TSTP Solution File: SWW470^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW470^1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:20:55 EDT 2023
% Result : Theorem 0.22s 0.66s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWW470^1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n020.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun Aug 27 19:33:59 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 % File : SWW470^1 : TPTP v8.1.2. Released v5.3.0.
% 0.22/0.51 % Domain : Software Verification
% 0.22/0.51 % Problem : Hoare's Logic with Procedures line 200, 100 axioms selected
% 0.22/0.51 % Version : Especial.
% 0.22/0.51 % English :
% 0.22/0.51
% 0.22/0.51 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.22/0.51 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.22/0.51 % Source : [Bla11]
% 0.22/0.51 % Names : hoare_100_thf_l200 [Bla11]
% 0.22/0.51
% 0.22/0.51 % Status : Theorem
% 0.22/0.51 % Rating : 0.38 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% 0.22/0.51 % Syntax : Number of formulae : 125 ( 25 unt; 27 typ; 0 def)
% 0.22/0.51 % Number of atoms : 422 ( 108 equ; 21 cnn)
% 0.22/0.51 % Maximal formula atoms : 9 ( 4 avg)
% 0.22/0.51 % Number of connectives : 854 ( 47 ~; 11 |; 31 &; 634 @)
% 0.22/0.51 % ( 22 <=>; 109 =>; 0 <=; 0 <~>)
% 0.22/0.51 % Maximal formula depth : 19 ( 8 avg)
% 0.22/0.51 % Number of types : 5 ( 4 usr)
% 0.22/0.51 % Number of type conns : 268 ( 268 >; 0 *; 0 +; 0 <<)
% 0.22/0.51 % Number of symbols : 29 ( 23 usr; 8 con; 0-4 aty)
% 0.22/0.51 % Number of variables : 307 ( 24 ^; 267 !; 16 ?; 307 :)
% 0.22/0.51 % SPC : TH0_THM_EQU_NAR
% 0.22/0.51
% 0.22/0.51 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.22/0.51 % 2011-08-09 19:02:36
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 %----Should-be-implicit typings (4)
% 0.22/0.51 thf(ty_ty_t__a,type,
% 0.22/0.51 x_a: $tType ).
% 0.22/0.51
% 0.22/0.51 thf(ty_ty_tc__Com__Ocom,type,
% 0.22/0.51 com: $tType ).
% 0.22/0.51
% 0.22/0.51 thf(ty_ty_tc__Com__Ostate,type,
% 0.22/0.51 state: $tType ).
% 0.22/0.51
% 0.22/0.51 thf(ty_ty_tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J,type,
% 0.22/0.51 hoare_669141180iple_a: $tType ).
% 0.22/0.51
% 0.22/0.51 %----Explicit typings (23)
% 0.22/0.51 thf(sy_c_Com_Ocom_OSKIP,type,
% 0.22/0.51 skip: com ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Com_Ocom_OSemi,type,
% 0.22/0.51 semi: com > com > com ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Ex,type,
% 0.22/0.51 ex: ( hoare_669141180iple_a > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_,type,
% 0.22/0.51 finite957651855iple_a: ( hoare_669141180iple_a > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Finite__Set_Ofold1Set_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__,type,
% 0.22/0.51 finite840267660iple_a: ( hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a ) > ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Finite__Set_Ofold1_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J,type,
% 0.22/0.51 finite684844060iple_a: ( hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a ) > ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Finite__Set_Ofold__graph_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_I,type,
% 0.22/0.51 finite590756294iple_a: ( hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a ) > hoare_669141180iple_a > ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_,type,
% 0.22/0.51 finite972428089iple_a: ( hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a ) > ( ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ghhkfsbqqq__Ot,type,
% 0.22/0.51 finite252461622iple_a: ( hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a ) > ( ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J,type,
% 0.22/0.51 the_Ho49089901iple_a: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ohoare__derivs_000t__a,type,
% 0.22/0.51 hoare_2128652938rivs_a: ( hoare_669141180iple_a > $o ) > ( hoare_669141180iple_a > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Otriple_Otriple_000t__a,type,
% 0.22/0.51 hoare_1295064928iple_a: ( x_a > state > $o ) > com > ( x_a > state > $o ) > hoare_669141180iple_a ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__O,type,
% 0.22/0.51 bot_bo280939947le_a_o: hoare_669141180iple_a > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 0.22/0.51 bot_bot_o: $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J,type,
% 0.22/0.51 collec1717965009iple_a: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J,type,
% 0.22/0.51 insert175534902iple_a: hoare_669141180iple_a > ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J,type,
% 0.22/0.51 the_el738790235iple_a: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J,type,
% 0.22/0.51 fequal182287803iple_a: hoare_669141180iple_a > hoare_669141180iple_a > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_c_member_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J,type,
% 0.22/0.51 member1016246415iple_a: hoare_669141180iple_a > ( hoare_669141180iple_a > $o ) > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_v_G,type,
% 0.22/0.51 g: hoare_669141180iple_a > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_v_P,type,
% 0.22/0.51 p: x_a > state > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_v_b,type,
% 0.22/0.51 b: state > $o ).
% 0.22/0.51
% 0.22/0.51 thf(sy_v_c,type,
% 0.22/0.51 c: com ).
% 0.22/0.51
% 0.22/0.51 %----Relevant facts (95)
% 0.22/0.51 thf(fact_0_empty,axiom,
% 0.22/0.51 ! [G_12: hoare_669141180iple_a > $o] : ( hoare_2128652938rivs_a @ G_12 @ bot_bo280939947le_a_o ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_1_triple_Oinject,axiom,
% 0.22/0.51 ! [Fun1_2: x_a > state > $o,Com_2: com,Fun2_2: x_a > state > $o,Fun1_1: x_a > state > $o,Com_1: com,Fun2_1: x_a > state > $o] :
% 0.22/0.51 ( ( ( hoare_1295064928iple_a @ Fun1_2 @ Com_2 @ Fun2_2 )
% 0.22/0.51 = ( hoare_1295064928iple_a @ Fun1_1 @ Com_1 @ Fun2_1 ) )
% 0.22/0.51 <=> ( ( Fun1_2 = Fun1_1 )
% 0.22/0.51 & ( Com_2 = Com_1 )
% 0.22/0.51 & ( Fun2_2 = Fun2_1 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_2_cut,axiom,
% 0.22/0.51 ! [G_11: hoare_669141180iple_a > $o,G_10: hoare_669141180iple_a > $o,Ts_1: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( hoare_2128652938rivs_a @ G_10 @ Ts_1 )
% 0.22/0.51 => ( ( hoare_2128652938rivs_a @ G_11 @ G_10 )
% 0.22/0.51 => ( hoare_2128652938rivs_a @ G_11 @ Ts_1 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_3_hoare__derivs_Oinsert,axiom,
% 0.22/0.51 ! [Ts: hoare_669141180iple_a > $o,G_9: hoare_669141180iple_a > $o,T: hoare_669141180iple_a] :
% 0.22/0.51 ( ( hoare_2128652938rivs_a @ G_9 @ ( insert175534902iple_a @ T @ bot_bo280939947le_a_o ) )
% 0.22/0.51 => ( ( hoare_2128652938rivs_a @ G_9 @ Ts )
% 0.22/0.51 => ( hoare_2128652938rivs_a @ G_9 @ ( insert175534902iple_a @ T @ Ts ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_4_constant,axiom,
% 0.22/0.51 ! [G_8: hoare_669141180iple_a > $o,P_25: x_a > state > $o,C_9: com,Q_11: x_a > state > $o,C_8: $o] :
% 0.22/0.51 ( ( C_8
% 0.22/0.51 => ( hoare_2128652938rivs_a @ G_8 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_25 @ C_9 @ Q_11 ) @ bot_bo280939947le_a_o ) ) )
% 0.22/0.51 => ( hoare_2128652938rivs_a @ G_8
% 0.22/0.51 @ ( insert175534902iple_a
% 0.22/0.51 @ ( hoare_1295064928iple_a
% 0.22/0.51 @ ^ [Z: x_a,S: state] : ( (&) @ ( P_25 @ Z @ S ) @ C_8 )
% 0.22/0.51 @ C_9
% 0.22/0.51 @ Q_11 )
% 0.22/0.51 @ bot_bo280939947le_a_o ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_5_escape,axiom,
% 0.22/0.51 ! [G_7: hoare_669141180iple_a > $o,C_7: com,Q_10: x_a > state > $o,P_24: x_a > state > $o] :
% 0.22/0.51 ( ! [Z: x_a,S: state] :
% 0.22/0.51 ( ( P_24 @ Z @ S )
% 0.22/0.51 => ( hoare_2128652938rivs_a @ G_7
% 0.22/0.51 @ ( insert175534902iple_a
% 0.22/0.51 @ ( hoare_1295064928iple_a
% 0.22/0.51 @ ^ [Za: x_a,S_1: state] : ( S_1 = S )
% 0.22/0.51 @ C_7
% 0.22/0.51 @ ^ [Z_6: x_a] : ( Q_10 @ Z ) )
% 0.22/0.51 @ bot_bo280939947le_a_o ) ) )
% 0.22/0.51 => ( hoare_2128652938rivs_a @ G_7 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_24 @ C_7 @ Q_10 ) @ bot_bo280939947le_a_o ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_6_conseq2,axiom,
% 0.22/0.51 ! [Q_9: x_a > state > $o,G_6: hoare_669141180iple_a > $o,P_23: x_a > state > $o,C_6: com,Q_8: x_a > state > $o] :
% 0.22/0.51 ( ( hoare_2128652938rivs_a @ G_6 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_23 @ C_6 @ Q_8 ) @ bot_bo280939947le_a_o ) )
% 0.22/0.51 => ( ! [Z: x_a,S: state] :
% 0.22/0.51 ( ( Q_8 @ Z @ S )
% 0.22/0.51 => ( Q_9 @ Z @ S ) )
% 0.22/0.51 => ( hoare_2128652938rivs_a @ G_6 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_23 @ C_6 @ Q_9 ) @ bot_bo280939947le_a_o ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_7_conseq1,axiom,
% 0.22/0.51 ! [P_22: x_a > state > $o,G_5: hoare_669141180iple_a > $o,P_21: x_a > state > $o,C_5: com,Q_7: x_a > state > $o] :
% 0.22/0.51 ( ( hoare_2128652938rivs_a @ G_5 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_21 @ C_5 @ Q_7 ) @ bot_bo280939947le_a_o ) )
% 0.22/0.51 => ( ! [Z: x_a,S: state] :
% 0.22/0.51 ( ( P_22 @ Z @ S )
% 0.22/0.51 => ( P_21 @ Z @ S ) )
% 0.22/0.51 => ( hoare_2128652938rivs_a @ G_5 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_22 @ C_5 @ Q_7 ) @ bot_bo280939947le_a_o ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_8_conseq12,axiom,
% 0.22/0.51 ! [Q_6: x_a > state > $o,P_20: x_a > state > $o,G_4: hoare_669141180iple_a > $o,P_19: x_a > state > $o,C_4: com,Q_5: x_a > state > $o] :
% 0.22/0.51 ( ( hoare_2128652938rivs_a @ G_4 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_19 @ C_4 @ Q_5 ) @ bot_bo280939947le_a_o ) )
% 0.22/0.51 => ( ! [Z: x_a,S: state] :
% 0.22/0.51 ( ( P_20 @ Z @ S )
% 0.22/0.51 => ! [S_1: state] :
% 0.22/0.51 ( ! [Z_6: x_a] :
% 0.22/0.51 ( ( P_19 @ Z_6 @ S )
% 0.22/0.51 => ( Q_5 @ Z_6 @ S_1 ) )
% 0.22/0.51 => ( Q_6 @ Z @ S_1 ) ) )
% 0.22/0.51 => ( hoare_2128652938rivs_a @ G_4 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_20 @ C_4 @ Q_6 ) @ bot_bo280939947le_a_o ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_9_insertE,axiom,
% 0.22/0.51 ! [A_64: hoare_669141180iple_a,B_14: hoare_669141180iple_a,A_63: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( member1016246415iple_a @ A_64 @ ( insert175534902iple_a @ B_14 @ A_63 ) )
% 0.22/0.51 => ( ( A_64 != B_14 )
% 0.22/0.51 => ( member1016246415iple_a @ A_64 @ A_63 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_10_insertCI,axiom,
% 0.22/0.51 ! [B_13: hoare_669141180iple_a,A_62: hoare_669141180iple_a,B_12: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( ~ ( member1016246415iple_a @ A_62 @ B_12 )
% 0.22/0.51 => ( A_62 = B_13 ) )
% 0.22/0.51 => ( member1016246415iple_a @ A_62 @ ( insert175534902iple_a @ B_13 @ B_12 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_11_emptyE,axiom,
% 0.22/0.51 ! [A_61: hoare_669141180iple_a] :
% 0.22/0.51 ~ ( member1016246415iple_a @ A_61 @ bot_bo280939947le_a_o ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_12_singleton__conv2,axiom,
% 0.22/0.51 ! [A_60: hoare_669141180iple_a] :
% 0.22/0.51 ( ( collec1717965009iple_a @ ( fequal182287803iple_a @ A_60 ) )
% 0.22/0.51 = ( insert175534902iple_a @ A_60 @ bot_bo280939947le_a_o ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_13_singleton__conv,axiom,
% 0.22/0.51 ! [A_59: hoare_669141180iple_a] :
% 0.22/0.51 ( ( collec1717965009iple_a
% 0.22/0.51 @ ^ [X_3: hoare_669141180iple_a] : ( X_3 = A_59 ) )
% 0.22/0.51 = ( insert175534902iple_a @ A_59 @ bot_bo280939947le_a_o ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_14_Collect__conv__if2,axiom,
% 0.22/0.51 ! [P_18: hoare_669141180iple_a > $o,A_58: hoare_669141180iple_a] :
% 0.22/0.51 ( ( ( P_18 @ A_58 )
% 0.22/0.51 => ( ( collec1717965009iple_a
% 0.22/0.51 @ ^ [X_3: hoare_669141180iple_a] : ( (&) @ ( A_58 = X_3 ) @ ( P_18 @ X_3 ) ) )
% 0.22/0.51 = ( insert175534902iple_a @ A_58 @ bot_bo280939947le_a_o ) ) )
% 0.22/0.51 & ( ~ ( P_18 @ A_58 )
% 0.22/0.51 => ( ( collec1717965009iple_a
% 0.22/0.51 @ ^ [X_3: hoare_669141180iple_a] : ( (&) @ ( A_58 = X_3 ) @ ( P_18 @ X_3 ) ) )
% 0.22/0.51 = bot_bo280939947le_a_o ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_15_Collect__conv__if,axiom,
% 0.22/0.51 ! [P_17: hoare_669141180iple_a > $o,A_57: hoare_669141180iple_a] :
% 0.22/0.51 ( ( ( P_17 @ A_57 )
% 0.22/0.51 => ( ( collec1717965009iple_a
% 0.22/0.51 @ ^ [X_3: hoare_669141180iple_a] : ( (&) @ ( X_3 = A_57 ) @ ( P_17 @ X_3 ) ) )
% 0.22/0.51 = ( insert175534902iple_a @ A_57 @ bot_bo280939947le_a_o ) ) )
% 0.22/0.51 & ( ~ ( P_17 @ A_57 )
% 0.22/0.51 => ( ( collec1717965009iple_a
% 0.22/0.51 @ ^ [X_3: hoare_669141180iple_a] : ( (&) @ ( X_3 = A_57 ) @ ( P_17 @ X_3 ) ) )
% 0.22/0.51 = bot_bo280939947le_a_o ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_16_equals0D,axiom,
% 0.22/0.51 ! [A_56: hoare_669141180iple_a,A_55: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( A_55 = bot_bo280939947le_a_o )
% 0.22/0.51 => ~ ( member1016246415iple_a @ A_56 @ A_55 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_17_Collect__empty__eq,axiom,
% 0.22/0.51 ! [P_16: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( ( collec1717965009iple_a @ P_16 )
% 0.22/0.51 = bot_bo280939947le_a_o )
% 0.22/0.51 <=> ! [X_3: hoare_669141180iple_a] :
% 0.22/0.51 ~ ( P_16 @ X_3 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_18_empty__iff,axiom,
% 0.22/0.51 ! [C_3: hoare_669141180iple_a] :
% 0.22/0.51 ~ ( member1016246415iple_a @ C_3 @ bot_bo280939947le_a_o ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_19_empty__Collect__eq,axiom,
% 0.22/0.51 ! [P_15: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( bot_bo280939947le_a_o
% 0.22/0.51 = ( collec1717965009iple_a @ P_15 ) )
% 0.22/0.51 <=> ! [X_3: hoare_669141180iple_a] :
% 0.22/0.51 ~ ( P_15 @ X_3 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_20_ex__in__conv,axiom,
% 0.22/0.51 ! [A_54: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ? [X_3: hoare_669141180iple_a] : ( member1016246415iple_a @ X_3 @ A_54 )
% 0.22/0.51 <=> ( A_54 != bot_bo280939947le_a_o ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_21_all__not__in__conv,axiom,
% 0.22/0.51 ! [A_53: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ! [X_3: hoare_669141180iple_a] :
% 0.22/0.51 ~ ( member1016246415iple_a @ X_3 @ A_53 )
% 0.22/0.51 <=> ( A_53 = bot_bo280939947le_a_o ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_22_empty__def,axiom,
% 0.22/0.51 ( bot_bo280939947le_a_o
% 0.22/0.51 = ( collec1717965009iple_a
% 0.22/0.51 @ ^ [X_3: hoare_669141180iple_a] : $false ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_23_insert__absorb,axiom,
% 0.22/0.51 ! [A_52: hoare_669141180iple_a,A_51: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( member1016246415iple_a @ A_52 @ A_51 )
% 0.22/0.51 => ( ( insert175534902iple_a @ A_52 @ A_51 )
% 0.22/0.51 = A_51 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_24_insertI2,axiom,
% 0.22/0.51 ! [B_11: hoare_669141180iple_a,A_50: hoare_669141180iple_a,B_10: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( member1016246415iple_a @ A_50 @ B_10 )
% 0.22/0.51 => ( member1016246415iple_a @ A_50 @ ( insert175534902iple_a @ B_11 @ B_10 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_25_insert__ident,axiom,
% 0.22/0.51 ! [B_9: hoare_669141180iple_a > $o,X_24: hoare_669141180iple_a,A_49: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ~ ( member1016246415iple_a @ X_24 @ A_49 )
% 0.22/0.51 => ( ~ ( member1016246415iple_a @ X_24 @ B_9 )
% 0.22/0.51 => ( ( ( insert175534902iple_a @ X_24 @ A_49 )
% 0.22/0.51 = ( insert175534902iple_a @ X_24 @ B_9 ) )
% 0.22/0.51 <=> ( A_49 = B_9 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_26_insert__code,axiom,
% 0.22/0.51 ! [Y_6: hoare_669141180iple_a,A_48: hoare_669141180iple_a > $o,X_23: hoare_669141180iple_a] :
% 0.22/0.51 ( ( insert175534902iple_a @ Y_6 @ A_48 @ X_23 )
% 0.22/0.51 <=> ( ( Y_6 = X_23 )
% 0.22/0.51 | ( A_48 @ X_23 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_27_insert__iff,axiom,
% 0.22/0.51 ! [A_47: hoare_669141180iple_a,B_8: hoare_669141180iple_a,A_46: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( member1016246415iple_a @ A_47 @ ( insert175534902iple_a @ B_8 @ A_46 ) )
% 0.22/0.51 <=> ( ( A_47 = B_8 )
% 0.22/0.51 | ( member1016246415iple_a @ A_47 @ A_46 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_28_insert__commute,axiom,
% 0.22/0.51 ! [X_22: hoare_669141180iple_a,Y_5: hoare_669141180iple_a,A_45: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( insert175534902iple_a @ X_22 @ ( insert175534902iple_a @ Y_5 @ A_45 ) )
% 0.22/0.51 = ( insert175534902iple_a @ Y_5 @ ( insert175534902iple_a @ X_22 @ A_45 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_29_insert__absorb2,axiom,
% 0.22/0.51 ! [X_21: hoare_669141180iple_a,A_44: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( insert175534902iple_a @ X_21 @ ( insert175534902iple_a @ X_21 @ A_44 ) )
% 0.22/0.51 = ( insert175534902iple_a @ X_21 @ A_44 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_30_insert__Collect,axiom,
% 0.22/0.51 ! [A_43: hoare_669141180iple_a,P_14: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( insert175534902iple_a @ A_43 @ ( collec1717965009iple_a @ P_14 ) )
% 0.22/0.51 = ( collec1717965009iple_a
% 0.22/0.51 @ ^ [U: hoare_669141180iple_a] : ( (=>) @ ( (~) @ ( U = A_43 ) ) @ ( P_14 @ U ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_31_insert__compr,axiom,
% 0.22/0.51 ! [A_42: hoare_669141180iple_a,B_7: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( insert175534902iple_a @ A_42 @ B_7 )
% 0.22/0.51 = ( collec1717965009iple_a
% 0.22/0.51 @ ^ [X_3: hoare_669141180iple_a] : ( (|) @ ( X_3 = A_42 ) @ ( member1016246415iple_a @ X_3 @ B_7 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_32_insertI1,axiom,
% 0.22/0.51 ! [A_41: hoare_669141180iple_a,B_6: hoare_669141180iple_a > $o] : ( member1016246415iple_a @ A_41 @ ( insert175534902iple_a @ A_41 @ B_6 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_33_insert__compr__raw,axiom,
% 0.22/0.51 ! [X_3: hoare_669141180iple_a,Xa: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( insert175534902iple_a @ X_3 @ Xa )
% 0.22/0.51 = ( collec1717965009iple_a
% 0.22/0.51 @ ^ [Y_1: hoare_669141180iple_a] : ( (|) @ ( Y_1 = X_3 ) @ ( member1016246415iple_a @ Y_1 @ Xa ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_34_singleton__inject,axiom,
% 0.22/0.51 ! [A_40: hoare_669141180iple_a,B_5: hoare_669141180iple_a] :
% 0.22/0.51 ( ( ( insert175534902iple_a @ A_40 @ bot_bo280939947le_a_o )
% 0.22/0.51 = ( insert175534902iple_a @ B_5 @ bot_bo280939947le_a_o ) )
% 0.22/0.51 => ( A_40 = B_5 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_35_singletonE,axiom,
% 0.22/0.51 ! [B_4: hoare_669141180iple_a,A_39: hoare_669141180iple_a] :
% 0.22/0.51 ( ( member1016246415iple_a @ B_4 @ ( insert175534902iple_a @ A_39 @ bot_bo280939947le_a_o ) )
% 0.22/0.51 => ( B_4 = A_39 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_36_doubleton__eq__iff,axiom,
% 0.22/0.51 ! [A_38: hoare_669141180iple_a,B_3: hoare_669141180iple_a,C_2: hoare_669141180iple_a,D_1: hoare_669141180iple_a] :
% 0.22/0.51 ( ( ( insert175534902iple_a @ A_38 @ ( insert175534902iple_a @ B_3 @ bot_bo280939947le_a_o ) )
% 0.22/0.51 = ( insert175534902iple_a @ C_2 @ ( insert175534902iple_a @ D_1 @ bot_bo280939947le_a_o ) ) )
% 0.22/0.51 <=> ( ( ( A_38 = C_2 )
% 0.22/0.51 & ( B_3 = D_1 ) )
% 0.22/0.51 | ( ( A_38 = D_1 )
% 0.22/0.51 & ( B_3 = C_2 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_37_singleton__iff,axiom,
% 0.22/0.51 ! [B_2: hoare_669141180iple_a,A_37: hoare_669141180iple_a] :
% 0.22/0.51 ( ( member1016246415iple_a @ B_2 @ ( insert175534902iple_a @ A_37 @ bot_bo280939947le_a_o ) )
% 0.22/0.51 <=> ( B_2 = A_37 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_38_insert__not__empty,axiom,
% 0.22/0.51 ! [A_36: hoare_669141180iple_a,A_35: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( insert175534902iple_a @ A_36 @ A_35 )
% 0.22/0.51 != bot_bo280939947le_a_o ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_39_empty__not__insert,axiom,
% 0.22/0.51 ! [A_34: hoare_669141180iple_a,A_33: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( bot_bo280939947le_a_o
% 0.22/0.51 != ( insert175534902iple_a @ A_34 @ A_33 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_40_the__elem__eq,axiom,
% 0.22/0.51 ! [X_20: hoare_669141180iple_a] :
% 0.22/0.51 ( ( the_el738790235iple_a @ ( insert175534902iple_a @ X_20 @ bot_bo280939947le_a_o ) )
% 0.22/0.51 = X_20 ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_41_bot__apply,axiom,
% 0.22/0.51 ! [X_19: hoare_669141180iple_a] :
% 0.22/0.51 ( ( bot_bo280939947le_a_o @ X_19 )
% 0.22/0.51 <=> bot_bot_o ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_42_bot__fun__def,axiom,
% 0.22/0.51 ! [X_3: hoare_669141180iple_a] :
% 0.22/0.51 ( ( bot_bo280939947le_a_o @ X_3 )
% 0.22/0.51 <=> bot_bot_o ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_43_hoare__derivs_OSkip,axiom,
% 0.22/0.51 ! [G_3: hoare_669141180iple_a > $o,P_13: x_a > state > $o] : ( hoare_2128652938rivs_a @ G_3 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_13 @ skip @ P_13 ) @ bot_bo280939947le_a_o ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_44_Comp,axiom,
% 0.22/0.51 ! [D: com,R: x_a > state > $o,G_2: hoare_669141180iple_a > $o,P_12: x_a > state > $o,C_1: com,Q_4: x_a > state > $o] :
% 0.22/0.51 ( ( hoare_2128652938rivs_a @ G_2 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_12 @ C_1 @ Q_4 ) @ bot_bo280939947le_a_o ) )
% 0.22/0.51 => ( ( hoare_2128652938rivs_a @ G_2 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ Q_4 @ D @ R ) @ bot_bo280939947le_a_o ) )
% 0.22/0.51 => ( hoare_2128652938rivs_a @ G_2 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_12 @ ( semi @ C_1 @ D ) @ R ) @ bot_bo280939947le_a_o ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_45_triple_Oexhaust,axiom,
% 0.22/0.51 ! [Y_4: hoare_669141180iple_a] :
% 0.22/0.51 ~ ! [Fun1: x_a > state > $o,Com: com,Fun2: x_a > state > $o] :
% 0.22/0.51 ( Y_4
% 0.22/0.51 != ( hoare_1295064928iple_a @ Fun1 @ Com @ Fun2 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_46_Set_Oset__insert,axiom,
% 0.22/0.51 ! [X_18: hoare_669141180iple_a,A_32: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( member1016246415iple_a @ X_18 @ A_32 )
% 0.22/0.51 => ~ ! [B_1: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( A_32
% 0.22/0.51 = ( insert175534902iple_a @ X_18 @ B_1 ) )
% 0.22/0.51 => ( member1016246415iple_a @ X_18 @ B_1 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_47_com_Osimps_I13_J,axiom,
% 0.22/0.51 ! [Com1: com,Com2: com] :
% 0.22/0.51 ( ( semi @ Com1 @ Com2 )
% 0.22/0.51 != skip ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_48_com_Osimps_I12_J,axiom,
% 0.22/0.51 ! [Com1: com,Com2: com] :
% 0.22/0.51 ( skip
% 0.22/0.51 != ( semi @ Com1 @ Com2 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_49_the__elem__def,axiom,
% 0.22/0.51 ! [X_17: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( the_el738790235iple_a @ X_17 )
% 0.22/0.51 = ( the_Ho49089901iple_a
% 0.22/0.51 @ ^ [X_3: hoare_669141180iple_a] :
% 0.22/0.51 ( X_17
% 0.22/0.51 = ( insert175534902iple_a @ X_3 @ bot_bo280939947le_a_o ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_50_mk__disjoint__insert,axiom,
% 0.22/0.51 ! [A_31: hoare_669141180iple_a,A_30: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( member1016246415iple_a @ A_31 @ A_30 )
% 0.22/0.51 => ? [B_1: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( A_30
% 0.22/0.51 = ( insert175534902iple_a @ A_31 @ B_1 ) )
% 0.22/0.51 & ~ ( member1016246415iple_a @ A_31 @ B_1 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_51_com_Osimps_I3_J,axiom,
% 0.22/0.51 ! [Com1_1: com,Com2_1: com,Com1: com,Com2: com] :
% 0.22/0.51 ( ( ( semi @ Com1_1 @ Com2_1 )
% 0.22/0.51 = ( semi @ Com1 @ Com2 ) )
% 0.22/0.51 <=> ( ( Com1_1 = Com1 )
% 0.22/0.51 & ( Com2_1 = Com2 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_52_the__sym__eq__trivial,axiom,
% 0.22/0.51 ! [X_16: hoare_669141180iple_a] :
% 0.22/0.51 ( ( the_Ho49089901iple_a @ ( fequal182287803iple_a @ X_16 ) )
% 0.22/0.51 = X_16 ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_53_the__eq__trivial,axiom,
% 0.22/0.51 ! [A_29: hoare_669141180iple_a] :
% 0.22/0.51 ( ( the_Ho49089901iple_a
% 0.22/0.51 @ ^ [X_3: hoare_669141180iple_a] : ( X_3 = A_29 ) )
% 0.22/0.51 = A_29 ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_54_If__def,axiom,
% 0.22/0.51 ! [X_15: hoare_669141180iple_a,Y_3: hoare_669141180iple_a,P_11: $o] :
% 0.22/0.51 ( ( P_11
% 0.22/0.51 => ( X_15
% 0.22/0.51 = ( the_Ho49089901iple_a
% 0.22/0.51 @ ^ [Z_7: hoare_669141180iple_a] : ( (&) @ ( (=>) @ P_11 @ ( Z_7 = X_15 ) ) @ ( (=>) @ ( (~) @ P_11 ) @ ( Z_7 = Y_3 ) ) ) ) ) )
% 0.22/0.51 & ( ~ P_11
% 0.22/0.51 => ( Y_3
% 0.22/0.51 = ( the_Ho49089901iple_a
% 0.22/0.51 @ ^ [Z_7: hoare_669141180iple_a] : ( (&) @ ( (=>) @ P_11 @ ( Z_7 = X_15 ) ) @ ( (=>) @ ( (~) @ P_11 ) @ ( Z_7 = Y_3 ) ) ) ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_55_equals0I,axiom,
% 0.22/0.51 ! [A_28: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ! [Y_1: hoare_669141180iple_a] :
% 0.22/0.51 ~ ( member1016246415iple_a @ Y_1 @ A_28 )
% 0.22/0.51 => ( A_28 = bot_bo280939947le_a_o ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_56_the__equality,axiom,
% 0.22/0.51 ! [P_10: hoare_669141180iple_a > $o,A_27: hoare_669141180iple_a] :
% 0.22/0.51 ( ( P_10 @ A_27 )
% 0.22/0.51 => ( ! [X_3: hoare_669141180iple_a] :
% 0.22/0.51 ( ( P_10 @ X_3 )
% 0.22/0.51 => ( X_3 = A_27 ) )
% 0.22/0.51 => ( ( the_Ho49089901iple_a @ P_10 )
% 0.22/0.51 = A_27 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_57_theI,axiom,
% 0.22/0.51 ! [P_9: hoare_669141180iple_a > $o,A_26: hoare_669141180iple_a] :
% 0.22/0.51 ( ( P_9 @ A_26 )
% 0.22/0.51 => ( ! [X_3: hoare_669141180iple_a] :
% 0.22/0.51 ( ( P_9 @ X_3 )
% 0.22/0.51 => ( X_3 = A_26 ) )
% 0.22/0.51 => ( P_9 @ ( the_Ho49089901iple_a @ P_9 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_58_the1__equality,axiom,
% 0.22/0.51 ! [A_25: hoare_669141180iple_a,P_8: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ? [X_3: hoare_669141180iple_a] :
% 0.22/0.51 ( ( P_8 @ X_3 )
% 0.22/0.51 & ! [Y_1: hoare_669141180iple_a] :
% 0.22/0.51 ( ( P_8 @ Y_1 )
% 0.22/0.51 => ( Y_1 = X_3 ) ) )
% 0.22/0.51 => ( ( P_8 @ A_25 )
% 0.22/0.51 => ( ( the_Ho49089901iple_a @ P_8 )
% 0.22/0.51 = A_25 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_59_theI_H,axiom,
% 0.22/0.51 ! [P_7: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ? [X_3: hoare_669141180iple_a] :
% 0.22/0.51 ( ( P_7 @ X_3 )
% 0.22/0.51 & ! [Y_1: hoare_669141180iple_a] :
% 0.22/0.51 ( ( P_7 @ Y_1 )
% 0.22/0.51 => ( Y_1 = X_3 ) ) )
% 0.22/0.51 => ( P_7 @ ( the_Ho49089901iple_a @ P_7 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_60_conseq,axiom,
% 0.22/0.51 ! [Q_2: x_a > state > $o,G_1: hoare_669141180iple_a > $o,C: com,P_5: x_a > state > $o] :
% 0.22/0.51 ( ! [Z: x_a,S: state] :
% 0.22/0.51 ( ( P_5 @ Z @ S )
% 0.22/0.51 => ? [P_6: x_a > state > $o,Q_3: x_a > state > $o] :
% 0.22/0.51 ( ( hoare_2128652938rivs_a @ G_1 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_6 @ C @ Q_3 ) @ bot_bo280939947le_a_o ) )
% 0.22/0.51 & ! [S_1: state] :
% 0.22/0.51 ( ! [Z_6: x_a] :
% 0.22/0.51 ( ( P_6 @ Z_6 @ S )
% 0.22/0.51 => ( Q_3 @ Z_6 @ S_1 ) )
% 0.22/0.51 => ( Q_2 @ Z @ S_1 ) ) ) )
% 0.22/0.51 => ( hoare_2128652938rivs_a @ G_1 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ P_5 @ C @ Q_2 ) @ bot_bo280939947le_a_o ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_61_nonempty__iff,axiom,
% 0.22/0.51 ! [A_24: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( A_24 != bot_bo280939947le_a_o )
% 0.22/0.51 <=> ? [X_3: hoare_669141180iple_a,B_1: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( A_24
% 0.22/0.51 = ( insert175534902iple_a @ X_3 @ B_1 ) )
% 0.22/0.51 & ~ ( member1016246415iple_a @ X_3 @ B_1 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_62_fold1Set__sing,axiom,
% 0.22/0.51 ! [F_31: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,A_23: hoare_669141180iple_a,B: hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite840267660iple_a @ F_31 @ ( insert175534902iple_a @ A_23 @ bot_bo280939947le_a_o ) @ B )
% 0.22/0.51 <=> ( A_23 = B ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_63_folding__one_Osingleton,axiom,
% 0.22/0.51 ! [X_14: hoare_669141180iple_a,F_30: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,F_29: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite972428089iple_a @ F_30 @ F_29 )
% 0.22/0.51 => ( ( F_29 @ ( insert175534902iple_a @ X_14 @ bot_bo280939947le_a_o ) )
% 0.22/0.51 = X_14 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_64_bot__empty__eq,axiom,
% 0.22/0.51 ! [X_3: hoare_669141180iple_a] :
% 0.22/0.51 ( ( bot_bo280939947le_a_o @ X_3 )
% 0.22/0.51 <=> ( member1016246415iple_a @ X_3 @ bot_bo280939947le_a_o ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_65_empty__fold1SetE,axiom,
% 0.22/0.51 ! [F_28: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,X_13: hoare_669141180iple_a] :
% 0.22/0.51 ~ ( finite840267660iple_a @ F_28 @ bot_bo280939947le_a_o @ X_13 ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_66_fold1Set__nonempty,axiom,
% 0.22/0.51 ! [F_27: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,A_22: hoare_669141180iple_a > $o,X_12: hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite840267660iple_a @ F_27 @ A_22 @ X_12 )
% 0.22/0.51 => ( A_22 != bot_bo280939947le_a_o ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_67_fold1Set_Ointros,axiom,
% 0.22/0.51 ! [F_26: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,A_21: hoare_669141180iple_a,A_20: hoare_669141180iple_a > $o,X_11: hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite590756294iple_a @ F_26 @ A_21 @ A_20 @ X_11 )
% 0.22/0.51 => ( ~ ( member1016246415iple_a @ A_21 @ A_20 )
% 0.22/0.51 => ( finite840267660iple_a @ F_26 @ ( insert175534902iple_a @ A_21 @ A_20 ) @ X_11 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_68_folding__one_Oinsert,axiom,
% 0.22/0.51 ! [X_10: hoare_669141180iple_a,A_19: hoare_669141180iple_a > $o,F_25: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,F_24: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite972428089iple_a @ F_25 @ F_24 )
% 0.22/0.51 => ( ( finite957651855iple_a @ A_19 )
% 0.22/0.51 => ( ~ ( member1016246415iple_a @ X_10 @ A_19 )
% 0.22/0.51 => ( ( A_19 != bot_bo280939947le_a_o )
% 0.22/0.51 => ( ( F_24 @ ( insert175534902iple_a @ X_10 @ A_19 ) )
% 0.22/0.51 = ( F_25 @ X_10 @ ( F_24 @ A_19 ) ) ) ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_69_fold1__def,axiom,
% 0.22/0.51 ! [F_23: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,A_18: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( finite684844060iple_a @ F_23 @ A_18 )
% 0.22/0.51 = ( the_Ho49089901iple_a @ ( finite840267660iple_a @ F_23 @ A_18 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_70_finite__Collect__conjI,axiom,
% 0.22/0.51 ! [Q_1: hoare_669141180iple_a > $o,P_4: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( ( finite957651855iple_a @ ( collec1717965009iple_a @ P_4 ) )
% 0.22/0.51 | ( finite957651855iple_a @ ( collec1717965009iple_a @ Q_1 ) ) )
% 0.22/0.51 => ( finite957651855iple_a
% 0.22/0.51 @ ( collec1717965009iple_a
% 0.22/0.51 @ ^ [X_3: hoare_669141180iple_a] : ( (&) @ ( P_4 @ X_3 ) @ ( Q_1 @ X_3 ) ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_71_finite_OemptyI,axiom,
% 0.22/0.51 finite957651855iple_a @ bot_bo280939947le_a_o ).
% 0.22/0.51
% 0.22/0.51 thf(fact_72_finite_OinsertI,axiom,
% 0.22/0.51 ! [A_17: hoare_669141180iple_a,A_16: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( finite957651855iple_a @ A_16 )
% 0.22/0.51 => ( finite957651855iple_a @ ( insert175534902iple_a @ A_17 @ A_16 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_73_mem__def,axiom,
% 0.22/0.51 ! [X_9: hoare_669141180iple_a,A_15: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( member1016246415iple_a @ X_9 @ A_15 )
% 0.22/0.51 <=> ( A_15 @ X_9 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_74_Collect__def,axiom,
% 0.22/0.51 ! [P_3: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( collec1717965009iple_a @ P_3 )
% 0.22/0.51 = P_3 ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_75_folding__one_Oeq__fold,axiom,
% 0.22/0.51 ! [A_14: hoare_669141180iple_a > $o,F_22: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,F_21: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite972428089iple_a @ F_22 @ F_21 )
% 0.22/0.51 => ( ( finite957651855iple_a @ A_14 )
% 0.22/0.51 => ( ( F_21 @ A_14 )
% 0.22/0.51 = ( finite684844060iple_a @ F_22 @ A_14 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_76_fold__graph_OemptyI,axiom,
% 0.22/0.51 ! [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 ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_77_empty__fold__graphE,axiom,
% 0.22/0.51 ! [F_19: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,Z_4: hoare_669141180iple_a,X_8: hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite590756294iple_a @ F_19 @ Z_4 @ bot_bo280939947le_a_o @ X_8 )
% 0.22/0.51 => ( X_8 = Z_4 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_78_fold__graph_OinsertI,axiom,
% 0.22/0.51 ! [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 > $o] :
% 0.22/0.51 ( ~ ( member1016246415iple_a @ X_7 @ A_13 )
% 0.22/0.51 => ( ( finite590756294iple_a @ F_18 @ Z_3 @ A_13 @ Y_2 )
% 0.22/0.51 => ( finite590756294iple_a @ F_18 @ Z_3 @ ( insert175534902iple_a @ X_7 @ A_13 ) @ ( F_18 @ X_7 @ Y_2 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_79_finite__Collect__disjI,axiom,
% 0.22/0.51 ! [P_2: hoare_669141180iple_a > $o,Q: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( finite957651855iple_a
% 0.22/0.51 @ ( collec1717965009iple_a
% 0.22/0.51 @ ^ [X_3: hoare_669141180iple_a] : ( (|) @ ( P_2 @ X_3 ) @ ( Q @ X_3 ) ) ) )
% 0.22/0.51 <=> ( ( finite957651855iple_a @ ( collec1717965009iple_a @ P_2 ) )
% 0.22/0.51 & ( finite957651855iple_a @ ( collec1717965009iple_a @ Q ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_80_finite__insert,axiom,
% 0.22/0.51 ! [A_12: hoare_669141180iple_a,A_11: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( finite957651855iple_a @ ( insert175534902iple_a @ A_12 @ A_11 ) )
% 0.22/0.51 <=> ( finite957651855iple_a @ A_11 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_81_fold1__singleton__def,axiom,
% 0.22/0.51 ! [A_10: hoare_669141180iple_a,G: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a,F_17: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a] :
% 0.22/0.51 ( ( G
% 0.22/0.51 = ( finite684844060iple_a @ F_17 ) )
% 0.22/0.51 => ( ( G @ ( insert175534902iple_a @ A_10 @ bot_bo280939947le_a_o ) )
% 0.22/0.51 = A_10 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_82_fold1__singleton,axiom,
% 0.22/0.51 ! [F_16: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,A_9: hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite684844060iple_a @ F_16 @ ( insert175534902iple_a @ A_9 @ bot_bo280939947le_a_o ) )
% 0.22/0.51 = A_9 ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_83_folding__one_Oclosed,axiom,
% 0.22/0.51 ! [A_8: hoare_669141180iple_a > $o,F_15: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,F_14: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite972428089iple_a @ F_15 @ F_14 )
% 0.22/0.51 => ( ( finite957651855iple_a @ A_8 )
% 0.22/0.51 => ( ( A_8 != bot_bo280939947le_a_o )
% 0.22/0.51 => ( ! [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 ) ) )
% 0.22/0.51 => ( member1016246415iple_a @ ( F_14 @ A_8 ) @ A_8 ) ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_84_insert__fold1SetE,axiom,
% 0.22/0.51 ! [F_13: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,A_7: hoare_669141180iple_a,X_6: hoare_669141180iple_a > $o,X_5: hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite840267660iple_a @ F_13 @ ( insert175534902iple_a @ A_7 @ X_6 ) @ X_5 )
% 0.22/0.51 => ~ ! [A_3: hoare_669141180iple_a,A_2: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( ( insert175534902iple_a @ A_7 @ X_6 )
% 0.22/0.51 = ( insert175534902iple_a @ A_3 @ A_2 ) )
% 0.22/0.51 => ( ( finite590756294iple_a @ F_13 @ A_3 @ A_2 @ X_5 )
% 0.22/0.51 => ( member1016246415iple_a @ A_3 @ A_2 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_85_finite__nonempty__imp__fold1Set,axiom,
% 0.22/0.51 ! [F_12: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,A_6: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( finite957651855iple_a @ A_6 )
% 0.22/0.51 => ( ( A_6 != bot_bo280939947le_a_o )
% 0.22/0.51 => ( ex @ ( finite840267660iple_a @ F_12 @ A_6 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_86_finite__induct,axiom,
% 0.22/0.51 ! [P_1: ( hoare_669141180iple_a > $o ) > $o,F_11: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( finite957651855iple_a @ F_11 )
% 0.22/0.51 => ( ( P_1 @ bot_bo280939947le_a_o )
% 0.22/0.51 => ( ! [X_3: hoare_669141180iple_a,F_5: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( finite957651855iple_a @ F_5 )
% 0.22/0.51 => ( ~ ( member1016246415iple_a @ X_3 @ F_5 )
% 0.22/0.51 => ( ( P_1 @ F_5 )
% 0.22/0.51 => ( P_1 @ ( insert175534902iple_a @ X_3 @ F_5 ) ) ) ) )
% 0.22/0.51 => ( P_1 @ F_11 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_87_finite_Osimps,axiom,
% 0.22/0.51 ! [A_5: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( finite957651855iple_a @ A_5 )
% 0.22/0.51 <=> ( ( A_5 = bot_bo280939947le_a_o )
% 0.22/0.51 | ? [A_2: hoare_669141180iple_a > $o,A_3: hoare_669141180iple_a] :
% 0.22/0.51 ( ( A_5
% 0.22/0.51 = ( insert175534902iple_a @ A_3 @ A_2 ) )
% 0.22/0.51 & ( finite957651855iple_a @ A_2 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_88_finite__imp__fold__graph,axiom,
% 0.22/0.51 ! [F_10: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,Z_2: hoare_669141180iple_a,A_4: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( finite957651855iple_a @ A_4 )
% 0.22/0.51 => ( ex @ ( finite590756294iple_a @ F_10 @ Z_2 @ A_4 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_89_fold1Set_Osimps,axiom,
% 0.22/0.51 ! [F_9: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,A1_1: hoare_669141180iple_a > $o,A2_1: hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite840267660iple_a @ F_9 @ A1_1 @ A2_1 )
% 0.22/0.51 <=> ? [A_3: hoare_669141180iple_a,A_2: hoare_669141180iple_a > $o,X_3: hoare_669141180iple_a] :
% 0.22/0.51 ( ( A1_1
% 0.22/0.51 = ( insert175534902iple_a @ A_3 @ A_2 ) )
% 0.22/0.51 & ( A2_1 = X_3 )
% 0.22/0.51 & ( finite590756294iple_a @ F_9 @ A_3 @ A_2 @ X_3 )
% 0.22/0.51 & ~ ( member1016246415iple_a @ A_3 @ A_2 ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_90_fold__graph_Osimps,axiom,
% 0.22/0.51 ! [F_8: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,Z_1: hoare_669141180iple_a,A1: hoare_669141180iple_a > $o,A2: hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite590756294iple_a @ F_8 @ Z_1 @ A1 @ A2 )
% 0.22/0.51 <=> ( ( ( A1 = bot_bo280939947le_a_o )
% 0.22/0.51 & ( A2 = Z_1 ) )
% 0.22/0.51 | ? [X_3: hoare_669141180iple_a,A_2: hoare_669141180iple_a > $o,Y_1: hoare_669141180iple_a] :
% 0.22/0.51 ( ( A1
% 0.22/0.51 = ( insert175534902iple_a @ X_3 @ A_2 ) )
% 0.22/0.51 & ( A2
% 0.22/0.51 = ( F_8 @ X_3 @ Y_1 ) )
% 0.22/0.51 & ~ ( member1016246415iple_a @ X_3 @ A_2 )
% 0.22/0.51 & ( finite590756294iple_a @ F_8 @ Z_1 @ A_2 @ Y_1 ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_91_folding__one__idem_Oinsert__idem,axiom,
% 0.22/0.51 ! [X_4: hoare_669141180iple_a,A_1: hoare_669141180iple_a > $o,F_7: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,F_6: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite252461622iple_a @ F_7 @ F_6 )
% 0.22/0.51 => ( ( finite957651855iple_a @ A_1 )
% 0.22/0.51 => ( ( A_1 != bot_bo280939947le_a_o )
% 0.22/0.51 => ( ( F_6 @ ( insert175534902iple_a @ X_4 @ A_1 ) )
% 0.22/0.51 = ( F_7 @ X_4 @ ( F_6 @ A_1 ) ) ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_92_finite__ne__induct,axiom,
% 0.22/0.51 ! [P: ( hoare_669141180iple_a > $o ) > $o,F_4: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( finite957651855iple_a @ F_4 )
% 0.22/0.51 => ( ( F_4 != bot_bo280939947le_a_o )
% 0.22/0.51 => ( ! [X_3: hoare_669141180iple_a] : ( P @ ( insert175534902iple_a @ X_3 @ bot_bo280939947le_a_o ) )
% 0.22/0.51 => ( ! [X_3: hoare_669141180iple_a,F_5: hoare_669141180iple_a > $o] :
% 0.22/0.51 ( ( finite957651855iple_a @ F_5 )
% 0.22/0.51 => ( ( F_5 != bot_bo280939947le_a_o )
% 0.22/0.51 => ( ~ ( member1016246415iple_a @ X_3 @ F_5 )
% 0.22/0.51 => ( ( P @ F_5 )
% 0.22/0.51 => ( P @ ( insert175534902iple_a @ X_3 @ F_5 ) ) ) ) ) )
% 0.22/0.51 => ( P @ F_4 ) ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_93_folding__one__idem_Oidem,axiom,
% 0.22/0.51 ! [X_2: hoare_669141180iple_a,F_3: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,F_2: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite252461622iple_a @ F_3 @ F_2 )
% 0.22/0.51 => ( ( F_3 @ X_2 @ X_2 )
% 0.22/0.51 = X_2 ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(fact_94_folding__one__idem_Oin__idem,axiom,
% 0.22/0.51 ! [X_1: hoare_669141180iple_a,A: hoare_669141180iple_a > $o,F_1: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,F: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
% 0.22/0.51 ( ( finite252461622iple_a @ F_1 @ F )
% 0.22/0.51 => ( ( finite957651855iple_a @ A )
% 0.22/0.51 => ( ( member1016246415iple_a @ X_1 @ A )
% 0.22/0.51 => ( ( F_1 @ X_1 @ ( F @ A ) )
% 0.22/0.51 = ( F @ A ) ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %----Helper facts (2)
% 0.22/0.51 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_,axiom,
% 0.22/0.51 ! [X: hoare_669141180iple_a,Y: hoare_669141180iple_a] :
% 0.22/0.51 ( ~ ( fequal182287803iple_a @ X @ Y )
% 0.22/0.51 | ( X = Y ) ) ).
% 0.22/0.51
% 0.22/0.51 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_,axiom,
% 0.22/0.51 ! [X: hoare_669141180iple_a,Y: hoare_669141180iple_a] :
% 0.22/0.51 ( ( X != Y )
% 0.22/0.51 | ( fequal182287803iple_a @ X @ Y ) ) ).
% 0.22/0.54
% 0.22/0.54 %----Conjectures (1)
% 0.22/0.54 thf(conj_0,conjecture,
% 0.22/0.54 ( hoare_2128652938rivs_a @ g
% 0.22/0.54 @ ( insert175534902iple_a
% 0.22/0.54 @ ( hoare_1295064928iple_a
% 0.22/0.54 @ ^ [Z: x_a,S: state] : $false
% 0.22/0.54 @ c
% 0.22/0.54 @ ^ [Z: x_a,S: state] : ( (&) @ ( p @ Z @ S ) @ ( (~) @ ( b @ S ) ) ) )
% 0.22/0.54 @ bot_bo280939947le_a_o ) ) ).
% 0.22/0.54
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.HkbEte2MGz/cvc5---1.0.5_11311.p...
% 0.22/0.54 (declare-sort $$unsorted 0)
% 0.22/0.54 (declare-sort tptp.x_a 0)
% 0.22/0.54 (declare-sort tptp.com 0)
% 0.22/0.54 (declare-sort tptp.state 0)
% 0.22/0.54 (declare-sort tptp.hoare_669141180iple_a 0)
% 0.22/0.54 (declare-fun tptp.skip () tptp.com)
% 0.22/0.54 (declare-fun tptp.semi (tptp.com tptp.com) tptp.com)
% 0.22/0.54 (declare-fun tptp.ex ((-> tptp.hoare_669141180iple_a Bool)) Bool)
% 0.22/0.54 (declare-fun tptp.finite957651855iple_a ((-> tptp.hoare_669141180iple_a Bool)) Bool)
% 0.22/0.54 (declare-fun tptp.finite840267660iple_a ((-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a) (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a) Bool)
% 0.22/0.54 (declare-fun tptp.finite684844060iple_a ((-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a) (-> tptp.hoare_669141180iple_a Bool)) tptp.hoare_669141180iple_a)
% 0.22/0.54 (declare-fun tptp.finite590756294iple_a ((-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a) tptp.hoare_669141180iple_a (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a) Bool)
% 0.22/0.54 (declare-fun tptp.finite972428089iple_a ((-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a) (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a)) Bool)
% 0.22/0.54 (declare-fun tptp.finite252461622iple_a ((-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a) (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a)) Bool)
% 0.22/0.54 (declare-fun tptp.the_Ho49089901iple_a ((-> tptp.hoare_669141180iple_a Bool)) tptp.hoare_669141180iple_a)
% 0.22/0.54 (declare-fun tptp.hoare_2128652938rivs_a ((-> tptp.hoare_669141180iple_a Bool) (-> tptp.hoare_669141180iple_a Bool)) Bool)
% 0.22/0.54 (declare-fun tptp.hoare_1295064928iple_a ((-> tptp.x_a tptp.state Bool) tptp.com (-> tptp.x_a tptp.state Bool)) tptp.hoare_669141180iple_a)
% 0.22/0.54 (declare-fun tptp.bot_bo280939947le_a_o (tptp.hoare_669141180iple_a) Bool)
% 0.22/0.54 (declare-fun tptp.bot_bot_o () Bool)
% 0.22/0.54 (declare-fun tptp.collec1717965009iple_a ((-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a) Bool)
% 0.22/0.54 (declare-fun tptp.insert175534902iple_a (tptp.hoare_669141180iple_a (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a) Bool)
% 0.22/0.54 (declare-fun tptp.the_el738790235iple_a ((-> tptp.hoare_669141180iple_a Bool)) tptp.hoare_669141180iple_a)
% 0.22/0.54 (declare-fun tptp.fequal182287803iple_a (tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a) Bool)
% 0.22/0.54 (declare-fun tptp.member1016246415iple_a (tptp.hoare_669141180iple_a (-> tptp.hoare_669141180iple_a Bool)) Bool)
% 0.22/0.54 (declare-fun tptp.g (tptp.hoare_669141180iple_a) Bool)
% 0.22/0.54 (declare-fun tptp.p (tptp.x_a tptp.state) Bool)
% 0.22/0.54 (declare-fun tptp.b (tptp.state) Bool)
% 0.22/0.54 (declare-fun tptp.c () tptp.com)
% 0.22/0.54 (assert (forall ((G_12 (-> tptp.hoare_669141180iple_a Bool))) (@ (@ tptp.hoare_2128652938rivs_a G_12) tptp.bot_bo280939947le_a_o)))
% 0.22/0.54 (assert (forall ((Fun1_2 (-> tptp.x_a tptp.state Bool)) (Com_2 tptp.com) (Fun2_2 (-> tptp.x_a tptp.state Bool)) (Fun1_1 (-> tptp.x_a tptp.state Bool)) (Com_1 tptp.com) (Fun2_1 (-> tptp.x_a tptp.state Bool))) (= (= (@ (@ (@ tptp.hoare_1295064928iple_a Fun1_2) Com_2) Fun2_2) (@ (@ (@ tptp.hoare_1295064928iple_a Fun1_1) Com_1) Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_2 Com_1) (= Fun2_2 Fun2_1)))))
% 0.22/0.54 (assert (forall ((G_11 (-> tptp.hoare_669141180iple_a Bool)) (G_10 (-> tptp.hoare_669141180iple_a Bool)) (Ts_1 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.hoare_2128652938rivs_a G_11))) (=> (@ (@ tptp.hoare_2128652938rivs_a G_10) Ts_1) (=> (@ _let_1 G_10) (@ _let_1 Ts_1))))))
% 0.22/0.54 (assert (forall ((Ts (-> tptp.hoare_669141180iple_a Bool)) (G_9 (-> tptp.hoare_669141180iple_a Bool)) (T tptp.hoare_669141180iple_a)) (let ((_let_1 (@ tptp.insert175534902iple_a T))) (let ((_let_2 (@ tptp.hoare_2128652938rivs_a G_9))) (=> (@ _let_2 (@ _let_1 tptp.bot_bo280939947le_a_o)) (=> (@ _let_2 Ts) (@ _let_2 (@ _let_1 Ts))))))))
% 0.22/0.54 (assert (forall ((G_8 (-> tptp.hoare_669141180iple_a Bool)) (P_25 (-> tptp.x_a tptp.state Bool)) (C_9 tptp.com) (Q_11 (-> tptp.x_a tptp.state Bool)) (C_8 Bool)) (let ((_let_1 (@ tptp.hoare_2128652938rivs_a G_8))) (=> (=> C_8 (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_25) C_9) Q_11)) tptp.bot_bo280939947le_a_o))) (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (lambda ((Z tptp.x_a) (S tptp.state)) (and (@ (@ P_25 Z) S) C_8))) C_9) Q_11)) tptp.bot_bo280939947le_a_o))))))
% 0.22/0.54 (assert (forall ((G_7 (-> tptp.hoare_669141180iple_a Bool)) (C_7 tptp.com) (Q_10 (-> tptp.x_a tptp.state Bool)) (P_24 (-> tptp.x_a tptp.state Bool))) (=> (forall ((Z tptp.x_a) (S tptp.state)) (=> (@ (@ P_24 Z) S) (@ (@ tptp.hoare_2128652938rivs_a G_7) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (lambda ((Za tptp.x_a) (S_1 tptp.state)) (= S_1 S))) C_7) (lambda ((Z_6 tptp.x_a) (__flatten_var_0 tptp.state)) (@ (@ Q_10 Z) __flatten_var_0)))) tptp.bot_bo280939947le_a_o)))) (@ (@ tptp.hoare_2128652938rivs_a G_7) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_24) C_7) Q_10)) tptp.bot_bo280939947le_a_o)))))
% 0.22/0.54 (assert (forall ((Q_9 (-> tptp.x_a tptp.state Bool)) (G_6 (-> tptp.hoare_669141180iple_a Bool)) (P_23 (-> tptp.x_a tptp.state Bool)) (C_6 tptp.com) (Q_8 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ (@ tptp.hoare_1295064928iple_a P_23) C_6))) (let ((_let_2 (@ tptp.hoare_2128652938rivs_a G_6))) (=> (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ _let_1 Q_8)) tptp.bot_bo280939947le_a_o)) (=> (forall ((Z tptp.x_a) (S tptp.state)) (=> (@ (@ Q_8 Z) S) (@ (@ Q_9 Z) S))) (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ _let_1 Q_9)) tptp.bot_bo280939947le_a_o))))))))
% 0.22/0.54 (assert (forall ((P_22 (-> tptp.x_a tptp.state Bool)) (G_5 (-> tptp.hoare_669141180iple_a Bool)) (P_21 (-> tptp.x_a tptp.state Bool)) (C_5 tptp.com) (Q_7 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_2128652938rivs_a G_5))) (=> (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_21) C_5) Q_7)) tptp.bot_bo280939947le_a_o)) (=> (forall ((Z tptp.x_a) (S tptp.state)) (=> (@ (@ P_22 Z) S) (@ (@ P_21 Z) S))) (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_22) C_5) Q_7)) tptp.bot_bo280939947le_a_o)))))))
% 0.22/0.54 (assert (forall ((Q_6 (-> tptp.x_a tptp.state Bool)) (P_20 (-> tptp.x_a tptp.state Bool)) (G_4 (-> tptp.hoare_669141180iple_a Bool)) (P_19 (-> tptp.x_a tptp.state Bool)) (C_4 tptp.com) (Q_5 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_2128652938rivs_a G_4))) (=> (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_19) C_4) Q_5)) tptp.bot_bo280939947le_a_o)) (=> (forall ((Z tptp.x_a) (S tptp.state)) (=> (@ (@ P_20 Z) S) (forall ((S_1 tptp.state)) (=> (forall ((Z_6 tptp.x_a)) (=> (@ (@ P_19 Z_6) S) (@ (@ Q_5 Z_6) S_1))) (@ (@ Q_6 Z) S_1))))) (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_20) C_4) Q_6)) tptp.bot_bo280939947le_a_o)))))))
% 0.22/0.54 (assert (forall ((A_64 tptp.hoare_669141180iple_a) (B_14 tptp.hoare_669141180iple_a) (A_63 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.member1016246415iple_a A_64))) (=> (@ _let_1 (@ (@ tptp.insert175534902iple_a B_14) A_63)) (=> (not (= A_64 B_14)) (@ _let_1 A_63))))))
% 0.22/0.54 (assert (forall ((B_13 tptp.hoare_669141180iple_a) (A_62 tptp.hoare_669141180iple_a) (B_12 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.member1016246415iple_a A_62))) (=> (=> (not (@ _let_1 B_12)) (= A_62 B_13)) (@ _let_1 (@ (@ tptp.insert175534902iple_a B_13) B_12))))))
% 0.22/0.54 (assert (forall ((A_61 tptp.hoare_669141180iple_a)) (not (@ (@ tptp.member1016246415iple_a A_61) tptp.bot_bo280939947le_a_o))))
% 0.22/0.54 (assert (forall ((A_60 tptp.hoare_669141180iple_a)) (= (@ tptp.collec1717965009iple_a (@ tptp.fequal182287803iple_a A_60)) (@ (@ tptp.insert175534902iple_a A_60) tptp.bot_bo280939947le_a_o))))
% 0.22/0.54 (assert (forall ((A_59 tptp.hoare_669141180iple_a)) (= (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (= X_3 A_59))) (@ (@ tptp.insert175534902iple_a A_59) tptp.bot_bo280939947le_a_o))))
% 0.22/0.54 (assert (forall ((P_18 (-> tptp.hoare_669141180iple_a Bool)) (A_58 tptp.hoare_669141180iple_a)) (let ((_let_1 (@ P_18 A_58))) (and (=> _let_1 (= (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (and (= A_58 X_3) (@ P_18 X_3)))) (@ (@ tptp.insert175534902iple_a A_58) tptp.bot_bo280939947le_a_o))) (=> (not _let_1) (= (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (and (= A_58 X_3) (@ P_18 X_3)))) tptp.bot_bo280939947le_a_o))))))
% 0.22/0.54 (assert (forall ((P_17 (-> tptp.hoare_669141180iple_a Bool)) (A_57 tptp.hoare_669141180iple_a)) (let ((_let_1 (@ P_17 A_57))) (and (=> _let_1 (= (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (and (= X_3 A_57) (@ P_17 X_3)))) (@ (@ tptp.insert175534902iple_a A_57) tptp.bot_bo280939947le_a_o))) (=> (not _let_1) (= (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (and (= X_3 A_57) (@ P_17 X_3)))) tptp.bot_bo280939947le_a_o))))))
% 0.22/0.54 (assert (forall ((A_56 tptp.hoare_669141180iple_a) (A_55 (-> tptp.hoare_669141180iple_a Bool))) (=> (= A_55 tptp.bot_bo280939947le_a_o) (not (@ (@ tptp.member1016246415iple_a A_56) A_55)))))
% 0.22/0.54 (assert (forall ((P_16 (-> tptp.hoare_669141180iple_a Bool))) (= (= (@ tptp.collec1717965009iple_a P_16) tptp.bot_bo280939947le_a_o) (forall ((X_3 tptp.hoare_669141180iple_a)) (not (@ P_16 X_3))))))
% 0.22/0.54 (assert (forall ((C_3 tptp.hoare_669141180iple_a)) (not (@ (@ tptp.member1016246415iple_a C_3) tptp.bot_bo280939947le_a_o))))
% 0.22/0.54 (assert (forall ((P_15 (-> tptp.hoare_669141180iple_a Bool))) (= (= tptp.bot_bo280939947le_a_o (@ tptp.collec1717965009iple_a P_15)) (forall ((X_3 tptp.hoare_669141180iple_a)) (not (@ P_15 X_3))))))
% 0.22/0.54 (assert (forall ((A_54 (-> tptp.hoare_669141180iple_a Bool))) (= (exists ((X_3 tptp.hoare_669141180iple_a)) (@ (@ tptp.member1016246415iple_a X_3) A_54)) (not (= A_54 tptp.bot_bo280939947le_a_o)))))
% 0.22/0.54 (assert (forall ((A_53 (-> tptp.hoare_669141180iple_a Bool))) (= (forall ((X_3 tptp.hoare_669141180iple_a)) (not (@ (@ tptp.member1016246415iple_a X_3) A_53))) (= A_53 tptp.bot_bo280939947le_a_o))))
% 0.22/0.54 (assert (= tptp.bot_bo280939947le_a_o (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) false))))
% 0.22/0.54 (assert (forall ((A_52 tptp.hoare_669141180iple_a) (A_51 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ (@ tptp.member1016246415iple_a A_52) A_51) (= (@ (@ tptp.insert175534902iple_a A_52) A_51) A_51))))
% 0.22/0.54 (assert (forall ((B_11 tptp.hoare_669141180iple_a) (A_50 tptp.hoare_669141180iple_a) (B_10 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.member1016246415iple_a A_50))) (=> (@ _let_1 B_10) (@ _let_1 (@ (@ tptp.insert175534902iple_a B_11) B_10))))))
% 0.22/0.54 (assert (forall ((B_9 (-> tptp.hoare_669141180iple_a Bool)) (X_24 tptp.hoare_669141180iple_a) (A_49 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.insert175534902iple_a X_24))) (let ((_let_2 (@ tptp.member1016246415iple_a X_24))) (=> (not (@ _let_2 A_49)) (=> (not (@ _let_2 B_9)) (= (= (@ _let_1 A_49) (@ _let_1 B_9)) (= A_49 B_9))))))))
% 0.22/0.54 (assert (forall ((Y_6 tptp.hoare_669141180iple_a) (A_48 (-> tptp.hoare_669141180iple_a Bool)) (X_23 tptp.hoare_669141180iple_a)) (= (@ (@ (@ tptp.insert175534902iple_a Y_6) A_48) X_23) (or (= Y_6 X_23) (@ A_48 X_23)))))
% 0.22/0.54 (assert (forall ((A_47 tptp.hoare_669141180iple_a) (B_8 tptp.hoare_669141180iple_a) (A_46 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.member1016246415iple_a A_47))) (= (@ _let_1 (@ (@ tptp.insert175534902iple_a B_8) A_46)) (or (= A_47 B_8) (@ _let_1 A_46))))))
% 0.22/0.54 (assert (forall ((X_22 tptp.hoare_669141180iple_a) (Y_5 tptp.hoare_669141180iple_a) (A_45 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.insert175534902iple_a X_22))) (let ((_let_2 (@ tptp.insert175534902iple_a Y_5))) (= (@ _let_1 (@ _let_2 A_45)) (@ _let_2 (@ _let_1 A_45)))))))
% 0.22/0.54 (assert (forall ((X_21 tptp.hoare_669141180iple_a) (A_44 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.insert175534902iple_a X_21))) (let ((_let_2 (@ _let_1 A_44))) (= (@ _let_1 _let_2) _let_2)))))
% 0.22/0.54 (assert (forall ((A_43 tptp.hoare_669141180iple_a) (P_14 (-> tptp.hoare_669141180iple_a Bool))) (= (@ (@ tptp.insert175534902iple_a A_43) (@ tptp.collec1717965009iple_a P_14)) (@ tptp.collec1717965009iple_a (lambda ((U tptp.hoare_669141180iple_a)) (=> (not (= U A_43)) (@ P_14 U)))))))
% 0.22/0.54 (assert (forall ((A_42 tptp.hoare_669141180iple_a) (B_7 (-> tptp.hoare_669141180iple_a Bool))) (= (@ (@ tptp.insert175534902iple_a A_42) B_7) (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (or (= X_3 A_42) (@ (@ tptp.member1016246415iple_a X_3) B_7)))))))
% 0.22/0.54 (assert (forall ((A_41 tptp.hoare_669141180iple_a) (B_6 (-> tptp.hoare_669141180iple_a Bool))) (@ (@ tptp.member1016246415iple_a A_41) (@ (@ tptp.insert175534902iple_a A_41) B_6))))
% 0.22/0.54 (assert (forall ((X_3 tptp.hoare_669141180iple_a) (Xa (-> tptp.hoare_669141180iple_a Bool))) (= (@ (@ tptp.insert175534902iple_a X_3) Xa) (@ tptp.collec1717965009iple_a (lambda ((Y_1 tptp.hoare_669141180iple_a)) (or (= Y_1 X_3) (@ (@ tptp.member1016246415iple_a Y_1) Xa)))))))
% 0.22/0.54 (assert (forall ((A_40 tptp.hoare_669141180iple_a) (B_5 tptp.hoare_669141180iple_a)) (=> (= (@ (@ tptp.insert175534902iple_a A_40) tptp.bot_bo280939947le_a_o) (@ (@ tptp.insert175534902iple_a B_5) tptp.bot_bo280939947le_a_o)) (= A_40 B_5))))
% 0.22/0.54 (assert (forall ((B_4 tptp.hoare_669141180iple_a) (A_39 tptp.hoare_669141180iple_a)) (=> (@ (@ tptp.member1016246415iple_a B_4) (@ (@ tptp.insert175534902iple_a A_39) tptp.bot_bo280939947le_a_o)) (= B_4 A_39))))
% 0.22/0.54 (assert (forall ((A_38 tptp.hoare_669141180iple_a) (B_3 tptp.hoare_669141180iple_a) (C_2 tptp.hoare_669141180iple_a) (D_1 tptp.hoare_669141180iple_a)) (= (= (@ (@ tptp.insert175534902iple_a A_38) (@ (@ tptp.insert175534902iple_a B_3) tptp.bot_bo280939947le_a_o)) (@ (@ tptp.insert175534902iple_a C_2) (@ (@ tptp.insert175534902iple_a D_1) tptp.bot_bo280939947le_a_o))) (or (and (= A_38 C_2) (= B_3 D_1)) (and (= A_38 D_1) (= B_3 C_2))))))
% 0.22/0.54 (assert (forall ((B_2 tptp.hoare_669141180iple_a) (A_37 tptp.hoare_669141180iple_a)) (= (@ (@ tptp.member1016246415iple_a B_2) (@ (@ tptp.insert175534902iple_a A_37) tptp.bot_bo280939947le_a_o)) (= B_2 A_37))))
% 0.22/0.54 (assert (forall ((A_36 tptp.hoare_669141180iple_a) (A_35 (-> tptp.hoare_669141180iple_a Bool))) (not (= (@ (@ tptp.insert175534902iple_a A_36) A_35) tptp.bot_bo280939947le_a_o))))
% 0.22/0.54 (assert (forall ((A_34 tptp.hoare_669141180iple_a) (A_33 (-> tptp.hoare_669141180iple_a Bool))) (not (= tptp.bot_bo280939947le_a_o (@ (@ tptp.insert175534902iple_a A_34) A_33)))))
% 0.22/0.54 (assert (forall ((X_20 tptp.hoare_669141180iple_a)) (= (@ tptp.the_el738790235iple_a (@ (@ tptp.insert175534902iple_a X_20) tptp.bot_bo280939947le_a_o)) X_20)))
% 0.22/0.54 (assert (forall ((X_19 tptp.hoare_669141180iple_a)) (= (@ tptp.bot_bo280939947le_a_o X_19) tptp.bot_bot_o)))
% 0.22/0.54 (assert (forall ((X_3 tptp.hoare_669141180iple_a)) (= (@ tptp.bot_bo280939947le_a_o X_3) tptp.bot_bot_o)))
% 0.22/0.54 (assert (forall ((G_3 (-> tptp.hoare_669141180iple_a Bool)) (P_13 (-> tptp.x_a tptp.state Bool))) (@ (@ tptp.hoare_2128652938rivs_a G_3) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_13) tptp.skip) P_13)) tptp.bot_bo280939947le_a_o))))
% 0.22/0.54 (assert (forall ((D tptp.com) (R (-> tptp.x_a tptp.state Bool)) (G_2 (-> tptp.hoare_669141180iple_a Bool)) (P_12 (-> tptp.x_a tptp.state Bool)) (C_1 tptp.com) (Q_4 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_1295064928iple_a P_12))) (let ((_let_2 (@ tptp.hoare_2128652938rivs_a G_2))) (=> (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ _let_1 C_1) Q_4)) tptp.bot_bo280939947le_a_o)) (=> (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a Q_4) D) R)) tptp.bot_bo280939947le_a_o)) (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ _let_1 (@ (@ tptp.semi C_1) D)) R)) tptp.bot_bo280939947le_a_o))))))))
% 0.22/0.54 (assert (forall ((Y_4 tptp.hoare_669141180iple_a)) (not (forall ((Fun1 (-> tptp.x_a tptp.state Bool)) (Com tptp.com) (Fun2 (-> tptp.x_a tptp.state Bool))) (not (= Y_4 (@ (@ (@ tptp.hoare_1295064928iple_a Fun1) Com) Fun2)))))))
% 0.22/0.54 (assert (forall ((X_18 tptp.hoare_669141180iple_a) (A_32 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ (@ tptp.member1016246415iple_a X_18) A_32) (not (forall ((B_1 (-> tptp.hoare_669141180iple_a Bool))) (=> (= A_32 (@ (@ tptp.insert175534902iple_a X_18) B_1)) (@ (@ tptp.member1016246415iple_a X_18) B_1)))))))
% 0.22/0.54 (assert (forall ((Com1 tptp.com) (Com2 tptp.com)) (not (= (@ (@ tptp.semi Com1) Com2) tptp.skip))))
% 0.22/0.54 (assert (forall ((Com1 tptp.com) (Com2 tptp.com)) (not (= tptp.skip (@ (@ tptp.semi Com1) Com2)))))
% 0.22/0.54 (assert (forall ((X_17 (-> tptp.hoare_669141180iple_a Bool))) (= (@ tptp.the_el738790235iple_a X_17) (@ tptp.the_Ho49089901iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (= X_17 (@ (@ tptp.insert175534902iple_a X_3) tptp.bot_bo280939947le_a_o)))))))
% 0.22/0.54 (assert (forall ((A_31 tptp.hoare_669141180iple_a) (A_30 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ (@ tptp.member1016246415iple_a A_31) A_30) (exists ((B_1 (-> tptp.hoare_669141180iple_a Bool))) (and (= A_30 (@ (@ tptp.insert175534902iple_a A_31) B_1)) (not (@ (@ tptp.member1016246415iple_a A_31) B_1)))))))
% 0.22/0.54 (assert (forall ((Com1_1 tptp.com) (Com2_1 tptp.com) (Com1 tptp.com) (Com2 tptp.com)) (= (= (@ (@ tptp.semi Com1_1) Com2_1) (@ (@ tptp.semi Com1) Com2)) (and (= Com1_1 Com1) (= Com2_1 Com2)))))
% 0.22/0.54 (assert (forall ((X_16 tptp.hoare_669141180iple_a)) (= (@ tptp.the_Ho49089901iple_a (@ tptp.fequal182287803iple_a X_16)) X_16)))
% 0.22/0.54 (assert (forall ((A_29 tptp.hoare_669141180iple_a)) (= (@ tptp.the_Ho49089901iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (= X_3 A_29))) A_29)))
% 0.22/0.54 (assert (forall ((X_15 tptp.hoare_669141180iple_a) (Y_3 tptp.hoare_669141180iple_a) (P_11 Bool)) (and (=> P_11 (= X_15 (@ tptp.the_Ho49089901iple_a (lambda ((Z_7 tptp.hoare_669141180iple_a)) (and (=> P_11 (= Z_7 X_15)) (=> (not P_11) (= Z_7 Y_3))))))) (=> (not P_11) (= Y_3 (@ tptp.the_Ho49089901iple_a (lambda ((Z_7 tptp.hoare_669141180iple_a)) (and (=> P_11 (= Z_7 X_15)) (=> (not P_11) (= Z_7 Y_3))))))))))
% 0.22/0.54 (assert (forall ((A_28 (-> tptp.hoare_669141180iple_a Bool))) (=> (forall ((Y_1 tptp.hoare_669141180iple_a)) (not (@ (@ tptp.member1016246415iple_a Y_1) A_28))) (= A_28 tptp.bot_bo280939947le_a_o))))
% 0.22/0.54 (assert (forall ((P_10 (-> tptp.hoare_669141180iple_a Bool)) (A_27 tptp.hoare_669141180iple_a)) (=> (@ P_10 A_27) (=> (forall ((X_3 tptp.hoare_669141180iple_a)) (=> (@ P_10 X_3) (= X_3 A_27))) (= (@ tptp.the_Ho49089901iple_a P_10) A_27)))))
% 0.22/0.54 (assert (forall ((P_9 (-> tptp.hoare_669141180iple_a Bool)) (A_26 tptp.hoare_669141180iple_a)) (=> (@ P_9 A_26) (=> (forall ((X_3 tptp.hoare_669141180iple_a)) (=> (@ P_9 X_3) (= X_3 A_26))) (@ P_9 (@ tptp.the_Ho49089901iple_a P_9))))))
% 0.22/0.54 (assert (forall ((A_25 tptp.hoare_669141180iple_a) (P_8 (-> tptp.hoare_669141180iple_a Bool))) (=> (exists ((X_3 tptp.hoare_669141180iple_a)) (and (@ P_8 X_3) (forall ((Y_1 tptp.hoare_669141180iple_a)) (=> (@ P_8 Y_1) (= Y_1 X_3))))) (=> (@ P_8 A_25) (= (@ tptp.the_Ho49089901iple_a P_8) A_25)))))
% 0.22/0.54 (assert (forall ((P_7 (-> tptp.hoare_669141180iple_a Bool))) (=> (exists ((X_3 tptp.hoare_669141180iple_a)) (and (@ P_7 X_3) (forall ((Y_1 tptp.hoare_669141180iple_a)) (=> (@ P_7 Y_1) (= Y_1 X_3))))) (@ P_7 (@ tptp.the_Ho49089901iple_a P_7)))))
% 0.22/0.54 (assert (forall ((Q_2 (-> tptp.x_a tptp.state Bool)) (G_1 (-> tptp.hoare_669141180iple_a Bool)) (C tptp.com) (P_5 (-> tptp.x_a tptp.state Bool))) (=> (forall ((Z tptp.x_a) (S tptp.state)) (=> (@ (@ P_5 Z) S) (exists ((P_6 (-> tptp.x_a tptp.state Bool)) (Q_3 (-> tptp.x_a tptp.state Bool))) (and (@ (@ tptp.hoare_2128652938rivs_a G_1) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_6) C) Q_3)) tptp.bot_bo280939947le_a_o)) (forall ((S_1 tptp.state)) (=> (forall ((Z_6 tptp.x_a)) (=> (@ (@ P_6 Z_6) S) (@ (@ Q_3 Z_6) S_1))) (@ (@ Q_2 Z) S_1))))))) (@ (@ tptp.hoare_2128652938rivs_a G_1) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_5) C) Q_2)) tptp.bot_bo280939947le_a_o)))))
% 0.22/0.54 (assert (forall ((A_24 (-> tptp.hoare_669141180iple_a Bool))) (= (not (= A_24 tptp.bot_bo280939947le_a_o)) (exists ((X_3 tptp.hoare_669141180iple_a) (B_1 (-> tptp.hoare_669141180iple_a Bool))) (and (= A_24 (@ (@ tptp.insert175534902iple_a X_3) B_1)) (not (@ (@ tptp.member1016246415iple_a X_3) B_1)))))))
% 0.22/0.54 (assert (forall ((F_31 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_23 tptp.hoare_669141180iple_a) (B tptp.hoare_669141180iple_a)) (= (@ (@ (@ tptp.finite840267660iple_a F_31) (@ (@ tptp.insert175534902iple_a A_23) tptp.bot_bo280939947le_a_o)) B) (= A_23 B))))
% 0.22/0.54 (assert (forall ((X_14 tptp.hoare_669141180iple_a) (F_30 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_29 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite972428089iple_a F_30) F_29) (= (@ F_29 (@ (@ tptp.insert175534902iple_a X_14) tptp.bot_bo280939947le_a_o)) X_14))))
% 0.22/0.54 (assert (forall ((X_3 tptp.hoare_669141180iple_a)) (= (@ tptp.bot_bo280939947le_a_o X_3) (@ (@ tptp.member1016246415iple_a X_3) tptp.bot_bo280939947le_a_o))))
% 0.22/0.54 (assert (forall ((F_28 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (X_13 tptp.hoare_669141180iple_a)) (not (@ (@ (@ tptp.finite840267660iple_a F_28) tptp.bot_bo280939947le_a_o) X_13))))
% 0.22/0.54 (assert (forall ((F_27 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_22 (-> tptp.hoare_669141180iple_a Bool)) (X_12 tptp.hoare_669141180iple_a)) (=> (@ (@ (@ tptp.finite840267660iple_a F_27) A_22) X_12) (not (= A_22 tptp.bot_bo280939947le_a_o)))))
% 0.22/0.54 (assert (forall ((F_26 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_21 tptp.hoare_669141180iple_a) (A_20 (-> tptp.hoare_669141180iple_a Bool)) (X_11 tptp.hoare_669141180iple_a)) (=> (@ (@ (@ (@ tptp.finite590756294iple_a F_26) A_21) A_20) X_11) (=> (not (@ (@ tptp.member1016246415iple_a A_21) A_20)) (@ (@ (@ tptp.finite840267660iple_a F_26) (@ (@ tptp.insert175534902iple_a A_21) A_20)) X_11)))))
% 0.22/0.54 (assert (forall ((X_10 tptp.hoare_669141180iple_a) (A_19 (-> tptp.hoare_669141180iple_a Bool)) (F_25 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_24 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite972428089iple_a F_25) F_24) (=> (@ tptp.finite957651855iple_a A_19) (=> (not (@ (@ tptp.member1016246415iple_a X_10) A_19)) (=> (not (= A_19 tptp.bot_bo280939947le_a_o)) (= (@ F_24 (@ (@ tptp.insert175534902iple_a X_10) A_19)) (@ (@ F_25 X_10) (@ F_24 A_19)))))))))
% 0.22/0.54 (assert (forall ((F_23 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_18 (-> tptp.hoare_669141180iple_a Bool))) (= (@ (@ tptp.finite684844060iple_a F_23) A_18) (@ tptp.the_Ho49089901iple_a (@ (@ tptp.finite840267660iple_a F_23) A_18)))))
% 0.22/0.54 (assert (forall ((Q_1 (-> tptp.hoare_669141180iple_a Bool)) (P_4 (-> tptp.hoare_669141180iple_a Bool))) (=> (or (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a P_4)) (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a Q_1))) (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (and (@ P_4 X_3) (@ Q_1 X_3))))))))
% 0.22/0.54 (assert (@ tptp.finite957651855iple_a tptp.bot_bo280939947le_a_o))
% 0.22/0.54 (assert (forall ((A_17 tptp.hoare_669141180iple_a) (A_16 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a A_16) (@ tptp.finite957651855iple_a (@ (@ tptp.insert175534902iple_a A_17) A_16)))))
% 0.22/0.54 (assert (forall ((X_9 tptp.hoare_669141180iple_a) (A_15 (-> tptp.hoare_669141180iple_a Bool))) (= (@ (@ tptp.member1016246415iple_a X_9) A_15) (@ A_15 X_9))))
% 0.22/0.54 (assert (forall ((P_3 (-> tptp.hoare_669141180iple_a Bool))) (= (@ tptp.collec1717965009iple_a P_3) P_3)))
% 0.22/0.54 (assert (forall ((A_14 (-> tptp.hoare_669141180iple_a Bool)) (F_22 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_21 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite972428089iple_a F_22) F_21) (=> (@ tptp.finite957651855iple_a A_14) (= (@ F_21 A_14) (@ (@ tptp.finite684844060iple_a F_22) A_14))))))
% 0.22/0.54 (assert (forall ((F_20 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (Z_5 tptp.hoare_669141180iple_a)) (@ (@ (@ (@ tptp.finite590756294iple_a F_20) Z_5) tptp.bot_bo280939947le_a_o) Z_5)))
% 0.22/0.54 (assert (forall ((F_19 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (Z_4 tptp.hoare_669141180iple_a) (X_8 tptp.hoare_669141180iple_a)) (=> (@ (@ (@ (@ tptp.finite590756294iple_a F_19) Z_4) tptp.bot_bo280939947le_a_o) X_8) (= X_8 Z_4))))
% 0.22/0.54 (assert (forall ((F_18 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (Z_3 tptp.hoare_669141180iple_a) (Y_2 tptp.hoare_669141180iple_a) (X_7 tptp.hoare_669141180iple_a) (A_13 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ (@ tptp.finite590756294iple_a F_18) Z_3))) (=> (not (@ (@ tptp.member1016246415iple_a X_7) A_13)) (=> (@ (@ _let_1 A_13) Y_2) (@ (@ _let_1 (@ (@ tptp.insert175534902iple_a X_7) A_13)) (@ (@ F_18 X_7) Y_2)))))))
% 0.22/0.54 (assert (forall ((P_2 (-> tptp.hoare_669141180iple_a Bool)) (Q (-> tptp.hoare_669141180iple_a Bool))) (= (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (or (@ P_2 X_3) (@ Q X_3))))) (and (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a P_2)) (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a Q))))))
% 0.22/0.54 (assert (forall ((A_12 tptp.hoare_669141180iple_a) (A_11 (-> tptp.hoare_669141180iple_a Bool))) (= (@ tptp.finite957651855iple_a (@ (@ tptp.insert175534902iple_a A_12) A_11)) (@ tptp.finite957651855iple_a A_11))))
% 0.22/0.54 (assert (forall ((A_10 tptp.hoare_669141180iple_a) (G (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a)) (F_17 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a))) (=> (= G (@ tptp.finite684844060iple_a F_17)) (= (@ G (@ (@ tptp.insert175534902iple_a A_10) tptp.bot_bo280939947le_a_o)) A_10))))
% 0.22/0.54 (assert (forall ((F_16 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_9 tptp.hoare_669141180iple_a)) (= (@ (@ tptp.finite684844060iple_a F_16) (@ (@ tptp.insert175534902iple_a A_9) tptp.bot_bo280939947le_a_o)) A_9)))
% 0.22/0.54 (assert (forall ((A_8 (-> tptp.hoare_669141180iple_a Bool)) (F_15 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_14 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite972428089iple_a F_15) F_14) (=> (@ tptp.finite957651855iple_a A_8) (=> (not (= A_8 tptp.bot_bo280939947le_a_o)) (=> (forall ((X_3 tptp.hoare_669141180iple_a) (Y_1 tptp.hoare_669141180iple_a)) (@ (@ tptp.member1016246415iple_a (@ (@ F_15 X_3) Y_1)) (@ (@ tptp.insert175534902iple_a X_3) (@ (@ tptp.insert175534902iple_a Y_1) tptp.bot_bo280939947le_a_o)))) (@ (@ tptp.member1016246415iple_a (@ F_14 A_8)) A_8)))))))
% 0.22/0.54 (assert (forall ((F_13 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_7 tptp.hoare_669141180iple_a) (X_6 (-> tptp.hoare_669141180iple_a Bool)) (X_5 tptp.hoare_669141180iple_a)) (=> (@ (@ (@ tptp.finite840267660iple_a F_13) (@ (@ tptp.insert175534902iple_a A_7) X_6)) X_5) (not (forall ((A_3 tptp.hoare_669141180iple_a) (A_2 (-> tptp.hoare_669141180iple_a Bool))) (=> (= (@ (@ tptp.insert175534902iple_a A_7) X_6) (@ (@ tptp.insert175534902iple_a A_3) A_2)) (=> (@ (@ (@ (@ tptp.finite590756294iple_a F_13) A_3) A_2) X_5) (@ (@ tptp.member1016246415iple_a A_3) A_2))))))))
% 0.22/0.54 (assert (forall ((F_12 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_6 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a A_6) (=> (not (= A_6 tptp.bot_bo280939947le_a_o)) (@ tptp.ex (@ (@ tptp.finite840267660iple_a F_12) A_6))))))
% 0.22/0.54 (assert (forall ((P_1 (-> (-> tptp.hoare_669141180iple_a Bool) Bool)) (F_11 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a F_11) (=> (@ P_1 tptp.bot_bo280939947le_a_o) (=> (forall ((X_3 tptp.hoare_669141180iple_a) (F_5 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a F_5) (=> (not (@ (@ tptp.member1016246415iple_a X_3) F_5)) (=> (@ P_1 F_5) (@ P_1 (@ (@ tptp.insert175534902iple_a X_3) F_5)))))) (@ P_1 F_11))))))
% 0.22/0.54 (assert (forall ((A_5 (-> tptp.hoare_669141180iple_a Bool))) (= (@ tptp.finite957651855iple_a A_5) (or (= A_5 tptp.bot_bo280939947le_a_o) (exists ((A_2 (-> tptp.hoare_669141180iple_a Bool)) (A_3 tptp.hoare_669141180iple_a)) (and (= A_5 (@ (@ tptp.insert175534902iple_a A_3) A_2)) (@ tptp.finite957651855iple_a A_2)))))))
% 0.22/0.54 (assert (forall ((F_10 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (Z_2 tptp.hoare_669141180iple_a) (A_4 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a A_4) (@ tptp.ex (@ (@ (@ tptp.finite590756294iple_a F_10) Z_2) A_4)))))
% 0.22/0.54 (assert (forall ((F_9 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A1_1 (-> tptp.hoare_669141180iple_a Bool)) (A2_1 tptp.hoare_669141180iple_a)) (= (@ (@ (@ tptp.finite840267660iple_a F_9) A1_1) A2_1) (exists ((A_3 tptp.hoare_669141180iple_a) (A_2 (-> tptp.hoare_669141180iple_a Bool)) (X_3 tptp.hoare_669141180iple_a)) (and (= A1_1 (@ (@ tptp.insert175534902iple_a A_3) A_2)) (= A2_1 X_3) (@ (@ (@ (@ tptp.finite590756294iple_a F_9) A_3) A_2) X_3) (not (@ (@ tptp.member1016246415iple_a A_3) A_2)))))))
% 0.22/0.54 (assert (forall ((F_8 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (Z_1 tptp.hoare_669141180iple_a) (A1 (-> tptp.hoare_669141180iple_a Bool)) (A2 tptp.hoare_669141180iple_a)) (= (@ (@ (@ (@ tptp.finite590756294iple_a F_8) Z_1) A1) A2) (or (and (= A1 tptp.bot_bo280939947le_a_o) (= A2 Z_1)) (exists ((X_3 tptp.hoare_669141180iple_a) (A_2 (-> tptp.hoare_669141180iple_a Bool)) (Y_1 tptp.hoare_669141180iple_a)) (and (= A1 (@ (@ tptp.insert175534902iple_a X_3) A_2)) (= A2 (@ (@ F_8 X_3) Y_1)) (not (@ (@ tptp.member1016246415iple_a X_3) A_2)) (@ (@ (@ (@ tptp.finite590756294iple_a F_8) Z_1) A_2) Y_1)))))))
% 0.22/0.54 (assert (forall ((X_4 tptp.hoare_669141180iple_a) (A_1 (-> tptp.hoare_669141180iple_a Bool)) (F_7 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_6 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite252461622iple_a F_7) F_6) (=> (@ tptp.finite957651855iple_a A_1) (=> (not (= A_1 tptp.bot_bo280939947le_a_o)) (= (@ F_6 (@ (@ tptp.insert175534902iple_a X_4) A_1)) (@ (@ F_7 X_4) (@ F_6 A_1))))))))
% 0.22/0.54 (assert (forall ((P (-> (-> tptp.hoare_669141180iple_a Bool) Bool)) (F_4 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a F_4) (=> (not (= F_4 tptp.bot_bo280939947le_a_o)) (=> (forall ((X_3 tptp.hoare_669141180iple_a)) (@ P (@ (@ tptp.insert175534902iple_a X_3) tptp.bot_bo280939947le_a_o))) (=> (forall ((X_3 tptp.hoare_669141180iple_a) (F_5 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a F_5) (=> (not (= F_5 tptp.bot_bo280939947le_a_o)) (=> (not (@ (@ tptp.member1016246415iple_a X_3) F_5)) (=> (@ P F_5) (@ P (@ (@ tptp.insert175534902iple_a X_3) F_5))))))) (@ P F_4)))))))
% 0.22/0.54 (assert (forall ((X_2 tptp.hoare_669141180iple_a) (F_3 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_2 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite252461622iple_a F_3) F_2) (= (@ (@ F_3 X_2) X_2) X_2))))
% 0.22/0.54 (assert (forall ((X_1 tptp.hoare_669141180iple_a) (A (-> tptp.hoare_669141180iple_a Bool)) (F_1 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (let ((_let_1 (@ F A))) (=> (@ (@ tptp.finite252461622iple_a F_1) F) (=> (@ tptp.finite957651855iple_a A) (=> (@ (@ tptp.member1016246415iple_a X_1) A) (= (@ (@ F_1 X_1) _let_1) _let_1)))))))
% 0.22/0.54 (assert (forall ((X tptp.hoare_669141180iple_a) (Y tptp.hoare_669141180iple_a)) (or (not (@ (@ tptp.fequal182287803iple_a X) Y)) (= X Y))))
% 0.22/0.54 (assert (forall ((X tptp.hoare_669141180iple_a) (Y tptp.hoare_669141180iple_a)) (or (not (= X Y)) (@ (@ tptp.fequal182287803iple_a X) Y))))
% 0.22/0.66 (assert (not (@ (@ tptp.hoare_2128652938rivs_a tptp.g) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (lambda ((Z tptp.x_a) (S tptp.state)) false)) tptp.c) (lambda ((Z tptp.x_a) (S tptp.state)) (and (@ (@ tptp.p Z) S) (not (@ tptp.b S)))))) tptp.bot_bo280939947le_a_o))))
% 0.22/0.66 (set-info :filename cvc5---1.0.5_11311)
% 0.22/0.66 (check-sat-assuming ( true ))
% 0.22/0.66 ------- get file name : TPTP file name is SWW470^1
% 0.22/0.66 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11311.smt2...
% 0.22/0.66 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.66 % SZS status Theorem for SWW470^1
% 0.22/0.66 % SZS output start Proof for SWW470^1
% 0.22/0.66 (
% 0.22/0.66 (let ((_let_1 (lambda ((Z tptp.x_a) (S tptp.state)) (and (@ (@ tptp.p Z) S) (not (@ tptp.b S)))))) (let ((_let_2 (@ tptp.hoare_2128652938rivs_a tptp.g))) (let ((_let_3 (not (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (lambda ((Z tptp.x_a) (S tptp.state)) false)) tptp.c) _let_1)) tptp.bot_bo280939947le_a_o))))) (let ((_let_4 (= tptp.bot_bo280939947le_a_o (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) false))))) (let ((_let_5 (forall ((G_8 (-> tptp.hoare_669141180iple_a Bool)) (P_25 (-> tptp.x_a tptp.state Bool)) (C_9 tptp.com) (Q_11 (-> tptp.x_a tptp.state Bool)) (C_8 Bool)) (let ((_let_1 (@ tptp.hoare_2128652938rivs_a G_8))) (=> (=> C_8 (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_25) C_9) Q_11)) tptp.bot_bo280939947le_a_o))) (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (lambda ((Z tptp.x_a) (S tptp.state)) (and (@ (@ P_25 Z) S) C_8))) C_9) Q_11)) tptp.bot_bo280939947le_a_o))))))) (let ((_let_6 (forall ((BOUND_VARIABLE_4830 |u_(-> tptp.hoare_669141180iple_a Bool)|) (BOUND_VARIABLE_2134 tptp.com) (BOUND_VARIABLE_4824 |u_(-> tptp.x_a tptp.state Bool)|)) (ho_44 (ho_62 k_61 BOUND_VARIABLE_4830) (ho_30 (ho_39 k_38 (ho_66 (ho_65 (ho_64 k_63 k_57) BOUND_VARIABLE_2134) BOUND_VARIABLE_4824)) (ho_30 k_37 k_36)))))) (let ((_let_7 (ho_44 (ho_62 k_61 k_88) (ho_30 (ho_39 k_38 (ho_66 (ho_65 (ho_64 k_63 k_57) tptp.c) k_22)) (ho_30 k_37 k_36))))) (let ((_let_8 (and (forall ((BOUND_VARIABLE_2130 (-> tptp.hoare_669141180iple_a Bool)) (BOUND_VARIABLE_2134 tptp.com) (BOUND_VARIABLE_2136 (-> tptp.x_a tptp.state Bool))) (@ (@ tptp.hoare_2128652938rivs_a BOUND_VARIABLE_2130) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a ll_4) BOUND_VARIABLE_2134) BOUND_VARIABLE_2136)) (@ tptp.collec1717965009iple_a ll_2)))) (forall ((BOUND_VARIABLE_2154 (-> tptp.hoare_669141180iple_a Bool)) (BOUND_VARIABLE_2156 (-> tptp.x_a tptp.state Bool)) (BOUND_VARIABLE_2158 tptp.com) (BOUND_VARIABLE_2160 (-> tptp.x_a tptp.state Bool)) (BOUND_VARIABLE_2162 Bool)) (let ((_let_1 (@ tptp.collec1717965009iple_a ll_2))) (let ((_let_2 (@ tptp.hoare_2128652938rivs_a BOUND_VARIABLE_2154))) (or (not (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a BOUND_VARIABLE_2156) BOUND_VARIABLE_2158) BOUND_VARIABLE_2160)) _let_1))) (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (@ (@ ll_3 BOUND_VARIABLE_2156) BOUND_VARIABLE_2162)) BOUND_VARIABLE_2158) BOUND_VARIABLE_2160)) _let_1))))))))) (let ((_let_9 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_10 (not (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a ll_4) tptp.c) ll_21)) (@ tptp.collec1717965009iple_a ll_2)))))) (let ((_let_11 (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (lambda ((BOUND_VARIABLE_3641 tptp.x_a) (BOUND_VARIABLE_3643 tptp.state)) false)) tptp.c) _let_1)))) (let ((_let_12 (_let_6))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_12) :args (k_88 tptp.c k_22 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_12)) :args ((or _let_7 (not _let_6)))) (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_9 :args ((not (@ _let_2 (@ _let_11 tptp.bot_bo280939947le_a_o))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (@ _let_2 (@ _let_11 (@ tptp.collec1717965009iple_a (lambda ((BOUND_VARIABLE_3604 tptp.hoare_669141180iple_a)) false))))) _let_10))) (PREPROCESS :args ((= _let_10 (not _let_7)))))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_9 :args ((and (forall ((BOUND_VARIABLE_2130 (-> tptp.hoare_669141180iple_a Bool)) (BOUND_VARIABLE_2134 tptp.com) (BOUND_VARIABLE_2136 (-> tptp.x_a tptp.state Bool))) (@ (@ tptp.hoare_2128652938rivs_a BOUND_VARIABLE_2130) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (lambda ((BOUND_VARIABLE_3641 tptp.x_a) (BOUND_VARIABLE_3643 tptp.state)) false)) BOUND_VARIABLE_2134) BOUND_VARIABLE_2136)) tptp.bot_bo280939947le_a_o))) (forall ((BOUND_VARIABLE_2154 (-> tptp.hoare_669141180iple_a Bool)) (BOUND_VARIABLE_2156 (-> tptp.x_a tptp.state Bool)) (BOUND_VARIABLE_2158 tptp.com) (BOUND_VARIABLE_2160 (-> tptp.x_a tptp.state Bool)) (BOUND_VARIABLE_2162 Bool)) (let ((_let_1 (@ tptp.hoare_2128652938rivs_a BOUND_VARIABLE_2154))) (or (not (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a BOUND_VARIABLE_2156) BOUND_VARIABLE_2158) BOUND_VARIABLE_2160)) tptp.bot_bo280939947le_a_o))) (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (lambda ((Z tptp.x_a) (S tptp.state)) (and (@ (@ BOUND_VARIABLE_2156 Z) S) BOUND_VARIABLE_2162))) BOUND_VARIABLE_2158) BOUND_VARIABLE_2160)) tptp.bot_bo280939947le_a_o)))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (forall ((BOUND_VARIABLE_2130 (-> tptp.hoare_669141180iple_a Bool)) (BOUND_VARIABLE_2134 tptp.com) (BOUND_VARIABLE_2136 (-> tptp.x_a tptp.state Bool))) (@ (@ tptp.hoare_2128652938rivs_a BOUND_VARIABLE_2130) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (lambda ((BOUND_VARIABLE_3641 tptp.x_a) (BOUND_VARIABLE_3643 tptp.state)) false)) BOUND_VARIABLE_2134) BOUND_VARIABLE_2136)) (@ tptp.collec1717965009iple_a (lambda ((BOUND_VARIABLE_3604 tptp.hoare_669141180iple_a)) false))))) (forall ((BOUND_VARIABLE_2154 (-> tptp.hoare_669141180iple_a Bool)) (BOUND_VARIABLE_2156 (-> tptp.x_a tptp.state Bool)) (BOUND_VARIABLE_2158 tptp.com) (BOUND_VARIABLE_2160 (-> tptp.x_a tptp.state Bool)) (BOUND_VARIABLE_2162 Bool)) (let ((_let_1 (@ tptp.collec1717965009iple_a (lambda ((BOUND_VARIABLE_3604 tptp.hoare_669141180iple_a)) false)))) (let ((_let_2 (@ tptp.hoare_2128652938rivs_a BOUND_VARIABLE_2154))) (or (not (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a BOUND_VARIABLE_2156) BOUND_VARIABLE_2158) BOUND_VARIABLE_2160)) _let_1))) (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (lambda ((Z tptp.x_a) (S tptp.state)) (and (@ (@ BOUND_VARIABLE_2156 Z) S) BOUND_VARIABLE_2162))) BOUND_VARIABLE_2158) BOUND_VARIABLE_2160)) _let_1))))))) _let_8))) (PREPROCESS :args ((= _let_8 (and _let_6 (forall ((BOUND_VARIABLE_4811 |u_(-> tptp.hoare_669141180iple_a Bool)|) (BOUND_VARIABLE_4803 |u_(-> tptp.x_a tptp.state Bool)|) (BOUND_VARIABLE_2158 tptp.com) (BOUND_VARIABLE_4802 |u_(-> tptp.x_a tptp.state Bool)|) (BOUND_VARIABLE_2162 Bool)) (let ((_let_1 (ho_30 k_37 k_36))) (let ((_let_2 (ho_62 k_61 BOUND_VARIABLE_4811))) (or (not (ho_44 _let_2 (ho_30 (ho_39 k_38 (ho_66 (ho_65 (ho_64 k_63 BOUND_VARIABLE_4803) BOUND_VARIABLE_2158) BOUND_VARIABLE_4802)) _let_1))) (ho_44 _let_2 (ho_30 (ho_39 k_38 (ho_66 (ho_65 (ho_64 k_63 (ho_60 (ho_59 k_58 BOUND_VARIABLE_4803) BOUND_VARIABLE_2162)) BOUND_VARIABLE_2158) BOUND_VARIABLE_4802)) _let_1)))))))))))) :args (0)) :args (false true _let_7 false _let_6)) :args ((forall ((G_12 (-> tptp.hoare_669141180iple_a Bool))) (@ (@ tptp.hoare_2128652938rivs_a G_12) tptp.bot_bo280939947le_a_o)) (forall ((Fun1_2 (-> tptp.x_a tptp.state Bool)) (Com_2 tptp.com) (Fun2_2 (-> tptp.x_a tptp.state Bool)) (Fun1_1 (-> tptp.x_a tptp.state Bool)) (Com_1 tptp.com) (Fun2_1 (-> tptp.x_a tptp.state Bool))) (= (= (@ (@ (@ tptp.hoare_1295064928iple_a Fun1_2) Com_2) Fun2_2) (@ (@ (@ tptp.hoare_1295064928iple_a Fun1_1) Com_1) Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_2 Com_1) (= Fun2_2 Fun2_1)))) (forall ((G_11 (-> tptp.hoare_669141180iple_a Bool)) (G_10 (-> tptp.hoare_669141180iple_a Bool)) (Ts_1 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.hoare_2128652938rivs_a G_11))) (=> (@ (@ tptp.hoare_2128652938rivs_a G_10) Ts_1) (=> (@ _let_1 G_10) (@ _let_1 Ts_1))))) (forall ((Ts (-> tptp.hoare_669141180iple_a Bool)) (G_9 (-> tptp.hoare_669141180iple_a Bool)) (T tptp.hoare_669141180iple_a)) (let ((_let_1 (@ tptp.insert175534902iple_a T))) (let ((_let_2 (@ tptp.hoare_2128652938rivs_a G_9))) (=> (@ _let_2 (@ _let_1 tptp.bot_bo280939947le_a_o)) (=> (@ _let_2 Ts) (@ _let_2 (@ _let_1 Ts))))))) _let_5 (forall ((G_7 (-> tptp.hoare_669141180iple_a Bool)) (C_7 tptp.com) (Q_10 (-> tptp.x_a tptp.state Bool)) (P_24 (-> tptp.x_a tptp.state Bool))) (=> (forall ((Z tptp.x_a) (S tptp.state)) (=> (@ (@ P_24 Z) S) (@ (@ tptp.hoare_2128652938rivs_a G_7) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a (lambda ((Za tptp.x_a) (S_1 tptp.state)) (= S_1 S))) C_7) (lambda ((Z_6 tptp.x_a) (__flatten_var_0 tptp.state)) (@ (@ Q_10 Z) __flatten_var_0)))) tptp.bot_bo280939947le_a_o)))) (@ (@ tptp.hoare_2128652938rivs_a G_7) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_24) C_7) Q_10)) tptp.bot_bo280939947le_a_o)))) (forall ((Q_9 (-> tptp.x_a tptp.state Bool)) (G_6 (-> tptp.hoare_669141180iple_a Bool)) (P_23 (-> tptp.x_a tptp.state Bool)) (C_6 tptp.com) (Q_8 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ (@ tptp.hoare_1295064928iple_a P_23) C_6))) (let ((_let_2 (@ tptp.hoare_2128652938rivs_a G_6))) (=> (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ _let_1 Q_8)) tptp.bot_bo280939947le_a_o)) (=> (forall ((Z tptp.x_a) (S tptp.state)) (=> (@ (@ Q_8 Z) S) (@ (@ Q_9 Z) S))) (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ _let_1 Q_9)) tptp.bot_bo280939947le_a_o))))))) (forall ((P_22 (-> tptp.x_a tptp.state Bool)) (G_5 (-> tptp.hoare_669141180iple_a Bool)) (P_21 (-> tptp.x_a tptp.state Bool)) (C_5 tptp.com) (Q_7 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_2128652938rivs_a G_5))) (=> (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_21) C_5) Q_7)) tptp.bot_bo280939947le_a_o)) (=> (forall ((Z tptp.x_a) (S tptp.state)) (=> (@ (@ P_22 Z) S) (@ (@ P_21 Z) S))) (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_22) C_5) Q_7)) tptp.bot_bo280939947le_a_o)))))) (forall ((Q_6 (-> tptp.x_a tptp.state Bool)) (P_20 (-> tptp.x_a tptp.state Bool)) (G_4 (-> tptp.hoare_669141180iple_a Bool)) (P_19 (-> tptp.x_a tptp.state Bool)) (C_4 tptp.com) (Q_5 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_2128652938rivs_a G_4))) (=> (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_19) C_4) Q_5)) tptp.bot_bo280939947le_a_o)) (=> (forall ((Z tptp.x_a) (S tptp.state)) (=> (@ (@ P_20 Z) S) (forall ((S_1 tptp.state)) (=> (forall ((Z_6 tptp.x_a)) (=> (@ (@ P_19 Z_6) S) (@ (@ Q_5 Z_6) S_1))) (@ (@ Q_6 Z) S_1))))) (@ _let_1 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_20) C_4) Q_6)) tptp.bot_bo280939947le_a_o)))))) (forall ((A_64 tptp.hoare_669141180iple_a) (B_14 tptp.hoare_669141180iple_a) (A_63 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.member1016246415iple_a A_64))) (=> (@ _let_1 (@ (@ tptp.insert175534902iple_a B_14) A_63)) (=> (not (= A_64 B_14)) (@ _let_1 A_63))))) (forall ((B_13 tptp.hoare_669141180iple_a) (A_62 tptp.hoare_669141180iple_a) (B_12 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.member1016246415iple_a A_62))) (=> (=> (not (@ _let_1 B_12)) (= A_62 B_13)) (@ _let_1 (@ (@ tptp.insert175534902iple_a B_13) B_12))))) (forall ((A_61 tptp.hoare_669141180iple_a)) (not (@ (@ tptp.member1016246415iple_a A_61) tptp.bot_bo280939947le_a_o))) (forall ((A_60 tptp.hoare_669141180iple_a)) (= (@ tptp.collec1717965009iple_a (@ tptp.fequal182287803iple_a A_60)) (@ (@ tptp.insert175534902iple_a A_60) tptp.bot_bo280939947le_a_o))) (forall ((A_59 tptp.hoare_669141180iple_a)) (= (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (= X_3 A_59))) (@ (@ tptp.insert175534902iple_a A_59) tptp.bot_bo280939947le_a_o))) (forall ((P_18 (-> tptp.hoare_669141180iple_a Bool)) (A_58 tptp.hoare_669141180iple_a)) (let ((_let_1 (@ P_18 A_58))) (and (=> _let_1 (= (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (and (= A_58 X_3) (@ P_18 X_3)))) (@ (@ tptp.insert175534902iple_a A_58) tptp.bot_bo280939947le_a_o))) (=> (not _let_1) (= (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (and (= A_58 X_3) (@ P_18 X_3)))) tptp.bot_bo280939947le_a_o))))) (forall ((P_17 (-> tptp.hoare_669141180iple_a Bool)) (A_57 tptp.hoare_669141180iple_a)) (let ((_let_1 (@ P_17 A_57))) (and (=> _let_1 (= (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (and (= X_3 A_57) (@ P_17 X_3)))) (@ (@ tptp.insert175534902iple_a A_57) tptp.bot_bo280939947le_a_o))) (=> (not _let_1) (= (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (and (= X_3 A_57) (@ P_17 X_3)))) tptp.bot_bo280939947le_a_o))))) (forall ((A_56 tptp.hoare_669141180iple_a) (A_55 (-> tptp.hoare_669141180iple_a Bool))) (=> (= A_55 tptp.bot_bo280939947le_a_o) (not (@ (@ tptp.member1016246415iple_a A_56) A_55)))) (forall ((P_16 (-> tptp.hoare_669141180iple_a Bool))) (= (= (@ tptp.collec1717965009iple_a P_16) tptp.bot_bo280939947le_a_o) (forall ((X_3 tptp.hoare_669141180iple_a)) (not (@ P_16 X_3))))) (forall ((C_3 tptp.hoare_669141180iple_a)) (not (@ (@ tptp.member1016246415iple_a C_3) tptp.bot_bo280939947le_a_o))) (forall ((P_15 (-> tptp.hoare_669141180iple_a Bool))) (= (= tptp.bot_bo280939947le_a_o (@ tptp.collec1717965009iple_a P_15)) (forall ((X_3 tptp.hoare_669141180iple_a)) (not (@ P_15 X_3))))) (forall ((A_54 (-> tptp.hoare_669141180iple_a Bool))) (= (exists ((X_3 tptp.hoare_669141180iple_a)) (@ (@ tptp.member1016246415iple_a X_3) A_54)) (not (= A_54 tptp.bot_bo280939947le_a_o)))) (forall ((A_53 (-> tptp.hoare_669141180iple_a Bool))) (= (forall ((X_3 tptp.hoare_669141180iple_a)) (not (@ (@ tptp.member1016246415iple_a X_3) A_53))) (= A_53 tptp.bot_bo280939947le_a_o))) _let_4 (forall ((A_52 tptp.hoare_669141180iple_a) (A_51 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ (@ tptp.member1016246415iple_a A_52) A_51) (= (@ (@ tptp.insert175534902iple_a A_52) A_51) A_51))) (forall ((B_11 tptp.hoare_669141180iple_a) (A_50 tptp.hoare_669141180iple_a) (B_10 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.member1016246415iple_a A_50))) (=> (@ _let_1 B_10) (@ _let_1 (@ (@ tptp.insert175534902iple_a B_11) B_10))))) (forall ((B_9 (-> tptp.hoare_669141180iple_a Bool)) (X_24 tptp.hoare_669141180iple_a) (A_49 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.insert175534902iple_a X_24))) (let ((_let_2 (@ tptp.member1016246415iple_a X_24))) (=> (not (@ _let_2 A_49)) (=> (not (@ _let_2 B_9)) (= (= (@ _let_1 A_49) (@ _let_1 B_9)) (= A_49 B_9))))))) (forall ((Y_6 tptp.hoare_669141180iple_a) (A_48 (-> tptp.hoare_669141180iple_a Bool)) (X_23 tptp.hoare_669141180iple_a)) (= (@ (@ (@ tptp.insert175534902iple_a Y_6) A_48) X_23) (or (= Y_6 X_23) (@ A_48 X_23)))) (forall ((A_47 tptp.hoare_669141180iple_a) (B_8 tptp.hoare_669141180iple_a) (A_46 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.member1016246415iple_a A_47))) (= (@ _let_1 (@ (@ tptp.insert175534902iple_a B_8) A_46)) (or (= A_47 B_8) (@ _let_1 A_46))))) (forall ((X_22 tptp.hoare_669141180iple_a) (Y_5 tptp.hoare_669141180iple_a) (A_45 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.insert175534902iple_a X_22))) (let ((_let_2 (@ tptp.insert175534902iple_a Y_5))) (= (@ _let_1 (@ _let_2 A_45)) (@ _let_2 (@ _let_1 A_45)))))) (forall ((X_21 tptp.hoare_669141180iple_a) (A_44 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ tptp.insert175534902iple_a X_21))) (let ((_let_2 (@ _let_1 A_44))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A_43 tptp.hoare_669141180iple_a) (P_14 (-> tptp.hoare_669141180iple_a Bool))) (= (@ (@ tptp.insert175534902iple_a A_43) (@ tptp.collec1717965009iple_a P_14)) (@ tptp.collec1717965009iple_a (lambda ((U tptp.hoare_669141180iple_a)) (=> (not (= U A_43)) (@ P_14 U)))))) (forall ((A_42 tptp.hoare_669141180iple_a) (B_7 (-> tptp.hoare_669141180iple_a Bool))) (= (@ (@ tptp.insert175534902iple_a A_42) B_7) (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (or (= X_3 A_42) (@ (@ tptp.member1016246415iple_a X_3) B_7)))))) (forall ((A_41 tptp.hoare_669141180iple_a) (B_6 (-> tptp.hoare_669141180iple_a Bool))) (@ (@ tptp.member1016246415iple_a A_41) (@ (@ tptp.insert175534902iple_a A_41) B_6))) (forall ((X_3 tptp.hoare_669141180iple_a) (Xa (-> tptp.hoare_669141180iple_a Bool))) (= (@ (@ tptp.insert175534902iple_a X_3) Xa) (@ tptp.collec1717965009iple_a (lambda ((Y_1 tptp.hoare_669141180iple_a)) (or (= Y_1 X_3) (@ (@ tptp.member1016246415iple_a Y_1) Xa)))))) (forall ((A_40 tptp.hoare_669141180iple_a) (B_5 tptp.hoare_669141180iple_a)) (=> (= (@ (@ tptp.insert175534902iple_a A_40) tptp.bot_bo280939947le_a_o) (@ (@ tptp.insert175534902iple_a B_5) tptp.bot_bo280939947le_a_o)) (= A_40 B_5))) (forall ((B_4 tptp.hoare_669141180iple_a) (A_39 tptp.hoare_669141180iple_a)) (=> (@ (@ tptp.member1016246415iple_a B_4) (@ (@ tptp.insert175534902iple_a A_39) tptp.bot_bo280939947le_a_o)) (= B_4 A_39))) (forall ((A_38 tptp.hoare_669141180iple_a) (B_3 tptp.hoare_669141180iple_a) (C_2 tptp.hoare_669141180iple_a) (D_1 tptp.hoare_669141180iple_a)) (= (= (@ (@ tptp.insert175534902iple_a A_38) (@ (@ tptp.insert175534902iple_a B_3) tptp.bot_bo280939947le_a_o)) (@ (@ tptp.insert175534902iple_a C_2) (@ (@ tptp.insert175534902iple_a D_1) tptp.bot_bo280939947le_a_o))) (or (and (= A_38 C_2) (= B_3 D_1)) (and (= A_38 D_1) (= B_3 C_2))))) (forall ((B_2 tptp.hoare_669141180iple_a) (A_37 tptp.hoare_669141180iple_a)) (= (@ (@ tptp.member1016246415iple_a B_2) (@ (@ tptp.insert175534902iple_a A_37) tptp.bot_bo280939947le_a_o)) (= B_2 A_37))) (forall ((A_36 tptp.hoare_669141180iple_a) (A_35 (-> tptp.hoare_669141180iple_a Bool))) (not (= (@ (@ tptp.insert175534902iple_a A_36) A_35) tptp.bot_bo280939947le_a_o))) (forall ((A_34 tptp.hoare_669141180iple_a) (A_33 (-> tptp.hoare_669141180iple_a Bool))) (not (= tptp.bot_bo280939947le_a_o (@ (@ tptp.insert175534902iple_a A_34) A_33)))) (forall ((X_20 tptp.hoare_669141180iple_a)) (= (@ tptp.the_el738790235iple_a (@ (@ tptp.insert175534902iple_a X_20) tptp.bot_bo280939947le_a_o)) X_20)) (forall ((X_19 tptp.hoare_669141180iple_a)) (= (@ tptp.bot_bo280939947le_a_o X_19) tptp.bot_bot_o)) (forall ((X_3 tptp.hoare_669141180iple_a)) (= (@ tptp.bot_bo280939947le_a_o X_3) tptp.bot_bot_o)) (forall ((G_3 (-> tptp.hoare_669141180iple_a Bool)) (P_13 (-> tptp.x_a tptp.state Bool))) (@ (@ tptp.hoare_2128652938rivs_a G_3) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_13) tptp.skip) P_13)) tptp.bot_bo280939947le_a_o))) (forall ((D tptp.com) (R (-> tptp.x_a tptp.state Bool)) (G_2 (-> tptp.hoare_669141180iple_a Bool)) (P_12 (-> tptp.x_a tptp.state Bool)) (C_1 tptp.com) (Q_4 (-> tptp.x_a tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_1295064928iple_a P_12))) (let ((_let_2 (@ tptp.hoare_2128652938rivs_a G_2))) (=> (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ _let_1 C_1) Q_4)) tptp.bot_bo280939947le_a_o)) (=> (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a Q_4) D) R)) tptp.bot_bo280939947le_a_o)) (@ _let_2 (@ (@ tptp.insert175534902iple_a (@ (@ _let_1 (@ (@ tptp.semi C_1) D)) R)) tptp.bot_bo280939947le_a_o))))))) (forall ((Y_4 tptp.hoare_669141180iple_a)) (not (forall ((Fun1 (-> tptp.x_a tptp.state Bool)) (Com tptp.com) (Fun2 (-> tptp.x_a tptp.state Bool))) (not (= Y_4 (@ (@ (@ tptp.hoare_1295064928iple_a Fun1) Com) Fun2)))))) (forall ((X_18 tptp.hoare_669141180iple_a) (A_32 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ (@ tptp.member1016246415iple_a X_18) A_32) (not (forall ((B_1 (-> tptp.hoare_669141180iple_a Bool))) (=> (= A_32 (@ (@ tptp.insert175534902iple_a X_18) B_1)) (@ (@ tptp.member1016246415iple_a X_18) B_1)))))) (forall ((Com1 tptp.com) (Com2 tptp.com)) (not (= (@ (@ tptp.semi Com1) Com2) tptp.skip))) (forall ((Com1 tptp.com) (Com2 tptp.com)) (not (= tptp.skip (@ (@ tptp.semi Com1) Com2)))) (forall ((X_17 (-> tptp.hoare_669141180iple_a Bool))) (= (@ tptp.the_el738790235iple_a X_17) (@ tptp.the_Ho49089901iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (= X_17 (@ (@ tptp.insert175534902iple_a X_3) tptp.bot_bo280939947le_a_o)))))) (forall ((A_31 tptp.hoare_669141180iple_a) (A_30 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ (@ tptp.member1016246415iple_a A_31) A_30) (exists ((B_1 (-> tptp.hoare_669141180iple_a Bool))) (and (= A_30 (@ (@ tptp.insert175534902iple_a A_31) B_1)) (not (@ (@ tptp.member1016246415iple_a A_31) B_1)))))) (forall ((Com1_1 tptp.com) (Com2_1 tptp.com) (Com1 tptp.com) (Com2 tptp.com)) (= (= (@ (@ tptp.semi Com1_1) Com2_1) (@ (@ tptp.semi Com1) Com2)) (and (= Com1_1 Com1) (= Com2_1 Com2)))) (forall ((X_16 tptp.hoare_669141180iple_a)) (= (@ tptp.the_Ho49089901iple_a (@ tptp.fequal182287803iple_a X_16)) X_16)) (forall ((A_29 tptp.hoare_669141180iple_a)) (= (@ tptp.the_Ho49089901iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (= X_3 A_29))) A_29)) (forall ((X_15 tptp.hoare_669141180iple_a) (Y_3 tptp.hoare_669141180iple_a) (P_11 Bool)) (and (=> P_11 (= X_15 (@ tptp.the_Ho49089901iple_a (lambda ((Z_7 tptp.hoare_669141180iple_a)) (and (=> P_11 (= Z_7 X_15)) (=> (not P_11) (= Z_7 Y_3))))))) (=> (not P_11) (= Y_3 (@ tptp.the_Ho49089901iple_a (lambda ((Z_7 tptp.hoare_669141180iple_a)) (and (=> P_11 (= Z_7 X_15)) (=> (not P_11) (= Z_7 Y_3))))))))) (forall ((A_28 (-> tptp.hoare_669141180iple_a Bool))) (=> (forall ((Y_1 tptp.hoare_669141180iple_a)) (not (@ (@ tptp.member1016246415iple_a Y_1) A_28))) (= A_28 tptp.bot_bo280939947le_a_o))) (forall ((P_10 (-> tptp.hoare_669141180iple_a Bool)) (A_27 tptp.hoare_669141180iple_a)) (=> (@ P_10 A_27) (=> (forall ((X_3 tptp.hoare_669141180iple_a)) (=> (@ P_10 X_3) (= X_3 A_27))) (= (@ tptp.the_Ho49089901iple_a P_10) A_27)))) (forall ((P_9 (-> tptp.hoare_669141180iple_a Bool)) (A_26 tptp.hoare_669141180iple_a)) (=> (@ P_9 A_26) (=> (forall ((X_3 tptp.hoare_669141180iple_a)) (=> (@ P_9 X_3) (= X_3 A_26))) (@ P_9 (@ tptp.the_Ho49089901iple_a P_9))))) (forall ((A_25 tptp.hoare_669141180iple_a) (P_8 (-> tptp.hoare_669141180iple_a Bool))) (=> (exists ((X_3 tptp.hoare_669141180iple_a)) (and (@ P_8 X_3) (forall ((Y_1 tptp.hoare_669141180iple_a)) (=> (@ P_8 Y_1) (= Y_1 X_3))))) (=> (@ P_8 A_25) (= (@ tptp.the_Ho49089901iple_a P_8) A_25)))) (forall ((P_7 (-> tptp.hoare_669141180iple_a Bool))) (=> (exists ((X_3 tptp.hoare_669141180iple_a)) (and (@ P_7 X_3) (forall ((Y_1 tptp.hoare_669141180iple_a)) (=> (@ P_7 Y_1) (= Y_1 X_3))))) (@ P_7 (@ tptp.the_Ho49089901iple_a P_7)))) (forall ((Q_2 (-> tptp.x_a tptp.state Bool)) (G_1 (-> tptp.hoare_669141180iple_a Bool)) (C tptp.com) (P_5 (-> tptp.x_a tptp.state Bool))) (=> (forall ((Z tptp.x_a) (S tptp.state)) (=> (@ (@ P_5 Z) S) (exists ((P_6 (-> tptp.x_a tptp.state Bool)) (Q_3 (-> tptp.x_a tptp.state Bool))) (and (@ (@ tptp.hoare_2128652938rivs_a G_1) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_6) C) Q_3)) tptp.bot_bo280939947le_a_o)) (forall ((S_1 tptp.state)) (=> (forall ((Z_6 tptp.x_a)) (=> (@ (@ P_6 Z_6) S) (@ (@ Q_3 Z_6) S_1))) (@ (@ Q_2 Z) S_1))))))) (@ (@ tptp.hoare_2128652938rivs_a G_1) (@ (@ tptp.insert175534902iple_a (@ (@ (@ tptp.hoare_1295064928iple_a P_5) C) Q_2)) tptp.bot_bo280939947le_a_o)))) (forall ((A_24 (-> tptp.hoare_669141180iple_a Bool))) (= (not (= A_24 tptp.bot_bo280939947le_a_o)) (exists ((X_3 tptp.hoare_669141180iple_a) (B_1 (-> tptp.hoare_669141180iple_a Bool))) (and (= A_24 (@ (@ tptp.insert175534902iple_a X_3) B_1)) (not (@ (@ tptp.member1016246415iple_a X_3) B_1)))))) (forall ((F_31 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_23 tptp.hoare_669141180iple_a) (B tptp.hoare_669141180iple_a)) (= (@ (@ (@ tptp.finite840267660iple_a F_31) (@ (@ tptp.insert175534902iple_a A_23) tptp.bot_bo280939947le_a_o)) B) (= A_23 B))) (forall ((X_14 tptp.hoare_669141180iple_a) (F_30 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_29 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite972428089iple_a F_30) F_29) (= (@ F_29 (@ (@ tptp.insert175534902iple_a X_14) tptp.bot_bo280939947le_a_o)) X_14))) (forall ((X_3 tptp.hoare_669141180iple_a)) (= (@ tptp.bot_bo280939947le_a_o X_3) (@ (@ tptp.member1016246415iple_a X_3) tptp.bot_bo280939947le_a_o))) (forall ((F_28 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (X_13 tptp.hoare_669141180iple_a)) (not (@ (@ (@ tptp.finite840267660iple_a F_28) tptp.bot_bo280939947le_a_o) X_13))) (forall ((F_27 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_22 (-> tptp.hoare_669141180iple_a Bool)) (X_12 tptp.hoare_669141180iple_a)) (=> (@ (@ (@ tptp.finite840267660iple_a F_27) A_22) X_12) (not (= A_22 tptp.bot_bo280939947le_a_o)))) (forall ((F_26 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_21 tptp.hoare_669141180iple_a) (A_20 (-> tptp.hoare_669141180iple_a Bool)) (X_11 tptp.hoare_669141180iple_a)) (=> (@ (@ (@ (@ tptp.finite590756294iple_a F_26) A_21) A_20) X_11) (=> (not (@ (@ tptp.member1016246415iple_a A_21) A_20)) (@ (@ (@ tptp.finite840267660iple_a F_26) (@ (@ tptp.insert175534902iple_a A_21) A_20)) X_11)))) (forall ((X_10 tptp.hoare_669141180iple_a) (A_19 (-> tptp.hoare_669141180iple_a Bool)) (F_25 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_24 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite972428089iple_a F_25) F_24) (=> (@ tptp.finite957651855iple_a A_19) (=> (not (@ (@ tptp.member1016246415iple_a X_10) A_19)) (=> (not (= A_19 tptp.bot_bo280939947le_a_o)) (= (@ F_24 (@ (@ tptp.insert175534902iple_a X_10) A_19)) (@ (@ F_25 X_10) (@ F_24 A_19)))))))) (forall ((F_23 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_18 (-> tptp.hoare_669141180iple_a Bool))) (= (@ (@ tptp.finite684844060iple_a F_23) A_18) (@ tptp.the_Ho49089901iple_a (@ (@ tptp.finite840267660iple_a F_23) A_18)))) (forall ((Q_1 (-> tptp.hoare_669141180iple_a Bool)) (P_4 (-> tptp.hoare_669141180iple_a Bool))) (=> (or (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a P_4)) (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a Q_1))) (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (and (@ P_4 X_3) (@ Q_1 X_3))))))) (@ tptp.finite957651855iple_a tptp.bot_bo280939947le_a_o) (forall ((A_17 tptp.hoare_669141180iple_a) (A_16 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a A_16) (@ tptp.finite957651855iple_a (@ (@ tptp.insert175534902iple_a A_17) A_16)))) (forall ((X_9 tptp.hoare_669141180iple_a) (A_15 (-> tptp.hoare_669141180iple_a Bool))) (= (@ (@ tptp.member1016246415iple_a X_9) A_15) (@ A_15 X_9))) (forall ((P_3 (-> tptp.hoare_669141180iple_a Bool))) (= (@ tptp.collec1717965009iple_a P_3) P_3)) (forall ((A_14 (-> tptp.hoare_669141180iple_a Bool)) (F_22 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_21 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite972428089iple_a F_22) F_21) (=> (@ tptp.finite957651855iple_a A_14) (= (@ F_21 A_14) (@ (@ tptp.finite684844060iple_a F_22) A_14))))) (forall ((F_20 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (Z_5 tptp.hoare_669141180iple_a)) (@ (@ (@ (@ tptp.finite590756294iple_a F_20) Z_5) tptp.bot_bo280939947le_a_o) Z_5)) (forall ((F_19 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (Z_4 tptp.hoare_669141180iple_a) (X_8 tptp.hoare_669141180iple_a)) (=> (@ (@ (@ (@ tptp.finite590756294iple_a F_19) Z_4) tptp.bot_bo280939947le_a_o) X_8) (= X_8 Z_4))) (forall ((F_18 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (Z_3 tptp.hoare_669141180iple_a) (Y_2 tptp.hoare_669141180iple_a) (X_7 tptp.hoare_669141180iple_a) (A_13 (-> tptp.hoare_669141180iple_a Bool))) (let ((_let_1 (@ (@ tptp.finite590756294iple_a F_18) Z_3))) (=> (not (@ (@ tptp.member1016246415iple_a X_7) A_13)) (=> (@ (@ _let_1 A_13) Y_2) (@ (@ _let_1 (@ (@ tptp.insert175534902iple_a X_7) A_13)) (@ (@ F_18 X_7) Y_2)))))) (forall ((P_2 (-> tptp.hoare_669141180iple_a Bool)) (Q (-> tptp.hoare_669141180iple_a Bool))) (= (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a (lambda ((X_3 tptp.hoare_669141180iple_a)) (or (@ P_2 X_3) (@ Q X_3))))) (and (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a P_2)) (@ tptp.finite957651855iple_a (@ tptp.collec1717965009iple_a Q))))) (forall ((A_12 tptp.hoare_669141180iple_a) (A_11 (-> tptp.hoare_669141180iple_a Bool))) (= (@ tptp.finite957651855iple_a (@ (@ tptp.insert175534902iple_a A_12) A_11)) (@ tptp.finite957651855iple_a A_11))) (forall ((A_10 tptp.hoare_669141180iple_a) (G (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a)) (F_17 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a))) (=> (= G (@ tptp.finite684844060iple_a F_17)) (= (@ G (@ (@ tptp.insert175534902iple_a A_10) tptp.bot_bo280939947le_a_o)) A_10))) (forall ((F_16 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_9 tptp.hoare_669141180iple_a)) (= (@ (@ tptp.finite684844060iple_a F_16) (@ (@ tptp.insert175534902iple_a A_9) tptp.bot_bo280939947le_a_o)) A_9)) (forall ((A_8 (-> tptp.hoare_669141180iple_a Bool)) (F_15 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_14 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite972428089iple_a F_15) F_14) (=> (@ tptp.finite957651855iple_a A_8) (=> (not (= A_8 tptp.bot_bo280939947le_a_o)) (=> (forall ((X_3 tptp.hoare_669141180iple_a) (Y_1 tptp.hoare_669141180iple_a)) (@ (@ tptp.member1016246415iple_a (@ (@ F_15 X_3) Y_1)) (@ (@ tptp.insert175534902iple_a X_3) (@ (@ tptp.insert175534902iple_a Y_1) tptp.bot_bo280939947le_a_o)))) (@ (@ tptp.member1016246415iple_a (@ F_14 A_8)) A_8)))))) (forall ((F_13 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_7 tptp.hoare_669141180iple_a) (X_6 (-> tptp.hoare_669141180iple_a Bool)) (X_5 tptp.hoare_669141180iple_a)) (=> (@ (@ (@ tptp.finite840267660iple_a F_13) (@ (@ tptp.insert175534902iple_a A_7) X_6)) X_5) (not (forall ((A_3 tptp.hoare_669141180iple_a) (A_2 (-> tptp.hoare_669141180iple_a Bool))) (=> (= (@ (@ tptp.insert175534902iple_a A_7) X_6) (@ (@ tptp.insert175534902iple_a A_3) A_2)) (=> (@ (@ (@ (@ tptp.finite590756294iple_a F_13) A_3) A_2) X_5) (@ (@ tptp.member1016246415iple_a A_3) A_2))))))) (forall ((F_12 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A_6 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a A_6) (=> (not (= A_6 tptp.bot_bo280939947le_a_o)) (@ tptp.ex (@ (@ tptp.finite840267660iple_a F_12) A_6))))) (forall ((P_1 (-> (-> tptp.hoare_669141180iple_a Bool) Bool)) (F_11 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a F_11) (=> (@ P_1 tptp.bot_bo280939947le_a_o) (=> (forall ((X_3 tptp.hoare_669141180iple_a) (F_5 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a F_5) (=> (not (@ (@ tptp.member1016246415iple_a X_3) F_5)) (=> (@ P_1 F_5) (@ P_1 (@ (@ tptp.insert175534902iple_a X_3) F_5)))))) (@ P_1 F_11))))) (forall ((A_5 (-> tptp.hoare_669141180iple_a Bool))) (= (@ tptp.finite957651855iple_a A_5) (or (= A_5 tptp.bot_bo280939947le_a_o) (exists ((A_2 (-> tptp.hoare_669141180iple_a Bool)) (A_3 tptp.hoare_669141180iple_a)) (and (= A_5 (@ (@ tptp.insert175534902iple_a A_3) A_2)) (@ tptp.finite957651855iple_a A_2)))))) (forall ((F_10 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (Z_2 tptp.hoare_669141180iple_a) (A_4 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a A_4) (@ tptp.ex (@ (@ (@ tptp.finite590756294iple_a F_10) Z_2) A_4)))) (forall ((F_9 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (A1_1 (-> tptp.hoare_669141180iple_a Bool)) (A2_1 tptp.hoare_669141180iple_a)) (= (@ (@ (@ tptp.finite840267660iple_a F_9) A1_1) A2_1) (exists ((A_3 tptp.hoare_669141180iple_a) (A_2 (-> tptp.hoare_669141180iple_a Bool)) (X_3 tptp.hoare_669141180iple_a)) (and (= A1_1 (@ (@ tptp.insert175534902iple_a A_3) A_2)) (= A2_1 X_3) (@ (@ (@ (@ tptp.finite590756294iple_a F_9) A_3) A_2) X_3) (not (@ (@ tptp.member1016246415iple_a A_3) A_2)))))) (forall ((F_8 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (Z_1 tptp.hoare_669141180iple_a) (A1 (-> tptp.hoare_669141180iple_a Bool)) (A2 tptp.hoare_669141180iple_a)) (= (@ (@ (@ (@ tptp.finite590756294iple_a F_8) Z_1) A1) A2) (or (and (= A1 tptp.bot_bo280939947le_a_o) (= A2 Z_1)) (exists ((X_3 tptp.hoare_669141180iple_a) (A_2 (-> tptp.hoare_669141180iple_a Bool)) (Y_1 tptp.hoare_669141180iple_a)) (and (= A1 (@ (@ tptp.insert175534902iple_a X_3) A_2)) (= A2 (@ (@ F_8 X_3) Y_1)) (not (@ (@ tptp.member1016246415iple_a X_3) A_2)) (@ (@ (@ (@ tptp.finite590756294iple_a F_8) Z_1) A_2) Y_1)))))) (forall ((X_4 tptp.hoare_669141180iple_a) (A_1 (-> tptp.hoare_669141180iple_a Bool)) (F_7 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_6 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite252461622iple_a F_7) F_6) (=> (@ tptp.finite957651855iple_a A_1) (=> (not (= A_1 tptp.bot_bo280939947le_a_o)) (= (@ F_6 (@ (@ tptp.insert175534902iple_a X_4) A_1)) (@ (@ F_7 X_4) (@ F_6 A_1))))))) (forall ((P (-> (-> tptp.hoare_669141180iple_a Bool) Bool)) (F_4 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a F_4) (=> (not (= F_4 tptp.bot_bo280939947le_a_o)) (=> (forall ((X_3 tptp.hoare_669141180iple_a)) (@ P (@ (@ tptp.insert175534902iple_a X_3) tptp.bot_bo280939947le_a_o))) (=> (forall ((X_3 tptp.hoare_669141180iple_a) (F_5 (-> tptp.hoare_669141180iple_a Bool))) (=> (@ tptp.finite957651855iple_a F_5) (=> (not (= F_5 tptp.bot_bo280939947le_a_o)) (=> (not (@ (@ tptp.member1016246415iple_a X_3) F_5)) (=> (@ P F_5) (@ P (@ (@ tptp.insert175534902iple_a X_3) F_5))))))) (@ P F_4)))))) (forall ((X_2 tptp.hoare_669141180iple_a) (F_3 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F_2 (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (=> (@ (@ tptp.finite252461622iple_a F_3) F_2) (= (@ (@ F_3 X_2) X_2) X_2))) (forall ((X_1 tptp.hoare_669141180iple_a) (A (-> tptp.hoare_669141180iple_a Bool)) (F_1 (-> tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a tptp.hoare_669141180iple_a)) (F (-> (-> tptp.hoare_669141180iple_a Bool) tptp.hoare_669141180iple_a))) (let ((_let_1 (@ F A))) (=> (@ (@ tptp.finite252461622iple_a F_1) F) (=> (@ tptp.finite957651855iple_a A) (=> (@ (@ tptp.member1016246415iple_a X_1) A) (= (@ (@ F_1 X_1) _let_1) _let_1)))))) (forall ((X tptp.hoare_669141180iple_a) (Y tptp.hoare_669141180iple_a)) (or (not (@ (@ tptp.fequal182287803iple_a X) Y)) (= X Y))) (forall ((X tptp.hoare_669141180iple_a) (Y tptp.hoare_669141180iple_a)) (or (not (= X Y)) (@ (@ tptp.fequal182287803iple_a X) Y))) _let_3 true)))))))))))))))
% 0.22/0.66 )
% 0.22/0.66 % SZS output end Proof for SWW470^1
% 0.22/0.66 % cvc5---1.0.5 exiting
% 0.22/0.66 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------