%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SWW470^1 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n089.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 13:37:20 EDT 2014

% Result   : Theorem 2.77s
% Output   : Proof 2.77s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SWW470^1 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n089.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 09:12:36 CDT 2014
% % CPUTime  : 2.77 
% 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 0x148f3b0>, <kernel.Type object at 0x148f518>) of role type named ty_ty_t__a
% Using role type
% Declaring x_a:Type
% FOF formula (<kernel.Constant object at 0x148f998>, <kernel.Type object at 0x1493248>) of role type named ty_ty_tc__Com__Ocom
% Using role type
% Declaring com:Type
% FOF formula (<kernel.Constant object at 0x148fa70>, <kernel.Type object at 0x1414368>) of role type named ty_ty_tc__Com__Ostate
% Using role type
% Declaring state:Type
% FOF formula (<kernel.Constant object at 0x148f518>, <kernel.Type object at 0x1414368>) 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 0x148f3b0>, <kernel.Constant object at 0x1414488>) of role type named sy_c_Com_Ocom_OSKIP
% Using role type
% Declaring skip:com
% FOF formula (<kernel.Constant object at 0x148f518>, <kernel.DependentProduct object at 0x1414320>) of role type named sy_c_Com_Ocom_OSemi
% Using role type
% Declaring semi:(com->(com->com))
% FOF formula (<kernel.Constant object at 0x148f3b0>, <kernel.DependentProduct object at 0x1414248>) of role type named sy_c_Ex
% Using role type
% Declaring _TPTP_ex:((hoare_669141180iple_a->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x148fa70>, <kernel.DependentProduct object at 0x1414128>) of role type named sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_
% Using role type
% Declaring finite957651855iple_a:((hoare_669141180iple_a->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x148fa70>, <kernel.DependentProduct object at 0x1414908>) of role type named sy_c_Finite__Set_Ofold1Set_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__
% Using role type
% Declaring finite840267660iple_a:((hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))->((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop)))
% FOF formula (<kernel.Constant object at 0x1414200>, <kernel.DependentProduct object at 0x14142d8>) of role type named sy_c_Finite__Set_Ofold1_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J
% Using role type
% Declaring finite684844060iple_a:((hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))->((hoare_669141180iple_a->Prop)->hoare_669141180iple_a))
% FOF formula (<kernel.Constant object at 0x1414488>, <kernel.DependentProduct object at 0x1414170>) of role type named sy_c_Finite__Set_Ofold__graph_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_I
% Using role type
% Declaring finite590756294iple_a:((hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))->(hoare_669141180iple_a->((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop))))
% FOF formula (<kernel.Constant object at 0x1414098>, <kernel.DependentProduct object at 0x1414200>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_
% Using role type
% Declaring finite972428089iple_a:((hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))->(((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)->Prop))
% FOF formula (<kernel.Constant object at 0x1414128>, <kernel.DependentProduct object at 0x1414488>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ghhkfsbqqq__Ot
% Using role type
% Declaring finite252461622iple_a:((hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))->(((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)->Prop))
% FOF formula (<kernel.Constant object at 0x14140e0>, <kernel.DependentProduct object at 0x1414050>) of role type named sy_c_HOL_OThe_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J
% Using role type
% Declaring the_Ho49089901iple_a:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)
% FOF formula (<kernel.Constant object at 0x1414560>, <kernel.DependentProduct object at 0x14143f8>) 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 0x14144d0>, <kernel.DependentProduct object at 0x1414128>) 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 0x14142d8>, <kernel.DependentProduct object at 0x14143f8>) 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 0x1414050>, <kernel.Sort object at 0xf21518>) of role type named sy_c_Orderings_Obot__class_Obot_000_Eo
% Using role type
% Declaring bot_bot_o:Prop
% FOF formula (<kernel.Constant object at 0x1414098>, <kernel.DependentProduct object at 0x14144d0>) 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 0x14143b0>, <kernel.DependentProduct object at 0x1414518>) 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 0x14148c0>, <kernel.DependentProduct object at 0x1053bd8>) of role type named sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J
% Using role type
% Declaring the_el738790235iple_a:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)
% FOF formula (<kernel.Constant object at 0x14144d0>, <kernel.DependentProduct object at 0x1053d40>) 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 0x1414050>, <kernel.DependentProduct object at 0x1053ab8>) 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 0x14148c0>, <kernel.DependentProduct object at 0x1053c20>) of role type named sy_v_G
% Using role type
% Declaring g:(hoare_669141180iple_a->Prop)
% FOF formula (<kernel.Constant object at 0x14144d0>, <kernel.DependentProduct object at 0x1053b48>) of role type named sy_v_P
% Using role type
% Declaring p:(x_a->(state->Prop))
% FOF formula (<kernel.Constant object at 0x14148c0>, <kernel.DependentProduct object at 0x1053878>) of role type named sy_v_b
% Using role type
% Declaring b:(state->Prop)
% FOF formula (<kernel.Constant object at 0x14144d0>, <kernel.Constant object at 0x1053878>) of role type named sy_v_c
% Using role type
% Declaring c:com
% FOF formula (forall (G_12:(hoare_669141180iple_a->Prop)), ((hoare_2128652938rivs_a G_12) bot_bo280939947le_a_o)) of role axiom named fact_0_empty
% A new axiom: (forall (G_12:(hoare_669141180iple_a->Prop)), ((hoare_2128652938rivs_a G_12) bot_bo280939947le_a_o))
% 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_1_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_11:(hoare_669141180iple_a->Prop)) (G_10:(hoare_669141180iple_a->Prop)) (Ts_1:(hoare_669141180iple_a->Prop)), (((hoare_2128652938rivs_a G_10) Ts_1)->(((hoare_2128652938rivs_a G_11) G_10)->((hoare_2128652938rivs_a G_11) Ts_1)))) of role axiom named fact_2_cut
% A new axiom: (forall (G_11:(hoare_669141180iple_a->Prop)) (G_10:(hoare_669141180iple_a->Prop)) (Ts_1:(hoare_669141180iple_a->Prop)), (((hoare_2128652938rivs_a G_10) Ts_1)->(((hoare_2128652938rivs_a G_11) G_10)->((hoare_2128652938rivs_a G_11) Ts_1))))
% FOF formula (forall (Ts:(hoare_669141180iple_a->Prop)) (G_9:(hoare_669141180iple_a->Prop)) (T:hoare_669141180iple_a), (((hoare_2128652938rivs_a G_9) ((insert175534902iple_a T) bot_bo280939947le_a_o))->(((hoare_2128652938rivs_a G_9) Ts)->((hoare_2128652938rivs_a G_9) ((insert175534902iple_a T) Ts))))) of role axiom named fact_3_hoare__derivs_Oinsert
% A new axiom: (forall (Ts:(hoare_669141180iple_a->Prop)) (G_9:(hoare_669141180iple_a->Prop)) (T:hoare_669141180iple_a), (((hoare_2128652938rivs_a G_9) ((insert175534902iple_a T) bot_bo280939947le_a_o))->(((hoare_2128652938rivs_a G_9) Ts)->((hoare_2128652938rivs_a G_9) ((insert175534902iple_a T) Ts)))))
% FOF formula (forall (G_8:(hoare_669141180iple_a->Prop)) (P_25:(x_a->(state->Prop))) (C_9:com) (Q_11:(x_a->(state->Prop))) (C_8:Prop), ((C_8->((hoare_2128652938rivs_a G_8) ((insert175534902iple_a (((hoare_1295064928iple_a P_25) C_9) Q_11)) bot_bo280939947le_a_o)))->((hoare_2128652938rivs_a G_8) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> ((and ((P_25 Z) S)) C_8))) C_9) Q_11)) bot_bo280939947le_a_o)))) of role axiom named fact_4_constant
% A new axiom: (forall (G_8:(hoare_669141180iple_a->Prop)) (P_25:(x_a->(state->Prop))) (C_9:com) (Q_11:(x_a->(state->Prop))) (C_8:Prop), ((C_8->((hoare_2128652938rivs_a G_8) ((insert175534902iple_a (((hoare_1295064928iple_a P_25) C_9) Q_11)) bot_bo280939947le_a_o)))->((hoare_2128652938rivs_a G_8) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> ((and ((P_25 Z) S)) C_8))) C_9) Q_11)) bot_bo280939947le_a_o))))
% FOF formula (forall (G_7:(hoare_669141180iple_a->Prop)) (C_7:com) (Q_10:(x_a->(state->Prop))) (P_24:(x_a->(state->Prop))), ((forall (Z:x_a) (S:state), (((P_24 Z) S)->((hoare_2128652938rivs_a G_7) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Za:x_a) (S_1:state)=> (((eq state) S_1) S))) C_7) (fun (Z_6:x_a)=> (Q_10 Z)))) bot_bo280939947le_a_o))))->((hoare_2128652938rivs_a G_7) ((insert175534902iple_a (((hoare_1295064928iple_a P_24) C_7) Q_10)) bot_bo280939947le_a_o)))) of role axiom named fact_5_escape
% A new axiom: (forall (G_7:(hoare_669141180iple_a->Prop)) (C_7:com) (Q_10:(x_a->(state->Prop))) (P_24:(x_a->(state->Prop))), ((forall (Z:x_a) (S:state), (((P_24 Z) S)->((hoare_2128652938rivs_a G_7) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Za:x_a) (S_1:state)=> (((eq state) S_1) S))) C_7) (fun (Z_6:x_a)=> (Q_10 Z)))) bot_bo280939947le_a_o))))->((hoare_2128652938rivs_a G_7) ((insert175534902iple_a (((hoare_1295064928iple_a P_24) C_7) Q_10)) bot_bo280939947le_a_o))))
% FOF formula (forall (Q_9:(x_a->(state->Prop))) (G_6:(hoare_669141180iple_a->Prop)) (P_23:(x_a->(state->Prop))) (C_6:com) (Q_8:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_6) ((insert175534902iple_a (((hoare_1295064928iple_a P_23) C_6) Q_8)) bot_bo280939947le_a_o))->((forall (Z:x_a) (S:state), (((Q_8 Z) S)->((Q_9 Z) S)))->((hoare_2128652938rivs_a G_6) ((insert175534902iple_a (((hoare_1295064928iple_a P_23) C_6) Q_9)) bot_bo280939947le_a_o))))) of role axiom named fact_6_conseq2
% A new axiom: (forall (Q_9:(x_a->(state->Prop))) (G_6:(hoare_669141180iple_a->Prop)) (P_23:(x_a->(state->Prop))) (C_6:com) (Q_8:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_6) ((insert175534902iple_a (((hoare_1295064928iple_a P_23) C_6) Q_8)) bot_bo280939947le_a_o))->((forall (Z:x_a) (S:state), (((Q_8 Z) S)->((Q_9 Z) S)))->((hoare_2128652938rivs_a G_6) ((insert175534902iple_a (((hoare_1295064928iple_a P_23) C_6) Q_9)) bot_bo280939947le_a_o)))))
% FOF formula (forall (P_22:(x_a->(state->Prop))) (G_5:(hoare_669141180iple_a->Prop)) (P_21:(x_a->(state->Prop))) (C_5:com) (Q_7:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_5) ((insert175534902iple_a (((hoare_1295064928iple_a P_21) C_5) Q_7)) bot_bo280939947le_a_o))->((forall (Z:x_a) (S:state), (((P_22 Z) S)->((P_21 Z) S)))->((hoare_2128652938rivs_a G_5) ((insert175534902iple_a (((hoare_1295064928iple_a P_22) C_5) Q_7)) bot_bo280939947le_a_o))))) of role axiom named fact_7_conseq1
% A new axiom: (forall (P_22:(x_a->(state->Prop))) (G_5:(hoare_669141180iple_a->Prop)) (P_21:(x_a->(state->Prop))) (C_5:com) (Q_7:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_5) ((insert175534902iple_a (((hoare_1295064928iple_a P_21) C_5) Q_7)) bot_bo280939947le_a_o))->((forall (Z:x_a) (S:state), (((P_22 Z) S)->((P_21 Z) S)))->((hoare_2128652938rivs_a G_5) ((insert175534902iple_a (((hoare_1295064928iple_a P_22) C_5) Q_7)) bot_bo280939947le_a_o)))))
% FOF formula (forall (Q_6:(x_a->(state->Prop))) (P_20:(x_a->(state->Prop))) (G_4:(hoare_669141180iple_a->Prop)) (P_19:(x_a->(state->Prop))) (C_4:com) (Q_5:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_4) ((insert175534902iple_a (((hoare_1295064928iple_a P_19) C_4) Q_5)) bot_bo280939947le_a_o))->((forall (Z:x_a) (S:state), (((P_20 Z) S)->(forall (S_1:state), ((forall (Z_6:x_a), (((P_19 Z_6) S)->((Q_5 Z_6) S_1)))->((Q_6 Z) S_1)))))->((hoare_2128652938rivs_a G_4) ((insert175534902iple_a (((hoare_1295064928iple_a P_20) C_4) Q_6)) bot_bo280939947le_a_o))))) of role axiom named fact_8_conseq12
% A new axiom: (forall (Q_6:(x_a->(state->Prop))) (P_20:(x_a->(state->Prop))) (G_4:(hoare_669141180iple_a->Prop)) (P_19:(x_a->(state->Prop))) (C_4:com) (Q_5:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_4) ((insert175534902iple_a (((hoare_1295064928iple_a P_19) C_4) Q_5)) bot_bo280939947le_a_o))->((forall (Z:x_a) (S:state), (((P_20 Z) S)->(forall (S_1:state), ((forall (Z_6:x_a), (((P_19 Z_6) S)->((Q_5 Z_6) S_1)))->((Q_6 Z) S_1)))))->((hoare_2128652938rivs_a G_4) ((insert175534902iple_a (((hoare_1295064928iple_a P_20) C_4) Q_6)) bot_bo280939947le_a_o)))))
% FOF formula (forall (A_64:hoare_669141180iple_a) (B_14:hoare_669141180iple_a) (A_63:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_64) ((insert175534902iple_a B_14) A_63))->((not (((eq hoare_669141180iple_a) A_64) B_14))->((member1016246415iple_a A_64) A_63)))) of role axiom named fact_9_insertE
% A new axiom: (forall (A_64:hoare_669141180iple_a) (B_14:hoare_669141180iple_a) (A_63:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_64) ((insert175534902iple_a B_14) A_63))->((not (((eq hoare_669141180iple_a) A_64) B_14))->((member1016246415iple_a A_64) A_63))))
% FOF formula (forall (B_13:hoare_669141180iple_a) (A_62:hoare_669141180iple_a) (B_12:(hoare_669141180iple_a->Prop)), (((((member1016246415iple_a A_62) B_12)->False)->(((eq hoare_669141180iple_a) A_62) B_13))->((member1016246415iple_a A_62) ((insert175534902iple_a B_13) B_12)))) of role axiom named fact_10_insertCI
% A new axiom: (forall (B_13:hoare_669141180iple_a) (A_62:hoare_669141180iple_a) (B_12:(hoare_669141180iple_a->Prop)), (((((member1016246415iple_a A_62) B_12)->False)->(((eq hoare_669141180iple_a) A_62) B_13))->((member1016246415iple_a A_62) ((insert175534902iple_a B_13) B_12))))
% FOF formula (forall (A_61:hoare_669141180iple_a), (((member1016246415iple_a A_61) bot_bo280939947le_a_o)->False)) of role axiom named fact_11_emptyE
% A new axiom: (forall (A_61:hoare_669141180iple_a), (((member1016246415iple_a A_61) bot_bo280939947le_a_o)->False))
% FOF formula (forall (A_60:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fequal182287803iple_a A_60))) ((insert175534902iple_a A_60) bot_bo280939947le_a_o))) of role axiom named fact_12_singleton__conv2
% A new axiom: (forall (A_60:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fequal182287803iple_a A_60))) ((insert175534902iple_a A_60) bot_bo280939947le_a_o)))
% FOF formula (forall (A_59:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> (((eq hoare_669141180iple_a) X_3) A_59)))) ((insert175534902iple_a A_59) bot_bo280939947le_a_o))) of role axiom named fact_13_singleton__conv
% A new axiom: (forall (A_59:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> (((eq hoare_669141180iple_a) X_3) A_59)))) ((insert175534902iple_a A_59) bot_bo280939947le_a_o)))
% FOF formula (forall (P_18:(hoare_669141180iple_a->Prop)) (A_58:hoare_669141180iple_a), ((and ((P_18 A_58)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_58) X_3)) (P_18 X_3))))) ((insert175534902iple_a A_58) bot_bo280939947le_a_o)))) (((P_18 A_58)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_58) X_3)) (P_18 X_3))))) bot_bo280939947le_a_o)))) of role axiom named fact_14_Collect__conv__if2
% A new axiom: (forall (P_18:(hoare_669141180iple_a->Prop)) (A_58:hoare_669141180iple_a), ((and ((P_18 A_58)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_58) X_3)) (P_18 X_3))))) ((insert175534902iple_a A_58) bot_bo280939947le_a_o)))) (((P_18 A_58)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_58) X_3)) (P_18 X_3))))) bot_bo280939947le_a_o))))
% FOF formula (forall (P_17:(hoare_669141180iple_a->Prop)) (A_57:hoare_669141180iple_a), ((and ((P_17 A_57)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X_3) A_57)) (P_17 X_3))))) ((insert175534902iple_a A_57) bot_bo280939947le_a_o)))) (((P_17 A_57)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X_3) A_57)) (P_17 X_3))))) bot_bo280939947le_a_o)))) of role axiom named fact_15_Collect__conv__if
% A new axiom: (forall (P_17:(hoare_669141180iple_a->Prop)) (A_57:hoare_669141180iple_a), ((and ((P_17 A_57)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X_3) A_57)) (P_17 X_3))))) ((insert175534902iple_a A_57) bot_bo280939947le_a_o)))) (((P_17 A_57)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X_3) A_57)) (P_17 X_3))))) bot_bo280939947le_a_o))))
% FOF formula (forall (A_56:hoare_669141180iple_a) (A_55:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) A_55) bot_bo280939947le_a_o)->(((member1016246415iple_a A_56) A_55)->False))) of role axiom named fact_16_equals0D
% A new axiom: (forall (A_56:hoare_669141180iple_a) (A_55:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) A_55) bot_bo280939947le_a_o)->(((member1016246415iple_a A_56) A_55)->False)))
% FOF formula (forall (P_16:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P_16)) bot_bo280939947le_a_o)) (forall (X_3:hoare_669141180iple_a), ((P_16 X_3)->False)))) of role axiom named fact_17_Collect__empty__eq
% A new axiom: (forall (P_16:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P_16)) bot_bo280939947le_a_o)) (forall (X_3:hoare_669141180iple_a), ((P_16 X_3)->False))))
% FOF formula (forall (C_3:hoare_669141180iple_a), (((member1016246415iple_a C_3) bot_bo280939947le_a_o)->False)) of role axiom named fact_18_empty__iff
% A new axiom: (forall (C_3:hoare_669141180iple_a), (((member1016246415iple_a C_3) bot_bo280939947le_a_o)->False))
% FOF formula (forall (P_15:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a P_15))) (forall (X_3:hoare_669141180iple_a), ((P_15 X_3)->False)))) of role axiom named fact_19_empty__Collect__eq
% A new axiom: (forall (P_15:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a P_15))) (forall (X_3:hoare_669141180iple_a), ((P_15 X_3)->False))))
% FOF formula (forall (A_54:(hoare_669141180iple_a->Prop)), ((iff ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((member1016246415iple_a X_3) A_54)))) (not (((eq (hoare_669141180iple_a->Prop)) A_54) bot_bo280939947le_a_o)))) of role axiom named fact_20_ex__in__conv
% A new axiom: (forall (A_54:(hoare_669141180iple_a->Prop)), ((iff ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((member1016246415iple_a X_3) A_54)))) (not (((eq (hoare_669141180iple_a->Prop)) A_54) bot_bo280939947le_a_o))))
% FOF formula (forall (A_53:(hoare_669141180iple_a->Prop)), ((iff (forall (X_3:hoare_669141180iple_a), (((member1016246415iple_a X_3) A_53)->False))) (((eq (hoare_669141180iple_a->Prop)) A_53) bot_bo280939947le_a_o))) of role axiom named fact_21_all__not__in__conv
% A new axiom: (forall (A_53:(hoare_669141180iple_a->Prop)), ((iff (forall (X_3:hoare_669141180iple_a), (((member1016246415iple_a X_3) A_53)->False))) (((eq (hoare_669141180iple_a->Prop)) A_53) bot_bo280939947le_a_o)))
% FOF formula (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> False))) of role axiom named fact_22_empty__def
% A new axiom: (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> False)))
% FOF formula (forall (A_52:hoare_669141180iple_a) (A_51:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_52) A_51)->(((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_52) A_51)) A_51))) of role axiom named fact_23_insert__absorb
% A new axiom: (forall (A_52:hoare_669141180iple_a) (A_51:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_52) A_51)->(((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_52) A_51)) A_51)))
% FOF formula (forall (B_11:hoare_669141180iple_a) (A_50:hoare_669141180iple_a) (B_10:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_50) B_10)->((member1016246415iple_a A_50) ((insert175534902iple_a B_11) B_10)))) of role axiom named fact_24_insertI2
% A new axiom: (forall (B_11:hoare_669141180iple_a) (A_50:hoare_669141180iple_a) (B_10:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_50) B_10)->((member1016246415iple_a A_50) ((insert175534902iple_a B_11) B_10))))
% FOF formula (forall (B_9:(hoare_669141180iple_a->Prop)) (X_24:hoare_669141180iple_a) (A_49:(hoare_669141180iple_a->Prop)), ((((member1016246415iple_a X_24) A_49)->False)->((((member1016246415iple_a X_24) B_9)->False)->((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_24) A_49)) ((insert175534902iple_a X_24) B_9))) (((eq (hoare_669141180iple_a->Prop)) A_49) B_9))))) of role axiom named fact_25_insert__ident
% A new axiom: (forall (B_9:(hoare_669141180iple_a->Prop)) (X_24:hoare_669141180iple_a) (A_49:(hoare_669141180iple_a->Prop)), ((((member1016246415iple_a X_24) A_49)->False)->((((member1016246415iple_a X_24) B_9)->False)->((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_24) A_49)) ((insert175534902iple_a X_24) B_9))) (((eq (hoare_669141180iple_a->Prop)) A_49) B_9)))))
% FOF formula (forall (Y_6:hoare_669141180iple_a) (A_48:(hoare_669141180iple_a->Prop)) (X_23:hoare_669141180iple_a), ((iff (((insert175534902iple_a Y_6) A_48) X_23)) ((or (((eq hoare_669141180iple_a) Y_6) X_23)) (A_48 X_23)))) of role axiom named fact_26_insert__code
% A new axiom: (forall (Y_6:hoare_669141180iple_a) (A_48:(hoare_669141180iple_a->Prop)) (X_23:hoare_669141180iple_a), ((iff (((insert175534902iple_a Y_6) A_48) X_23)) ((or (((eq hoare_669141180iple_a) Y_6) X_23)) (A_48 X_23))))
% FOF formula (forall (A_47:hoare_669141180iple_a) (B_8:hoare_669141180iple_a) (A_46:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a A_47) ((insert175534902iple_a B_8) A_46))) ((or (((eq hoare_669141180iple_a) A_47) B_8)) ((member1016246415iple_a A_47) A_46)))) of role axiom named fact_27_insert__iff
% A new axiom: (forall (A_47:hoare_669141180iple_a) (B_8:hoare_669141180iple_a) (A_46:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a A_47) ((insert175534902iple_a B_8) A_46))) ((or (((eq hoare_669141180iple_a) A_47) B_8)) ((member1016246415iple_a A_47) A_46))))
% FOF formula (forall (X_22:hoare_669141180iple_a) (Y_5:hoare_669141180iple_a) (A_45:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_22) ((insert175534902iple_a Y_5) A_45))) ((insert175534902iple_a Y_5) ((insert175534902iple_a X_22) A_45)))) of role axiom named fact_28_insert__commute
% A new axiom: (forall (X_22:hoare_669141180iple_a) (Y_5:hoare_669141180iple_a) (A_45:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_22) ((insert175534902iple_a Y_5) A_45))) ((insert175534902iple_a Y_5) ((insert175534902iple_a X_22) A_45))))
% FOF formula (forall (X_21:hoare_669141180iple_a) (A_44:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_21) ((insert175534902iple_a X_21) A_44))) ((insert175534902iple_a X_21) A_44))) of role axiom named fact_29_insert__absorb2
% A new axiom: (forall (X_21:hoare_669141180iple_a) (A_44:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_21) ((insert175534902iple_a X_21) A_44))) ((insert175534902iple_a X_21) A_44)))
% FOF formula (forall (A_43:hoare_669141180iple_a) (P_14:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_43) (collec1717965009iple_a P_14))) (collec1717965009iple_a (fun (U:hoare_669141180iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_669141180iple_a) U) A_43))) (P_14 U)))))) of role axiom named fact_30_insert__Collect
% A new axiom: (forall (A_43:hoare_669141180iple_a) (P_14:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_43) (collec1717965009iple_a P_14))) (collec1717965009iple_a (fun (U:hoare_669141180iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_669141180iple_a) U) A_43))) (P_14 U))))))
% FOF formula (forall (A_42:hoare_669141180iple_a) (B_7:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_42) B_7)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) X_3) A_42)) ((member1016246415iple_a X_3) B_7)))))) of role axiom named fact_31_insert__compr
% A new axiom: (forall (A_42:hoare_669141180iple_a) (B_7:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_42) B_7)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) X_3) A_42)) ((member1016246415iple_a X_3) B_7))))))
% FOF formula (forall (A_41:hoare_669141180iple_a) (B_6:(hoare_669141180iple_a->Prop)), ((member1016246415iple_a A_41) ((insert175534902iple_a A_41) B_6))) of role axiom named fact_32_insertI1
% A new axiom: (forall (A_41:hoare_669141180iple_a) (B_6:(hoare_669141180iple_a->Prop)), ((member1016246415iple_a A_41) ((insert175534902iple_a A_41) B_6)))
% FOF formula (forall (X_3:hoare_669141180iple_a) (Xa:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_3) Xa)) (collec1717965009iple_a (fun (Y_1:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) Y_1) X_3)) ((member1016246415iple_a Y_1) Xa)))))) of role axiom named fact_33_insert__compr__raw
% A new axiom: (forall (X_3:hoare_669141180iple_a) (Xa:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_3) Xa)) (collec1717965009iple_a (fun (Y_1:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) Y_1) X_3)) ((member1016246415iple_a Y_1) Xa))))))
% FOF formula (forall (A_40:hoare_669141180iple_a) (B_5:hoare_669141180iple_a), ((((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_40) bot_bo280939947le_a_o)) ((insert175534902iple_a B_5) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) A_40) B_5))) of role axiom named fact_34_singleton__inject
% A new axiom: (forall (A_40:hoare_669141180iple_a) (B_5:hoare_669141180iple_a), ((((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_40) bot_bo280939947le_a_o)) ((insert175534902iple_a B_5) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) A_40) B_5)))
% FOF formula (forall (B_4:hoare_669141180iple_a) (A_39:hoare_669141180iple_a), (((member1016246415iple_a B_4) ((insert175534902iple_a A_39) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) B_4) A_39))) of role axiom named fact_35_singletonE
% A new axiom: (forall (B_4:hoare_669141180iple_a) (A_39:hoare_669141180iple_a), (((member1016246415iple_a B_4) ((insert175534902iple_a A_39) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) B_4) A_39)))
% FOF formula (forall (A_38:hoare_669141180iple_a) (B_3:hoare_669141180iple_a) (C_2:hoare_669141180iple_a) (D_1:hoare_669141180iple_a), ((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_38) ((insert175534902iple_a B_3) bot_bo280939947le_a_o))) ((insert175534902iple_a C_2) ((insert175534902iple_a D_1) bot_bo280939947le_a_o)))) ((or ((and (((eq hoare_669141180iple_a) A_38) C_2)) (((eq hoare_669141180iple_a) B_3) D_1))) ((and (((eq hoare_669141180iple_a) A_38) D_1)) (((eq hoare_669141180iple_a) B_3) C_2))))) of role axiom named fact_36_doubleton__eq__iff
% A new axiom: (forall (A_38:hoare_669141180iple_a) (B_3:hoare_669141180iple_a) (C_2:hoare_669141180iple_a) (D_1:hoare_669141180iple_a), ((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_38) ((insert175534902iple_a B_3) bot_bo280939947le_a_o))) ((insert175534902iple_a C_2) ((insert175534902iple_a D_1) bot_bo280939947le_a_o)))) ((or ((and (((eq hoare_669141180iple_a) A_38) C_2)) (((eq hoare_669141180iple_a) B_3) D_1))) ((and (((eq hoare_669141180iple_a) A_38) D_1)) (((eq hoare_669141180iple_a) B_3) C_2)))))
% FOF formula (forall (B_2:hoare_669141180iple_a) (A_37:hoare_669141180iple_a), ((iff ((member1016246415iple_a B_2) ((insert175534902iple_a A_37) bot_bo280939947le_a_o))) (((eq hoare_669141180iple_a) B_2) A_37))) of role axiom named fact_37_singleton__iff
% A new axiom: (forall (B_2:hoare_669141180iple_a) (A_37:hoare_669141180iple_a), ((iff ((member1016246415iple_a B_2) ((insert175534902iple_a A_37) bot_bo280939947le_a_o))) (((eq hoare_669141180iple_a) B_2) A_37)))
% FOF formula (forall (A_36:hoare_669141180iple_a) (A_35:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_36) A_35)) bot_bo280939947le_a_o))) of role axiom named fact_38_insert__not__empty
% A new axiom: (forall (A_36:hoare_669141180iple_a) (A_35:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_36) A_35)) bot_bo280939947le_a_o)))
% FOF formula (forall (A_34:hoare_669141180iple_a) (A_33:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) ((insert175534902iple_a A_34) A_33)))) of role axiom named fact_39_empty__not__insert
% A new axiom: (forall (A_34:hoare_669141180iple_a) (A_33:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) ((insert175534902iple_a A_34) A_33))))
% FOF formula (forall (X_20:hoare_669141180iple_a), (((eq hoare_669141180iple_a) (the_el738790235iple_a ((insert175534902iple_a X_20) bot_bo280939947le_a_o))) X_20)) of role axiom named fact_40_the__elem__eq
% A new axiom: (forall (X_20:hoare_669141180iple_a), (((eq hoare_669141180iple_a) (the_el738790235iple_a ((insert175534902iple_a X_20) bot_bo280939947le_a_o))) X_20))
% FOF formula (forall (X_19:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X_19)) bot_bot_o)) of role axiom named fact_41_bot__apply
% A new axiom: (forall (X_19:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X_19)) bot_bot_o))
% FOF formula (forall (X_3:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X_3)) bot_bot_o)) of role axiom named fact_42_bot__fun__def
% A new axiom: (forall (X_3:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X_3)) bot_bot_o))
% FOF formula (forall (G_3:(hoare_669141180iple_a->Prop)) (P_13:(x_a->(state->Prop))), ((hoare_2128652938rivs_a G_3) ((insert175534902iple_a (((hoare_1295064928iple_a P_13) skip) P_13)) bot_bo280939947le_a_o))) of role axiom named fact_43_hoare__derivs_OSkip
% A new axiom: (forall (G_3:(hoare_669141180iple_a->Prop)) (P_13:(x_a->(state->Prop))), ((hoare_2128652938rivs_a G_3) ((insert175534902iple_a (((hoare_1295064928iple_a P_13) skip) P_13)) bot_bo280939947le_a_o)))
% FOF formula (forall (D:com) (R:(x_a->(state->Prop))) (G_2:(hoare_669141180iple_a->Prop)) (P_12:(x_a->(state->Prop))) (C_1:com) (Q_4:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_2) ((insert175534902iple_a (((hoare_1295064928iple_a P_12) C_1) Q_4)) bot_bo280939947le_a_o))->(((hoare_2128652938rivs_a G_2) ((insert175534902iple_a (((hoare_1295064928iple_a Q_4) D) R)) bot_bo280939947le_a_o))->((hoare_2128652938rivs_a G_2) ((insert175534902iple_a (((hoare_1295064928iple_a P_12) ((semi C_1) D)) R)) bot_bo280939947le_a_o))))) of role axiom named fact_44_Comp
% A new axiom: (forall (D:com) (R:(x_a->(state->Prop))) (G_2:(hoare_669141180iple_a->Prop)) (P_12:(x_a->(state->Prop))) (C_1:com) (Q_4:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_2) ((insert175534902iple_a (((hoare_1295064928iple_a P_12) C_1) Q_4)) bot_bo280939947le_a_o))->(((hoare_2128652938rivs_a G_2) ((insert175534902iple_a (((hoare_1295064928iple_a Q_4) D) R)) bot_bo280939947le_a_o))->((hoare_2128652938rivs_a G_2) ((insert175534902iple_a (((hoare_1295064928iple_a P_12) ((semi C_1) D)) R)) bot_bo280939947le_a_o)))))
% 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_45_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 (X_18:hoare_669141180iple_a) (A_32:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_18) A_32)->((forall (B_1:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) A_32) ((insert175534902iple_a X_18) B_1))->((member1016246415iple_a X_18) B_1)))->False))) of role axiom named fact_46_Set_Oset__insert
% A new axiom: (forall (X_18:hoare_669141180iple_a) (A_32:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_18) A_32)->((forall (B_1:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) A_32) ((insert175534902iple_a X_18) B_1))->((member1016246415iple_a X_18) B_1)))->False)))
% FOF formula (forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip))) of role axiom named fact_47_com_Osimps_I13_J
% A new axiom: (forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip)))
% FOF formula (forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2)))) of role axiom named fact_48_com_Osimps_I12_J
% A new axiom: (forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2))))
% FOF formula (forall (X_17:(hoare_669141180iple_a->Prop)), (((eq hoare_669141180iple_a) (the_el738790235iple_a X_17)) (the_Ho49089901iple_a (fun (X_3:hoare_669141180iple_a)=> (((eq (hoare_669141180iple_a->Prop)) X_17) ((insert175534902iple_a X_3) bot_bo280939947le_a_o)))))) of role axiom named fact_49_the__elem__def
% A new axiom: (forall (X_17:(hoare_669141180iple_a->Prop)), (((eq hoare_669141180iple_a) (the_el738790235iple_a X_17)) (the_Ho49089901iple_a (fun (X_3:hoare_669141180iple_a)=> (((eq (hoare_669141180iple_a->Prop)) X_17) ((insert175534902iple_a X_3) bot_bo280939947le_a_o))))))
% FOF formula (forall (A_31:hoare_669141180iple_a) (A_30:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_31) A_30)->((ex (hoare_669141180iple_a->Prop)) (fun (B_1:(hoare_669141180iple_a->Prop))=> ((and (((eq (hoare_669141180iple_a->Prop)) A_30) ((insert175534902iple_a A_31) B_1))) (((member1016246415iple_a A_31) B_1)->False)))))) of role axiom named fact_50_mk__disjoint__insert
% A new axiom: (forall (A_31:hoare_669141180iple_a) (A_30:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_31) A_30)->((ex (hoare_669141180iple_a->Prop)) (fun (B_1:(hoare_669141180iple_a->Prop))=> ((and (((eq (hoare_669141180iple_a->Prop)) A_30) ((insert175534902iple_a A_31) B_1))) (((member1016246415iple_a A_31) B_1)->False))))))
% FOF formula (forall (Com1_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2)))) of role axiom named fact_51_com_Osimps_I3_J
% A new axiom: (forall (Com1_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2))))
% FOF formula (forall (X_16:hoare_669141180iple_a), (((eq hoare_669141180iple_a) (the_Ho49089901iple_a (fequal182287803iple_a X_16))) X_16)) of role axiom named fact_52_the__sym__eq__trivial
% A new axiom: (forall (X_16:hoare_669141180iple_a), (((eq hoare_669141180iple_a) (the_Ho49089901iple_a (fequal182287803iple_a X_16))) X_16))
% FOF formula (forall (A_29:hoare_669141180iple_a), (((eq hoare_669141180iple_a) (the_Ho49089901iple_a (fun (X_3:hoare_669141180iple_a)=> (((eq hoare_669141180iple_a) X_3) A_29)))) A_29)) of role axiom named fact_53_the__eq__trivial
% A new axiom: (forall (A_29:hoare_669141180iple_a), (((eq hoare_669141180iple_a) (the_Ho49089901iple_a (fun (X_3:hoare_669141180iple_a)=> (((eq hoare_669141180iple_a) X_3) A_29)))) A_29))
% FOF formula (forall (X_15:hoare_669141180iple_a) (Y_3:hoare_669141180iple_a) (P_11:Prop), ((and (P_11->(((eq hoare_669141180iple_a) X_15) (the_Ho49089901iple_a (fun (Z_7:hoare_669141180iple_a)=> ((and (((fun (X:Prop) (Y:Prop)=> (X->Y)) P_11) (((eq hoare_669141180iple_a) Z_7) X_15))) (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not P_11)) (((eq hoare_669141180iple_a) Z_7) Y_3)))))))) ((P_11->False)->(((eq hoare_669141180iple_a) Y_3) (the_Ho49089901iple_a (fun (Z_7:hoare_669141180iple_a)=> ((and (((fun (X:Prop) (Y:Prop)=> (X->Y)) P_11) (((eq hoare_669141180iple_a) Z_7) X_15))) (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not P_11)) (((eq hoare_669141180iple_a) Z_7) Y_3))))))))) of role axiom named fact_54_If__def
% A new axiom: (forall (X_15:hoare_669141180iple_a) (Y_3:hoare_669141180iple_a) (P_11:Prop), ((and (P_11->(((eq hoare_669141180iple_a) X_15) (the_Ho49089901iple_a (fun (Z_7:hoare_669141180iple_a)=> ((and (((fun (X:Prop) (Y:Prop)=> (X->Y)) P_11) (((eq hoare_669141180iple_a) Z_7) X_15))) (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not P_11)) (((eq hoare_669141180iple_a) Z_7) Y_3)))))))) ((P_11->False)->(((eq hoare_669141180iple_a) Y_3) (the_Ho49089901iple_a (fun (Z_7:hoare_669141180iple_a)=> ((and (((fun (X:Prop) (Y:Prop)=> (X->Y)) P_11) (((eq hoare_669141180iple_a) Z_7) X_15))) (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not P_11)) (((eq hoare_669141180iple_a) Z_7) Y_3)))))))))
% FOF formula (forall (A_28:(hoare_669141180iple_a->Prop)), ((forall (Y_1:hoare_669141180iple_a), (((member1016246415iple_a Y_1) A_28)->False))->(((eq (hoare_669141180iple_a->Prop)) A_28) bot_bo280939947le_a_o))) of role axiom named fact_55_equals0I
% A new axiom: (forall (A_28:(hoare_669141180iple_a->Prop)), ((forall (Y_1:hoare_669141180iple_a), (((member1016246415iple_a Y_1) A_28)->False))->(((eq (hoare_669141180iple_a->Prop)) A_28) bot_bo280939947le_a_o)))
% FOF formula (forall (P_10:(hoare_669141180iple_a->Prop)) (A_27:hoare_669141180iple_a), ((P_10 A_27)->((forall (X_3:hoare_669141180iple_a), ((P_10 X_3)->(((eq hoare_669141180iple_a) X_3) A_27)))->(((eq hoare_669141180iple_a) (the_Ho49089901iple_a P_10)) A_27)))) of role axiom named fact_56_the__equality
% A new axiom: (forall (P_10:(hoare_669141180iple_a->Prop)) (A_27:hoare_669141180iple_a), ((P_10 A_27)->((forall (X_3:hoare_669141180iple_a), ((P_10 X_3)->(((eq hoare_669141180iple_a) X_3) A_27)))->(((eq hoare_669141180iple_a) (the_Ho49089901iple_a P_10)) A_27))))
% FOF formula (forall (P_9:(hoare_669141180iple_a->Prop)) (A_26:hoare_669141180iple_a), ((P_9 A_26)->((forall (X_3:hoare_669141180iple_a), ((P_9 X_3)->(((eq hoare_669141180iple_a) X_3) A_26)))->(P_9 (the_Ho49089901iple_a P_9))))) of role axiom named fact_57_theI
% A new axiom: (forall (P_9:(hoare_669141180iple_a->Prop)) (A_26:hoare_669141180iple_a), ((P_9 A_26)->((forall (X_3:hoare_669141180iple_a), ((P_9 X_3)->(((eq hoare_669141180iple_a) X_3) A_26)))->(P_9 (the_Ho49089901iple_a P_9)))))
% FOF formula (forall (A_25:hoare_669141180iple_a) (P_8:(hoare_669141180iple_a->Prop)), (((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((and (P_8 X_3)) (forall (Y_1:hoare_669141180iple_a), ((P_8 Y_1)->(((eq hoare_669141180iple_a) Y_1) X_3))))))->((P_8 A_25)->(((eq hoare_669141180iple_a) (the_Ho49089901iple_a P_8)) A_25)))) of role axiom named fact_58_the1__equality
% A new axiom: (forall (A_25:hoare_669141180iple_a) (P_8:(hoare_669141180iple_a->Prop)), (((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((and (P_8 X_3)) (forall (Y_1:hoare_669141180iple_a), ((P_8 Y_1)->(((eq hoare_669141180iple_a) Y_1) X_3))))))->((P_8 A_25)->(((eq hoare_669141180iple_a) (the_Ho49089901iple_a P_8)) A_25))))
% FOF formula (forall (P_7:(hoare_669141180iple_a->Prop)), (((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((and (P_7 X_3)) (forall (Y_1:hoare_669141180iple_a), ((P_7 Y_1)->(((eq hoare_669141180iple_a) Y_1) X_3))))))->(P_7 (the_Ho49089901iple_a P_7)))) of role axiom named fact_59_theI_H
% A new axiom: (forall (P_7:(hoare_669141180iple_a->Prop)), (((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((and (P_7 X_3)) (forall (Y_1:hoare_669141180iple_a), ((P_7 Y_1)->(((eq hoare_669141180iple_a) Y_1) X_3))))))->(P_7 (the_Ho49089901iple_a P_7))))
% FOF formula (forall (Q_2:(x_a->(state->Prop))) (G_1:(hoare_669141180iple_a->Prop)) (C:com) (P_5:(x_a->(state->Prop))), ((forall (Z:x_a) (S:state), (((P_5 Z) S)->((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a G_1) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) C) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((Q_2 Z) S_1))))))))))->((hoare_2128652938rivs_a G_1) ((insert175534902iple_a (((hoare_1295064928iple_a P_5) C) Q_2)) bot_bo280939947le_a_o)))) of role axiom named fact_60_conseq
% A new axiom: (forall (Q_2:(x_a->(state->Prop))) (G_1:(hoare_669141180iple_a->Prop)) (C:com) (P_5:(x_a->(state->Prop))), ((forall (Z:x_a) (S:state), (((P_5 Z) S)->((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a G_1) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) C) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((Q_2 Z) S_1))))))))))->((hoare_2128652938rivs_a G_1) ((insert175534902iple_a (((hoare_1295064928iple_a P_5) C) Q_2)) bot_bo280939947le_a_o))))
% FOF formula (forall (A_24:(hoare_669141180iple_a->Prop)), ((iff (not (((eq (hoare_669141180iple_a->Prop)) A_24) bot_bo280939947le_a_o))) ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((ex (hoare_669141180iple_a->Prop)) (fun (B_1:(hoare_669141180iple_a->Prop))=> ((and (((eq (hoare_669141180iple_a->Prop)) A_24) ((insert175534902iple_a X_3) B_1))) (((member1016246415iple_a X_3) B_1)->False)))))))) of role axiom named fact_61_nonempty__iff
% A new axiom: (forall (A_24:(hoare_669141180iple_a->Prop)), ((iff (not (((eq (hoare_669141180iple_a->Prop)) A_24) bot_bo280939947le_a_o))) ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((ex (hoare_669141180iple_a->Prop)) (fun (B_1:(hoare_669141180iple_a->Prop))=> ((and (((eq (hoare_669141180iple_a->Prop)) A_24) ((insert175534902iple_a X_3) B_1))) (((member1016246415iple_a X_3) B_1)->False))))))))
% FOF formula (forall (F_31:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_23:hoare_669141180iple_a) (B:hoare_669141180iple_a), ((iff (((finite840267660iple_a F_31) ((insert175534902iple_a A_23) bot_bo280939947le_a_o)) B)) (((eq hoare_669141180iple_a) A_23) B))) of role axiom named fact_62_fold1Set__sing
% A new axiom: (forall (F_31:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_23:hoare_669141180iple_a) (B:hoare_669141180iple_a), ((iff (((finite840267660iple_a F_31) ((insert175534902iple_a A_23) bot_bo280939947le_a_o)) B)) (((eq hoare_669141180iple_a) A_23) B)))
% FOF formula (forall (X_14:hoare_669141180iple_a) (F_30:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_29:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_30) F_29)->(((eq hoare_669141180iple_a) (F_29 ((insert175534902iple_a X_14) bot_bo280939947le_a_o))) X_14))) of role axiom named fact_63_folding__one_Osingleton
% A new axiom: (forall (X_14:hoare_669141180iple_a) (F_30:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_29:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_30) F_29)->(((eq hoare_669141180iple_a) (F_29 ((insert175534902iple_a X_14) bot_bo280939947le_a_o))) X_14)))
% FOF formula (forall (X_3:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X_3)) ((member1016246415iple_a X_3) bot_bo280939947le_a_o))) of role axiom named fact_64_bot__empty__eq
% A new axiom: (forall (X_3:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X_3)) ((member1016246415iple_a X_3) bot_bo280939947le_a_o)))
% FOF formula (forall (F_28:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (X_13:hoare_669141180iple_a), ((((finite840267660iple_a F_28) bot_bo280939947le_a_o) X_13)->False)) of role axiom named fact_65_empty__fold1SetE
% A new axiom: (forall (F_28:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (X_13:hoare_669141180iple_a), ((((finite840267660iple_a F_28) bot_bo280939947le_a_o) X_13)->False))
% FOF formula (forall (F_27:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_22:(hoare_669141180iple_a->Prop)) (X_12:hoare_669141180iple_a), ((((finite840267660iple_a F_27) A_22) X_12)->(not (((eq (hoare_669141180iple_a->Prop)) A_22) bot_bo280939947le_a_o)))) of role axiom named fact_66_fold1Set__nonempty
% A new axiom: (forall (F_27:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_22:(hoare_669141180iple_a->Prop)) (X_12:hoare_669141180iple_a), ((((finite840267660iple_a F_27) A_22) X_12)->(not (((eq (hoare_669141180iple_a->Prop)) A_22) bot_bo280939947le_a_o))))
% FOF formula (forall (F_26:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_21:hoare_669141180iple_a) (A_20:(hoare_669141180iple_a->Prop)) (X_11:hoare_669141180iple_a), (((((finite590756294iple_a F_26) A_21) A_20) X_11)->((((member1016246415iple_a A_21) A_20)->False)->(((finite840267660iple_a F_26) ((insert175534902iple_a A_21) A_20)) X_11)))) of role axiom named fact_67_fold1Set_Ointros
% A new axiom: (forall (F_26:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_21:hoare_669141180iple_a) (A_20:(hoare_669141180iple_a->Prop)) (X_11:hoare_669141180iple_a), (((((finite590756294iple_a F_26) A_21) A_20) X_11)->((((member1016246415iple_a A_21) A_20)->False)->(((finite840267660iple_a F_26) ((insert175534902iple_a A_21) A_20)) X_11))))
% FOF formula (forall (X_10:hoare_669141180iple_a) (A_19:(hoare_669141180iple_a->Prop)) (F_25:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_24:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_25) F_24)->((finite957651855iple_a A_19)->((((member1016246415iple_a X_10) A_19)->False)->((not (((eq (hoare_669141180iple_a->Prop)) A_19) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) (F_24 ((insert175534902iple_a X_10) A_19))) ((F_25 X_10) (F_24 A_19)))))))) of role axiom named fact_68_folding__one_Oinsert
% A new axiom: (forall (X_10:hoare_669141180iple_a) (A_19:(hoare_669141180iple_a->Prop)) (F_25:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_24:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_25) F_24)->((finite957651855iple_a A_19)->((((member1016246415iple_a X_10) A_19)->False)->((not (((eq (hoare_669141180iple_a->Prop)) A_19) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) (F_24 ((insert175534902iple_a X_10) A_19))) ((F_25 X_10) (F_24 A_19))))))))
% FOF formula (forall (F_23:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_18:(hoare_669141180iple_a->Prop)), (((eq hoare_669141180iple_a) ((finite684844060iple_a F_23) A_18)) (the_Ho49089901iple_a ((finite840267660iple_a F_23) A_18)))) of role axiom named fact_69_fold1__def
% A new axiom: (forall (F_23:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_18:(hoare_669141180iple_a->Prop)), (((eq hoare_669141180iple_a) ((finite684844060iple_a F_23) A_18)) (the_Ho49089901iple_a ((finite840267660iple_a F_23) A_18))))
% FOF formula (forall (Q_1:(hoare_669141180iple_a->Prop)) (P_4:(hoare_669141180iple_a->Prop)), (((or (finite957651855iple_a (collec1717965009iple_a P_4))) (finite957651855iple_a (collec1717965009iple_a Q_1)))->(finite957651855iple_a (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (P_4 X_3)) (Q_1 X_3))))))) of role axiom named fact_70_finite__Collect__conjI
% A new axiom: (forall (Q_1:(hoare_669141180iple_a->Prop)) (P_4:(hoare_669141180iple_a->Prop)), (((or (finite957651855iple_a (collec1717965009iple_a P_4))) (finite957651855iple_a (collec1717965009iple_a Q_1)))->(finite957651855iple_a (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (P_4 X_3)) (Q_1 X_3)))))))
% FOF formula (finite957651855iple_a bot_bo280939947le_a_o) of role axiom named fact_71_finite_OemptyI
% A new axiom: (finite957651855iple_a bot_bo280939947le_a_o)
% FOF formula (forall (A_17:hoare_669141180iple_a) (A_16:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a A_16)->(finite957651855iple_a ((insert175534902iple_a A_17) A_16)))) of role axiom named fact_72_finite_OinsertI
% A new axiom: (forall (A_17:hoare_669141180iple_a) (A_16:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a A_16)->(finite957651855iple_a ((insert175534902iple_a A_17) A_16))))
% FOF formula (forall (X_9:hoare_669141180iple_a) (A_15:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a X_9) A_15)) (A_15 X_9))) of role axiom named fact_73_mem__def
% A new axiom: (forall (X_9:hoare_669141180iple_a) (A_15:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a X_9) A_15)) (A_15 X_9)))
% FOF formula (forall (P_3:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P_3)) P_3)) of role axiom named fact_74_Collect__def
% A new axiom: (forall (P_3:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P_3)) P_3))
% FOF formula (forall (A_14:(hoare_669141180iple_a->Prop)) (F_22:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_21:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_22) F_21)->((finite957651855iple_a A_14)->(((eq hoare_669141180iple_a) (F_21 A_14)) ((finite684844060iple_a F_22) A_14))))) of role axiom named fact_75_folding__one_Oeq__fold
% A new axiom: (forall (A_14:(hoare_669141180iple_a->Prop)) (F_22:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_21:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_22) F_21)->((finite957651855iple_a A_14)->(((eq hoare_669141180iple_a) (F_21 A_14)) ((finite684844060iple_a F_22) A_14)))))
% FOF formula (forall (F_20:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_5:hoare_669141180iple_a), ((((finite590756294iple_a F_20) Z_5) bot_bo280939947le_a_o) Z_5)) of role axiom named fact_76_fold__graph_OemptyI
% A new axiom: (forall (F_20:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_5:hoare_669141180iple_a), ((((finite590756294iple_a F_20) Z_5) bot_bo280939947le_a_o) Z_5))
% FOF formula (forall (F_19:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_4:hoare_669141180iple_a) (X_8:hoare_669141180iple_a), (((((finite590756294iple_a F_19) Z_4) bot_bo280939947le_a_o) X_8)->(((eq hoare_669141180iple_a) X_8) Z_4))) of role axiom named fact_77_empty__fold__graphE
% A new axiom: (forall (F_19:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_4:hoare_669141180iple_a) (X_8:hoare_669141180iple_a), (((((finite590756294iple_a F_19) Z_4) bot_bo280939947le_a_o) X_8)->(((eq hoare_669141180iple_a) X_8) Z_4)))
% FOF formula (forall (F_18:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_3:hoare_669141180iple_a) (Y_2:hoare_669141180iple_a) (X_7:hoare_669141180iple_a) (A_13:(hoare_669141180iple_a->Prop)), ((((member1016246415iple_a X_7) A_13)->False)->(((((finite590756294iple_a F_18) Z_3) A_13) Y_2)->((((finite590756294iple_a F_18) Z_3) ((insert175534902iple_a X_7) A_13)) ((F_18 X_7) Y_2))))) of role axiom named fact_78_fold__graph_OinsertI
% A new axiom: (forall (F_18:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_3:hoare_669141180iple_a) (Y_2:hoare_669141180iple_a) (X_7:hoare_669141180iple_a) (A_13:(hoare_669141180iple_a->Prop)), ((((member1016246415iple_a X_7) A_13)->False)->(((((finite590756294iple_a F_18) Z_3) A_13) Y_2)->((((finite590756294iple_a F_18) Z_3) ((insert175534902iple_a X_7) A_13)) ((F_18 X_7) Y_2)))))
% FOF formula (forall (P_2:(hoare_669141180iple_a->Prop)) (Q:(hoare_669141180iple_a->Prop)), ((iff (finite957651855iple_a (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((or (P_2 X_3)) (Q X_3)))))) ((and (finite957651855iple_a (collec1717965009iple_a P_2))) (finite957651855iple_a (collec1717965009iple_a Q))))) of role axiom named fact_79_finite__Collect__disjI
% A new axiom: (forall (P_2:(hoare_669141180iple_a->Prop)) (Q:(hoare_669141180iple_a->Prop)), ((iff (finite957651855iple_a (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((or (P_2 X_3)) (Q X_3)))))) ((and (finite957651855iple_a (collec1717965009iple_a P_2))) (finite957651855iple_a (collec1717965009iple_a Q)))))
% FOF formula (forall (A_12:hoare_669141180iple_a) (A_11:(hoare_669141180iple_a->Prop)), ((iff (finite957651855iple_a ((insert175534902iple_a A_12) A_11))) (finite957651855iple_a A_11))) of role axiom named fact_80_finite__insert
% A new axiom: (forall (A_12:hoare_669141180iple_a) (A_11:(hoare_669141180iple_a->Prop)), ((iff (finite957651855iple_a ((insert175534902iple_a A_12) A_11))) (finite957651855iple_a A_11)))
% FOF formula (forall (A_10:hoare_669141180iple_a) (G:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)) (F_17:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))), ((((eq ((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)) G) (finite684844060iple_a F_17))->(((eq hoare_669141180iple_a) (G ((insert175534902iple_a A_10) bot_bo280939947le_a_o))) A_10))) of role axiom named fact_81_fold1__singleton__def
% A new axiom: (forall (A_10:hoare_669141180iple_a) (G:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)) (F_17:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))), ((((eq ((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)) G) (finite684844060iple_a F_17))->(((eq hoare_669141180iple_a) (G ((insert175534902iple_a A_10) bot_bo280939947le_a_o))) A_10)))
% FOF formula (forall (F_16:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_9:hoare_669141180iple_a), (((eq hoare_669141180iple_a) ((finite684844060iple_a F_16) ((insert175534902iple_a A_9) bot_bo280939947le_a_o))) A_9)) of role axiom named fact_82_fold1__singleton
% A new axiom: (forall (F_16:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_9:hoare_669141180iple_a), (((eq hoare_669141180iple_a) ((finite684844060iple_a F_16) ((insert175534902iple_a A_9) bot_bo280939947le_a_o))) A_9))
% FOF formula (forall (A_8:(hoare_669141180iple_a->Prop)) (F_15:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_14:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_15) F_14)->((finite957651855iple_a A_8)->((not (((eq (hoare_669141180iple_a->Prop)) A_8) bot_bo280939947le_a_o))->((forall (X_3:hoare_669141180iple_a) (Y_1:hoare_669141180iple_a), ((member1016246415iple_a ((F_15 X_3) Y_1)) ((insert175534902iple_a X_3) ((insert175534902iple_a Y_1) bot_bo280939947le_a_o))))->((member1016246415iple_a (F_14 A_8)) A_8)))))) of role axiom named fact_83_folding__one_Oclosed
% A new axiom: (forall (A_8:(hoare_669141180iple_a->Prop)) (F_15:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_14:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_15) F_14)->((finite957651855iple_a A_8)->((not (((eq (hoare_669141180iple_a->Prop)) A_8) bot_bo280939947le_a_o))->((forall (X_3:hoare_669141180iple_a) (Y_1:hoare_669141180iple_a), ((member1016246415iple_a ((F_15 X_3) Y_1)) ((insert175534902iple_a X_3) ((insert175534902iple_a Y_1) bot_bo280939947le_a_o))))->((member1016246415iple_a (F_14 A_8)) A_8))))))
% FOF formula (forall (F_13:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_7:hoare_669141180iple_a) (X_6:(hoare_669141180iple_a->Prop)) (X_5:hoare_669141180iple_a), ((((finite840267660iple_a F_13) ((insert175534902iple_a A_7) X_6)) X_5)->((forall (A_3:hoare_669141180iple_a) (A_2:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_7) X_6)) ((insert175534902iple_a A_3) A_2))->(((((finite590756294iple_a F_13) A_3) A_2) X_5)->((member1016246415iple_a A_3) A_2))))->False))) of role axiom named fact_84_insert__fold1SetE
% A new axiom: (forall (F_13:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_7:hoare_669141180iple_a) (X_6:(hoare_669141180iple_a->Prop)) (X_5:hoare_669141180iple_a), ((((finite840267660iple_a F_13) ((insert175534902iple_a A_7) X_6)) X_5)->((forall (A_3:hoare_669141180iple_a) (A_2:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_7) X_6)) ((insert175534902iple_a A_3) A_2))->(((((finite590756294iple_a F_13) A_3) A_2) X_5)->((member1016246415iple_a A_3) A_2))))->False)))
% FOF formula (forall (F_12:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_6:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a A_6)->((not (((eq (hoare_669141180iple_a->Prop)) A_6) bot_bo280939947le_a_o))->(_TPTP_ex ((finite840267660iple_a F_12) A_6))))) of role axiom named fact_85_finite__nonempty__imp__fold1Set
% A new axiom: (forall (F_12:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_6:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a A_6)->((not (((eq (hoare_669141180iple_a->Prop)) A_6) bot_bo280939947le_a_o))->(_TPTP_ex ((finite840267660iple_a F_12) A_6)))))
% FOF formula (forall (P_1:((hoare_669141180iple_a->Prop)->Prop)) (F_11:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_11)->((P_1 bot_bo280939947le_a_o)->((forall (X_3:hoare_669141180iple_a) (F_5:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_5)->((((member1016246415iple_a X_3) F_5)->False)->((P_1 F_5)->(P_1 ((insert175534902iple_a X_3) F_5))))))->(P_1 F_11))))) of role axiom named fact_86_finite__induct
% A new axiom: (forall (P_1:((hoare_669141180iple_a->Prop)->Prop)) (F_11:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_11)->((P_1 bot_bo280939947le_a_o)->((forall (X_3:hoare_669141180iple_a) (F_5:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_5)->((((member1016246415iple_a X_3) F_5)->False)->((P_1 F_5)->(P_1 ((insert175534902iple_a X_3) F_5))))))->(P_1 F_11)))))
% FOF formula (forall (A_5:(hoare_669141180iple_a->Prop)), ((iff (finite957651855iple_a A_5)) ((or (((eq (hoare_669141180iple_a->Prop)) A_5) bot_bo280939947le_a_o)) ((ex (hoare_669141180iple_a->Prop)) (fun (A_2:(hoare_669141180iple_a->Prop))=> ((ex hoare_669141180iple_a) (fun (A_3:hoare_669141180iple_a)=> ((and (((eq (hoare_669141180iple_a->Prop)) A_5) ((insert175534902iple_a A_3) A_2))) (finite957651855iple_a A_2))))))))) of role axiom named fact_87_finite_Osimps
% A new axiom: (forall (A_5:(hoare_669141180iple_a->Prop)), ((iff (finite957651855iple_a A_5)) ((or (((eq (hoare_669141180iple_a->Prop)) A_5) bot_bo280939947le_a_o)) ((ex (hoare_669141180iple_a->Prop)) (fun (A_2:(hoare_669141180iple_a->Prop))=> ((ex hoare_669141180iple_a) (fun (A_3:hoare_669141180iple_a)=> ((and (((eq (hoare_669141180iple_a->Prop)) A_5) ((insert175534902iple_a A_3) A_2))) (finite957651855iple_a A_2)))))))))
% FOF formula (forall (F_10:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_2:hoare_669141180iple_a) (A_4:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a A_4)->(_TPTP_ex (((finite590756294iple_a F_10) Z_2) A_4)))) of role axiom named fact_88_finite__imp__fold__graph
% A new axiom: (forall (F_10:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_2:hoare_669141180iple_a) (A_4:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a A_4)->(_TPTP_ex (((finite590756294iple_a F_10) Z_2) A_4))))
% FOF formula (forall (F_9:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A1_1:(hoare_669141180iple_a->Prop)) (A2_1:hoare_669141180iple_a), ((iff (((finite840267660iple_a F_9) A1_1) A2_1)) ((ex hoare_669141180iple_a) (fun (A_3:hoare_669141180iple_a)=> ((ex (hoare_669141180iple_a->Prop)) (fun (A_2:(hoare_669141180iple_a->Prop))=> ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((and ((and ((and (((eq (hoare_669141180iple_a->Prop)) A1_1) ((insert175534902iple_a A_3) A_2))) (((eq hoare_669141180iple_a) A2_1) X_3))) ((((finite590756294iple_a F_9) A_3) A_2) X_3))) (((member1016246415iple_a A_3) A_2)->False)))))))))) of role axiom named fact_89_fold1Set_Osimps
% A new axiom: (forall (F_9:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A1_1:(hoare_669141180iple_a->Prop)) (A2_1:hoare_669141180iple_a), ((iff (((finite840267660iple_a F_9) A1_1) A2_1)) ((ex hoare_669141180iple_a) (fun (A_3:hoare_669141180iple_a)=> ((ex (hoare_669141180iple_a->Prop)) (fun (A_2:(hoare_669141180iple_a->Prop))=> ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((and ((and ((and (((eq (hoare_669141180iple_a->Prop)) A1_1) ((insert175534902iple_a A_3) A_2))) (((eq hoare_669141180iple_a) A2_1) X_3))) ((((finite590756294iple_a F_9) A_3) A_2) X_3))) (((member1016246415iple_a A_3) A_2)->False))))))))))
% FOF formula (forall (F_8:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_1:hoare_669141180iple_a) (A1:(hoare_669141180iple_a->Prop)) (A2:hoare_669141180iple_a), ((iff ((((finite590756294iple_a F_8) Z_1) A1) A2)) ((or ((and (((eq (hoare_669141180iple_a->Prop)) A1) bot_bo280939947le_a_o)) (((eq hoare_669141180iple_a) A2) Z_1))) ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((ex (hoare_669141180iple_a->Prop)) (fun (A_2:(hoare_669141180iple_a->Prop))=> ((ex hoare_669141180iple_a) (fun (Y_1:hoare_669141180iple_a)=> ((and ((and ((and (((eq (hoare_669141180iple_a->Prop)) A1) ((insert175534902iple_a X_3) A_2))) (((eq hoare_669141180iple_a) A2) ((F_8 X_3) Y_1)))) (((member1016246415iple_a X_3) A_2)->False))) ((((finite590756294iple_a F_8) Z_1) A_2) Y_1))))))))))) of role axiom named fact_90_fold__graph_Osimps
% A new axiom: (forall (F_8:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_1:hoare_669141180iple_a) (A1:(hoare_669141180iple_a->Prop)) (A2:hoare_669141180iple_a), ((iff ((((finite590756294iple_a F_8) Z_1) A1) A2)) ((or ((and (((eq (hoare_669141180iple_a->Prop)) A1) bot_bo280939947le_a_o)) (((eq hoare_669141180iple_a) A2) Z_1))) ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((ex (hoare_669141180iple_a->Prop)) (fun (A_2:(hoare_669141180iple_a->Prop))=> ((ex hoare_669141180iple_a) (fun (Y_1:hoare_669141180iple_a)=> ((and ((and ((and (((eq (hoare_669141180iple_a->Prop)) A1) ((insert175534902iple_a X_3) A_2))) (((eq hoare_669141180iple_a) A2) ((F_8 X_3) Y_1)))) (((member1016246415iple_a X_3) A_2)->False))) ((((finite590756294iple_a F_8) Z_1) A_2) Y_1)))))))))))
% FOF formula (forall (X_4:hoare_669141180iple_a) (A_1:(hoare_669141180iple_a->Prop)) (F_7:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_6:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite252461622iple_a F_7) F_6)->((finite957651855iple_a A_1)->((not (((eq (hoare_669141180iple_a->Prop)) A_1) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) (F_6 ((insert175534902iple_a X_4) A_1))) ((F_7 X_4) (F_6 A_1))))))) of role axiom named fact_91_folding__one__idem_Oinsert__idem
% A new axiom: (forall (X_4:hoare_669141180iple_a) (A_1:(hoare_669141180iple_a->Prop)) (F_7:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_6:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite252461622iple_a F_7) F_6)->((finite957651855iple_a A_1)->((not (((eq (hoare_669141180iple_a->Prop)) A_1) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) (F_6 ((insert175534902iple_a X_4) A_1))) ((F_7 X_4) (F_6 A_1)))))))
% FOF formula (forall (P:((hoare_669141180iple_a->Prop)->Prop)) (F_4:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_4)->((not (((eq (hoare_669141180iple_a->Prop)) F_4) bot_bo280939947le_a_o))->((forall (X_3:hoare_669141180iple_a), (P ((insert175534902iple_a X_3) bot_bo280939947le_a_o)))->((forall (X_3:hoare_669141180iple_a) (F_5:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_5)->((not (((eq (hoare_669141180iple_a->Prop)) F_5) bot_bo280939947le_a_o))->((((member1016246415iple_a X_3) F_5)->False)->((P F_5)->(P ((insert175534902iple_a X_3) F_5)))))))->(P F_4)))))) of role axiom named fact_92_finite__ne__induct
% A new axiom: (forall (P:((hoare_669141180iple_a->Prop)->Prop)) (F_4:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_4)->((not (((eq (hoare_669141180iple_a->Prop)) F_4) bot_bo280939947le_a_o))->((forall (X_3:hoare_669141180iple_a), (P ((insert175534902iple_a X_3) bot_bo280939947le_a_o)))->((forall (X_3:hoare_669141180iple_a) (F_5:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_5)->((not (((eq (hoare_669141180iple_a->Prop)) F_5) bot_bo280939947le_a_o))->((((member1016246415iple_a X_3) F_5)->False)->((P F_5)->(P ((insert175534902iple_a X_3) F_5)))))))->(P F_4))))))
% FOF formula (forall (X_2:hoare_669141180iple_a) (F_3:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_2:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite252461622iple_a F_3) F_2)->(((eq hoare_669141180iple_a) ((F_3 X_2) X_2)) X_2))) of role axiom named fact_93_folding__one__idem_Oidem
% A new axiom: (forall (X_2:hoare_669141180iple_a) (F_3:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_2:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite252461622iple_a F_3) F_2)->(((eq hoare_669141180iple_a) ((F_3 X_2) X_2)) X_2)))
% FOF formula (forall (X_1:hoare_669141180iple_a) (A:(hoare_669141180iple_a->Prop)) (F_1:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite252461622iple_a F_1) F)->((finite957651855iple_a A)->(((member1016246415iple_a X_1) A)->(((eq hoare_669141180iple_a) ((F_1 X_1) (F A))) (F A)))))) of role axiom named fact_94_folding__one__idem_Oin__idem
% A new axiom: (forall (X_1:hoare_669141180iple_a) (A:(hoare_669141180iple_a->Prop)) (F_1:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite252461622iple_a F_1) F)->((finite957651855iple_a A)->(((member1016246415iple_a X_1) A)->(((eq hoare_669141180iple_a) ((F_1 X_1) (F A))) (F A))))))
% FOF formula (forall (X:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (((fequal182287803iple_a X) Y)->False)) (((eq hoare_669141180iple_a) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_
% A new axiom: (forall (X:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (((fequal182287803iple_a X) Y)->False)) (((eq hoare_669141180iple_a) X) Y)))
% FOF formula (forall (X:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (not (((eq hoare_669141180iple_a) X) Y))) ((fequal182287803iple_a X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_
% A new axiom: (forall (X:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (not (((eq hoare_669141180iple_a) X) Y))) ((fequal182287803iple_a X) Y)))
% FOF formula ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> False)) c) (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S)))))) bot_bo280939947le_a_o)) of role conjecture named conj_0
% Conjecture to prove = ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> False)) c) (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S)))))) bot_bo280939947le_a_o)):Prop
% Parameter x_a_DUMMY:x_a.
% Parameter state_DUMMY:state.
% Parameter hoare_669141180iple_a_DUMMY:hoare_669141180iple_a.
% We need to prove ['((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> False)) c) (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S)))))) bot_bo280939947le_a_o))']
% Parameter x_a:Type.
% Parameter com:Type.
% Parameter state:Type.
% Parameter hoare_669141180iple_a:Type.
% Parameter skip:com.
% Parameter semi:(com->(com->com)).
% Parameter _TPTP_ex:((hoare_669141180iple_a->Prop)->Prop).
% Parameter finite957651855iple_a:((hoare_669141180iple_a->Prop)->Prop).
% Parameter finite840267660iple_a:((hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))->((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop))).
% Parameter finite684844060iple_a:((hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))->((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)).
% Parameter finite590756294iple_a:((hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))->(hoare_669141180iple_a->((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop)))).
% Parameter finite972428089iple_a:((hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))->(((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)->Prop)).
% Parameter finite252461622iple_a:((hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))->(((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)->Prop)).
% Parameter the_Ho49089901iple_a:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a).
% Parameter hoare_2128652938rivs_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 bot_bo280939947le_a_o:(hoare_669141180iple_a->Prop).
% Parameter bot_bot_o:Prop.
% Parameter collec1717965009iple_a:((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop)).
% Parameter insert175534902iple_a:(hoare_669141180iple_a->((hoare_669141180iple_a->Prop)->(hoare_669141180iple_a->Prop))).
% Parameter the_el738790235iple_a:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a).
% Parameter fequal182287803iple_a:(hoare_669141180iple_a->(hoare_669141180iple_a->Prop)).
% Parameter member1016246415iple_a:(hoare_669141180iple_a->((hoare_669141180iple_a->Prop)->Prop)).
% Parameter g:(hoare_669141180iple_a->Prop).
% Parameter p:(x_a->(state->Prop)).
% Parameter b:(state->Prop).
% Parameter c:com.
% Axiom fact_0_empty:(forall (G_12:(hoare_669141180iple_a->Prop)), ((hoare_2128652938rivs_a G_12) bot_bo280939947le_a_o)).
% Axiom fact_1_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_2_cut:(forall (G_11:(hoare_669141180iple_a->Prop)) (G_10:(hoare_669141180iple_a->Prop)) (Ts_1:(hoare_669141180iple_a->Prop)), (((hoare_2128652938rivs_a G_10) Ts_1)->(((hoare_2128652938rivs_a G_11) G_10)->((hoare_2128652938rivs_a G_11) Ts_1)))).
% Axiom fact_3_hoare__derivs_Oinsert:(forall (Ts:(hoare_669141180iple_a->Prop)) (G_9:(hoare_669141180iple_a->Prop)) (T:hoare_669141180iple_a), (((hoare_2128652938rivs_a G_9) ((insert175534902iple_a T) bot_bo280939947le_a_o))->(((hoare_2128652938rivs_a G_9) Ts)->((hoare_2128652938rivs_a G_9) ((insert175534902iple_a T) Ts))))).
% Axiom fact_4_constant:(forall (G_8:(hoare_669141180iple_a->Prop)) (P_25:(x_a->(state->Prop))) (C_9:com) (Q_11:(x_a->(state->Prop))) (C_8:Prop), ((C_8->((hoare_2128652938rivs_a G_8) ((insert175534902iple_a (((hoare_1295064928iple_a P_25) C_9) Q_11)) bot_bo280939947le_a_o)))->((hoare_2128652938rivs_a G_8) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> ((and ((P_25 Z) S)) C_8))) C_9) Q_11)) bot_bo280939947le_a_o)))).
% Axiom fact_5_escape:(forall (G_7:(hoare_669141180iple_a->Prop)) (C_7:com) (Q_10:(x_a->(state->Prop))) (P_24:(x_a->(state->Prop))), ((forall (Z:x_a) (S:state), (((P_24 Z) S)->((hoare_2128652938rivs_a G_7) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Za:x_a) (S_1:state)=> (((eq state) S_1) S))) C_7) (fun (Z_6:x_a)=> (Q_10 Z)))) bot_bo280939947le_a_o))))->((hoare_2128652938rivs_a G_7) ((insert175534902iple_a (((hoare_1295064928iple_a P_24) C_7) Q_10)) bot_bo280939947le_a_o)))).
% Axiom fact_6_conseq2:(forall (Q_9:(x_a->(state->Prop))) (G_6:(hoare_669141180iple_a->Prop)) (P_23:(x_a->(state->Prop))) (C_6:com) (Q_8:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_6) ((insert175534902iple_a (((hoare_1295064928iple_a P_23) C_6) Q_8)) bot_bo280939947le_a_o))->((forall (Z:x_a) (S:state), (((Q_8 Z) S)->((Q_9 Z) S)))->((hoare_2128652938rivs_a G_6) ((insert175534902iple_a (((hoare_1295064928iple_a P_23) C_6) Q_9)) bot_bo280939947le_a_o))))).
% Axiom fact_7_conseq1:(forall (P_22:(x_a->(state->Prop))) (G_5:(hoare_669141180iple_a->Prop)) (P_21:(x_a->(state->Prop))) (C_5:com) (Q_7:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_5) ((insert175534902iple_a (((hoare_1295064928iple_a P_21) C_5) Q_7)) bot_bo280939947le_a_o))->((forall (Z:x_a) (S:state), (((P_22 Z) S)->((P_21 Z) S)))->((hoare_2128652938rivs_a G_5) ((insert175534902iple_a (((hoare_1295064928iple_a P_22) C_5) Q_7)) bot_bo280939947le_a_o))))).
% Axiom fact_8_conseq12:(forall (Q_6:(x_a->(state->Prop))) (P_20:(x_a->(state->Prop))) (G_4:(hoare_669141180iple_a->Prop)) (P_19:(x_a->(state->Prop))) (C_4:com) (Q_5:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_4) ((insert175534902iple_a (((hoare_1295064928iple_a P_19) C_4) Q_5)) bot_bo280939947le_a_o))->((forall (Z:x_a) (S:state), (((P_20 Z) S)->(forall (S_1:state), ((forall (Z_6:x_a), (((P_19 Z_6) S)->((Q_5 Z_6) S_1)))->((Q_6 Z) S_1)))))->((hoare_2128652938rivs_a G_4) ((insert175534902iple_a (((hoare_1295064928iple_a P_20) C_4) Q_6)) bot_bo280939947le_a_o))))).
% Axiom fact_9_insertE:(forall (A_64:hoare_669141180iple_a) (B_14:hoare_669141180iple_a) (A_63:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_64) ((insert175534902iple_a B_14) A_63))->((not (((eq hoare_669141180iple_a) A_64) B_14))->((member1016246415iple_a A_64) A_63)))).
% Axiom fact_10_insertCI:(forall (B_13:hoare_669141180iple_a) (A_62:hoare_669141180iple_a) (B_12:(hoare_669141180iple_a->Prop)), (((((member1016246415iple_a A_62) B_12)->False)->(((eq hoare_669141180iple_a) A_62) B_13))->((member1016246415iple_a A_62) ((insert175534902iple_a B_13) B_12)))).
% Axiom fact_11_emptyE:(forall (A_61:hoare_669141180iple_a), (((member1016246415iple_a A_61) bot_bo280939947le_a_o)->False)).
% Axiom fact_12_singleton__conv2:(forall (A_60:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fequal182287803iple_a A_60))) ((insert175534902iple_a A_60) bot_bo280939947le_a_o))).
% Axiom fact_13_singleton__conv:(forall (A_59:hoare_669141180iple_a), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> (((eq hoare_669141180iple_a) X_3) A_59)))) ((insert175534902iple_a A_59) bot_bo280939947le_a_o))).
% Axiom fact_14_Collect__conv__if2:(forall (P_18:(hoare_669141180iple_a->Prop)) (A_58:hoare_669141180iple_a), ((and ((P_18 A_58)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_58) X_3)) (P_18 X_3))))) ((insert175534902iple_a A_58) bot_bo280939947le_a_o)))) (((P_18 A_58)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) A_58) X_3)) (P_18 X_3))))) bot_bo280939947le_a_o)))).
% Axiom fact_15_Collect__conv__if:(forall (P_17:(hoare_669141180iple_a->Prop)) (A_57:hoare_669141180iple_a), ((and ((P_17 A_57)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X_3) A_57)) (P_17 X_3))))) ((insert175534902iple_a A_57) bot_bo280939947le_a_o)))) (((P_17 A_57)->False)->(((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (((eq hoare_669141180iple_a) X_3) A_57)) (P_17 X_3))))) bot_bo280939947le_a_o)))).
% Axiom fact_16_equals0D:(forall (A_56:hoare_669141180iple_a) (A_55:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) A_55) bot_bo280939947le_a_o)->(((member1016246415iple_a A_56) A_55)->False))).
% Axiom fact_17_Collect__empty__eq:(forall (P_16:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P_16)) bot_bo280939947le_a_o)) (forall (X_3:hoare_669141180iple_a), ((P_16 X_3)->False)))).
% Axiom fact_18_empty__iff:(forall (C_3:hoare_669141180iple_a), (((member1016246415iple_a C_3) bot_bo280939947le_a_o)->False)).
% Axiom fact_19_empty__Collect__eq:(forall (P_15:(hoare_669141180iple_a->Prop)), ((iff (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a P_15))) (forall (X_3:hoare_669141180iple_a), ((P_15 X_3)->False)))).
% Axiom fact_20_ex__in__conv:(forall (A_54:(hoare_669141180iple_a->Prop)), ((iff ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((member1016246415iple_a X_3) A_54)))) (not (((eq (hoare_669141180iple_a->Prop)) A_54) bot_bo280939947le_a_o)))).
% Axiom fact_21_all__not__in__conv:(forall (A_53:(hoare_669141180iple_a->Prop)), ((iff (forall (X_3:hoare_669141180iple_a), (((member1016246415iple_a X_3) A_53)->False))) (((eq (hoare_669141180iple_a->Prop)) A_53) bot_bo280939947le_a_o))).
% Axiom fact_22_empty__def:(((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> False))).
% Axiom fact_23_insert__absorb:(forall (A_52:hoare_669141180iple_a) (A_51:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_52) A_51)->(((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_52) A_51)) A_51))).
% Axiom fact_24_insertI2:(forall (B_11:hoare_669141180iple_a) (A_50:hoare_669141180iple_a) (B_10:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_50) B_10)->((member1016246415iple_a A_50) ((insert175534902iple_a B_11) B_10)))).
% Axiom fact_25_insert__ident:(forall (B_9:(hoare_669141180iple_a->Prop)) (X_24:hoare_669141180iple_a) (A_49:(hoare_669141180iple_a->Prop)), ((((member1016246415iple_a X_24) A_49)->False)->((((member1016246415iple_a X_24) B_9)->False)->((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_24) A_49)) ((insert175534902iple_a X_24) B_9))) (((eq (hoare_669141180iple_a->Prop)) A_49) B_9))))).
% Axiom fact_26_insert__code:(forall (Y_6:hoare_669141180iple_a) (A_48:(hoare_669141180iple_a->Prop)) (X_23:hoare_669141180iple_a), ((iff (((insert175534902iple_a Y_6) A_48) X_23)) ((or (((eq hoare_669141180iple_a) Y_6) X_23)) (A_48 X_23)))).
% Axiom fact_27_insert__iff:(forall (A_47:hoare_669141180iple_a) (B_8:hoare_669141180iple_a) (A_46:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a A_47) ((insert175534902iple_a B_8) A_46))) ((or (((eq hoare_669141180iple_a) A_47) B_8)) ((member1016246415iple_a A_47) A_46)))).
% Axiom fact_28_insert__commute:(forall (X_22:hoare_669141180iple_a) (Y_5:hoare_669141180iple_a) (A_45:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_22) ((insert175534902iple_a Y_5) A_45))) ((insert175534902iple_a Y_5) ((insert175534902iple_a X_22) A_45)))).
% Axiom fact_29_insert__absorb2:(forall (X_21:hoare_669141180iple_a) (A_44:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_21) ((insert175534902iple_a X_21) A_44))) ((insert175534902iple_a X_21) A_44))).
% Axiom fact_30_insert__Collect:(forall (A_43:hoare_669141180iple_a) (P_14:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_43) (collec1717965009iple_a P_14))) (collec1717965009iple_a (fun (U:hoare_669141180iple_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_669141180iple_a) U) A_43))) (P_14 U)))))).
% Axiom fact_31_insert__compr:(forall (A_42:hoare_669141180iple_a) (B_7:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_42) B_7)) (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) X_3) A_42)) ((member1016246415iple_a X_3) B_7)))))).
% Axiom fact_32_insertI1:(forall (A_41:hoare_669141180iple_a) (B_6:(hoare_669141180iple_a->Prop)), ((member1016246415iple_a A_41) ((insert175534902iple_a A_41) B_6))).
% Axiom fact_33_insert__compr__raw:(forall (X_3:hoare_669141180iple_a) (Xa:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a X_3) Xa)) (collec1717965009iple_a (fun (Y_1:hoare_669141180iple_a)=> ((or (((eq hoare_669141180iple_a) Y_1) X_3)) ((member1016246415iple_a Y_1) Xa)))))).
% Axiom fact_34_singleton__inject:(forall (A_40:hoare_669141180iple_a) (B_5:hoare_669141180iple_a), ((((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_40) bot_bo280939947le_a_o)) ((insert175534902iple_a B_5) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) A_40) B_5))).
% Axiom fact_35_singletonE:(forall (B_4:hoare_669141180iple_a) (A_39:hoare_669141180iple_a), (((member1016246415iple_a B_4) ((insert175534902iple_a A_39) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) B_4) A_39))).
% Axiom fact_36_doubleton__eq__iff:(forall (A_38:hoare_669141180iple_a) (B_3:hoare_669141180iple_a) (C_2:hoare_669141180iple_a) (D_1:hoare_669141180iple_a), ((iff (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_38) ((insert175534902iple_a B_3) bot_bo280939947le_a_o))) ((insert175534902iple_a C_2) ((insert175534902iple_a D_1) bot_bo280939947le_a_o)))) ((or ((and (((eq hoare_669141180iple_a) A_38) C_2)) (((eq hoare_669141180iple_a) B_3) D_1))) ((and (((eq hoare_669141180iple_a) A_38) D_1)) (((eq hoare_669141180iple_a) B_3) C_2))))).
% Axiom fact_37_singleton__iff:(forall (B_2:hoare_669141180iple_a) (A_37:hoare_669141180iple_a), ((iff ((member1016246415iple_a B_2) ((insert175534902iple_a A_37) bot_bo280939947le_a_o))) (((eq hoare_669141180iple_a) B_2) A_37))).
% Axiom fact_38_insert__not__empty:(forall (A_36:hoare_669141180iple_a) (A_35:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_36) A_35)) bot_bo280939947le_a_o))).
% Axiom fact_39_empty__not__insert:(forall (A_34:hoare_669141180iple_a) (A_33:(hoare_669141180iple_a->Prop)), (not (((eq (hoare_669141180iple_a->Prop)) bot_bo280939947le_a_o) ((insert175534902iple_a A_34) A_33)))).
% Axiom fact_40_the__elem__eq:(forall (X_20:hoare_669141180iple_a), (((eq hoare_669141180iple_a) (the_el738790235iple_a ((insert175534902iple_a X_20) bot_bo280939947le_a_o))) X_20)).
% Axiom fact_41_bot__apply:(forall (X_19:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X_19)) bot_bot_o)).
% Axiom fact_42_bot__fun__def:(forall (X_3:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X_3)) bot_bot_o)).
% Axiom fact_43_hoare__derivs_OSkip:(forall (G_3:(hoare_669141180iple_a->Prop)) (P_13:(x_a->(state->Prop))), ((hoare_2128652938rivs_a G_3) ((insert175534902iple_a (((hoare_1295064928iple_a P_13) skip) P_13)) bot_bo280939947le_a_o))).
% Axiom fact_44_Comp:(forall (D:com) (R:(x_a->(state->Prop))) (G_2:(hoare_669141180iple_a->Prop)) (P_12:(x_a->(state->Prop))) (C_1:com) (Q_4:(x_a->(state->Prop))), (((hoare_2128652938rivs_a G_2) ((insert175534902iple_a (((hoare_1295064928iple_a P_12) C_1) Q_4)) bot_bo280939947le_a_o))->(((hoare_2128652938rivs_a G_2) ((insert175534902iple_a (((hoare_1295064928iple_a Q_4) D) R)) bot_bo280939947le_a_o))->((hoare_2128652938rivs_a G_2) ((insert175534902iple_a (((hoare_1295064928iple_a P_12) ((semi C_1) D)) R)) bot_bo280939947le_a_o))))).
% Axiom fact_45_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_46_Set_Oset__insert:(forall (X_18:hoare_669141180iple_a) (A_32:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a X_18) A_32)->((forall (B_1:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) A_32) ((insert175534902iple_a X_18) B_1))->((member1016246415iple_a X_18) B_1)))->False))).
% Axiom fact_47_com_Osimps_I13_J:(forall (Com1:com) (Com2:com), (not (((eq com) ((semi Com1) Com2)) skip))).
% Axiom fact_48_com_Osimps_I12_J:(forall (Com1:com) (Com2:com), (not (((eq com) skip) ((semi Com1) Com2)))).
% Axiom fact_49_the__elem__def:(forall (X_17:(hoare_669141180iple_a->Prop)), (((eq hoare_669141180iple_a) (the_el738790235iple_a X_17)) (the_Ho49089901iple_a (fun (X_3:hoare_669141180iple_a)=> (((eq (hoare_669141180iple_a->Prop)) X_17) ((insert175534902iple_a X_3) bot_bo280939947le_a_o)))))).
% Axiom fact_50_mk__disjoint__insert:(forall (A_31:hoare_669141180iple_a) (A_30:(hoare_669141180iple_a->Prop)), (((member1016246415iple_a A_31) A_30)->((ex (hoare_669141180iple_a->Prop)) (fun (B_1:(hoare_669141180iple_a->Prop))=> ((and (((eq (hoare_669141180iple_a->Prop)) A_30) ((insert175534902iple_a A_31) B_1))) (((member1016246415iple_a A_31) B_1)->False)))))).
% Axiom fact_51_com_Osimps_I3_J:(forall (Com1_1:com) (Com2_1:com) (Com1:com) (Com2:com), ((iff (((eq com) ((semi Com1_1) Com2_1)) ((semi Com1) Com2))) ((and (((eq com) Com1_1) Com1)) (((eq com) Com2_1) Com2)))).
% Axiom fact_52_the__sym__eq__trivial:(forall (X_16:hoare_669141180iple_a), (((eq hoare_669141180iple_a) (the_Ho49089901iple_a (fequal182287803iple_a X_16))) X_16)).
% Axiom fact_53_the__eq__trivial:(forall (A_29:hoare_669141180iple_a), (((eq hoare_669141180iple_a) (the_Ho49089901iple_a (fun (X_3:hoare_669141180iple_a)=> (((eq hoare_669141180iple_a) X_3) A_29)))) A_29)).
% Axiom fact_54_If__def:(forall (X_15:hoare_669141180iple_a) (Y_3:hoare_669141180iple_a) (P_11:Prop), ((and (P_11->(((eq hoare_669141180iple_a) X_15) (the_Ho49089901iple_a (fun (Z_7:hoare_669141180iple_a)=> ((and (((fun (X:Prop) (Y:Prop)=> (X->Y)) P_11) (((eq hoare_669141180iple_a) Z_7) X_15))) (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not P_11)) (((eq hoare_669141180iple_a) Z_7) Y_3)))))))) ((P_11->False)->(((eq hoare_669141180iple_a) Y_3) (the_Ho49089901iple_a (fun (Z_7:hoare_669141180iple_a)=> ((and (((fun (X:Prop) (Y:Prop)=> (X->Y)) P_11) (((eq hoare_669141180iple_a) Z_7) X_15))) (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not P_11)) (((eq hoare_669141180iple_a) Z_7) Y_3))))))))).
% Axiom fact_55_equals0I:(forall (A_28:(hoare_669141180iple_a->Prop)), ((forall (Y_1:hoare_669141180iple_a), (((member1016246415iple_a Y_1) A_28)->False))->(((eq (hoare_669141180iple_a->Prop)) A_28) bot_bo280939947le_a_o))).
% Axiom fact_56_the__equality:(forall (P_10:(hoare_669141180iple_a->Prop)) (A_27:hoare_669141180iple_a), ((P_10 A_27)->((forall (X_3:hoare_669141180iple_a), ((P_10 X_3)->(((eq hoare_669141180iple_a) X_3) A_27)))->(((eq hoare_669141180iple_a) (the_Ho49089901iple_a P_10)) A_27)))).
% Axiom fact_57_theI:(forall (P_9:(hoare_669141180iple_a->Prop)) (A_26:hoare_669141180iple_a), ((P_9 A_26)->((forall (X_3:hoare_669141180iple_a), ((P_9 X_3)->(((eq hoare_669141180iple_a) X_3) A_26)))->(P_9 (the_Ho49089901iple_a P_9))))).
% Axiom fact_58_the1__equality:(forall (A_25:hoare_669141180iple_a) (P_8:(hoare_669141180iple_a->Prop)), (((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((and (P_8 X_3)) (forall (Y_1:hoare_669141180iple_a), ((P_8 Y_1)->(((eq hoare_669141180iple_a) Y_1) X_3))))))->((P_8 A_25)->(((eq hoare_669141180iple_a) (the_Ho49089901iple_a P_8)) A_25)))).
% Axiom fact_59_theI_H:(forall (P_7:(hoare_669141180iple_a->Prop)), (((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((and (P_7 X_3)) (forall (Y_1:hoare_669141180iple_a), ((P_7 Y_1)->(((eq hoare_669141180iple_a) Y_1) X_3))))))->(P_7 (the_Ho49089901iple_a P_7)))).
% Axiom fact_60_conseq:(forall (Q_2:(x_a->(state->Prop))) (G_1:(hoare_669141180iple_a->Prop)) (C:com) (P_5:(x_a->(state->Prop))), ((forall (Z:x_a) (S:state), (((P_5 Z) S)->((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a G_1) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) C) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((Q_2 Z) S_1))))))))))->((hoare_2128652938rivs_a G_1) ((insert175534902iple_a (((hoare_1295064928iple_a P_5) C) Q_2)) bot_bo280939947le_a_o)))).
% Axiom fact_61_nonempty__iff:(forall (A_24:(hoare_669141180iple_a->Prop)), ((iff (not (((eq (hoare_669141180iple_a->Prop)) A_24) bot_bo280939947le_a_o))) ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((ex (hoare_669141180iple_a->Prop)) (fun (B_1:(hoare_669141180iple_a->Prop))=> ((and (((eq (hoare_669141180iple_a->Prop)) A_24) ((insert175534902iple_a X_3) B_1))) (((member1016246415iple_a X_3) B_1)->False)))))))).
% Axiom fact_62_fold1Set__sing:(forall (F_31:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_23:hoare_669141180iple_a) (B:hoare_669141180iple_a), ((iff (((finite840267660iple_a F_31) ((insert175534902iple_a A_23) bot_bo280939947le_a_o)) B)) (((eq hoare_669141180iple_a) A_23) B))).
% Axiom fact_63_folding__one_Osingleton:(forall (X_14:hoare_669141180iple_a) (F_30:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_29:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_30) F_29)->(((eq hoare_669141180iple_a) (F_29 ((insert175534902iple_a X_14) bot_bo280939947le_a_o))) X_14))).
% Axiom fact_64_bot__empty__eq:(forall (X_3:hoare_669141180iple_a), ((iff (bot_bo280939947le_a_o X_3)) ((member1016246415iple_a X_3) bot_bo280939947le_a_o))).
% Axiom fact_65_empty__fold1SetE:(forall (F_28:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (X_13:hoare_669141180iple_a), ((((finite840267660iple_a F_28) bot_bo280939947le_a_o) X_13)->False)).
% Axiom fact_66_fold1Set__nonempty:(forall (F_27:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_22:(hoare_669141180iple_a->Prop)) (X_12:hoare_669141180iple_a), ((((finite840267660iple_a F_27) A_22) X_12)->(not (((eq (hoare_669141180iple_a->Prop)) A_22) bot_bo280939947le_a_o)))).
% Axiom fact_67_fold1Set_Ointros:(forall (F_26:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_21:hoare_669141180iple_a) (A_20:(hoare_669141180iple_a->Prop)) (X_11:hoare_669141180iple_a), (((((finite590756294iple_a F_26) A_21) A_20) X_11)->((((member1016246415iple_a A_21) A_20)->False)->(((finite840267660iple_a F_26) ((insert175534902iple_a A_21) A_20)) X_11)))).
% Axiom fact_68_folding__one_Oinsert:(forall (X_10:hoare_669141180iple_a) (A_19:(hoare_669141180iple_a->Prop)) (F_25:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_24:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_25) F_24)->((finite957651855iple_a A_19)->((((member1016246415iple_a X_10) A_19)->False)->((not (((eq (hoare_669141180iple_a->Prop)) A_19) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) (F_24 ((insert175534902iple_a X_10) A_19))) ((F_25 X_10) (F_24 A_19)))))))).
% Axiom fact_69_fold1__def:(forall (F_23:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_18:(hoare_669141180iple_a->Prop)), (((eq hoare_669141180iple_a) ((finite684844060iple_a F_23) A_18)) (the_Ho49089901iple_a ((finite840267660iple_a F_23) A_18)))).
% Axiom fact_70_finite__Collect__conjI:(forall (Q_1:(hoare_669141180iple_a->Prop)) (P_4:(hoare_669141180iple_a->Prop)), (((or (finite957651855iple_a (collec1717965009iple_a P_4))) (finite957651855iple_a (collec1717965009iple_a Q_1)))->(finite957651855iple_a (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((and (P_4 X_3)) (Q_1 X_3))))))).
% Axiom fact_71_finite_OemptyI:(finite957651855iple_a bot_bo280939947le_a_o).
% Axiom fact_72_finite_OinsertI:(forall (A_17:hoare_669141180iple_a) (A_16:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a A_16)->(finite957651855iple_a ((insert175534902iple_a A_17) A_16)))).
% Axiom fact_73_mem__def:(forall (X_9:hoare_669141180iple_a) (A_15:(hoare_669141180iple_a->Prop)), ((iff ((member1016246415iple_a X_9) A_15)) (A_15 X_9))).
% Axiom fact_74_Collect__def:(forall (P_3:(hoare_669141180iple_a->Prop)), (((eq (hoare_669141180iple_a->Prop)) (collec1717965009iple_a P_3)) P_3)).
% Axiom fact_75_folding__one_Oeq__fold:(forall (A_14:(hoare_669141180iple_a->Prop)) (F_22:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_21:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_22) F_21)->((finite957651855iple_a A_14)->(((eq hoare_669141180iple_a) (F_21 A_14)) ((finite684844060iple_a F_22) A_14))))).
% Axiom fact_76_fold__graph_OemptyI:(forall (F_20:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_5:hoare_669141180iple_a), ((((finite590756294iple_a F_20) Z_5) bot_bo280939947le_a_o) Z_5)).
% Axiom fact_77_empty__fold__graphE:(forall (F_19:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_4:hoare_669141180iple_a) (X_8:hoare_669141180iple_a), (((((finite590756294iple_a F_19) Z_4) bot_bo280939947le_a_o) X_8)->(((eq hoare_669141180iple_a) X_8) Z_4))).
% Axiom fact_78_fold__graph_OinsertI:(forall (F_18:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_3:hoare_669141180iple_a) (Y_2:hoare_669141180iple_a) (X_7:hoare_669141180iple_a) (A_13:(hoare_669141180iple_a->Prop)), ((((member1016246415iple_a X_7) A_13)->False)->(((((finite590756294iple_a F_18) Z_3) A_13) Y_2)->((((finite590756294iple_a F_18) Z_3) ((insert175534902iple_a X_7) A_13)) ((F_18 X_7) Y_2))))).
% Axiom fact_79_finite__Collect__disjI:(forall (P_2:(hoare_669141180iple_a->Prop)) (Q:(hoare_669141180iple_a->Prop)), ((iff (finite957651855iple_a (collec1717965009iple_a (fun (X_3:hoare_669141180iple_a)=> ((or (P_2 X_3)) (Q X_3)))))) ((and (finite957651855iple_a (collec1717965009iple_a P_2))) (finite957651855iple_a (collec1717965009iple_a Q))))).
% Axiom fact_80_finite__insert:(forall (A_12:hoare_669141180iple_a) (A_11:(hoare_669141180iple_a->Prop)), ((iff (finite957651855iple_a ((insert175534902iple_a A_12) A_11))) (finite957651855iple_a A_11))).
% Axiom fact_81_fold1__singleton__def:(forall (A_10:hoare_669141180iple_a) (G:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)) (F_17:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))), ((((eq ((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)) G) (finite684844060iple_a F_17))->(((eq hoare_669141180iple_a) (G ((insert175534902iple_a A_10) bot_bo280939947le_a_o))) A_10))).
% Axiom fact_82_fold1__singleton:(forall (F_16:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_9:hoare_669141180iple_a), (((eq hoare_669141180iple_a) ((finite684844060iple_a F_16) ((insert175534902iple_a A_9) bot_bo280939947le_a_o))) A_9)).
% Axiom fact_83_folding__one_Oclosed:(forall (A_8:(hoare_669141180iple_a->Prop)) (F_15:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_14:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite972428089iple_a F_15) F_14)->((finite957651855iple_a A_8)->((not (((eq (hoare_669141180iple_a->Prop)) A_8) bot_bo280939947le_a_o))->((forall (X_3:hoare_669141180iple_a) (Y_1:hoare_669141180iple_a), ((member1016246415iple_a ((F_15 X_3) Y_1)) ((insert175534902iple_a X_3) ((insert175534902iple_a Y_1) bot_bo280939947le_a_o))))->((member1016246415iple_a (F_14 A_8)) A_8)))))).
% Axiom fact_84_insert__fold1SetE:(forall (F_13:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_7:hoare_669141180iple_a) (X_6:(hoare_669141180iple_a->Prop)) (X_5:hoare_669141180iple_a), ((((finite840267660iple_a F_13) ((insert175534902iple_a A_7) X_6)) X_5)->((forall (A_3:hoare_669141180iple_a) (A_2:(hoare_669141180iple_a->Prop)), ((((eq (hoare_669141180iple_a->Prop)) ((insert175534902iple_a A_7) X_6)) ((insert175534902iple_a A_3) A_2))->(((((finite590756294iple_a F_13) A_3) A_2) X_5)->((member1016246415iple_a A_3) A_2))))->False))).
% Axiom fact_85_finite__nonempty__imp__fold1Set:(forall (F_12:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A_6:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a A_6)->((not (((eq (hoare_669141180iple_a->Prop)) A_6) bot_bo280939947le_a_o))->(_TPTP_ex ((finite840267660iple_a F_12) A_6))))).
% Axiom fact_86_finite__induct:(forall (P_1:((hoare_669141180iple_a->Prop)->Prop)) (F_11:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_11)->((P_1 bot_bo280939947le_a_o)->((forall (X_3:hoare_669141180iple_a) (F_5:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_5)->((((member1016246415iple_a X_3) F_5)->False)->((P_1 F_5)->(P_1 ((insert175534902iple_a X_3) F_5))))))->(P_1 F_11))))).
% Axiom fact_87_finite_Osimps:(forall (A_5:(hoare_669141180iple_a->Prop)), ((iff (finite957651855iple_a A_5)) ((or (((eq (hoare_669141180iple_a->Prop)) A_5) bot_bo280939947le_a_o)) ((ex (hoare_669141180iple_a->Prop)) (fun (A_2:(hoare_669141180iple_a->Prop))=> ((ex hoare_669141180iple_a) (fun (A_3:hoare_669141180iple_a)=> ((and (((eq (hoare_669141180iple_a->Prop)) A_5) ((insert175534902iple_a A_3) A_2))) (finite957651855iple_a A_2))))))))).
% Axiom fact_88_finite__imp__fold__graph:(forall (F_10:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_2:hoare_669141180iple_a) (A_4:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a A_4)->(_TPTP_ex (((finite590756294iple_a F_10) Z_2) A_4)))).
% Axiom fact_89_fold1Set_Osimps:(forall (F_9:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (A1_1:(hoare_669141180iple_a->Prop)) (A2_1:hoare_669141180iple_a), ((iff (((finite840267660iple_a F_9) A1_1) A2_1)) ((ex hoare_669141180iple_a) (fun (A_3:hoare_669141180iple_a)=> ((ex (hoare_669141180iple_a->Prop)) (fun (A_2:(hoare_669141180iple_a->Prop))=> ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((and ((and ((and (((eq (hoare_669141180iple_a->Prop)) A1_1) ((insert175534902iple_a A_3) A_2))) (((eq hoare_669141180iple_a) A2_1) X_3))) ((((finite590756294iple_a F_9) A_3) A_2) X_3))) (((member1016246415iple_a A_3) A_2)->False)))))))))).
% Axiom fact_90_fold__graph_Osimps:(forall (F_8:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (Z_1:hoare_669141180iple_a) (A1:(hoare_669141180iple_a->Prop)) (A2:hoare_669141180iple_a), ((iff ((((finite590756294iple_a F_8) Z_1) A1) A2)) ((or ((and (((eq (hoare_669141180iple_a->Prop)) A1) bot_bo280939947le_a_o)) (((eq hoare_669141180iple_a) A2) Z_1))) ((ex hoare_669141180iple_a) (fun (X_3:hoare_669141180iple_a)=> ((ex (hoare_669141180iple_a->Prop)) (fun (A_2:(hoare_669141180iple_a->Prop))=> ((ex hoare_669141180iple_a) (fun (Y_1:hoare_669141180iple_a)=> ((and ((and ((and (((eq (hoare_669141180iple_a->Prop)) A1) ((insert175534902iple_a X_3) A_2))) (((eq hoare_669141180iple_a) A2) ((F_8 X_3) Y_1)))) (((member1016246415iple_a X_3) A_2)->False))) ((((finite590756294iple_a F_8) Z_1) A_2) Y_1))))))))))).
% Axiom fact_91_folding__one__idem_Oinsert__idem:(forall (X_4:hoare_669141180iple_a) (A_1:(hoare_669141180iple_a->Prop)) (F_7:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_6:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite252461622iple_a F_7) F_6)->((finite957651855iple_a A_1)->((not (((eq (hoare_669141180iple_a->Prop)) A_1) bot_bo280939947le_a_o))->(((eq hoare_669141180iple_a) (F_6 ((insert175534902iple_a X_4) A_1))) ((F_7 X_4) (F_6 A_1))))))).
% Axiom fact_92_finite__ne__induct:(forall (P:((hoare_669141180iple_a->Prop)->Prop)) (F_4:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_4)->((not (((eq (hoare_669141180iple_a->Prop)) F_4) bot_bo280939947le_a_o))->((forall (X_3:hoare_669141180iple_a), (P ((insert175534902iple_a X_3) bot_bo280939947le_a_o)))->((forall (X_3:hoare_669141180iple_a) (F_5:(hoare_669141180iple_a->Prop)), ((finite957651855iple_a F_5)->((not (((eq (hoare_669141180iple_a->Prop)) F_5) bot_bo280939947le_a_o))->((((member1016246415iple_a X_3) F_5)->False)->((P F_5)->(P ((insert175534902iple_a X_3) F_5)))))))->(P F_4)))))).
% Axiom fact_93_folding__one__idem_Oidem:(forall (X_2:hoare_669141180iple_a) (F_3:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F_2:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite252461622iple_a F_3) F_2)->(((eq hoare_669141180iple_a) ((F_3 X_2) X_2)) X_2))).
% Axiom fact_94_folding__one__idem_Oin__idem:(forall (X_1:hoare_669141180iple_a) (A:(hoare_669141180iple_a->Prop)) (F_1:(hoare_669141180iple_a->(hoare_669141180iple_a->hoare_669141180iple_a))) (F:((hoare_669141180iple_a->Prop)->hoare_669141180iple_a)), (((finite252461622iple_a F_1) F)->((finite957651855iple_a A)->(((member1016246415iple_a X_1) A)->(((eq hoare_669141180iple_a) ((F_1 X_1) (F A))) (F A)))))).
% Axiom help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_:(forall (X:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (((fequal182287803iple_a X) Y)->False)) (((eq hoare_669141180iple_a) X) Y))).
% Axiom help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_:(forall (X:hoare_669141180iple_a) (Y:hoare_669141180iple_a), ((or (not (((eq hoare_669141180iple_a) X) Y))) ((fequal182287803iple_a X) Y))).
% Trying to prove ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> False)) c) (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S)))))) bot_bo280939947le_a_o))
% Found False_rect00:=(False_rect0 ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))):((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))
% Found (False_rect0 ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))) as proof of ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))
% Found ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))) as proof of ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))
% Found (fun (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1)))))))))))) as proof of ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))
% Found (fun (S:state) (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1)))))))))))) as proof of (False->((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1)))))))))))
% Found (fun (Z:x_a) (S:state) (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1)))))))))))) as proof of (forall (S:state), (False->((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))))
% Found (fun (Z:x_a) (S:state) (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1)))))))))))) as proof of (forall (Z:x_a) (S:state), (False->((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))))
% Found (fact_60_conseq0000 (fun (Z:x_a) (S:state) (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))))) as proof of ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> False)) c) (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S)))))) bot_bo280939947le_a_o))
% Found ((fact_60_conseq000 (fun (Z:x_a) (S:state)=> False)) (fun (Z:x_a) (S:state) (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))))) as proof of ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> False)) c) (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S)))))) bot_bo280939947le_a_o))
% Found (((fact_60_conseq00 c) (fun (Z:x_a) (S:state)=> False)) (fun (Z:x_a) (S:state) (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))))) as proof of ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> False)) c) (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S)))))) bot_bo280939947le_a_o))
% Found ((((fact_60_conseq0 g) c) (fun (Z:x_a) (S:state)=> False)) (fun (Z:x_a) (S:state) (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))))) as proof of ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> False)) c) (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S)))))) bot_bo280939947le_a_o))
% Found (((((fact_60_conseq (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S))))) g) c) (fun (Z:x_a) (S:state)=> False)) (fun (Z:x_a) (S:state) (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))))) as proof of ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> False)) c) (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S)))))) bot_bo280939947le_a_o))
% Found (((((fact_60_conseq (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S))))) g) c) (fun (Z:x_a) (S:state)=> False)) (fun (Z:x_a) (S:state) (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1))))))))))))) as proof of ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a (fun (Z:x_a) (S:state)=> False)) c) (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S)))))) bot_bo280939947le_a_o))
% Got proof (((((fact_60_conseq (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S))))) g) c) (fun (Z:x_a) (S:state)=> False)) (fun (Z:x_a) (S:state) (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1)))))))))))))
% Time elapsed = 2.176457s
% node=114 cost=217.000000 depth=11
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (((((fact_60_conseq (fun (Z:x_a) (S:state)=> ((and ((p Z) S)) (not (b S))))) g) c) (fun (Z:x_a) (S:state)=> False)) (fun (Z:x_a) (S:state) (x:False)=> ((fun (P:Type)=> ((False_rect P) x)) ((ex (x_a->(state->Prop))) (fun (P_6:(x_a->(state->Prop)))=> ((ex (x_a->(state->Prop))) (fun (Q_3:(x_a->(state->Prop)))=> ((and ((hoare_2128652938rivs_a g) ((insert175534902iple_a (((hoare_1295064928iple_a P_6) c) Q_3)) bot_bo280939947le_a_o))) (forall (S_1:state), ((forall (Z_6:x_a), (((P_6 Z_6) S)->((Q_3 Z_6) S_1)))->((and ((p Z) S_1)) (not (b S_1)))))))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------