_669141180iple_a:Type
% FOF formula (<kernel.Constant object at 0x2bc76c8>, <kernel.Type object at 0x2bc7b90>) of role type named ty_ty_tc__Nat__Onat
% Using role type
% Declaring nat:Type
% FOF formula (<kernel.Constant object at 0x2bc7368>, <kernel.Type object at 0x2970d88>) 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 0x2bc71b8>, <kernel.DependentProduct object at 0x2970bd8>) of role type named sy_c_Com_Obody
% Using role type
% Declaring body_1:(pname->option_com)
% FOF formula (<kernel.Constant object at 0x2bc7248>, <kernel.DependentProduct object at 0x2970cb0>) of role type named sy_c_Com_Ocom_OBODY
% Using role type
% Declaring body:(pname->com)
% FOF formula (<kernel.Constant object at 0x2bc71b8>, <kernel.Constant object at 0x2970bd8>) 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 0x2bc7248>, <kernel.DependentProduct object at 0x2970ab8>) of role type named sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ohoare__derivs_000t__a
% Using role type
% Declaring hoare_2128652938rivs_a:((hoare_669141180iple_a->Prop)->((hoare_669141180iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x2bc76c8>, <kernel.DependentProduct object at 0x2970b90>) of role type named sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ohoare__valids_000t__a
% Using role type
% Declaring hoare_319002636lids_a:((hoare_669141180iple_a->Prop)->((hoare_669141180iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x2bc76c8>, <kernel.DependentProduct object at 0x2970cb0>) of role type named sy_c_Hoare__Mirabelle__ghhkfsbqqq_Otriple_Otriple_000t__a
% Using role type
% Declaring hoare_1295064928iple_a:((x_a->(state->Prop))->(com->((x_a->(state->Prop))->hoare_669141180iple_a)))
% FOF formula (<kernel.Constant object at 0x2970c20>, <kernel.DependentProduct object at 0x2970b48>) of role type named sy_c_Hoare__Mirabelle__ghhkfsbqqq_Otriple__valid_000t__a
% Using role type
% Declaring hoare_2082685510alid_a:(nat->(hoare_669141180iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x2970d40>, <kernel.DependentProduct object at 0x2970a28>) 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 0x2970cb0>, <kernel.DependentProduct object at 0x2970a70>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____g
% Using role type
% Declaring semila1689936973le_a_o:((hoare_669141180iple_a->Prop)->((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x2970ab8>, <kernel.DependentProduct object at 0x2970a28>) 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 0x2970d40>, <kernel.DependentProduct object at 0x2970830>) of role type named sy_c_Nat_OSuc
% Using role type
% Declaring suc:(nat->nat)
% FOF formula (<kernel.Constant object at 0x2970a70>, <kernel.DependentProduct object at 0x2970cb0>) of role type named sy_c_Natural_Oevalc
% Using role type
% Declaring evalc:(com->(state->(state->Prop)))
% FOF formula (<kernel.Constant object at 0x2970bd8>, <kernel.DependentProduct object at 0x29705a8>) 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 0x2970b00>, <kernel.DependentProduct object at 0x2970c20>) 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 0x2970cb0>, <kernel.DependentProduct object at 0x2970a70>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__O
% Using role type
% Declaring bot_bo280939947le_a_o:(hoare_669141180iple_a->Prop)
% FOF formula (<kernel.Constant object at 0x2970bd8>, <kernel.DependentProduct object at 0x2970638>) 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 0x2970c20>, <kernel.DependentProduct object at 0x2970a70>) of role type named sy_c_Set_OCollect_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J
% Using role type
% Declaring collec1717965009iple_a:((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x29707a0>, <kernel.DependentProduct object at 0x29702d8>) 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 0x2970b00>, <kernel.DependentProduct object at 0x2970248>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otri
% Using role type
% Declaring image_957198589iple_a:((pname->hoare_669141180iple_a)->((pname->Prop)->(hoare_669141180iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x29705f0>, <kernel.DependentProduct object at 0x2970320>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_000tc__
% Using role type
% Declaring image_225123213_pname:((hoare_669141180iple_a->pname)->((hoare_669141180iple_a->Prop)->(pname->Prop)))
% FOF formula (<kernel.Constant object at 0x2970a70>, <kernel.DependentProduct object at 0x29701b8>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_000tc___001
% Using role type
% Declaring image_1033305477iple_a:((hoare_669141180iple_a->hoare_669141180iple_a)->((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x2970a28>, <kernel.DependentProduct object at 0x29703b0>) 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 0x2970248>, <kernel.DependentProduct object at 0x2970b00>) of role type named sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J
% Using role type
% Declaring insert175534902iple_a:(hoare_669141180iple_a->((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x29702d8>, <kernel.DependentProduct object at 0x2970248>) 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 0x2970a28>, <kernel.DependentProduct object at 0x29707a0>) of role type named sy_c_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J
% Using role type
% Declaring fequal182287803iple_a:(hoare_669141180iple_a->(hoare_669141180iple_a->Prop))
% FOF formula (<kernel.Constant object at 0x29701b8>, <kernel.DependentProduct object at 0x2970170>) 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 0x2970248>, <kernel.DependentProduct object at 0x2970a28>) of role type named sy_c_member_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J
% Using role type
% Declaring member1016246415iple_a:(hoare_669141180iple_a->((hoare_669141180iple_a->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x29707a0>, <kernel.DependentProduct object at 0x2970098>) of role type named sy_v_G
% Using role type
% Declaring g:(hoare_669141180iple_a->Prop)
% FOF formula (<kernel.Constant object at 0x29701b8>, <kernel.DependentProduct object at 0x2970638>) of role type named sy_v_P
% Using role type
% Declaring p:(pname->(x_a->(state->Prop)))
% FOF formula (<kernel.Constant object at 0x2970a28>, <kernel.DependentProduct object at 0x2970248>) of role type named sy_v_Procs
% Using role type
% Declaring procs:(pname->Prop)
% FOF formula (<kernel.Constant object at 0x2970098>, <kernel.DependentProduct object at 0x29700e0>) of role type named sy_v_Q
% Using role type
% Declaring q:(pname->(x_a->(state->Prop)))
% FOF formula (<kernel.Constant object at 0x2970638>, <kernel.Constant object at 0x29700e0>) of role type named sy_v_n
% Using role type
% Declaring n:nat
% FOF formula (forall (Fun1_2:(x_a->(state->Prop))) (Com_2:com) (Fun2_2:(x_a->(state->Prop))) (Fun1_1:(x_a->(state->Prop))) (Com_1:com) (Fun2_1:(x_a->(state->Prop))), ((iff (((eq hoare_669141180iple_a) (((hoare_1295064928iple_a Fun1_2) Com_2) Fun2_2)) (((hoare_1295064928iple_a Fun1_1) Com_1) Fun2_1))) ((and ((and (((eq (x_a->(state->Prop))) Fun1_2) Fun1_1)) (((eq com) Com_2) Com_1))) (((eq (x_a->(state->Prop))) Fun2_2) Fun2_1)))) of role axiom named fact_0_triple_Oinject
% A new axiom: (forall (Fun1_2:(x_a->(state->Prop))) (Com_2:com) (Fun2_2:(x_a->(state->Prop))) (Fun1_1:(x_a->(state->Prop))) (Com_1:com) (Fun2_1:(x_a->(state->Prop))), ((iff (((eq hoare_669141180iple_a) (((hoare_1295064928iple_a Fun1_2) Com_2) Fun2_2)) (((hoare_1295064928iple_a Fun1_1) Com_1) Fun2_1))) ((and ((and (((eq (x_a->(state->Prop))) Fun1_2) Fun1_1)) (((eq com) Com_2) Com_1))) (((eq (x_a->(state->Prop))) Fun2_2) Fun2_1))))
% FOF formula (forall (G_10:(hoare_669141180iple_a->Prop)) (Ts_3:(hoare_669141180iple_a->Prop)), ((iff ((hoare_319002636lids_a G_10) Ts_3)) (forall (N:nat), ((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) G_10)->((hoare_2082685510alid_a N) X)))->(forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) Ts_3)->((hoare_2082685510alid_a N) X))))))) of role axiom named fact_1_hoare__valids__def
% A new axiom: (forall (G_10:(hoare_669141180iple_a->Prop)) (Ts_3:(hoare_669141180iple_a->Prop)), ((iff ((hoare_319002636lids_a G_10) Ts_3)) (forall (N:nat), ((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) G_10)->((hoare_2082685510alid_a N) X)))->(forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) Ts_3)->((hoare_2082685510alid_a N) X)))))))
% FOF formula (forall (G_9:(hoare_669141180iple_a->Prop)) (P_14:(pname->(x_a->(state->Prop)))) (Q_4:(pname->(x_a->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_2128652938rivs_a ((semila1689936973le_a_o G_9) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_14 P_9)) (body P_9)) (Q_4 P_9)))) Procs_1))) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_14 P_9)) (the_com (body_1 P_9))) (Q_4 P_9)))) Procs_1))->((hoare_2128652938rivs_a G_9) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_14 P_9)) (body P_9)) (Q_4 P_9)))) Procs_1)))) of role axiom named fact_2_hoare__derivs_OBody
% A new axiom: (forall (G_9:(hoare_669141180iple_a->Prop)) (P_14:(pname->(x_a->(state->Prop)))) (Q_4:(pname->(x_a->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_2128652938rivs_a ((semila1689936973le_a_o G_9) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_14 P_9)) (body P_9)) (Q_4 P_9)))) Procs_1))) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_14 P_9)) (the_com (body_1 P_9))) (Q_4 P_9)))) Procs_1))->((hoare_2128652938rivs_a G_9) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_14 P_9)) (body P_9)) (Q_4 P_9)))) Procs_1))))
% FOF formula (forall (C_13:hoare_669141180iple_a) (A_65:(hoare_669141180iple_a->Prop)) (B_36:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a C_13) ((semila1689936973le_a_o A_65) B_36))->((((member1016246415iple_a C_13) A_65)->False)->((member1016246415iple_a C_13) B_36)))) of role axiom named fact_3_UnE
% A new axiom: (forall (C_13:hoare_669141180iple_a) (A_65:(hoare_669141180iple_a->Prop)) (B_36:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a C_13) ((semila1689936973le_a_o A_65) B_36))->((((member1016246415iple_a C_13) A_65)->False)->((member1016246415iple_a C_13) B_36))))
% FOF formula (forall (C_13:pname) (A_65:(pname->Prop)) (B_36:(pname->Prop)), (((member_pname C_13) ((semila1780557381name_o A_65) B_36))->((((member_pname C_13) A_65)->False)->((member_pname C_13) B_36)))) of role axiom named fact_4_UnE
% A new axiom: (forall (C_13:pname) (A_65:(pname->Prop)) (B_36:(pname->Prop)), (((member_pname C_13) ((semila1780557381name_o A_65) B_36))->((((member_pname C_13) A_65)->False)->((member_pname C_13) B_36))))
% FOF formula (forall (A_64:(hoare_669141180iple_a->Prop)) (B_35:(hoare_669141180iple_a->Prop)) (X_24:hoare_669141180iple_a), ((((semila1689936973le_a_o A_64) B_35) X_24)->(((A_64 X_24)->False)->(B_35 X_24)))) of role axiom named fact_5_sup1E
% A new axiom: (forall (A_64:(hoare_669141180iple_a->Prop)) (B_35:(hoare_669141180iple_a->Prop)) (X_24:hoare_669141180iple_a), ((((semila1689936973le_a_o A_64) B_35) X_24)->(((A_64 X_24)->False)->(B_35 X_24))))
% FOF formula (forall (A_64:(pname->Prop)) (B_35:(pname->Prop)) (X_24:pname), ((((semila1780557381name_o A_64) B_35) X_24)->(((A_64 X_24)->False)->(B_35 X_24)))) of role axiom named fact_6_sup1E
% A new axiom: (forall (A_64:(pname->Prop)) (B_35:(pname->Prop)) (X_24:pname), ((((semila1780557381name_o A_64) B_35) X_24)->(((A_64 X_24)->False)->(B_35 X_24))))
% FOF formula (forall (A_63:(hoare_669141180iple_a->Prop)) (B_34:(hoare_669141180iple_a->Prop)) (X_23:hoare_669141180iple_a), ((((B_34 X_23)->False)->(A_63 X_23))->(((semila1689936973le_a_o A_63) B_34) X_23))) of role axiom named fact_7_sup1CI
% A new axiom: (forall (A_63:(hoare_669141180iple_a->Prop)) (B_34:(hoare_669141180iple_a->Prop)) (X_23:hoare_669141180iple_a), ((((B_34 X_23)->False)->(A_63 X_23))->(((semila1689936973le_a_o A_63) B_34) X_23)))
% FOF formula (forall (A_63:(pname->Prop)) (B_34:(pname->Prop)) (X_23:pname), ((((B_34 X_23)->False)->(A_63 X_23))->(((semila1780557381name_o A_63) B_34) X_23))) of role axiom named fact_8_sup1CI
% A new axiom: (forall (A_63:(pname->Prop)) (B_34:(pname->Prop)) (X_23:pname), ((((B_34 X_23)->False)->(A_63 X_23))->(((semila1780557381name_o A_63) B_34) X_23)))
% FOF formula (forall (A_62:(hoare_669141180iple_a->Prop)) (C_12:hoare_669141180iple_a) (B_33:(hoare_669141180iple_a->Prop)), (((((member1016246415iple_a C_12) B_33)->False)->((member1016246415iple_a C_12) A_62))->((member1016246415iple_a C_12) ((semila1689936973le_a_o A_62) B_33)))) of role axiom named fact_9_UnCI
% A new axiom: (forall (A_62:(hoare_669141180iple_a->Prop)) (C_12:hoare_669141180iple_a) (B_33:(hoare_669141180iple_a->Prop)), (((((member1016246415iple_a C_12) B_33)->False)->((member1016246415iple_a C_12) A_62))->((member1016246415iple_a C_12) ((semila1689936973le_a_o A_62) B_33))))
% FOF formula (forall (A_62:(pname->Prop)) (C_12:pname) (B_33:(pname->Prop)), (((((member_pname C_12) B_33)->False)->((member_pname C_12) A_62))->((member_pname C_12) ((semila1780557381name_o A_62) B_33)))) of role axiom named fact_10_UnCI
% A new axiom: (forall (A_62:(pname->Prop)) (C_12:pname) (B_33:(pname->Prop)), (((((member_pname C_12) B_33)->False)->((member_pname C_12) A_62))->((member_pname C_12) ((semila1780557381name_o A_62) B_33))))
% FOF formula (forall (A_61:(pname->Prop)) (B_32:hoare_669141180iple_a) (F_9:(pname->hoare_669141180iple_a)) (X_22:pname), ((((eq hoare_669141180iple_a) B_32) (F_9 X_22))->(((member_pname X_22) A_61)->((member1016246415iple_a B_32) ((image_957198589iple_a F_9) A_61))))) of role axiom named fact_11_image__eqI
% A new axiom: (forall (A_61:(pname->Prop)) (B_32:hoare_669141180iple_a) (F_9:(pname->hoare_669141180iple_a)) (X_22:pname), ((((eq hoare_669141180iple_a) B_32) (F_9 X_22))->(((member_pname X_22) A_61)->((member1016246415iple_a B_32) ((image_957198589iple_a F_9) A_61)))))
% FOF formula (forall (A_61:(hoare_669141180iple_a->Prop)) (B_32:pname) (F_9:(hoare_669141180iple_a->pname)) (X_22:hoare_669141180iple_a), ((((eq pname) B_32) (F_9 X_22))->(((member1016246415iple_a X_22) A_61)->((member_pname B_32) ((image_225123213_pname F_9) A_61))))) of role axiom named fact_12_image__eqI
% A new axiom: (forall (A_61:(hoare_669141180iple_a->Prop)) (B_32:pname) (F_9:(hoare_669141180iple_a->pname)) (X_22:hoare_669141180iple_a), ((((eq pname) B_32) (F_9 X_22))->(((member1016246415iple_a X_22) A_61)->((member_pname B_32) ((image_225123213_pname F_9) A_61)))))
% FOF formula (forall (F_8:(pname->hoare_669141180iple_a)) (A_60:(pname->Prop)) (B_31:(pname->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a F_8) ((semila1780557381name_o A_60) B_31))) ((semila1689936973le_a_o ((image_957198589iple_a F_8) A_60)) ((image_957198589iple_a F_8) B_31)))) of role axiom named fact_13_image__Un
% A new axiom: (forall (F_8:(pname->hoare_669141180iple_a)) (A_60:(pname->Prop)) (B_31:(pname->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a F_8) ((semila1780557381name_o A_60) B_31))) ((semila1689936973le_a_o ((image_957198589iple_a F_8) A_60)) ((image_957198589iple_a F_8) B_31))))
% FOF formula (forall (F_8:(hoare_669141180iple_a->pname)) (A_60:(hoare_669141180iple_a->Prop)) (B_31:(hoare_669141180iple_a->Prop)), (((eq (pname->Prop)) ((image_225123213_pname F_8) ((semila1689936973le_a_o A_60) B_31))) ((semila1780557381name_o ((image_225123213_pname F_8) A_60)) ((image_225123213_pname F_8) B_31)))) of role axiom named fact_14_image__Un
% A new axiom: (forall (F_8:(hoare_669141180iple_a->pname)) (A_60:(hoare_669141180iple_a->Prop)) (B_31:(hoare_669141180iple_a->Prop)), (((eq (pname->Prop)) ((image_225123213_pname F_8) ((semila1689936973le_a_o A_60) B_31))) ((semila1780557381name_o ((image_225123213_pname F_8) A_60)) ((image_225123213_pname F_8) B_31))))
% FOF formula (forall (F_7:(hoare_669141180iple_a->Prop)) (G_8:(hoare_669141180iple_a->Prop)) (X:hoare_669141180iple_a), ((iff (((semila1689936973le_a_o F_7) G_8) X)) ((semila10642723_sup_o (F_7 X)) (G_8 X)))) of role axiom named fact_15_sup__fun__def
% A new axiom: (forall (F_7:(hoare_669141180iple_a->Prop)) (G_8:(hoare_669141180iple_a->Prop)) (X:hoare_669141180iple_a), ((iff (((semila1689936973le_a_o F_7) G_8) X)) ((semila10642723_sup_o (F_7 X)) (G_8 X))))
% FOF formula (forall (F_7:(pname->Prop)) (G_8:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o F_7) G_8) X)) ((semila10642723_sup_o (F_7 X)) (G_8 X)))) of role axiom named fact_16_sup__fun__def
% A new axiom: (forall (F_7:(pname->Prop)) (G_8:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o F_7) G_8) X)) ((semila10642723_sup_o (F_7 X)) (G_8 X))))
% FOF formula (forall (F_6:(hoare_669141180iple_a->Prop)) (G_7:(hoare_669141180iple_a->Prop)) (X_21:hoare_669141180iple_a), ((iff (((semila1689936973le_a_o F_6) G_7) X_21)) ((semila10642723_sup_o (F_6 X_21)) (G_7 X_21)))) of role axiom named fact_17_sup__apply
% A new axiom: (forall (F_6:(hoare_669141180iple_a->Prop)) (G_7:(hoare_669141180iple_a->Prop)) (X_21:hoare_669141180iple_a), ((iff (((semila1689936973le_a_o F_6) G_7) X_21)) ((semila10642723_sup_o (F_6 X_21)) (G_7 X_21))))
% FOF formula (forall (F_6:(pname->Prop)) (G_7:(pname->Prop)) (X_21:pname), ((iff (((semila1780557381name_o F_6) G_7) X_21)) ((semila10642723_sup_o (F_6 X_21)) (G_7 X_21)))) of role axiom named fact_18_sup__apply
% A new axiom: (forall (F_6:(pname->Prop)) (G_7:(pname->Prop)) (X_21:pname), ((iff (((semila1780557381name_o F_6) G_7) X_21)) ((semila10642723_sup_o (F_6 X_21)) (G_7 X_21))))
% FOF formula (forall (G_6:(hoare_669141180iple_a->Prop)) (G_5:(hoare_669141180iple_a->Prop)) (Ts_2:(hoare_669141180iple_a->Prop)), (((hoare_2128652938rivs_a G_5) Ts_2)->(((hoare_2128652938rivs_a G_6) G_5)->((hoare_2128652938rivs_a G_6) Ts_2)))) of role axiom named fact_19_cut
% A new axiom: (forall (G_6:(hoare_669141180iple_a->Prop)) (G_5:(hoare_669141180iple_a->Prop)) (Ts_2:(hoare_669141180iple_a->Prop)), (((hoare_2128652938rivs_a G_5) Ts_2)->(((hoare_2128652938rivs_a G_6) G_5)->((hoare_2128652938rivs_a G_6) Ts_2))))
% FOF formula (forall (X_20:(hoare_669141180iple_a->Prop)) (Y_12:(hoare_669141180iple_a->Prop)) (Z_4:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o X_20) Y_12)) Z_4)) ((semila1689936973le_a_o X_20) ((semila1689936973le_a_o Y_12) Z_4)))) of role axiom named fact_20_sup__assoc
% A new axiom: (forall (X_20:(hoare_669141180iple_a->Prop)) (Y_12:(hoare_669141180iple_a->Prop)) (Z_4:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o X_20) Y_12)) Z_4)) ((semila1689936973le_a_o X_20) ((semila1689936973le_a_o Y_12) Z_4))))
% FOF formula (forall (X_20:(pname->Prop)) (Y_12:(pname->Prop)) (Z_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_20) Y_12)) Z_4)) ((semila1780557381name_o X_20) ((semila1780557381name_o Y_12) Z_4)))) of role axiom named fact_21_sup__assoc
% A new axiom: (forall (X_20:(pname->Prop)) (Y_12:(pname->Prop)) (Z_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_20) Y_12)) Z_4)) ((semila1780557381name_o X_20) ((semila1780557381name_o Y_12) Z_4))))
% FOF formula (forall (X_20:Prop) (Y_12:Prop) (Z_4:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_20) Y_12)) Z_4)) ((semila10642723_sup_o X_20) ((semila10642723_sup_o Y_12) Z_4)))) of role axiom named fact_22_sup__assoc
% A new axiom: (forall (X_20:Prop) (Y_12:Prop) (Z_4:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_20) Y_12)) Z_4)) ((semila10642723_sup_o X_20) ((semila10642723_sup_o Y_12) Z_4))))
% FOF formula (forall (X_19:(hoare_669141180iple_a->Prop)) (Y_11:(hoare_669141180iple_a->Prop)) (Z_3:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o X_19) Y_11)) Z_3)) ((semila1689936973le_a_o X_19) ((semila1689936973le_a_o Y_11) Z_3)))) of role axiom named fact_23_inf__sup__aci_I6_J
% A new axiom: (forall (X_19:(hoare_669141180iple_a->Prop)) (Y_11:(hoare_669141180iple_a->Prop)) (Z_3:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o X_19) Y_11)) Z_3)) ((semila1689936973le_a_o X_19) ((semila1689936973le_a_o Y_11) Z_3))))
% FOF formula (forall (X_19:(pname->Prop)) (Y_11:(pname->Prop)) (Z_3:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_19) Y_11)) Z_3)) ((semila1780557381name_o X_19) ((semila1780557381name_o Y_11) Z_3)))) of role axiom named fact_24_inf__sup__aci_I6_J
% A new axiom: (forall (X_19:(pname->Prop)) (Y_11:(pname->Prop)) (Z_3:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_19) Y_11)) Z_3)) ((semila1780557381name_o X_19) ((semila1780557381name_o Y_11) Z_3))))
% FOF formula (forall (X_19:Prop) (Y_11:Prop) (Z_3:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_19) Y_11)) Z_3)) ((semila10642723_sup_o X_19) ((semila10642723_sup_o Y_11) Z_3)))) of role axiom named fact_25_inf__sup__aci_I6_J
% A new axiom: (forall (X_19:Prop) (Y_11:Prop) (Z_3:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_19) Y_11)) Z_3)) ((semila10642723_sup_o X_19) ((semila10642723_sup_o Y_11) Z_3))))
% FOF formula (forall (A_59:(hoare_669141180iple_a->Prop)) (B_30:(hoare_669141180iple_a->Prop)) (C_11:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o A_59) B_30)) C_11)) ((semila1689936973le_a_o A_59) ((semila1689936973le_a_o B_30) C_11)))) of role axiom named fact_26_sup_Oassoc
% A new axiom: (forall (A_59:(hoare_669141180iple_a->Prop)) (B_30:(hoare_669141180iple_a->Prop)) (C_11:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o A_59) B_30)) C_11)) ((semila1689936973le_a_o A_59) ((semila1689936973le_a_o B_30) C_11))))
% FOF formula (forall (A_59:(pname->Prop)) (B_30:(pname->Prop)) (C_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_59) B_30)) C_11)) ((semila1780557381name_o A_59) ((semila1780557381name_o B_30) C_11)))) of role axiom named fact_27_sup_Oassoc
% A new axiom: (forall (A_59:(pname->Prop)) (B_30:(pname->Prop)) (C_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_59) B_30)) C_11)) ((semila1780557381name_o A_59) ((semila1780557381name_o B_30) C_11))))
% FOF formula (forall (A_59:Prop) (B_30:Prop) (C_11:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_59) B_30)) C_11)) ((semila10642723_sup_o A_59) ((semila10642723_sup_o B_30) C_11)))) of role axiom named fact_28_sup_Oassoc
% A new axiom: (forall (A_59:Prop) (B_30:Prop) (C_11:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_59) B_30)) C_11)) ((semila10642723_sup_o A_59) ((semila10642723_sup_o B_30) C_11))))
% FOF formula (forall (X_18:(hoare_669141180iple_a->Prop)) (Y_10:(hoare_669141180iple_a->Prop)) (Z_2:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_18) ((semila1689936973le_a_o Y_10) Z_2))) ((semila1689936973le_a_o Y_10) ((semila1689936973le_a_o X_18) Z_2)))) of role axiom named fact_29_sup__left__commute
% A new axiom: (forall (X_18:(hoare_669141180iple_a->Prop)) (Y_10:(hoare_669141180iple_a->Prop)) (Z_2:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_18) ((semila1689936973le_a_o Y_10) Z_2))) ((semila1689936973le_a_o Y_10) ((semila1689936973le_a_o X_18) Z_2))))
% FOF formula (forall (X_18:(pname->Prop)) (Y_10:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_18) ((semila1780557381name_o Y_10) Z_2))) ((semila1780557381name_o Y_10) ((semila1780557381name_o X_18) Z_2)))) of role axiom named fact_30_sup__left__commute
% A new axiom: (forall (X_18:(pname->Prop)) (Y_10:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_18) ((semila1780557381name_o Y_10) Z_2))) ((semila1780557381name_o Y_10) ((semila1780557381name_o X_18) Z_2))))
% FOF formula (forall (X_18:Prop) (Y_10:Prop) (Z_2:Prop), ((iff ((semila10642723_sup_o X_18) ((semila10642723_sup_o Y_10) Z_2))) ((semila10642723_sup_o Y_10) ((semila10642723_sup_o X_18) Z_2)))) of role axiom named fact_31_sup__left__commute
% A new axiom: (forall (X_18:Prop) (Y_10:Prop) (Z_2:Prop), ((iff ((semila10642723_sup_o X_18) ((semila10642723_sup_o Y_10) Z_2))) ((semila10642723_sup_o Y_10) ((semila10642723_sup_o X_18) Z_2))))
% FOF formula (forall (X_17:(hoare_669141180iple_a->Prop)) (Y_9:(hoare_669141180iple_a->Prop)) (Z_1:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_17) ((semila1689936973le_a_o Y_9) Z_1))) ((semila1689936973le_a_o Y_9) ((semila1689936973le_a_o X_17) Z_1)))) of role axiom named fact_32_inf__sup__aci_I7_J
% A new axiom: (forall (X_17:(hoare_669141180iple_a->Prop)) (Y_9:(hoare_669141180iple_a->Prop)) (Z_1:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_17) ((semila1689936973le_a_o Y_9) Z_1))) ((semila1689936973le_a_o Y_9) ((semila1689936973le_a_o X_17) Z_1))))
% FOF formula (forall (X_17:(pname->Prop)) (Y_9:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_17) ((semila1780557381name_o Y_9) Z_1))) ((semila1780557381name_o Y_9) ((semila1780557381name_o X_17) Z_1)))) of role axiom named fact_33_inf__sup__aci_I7_J
% A new axiom: (forall (X_17:(pname->Prop)) (Y_9:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_17) ((semila1780557381name_o Y_9) Z_1))) ((semila1780557381name_o Y_9) ((semila1780557381name_o X_17) Z_1))))
% FOF formula (forall (X_17:Prop) (Y_9:Prop) (Z_1:Prop), ((iff ((semila10642723_sup_o X_17) ((semila10642723_sup_o Y_9) Z_1))) ((semila10642723_sup_o Y_9) ((semila10642723_sup_o X_17) Z_1)))) of role axiom named fact_34_inf__sup__aci_I7_J
% A new axiom: (forall (X_17:Prop) (Y_9:Prop) (Z_1:Prop), ((iff ((semila10642723_sup_o X_17) ((semila10642723_sup_o Y_9) Z_1))) ((semila10642723_sup_o Y_9) ((semila10642723_sup_o X_17) Z_1))))
% FOF formula (forall (B_29:(hoare_669141180iple_a->Prop)) (A_58:(hoare_669141180iple_a->Prop)) (C_10:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o B_29) ((semila1689936973le_a_o A_58) C_10))) ((semila1689936973le_a_o A_58) ((semila1689936973le_a_o B_29) C_10)))) of role axiom named fact_35_sup_Oleft__commute
% A new axiom: (forall (B_29:(hoare_669141180iple_a->Prop)) (A_58:(hoare_669141180iple_a->Prop)) (C_10:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o B_29) ((semila1689936973le_a_o A_58) C_10))) ((semila1689936973le_a_o A_58) ((semila1689936973le_a_o B_29) C_10))))
% FOF formula (forall (B_29:(pname->Prop)) (A_58:(pname->Prop)) (C_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_29) ((semila1780557381name_o A_58) C_10))) ((semila1780557381name_o A_58) ((semila1780557381name_o B_29) C_10)))) of role axiom named fact_36_sup_Oleft__commute
% A new axiom: (forall (B_29:(pname->Prop)) (A_58:(pname->Prop)) (C_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_29) ((semila1780557381name_o A_58) C_10))) ((semila1780557381name_o A_58) ((semila1780557381name_o B_29) C_10))))
% FOF formula (forall (B_29:Prop) (A_58:Prop) (C_10:Prop), ((iff ((semila10642723_sup_o B_29) ((semila10642723_sup_o A_58) C_10))) ((semila10642723_sup_o A_58) ((semila10642723_sup_o B_29) C_10)))) of role axiom named fact_37_sup_Oleft__commute
% A new axiom: (forall (B_29:Prop) (A_58:Prop) (C_10:Prop), ((iff ((semila10642723_sup_o B_29) ((semila10642723_sup_o A_58) C_10))) ((semila10642723_sup_o A_58) ((semila10642723_sup_o B_29) C_10))))
% FOF formula (forall (X_16:(hoare_669141180iple_a->Prop)) (Y_8:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_16) ((semila1689936973le_a_o X_16) Y_8))) ((semila1689936973le_a_o X_16) Y_8))) of role axiom named fact_38_sup__left__idem
% A new axiom: (forall (X_16:(hoare_669141180iple_a->Prop)) (Y_8:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_16) ((semila1689936973le_a_o X_16) Y_8))) ((semila1689936973le_a_o X_16) Y_8)))
% FOF formula (forall (X_16:(pname->Prop)) (Y_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_16) ((semila1780557381name_o X_16) Y_8))) ((semila1780557381name_o X_16) Y_8))) of role axiom named fact_39_sup__left__idem
% A new axiom: (forall (X_16:(pname->Prop)) (Y_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_16) ((semila1780557381name_o X_16) Y_8))) ((semila1780557381name_o X_16) Y_8)))
% FOF formula (forall (X_16:Prop) (Y_8:Prop), ((iff ((semila10642723_sup_o X_16) ((semila10642723_sup_o X_16) Y_8))) ((semila10642723_sup_o X_16) Y_8))) of role axiom named fact_40_sup__left__idem
% A new axiom: (forall (X_16:Prop) (Y_8:Prop), ((iff ((semila10642723_sup_o X_16) ((semila10642723_sup_o X_16) Y_8))) ((semila10642723_sup_o X_16) Y_8)))
% FOF formula (forall (X_15:(hoare_669141180iple_a->Prop)) (Y_7:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_15) ((semila1689936973le_a_o X_15) Y_7))) ((semila1689936973le_a_o X_15) Y_7))) of role axiom named fact_41_inf__sup__aci_I8_J
% A new axiom: (forall (X_15:(hoare_669141180iple_a->Prop)) (Y_7:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_15) ((semila1689936973le_a_o X_15) Y_7))) ((semila1689936973le_a_o X_15) Y_7)))
% FOF formula (forall (X_15:(pname->Prop)) (Y_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_15) ((semila1780557381name_o X_15) Y_7))) ((semila1780557381name_o X_15) Y_7))) of role axiom named fact_42_inf__sup__aci_I8_J
% A new axiom: (forall (X_15:(pname->Prop)) (Y_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_15) ((semila1780557381name_o X_15) Y_7))) ((semila1780557381name_o X_15) Y_7)))
% FOF formula (forall (X_15:Prop) (Y_7:Prop), ((iff ((semila10642723_sup_o X_15) ((semila10642723_sup_o X_15) Y_7))) ((semila10642723_sup_o X_15) Y_7))) of role axiom named fact_43_inf__sup__aci_I8_J
% A new axiom: (forall (X_15:Prop) (Y_7:Prop), ((iff ((semila10642723_sup_o X_15) ((semila10642723_sup_o X_15) Y_7))) ((semila10642723_sup_o X_15) Y_7)))
% FOF formula (forall (A_57:(hoare_669141180iple_a->Prop)) (B_28:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_57) ((semila1689936973le_a_o A_57) B_28))) ((semila1689936973le_a_o A_57) B_28))) of role axiom named fact_44_sup_Oleft__idem
% A new axiom: (forall (A_57:(hoare_669141180iple_a->Prop)) (B_28:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_57) ((semila1689936973le_a_o A_57) B_28))) ((semila1689936973le_a_o A_57) B_28)))
% FOF formula (forall (A_57:(pname->Prop)) (B_28:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_57) ((semila1780557381name_o A_57) B_28))) ((semila1780557381name_o A_57) B_28))) of role axiom named fact_45_sup_Oleft__idem
% A new axiom: (forall (A_57:(pname->Prop)) (B_28:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_57) ((semila1780557381name_o A_57) B_28))) ((semila1780557381name_o A_57) B_28)))
% FOF formula (forall (A_57:Prop) (B_28:Prop), ((iff ((semila10642723_sup_o A_57) ((semila10642723_sup_o A_57) B_28))) ((semila10642723_sup_o A_57) B_28))) of role axiom named fact_46_sup_Oleft__idem
% A new axiom: (forall (A_57:Prop) (B_28:Prop), ((iff ((semila10642723_sup_o A_57) ((semila10642723_sup_o A_57) B_28))) ((semila10642723_sup_o A_57) B_28)))
% FOF formula (forall (X_14:(hoare_669141180iple_a->Prop)) (Y_6:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_14) Y_6)) ((semila1689936973le_a_o Y_6) X_14))) of role axiom named fact_47_sup__commute
% A new axiom: (forall (X_14:(hoare_669141180iple_a->Prop)) (Y_6:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_14) Y_6)) ((semila1689936973le_a_o Y_6) X_14)))
% FOF formula (forall (X_14:(pname->Prop)) (Y_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_14) Y_6)) ((semila1780557381name_o Y_6) X_14))) of role axiom named fact_48_sup__commute
% A new axiom: (forall (X_14:(pname->Prop)) (Y_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_14) Y_6)) ((semila1780557381name_o Y_6) X_14)))
% FOF formula (forall (X_14:Prop) (Y_6:Prop), ((iff ((semila10642723_sup_o X_14) Y_6)) ((semila10642723_sup_o Y_6) X_14))) of role axiom named fact_49_sup__commute
% A new axiom: (forall (X_14:Prop) (Y_6:Prop), ((iff ((semila10642723_sup_o X_14) Y_6)) ((semila10642723_sup_o Y_6) X_14)))
% FOF formula (forall (X_13:(hoare_669141180iple_a->Prop)) (Y_5:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_13) Y_5)) ((semila1689936973le_a_o Y_5) X_13))) of role axiom named fact_50_inf__sup__aci_I5_J
% A new axiom: (forall (X_13:(hoare_669141180iple_a->Prop)) (Y_5:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_13) Y_5)) ((semila1689936973le_a_o Y_5) X_13)))
% FOF formula (forall (X_13:(pname->Prop)) (Y_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_13) Y_5)) ((semila1780557381name_o Y_5) X_13))) of role axiom named fact_51_inf__sup__aci_I5_J
% A new axiom: (forall (X_13:(pname->Prop)) (Y_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_13) Y_5)) ((semila1780557381name_o Y_5) X_13)))
% FOF formula (forall (X_13:Prop) (Y_5:Prop), ((iff ((semila10642723_sup_o X_13) Y_5)) ((semila10642723_sup_o Y_5) X_13))) of role axiom named fact_52_inf__sup__aci_I5_J
% A new axiom: (forall (X_13:Prop) (Y_5:Prop), ((iff ((semila10642723_sup_o X_13) Y_5)) ((semila10642723_sup_o Y_5) X_13)))
% FOF formula (forall (A_56:(hoare_669141180iple_a->Prop)) (B_27:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_56) B_27)) ((semila1689936973le_a_o B_27) A_56))) of role axiom named fact_53_sup_Ocommute
% A new axiom: (forall (A_56:(hoare_669141180iple_a->Prop)) (B_27:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_56) B_27)) ((semila1689936973le_a_o B_27) A_56)))
% FOF formula (forall (A_56:(pname->Prop)) (B_27:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_56) B_27)) ((semila1780557381name_o B_27) A_56))) of role axiom named fact_54_sup_Ocommute
% A new axiom: (forall (A_56:(pname->Prop)) (B_27:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_56) B_27)) ((semila1780557381name_o B_27) A_56)))
% FOF formula (forall (A_56:Prop) (B_27:Prop), ((iff ((semila10642723_sup_o A_56) B_27)) ((semila10642723_sup_o B_27) A_56))) of role axiom named fact_55_sup_Ocommute
% A new axiom: (forall (A_56:Prop) (B_27:Prop), ((iff ((semila10642723_sup_o A_56) B_27)) ((semila10642723_sup_o B_27) A_56)))
% FOF formula (forall (X_12:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_12) X_12)) X_12)) of role axiom named fact_56_sup__idem
% A new axiom: (forall (X_12:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_12) X_12)) X_12))
% FOF formula (forall (X_12:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_12) X_12)) X_12)) of role axiom named fact_57_sup__idem
% A new axiom: (forall (X_12:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_12) X_12)) X_12))
% FOF formula (forall (X_12:Prop), ((iff ((semila10642723_sup_o X_12) X_12)) X_12)) of role axiom named fact_58_sup__idem
% A new axiom: (forall (X_12:Prop), ((iff ((semila10642723_sup_o X_12) X_12)) X_12))
% FOF formula (forall (A_55:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_55) A_55)) A_55)) of role axiom named fact_59_sup_Oidem
% A new axiom: (forall (A_55:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_55) A_55)) A_55))
% FOF formula (forall (A_55:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_55) A_55)) A_55)) of role axiom named fact_60_sup_Oidem
% A new axiom: (forall (A_55:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_55) A_55)) A_55))
% FOF formula (forall (A_55:Prop), ((iff ((semila10642723_sup_o A_55) A_55)) A_55)) of role axiom named fact_61_sup_Oidem
% A new axiom: (forall (A_55:Prop), ((iff ((semila10642723_sup_o A_55) A_55)) A_55))
% FOF formula (forall (B_26:pname) (F_5:(hoare_669141180iple_a->pname)) (X_11:hoare_669141180iple_a) (A_54:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_11) A_54)->((((eq pname) B_26) (F_5 X_11))->((member_pname B_26) ((image_225123213_pname F_5) A_54))))) of role axiom named fact_62_rev__image__eqI
% A new axiom: (forall (B_26:pname) (F_5:(hoare_669141180iple_a->pname)) (X_11:hoare_669141180iple_a) (A_54:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_11) A_54)->((((eq pname) B_26) (F_5 X_11))->((member_pname B_26) ((image_225123213_pname F_5) A_54)))))
% FOF formula (forall (B_26:hoare_669141180iple_a) (F_5:(pname->hoare_669141180iple_a)) (X_11:pname) (A_54:(pname->Prop)), (((member_pname X_11) A_54)->((((eq hoare_669141180iple_a) B_26) (F_5 X_11))->((member1016246415iple_a B_26) ((image_957198589iple_a F_5) A_54))))) of role axiom named fact_63_rev__image__eqI
% A new axiom: (forall (B_26:hoare_669141180iple_a) (F_5:(pname->hoare_669141180iple_a)) (X_11:pname) (A_54:(pname->Prop)), (((member_pname X_11) A_54)->((((eq hoare_669141180iple_a) B_26) (F_5 X_11))->((member1016246415iple_a B_26) ((image_957198589iple_a F_5) A_54)))))
% FOF formula (forall (F_4:(hoare_669141180iple_a->pname)) (X_10:hoare_669141180iple_a) (A_53:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_10) A_53)->((member_pname (F_4 X_10)) ((image_225123213_pname F_4) A_53)))) of role axiom named fact_64_imageI
% A new axiom: (forall (F_4:(hoare_669141180iple_a->pname)) (X_10:hoare_669141180iple_a) (A_53:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_10) A_53)->((member_pname (F_4 X_10)) ((image_225123213_pname F_4) A_53))))
% FOF formula (forall (F_4:(pname->hoare_669141180iple_a)) (X_10:pname) (A_53:(pname->Prop)), (((member_pname X_10) A_53)->((member1016246415iple_a (F_4 X_10)) ((image_957198589iple_a F_4) A_53)))) of role axiom named fact_65_imageI
% A new axiom: (forall (F_4:(pname->hoare_669141180iple_a)) (X_10:pname) (A_53:(pname->Prop)), (((member_pname X_10) A_53)->((member1016246415iple_a (F_4 X_10)) ((image_957198589iple_a F_4) A_53))))
% FOF formula (forall (Z:pname) (F_3:(hoare_669141180iple_a->pname)) (A_52:(hoare_669141180iple_a->Prop)), ((iff ((member_pname Z) ((image_225123213_pname F_3) A_52))) ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) A_52)) (((eq pname) Z) (F_3 X))))))) of role axiom named fact_66_image__iff
% A new axiom: (forall (Z:pname) (F_3:(hoare_669141180iple_a->pname)) (A_52:(hoare_669141180iple_a->Prop)), ((iff ((member_pname Z) ((image_225123213_pname F_3) A_52))) ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) A_52)) (((eq pname) Z) (F_3 X)))))))
% FOF formula (forall (Z:hoare_669141180iple_a) (F_3:(pname->hoare_669141180iple_a)) (A_52:(pname->Prop)), ((iff ((member1016246415iple_a Z) ((image_957198589iple_a F_3) A_52))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_52)) (((eq hoare_669141180iple_a) Z) (F_3 X))))))) of role axiom named fact_67_image__iff
% A new axiom: (forall (Z:hoare_669141180iple_a) (F_3:(pname->hoare_669141180iple_a)) (A_52:(pname->Prop)), ((iff ((member1016246415iple_a Z) ((image_957198589iple_a F_3) A_52))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_52)) (((eq hoare_669141180iple_a) Z) (F_3 X)))))))
% FOF formula (forall (A_51:(hoare_669141180iple_a->Prop)) (C_9:hoare_669141180iple_a) (B_25:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a C_9) B_25)->((member1016246415iple_a C_9) ((semila1689936973le_a_o A_51) B_25)))) of role axiom named fact_68_UnI2
% A new axiom: (forall (A_51:(hoare_669141180iple_a->Prop)) (C_9:hoare_669141180iple_a) (B_25:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a C_9) B_25)->((member1016246415iple_a C_9) ((semila1689936973le_a_o A_51) B_25))))
% FOF formula (forall (A_51:(pname->Prop)) (C_9:pname) (B_25:(pname->Prop)), (((member_pname C_9) B_25)->((member_pname C_9) ((semila1780557381name_o A_51) B_25)))) of role axiom named fact_69_UnI2
% A new axiom: (forall (A_51:(pname->Prop)) (C_9:pname) (B_25:(pname->Prop)), (((member_pname C_9) B_25)->((member_pname C_9) ((semila1780557381name_o A_51) B_25))))
% FOF formula (forall (B_24:(hoare_669141180iple_a->Prop)) (C_8:hoare_669141180iple_a) (A_50:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a C_8) A_50)->((member1016246415iple_a C_8) ((semila1689936973le_a_o A_50) B_24)))) of role axiom named fact_70_UnI1
% A new axiom: (forall (B_24:(hoare_669141180iple_a->Prop)) (C_8:hoare_669141180iple_a) (A_50:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a C_8) A_50)->((member1016246415iple_a C_8) ((semila1689936973le_a_o A_50) B_24))))
% FOF formula (forall (B_24:(pname->Prop)) (C_8:pname) (A_50:(pname->Prop)), (((member_pname C_8) A_50)->((member_pname C_8) ((semila1780557381name_o A_50) B_24)))) of role axiom named fact_71_UnI1
% A new axiom: (forall (B_24:(pname->Prop)) (C_8:pname) (A_50:(pname->Prop)), (((member_pname C_8) A_50)->((member_pname C_8) ((semila1780557381name_o A_50) B_24))))
% FOF formula (forall (A_49:(hoare_669141180iple_a->Prop)) (B_23:(hoare_669141180iple_a->Prop)) (X_9:hoare_669141180iple_a), ((B_23 X_9)->(((semila1689936973le_a_o A_49) B_23) X_9))) of role axiom named fact_72_sup1I2
% A new axiom: (forall (A_49:(hoare_669141180iple_a->Prop)) (B_23:(hoare_669141180iple_a->Prop)) (X_9:hoare_669141180iple_a), ((B_23 X_9)->(((semila1689936973le_a_o A_49) B_23) X_9)))
% FOF formula (forall (A_49:(pname->Prop)) (B_23:(pname->Prop)) (X_9:pname), ((B_23 X_9)->(((semila1780557381name_o A_49) B_23) X_9))) of role axiom named fact_73_sup1I2
% A new axiom: (forall (A_49:(pname->Prop)) (B_23:(pname->Prop)) (X_9:pname), ((B_23 X_9)->(((semila1780557381name_o A_49) B_23) X_9)))
% FOF formula (forall (B_22:(hoare_669141180iple_a->Prop)) (A_48:(hoare_669141180iple_a->Prop)) (X_8:hoare_669141180iple_a), ((A_48 X_8)->(((semila1689936973le_a_o A_48) B_22) X_8))) of role axiom named fact_74_sup1I1
% A new axiom: (forall (B_22:(hoare_669141180iple_a->Prop)) (A_48:(hoare_669141180iple_a->Prop)) (X_8:hoare_669141180iple_a), ((A_48 X_8)->(((semila1689936973le_a_o A_48) B_22) X_8)))
% FOF formula (forall (B_22:(pname->Prop)) (A_48:(pname->Prop)) (X_8:pname), ((A_48 X_8)->(((semila1780557381name_o A_48) B_22) X_8))) of role axiom named fact_75_sup1I1
% A new axiom: (forall (B_22:(pname->Prop)) (A_48:(pname->Prop)) (X_8:pname), ((A_48 X_8)->(((semila1780557381name_o A_48) B_22) X_8)))
% FOF formula (forall (P_13:(hoare_669141180iple_a->Prop)) (A_47:(hoare_669141180iple_a->Prop)) (B_21:(hoare_669141180iple_a->Prop)), ((iff (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((semila1689936973le_a_o A_47) B_21))->(P_13 X)))) ((and (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) A_47)->(P_13 X)))) (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) B_21)->(P_13 X)))))) of role axiom named fact_76_ball__Un
% A new axiom: (forall (P_13:(hoare_669141180iple_a->Prop)) (A_47:(hoare_669141180iple_a->Prop)) (B_21:(hoare_669141180iple_a->Prop)), ((iff (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((semila1689936973le_a_o A_47) B_21))->(P_13 X)))) ((and (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) A_47)->(P_13 X)))) (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) B_21)->(P_13 X))))))
% FOF formula (forall (P_13:(pname->Prop)) (A_47:(pname->Prop)) (B_21:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) ((semila1780557381name_o A_47) B_21))->(P_13 X)))) ((and (forall (X:pname), (((member_pname X) A_47)->(P_13 X)))) (forall (X:pname), (((member_pname X) B_21)->(P_13 X)))))) of role axiom named fact_77_ball__Un
% A new axiom: (forall (P_13:(pname->Prop)) (A_47:(pname->Prop)) (B_21:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) ((semila1780557381name_o A_47) B_21))->(P_13 X)))) ((and (forall (X:pname), (((member_pname X) A_47)->(P_13 X)))) (forall (X:pname), (((member_pname X) B_21)->(P_13 X))))))
% FOF formula (forall (P_12:(hoare_669141180iple_a->Prop)) (A_46:(hoare_669141180iple_a->Prop)) (B_20:(hoare_669141180iple_a->Prop)), ((iff ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) ((semila1689936973le_a_o A_46) B_20))) (P_12 X))))) ((or ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) A_46)) (P_12 X))))) ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) B_20)) (P_12 X))))))) of role axiom named fact_78_bex__Un
% A new axiom: (forall (P_12:(hoare_669141180iple_a->Prop)) (A_46:(hoare_669141180iple_a->Prop)) (B_20:(hoare_669141180iple_a->Prop)), ((iff ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) ((semila1689936973le_a_o A_46) B_20))) (P_12 X))))) ((or ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) A_46)) (P_12 X))))) ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) B_20)) (P_12 X)))))))
% FOF formula (forall (P_12:(pname->Prop)) (A_46:(pname->Prop)) (B_20:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((and ((member_pname X) ((semila1780557381name_o A_46) B_20))) (P_12 X))))) ((or ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_46)) (P_12 X))))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) B_20)) (P_12 X))))))) of role axiom named fact_79_bex__Un
% A new axiom: (forall (P_12:(pname->Prop)) (A_46:(pname->Prop)) (B_20:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((and ((member_pname X) ((semila1780557381name_o A_46) B_20))) (P_12 X))))) ((or ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_46)) (P_12 X))))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) B_20)) (P_12 X)))))))
% FOF formula (forall (A_45:(hoare_669141180iple_a->Prop)) (B_19:(hoare_669141180iple_a->Prop)) (C_7:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o A_45) B_19)) C_7)) ((semila1689936973le_a_o A_45) ((semila1689936973le_a_o B_19) C_7)))) of role axiom named fact_80_Un__assoc
% A new axiom: (forall (A_45:(hoare_669141180iple_a->Prop)) (B_19:(hoare_669141180iple_a->Prop)) (C_7:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o A_45) B_19)) C_7)) ((semila1689936973le_a_o A_45) ((semila1689936973le_a_o B_19) C_7))))
% FOF formula (forall (A_45:(pname->Prop)) (B_19:(pname->Prop)) (C_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_45) B_19)) C_7)) ((semila1780557381name_o A_45) ((semila1780557381name_o B_19) C_7)))) of role axiom named fact_81_Un__assoc
% A new axiom: (forall (A_45:(pname->Prop)) (B_19:(pname->Prop)) (C_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_45) B_19)) C_7)) ((semila1780557381name_o A_45) ((semila1780557381name_o B_19) C_7))))
% FOF formula (forall (C_6:hoare_669141180iple_a) (A_44:(hoare_669141180iple_a->Prop)) (B_18:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a C_6) ((semila1689936973le_a_o A_44) B_18))) ((or ((member1016246415iple_a C_6) A_44)) ((member1016246415iple_a C_6) B_18)))) of role axiom named fact_82_Un__iff
% A new axiom: (forall (C_6:hoare_669141180iple_a) (A_44:(hoare_669141180iple_a->Prop)) (B_18:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a C_6) ((semila1689936973le_a_o A_44) B_18))) ((or ((member1016246415iple_a C_6) A_44)) ((member1016246415iple_a C_6) B_18))))
% FOF formula (forall (C_6:pname) (A_44:(pname->Prop)) (B_18:(pname->Prop)), ((iff ((member_pname C_6) ((semila1780557381name_o A_44) B_18))) ((or ((member_pname C_6) A_44)) ((member_pname C_6) B_18)))) of role axiom named fact_83_Un__iff
% A new axiom: (forall (C_6:pname) (A_44:(pname->Prop)) (B_18:(pname->Prop)), ((iff ((member_pname C_6) ((semila1780557381name_o A_44) B_18))) ((or ((member_pname C_6) A_44)) ((member_pname C_6) B_18))))
% FOF formula (forall (A_43:(hoare_669141180iple_a->Prop)) (B_17:(hoare_669141180iple_a->Prop)) (C_5:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_43) ((semila1689936973le_a_o B_17) C_5))) ((semila1689936973le_a_o B_17) ((semila1689936973le_a_o A_43) C_5)))) of role axiom named fact_84_Un__left__commute
% A new axiom: (forall (A_43:(hoare_669141180iple_a->Prop)) (B_17:(hoare_669141180iple_a->Prop)) (C_5:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_43) ((semila1689936973le_a_o B_17) C_5))) ((semila1689936973le_a_o B_17) ((semila1689936973le_a_o A_43) C_5))))
% FOF formula (forall (A_43:(pname->Prop)) (B_17:(pname->Prop)) (C_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_43) ((semila1780557381name_o B_17) C_5))) ((semila1780557381name_o B_17) ((semila1780557381name_o A_43) C_5)))) of role axiom named fact_85_Un__left__commute
% A new axiom: (forall (A_43:(pname->Prop)) (B_17:(pname->Prop)) (C_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_43) ((semila1780557381name_o B_17) C_5))) ((semila1780557381name_o B_17) ((semila1780557381name_o A_43) C_5))))
% FOF formula (forall (A_42:(hoare_669141180iple_a->Prop)) (B_16:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_42) ((semila1689936973le_a_o A_42) B_16))) ((semila1689936973le_a_o A_42) B_16))) of role axiom named fact_86_Un__left__absorb
% A new axiom: (forall (A_42:(hoare_669141180iple_a->Prop)) (B_16:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_42) ((semila1689936973le_a_o A_42) B_16))) ((semila1689936973le_a_o A_42) B_16)))
% FOF formula (forall (A_42:(pname->Prop)) (B_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_42) ((semila1780557381name_o A_42) B_16))) ((semila1780557381name_o A_42) B_16))) of role axiom named fact_87_Un__left__absorb
% A new axiom: (forall (A_42:(pname->Prop)) (B_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_42) ((semila1780557381name_o A_42) B_16))) ((semila1780557381name_o A_42) B_16)))
% FOF formula (forall (A_41:(hoare_669141180iple_a->Prop)) (B_15:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_41) B_15)) ((semila1689936973le_a_o B_15) A_41))) of role axiom named fact_88_Un__commute
% A new axiom: (forall (A_41:(hoare_669141180iple_a->Prop)) (B_15:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_41) B_15)) ((semila1689936973le_a_o B_15) A_41)))
% FOF formula (forall (A_41:(pname->Prop)) (B_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_41) B_15)) ((semila1780557381name_o B_15) A_41))) of role axiom named fact_89_Un__commute
% A new axiom: (forall (A_41:(pname->Prop)) (B_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_41) B_15)) ((semila1780557381name_o B_15) A_41)))
% FOF formula (forall (A_40:(hoare_669141180iple_a->Prop)) (B_14:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_40) B_14)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((or ((member1016246415iple_a X) A_40)) ((member1016246415iple_a X) B_14)))))) of role axiom named fact_90_Un__def
% A new axiom: (forall (A_40:(hoare_669141180iple_a->Prop)) (B_14:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_40) B_14)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((or ((member1016246415iple_a X) A_40)) ((member1016246415iple_a X) B_14))))))
% FOF formula (forall (A_40:(pname->Prop)) (B_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_40) B_14)) (collect_pname (fun (X:pname)=> ((or ((member_pname X) A_40)) ((member_pname X) B_14)))))) of role axiom named fact_91_Un__def
% A new axiom: (forall (A_40:(pname->Prop)) (B_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_40) B_14)) (collect_pname (fun (X:pname)=> ((or ((member_pname X) A_40)) ((member_pname X) B_14))))))
% FOF formula (forall (A_39:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_39) A_39)) A_39)) of role axiom named fact_92_Un__absorb
% A new axiom: (forall (A_39:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_39) A_39)) A_39))
% FOF formula (forall (A_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_39) A_39)) A_39)) of role axiom named fact_93_Un__absorb
% A new axiom: (forall (A_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_39) A_39)) A_39))
% FOF formula (forall (F_2:(pname->hoare_669141180iple_a)) (G_4:(hoare_669141180iple_a->pname)) (A_38:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a F_2) ((image_225123213_pname G_4) A_38))) ((image_1033305477iple_a (fun (X:hoare_669141180iple_a)=> (F_2 (G_4 X)))) A_38))) of role axiom named fact_94_image__image
% A new axiom: (forall (F_2:(pname->hoare_669141180iple_a)) (G_4:(hoare_669141180iple_a->pname)) (A_38:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a F_2) ((image_225123213_pname G_4) A_38))) ((image_1033305477iple_a (fun (X:hoare_669141180iple_a)=> (F_2 (G_4 X)))) A_38)))
% FOF formula (forall (F_2:(hoare_669141180iple_a->pname)) (G_4:(pname->hoare_669141180iple_a)) (A_38:(pname->Prop)), (((eq (pname->Prop)) ((image_225123213_pname F_2) ((image_957198589iple_a G_4) A_38))) ((image_pname_pname (fun (X:pname)=> (F_2 (G_4 X)))) A_38))) of role axiom named fact_95_image__image
% A new axiom: (forall (F_2:(hoare_669141180iple_a->pname)) (G_4:(pname->hoare_669141180iple_a)) (A_38:(pname->Prop)), (((eq (pname->Prop)) ((image_225123213_pname F_2) ((image_957198589iple_a G_4) A_38))) ((image_pname_pname (fun (X:pname)=> (F_2 (G_4 X)))) A_38)))
% FOF formula (forall (R:(hoare_669141180iple_a->Prop)) (S_1:(hoare_669141180iple_a->Prop)) (X:hoare_669141180iple_a), ((iff (((semila1689936973le_a_o (fun (Y_1:hoare_669141180iple_a)=> ((member1016246415iple_a Y_1) R))) (fun (Y_1:hoare_669141180iple_a)=> ((member1016246415iple_a Y_1) S_1))) X)) ((member1016246415iple_a X) ((semila1689936973le_a_o R) S_1)))) of role axiom named fact_96_sup__Un__eq
% A new axiom: (forall (R:(hoare_669141180iple_a->Prop)) (S_1:(hoare_669141180iple_a->Prop)) (X:hoare_669141180iple_a), ((iff (((semila1689936973le_a_o (fun (Y_1:hoare_669141180iple_a)=> ((member1016246415iple_a Y_1) R))) (fun (Y_1:hoare_669141180iple_a)=> ((member1016246415iple_a Y_1) S_1))) X)) ((member1016246415iple_a X) ((semila1689936973le_a_o R) S_1))))
% FOF formula (forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o (fun (Y_1:pname)=> ((member_pname Y_1) R))) (fun (Y_1:pname)=> ((member_pname Y_1) S_1))) X)) ((member_pname X) ((semila1780557381name_o R) S_1)))) of role axiom named fact_97_sup__Un__eq
% A new axiom: (forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o (fun (Y_1:pname)=> ((member_pname Y_1) R))) (fun (Y_1:pname)=> ((member_pname Y_1) S_1))) X)) ((member_pname X) ((semila1780557381name_o R) S_1))))
% FOF formula (forall (P_11:(hoare_669141180iple_a->Prop)) (Q_3:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((or (P_11 X)) (Q_3 X))))) ((semila1689936973le_a_o (collec1717965009iple_a P_11)) (collec1717965009iple_a Q_3)))) of role axiom named fact_98_Collect__disj__eq
% A new axiom: (forall (P_11:(hoare_669141180iple_a->Prop)) (Q_3:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((or (P_11 X)) (Q_3 X))))) ((semila1689936973le_a_o (collec1717965009iple_a P_11)) (collec1717965009iple_a Q_3))))
% FOF formula (forall (P_11:(pname->Prop)) (Q_3:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((or (P_11 X)) (Q_3 X))))) ((semila1780557381name_o (collect_pname P_11)) (collect_pname Q_3)))) of role axiom named fact_99_Collect__disj__eq
% A new axiom: (forall (P_11:(pname->Prop)) (Q_3:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((or (P_11 X)) (Q_3 X))))) ((semila1780557381name_o (collect_pname P_11)) (collect_pname Q_3))))
% FOF formula (forall (B_13:pname) (F_1:(hoare_669141180iple_a->pname)) (A_37:(hoare_669141180iple_a->Prop)), (((member_pname B_13) ((image_225123213_pname F_1) A_37))->((forall (X:hoare_669141180iple_a), ((((eq pname) B_13) (F_1 X))->(((member1016246415iple_a X) A_37)->False)))->False))) of role axiom named fact_100_imageE
% A new axiom: (forall (B_13:pname) (F_1:(hoare_669141180iple_a->pname)) (A_37:(hoare_669141180iple_a->Prop)), (((member_pname B_13) ((image_225123213_pname F_1) A_37))->((forall (X:hoare_669141180iple_a), ((((eq pname) B_13) (F_1 X))->(((member1016246415iple_a X) A_37)->False)))->False)))
% FOF formula (forall (B_13:hoare_669141180iple_a) (F_1:(pname->hoare_669141180iple_a)) (A_37:(pname->Prop)), (((member1016246415iple_a B_13) ((image_957198589iple_a F_1) A_37))->((forall (X:pname), ((((eq hoare_669141180iple_a) B_13) (F_1 X))->(((member_pname X) A_37)->False)))->False))) of role axiom named fact_101_imageE
% A new axiom: (forall (B_13:hoare_669141180iple_a) (F_1:(pname->hoare_669141180iple_a)) (A_37:(pname->Prop)), (((member1016246415iple_a B_13) ((image_957198589iple_a F_1) A_37))->((forall (X:pname), ((((eq hoare_669141180iple_a) B_13) (F_1 X))->(((member_pname X) A_37)->False)))->False)))
% FOF formula (forall (N_2:nat) (P_10:(x_a->(state->Prop))) (Pn_4:pname) (Q_2:(x_a->(state->Prop))), ((iff ((hoare_2082685510alid_a N_2) (((hoare_1295064928iple_a P_10) (the_com (body_1 Pn_4))) Q_2))) ((hoare_2082685510alid_a (suc N_2)) (((hoare_1295064928iple_a P_10) (body Pn_4)) Q_2)))) of role axiom named fact_102_Body__triple__valid__Suc
% A new axiom: (forall (N_2:nat) (P_10:(x_a->(state->Prop))) (Pn_4:pname) (Q_2:(x_a->(state->Prop))), ((iff ((hoare_2082685510alid_a N_2) (((hoare_1295064928iple_a P_10) (the_com (body_1 Pn_4))) Q_2))) ((hoare_2082685510alid_a (suc N_2)) (((hoare_1295064928iple_a P_10) (body Pn_4)) Q_2))))
% FOF formula (forall (Y_4:hoare_669141180iple_a), ((forall (Fun1:(x_a->(state->Prop))) (Com:com) (Fun2:(x_a->(state->Prop))), (not (((eq hoare_669141180iple_a) Y_4) (((hoare_1295064928iple_a Fun1) Com) Fun2))))->False)) of role axiom named fact_103_triple_Oexhaust
% A new axiom: (forall (Y_4:hoare_669141180iple_a), ((forall (Fun1:(x_a->(state->Prop))) (Com:com) (Fun2:(x_a->(state->Prop))), (not (((eq hoare_669141180iple_a) Y_4) (((hoare_1295064928iple_a Fun1) Com) Fun2))))->False))
% FOF formula (forall (Pn_3:pname) (G_3:(hoare_669141180iple_a->Prop)) (P_8:(pname->(x_a->(state->Prop)))) (Q_1:(pname->(x_a->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_2128652938rivs_a ((semila1689936973le_a_o G_3) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_8 P_9)) (body P_9)) (Q_1 P_9)))) Procs))) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_8 P_9)) (the_com (body_1 P_9))) (Q_1 P_9)))) Procs))->(((member_pname Pn_3) Procs)->((hoare_2128652938rivs_a G_3) ((insert175534902iple_a (((hoare_1295064928iple_a (P_8 Pn_3)) (body Pn_3)) (Q_1 Pn_3))) bot_bo280939947le_a_o))))) of role axiom named fact_104_Body1
% A new axiom: (forall (Pn_3:pname) (G_3:(hoare_669141180iple_a->Prop)) (P_8:(pname->(x_a->(state->Prop)))) (Q_1:(pname->(x_a->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_2128652938rivs_a ((semila1689936973le_a_o G_3) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_8 P_9)) (body P_9)) (Q_1 P_9)))) Procs))) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_8 P_9)) (the_com (body_1 P_9))) (Q_1 P_9)))) Procs))->(((member_pname Pn_3) Procs)->((hoare_2128652938rivs_a G_3) ((insert175534902iple_a (((hoare_1295064928iple_a (P_8 Pn_3)) (body Pn_3)) (Q_1 Pn_3))) bot_bo280939947le_a_o)))))
% FOF formula (forall (F:(hoare_669141180iple_a->pname)) (G_2:(hoare_669141180iple_a->pname)) (M:(hoare_669141180iple_a->Prop)) (N_1:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) M) N_1)->((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) N_1)->(((eq pname) (F X)) (G_2 X))))->(((eq (pname->Prop)) ((image_225123213_pname F) M)) ((image_225123213_pname G_2) N_1))))) of role axiom named fact_105_image__cong
% A new axiom: (forall (F:(hoare_669141180iple_a->pname)) (G_2:(hoare_669141180iple_a->pname)) (M:(hoare_669141180iple_a->Prop)) (N_1:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) M) N_1)->((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) N_1)->(((eq pname) (F X)) (G_2 X))))->(((eq (pname->Prop)) ((image_225123213_pname F) M)) ((image_225123213_pname G_2) N_1)))))
% FOF formula (forall (F:(pname->hoare_669141180iple_a)) (G_2:(pname->hoare_669141180iple_a)) (M:(pname->Prop)) (N_1:(pname->Prop)), ((((eq (pname->Prop)) M) N_1)->((forall (X:pname), (((member_pname X) N_1)->(((eq hoare_669141180iple_a) (F X)) (G_2 X))))->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a F) M)) ((image_957198589iple_a G_2) N_1))))) of role axiom named fact_106_image__cong
% A new axiom: (forall (F:(pname->hoare_669141180iple_a)) (G_2:(pname->hoare_669141180iple_a)) (M:(pname->Prop)) (N_1:(pname->Prop)), ((((eq (pname->Prop)) M) N_1)->((forall (X:pname), (((member_pname X) N_1)->(((eq hoare_669141180iple_a) (F X)) (G_2 X))))->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a F) M)) ((image_957198589iple_a G_2) N_1)))))
% FOF formula (forall (P_7:(x_a->(state->Prop))) (Pn_2:pname) (Q:(x_a->(state->Prop))), ((hoare_2082685510alid_a zero_zero_nat) (((hoare_1295064928iple_a P_7) (body Pn_2)) Q))) of role axiom named fact_107_Body__triple__valid__0
% A new axiom: (forall (P_7:(x_a->(state->Prop))) (Pn_2:pname) (Q:(x_a->(state->Prop))), ((hoare_2082685510alid_a zero_zero_nat) (((hoare_1295064928iple_a P_7) (body Pn_2)) Q)))
% 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_108_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_109_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 (A_36:hoare_669141180iple_a), (((member1016246415iple_a A_36) bot_bo280939947le_a_o)->False)) of role axiom named fact_110_emptyE
% A new axiom: (forall (A_36:hoare_669141180iple_a), (((member1016246415iple_a A_36) bot_bo280939947le_a_o)->False))
% FOF formula (forall (A_36:pname), (((member_pname A_36) bot_bot_pname_o)->False)) of role axiom named fact_111_emptyE
% A new axiom: (forall (A_36:pname), (((member_pname A_36) bot_bot_pname_o)->False))
% FOF formula (forall (A_35:hoare_669141180iple_a) (B_12:hoare_669141180iple_a) (A_34:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_35) ((insert175534902iple_a B_12) A_34))->((not (((eq hoare_669141180iple_a) A_35) B_12))->((member1016246415iple_a A_35) A_34)))) of role axiom named fact_112_insertE
% A new axiom: (forall (A_35:hoare_669141180iple_a) (B_12:hoare_669141180iple_a) (A_34:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_35) ((insert175534902iple_a B_12) A_34))->((not (((eq hoare_669141180iple_a) A_35) B_12))->((member1016246415iple_a A_35) A_34))))
% FOF formula (forall (A_35:pname) (B_12:pname) (A_34:(pname->Prop)), (((member_pname A_35) ((insert_pname B_12) A_34))->((not (((eq pname) A_35) B_12))->((member_pname A_35) A_34)))) of role axiom named fact_113_insertE
% A new axiom: (forall (A_35:pname) (B_12:pname) (A_34:(pname->Prop)), (((member_pname A_35) ((insert_pname B_12) A_34))->((not (((eq pname) A_35) B_12))->((member_pname A_35) A_34))))
% FOF formula (forall (B_11:hoare_669141180iple_a) (A_33:hoare_669141180iple_a) (B_10:(hoare_669141180iple_a->Prop)), (((((member1016246415iple_a A_33) B_10)->False)->(((eq hoare_669141180iple_a) A_33) B_11))->((member1016246415iple_a A_33) ((insert175534902iple_a B_11) B_10)))) of role axiom named fact_114_insertCI
% A new axiom: (forall (B_11:hoare_669141180iple_a) (A_33:hoare_669141180iple_a) (B_10:(hoare_669141180iple_a->Prop)), (((((member1016246415iple_a A_33) B_10)->False)->(((eq hoare_669141180iple_a) A_33) B_11))->((member1016246415iple_a A_33) ((insert175534902iple_a B_11) B_10))))
% FOF formula (forall (B_11:pname) (A_33:pname) (B_10:(pname->Prop)), (((((member_pname A_33) B_10)->False)->(((eq pname) A_33) B_11))->((member_pname A_33) ((insert_pname B_11) B_10)))) of role axiom named fact_115_insertCI
% A new axiom: (forall (B_11:pname) (A_33:pname) (B_10:(pname->Prop)), (((((member_pname A_33) B_10)->False)->(((eq pname) A_33) B_11))->((member_pname A_33) ((insert_pname B_11) B_10))))
% FOF formula (forall (P_6:pname) (S:state) (S1:state), ((((evalc (body P_6)) S) S1)->(((evalc (the_com (body_1 P_6))) S) S1))) of role axiom named fact_116_evalc__elim__cases_I6_J
% A new axiom: (forall (P_6:pname) (S:state) (S1:state), ((((evalc (body P_6)) S) S1)->(((evalc (the_com (body_1 P_6))) S) S1)))
% FOF formula (forall (A_32:hoare_669141180iple_a) (A_31:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) ((insert175534902iple_a A_32) A_31)))) of role axiom named fact_117_empty__not__insert
% A new axiom: (forall (A_32:hoare_669141180iple_a) (A_31:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) ((insert175534902iple_a A_32) A_31))))
% FOF formula (forall (A_32:pname) (A_31:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_32) A_31)))) of role axiom named fact_118_empty__not__insert
% A new axiom: (forall (A_32:pname) (A_31:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_32) A_31))))
% FOF formula (forall (A_30:hoare_669141180iple_a) (A_29:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_30) A_29)) bot_bo280939947le_a_o))) of role axiom named fact_119_insert__not__empty
% A new axiom: (forall (A_30:hoare_669141180iple_a) (A_29:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_30) A_29)) bot_bo280939947le_a_o)))
% FOF formula (forall (A_30:pname) (A_29:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_30) A_29)) bot_bot_pname_o))) of role axiom named fact_120_insert__not__empty
% A new axiom: (forall (A_30:pname) (A_29:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_30) A_29)) bot_bot_pname_o)))
% FOF formula (forall (X:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X)) ((member1016246415iple_a X) bot_bo280939947le_a_o))) of role axiom named fact_121_bot__empty__eq
% A new axiom: (forall (X:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X)) ((member1016246415iple_a X) bot_bo280939947le_a_o)))
% FOF formula (forall (X:pname), ((iff (bot_bot_pname_o X)) ((member_pname X) bot_bot_pname_o))) of role axiom named fact_122_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_123_empty__def
% A new axiom: (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X:pname)=> False)))
% FOF formula (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> False))) of role axiom named fact_124_empty__def
% A new axiom: (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> False)))
% FOF formula (forall (A_28:hoare_669141180iple_a) (B_9:(hoare_669141180iple_a->Prop)), ((member1016246415iple_a A_28) ((insert175534902iple_a A_28) B_9))) of role axiom named fact_125_insertI1
% A new axiom: (forall (A_28:hoare_669141180iple_a) (B_9:(hoare_669141180iple_a->Prop)), ((member1016246415iple_a A_28) ((insert175534902iple_a A_28) B_9)))
% FOF formula (forall (A_28:pname) (B_9:(pname->Prop)), ((member_pname A_28) ((insert_pname A_28) B_9))) of role axiom named fact_126_insertI1
% A new axiom: (forall (A_28:pname) (B_9:(pname->Prop)), ((member_pname A_28) ((insert_pname A_28) B_9)))
% FOF formula (forall (A_27:(hoare_669141180iple_a->Prop)), ((iff (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) A_27)->False))) (((eq (hoare_669141180iple_a->Prop)) A_27) bot_bo280939947le_a_o))) of role axiom named fact_127_all__not__in__conv
% A new axiom: (forall (A_27:(hoare_669141180iple_a->Prop)), ((iff (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) A_27)->False))) (((eq (hoare_669141180iple_a->Prop)) A_27) bot_bo280939947le_a_o)))
% FOF formula (forall (A_27:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) A_27)->False))) (((eq (pname->Prop)) A_27) bot_bot_pname_o))) of role axiom named fact_128_all__not__in__conv
% A new axiom: (forall (A_27:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) A_27)->False))) (((eq (pname->Prop)) A_27) bot_bot_pname_o)))
% FOF formula (forall (A_26:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fequal182287803iple_a A_26))) ((insert175534902iple_a A_26) bot_bo280939947le_a_o))) of role axiom named fact_129_singleton__conv2
% A new axiom: (forall (A_26:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fequal182287803iple_a A_26))) ((insert175534902iple_a A_26) bot_bo280939947le_a_o)))
% FOF formula (forall (A_26:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_26))) ((insert_pname A_26) bot_bot_pname_o))) of role axiom named fact_130_singleton__conv2
% A new axiom: (forall (A_26:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_26))) ((insert_pname A_26) bot_bot_pname_o)))
% FOF formula (forall (A_25:(hoare_669141180iple_a->Prop)), ((iff ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((member1016246415iple_a X) A_25)))) (not (((eq (hoare_669141180iple_a->Prop)) A_25) bot_bo280939947le_a_o)))) of role axiom named fact_131_ex__in__conv
% A new axiom: (forall (A_25:(hoare_669141180iple_a->Prop)), ((iff ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((member1016246415iple_a X) A_25)))) (not (((eq (hoare_669141180iple_a->Prop)) A_25) bot_bo280939947le_a_o))))
% FOF formula (forall (A_25:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((member_pname X) A_25)))) (not (((eq (pname->Prop)) A_25) bot_bot_pname_o)))) of role axiom named fact_132_ex__in__conv
% A new axiom: (forall (A_25:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((member_pname X) A_25)))) (not (((eq (pname->Prop)) A_25) bot_bot_pname_o))))
% FOF formula (forall (A_24:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> (((eq hoare_669141180iple_a) X) A_24)))) ((insert175534902iple_a A_24) bot_bo280939947le_a_o))) of role axiom named fact_133_singleton__conv
% A new axiom: (forall (A_24:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> (((eq hoare_669141180iple_a) X) A_24)))) ((insert175534902iple_a A_24) bot_bo280939947le_a_o)))
% FOF formula (forall (A_24:pname), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> (((eq pname) X) A_24)))) ((insert_pname A_24) bot_bot_pname_o))) of role axiom named fact_134_singleton__conv
% A new axiom: (forall (A_24:pname), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> (((eq pname) X) A_24)))) ((insert_pname A_24) bot_bot_pname_o)))
% FOF formula (forall (P_5:(hoare_669141180iple_a->Prop)) (A_23:hoare_669141180iple_a), ((and ((P_5 A_23)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_23) X)) (P_5 X))))) ((insert175534902iple_a A_23) bot_bo280939947le_a_o)))) (((P_5 A_23)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_23) X)) (P_5 X))))) bot_bo280939947le_a_o)))) of role axiom named fact_135_Collect__conv__if2
% A new axiom: (forall (P_5:(hoare_669141180iple_a->Prop)) (A_23:hoare_669141180iple_a), ((and ((P_5 A_23)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_23) X)) (P_5 X))))) ((insert175534902iple_a A_23) bot_bo280939947le_a_o)))) (((P_5 A_23)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_23) X)) (P_5 X))))) bot_bo280939947le_a_o))))
% FOF formula (forall (P_5:(pname->Prop)) (A_23:pname), ((and ((P_5 A_23)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_23) X)) (P_5 X))))) ((insert_pname A_23) bot_bot_pname_o)))) (((P_5 A_23)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_23) X)) (P_5 X))))) bot_bot_pname_o)))) of role axiom named fact_136_Collect__conv__if2
% A new axiom: (forall (P_5:(pname->Prop)) (A_23:pname), ((and ((P_5 A_23)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_23) X)) (P_5 X))))) ((insert_pname A_23) bot_bot_pname_o)))) (((P_5 A_23)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_23) X)) (P_5 X))))) bot_bot_pname_o))))
% FOF formula (forall (P_4:(hoare_669141180iple_a->Prop)) (A_22:hoare_669141180iple_a), ((and ((P_4 A_22)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X) A_22)) (P_4 X))))) ((insert175534902iple_a A_22) bot_bo280939947le_a_o)))) (((P_4 A_22)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X) A_22)) (P_4 X))))) bot_bo280939947le_a_o)))) of role axiom named fact_137_Collect__conv__if
% A new axiom: (forall (P_4:(hoare_669141180iple_a->Prop)) (A_22:hoare_669141180iple_a), ((and ((P_4 A_22)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X) A_22)) (P_4 X))))) ((insert175534902iple_a A_22) bot_bo280939947le_a_o)))) (((P_4 A_22)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X) A_22)) (P_4 X))))) bot_bo280939947le_a_o))))
% FOF formula (forall (P_4:(pname->Prop)) (A_22:pname), ((and ((P_4 A_22)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_22)) (P_4 X))))) ((insert_pname A_22) bot_bot_pname_o)))) (((P_4 A_22)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_22)) (P_4 X))))) bot_bot_pname_o)))) of role axiom named fact_138_Collect__conv__if
% A new axiom: (forall (P_4:(pname->Prop)) (A_22:pname), ((and ((P_4 A_22)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_22)) (P_4 X))))) ((insert_pname A_22) bot_bot_pname_o)))) (((P_4 A_22)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_22)) (P_4 X))))) bot_bot_pname_o))))
% FOF formula (forall (P_3:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_3))) (forall (X:pname), ((P_3 X)->False)))) of role axiom named fact_139_empty__Collect__eq
% A new axiom: (forall (P_3:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_3))) (forall (X:pname), ((P_3 X)->False))))
% FOF formula (forall (P_3:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a P_3))) (forall (X:hoare_669141180iple_a), ((P_3 X)->False)))) of role axiom named fact_140_empty__Collect__eq
% A new axiom: (forall (P_3:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a P_3))) (forall (X:hoare_669141180iple_a), ((P_3 X)->False))))
% FOF formula (forall (C_4:hoare_669141180iple_a), (((member1016246415iple_a C_4) bot_bo280939947le_a_o)->False)) of role axiom named fact_141_empty__iff
% A new axiom: (forall (C_4:hoare_669141180iple_a), (((member1016246415iple_a C_4) bot_bo280939947le_a_o)->False))
% FOF formula (forall (C_4:pname), (((member_pname C_4) bot_bot_pname_o)->False)) of role axiom named fact_142_empty__iff
% A new axiom: (forall (C_4:pname), (((member_pname C_4) bot_bot_pname_o)->False))
% FOF formula (forall (X_7:hoare_669141180iple_a) (A_21:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a X_7) A_21)) (A_21 X_7))) of role axiom named fact_143_mem__def
% A new axiom: (forall (X_7:hoare_669141180iple_a) (A_21:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a X_7) A_21)) (A_21 X_7)))
% FOF formula (forall (X_7:pname) (A_21:(pname->Prop)), ((iff ((member_pname X_7) A_21)) (A_21 X_7))) of role axiom named fact_144_mem__def
% A new axiom: (forall (X_7:pname) (A_21:(pname->Prop)), ((iff ((member_pname X_7) A_21)) (A_21 X_7)))
% FOF formula (forall (P_2:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_2)) P_2)) of role axiom named fact_145_Collect__def
% A new axiom: (forall (P_2:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_2)) P_2))
% FOF formula (forall (P_2:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P_2)) P_2)) of role axiom named fact_146_Collect__def
% A new axiom: (forall (P_2:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P_2)) P_2))
% FOF formula (forall (A_20:hoare_669141180iple_a) (B_8:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_20) B_8)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) X) A_20)) ((member1016246415iple_a X) B_8)))))) of role axiom named fact_147_insert__compr
% A new axiom: (forall (A_20:hoare_669141180iple_a) (B_8:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_20) B_8)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) X) A_20)) ((member1016246415iple_a X) B_8))))))
% FOF formula (forall (A_20:pname) (B_8:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_20) B_8)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_20)) ((member_pname X) B_8)))))) of role axiom named fact_148_insert__compr
% A new axiom: (forall (A_20:pname) (B_8:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_20) B_8)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_20)) ((member_pname X) B_8))))))
% FOF formula (forall (A_19:hoare_669141180iple_a) (A_18:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_19) A_18)) ((semila1689936973le_a_o ((insert175534902iple_a A_19) bot_bo280939947le_a_o)) A_18))) of role axiom named fact_149_insert__is__Un
% A new axiom: (forall (A_19:hoare_669141180iple_a) (A_18:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_19) A_18)) ((semila1689936973le_a_o ((insert175534902iple_a A_19) bot_bo280939947le_a_o)) A_18)))
% FOF formula (forall (A_19:pname) (A_18:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_19) A_18)) ((semila1780557381name_o ((insert_pname A_19) bot_bot_pname_o)) A_18))) of role axiom named fact_150_insert__is__Un
% A new axiom: (forall (A_19:pname) (A_18:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_19) A_18)) ((semila1780557381name_o ((insert_pname A_19) bot_bot_pname_o)) A_18)))
% FOF formula (forall (A_17:hoare_669141180iple_a) (P_1:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_17) (collec1717965009iple_a P_1))) (collec1717965009iple_a (fun (U_1:hoare_669141180iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_669141180iple_a) U_1) A_17))) (P_1 U_1)))))) of role axiom named fact_151_insert__Collect
% A new axiom: (forall (A_17:hoare_669141180iple_a) (P_1:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_17) (collec1717965009iple_a P_1))) (collec1717965009iple_a (fun (U_1:hoare_669141180iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_669141180iple_a) U_1) A_17))) (P_1 U_1))))))
% FOF formula (forall (A_17:pname) (P_1:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_17) (collect_pname P_1))) (collect_pname (fun (U_1:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_1) A_17))) (P_1 U_1)))))) of role axiom named fact_152_insert__Collect
% A new axiom: (forall (A_17:pname) (P_1:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_17) (collect_pname P_1))) (collect_pname (fun (U_1:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_1) A_17))) (P_1 U_1))))))
% FOF formula (forall (B_7:hoare_669141180iple_a) (A_16:hoare_669141180iple_a), ((iff ((member1016246415iple_a B_7) ((insert175534902iple_a A_16) bot_bo280939947le_a_o))) (((eq hoare_669141180iple_a) B_7) A_16))) of role axiom named fact_153_singleton__iff
% A new axiom: (forall (B_7:hoare_669141180iple_a) (A_16:hoare_669141180iple_a), ((iff ((member1016246415iple_a B_7) ((insert175534902iple_a A_16) bot_bo280939947le_a_o))) (((eq hoare_669141180iple_a) B_7) A_16)))
% FOF formula (forall (B_7:pname) (A_16:pname), ((iff ((member_pname B_7) ((insert_pname A_16) bot_bot_pname_o))) (((eq pname) B_7) A_16))) of role axiom named fact_154_singleton__iff
% A new axiom: (forall (B_7:pname) (A_16:pname), ((iff ((member_pname B_7) ((insert_pname A_16) bot_bot_pname_o))) (((eq pname) B_7) A_16)))
% FOF formula (forall (X_6:hoare_669141180iple_a) (A_15:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_6) ((insert175534902iple_a X_6) A_15))) ((insert175534902iple_a X_6) A_15))) of role axiom named fact_155_insert__absorb2
% A new axiom: (forall (X_6:hoare_669141180iple_a) (A_15:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_6) ((insert175534902iple_a X_6) A_15))) ((insert175534902iple_a X_6) A_15)))
% FOF formula (forall (X_6:pname) (A_15:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_6) ((insert_pname X_6) A_15))) ((insert_pname X_6) A_15))) of role axiom named fact_156_insert__absorb2
% A new axiom: (forall (X_6:pname) (A_15:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_6) ((insert_pname X_6) A_15))) ((insert_pname X_6) A_15)))
% FOF formula (forall (X_5:hoare_669141180iple_a) (Y_3:hoare_669141180iple_a) (A_14:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_5) ((insert175534902iple_a Y_3) A_14))) ((insert175534902iple_a Y_3) ((insert175534902iple_a X_5) A_14)))) of role axiom named fact_157_insert__commute
% A new axiom: (forall (X_5:hoare_669141180iple_a) (Y_3:hoare_669141180iple_a) (A_14:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_5) ((insert175534902iple_a Y_3) A_14))) ((insert175534902iple_a Y_3) ((insert175534902iple_a X_5) A_14))))
% FOF formula (forall (X_5:pname) (Y_3:pname) (A_14:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_5) ((insert_pname Y_3) A_14))) ((insert_pname Y_3) ((insert_pname X_5) A_14)))) of role axiom named fact_158_insert__commute
% A new axiom: (forall (X_5:pname) (Y_3:pname) (A_14:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_5) ((insert_pname Y_3) A_14))) ((insert_pname Y_3) ((insert_pname X_5) A_14))))
% FOF formula (forall (A_13:hoare_669141180iple_a) (B_6:hoare_669141180iple_a) (A_12:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a A_13) ((insert175534902iple_a B_6) A_12))) ((or (((eq hoare_669141180iple_a) A_13) B_6)) ((member1016246415iple_a A_13) A_12)))) of role axiom named fact_159_insert__iff
% A new axiom: (forall (A_13:hoare_669141180iple_a) (B_6:hoare_669141180iple_a) (A_12:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a A_13) ((insert175534902iple_a B_6) A_12))) ((or (((eq hoare_669141180iple_a) A_13) B_6)) ((member1016246415iple_a A_13) A_12))))
% FOF formula (forall (A_13:pname) (B_6:pname) (A_12:(pname->Prop)), ((iff ((member_pname A_13) ((insert_pname B_6) A_12))) ((or (((eq pname) A_13) B_6)) ((member_pname A_13) A_12)))) of role axiom named fact_160_insert__iff
% A new axiom: (forall (A_13:pname) (B_6:pname) (A_12:(pname->Prop)), ((iff ((member_pname A_13) ((insert_pname B_6) A_12))) ((or (((eq pname) A_13) B_6)) ((member_pname A_13) A_12))))
% FOF formula (forall (P:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P)) bot_bot_pname_o)) (forall (X:pname), ((P X)->False)))) of role axiom named fact_161_Collect__empty__eq
% A new axiom: (forall (P:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P)) bot_bot_pname_o)) (forall (X:pname), ((P X)->False))))
% FOF formula (forall (P:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P)) bot_bo280939947le_a_o)) (forall (X:hoare_669141180iple_a), ((P X)->False)))) of role axiom named fact_162_Collect__empty__eq
% A new axiom: (forall (P:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P)) bot_bo280939947le_a_o)) (forall (X:hoare_669141180iple_a), ((P X)->False))))
% FOF formula (forall (A_11:hoare_669141180iple_a) (B_5:hoare_669141180iple_a) (C_3:hoare_669141180iple_a) (D:hoare_669141180iple_a), ((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_11) ((insert175534902iple_a B_5) bot_bo280939947le_a_o))) ((insert175534902iple_a C_3) ((insert175534902iple_a D) bot_bo280939947le_a_o)))) ((or ((and (((eq hoare_669141180iple_a) A_11) C_3)) (((eq hoare_669141180iple_a) B_5) D))) ((and (((eq hoare_669141180iple_a) A_11) D)) (((eq hoare_669141180iple_a) B_5) C_3))))) of role axiom named fact_163_doubleton__eq__iff
% A new axiom: (forall (A_11:hoare_669141180iple_a) (B_5:hoare_669141180iple_a) (C_3:hoare_669141180iple_a) (D:hoare_669141180iple_a), ((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_11) ((insert175534902iple_a B_5) bot_bo280939947le_a_o))) ((insert175534902iple_a C_3) ((insert175534902iple_a D) bot_bo280939947le_a_o)))) ((or ((and (((eq hoare_669141180iple_a) A_11) C_3)) (((eq hoare_669141180iple_a) B_5) D))) ((and (((eq hoare_669141180iple_a) A_11) D)) (((eq hoare_669141180iple_a) B_5) C_3)))))
% FOF formula (forall (A_11:pname) (B_5:pname) (C_3:pname) (D:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_11) ((insert_pname B_5) bot_bot_pname_o))) ((insert_pname C_3) ((insert_pname D) bot_bot_pname_o)))) ((or ((and (((eq pname) A_11) C_3)) (((eq pname) B_5) D))) ((and (((eq pname) A_11) D)) (((eq pname) B_5) C_3))))) of role axiom named fact_164_doubleton__eq__iff
% A new axiom: (forall (A_11:pname) (B_5:pname) (C_3:pname) (D:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_11) ((insert_pname B_5) bot_bot_pname_o))) ((insert_pname C_3) ((insert_pname D) bot_bot_pname_o)))) ((or ((and (((eq pname) A_11) C_3)) (((eq pname) B_5) D))) ((and (((eq pname) A_11) D)) (((eq pname) B_5) C_3)))))
% FOF formula (forall (Y_2:hoare_669141180iple_a) (A_10:(hoare_669141180iple_a->Prop)) (X_4:hoare_669141180iple_a), ((iff (((insert175534902iple_a Y_2) A_10) X_4)) ((or (((eq hoare_669141180iple_a) Y_2) X_4)) (A_10 X_4)))) of role axiom named fact_165_insert__code
% A new axiom: (forall (Y_2:hoare_669141180iple_a) (A_10:(hoare_669141180iple_a->Prop)) (X_4:hoare_669141180iple_a), ((iff (((insert175534902iple_a Y_2) A_10) X_4)) ((or (((eq hoare_669141180iple_a) Y_2) X_4)) (A_10 X_4))))
% FOF formula (forall (Y_2:pname) (A_10:(pname->Prop)) (X_4:pname), ((iff (((insert_pname Y_2) A_10) X_4)) ((or (((eq pname) Y_2) X_4)) (A_10 X_4)))) of role axiom named fact_166_insert__code
% A new axiom: (forall (Y_2:pname) (A_10:(pname->Prop)) (X_4:pname), ((iff (((insert_pname Y_2) A_10) X_4)) ((or (((eq pname) Y_2) X_4)) (A_10 X_4))))
% FOF formula (forall (X:hoare_669141180iple_a) (Xa:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X) Xa)) (collec1717965009iple_a (fun (Y_1:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) Y_1) X)) ((member1016246415iple_a Y_1) Xa)))))) of role axiom named fact_167_insert__compr__raw
% A new axiom: (forall (X:hoare_669141180iple_a) (Xa:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X) Xa)) (collec1717965009iple_a (fun (Y_1:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) Y_1) X)) ((member1016246415iple_a Y_1) Xa))))))
% FOF formula (forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y_1:pname)=> ((or (((eq pname) Y_1) X)) ((member_pname Y_1) Xa)))))) of role axiom named fact_168_insert__compr__raw
% A new axiom: (forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y_1:pname)=> ((or (((eq pname) Y_1) X)) ((member_pname Y_1) Xa))))))
% FOF formula (forall (B_4:(hoare_669141180iple_a->Prop)) (X_3:hoare_669141180iple_a) (A_9:(hoare_669141180iple_a->Prop)), ((((member1016246415iple_a X_3) A_9)->False)->((((member1016246415iple_a X_3) B_4)->False)->((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_3) A_9)) ((insert175534902iple_a X_3) B_4))) (((eq (hoare_669141180iple_a->Prop)) A_9) B_4))))) of role axiom named fact_169_insert__ident
% A new axiom: (forall (B_4:(hoare_669141180iple_a->Prop)) (X_3:hoare_669141180iple_a) (A_9:(hoare_669141180iple_a->Prop)), ((((member1016246415iple_a X_3) A_9)->False)->((((member1016246415iple_a X_3) B_4)->False)->((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_3) A_9)) ((insert175534902iple_a X_3) B_4))) (((eq (hoare_669141180iple_a->Prop)) A_9) B_4)))))
% FOF formula (forall (B_4:(pname->Prop)) (X_3:pname) (A_9:(pname->Prop)), ((((member_pname X_3) A_9)->False)->((((member_pname X_3) B_4)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_3) A_9)) ((insert_pname X_3) B_4))) (((eq (pname->Prop)) A_9) B_4))))) of role axiom named fact_170_insert__ident
% A new axiom: (forall (B_4:(pname->Prop)) (X_3:pname) (A_9:(pname->Prop)), ((((member_pname X_3) A_9)->False)->((((member_pname X_3) B_4)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_3) A_9)) ((insert_pname X_3) B_4))) (((eq (pname->Prop)) A_9) B_4)))))
% FOF formula (forall (A_8:hoare_669141180iple_a) (A_7:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) A_7) bot_bo280939947le_a_o)->(((member1016246415iple_a A_8) A_7)->False))) of role axiom named fact_171_equals0D
% A new axiom: (forall (A_8:hoare_669141180iple_a) (A_7:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) A_7) bot_bo280939947le_a_o)->(((member1016246415iple_a A_8) A_7)->False)))
% FOF formula (forall (A_8:pname) (A_7:(pname->Prop)), ((((eq (pname->Prop)) A_7) bot_bot_pname_o)->(((member_pname A_8) A_7)->False))) of role axiom named fact_172_equals0D
% A new axiom: (forall (A_8:pname) (A_7:(pname->Prop)), ((((eq (pname->Prop)) A_7) bot_bot_pname_o)->(((member_pname A_8) A_7)->False)))
% FOF formula (forall (B_3:hoare_669141180iple_a) (A_6:hoare_669141180iple_a) (B_2:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_6) B_2)->((member1016246415iple_a A_6) ((insert175534902iple_a B_3) B_2)))) of role axiom named fact_173_insertI2
% A new axiom: (forall (B_3:hoare_669141180iple_a) (A_6:hoare_669141180iple_a) (B_2:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_6) B_2)->((member1016246415iple_a A_6) ((insert175534902iple_a B_3) B_2))))
% FOF formula (forall (B_3:pname) (A_6:pname) (B_2:(pname->Prop)), (((member_pname A_6) B_2)->((member_pname A_6) ((insert_pname B_3) B_2)))) of role axiom named fact_174_insertI2
% A new axiom: (forall (B_3:pname) (A_6:pname) (B_2:(pname->Prop)), (((member_pname A_6) B_2)->((member_pname A_6) ((insert_pname B_3) B_2))))
% FOF formula (forall (A_5:hoare_669141180iple_a) (A_4:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_5) A_4)->(((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_5) A_4)) A_4))) of role axiom named fact_175_insert__absorb
% A new axiom: (forall (A_5:hoare_669141180iple_a) (A_4:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_5) A_4)->(((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_5) A_4)) A_4)))
% FOF formula (forall (A_5:pname) (A_4:(pname->Prop)), (((member_pname A_5) A_4)->(((eq (pname->Prop)) ((insert_pname A_5) A_4)) A_4))) of role axiom named fact_176_insert__absorb
% A new axiom: (forall (A_5:pname) (A_4:(pname->Prop)), (((member_pname A_5) A_4)->(((eq (pname->Prop)) ((insert_pname A_5) A_4)) A_4)))
% FOF formula (forall (Ts_1:(hoare_669141180iple_a->Prop)) (G_1:(hoare_669141180iple_a->Prop)) (T_2:hoare_669141180iple_a), (((hoare_2128652938rivs_a G_1) ((insert175534902iple_a T_2) bot_bo280939947le_a_o))->(((hoare_2128652938rivs_a G_1) Ts_1)->((hoare_2128652938rivs_a G_1) ((insert175534902iple_a T_2) Ts_1))))) of role axiom named fact_177_hoare__derivs_Oinsert
% A new axiom: (forall (Ts_1:(hoare_669141180iple_a->Prop)) (G_1:(hoare_669141180iple_a->Prop)) (T_2:hoare_669141180iple_a), (((hoare_2128652938rivs_a G_1) ((insert175534902iple_a T_2) bot_bo280939947le_a_o))->(((hoare_2128652938rivs_a G_1) Ts_1)->((hoare_2128652938rivs_a G_1) ((insert175534902iple_a T_2) Ts_1)))))
% FOF formula (forall (B_1:hoare_669141180iple_a) (A_3:hoare_669141180iple_a), (((member1016246415iple_a B_1) ((insert175534902iple_a A_3) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) B_1) A_3))) of role axiom named fact_178_singletonE
% A new axiom: (forall (B_1:hoare_669141180iple_a) (A_3:hoare_669141180iple_a), (((member1016246415iple_a B_1) ((insert175534902iple_a A_3) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) B_1) A_3)))
% FOF formula (forall (B_1:pname) (A_3:pname), (((member_pname B_1) ((insert_pname A_3) bot_bot_pname_o))->(((eq pname) B_1) A_3))) of role axiom named fact_179_singletonE
% A new axiom: (forall (B_1:pname) (A_3:pname), (((member_pname B_1) ((insert_pname A_3) bot_bot_pname_o))->(((eq pname) B_1) A_3)))
% FOF formula (forall (G:(hoare_669141180iple_a->Prop)) (T_1:hoare_669141180iple_a) (Ts:(hoare_669141180iple_a->Prop)), (((hoare_2128652938rivs_a G) ((insert175534902iple_a T_1) Ts))->((and ((hoare_2128652938rivs_a G) ((insert175534902iple_a T_1) bot_bo280939947le_a_o))) ((hoare_2128652938rivs_a G) Ts)))) of role axiom named fact_180_derivs__insertD
% A new axiom: (forall (G:(hoare_669141180iple_a->Prop)) (T_1:hoare_669141180iple_a) (Ts:(hoare_669141180iple_a->Prop)), (((hoare_2128652938rivs_a G) ((insert175534902iple_a T_1) Ts))->((and ((hoare_2128652938rivs_a G) ((insert175534902iple_a T_1) bot_bo280939947le_a_o))) ((hoare_2128652938rivs_a G) Ts))))
% FOF formula (forall (A_2:hoare_669141180iple_a) (B:hoare_669141180iple_a), ((((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_2) bot_bo280939947le_a_o)) ((insert175534902iple_a B) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) A_2) B))) of role axiom named fact_181_singleton__inject
% A new axiom: (forall (A_2:hoare_669141180iple_a) (B:hoare_669141180iple_a), ((((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_2) bot_bo280939947le_a_o)) ((insert175534902iple_a B) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) A_2) B)))
% FOF formula (forall (A_2:pname) (B:pname), ((((eq (pname->Prop)) ((insert_pname A_2) bot_bot_pname_o)) ((insert_pname B) bot_bot_pname_o))->(((eq pname) A_2) B))) of role axiom named fact_182_singleton__inject
% A new axiom: (forall (A_2:pname) (B:pname), ((((eq (pname->Prop)) ((insert_pname A_2) bot_bot_pname_o)) ((insert_pname B) bot_bot_pname_o))->(((eq pname) A_2) B)))
% FOF formula (forall (U:state) (C_2:com) (S:state) (T:state), ((((evalc C_2) S) T)->((((evalc C_2) S) U)->(((eq state) U) T)))) of role axiom named fact_183_com__det
% A new axiom: (forall (U:state) (C_2:com) (S:state) (T:state), ((((evalc C_2) S) T)->((((evalc C_2) S) U)->(((eq state) U) T))))
% FOF formula (forall (C_1:pname) (A_1:(hoare_669141180iple_a->Prop)), ((and ((((eq (hoare_669141180iple_a->Prop)) A_1) bot_bo280939947le_a_o)->(((eq (pname->Prop)) ((image_225123213_pname (fun (X:hoare_669141180iple_a)=> C_1)) A_1)) bot_bot_pname_o))) ((not (((eq (hoare_669141180iple_a->Prop)) A_1) bot_bo280939947le_a_o))->(((eq (pname->Prop)) ((image_225123213_pname (fun (X:hoare_669141180iple_a)=> C_1)) A_1)) ((insert_pname C_1) bot_bot_pname_o))))) of role axiom named fact_184_image__constant__conv
% A new axiom: (forall (C_1:pname) (A_1:(hoare_669141180iple_a->Prop)), ((and ((((eq (hoare_669141180iple_a->Prop)) A_1) bot_bo280939947le_a_o)->(((eq (pname->Prop)) ((image_225123213_pname (fun (X:hoare_669141180iple_a)=> C_1)) A_1)) bot_bot_pname_o))) ((not (((eq (hoare_669141180iple_a->Prop)) A_1) bot_bo280939947le_a_o))->(((eq (pname->Prop)) ((image_225123213_pname (fun (X:hoare_669141180iple_a)=> C_1)) A_1)) ((insert_pname C_1) bot_bot_pname_o)))))
% FOF formula (forall (C_1:hoare_669141180iple_a) (A_1:(pname->Prop)), ((and ((((eq (pname->Prop)) A_1) bot_bot_pname_o)->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a (fun (X:pname)=> C_1)) A_1)) bot_bo280939947le_a_o))) ((not (((eq (pname->Prop)) A_1) bot_bot_pname_o))->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a (fun (X:pname)=> C_1)) A_1)) ((insert175534902iple_a C_1) bot_bo280939947le_a_o))))) of role axiom named fact_185_image__constant__conv
% A new axiom: (forall (C_1:hoare_669141180iple_a) (A_1:(pname->Prop)), ((and ((((eq (pname->Prop)) A_1) bot_bot_pname_o)->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a (fun (X:pname)=> C_1)) A_1)) bot_bo280939947le_a_o))) ((not (((eq (pname->Prop)) A_1) bot_bot_pname_o))->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a (fun (X:pname)=> C_1)) A_1)) ((insert175534902iple_a C_1) bot_bo280939947le_a_o)))))
% FOF formula (forall (C:pname) (X_2:hoare_669141180iple_a) (A:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_2) A)->(((eq (pname->Prop)) ((image_225123213_pname (fun (X:hoare_669141180iple_a)=> C)) A)) ((insert_pname C) bot_bot_pname_o)))) of role axiom named fact_186_image__constant
% A new axiom: (forall (C:pname) (X_2:hoare_669141180iple_a) (A:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_2) A)->(((eq (pname->Prop)) ((image_225123213_pname (fun (X:hoare_669141180iple_a)=> C)) A)) ((insert_pname C) bot_bot_pname_o))))
% FOF formula (forall (C:hoare_669141180iple_a) (X_2:hoare_669141180iple_a) (A:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_2) A)->(((eq (hoare_669141180iple_a->Prop)) ((image_1033305477iple_a (fun (X:hoare_669141180iple_a)=> C)) A)) ((insert175534902iple_a C) bot_bo280939947le_a_o)))) of role axiom named fact_187_image__constant
% A new axiom: (forall (C:hoare_669141180iple_a) (X_2:hoare_669141180iple_a) (A:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_2) A)->(((eq (hoare_669141180iple_a->Prop)) ((image_1033305477iple_a (fun (X:hoare_669141180iple_a)=> C)) A)) ((insert175534902iple_a C) bot_bo280939947le_a_o))))
% FOF formula (forall (C:pname) (X_2:pname) (A:(pname->Prop)), (((member_pname X_2) A)->(((eq (pname->Prop)) ((image_pname_pname (fun (X:pname)=> C)) A)) ((insert_pname C) bot_bot_pname_o)))) of role axiom named fact_188_image__constant
% A new axiom: (forall (C:pname) (X_2:pname) (A:(pname->Prop)), (((member_pname X_2) A)->(((eq (pname->Prop)) ((image_pname_pname (fun (X:pname)=> C)) A)) ((insert_pname C) bot_bot_pname_o))))
% FOF formula (forall (C:hoare_669141180iple_a) (X_2:pname) (A:(pname->Prop)), (((member_pname X_2) A)->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a (fun (X:pname)=> C)) A)) ((insert175534902iple_a C) bot_bo280939947le_a_o)))) of role axiom named fact_189_image__constant
% A new axiom: (forall (C:hoare_669141180iple_a) (X_2:pname) (A:(pname->Prop)), (((member_pname X_2) A)->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a (fun (X:pname)=> C)) A)) ((insert175534902iple_a C) bot_bo280939947le_a_o))))
% 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:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (((fequal182287803iple_a X_1) Y)->False)) (((eq hoare_669141180iple_a) X_1) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_
% A new axiom: (forall (X_1:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (((fequal182287803iple_a X_1) Y)->False)) (((eq hoare_669141180iple_a) X_1) Y)))
% FOF formula (forall (X_1:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (not (((eq hoare_669141180iple_a) X_1) Y))) ((fequal182287803iple_a X_1) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_
% A new axiom: (forall (X_1:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (not (((eq hoare_669141180iple_a) X_1) Y))) ((fequal182287803iple_a X_1) Y)))
% FOF formula (forall (N:nat), ((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((semila1689936973le_a_o g) ((image_957198589iple_a (fun (Pn:pname)=> (((hoare_1295064928iple_a (p Pn)) (body Pn)) (q Pn)))) procs)))->((hoare_2082685510alid_a N) X)))->(forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((image_957198589iple_a (fun (Pn:pname)=> (((hoare_1295064928iple_a (p Pn)) (the_com (body_1 Pn))) (q Pn)))) procs))->((hoare_2082685510alid_a N) X))))) of role hypothesis named conj_0
% A new axiom: (forall (N:nat), ((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((semila1689936973le_a_o g) ((image_957198589iple_a (fun (Pn:pname)=> (((hoare_1295064928iple_a (p Pn)) (body Pn)) (q Pn)))) procs)))->((hoare_2082685510alid_a N) X)))->(forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((image_957198589iple_a (fun (Pn:pname)=> (((hoare_1295064928iple_a (p Pn)) (the_com (body_1 Pn))) (q Pn)))) procs))->((hoare_2082685510alid_a N) X)))))
% FOF formula ((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) g)->((hoare_2082685510alid_a n) X)))->(forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((image_957198589iple_a (fun (Pn:pname)=> (((hoare_1295064928iple_a (p Pn)) (body Pn)) (q Pn)))) procs))->((hoare_2082685510alid_a n) X)))) of role conjecture named conj_1
% Conjecture to prove = ((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) g)->((hoare_2082685510alid_a n) X)))->(forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((image_957198589iple_a (fun (Pn:pname)=> (((hoare_1295064928iple_a (p Pn)) (body Pn)) (q Pn)))) procs))->((hoare_2082685510alid_a n) X)))):Prop
% Parameter x_a_DUMMY:x_a.
% Parameter com_DUMMY:com.
% Parameter pname_DUMMY:pname.
% Parameter state_DUMMY:state.
% Parameter hoare_669141180iple_a_DUMMY:hoare_669141180iple_a.
% Parameter option_com_DUMMY:option_com.
% We need to prove ['((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) g)->((hoare_2082685510alid_a n) X)))->(forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((image_957198589iple_a (fun (Pn:pname)=> (((hoare_1295064928iple_a (p Pn)) (body Pn)) (q Pn)))) procs))->((hoare_2082685510alid_a n) X))))']
% Parameter x_a:Type.
% Parameter com:Type.
% Parameter pname:Type.
% Parameter state:Type.
% Parameter hoare_669141180iple_a:Type.
% Parameter nat:Type.
% Parameter option_com:Type.
% Parameter body_1:(pname->option_com).
% Parameter body:(pname->com).
% Parameter zero_zero_nat:nat.
% Parameter hoare_2128652938rivs_a:((hoare_669141180iple_a->Prop)->((hoare_669141180iple_a->Prop)->Prop)).
% Parameter hoare_319002636lids_a:((hoare_669141180iple_a->Prop)->((hoare_669141180iple_a->Prop)->Prop)).
% Parameter hoare_1295064928iple_a:((x_a->(state->Prop))->(com->((x_a->(state->Prop))->hoare_669141180iple_a))).
% Parameter hoare_2082685510alid_a:(nat->(hoare_669141180iple_a->Prop)).
% Parameter semila1780557381name_o:((pname->Prop)->((pname->Prop)->(pname->Prop))).
% Parameter semila1689936973le_a_o:((hoare_669141180iple_a->Prop)->((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop))).
% Parameter semila10642723_sup_o:(Prop->(Prop->Prop)).
% Parameter suc:(nat->nat).
% Parameter evalc:(com->(state->(state->Prop))).
% Parameter the_com:(option_com->com).
% Parameter bot_bot_pname_o:(pname->Prop).
% Parameter bot_bo280939947le_a_o:(hoare_669141180iple_a->Prop).
% Parameter collect_pname:((pname->Prop)->(pname->Prop)).
% Parameter collec1717965009iple_a:((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop)).
% Parameter image_pname_pname:((pname->pname)->((pname->Prop)->(pname->Prop))).
% Parameter image_957198589iple_a:((pname->hoare_669141180iple_a)->((pname->Prop)->(hoare_669141180iple_a->Prop))).
% Parameter image_225123213_pname:((hoare_669141180iple_a->pname)->((hoare_669141180iple_a->Prop)->(pname->Prop))).
% Parameter image_1033305477iple_a:((hoare_669141180iple_a->hoare_669141180iple_a)->((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop))).
% Parameter insert_pname:(pname->((pname->Prop)->(pname->Prop))).
% Parameter insert175534902iple_a:(hoare_669141180iple_a->((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop))).
% Parameter fequal_pname:(pname->(pname->Prop)).
% Parameter fequal182287803iple_a:(hoare_669141180iple_a->(hoare_669141180iple_a->Prop)).
% Parameter member_pname:(pname->((pname->Prop)->Prop)).
% Parameter member1016246415iple_a:(hoare_669141180iple_a->((hoare_669141180iple_a->Prop)->Prop)).
% Parameter g:(hoare_669141180iple_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_2:(x_a->(state->Prop))) (Com_2:com) (Fun2_2:(x_a->(state->Prop))) (Fun1_1:(x_a->(state->Prop))) (Com_1:com) (Fun2_1:(x_a->(state->Prop))), ((iff (((eq hoare_669141180iple_a) (((hoare_1295064928iple_a Fun1_2) Com_2) Fun2_2)) (((hoare_1295064928iple_a Fun1_1) Com_1) Fun2_1))) ((and ((and (((eq (x_a->(state->Prop))) Fun1_2) Fun1_1)) (((eq com) Com_2) Com_1))) (((eq (x_a->(state->Prop))) Fun2_2) Fun2_1)))).
% Axiom fact_1_hoare__valids__def:(forall (G_10:(hoare_669141180iple_a->Prop)) (Ts_3:(hoare_669141180iple_a->Prop)), ((iff ((hoare_319002636lids_a G_10) Ts_3)) (forall (N:nat), ((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) G_10)->((hoare_2082685510alid_a N) X)))->(forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) Ts_3)->((hoare_2082685510alid_a N) X))))))).
% Axiom fact_2_hoare__derivs_OBody:(forall (G_9:(hoare_669141180iple_a->Prop)) (P_14:(pname->(x_a->(state->Prop)))) (Q_4:(pname->(x_a->(state->Prop)))) (Procs_1:(pname->Prop)), (((hoare_2128652938rivs_a ((semila1689936973le_a_o G_9) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_14 P_9)) (body P_9)) (Q_4 P_9)))) Procs_1))) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_14 P_9)) (the_com (body_1 P_9))) (Q_4 P_9)))) Procs_1))->((hoare_2128652938rivs_a G_9) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_14 P_9)) (body P_9)) (Q_4 P_9)))) Procs_1)))).
% Axiom fact_3_UnE:(forall (C_13:hoare_669141180iple_a) (A_65:(hoare_669141180iple_a->Prop)) (B_36:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a C_13) ((semila1689936973le_a_o A_65) B_36))->((((member1016246415iple_a C_13) A_65)->False)->((member1016246415iple_a C_13) B_36)))).
% Axiom fact_4_UnE:(forall (C_13:pname) (A_65:(pname->Prop)) (B_36:(pname->Prop)), (((member_pname C_13) ((semila1780557381name_o A_65) B_36))->((((member_pname C_13) A_65)->False)->((member_pname C_13) B_36)))).
% Axiom fact_5_sup1E:(forall (A_64:(hoare_669141180iple_a->Prop)) (B_35:(hoare_669141180iple_a->Prop)) (X_24:hoare_669141180iple_a), ((((semila1689936973le_a_o A_64) B_35) X_24)->(((A_64 X_24)->False)->(B_35 X_24)))).
% Axiom fact_6_sup1E:(forall (A_64:(pname->Prop)) (B_35:(pname->Prop)) (X_24:pname), ((((semila1780557381name_o A_64) B_35) X_24)->(((A_64 X_24)->False)->(B_35 X_24)))).
% Axiom fact_7_sup1CI:(forall (A_63:(hoare_669141180iple_a->Prop)) (B_34:(hoare_669141180iple_a->Prop)) (X_23:hoare_669141180iple_a), ((((B_34 X_23)->False)->(A_63 X_23))->(((semila1689936973le_a_o A_63) B_34) X_23))).
% Axiom fact_8_sup1CI:(forall (A_63:(pname->Prop)) (B_34:(pname->Prop)) (X_23:pname), ((((B_34 X_23)->False)->(A_63 X_23))->(((semila1780557381name_o A_63) B_34) X_23))).
% Axiom fact_9_UnCI:(forall (A_62:(hoare_669141180iple_a->Prop)) (C_12:hoare_669141180iple_a) (B_33:(hoare_669141180iple_a->Prop)), (((((member1016246415iple_a C_12) B_33)->False)->((member1016246415iple_a C_12) A_62))->((member1016246415iple_a C_12) ((semila1689936973le_a_o A_62) B_33)))).
% Axiom fact_10_UnCI:(forall (A_62:(pname->Prop)) (C_12:pname) (B_33:(pname->Prop)), (((((member_pname C_12) B_33)->False)->((member_pname C_12) A_62))->((member_pname C_12) ((semila1780557381name_o A_62) B_33)))).
% Axiom fact_11_image__eqI:(forall (A_61:(pname->Prop)) (B_32:hoare_669141180iple_a) (F_9:(pname->hoare_669141180iple_a)) (X_22:pname), ((((eq hoare_669141180iple_a) B_32) (F_9 X_22))->(((member_pname X_22) A_61)->((member1016246415iple_a B_32) ((image_957198589iple_a F_9) A_61))))).
% Axiom fact_12_image__eqI:(forall (A_61:(hoare_669141180iple_a->Prop)) (B_32:pname) (F_9:(hoare_669141180iple_a->pname)) (X_22:hoare_669141180iple_a), ((((eq pname) B_32) (F_9 X_22))->(((member1016246415iple_a X_22) A_61)->((member_pname B_32) ((image_225123213_pname F_9) A_61))))).
% Axiom fact_13_image__Un:(forall (F_8:(pname->hoare_669141180iple_a)) (A_60:(pname->Prop)) (B_31:(pname->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a F_8) ((semila1780557381name_o A_60) B_31))) ((semila1689936973le_a_o ((image_957198589iple_a F_8) A_60)) ((image_957198589iple_a F_8) B_31)))).
% Axiom fact_14_image__Un:(forall (F_8:(hoare_669141180iple_a->pname)) (A_60:(hoare_669141180iple_a->Prop)) (B_31:(hoare_669141180iple_a->Prop)), (((eq (pname->Prop)) ((image_225123213_pname F_8) ((semila1689936973le_a_o A_60) B_31))) ((semila1780557381name_o ((image_225123213_pname F_8) A_60)) ((image_225123213_pname F_8) B_31)))).
% Axiom fact_15_sup__fun__def:(forall (F_7:(hoare_669141180iple_a->Prop)) (G_8:(hoare_669141180iple_a->Prop)) (X:hoare_669141180iple_a), ((iff (((semila1689936973le_a_o F_7) G_8) X)) ((semila10642723_sup_o (F_7 X)) (G_8 X)))).
% Axiom fact_16_sup__fun__def:(forall (F_7:(pname->Prop)) (G_8:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o F_7) G_8) X)) ((semila10642723_sup_o (F_7 X)) (G_8 X)))).
% Axiom fact_17_sup__apply:(forall (F_6:(hoare_669141180iple_a->Prop)) (G_7:(hoare_669141180iple_a->Prop)) (X_21:hoare_669141180iple_a), ((iff (((semila1689936973le_a_o F_6) G_7) X_21)) ((semila10642723_sup_o (F_6 X_21)) (G_7 X_21)))).
% Axiom fact_18_sup__apply:(forall (F_6:(pname->Prop)) (G_7:(pname->Prop)) (X_21:pname), ((iff (((semila1780557381name_o F_6) G_7) X_21)) ((semila10642723_sup_o (F_6 X_21)) (G_7 X_21)))).
% Axiom fact_19_cut:(forall (G_6:(hoare_669141180iple_a->Prop)) (G_5:(hoare_669141180iple_a->Prop)) (Ts_2:(hoare_669141180iple_a->Prop)), (((hoare_2128652938rivs_a G_5) Ts_2)->(((hoare_2128652938rivs_a G_6) G_5)->((hoare_2128652938rivs_a G_6) Ts_2)))).
% Axiom fact_20_sup__assoc:(forall (X_20:(hoare_669141180iple_a->Prop)) (Y_12:(hoare_669141180iple_a->Prop)) (Z_4:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o X_20) Y_12)) Z_4)) ((semila1689936973le_a_o X_20) ((semila1689936973le_a_o Y_12) Z_4)))).
% Axiom fact_21_sup__assoc:(forall (X_20:(pname->Prop)) (Y_12:(pname->Prop)) (Z_4:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_20) Y_12)) Z_4)) ((semila1780557381name_o X_20) ((semila1780557381name_o Y_12) Z_4)))).
% Axiom fact_22_sup__assoc:(forall (X_20:Prop) (Y_12:Prop) (Z_4:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_20) Y_12)) Z_4)) ((semila10642723_sup_o X_20) ((semila10642723_sup_o Y_12) Z_4)))).
% Axiom fact_23_inf__sup__aci_I6_J:(forall (X_19:(hoare_669141180iple_a->Prop)) (Y_11:(hoare_669141180iple_a->Prop)) (Z_3:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o X_19) Y_11)) Z_3)) ((semila1689936973le_a_o X_19) ((semila1689936973le_a_o Y_11) Z_3)))).
% Axiom fact_24_inf__sup__aci_I6_J:(forall (X_19:(pname->Prop)) (Y_11:(pname->Prop)) (Z_3:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o X_19) Y_11)) Z_3)) ((semila1780557381name_o X_19) ((semila1780557381name_o Y_11) Z_3)))).
% Axiom fact_25_inf__sup__aci_I6_J:(forall (X_19:Prop) (Y_11:Prop) (Z_3:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o X_19) Y_11)) Z_3)) ((semila10642723_sup_o X_19) ((semila10642723_sup_o Y_11) Z_3)))).
% Axiom fact_26_sup_Oassoc:(forall (A_59:(hoare_669141180iple_a->Prop)) (B_30:(hoare_669141180iple_a->Prop)) (C_11:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o A_59) B_30)) C_11)) ((semila1689936973le_a_o A_59) ((semila1689936973le_a_o B_30) C_11)))).
% Axiom fact_27_sup_Oassoc:(forall (A_59:(pname->Prop)) (B_30:(pname->Prop)) (C_11:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_59) B_30)) C_11)) ((semila1780557381name_o A_59) ((semila1780557381name_o B_30) C_11)))).
% Axiom fact_28_sup_Oassoc:(forall (A_59:Prop) (B_30:Prop) (C_11:Prop), ((iff ((semila10642723_sup_o ((semila10642723_sup_o A_59) B_30)) C_11)) ((semila10642723_sup_o A_59) ((semila10642723_sup_o B_30) C_11)))).
% Axiom fact_29_sup__left__commute:(forall (X_18:(hoare_669141180iple_a->Prop)) (Y_10:(hoare_669141180iple_a->Prop)) (Z_2:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_18) ((semila1689936973le_a_o Y_10) Z_2))) ((semila1689936973le_a_o Y_10) ((semila1689936973le_a_o X_18) Z_2)))).
% Axiom fact_30_sup__left__commute:(forall (X_18:(pname->Prop)) (Y_10:(pname->Prop)) (Z_2:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_18) ((semila1780557381name_o Y_10) Z_2))) ((semila1780557381name_o Y_10) ((semila1780557381name_o X_18) Z_2)))).
% Axiom fact_31_sup__left__commute:(forall (X_18:Prop) (Y_10:Prop) (Z_2:Prop), ((iff ((semila10642723_sup_o X_18) ((semila10642723_sup_o Y_10) Z_2))) ((semila10642723_sup_o Y_10) ((semila10642723_sup_o X_18) Z_2)))).
% Axiom fact_32_inf__sup__aci_I7_J:(forall (X_17:(hoare_669141180iple_a->Prop)) (Y_9:(hoare_669141180iple_a->Prop)) (Z_1:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_17) ((semila1689936973le_a_o Y_9) Z_1))) ((semila1689936973le_a_o Y_9) ((semila1689936973le_a_o X_17) Z_1)))).
% Axiom fact_33_inf__sup__aci_I7_J:(forall (X_17:(pname->Prop)) (Y_9:(pname->Prop)) (Z_1:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_17) ((semila1780557381name_o Y_9) Z_1))) ((semila1780557381name_o Y_9) ((semila1780557381name_o X_17) Z_1)))).
% Axiom fact_34_inf__sup__aci_I7_J:(forall (X_17:Prop) (Y_9:Prop) (Z_1:Prop), ((iff ((semila10642723_sup_o X_17) ((semila10642723_sup_o Y_9) Z_1))) ((semila10642723_sup_o Y_9) ((semila10642723_sup_o X_17) Z_1)))).
% Axiom fact_35_sup_Oleft__commute:(forall (B_29:(hoare_669141180iple_a->Prop)) (A_58:(hoare_669141180iple_a->Prop)) (C_10:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o B_29) ((semila1689936973le_a_o A_58) C_10))) ((semila1689936973le_a_o A_58) ((semila1689936973le_a_o B_29) C_10)))).
% Axiom fact_36_sup_Oleft__commute:(forall (B_29:(pname->Prop)) (A_58:(pname->Prop)) (C_10:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o B_29) ((semila1780557381name_o A_58) C_10))) ((semila1780557381name_o A_58) ((semila1780557381name_o B_29) C_10)))).
% Axiom fact_37_sup_Oleft__commute:(forall (B_29:Prop) (A_58:Prop) (C_10:Prop), ((iff ((semila10642723_sup_o B_29) ((semila10642723_sup_o A_58) C_10))) ((semila10642723_sup_o A_58) ((semila10642723_sup_o B_29) C_10)))).
% Axiom fact_38_sup__left__idem:(forall (X_16:(hoare_669141180iple_a->Prop)) (Y_8:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_16) ((semila1689936973le_a_o X_16) Y_8))) ((semila1689936973le_a_o X_16) Y_8))).
% Axiom fact_39_sup__left__idem:(forall (X_16:(pname->Prop)) (Y_8:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_16) ((semila1780557381name_o X_16) Y_8))) ((semila1780557381name_o X_16) Y_8))).
% Axiom fact_40_sup__left__idem:(forall (X_16:Prop) (Y_8:Prop), ((iff ((semila10642723_sup_o X_16) ((semila10642723_sup_o X_16) Y_8))) ((semila10642723_sup_o X_16) Y_8))).
% Axiom fact_41_inf__sup__aci_I8_J:(forall (X_15:(hoare_669141180iple_a->Prop)) (Y_7:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_15) ((semila1689936973le_a_o X_15) Y_7))) ((semila1689936973le_a_o X_15) Y_7))).
% Axiom fact_42_inf__sup__aci_I8_J:(forall (X_15:(pname->Prop)) (Y_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_15) ((semila1780557381name_o X_15) Y_7))) ((semila1780557381name_o X_15) Y_7))).
% Axiom fact_43_inf__sup__aci_I8_J:(forall (X_15:Prop) (Y_7:Prop), ((iff ((semila10642723_sup_o X_15) ((semila10642723_sup_o X_15) Y_7))) ((semila10642723_sup_o X_15) Y_7))).
% Axiom fact_44_sup_Oleft__idem:(forall (A_57:(hoare_669141180iple_a->Prop)) (B_28:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_57) ((semila1689936973le_a_o A_57) B_28))) ((semila1689936973le_a_o A_57) B_28))).
% Axiom fact_45_sup_Oleft__idem:(forall (A_57:(pname->Prop)) (B_28:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_57) ((semila1780557381name_o A_57) B_28))) ((semila1780557381name_o A_57) B_28))).
% Axiom fact_46_sup_Oleft__idem:(forall (A_57:Prop) (B_28:Prop), ((iff ((semila10642723_sup_o A_57) ((semila10642723_sup_o A_57) B_28))) ((semila10642723_sup_o A_57) B_28))).
% Axiom fact_47_sup__commute:(forall (X_14:(hoare_669141180iple_a->Prop)) (Y_6:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_14) Y_6)) ((semila1689936973le_a_o Y_6) X_14))).
% Axiom fact_48_sup__commute:(forall (X_14:(pname->Prop)) (Y_6:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_14) Y_6)) ((semila1780557381name_o Y_6) X_14))).
% Axiom fact_49_sup__commute:(forall (X_14:Prop) (Y_6:Prop), ((iff ((semila10642723_sup_o X_14) Y_6)) ((semila10642723_sup_o Y_6) X_14))).
% Axiom fact_50_inf__sup__aci_I5_J:(forall (X_13:(hoare_669141180iple_a->Prop)) (Y_5:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_13) Y_5)) ((semila1689936973le_a_o Y_5) X_13))).
% Axiom fact_51_inf__sup__aci_I5_J:(forall (X_13:(pname->Prop)) (Y_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_13) Y_5)) ((semila1780557381name_o Y_5) X_13))).
% Axiom fact_52_inf__sup__aci_I5_J:(forall (X_13:Prop) (Y_5:Prop), ((iff ((semila10642723_sup_o X_13) Y_5)) ((semila10642723_sup_o Y_5) X_13))).
% Axiom fact_53_sup_Ocommute:(forall (A_56:(hoare_669141180iple_a->Prop)) (B_27:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_56) B_27)) ((semila1689936973le_a_o B_27) A_56))).
% Axiom fact_54_sup_Ocommute:(forall (A_56:(pname->Prop)) (B_27:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_56) B_27)) ((semila1780557381name_o B_27) A_56))).
% Axiom fact_55_sup_Ocommute:(forall (A_56:Prop) (B_27:Prop), ((iff ((semila10642723_sup_o A_56) B_27)) ((semila10642723_sup_o B_27) A_56))).
% Axiom fact_56_sup__idem:(forall (X_12:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o X_12) X_12)) X_12)).
% Axiom fact_57_sup__idem:(forall (X_12:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o X_12) X_12)) X_12)).
% Axiom fact_58_sup__idem:(forall (X_12:Prop), ((iff ((semila10642723_sup_o X_12) X_12)) X_12)).
% Axiom fact_59_sup_Oidem:(forall (A_55:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_55) A_55)) A_55)).
% Axiom fact_60_sup_Oidem:(forall (A_55:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_55) A_55)) A_55)).
% Axiom fact_61_sup_Oidem:(forall (A_55:Prop), ((iff ((semila10642723_sup_o A_55) A_55)) A_55)).
% Axiom fact_62_rev__image__eqI:(forall (B_26:pname) (F_5:(hoare_669141180iple_a->pname)) (X_11:hoare_669141180iple_a) (A_54:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_11) A_54)->((((eq pname) B_26) (F_5 X_11))->((member_pname B_26) ((image_225123213_pname F_5) A_54))))).
% Axiom fact_63_rev__image__eqI:(forall (B_26:hoare_669141180iple_a) (F_5:(pname->hoare_669141180iple_a)) (X_11:pname) (A_54:(pname->Prop)), (((member_pname X_11) A_54)->((((eq hoare_669141180iple_a) B_26) (F_5 X_11))->((member1016246415iple_a B_26) ((image_957198589iple_a F_5) A_54))))).
% Axiom fact_64_imageI:(forall (F_4:(hoare_669141180iple_a->pname)) (X_10:hoare_669141180iple_a) (A_53:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_10) A_53)->((member_pname (F_4 X_10)) ((image_225123213_pname F_4) A_53)))).
% Axiom fact_65_imageI:(forall (F_4:(pname->hoare_669141180iple_a)) (X_10:pname) (A_53:(pname->Prop)), (((member_pname X_10) A_53)->((member1016246415iple_a (F_4 X_10)) ((image_957198589iple_a F_4) A_53)))).
% Axiom fact_66_image__iff:(forall (Z:pname) (F_3:(hoare_669141180iple_a->pname)) (A_52:(hoare_669141180iple_a->Prop)), ((iff ((member_pname Z) ((image_225123213_pname F_3) A_52))) ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) A_52)) (((eq pname) Z) (F_3 X))))))).
% Axiom fact_67_image__iff:(forall (Z:hoare_669141180iple_a) (F_3:(pname->hoare_669141180iple_a)) (A_52:(pname->Prop)), ((iff ((member1016246415iple_a Z) ((image_957198589iple_a F_3) A_52))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_52)) (((eq hoare_669141180iple_a) Z) (F_3 X))))))).
% Axiom fact_68_UnI2:(forall (A_51:(hoare_669141180iple_a->Prop)) (C_9:hoare_669141180iple_a) (B_25:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a C_9) B_25)->((member1016246415iple_a C_9) ((semila1689936973le_a_o A_51) B_25)))).
% Axiom fact_69_UnI2:(forall (A_51:(pname->Prop)) (C_9:pname) (B_25:(pname->Prop)), (((member_pname C_9) B_25)->((member_pname C_9) ((semila1780557381name_o A_51) B_25)))).
% Axiom fact_70_UnI1:(forall (B_24:(hoare_669141180iple_a->Prop)) (C_8:hoare_669141180iple_a) (A_50:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a C_8) A_50)->((member1016246415iple_a C_8) ((semila1689936973le_a_o A_50) B_24)))).
% Axiom fact_71_UnI1:(forall (B_24:(pname->Prop)) (C_8:pname) (A_50:(pname->Prop)), (((member_pname C_8) A_50)->((member_pname C_8) ((semila1780557381name_o A_50) B_24)))).
% Axiom fact_72_sup1I2:(forall (A_49:(hoare_669141180iple_a->Prop)) (B_23:(hoare_669141180iple_a->Prop)) (X_9:hoare_669141180iple_a), ((B_23 X_9)->(((semila1689936973le_a_o A_49) B_23) X_9))).
% Axiom fact_73_sup1I2:(forall (A_49:(pname->Prop)) (B_23:(pname->Prop)) (X_9:pname), ((B_23 X_9)->(((semila1780557381name_o A_49) B_23) X_9))).
% Axiom fact_74_sup1I1:(forall (B_22:(hoare_669141180iple_a->Prop)) (A_48:(hoare_669141180iple_a->Prop)) (X_8:hoare_669141180iple_a), ((A_48 X_8)->(((semila1689936973le_a_o A_48) B_22) X_8))).
% Axiom fact_75_sup1I1:(forall (B_22:(pname->Prop)) (A_48:(pname->Prop)) (X_8:pname), ((A_48 X_8)->(((semila1780557381name_o A_48) B_22) X_8))).
% Axiom fact_76_ball__Un:(forall (P_13:(hoare_669141180iple_a->Prop)) (A_47:(hoare_669141180iple_a->Prop)) (B_21:(hoare_669141180iple_a->Prop)), ((iff (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((semila1689936973le_a_o A_47) B_21))->(P_13 X)))) ((and (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) A_47)->(P_13 X)))) (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) B_21)->(P_13 X)))))).
% Axiom fact_77_ball__Un:(forall (P_13:(pname->Prop)) (A_47:(pname->Prop)) (B_21:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) ((semila1780557381name_o A_47) B_21))->(P_13 X)))) ((and (forall (X:pname), (((member_pname X) A_47)->(P_13 X)))) (forall (X:pname), (((member_pname X) B_21)->(P_13 X)))))).
% Axiom fact_78_bex__Un:(forall (P_12:(hoare_669141180iple_a->Prop)) (A_46:(hoare_669141180iple_a->Prop)) (B_20:(hoare_669141180iple_a->Prop)), ((iff ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) ((semila1689936973le_a_o A_46) B_20))) (P_12 X))))) ((or ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) A_46)) (P_12 X))))) ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((and ((member1016246415iple_a X) B_20)) (P_12 X))))))).
% Axiom fact_79_bex__Un:(forall (P_12:(pname->Prop)) (A_46:(pname->Prop)) (B_20:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((and ((member_pname X) ((semila1780557381name_o A_46) B_20))) (P_12 X))))) ((or ((ex pname) (fun (X:pname)=> ((and ((member_pname X) A_46)) (P_12 X))))) ((ex pname) (fun (X:pname)=> ((and ((member_pname X) B_20)) (P_12 X))))))).
% Axiom fact_80_Un__assoc:(forall (A_45:(hoare_669141180iple_a->Prop)) (B_19:(hoare_669141180iple_a->Prop)) (C_7:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o ((semila1689936973le_a_o A_45) B_19)) C_7)) ((semila1689936973le_a_o A_45) ((semila1689936973le_a_o B_19) C_7)))).
% Axiom fact_81_Un__assoc:(forall (A_45:(pname->Prop)) (B_19:(pname->Prop)) (C_7:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o ((semila1780557381name_o A_45) B_19)) C_7)) ((semila1780557381name_o A_45) ((semila1780557381name_o B_19) C_7)))).
% Axiom fact_82_Un__iff:(forall (C_6:hoare_669141180iple_a) (A_44:(hoare_669141180iple_a->Prop)) (B_18:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a C_6) ((semila1689936973le_a_o A_44) B_18))) ((or ((member1016246415iple_a C_6) A_44)) ((member1016246415iple_a C_6) B_18)))).
% Axiom fact_83_Un__iff:(forall (C_6:pname) (A_44:(pname->Prop)) (B_18:(pname->Prop)), ((iff ((member_pname C_6) ((semila1780557381name_o A_44) B_18))) ((or ((member_pname C_6) A_44)) ((member_pname C_6) B_18)))).
% Axiom fact_84_Un__left__commute:(forall (A_43:(hoare_669141180iple_a->Prop)) (B_17:(hoare_669141180iple_a->Prop)) (C_5:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_43) ((semila1689936973le_a_o B_17) C_5))) ((semila1689936973le_a_o B_17) ((semila1689936973le_a_o A_43) C_5)))).
% Axiom fact_85_Un__left__commute:(forall (A_43:(pname->Prop)) (B_17:(pname->Prop)) (C_5:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_43) ((semila1780557381name_o B_17) C_5))) ((semila1780557381name_o B_17) ((semila1780557381name_o A_43) C_5)))).
% Axiom fact_86_Un__left__absorb:(forall (A_42:(hoare_669141180iple_a->Prop)) (B_16:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_42) ((semila1689936973le_a_o A_42) B_16))) ((semila1689936973le_a_o A_42) B_16))).
% Axiom fact_87_Un__left__absorb:(forall (A_42:(pname->Prop)) (B_16:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_42) ((semila1780557381name_o A_42) B_16))) ((semila1780557381name_o A_42) B_16))).
% Axiom fact_88_Un__commute:(forall (A_41:(hoare_669141180iple_a->Prop)) (B_15:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_41) B_15)) ((semila1689936973le_a_o B_15) A_41))).
% Axiom fact_89_Un__commute:(forall (A_41:(pname->Prop)) (B_15:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_41) B_15)) ((semila1780557381name_o B_15) A_41))).
% Axiom fact_90_Un__def:(forall (A_40:(hoare_669141180iple_a->Prop)) (B_14:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_40) B_14)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((or ((member1016246415iple_a X) A_40)) ((member1016246415iple_a X) B_14)))))).
% Axiom fact_91_Un__def:(forall (A_40:(pname->Prop)) (B_14:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_40) B_14)) (collect_pname (fun (X:pname)=> ((or ((member_pname X) A_40)) ((member_pname X) B_14)))))).
% Axiom fact_92_Un__absorb:(forall (A_39:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((semila1689936973le_a_o A_39) A_39)) A_39)).
% Axiom fact_93_Un__absorb:(forall (A_39:(pname->Prop)), (((eq (pname->Prop)) ((semila1780557381name_o A_39) A_39)) A_39)).
% Axiom fact_94_image__image:(forall (F_2:(pname->hoare_669141180iple_a)) (G_4:(hoare_669141180iple_a->pname)) (A_38:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a F_2) ((image_225123213_pname G_4) A_38))) ((image_1033305477iple_a (fun (X:hoare_669141180iple_a)=> (F_2 (G_4 X)))) A_38))).
% Axiom fact_95_image__image:(forall (F_2:(hoare_669141180iple_a->pname)) (G_4:(pname->hoare_669141180iple_a)) (A_38:(pname->Prop)), (((eq (pname->Prop)) ((image_225123213_pname F_2) ((image_957198589iple_a G_4) A_38))) ((image_pname_pname (fun (X:pname)=> (F_2 (G_4 X)))) A_38))).
% Axiom fact_96_sup__Un__eq:(forall (R:(hoare_669141180iple_a->Prop)) (S_1:(hoare_669141180iple_a->Prop)) (X:hoare_669141180iple_a), ((iff (((semila1689936973le_a_o (fun (Y_1:hoare_669141180iple_a)=> ((member1016246415iple_a Y_1) R))) (fun (Y_1:hoare_669141180iple_a)=> ((member1016246415iple_a Y_1) S_1))) X)) ((member1016246415iple_a X) ((semila1689936973le_a_o R) S_1)))).
% Axiom fact_97_sup__Un__eq:(forall (R:(pname->Prop)) (S_1:(pname->Prop)) (X:pname), ((iff (((semila1780557381name_o (fun (Y_1:pname)=> ((member_pname Y_1) R))) (fun (Y_1:pname)=> ((member_pname Y_1) S_1))) X)) ((member_pname X) ((semila1780557381name_o R) S_1)))).
% Axiom fact_98_Collect__disj__eq:(forall (P_11:(hoare_669141180iple_a->Prop)) (Q_3:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((or (P_11 X)) (Q_3 X))))) ((semila1689936973le_a_o (collec1717965009iple_a P_11)) (collec1717965009iple_a Q_3)))).
% Axiom fact_99_Collect__disj__eq:(forall (P_11:(pname->Prop)) (Q_3:(pname->Prop)), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((or (P_11 X)) (Q_3 X))))) ((semila1780557381name_o (collect_pname P_11)) (collect_pname Q_3)))).
% Axiom fact_100_imageE:(forall (B_13:pname) (F_1:(hoare_669141180iple_a->pname)) (A_37:(hoare_669141180iple_a->Prop)), (((member_pname B_13) ((image_225123213_pname F_1) A_37))->((forall (X:hoare_669141180iple_a), ((((eq pname) B_13) (F_1 X))->(((member1016246415iple_a X) A_37)->False)))->False))).
% Axiom fact_101_imageE:(forall (B_13:hoare_669141180iple_a) (F_1:(pname->hoare_669141180iple_a)) (A_37:(pname->Prop)), (((member1016246415iple_a B_13) ((image_957198589iple_a F_1) A_37))->((forall (X:pname), ((((eq hoare_669141180iple_a) B_13) (F_1 X))->(((member_pname X) A_37)->False)))->False))).
% Axiom fact_102_Body__triple__valid__Suc:(forall (N_2:nat) (P_10:(x_a->(state->Prop))) (Pn_4:pname) (Q_2:(x_a->(state->Prop))), ((iff ((hoare_2082685510alid_a N_2) (((hoare_1295064928iple_a P_10) (the_com (body_1 Pn_4))) Q_2))) ((hoare_2082685510alid_a (suc N_2)) (((hoare_1295064928iple_a P_10) (body Pn_4)) Q_2)))).
% Axiom fact_103_triple_Oexhaust:(forall (Y_4:hoare_669141180iple_a), ((forall (Fun1:(x_a->(state->Prop))) (Com:com) (Fun2:(x_a->(state->Prop))), (not (((eq hoare_669141180iple_a) Y_4) (((hoare_1295064928iple_a Fun1) Com) Fun2))))->False)).
% Axiom fact_104_Body1:(forall (Pn_3:pname) (G_3:(hoare_669141180iple_a->Prop)) (P_8:(pname->(x_a->(state->Prop)))) (Q_1:(pname->(x_a->(state->Prop)))) (Procs:(pname->Prop)), (((hoare_2128652938rivs_a ((semila1689936973le_a_o G_3) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_8 P_9)) (body P_9)) (Q_1 P_9)))) Procs))) ((image_957198589iple_a (fun (P_9:pname)=> (((hoare_1295064928iple_a (P_8 P_9)) (the_com (body_1 P_9))) (Q_1 P_9)))) Procs))->(((member_pname Pn_3) Procs)->((hoare_2128652938rivs_a G_3) ((insert175534902iple_a (((hoare_1295064928iple_a (P_8 Pn_3)) (body Pn_3)) (Q_1 Pn_3))) bot_bo280939947le_a_o))))).
% Axiom fact_105_image__cong:(forall (F:(hoare_669141180iple_a->pname)) (G_2:(hoare_669141180iple_a->pname)) (M:(hoare_669141180iple_a->Prop)) (N_1:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) M) N_1)->((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) N_1)->(((eq pname) (F X)) (G_2 X))))->(((eq (pname->Prop)) ((image_225123213_pname F) M)) ((image_225123213_pname G_2) N_1))))).
% Axiom fact_106_image__cong:(forall (F:(pname->hoare_669141180iple_a)) (G_2:(pname->hoare_669141180iple_a)) (M:(pname->Prop)) (N_1:(pname->Prop)), ((((eq (pname->Prop)) M) N_1)->((forall (X:pname), (((member_pname X) N_1)->(((eq hoare_669141180iple_a) (F X)) (G_2 X))))->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a F) M)) ((image_957198589iple_a G_2) N_1))))).
% Axiom fact_107_Body__triple__valid__0:(forall (P_7:(x_a->(state->Prop))) (Pn_2:pname) (Q:(x_a->(state->Prop))), ((hoare_2082685510alid_a zero_zero_nat) (((hoare_1295064928iple_a P_7) (body Pn_2)) Q))).
% Axiom fact_108_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_109_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_110_emptyE:(forall (A_36:hoare_669141180iple_a), (((member1016246415iple_a A_36) bot_bo280939947le_a_o)->False)).
% Axiom fact_111_emptyE:(forall (A_36:pname), (((member_pname A_36) bot_bot_pname_o)->False)).
% Axiom fact_112_insertE:(forall (A_35:hoare_669141180iple_a) (B_12:hoare_669141180iple_a) (A_34:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_35) ((insert175534902iple_a B_12) A_34))->((not (((eq hoare_669141180iple_a) A_35) B_12))->((member1016246415iple_a A_35) A_34)))).
% Axiom fact_113_insertE:(forall (A_35:pname) (B_12:pname) (A_34:(pname->Prop)), (((member_pname A_35) ((insert_pname B_12) A_34))->((not (((eq pname) A_35) B_12))->((member_pname A_35) A_34)))).
% Axiom fact_114_insertCI:(forall (B_11:hoare_669141180iple_a) (A_33:hoare_669141180iple_a) (B_10:(hoare_669141180iple_a->Prop)), (((((member1016246415iple_a A_33) B_10)->False)->(((eq hoare_669141180iple_a) A_33) B_11))->((member1016246415iple_a A_33) ((insert175534902iple_a B_11) B_10)))).
% Axiom fact_115_insertCI:(forall (B_11:pname) (A_33:pname) (B_10:(pname->Prop)), (((((member_pname A_33) B_10)->False)->(((eq pname) A_33) B_11))->((member_pname A_33) ((insert_pname B_11) B_10)))).
% Axiom fact_116_evalc__elim__cases_I6_J:(forall (P_6:pname) (S:state) (S1:state), ((((evalc (body P_6)) S) S1)->(((evalc (the_com (body_1 P_6))) S) S1))).
% Axiom fact_117_empty__not__insert:(forall (A_32:hoare_669141180iple_a) (A_31:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) ((insert175534902iple_a A_32) A_31)))).
% Axiom fact_118_empty__not__insert:(forall (A_32:pname) (A_31:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_32) A_31)))).
% Axiom fact_119_insert__not__empty:(forall (A_30:hoare_669141180iple_a) (A_29:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_30) A_29)) bot_bo280939947le_a_o))).
% Axiom fact_120_insert__not__empty:(forall (A_30:pname) (A_29:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_30) A_29)) bot_bot_pname_o))).
% Axiom fact_121_bot__empty__eq:(forall (X:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X)) ((member1016246415iple_a X) bot_bo280939947le_a_o))).
% Axiom fact_122_bot__empty__eq:(forall (X:pname), ((iff (bot_bot_pname_o X)) ((member_pname X) bot_bot_pname_o))).
% Axiom fact_123_empty__def:(((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X:pname)=> False))).
% Axiom fact_124_empty__def:(((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> False))).
% Axiom fact_125_insertI1:(forall (A_28:hoare_669141180iple_a) (B_9:(hoare_669141180iple_a->Prop)), ((member1016246415iple_a A_28) ((insert175534902iple_a A_28) B_9))).
% Axiom fact_126_insertI1:(forall (A_28:pname) (B_9:(pname->Prop)), ((member_pname A_28) ((insert_pname A_28) B_9))).
% Axiom fact_127_all__not__in__conv:(forall (A_27:(hoare_669141180iple_a->Prop)), ((iff (forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) A_27)->False))) (((eq (hoare_669141180iple_a->Prop)) A_27) bot_bo280939947le_a_o))).
% Axiom fact_128_all__not__in__conv:(forall (A_27:(pname->Prop)), ((iff (forall (X:pname), (((member_pname X) A_27)->False))) (((eq (pname->Prop)) A_27) bot_bot_pname_o))).
% Axiom fact_129_singleton__conv2:(forall (A_26:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fequal182287803iple_a A_26))) ((insert175534902iple_a A_26) bot_bo280939947le_a_o))).
% Axiom fact_130_singleton__conv2:(forall (A_26:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_26))) ((insert_pname A_26) bot_bot_pname_o))).
% Axiom fact_131_ex__in__conv:(forall (A_25:(hoare_669141180iple_a->Prop)), ((iff ((ex hoare_669141180iple_a) (fun (X:hoare_669141180iple_a)=> ((member1016246415iple_a X) A_25)))) (not (((eq (hoare_669141180iple_a->Prop)) A_25) bot_bo280939947le_a_o)))).
% Axiom fact_132_ex__in__conv:(forall (A_25:(pname->Prop)), ((iff ((ex pname) (fun (X:pname)=> ((member_pname X) A_25)))) (not (((eq (pname->Prop)) A_25) bot_bot_pname_o)))).
% Axiom fact_133_singleton__conv:(forall (A_24:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> (((eq hoare_669141180iple_a) X) A_24)))) ((insert175534902iple_a A_24) bot_bo280939947le_a_o))).
% Axiom fact_134_singleton__conv:(forall (A_24:pname), (((eq (pname->Prop)) (collect_pname (fun (X:pname)=> (((eq pname) X) A_24)))) ((insert_pname A_24) bot_bot_pname_o))).
% Axiom fact_135_Collect__conv__if2:(forall (P_5:(hoare_669141180iple_a->Prop)) (A_23:hoare_669141180iple_a), ((and ((P_5 A_23)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_23) X)) (P_5 X))))) ((insert175534902iple_a A_23) bot_bo280939947le_a_o)))) (((P_5 A_23)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_23) X)) (P_5 X))))) bot_bo280939947le_a_o)))).
% Axiom fact_136_Collect__conv__if2:(forall (P_5:(pname->Prop)) (A_23:pname), ((and ((P_5 A_23)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_23) X)) (P_5 X))))) ((insert_pname A_23) bot_bot_pname_o)))) (((P_5 A_23)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) A_23) X)) (P_5 X))))) bot_bot_pname_o)))).
% Axiom fact_137_Collect__conv__if:(forall (P_4:(hoare_669141180iple_a->Prop)) (A_22:hoare_669141180iple_a), ((and ((P_4 A_22)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X) A_22)) (P_4 X))))) ((insert175534902iple_a A_22) bot_bo280939947le_a_o)))) (((P_4 A_22)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X) A_22)) (P_4 X))))) bot_bo280939947le_a_o)))).
% Axiom fact_138_Collect__conv__if:(forall (P_4:(pname->Prop)) (A_22:pname), ((and ((P_4 A_22)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_22)) (P_4 X))))) ((insert_pname A_22) bot_bot_pname_o)))) (((P_4 A_22)->False)->(((eq (pname->Prop)) (collect_pname (fun (X:pname)=> ((and (((eq pname) X) A_22)) (P_4 X))))) bot_bot_pname_o)))).
% Axiom fact_139_empty__Collect__eq:(forall (P_3:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_3))) (forall (X:pname), ((P_3 X)->False)))).
% Axiom fact_140_empty__Collect__eq:(forall (P_3:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a P_3))) (forall (X:hoare_669141180iple_a), ((P_3 X)->False)))).
% Axiom fact_141_empty__iff:(forall (C_4:hoare_669141180iple_a), (((member1016246415iple_a C_4) bot_bo280939947le_a_o)->False)).
% Axiom fact_142_empty__iff:(forall (C_4:pname), (((member_pname C_4) bot_bot_pname_o)->False)).
% Axiom fact_143_mem__def:(forall (X_7:hoare_669141180iple_a) (A_21:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a X_7) A_21)) (A_21 X_7))).
% Axiom fact_144_mem__def:(forall (X_7:pname) (A_21:(pname->Prop)), ((iff ((member_pname X_7) A_21)) (A_21 X_7))).
% Axiom fact_145_Collect__def:(forall (P_2:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_2)) P_2)).
% Axiom fact_146_Collect__def:(forall (P_2:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P_2)) P_2)).
% Axiom fact_147_insert__compr:(forall (A_20:hoare_669141180iple_a) (B_8:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_20) B_8)) (collec1717965009iple_a (fun (X:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) X) A_20)) ((member1016246415iple_a X) B_8)))))).
% Axiom fact_148_insert__compr:(forall (A_20:pname) (B_8:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_20) B_8)) (collect_pname (fun (X:pname)=> ((or (((eq pname) X) A_20)) ((member_pname X) B_8)))))).
% Axiom fact_149_insert__is__Un:(forall (A_19:hoare_669141180iple_a) (A_18:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_19) A_18)) ((semila1689936973le_a_o ((insert175534902iple_a A_19) bot_bo280939947le_a_o)) A_18))).
% Axiom fact_150_insert__is__Un:(forall (A_19:pname) (A_18:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_19) A_18)) ((semila1780557381name_o ((insert_pname A_19) bot_bot_pname_o)) A_18))).
% Axiom fact_151_insert__Collect:(forall (A_17:hoare_669141180iple_a) (P_1:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_17) (collec1717965009iple_a P_1))) (collec1717965009iple_a (fun (U_1:hoare_669141180iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_669141180iple_a) U_1) A_17))) (P_1 U_1)))))).
% Axiom fact_152_insert__Collect:(forall (A_17:pname) (P_1:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_17) (collect_pname P_1))) (collect_pname (fun (U_1:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U_1) A_17))) (P_1 U_1)))))).
% Axiom fact_153_singleton__iff:(forall (B_7:hoare_669141180iple_a) (A_16:hoare_669141180iple_a), ((iff ((member1016246415iple_a B_7) ((insert175534902iple_a A_16) bot_bo280939947le_a_o))) (((eq hoare_669141180iple_a) B_7) A_16))).
% Axiom fact_154_singleton__iff:(forall (B_7:pname) (A_16:pname), ((iff ((member_pname B_7) ((insert_pname A_16) bot_bot_pname_o))) (((eq pname) B_7) A_16))).
% Axiom fact_155_insert__absorb2:(forall (X_6:hoare_669141180iple_a) (A_15:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_6) ((insert175534902iple_a X_6) A_15))) ((insert175534902iple_a X_6) A_15))).
% Axiom fact_156_insert__absorb2:(forall (X_6:pname) (A_15:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_6) ((insert_pname X_6) A_15))) ((insert_pname X_6) A_15))).
% Axiom fact_157_insert__commute:(forall (X_5:hoare_669141180iple_a) (Y_3:hoare_669141180iple_a) (A_14:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_5) ((insert175534902iple_a Y_3) A_14))) ((insert175534902iple_a Y_3) ((insert175534902iple_a X_5) A_14)))).
% Axiom fact_158_insert__commute:(forall (X_5:pname) (Y_3:pname) (A_14:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_5) ((insert_pname Y_3) A_14))) ((insert_pname Y_3) ((insert_pname X_5) A_14)))).
% Axiom fact_159_insert__iff:(forall (A_13:hoare_669141180iple_a) (B_6:hoare_669141180iple_a) (A_12:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a A_13) ((insert175534902iple_a B_6) A_12))) ((or (((eq hoare_669141180iple_a) A_13) B_6)) ((member1016246415iple_a A_13) A_12)))).
% Axiom fact_160_insert__iff:(forall (A_13:pname) (B_6:pname) (A_12:(pname->Prop)), ((iff ((member_pname A_13) ((insert_pname B_6) A_12))) ((or (((eq pname) A_13) B_6)) ((member_pname A_13) A_12)))).
% Axiom fact_161_Collect__empty__eq:(forall (P:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P)) bot_bot_pname_o)) (forall (X:pname), ((P X)->False)))).
% Axiom fact_162_Collect__empty__eq:(forall (P:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P)) bot_bo280939947le_a_o)) (forall (X:hoare_669141180iple_a), ((P X)->False)))).
% Axiom fact_163_doubleton__eq__iff:(forall (A_11:hoare_669141180iple_a) (B_5:hoare_669141180iple_a) (C_3:hoare_669141180iple_a) (D:hoare_669141180iple_a), ((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_11) ((insert175534902iple_a B_5) bot_bo280939947le_a_o))) ((insert175534902iple_a C_3) ((insert175534902iple_a D) bot_bo280939947le_a_o)))) ((or ((and (((eq hoare_669141180iple_a) A_11) C_3)) (((eq hoare_669141180iple_a) B_5) D))) ((and (((eq hoare_669141180iple_a) A_11) D)) (((eq hoare_669141180iple_a) B_5) C_3))))).
% Axiom fact_164_doubleton__eq__iff:(forall (A_11:pname) (B_5:pname) (C_3:pname) (D:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_11) ((insert_pname B_5) bot_bot_pname_o))) ((insert_pname C_3) ((insert_pname D) bot_bot_pname_o)))) ((or ((and (((eq pname) A_11) C_3)) (((eq pname) B_5) D))) ((and (((eq pname) A_11) D)) (((eq pname) B_5) C_3))))).
% Axiom fact_165_insert__code:(forall (Y_2:hoare_669141180iple_a) (A_10:(hoare_669141180iple_a->Prop)) (X_4:hoare_669141180iple_a), ((iff (((insert175534902iple_a Y_2) A_10) X_4)) ((or (((eq hoare_669141180iple_a) Y_2) X_4)) (A_10 X_4)))).
% Axiom fact_166_insert__code:(forall (Y_2:pname) (A_10:(pname->Prop)) (X_4:pname), ((iff (((insert_pname Y_2) A_10) X_4)) ((or (((eq pname) Y_2) X_4)) (A_10 X_4)))).
% Axiom fact_167_insert__compr__raw:(forall (X:hoare_669141180iple_a) (Xa:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X) Xa)) (collec1717965009iple_a (fun (Y_1:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) Y_1) X)) ((member1016246415iple_a Y_1) Xa)))))).
% Axiom fact_168_insert__compr__raw:(forall (X:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X) Xa)) (collect_pname (fun (Y_1:pname)=> ((or (((eq pname) Y_1) X)) ((member_pname Y_1) Xa)))))).
% Axiom fact_169_insert__ident:(forall (B_4:(hoare_669141180iple_a->Prop)) (X_3:hoare_669141180iple_a) (A_9:(hoare_669141180iple_a->Prop)), ((((member1016246415iple_a X_3) A_9)->False)->((((member1016246415iple_a X_3) B_4)->False)->((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_3) A_9)) ((insert175534902iple_a X_3) B_4))) (((eq (hoare_669141180iple_a->Prop)) A_9) B_4))))).
% Axiom fact_170_insert__ident:(forall (B_4:(pname->Prop)) (X_3:pname) (A_9:(pname->Prop)), ((((member_pname X_3) A_9)->False)->((((member_pname X_3) B_4)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_3) A_9)) ((insert_pname X_3) B_4))) (((eq (pname->Prop)) A_9) B_4))))).
% Axiom fact_171_equals0D:(forall (A_8:hoare_669141180iple_a) (A_7:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) A_7) bot_bo280939947le_a_o)->(((member1016246415iple_a A_8) A_7)->False))).
% Axiom fact_172_equals0D:(forall (A_8:pname) (A_7:(pname->Prop)), ((((eq (pname->Prop)) A_7) bot_bot_pname_o)->(((member_pname A_8) A_7)->False))).
% Axiom fact_173_insertI2:(forall (B_3:hoare_669141180iple_a) (A_6:hoare_669141180iple_a) (B_2:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_6) B_2)->((member1016246415iple_a A_6) ((insert175534902iple_a B_3) B_2)))).
% Axiom fact_174_insertI2:(forall (B_3:pname) (A_6:pname) (B_2:(pname->Prop)), (((member_pname A_6) B_2)->((member_pname A_6) ((insert_pname B_3) B_2)))).
% Axiom fact_175_insert__absorb:(forall (A_5:hoare_669141180iple_a) (A_4:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_5) A_4)->(((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_5) A_4)) A_4))).
% Axiom fact_176_insert__absorb:(forall (A_5:pname) (A_4:(pname->Prop)), (((member_pname A_5) A_4)->(((eq (pname->Prop)) ((insert_pname A_5) A_4)) A_4))).
% Axiom fact_177_hoare__derivs_Oinsert:(forall (Ts_1:(hoare_669141180iple_a->Prop)) (G_1:(hoare_669141180iple_a->Prop)) (T_2:hoare_669141180iple_a), (((hoare_2128652938rivs_a G_1) ((insert175534902iple_a T_2) bot_bo280939947le_a_o))->(((hoare_2128652938rivs_a G_1) Ts_1)->((hoare_2128652938rivs_a G_1) ((insert175534902iple_a T_2) Ts_1))))).
% Axiom fact_178_singletonE:(forall (B_1:hoare_669141180iple_a) (A_3:hoare_669141180iple_a), (((member1016246415iple_a B_1) ((insert175534902iple_a A_3) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) B_1) A_3))).
% Axiom fact_179_singletonE:(forall (B_1:pname) (A_3:pname), (((member_pname B_1) ((insert_pname A_3) bot_bot_pname_o))->(((eq pname) B_1) A_3))).
% Axiom fact_180_derivs__insertD:(forall (G:(hoare_669141180iple_a->Prop)) (T_1:hoare_669141180iple_a) (Ts:(hoare_669141180iple_a->Prop)), (((hoare_2128652938rivs_a G) ((insert175534902iple_a T_1) Ts))->((and ((hoare_2128652938rivs_a G) ((insert175534902iple_a T_1) bot_bo280939947le_a_o))) ((hoare_2128652938rivs_a G) Ts)))).
% Axiom fact_181_singleton__inject:(forall (A_2:hoare_669141180iple_a) (B:hoare_669141180iple_a), ((((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_2) bot_bo280939947le_a_o)) ((insert175534902iple_a B) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) A_2) B))).
% Axiom fact_182_singleton__inject:(forall (A_2:pname) (B:pname), ((((eq (pname->Prop)) ((insert_pname A_2) bot_bot_pname_o)) ((insert_pname B) bot_bot_pname_o))->(((eq pname) A_2) B))).
% Axiom fact_183_com__det:(forall (U:state) (C_2:com) (S:state) (T:state), ((((evalc C_2) S) T)->((((evalc C_2) S) U)->(((eq state) U) T)))).
% Axiom fact_184_image__constant__conv:(forall (C_1:pname) (A_1:(hoare_669141180iple_a->Prop)), ((and ((((eq (hoare_669141180iple_a->Prop)) A_1) bot_bo280939947le_a_o)->(((eq (pname->Prop)) ((image_225123213_pname (fun (X:hoare_669141180iple_a)=> C_1)) A_1)) bot_bot_pname_o))) ((not (((eq (hoare_669141180iple_a->Prop)) A_1) bot_bo280939947le_a_o))->(((eq (pname->Prop)) ((image_225123213_pname (fun (X:hoare_669141180iple_a)=> C_1)) A_1)) ((insert_pname C_1) bot_bot_pname_o))))).
% Axiom fact_185_image__constant__conv:(forall (C_1:hoare_669141180iple_a) (A_1:(pname->Prop)), ((and ((((eq (pname->Prop)) A_1) bot_bot_pname_o)->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a (fun (X:pname)=> C_1)) A_1)) bot_bo280939947le_a_o))) ((not (((eq (pname->Prop)) A_1) bot_bot_pname_o))->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a (fun (X:pname)=> C_1)) A_1)) ((insert175534902iple_a C_1) bot_bo280939947le_a_o))))).
% Axiom fact_186_image__constant:(forall (C:pname) (X_2:hoare_669141180iple_a) (A:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_2) A)->(((eq (pname->Prop)) ((image_225123213_pname (fun (X:hoare_669141180iple_a)=> C)) A)) ((insert_pname C) bot_bot_pname_o)))).
% Axiom fact_187_image__constant:(forall (C:hoare_669141180iple_a) (X_2:hoare_669141180iple_a) (A:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_2) A)->(((eq (hoare_669141180iple_a->Prop)) ((image_1033305477iple_a (fun (X:hoare_669141180iple_a)=> C)) A)) ((insert175534902iple_a C) bot_bo280939947le_a_o)))).
% Axiom fact_188_image__constant:(forall (C:pname) (X_2:pname) (A:(pname->Prop)), (((member_pname X_2) A)->(((eq (pname->Prop)) ((image_pname_pname (fun (X:pname)=> C)) A)) ((insert_pname C) bot_bot_pname_o)))).
% Axiom fact_189_image__constant:(forall (C:hoare_669141180iple_a) (X_2:pname) (A:(pname->Prop)), (((member_pname X_2) A)->(((eq (hoare_669141180iple_a->Prop)) ((image_957198589iple_a (fun (X:pname)=> C)) A)) ((insert175534902iple_a C) bot_bo280939947le_a_o)))).
% 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__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_:(forall (X_1:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (((fequal182287803iple_a X_1) Y)->False)) (((eq hoare_669141180iple_a) X_1) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_:(forall (X_1:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (not (((eq hoare_669141180iple_a) X_1) Y))) ((fequal182287803iple_a X_1) Y))).
% Axiom conj_0:(forall (N:nat), ((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((semila1689936973le_a_o g) ((image_957198589iple_a (fun (Pn:pname)=> (((hoare_1295064928iple_a (p Pn)) (body Pn)) (q Pn)))) procs)))->((hoare_2082685510alid_a N) X)))->(forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((image_957198589iple_a (fun (Pn:pname)=> (((hoare_1295064928iple_a (p Pn)) (the_com (body_1 Pn))) (q Pn)))) procs))->((hoare_2082685510alid_a N) X))))).
% Trying to prove ((forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) g)->((hoare_2082685510alid_a n) X)))->(forall (X:hoare_669141180iple_a), (((member1016246415iple_a X) ((image_957198589iple_a (fun (Pn:pname)=> (((hoare_1295064928iple_a (p Pn)) (body Pn)) (q Pn)))) procs))->((hoare_2082685510alid_a n) X))))
% Found x1:(A_64 X)
% Found x1 as proof of False
% Found (fun (x1:(A_64 X))=> x1) as proof of False
% Found (fun (x1:(A_64 X))=> x1) as proof of ((A_64 X)->False)
% Found x1:(A_64 pname_DUMMY)
% Found x1 as proof of False
% Found (fun (x1:(A_64 pname_DUMMY))=> x1) as proof of False
% Found (fun (x1:(A_64 pname_DUMMY))=> x1) as proof of ((A_64 pname_DUMMY)->False)
% Found x1:(A_64 hoare_669141180iple_a_DUMMY)
% Found x1 as proof of False
% Found (fun (x1:(A_64 hoare_669141180iple_a_DUMMY))=> x1) as proof of False
% Found (fun (x1:(A_64 hoare_669141180iple_a_DUMMY))=> x1) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_124_empty__def0:=(fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_124_empty__def0:=(fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found x2:(A_64 X)
% Found x2 as proof of False
% Found (fun (x2:(A_64 X))=> x2) as proof of False
% Found (fun (x2:(A_64 X))=> x2) as proof of ((A_64 X)->False)
% Found fact_124_empty__def0:=(fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 X))):((A_64 X)->(A_64 X))
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found x2:(A_64 hoare_669141180iple_a_DUMMY)
% Found x2 as proof of False
% Found (fun (x2:(A_64 hoare_669141180iple_a_DUMMY))=> x2) as proof of False
% Found (fun (x2:(A_64 hoare_669141180iple_a_DUMMY))=> x2) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found x2:(A_64 pname_DUMMY)
% Found x2 as proof of False
% Found (fun (x2:(A_64 pname_DUMMY))=> x2) as proof of False
% Found (fun (x2:(A_64 pname_DUMMY))=> x2) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x2:(pname->Prop))=> (A_64 X))):((A_64 X)->(A_64 X))
% Found (fact_123_empty__def (fun (x2:(pname->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found (fact_123_empty__def (fun (x2:(pname->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found x1:(A_64 pname_DUMMY)
% Found x1 as proof of False
% Found (fun (x1:(A_64 pname_DUMMY))=> x1) as proof of False
% Found (fun (x1:(A_64 pname_DUMMY))=> x1) as proof of ((A_64 pname_DUMMY)->False)
% Found x1:(A_64 hoare_669141180iple_a_DUMMY)
% Found x1 as proof of False
% Found (fun (x1:(A_64 hoare_669141180iple_a_DUMMY))=> x1) as proof of False
% Found (fun (x1:(A_64 hoare_669141180iple_a_DUMMY))=> x1) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x2:(pname->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_123_empty__def (fun (x2:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_123_empty__def (fun (x2:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x2:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_123_empty__def (fun (x2:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_123_empty__def (fun (x2:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found x1:(A_64 X)
% Found x1 as proof of False
% Found (fun (x1:(A_64 X))=> x1) as proof of False
% Found (fun (x1:(A_64 X))=> x1) as proof of ((A_64 X)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found x2:(A_64 X)
% Found x2 as proof of False
% Found (fun (x2:(A_64 X))=> x2) as proof of False
% Found (fun (x2:(A_64 X))=> x2) as proof of ((A_64 X)->False)
% Found x2:(A_64 pname_DUMMY)
% Found x2 as proof of False
% Found (fun (x2:(A_64 pname_DUMMY))=> x2) as proof of False
% Found (fun (x2:(A_64 pname_DUMMY))=> x2) as proof of ((A_64 pname_DUMMY)->False)
% Found x2:(A_64 hoare_669141180iple_a_DUMMY)
% Found x2 as proof of False
% Found (fun (x2:(A_64 hoare_669141180iple_a_DUMMY))=> x2) as proof of False
% Found (fun (x2:(A_64 hoare_669141180iple_a_DUMMY))=> x2) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_124_empty__def0:=(fact_124_empty__def (fun (x2:(hoare_669141180iple_a->Prop))=> (A_64 X))):((A_64 X)->(A_64 X))
% Found (fact_124_empty__def (fun (x2:(hoare_669141180iple_a->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found (fact_124_empty__def (fun (x2:(hoare_669141180iple_a->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found fact_124_empty__def0:=(fact_124_empty__def (fun (x2:(hoare_669141180iple_a->Prop))=> (A_64 X))):((A_64 X)->(A_64 X))
% Found (fact_124_empty__def (fun (x2:(hoare_669141180iple_a->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found (fact_124_empty__def (fun (x2:(hoare_669141180iple_a->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_124_empty__def0:=(fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_124_empty__def0:=(fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_124_empty__def0:=(fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_124_empty__def0:=(fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 X))):((A_64 X)->(A_64 X))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 X))):((A_64 X)->(A_64 X))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 X))) as proof of ((A_64 X)->False)
% Found fact_124_empty__def0:=(fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_124_empty__def (fun (x1:(hoare_669141180iple_a->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))) as proof of ((A_64 hoare_669141180iple_a_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))):((A_64 pname_DUMMY)->(A_64 pname_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found (fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 pname_DUMMY))) as proof of ((A_64 pname_DUMMY)->False)
% Found fact_123_empty__def0:=(fact_123_empty__def (fun (x1:(pname->Prop))=> (A_64 hoare_669141180iple_a_DUMMY))):((A_64 hoare_669141180iple_a_DUMMY)->(A_64 hoare_669141180iple_a_DUMMY))
% Found (fact_123_empty__def (fun (x1:(pname->Pr
% EOF
%------------------------------------------------------------------------------