TSTP Solution File: SWW472^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW472^1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n006.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 00:21:01 EDT 2023
% Result : Timeout 299.97s 300.21s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SWW472^1 : TPTP v8.1.2. Released v5.3.0.
% 0.14/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 21:46:51 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 % File : SWW472^1 : TPTP v8.1.2. Released v5.3.0.
% 0.21/0.51 % Domain : Software Verification
% 0.21/0.51 % Problem : Hoare's Logic with Procedures line 327, 100 axioms selected
% 0.21/0.51 % Version : Especial.
% 0.21/0.51 % English :
% 0.21/0.51
% 0.21/0.51 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.21/0.51 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.21/0.51 % Source : [Bla11]
% 0.21/0.51 % Names : hoare_100_thf_l327 [Bla11]
% 0.21/0.51
% 0.21/0.51 % Status : Theorem
% 0.21/0.51 % Rating : 1.00 v5.3.0
% 0.21/0.51 % Syntax : Number of formulae : 120 ( 19 unt; 27 typ; 0 def)
% 0.21/0.51 % Number of atoms : 406 ( 84 equ; 3 cnn)
% 0.21/0.51 % Maximal formula atoms : 9 ( 4 avg)
% 0.21/0.51 % Number of connectives : 802 ( 43 ~; 6 |; 18 &; 614 @)
% 0.21/0.51 % ( 22 <=>; 99 =>; 0 <=; 0 <~>)
% 0.21/0.51 % Maximal formula depth : 18 ( 8 avg)
% 0.21/0.51 % Number of types : 4 ( 3 usr)
% 0.21/0.51 % Number of type conns : 284 ( 284 >; 0 *; 0 +; 0 <<)
% 0.21/0.51 % Number of symbols : 29 ( 24 usr; 7 con; 0-4 aty)
% 0.21/0.51 % Number of variables : 273 ( 3 ^; 256 !; 14 ?; 273 :)
% 0.21/0.51 % SPC : TH0_THM_EQU_NAR
% 0.21/0.51
% 0.21/0.51 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.21/0.51 % 2011-08-09 19:16:50
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 %----Should-be-implicit typings (3)
% 0.21/0.51 thf(ty_ty_tc__Com__Ocom,type,
% 0.21/0.51 com: $tType ).
% 0.21/0.51
% 0.21/0.51 thf(ty_ty_tc__Com__Ostate,type,
% 0.21/0.51 state: $tType ).
% 0.21/0.51
% 0.21/0.51 thf(ty_ty_tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J,type,
% 0.21/0.51 hoare_1262092251_state: $tType ).
% 0.21/0.51
% 0.21/0.51 %----Explicit typings (24)
% 0.21/0.51 thf(sy_c_Big__Operators_Osemilattice__big_000tc__Hoare____Mirabelle____ghhkfsbqqq__O,type,
% 0.21/0.51 big_se1697321605_state: ( hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state ) > ( ( hoare_1262092251_state > $o ) > hoare_1262092251_state ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Com_Ocom_OSKIP,type,
% 0.21/0.51 skip: com ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Com_Ocom_OSemi,type,
% 0.21/0.51 semi: com > com > com ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Ex,type,
% 0.21/0.51 ex: ( hoare_1262092251_state > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__C,type,
% 0.21/0.51 finite1178804552_state: ( hoare_1262092251_state > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Finite__Set_Ofold1Set_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc_,type,
% 0.21/0.51 finite403475723_state: ( hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state ) > ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Finite__Set_Ofold1_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Co,type,
% 0.21/0.51 finite1740352635_state: ( hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state ) > ( hoare_1262092251_state > $o ) > hoare_1262092251_state ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Finite__Set_Ofold__graph_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_I,type,
% 0.21/0.51 finite975744042_state: ( hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state ) > hoare_1262092251_state > ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_,type,
% 0.21/0.51 finite1168661790_state: ( hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state ) > ( ( hoare_1262092251_state > $o ) > hoare_1262092251_state ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ghhkfsbqqq__Ot,type,
% 0.21/0.51 finite900773345_state: ( hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state ) > ( ( hoare_1262092251_state > $o ) > hoare_1262092251_state ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__,type,
% 0.21/0.51 minus_2758725tate_o: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_OMGT,type,
% 0.21/0.51 hoare_Mirabelle_MGT: com > hoare_1262092251_state ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ohoare__derivs_000tc__Com__Ostate,type,
% 0.21/0.51 hoare_930741239_state: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ohoare__valids_000tc__Com__Ostate,type,
% 0.21/0.51 hoare_1337152501_state: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Otriple_Otriple_000tc__Com__Ostate,type,
% 0.21/0.51 hoare_951399329_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1262092251_state ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__O,type,
% 0.21/0.51 bot_bo113204042tate_o: hoare_1262092251_state > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 0.21/0.51 bot_bot_o: $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost,type,
% 0.21/0.51 collec1121927558_state: ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Osta,type,
% 0.21/0.51 insert81609953_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__O,type,
% 0.21/0.51 the_el417915516_state: ( hoare_1262092251_state > $o ) > hoare_1262092251_state ).
% 0.21/0.51
% 0.21/0.51 thf(sy_c_member_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J,type,
% 0.21/0.51 member5164104_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_v_P,type,
% 0.21/0.51 p: state > state > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_v_Q,type,
% 0.21/0.51 q: state > state > $o ).
% 0.21/0.51
% 0.21/0.51 thf(sy_v_c,type,
% 0.21/0.51 c: com ).
% 0.21/0.51
% 0.21/0.51 %----Relevant facts (90)
% 0.21/0.51 thf(fact_0_empty,axiom,
% 0.21/0.51 ! [G_12: hoare_1262092251_state > $o] : ( hoare_930741239_state @ G_12 @ bot_bo113204042tate_o ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_1_triple_Oinject,axiom,
% 0.21/0.51 ! [Fun1_2: state > state > $o,Com_2: com,Fun2_2: state > state > $o,Fun1_1: state > state > $o,Com_1: com,Fun2_1: state > state > $o] :
% 0.21/0.51 ( ( ( hoare_951399329_state @ Fun1_2 @ Com_2 @ Fun2_2 )
% 0.21/0.51 = ( hoare_951399329_state @ Fun1_1 @ Com_1 @ Fun2_1 ) )
% 0.21/0.51 <=> ( ( Fun1_2 = Fun1_1 )
% 0.21/0.51 & ( Com_2 = Com_1 )
% 0.21/0.51 & ( Fun2_2 = Fun2_1 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_2_hoare__sound,axiom,
% 0.21/0.51 ! [G_11: hoare_1262092251_state > $o,Ts_3: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( hoare_930741239_state @ G_11 @ Ts_3 )
% 0.21/0.51 => ( hoare_1337152501_state @ G_11 @ Ts_3 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_3_cut,axiom,
% 0.21/0.51 ! [G_10: hoare_1262092251_state > $o,G_9: hoare_1262092251_state > $o,Ts_2: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( hoare_930741239_state @ G_9 @ Ts_2 )
% 0.21/0.51 => ( ( hoare_930741239_state @ G_10 @ G_9 )
% 0.21/0.51 => ( hoare_930741239_state @ G_10 @ Ts_2 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_4_hoare__derivs_Oinsert,axiom,
% 0.21/0.51 ! [Ts_1: hoare_1262092251_state > $o,G_8: hoare_1262092251_state > $o,T_1: hoare_1262092251_state] :
% 0.21/0.51 ( ( hoare_930741239_state @ G_8 @ ( insert81609953_state @ T_1 @ bot_bo113204042tate_o ) )
% 0.21/0.51 => ( ( hoare_930741239_state @ G_8 @ Ts_1 )
% 0.21/0.51 => ( hoare_930741239_state @ G_8 @ ( insert81609953_state @ T_1 @ Ts_1 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_5_derivs__insertD,axiom,
% 0.21/0.51 ! [G_7: hoare_1262092251_state > $o,T: hoare_1262092251_state,Ts: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( hoare_930741239_state @ G_7 @ ( insert81609953_state @ T @ Ts ) )
% 0.21/0.51 => ( ( hoare_930741239_state @ G_7 @ ( insert81609953_state @ T @ bot_bo113204042tate_o ) )
% 0.21/0.51 & ( hoare_930741239_state @ G_7 @ Ts ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_6_conseq2,axiom,
% 0.21/0.51 ! [Q_7: state > state > $o,G_6: hoare_1262092251_state > $o,P_14: state > state > $o,C_8: com,Q_6: state > state > $o] :
% 0.21/0.51 ( ( hoare_930741239_state @ G_6 @ ( insert81609953_state @ ( hoare_951399329_state @ P_14 @ C_8 @ Q_6 ) @ bot_bo113204042tate_o ) )
% 0.21/0.51 => ( ! [Z_5: state,S: state] :
% 0.21/0.51 ( ( Q_6 @ Z_5 @ S )
% 0.21/0.51 => ( Q_7 @ Z_5 @ S ) )
% 0.21/0.51 => ( hoare_930741239_state @ G_6 @ ( insert81609953_state @ ( hoare_951399329_state @ P_14 @ C_8 @ Q_7 ) @ bot_bo113204042tate_o ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_7_conseq1,axiom,
% 0.21/0.51 ! [P_13: state > state > $o,G_5: hoare_1262092251_state > $o,P_12: state > state > $o,C_7: com,Q_5: state > state > $o] :
% 0.21/0.51 ( ( hoare_930741239_state @ G_5 @ ( insert81609953_state @ ( hoare_951399329_state @ P_12 @ C_7 @ Q_5 ) @ bot_bo113204042tate_o ) )
% 0.21/0.51 => ( ! [Z_5: state,S: state] :
% 0.21/0.51 ( ( P_13 @ Z_5 @ S )
% 0.21/0.51 => ( P_12 @ Z_5 @ S ) )
% 0.21/0.51 => ( hoare_930741239_state @ G_5 @ ( insert81609953_state @ ( hoare_951399329_state @ P_13 @ C_7 @ Q_5 ) @ bot_bo113204042tate_o ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_8_insertE,axiom,
% 0.21/0.51 ! [A_71: hoare_1262092251_state,B_20: hoare_1262092251_state,A_70: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( member5164104_state @ A_71 @ ( insert81609953_state @ B_20 @ A_70 ) )
% 0.21/0.51 => ( ( A_71 != B_20 )
% 0.21/0.51 => ( member5164104_state @ A_71 @ A_70 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_9_insertCI,axiom,
% 0.21/0.51 ! [B_19: hoare_1262092251_state,A_69: hoare_1262092251_state,B_18: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( ~ ( member5164104_state @ A_69 @ B_18 )
% 0.21/0.51 => ( A_69 = B_19 ) )
% 0.21/0.51 => ( member5164104_state @ A_69 @ ( insert81609953_state @ B_19 @ B_18 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_10_conseq12,axiom,
% 0.21/0.51 ! [Q_4: state > state > $o,P_11: state > state > $o,G_4: hoare_1262092251_state > $o,P_10: state > state > $o,C_6: com,Q_3: state > state > $o] :
% 0.21/0.51 ( ( hoare_930741239_state @ G_4 @ ( insert81609953_state @ ( hoare_951399329_state @ P_10 @ C_6 @ Q_3 ) @ bot_bo113204042tate_o ) )
% 0.21/0.51 => ( ! [Z_5: state,S: state] :
% 0.21/0.51 ( ( P_11 @ Z_5 @ S )
% 0.21/0.51 => ! [S_1: state] :
% 0.21/0.51 ( ! [Z_6: state] :
% 0.21/0.51 ( ( P_10 @ Z_6 @ S )
% 0.21/0.51 => ( Q_3 @ Z_6 @ S_1 ) )
% 0.21/0.51 => ( Q_4 @ Z_5 @ S_1 ) ) )
% 0.21/0.51 => ( hoare_930741239_state @ G_4 @ ( insert81609953_state @ ( hoare_951399329_state @ P_11 @ C_6 @ Q_4 ) @ bot_bo113204042tate_o ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_11_emptyE,axiom,
% 0.21/0.51 ! [A_68: hoare_1262092251_state] :
% 0.21/0.51 ~ ( member5164104_state @ A_68 @ bot_bo113204042tate_o ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_12_empty__not__insert,axiom,
% 0.21/0.51 ! [A_67: hoare_1262092251_state,A_66: hoare_1262092251_state > $o] :
% 0.21/0.51 ( bot_bo113204042tate_o
% 0.21/0.51 != ( insert81609953_state @ A_67 @ A_66 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_13_insert__not__empty,axiom,
% 0.21/0.51 ! [A_65: hoare_1262092251_state,A_64: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( insert81609953_state @ A_65 @ A_64 )
% 0.21/0.51 != bot_bo113204042tate_o ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_14_singleton__iff,axiom,
% 0.21/0.51 ! [B_17: hoare_1262092251_state,A_63: hoare_1262092251_state] :
% 0.21/0.51 ( ( member5164104_state @ B_17 @ ( insert81609953_state @ A_63 @ bot_bo113204042tate_o ) )
% 0.21/0.51 <=> ( B_17 = A_63 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_15_doubleton__eq__iff,axiom,
% 0.21/0.51 ! [A_62: hoare_1262092251_state,B_16: hoare_1262092251_state,C_5: hoare_1262092251_state,D_1: hoare_1262092251_state] :
% 0.21/0.51 ( ( ( insert81609953_state @ A_62 @ ( insert81609953_state @ B_16 @ bot_bo113204042tate_o ) )
% 0.21/0.51 = ( insert81609953_state @ C_5 @ ( insert81609953_state @ D_1 @ bot_bo113204042tate_o ) ) )
% 0.21/0.51 <=> ( ( ( A_62 = C_5 )
% 0.21/0.51 & ( B_16 = D_1 ) )
% 0.21/0.51 | ( ( A_62 = D_1 )
% 0.21/0.51 & ( B_16 = C_5 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_16_equals0D,axiom,
% 0.21/0.51 ! [A_61: hoare_1262092251_state,A_60: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( A_60 = bot_bo113204042tate_o )
% 0.21/0.51 => ~ ( member5164104_state @ A_61 @ A_60 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_17_Collect__empty__eq,axiom,
% 0.21/0.51 ! [P_9: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( ( collec1121927558_state @ P_9 )
% 0.21/0.51 = bot_bo113204042tate_o )
% 0.21/0.51 <=> ! [X_2: hoare_1262092251_state] :
% 0.21/0.51 ~ ( P_9 @ X_2 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_18_empty__iff,axiom,
% 0.21/0.51 ! [C_4: hoare_1262092251_state] :
% 0.21/0.51 ~ ( member5164104_state @ C_4 @ bot_bo113204042tate_o ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_19_empty__Collect__eq,axiom,
% 0.21/0.51 ! [P_8: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( bot_bo113204042tate_o
% 0.21/0.51 = ( collec1121927558_state @ P_8 ) )
% 0.21/0.51 <=> ! [X_2: hoare_1262092251_state] :
% 0.21/0.51 ~ ( P_8 @ X_2 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_20_ex__in__conv,axiom,
% 0.21/0.51 ! [A_59: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ? [X_2: hoare_1262092251_state] : ( member5164104_state @ X_2 @ A_59 )
% 0.21/0.51 <=> ( A_59 != bot_bo113204042tate_o ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_21_all__not__in__conv,axiom,
% 0.21/0.51 ! [A_58: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ! [X_2: hoare_1262092251_state] :
% 0.21/0.51 ~ ( member5164104_state @ X_2 @ A_58 )
% 0.21/0.51 <=> ( A_58 = bot_bo113204042tate_o ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_22_empty__def,axiom,
% 0.21/0.51 ( bot_bo113204042tate_o
% 0.21/0.51 = ( collec1121927558_state
% 0.21/0.51 @ ^ [X_2: hoare_1262092251_state] : $false ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_23_insert__absorb,axiom,
% 0.21/0.51 ! [A_57: hoare_1262092251_state,A_56: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( member5164104_state @ A_57 @ A_56 )
% 0.21/0.51 => ( ( insert81609953_state @ A_57 @ A_56 )
% 0.21/0.51 = A_56 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_24_insertI2,axiom,
% 0.21/0.51 ! [B_15: hoare_1262092251_state,A_55: hoare_1262092251_state,B_14: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( member5164104_state @ A_55 @ B_14 )
% 0.21/0.51 => ( member5164104_state @ A_55 @ ( insert81609953_state @ B_15 @ B_14 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_25_insert__ident,axiom,
% 0.21/0.51 ! [B_13: hoare_1262092251_state > $o,X_22: hoare_1262092251_state,A_54: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ~ ( member5164104_state @ X_22 @ A_54 )
% 0.21/0.51 => ( ~ ( member5164104_state @ X_22 @ B_13 )
% 0.21/0.51 => ( ( ( insert81609953_state @ X_22 @ A_54 )
% 0.21/0.51 = ( insert81609953_state @ X_22 @ B_13 ) )
% 0.21/0.51 <=> ( A_54 = B_13 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_26_insert__code,axiom,
% 0.21/0.51 ! [Y_4: hoare_1262092251_state,A_53: hoare_1262092251_state > $o,X_21: hoare_1262092251_state] :
% 0.21/0.51 ( ( insert81609953_state @ Y_4 @ A_53 @ X_21 )
% 0.21/0.51 <=> ( ( Y_4 = X_21 )
% 0.21/0.51 | ( A_53 @ X_21 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_27_insert__iff,axiom,
% 0.21/0.51 ! [A_52: hoare_1262092251_state,B_12: hoare_1262092251_state,A_51: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( member5164104_state @ A_52 @ ( insert81609953_state @ B_12 @ A_51 ) )
% 0.21/0.51 <=> ( ( A_52 = B_12 )
% 0.21/0.51 | ( member5164104_state @ A_52 @ A_51 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_28_insert__commute,axiom,
% 0.21/0.51 ! [X_20: hoare_1262092251_state,Y_3: hoare_1262092251_state,A_50: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( insert81609953_state @ X_20 @ ( insert81609953_state @ Y_3 @ A_50 ) )
% 0.21/0.51 = ( insert81609953_state @ Y_3 @ ( insert81609953_state @ X_20 @ A_50 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_29_insert__absorb2,axiom,
% 0.21/0.51 ! [X_19: hoare_1262092251_state,A_49: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( insert81609953_state @ X_19 @ ( insert81609953_state @ X_19 @ A_49 ) )
% 0.21/0.51 = ( insert81609953_state @ X_19 @ A_49 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_30_insert__Collect,axiom,
% 0.21/0.51 ! [A_48: hoare_1262092251_state,P_7: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( insert81609953_state @ A_48 @ ( collec1121927558_state @ P_7 ) )
% 0.21/0.51 = ( collec1121927558_state
% 0.21/0.51 @ ^ [U: hoare_1262092251_state] : ( (=>) @ ( (~) @ ( U = A_48 ) ) @ ( P_7 @ U ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_31_insert__compr,axiom,
% 0.21/0.51 ! [A_47: hoare_1262092251_state,B_11: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( insert81609953_state @ A_47 @ B_11 )
% 0.21/0.51 = ( collec1121927558_state
% 0.21/0.51 @ ^ [X_2: hoare_1262092251_state] : ( (|) @ ( X_2 = A_47 ) @ ( member5164104_state @ X_2 @ B_11 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_32_insertI1,axiom,
% 0.21/0.51 ! [A_46: hoare_1262092251_state,B_10: hoare_1262092251_state > $o] : ( member5164104_state @ A_46 @ ( insert81609953_state @ A_46 @ B_10 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_33_singleton__inject,axiom,
% 0.21/0.51 ! [A_45: hoare_1262092251_state,B_9: hoare_1262092251_state] :
% 0.21/0.51 ( ( ( insert81609953_state @ A_45 @ bot_bo113204042tate_o )
% 0.21/0.51 = ( insert81609953_state @ B_9 @ bot_bo113204042tate_o ) )
% 0.21/0.51 => ( A_45 = B_9 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_34_singletonE,axiom,
% 0.21/0.51 ! [B_8: hoare_1262092251_state,A_44: hoare_1262092251_state] :
% 0.21/0.51 ( ( member5164104_state @ B_8 @ ( insert81609953_state @ A_44 @ bot_bo113204042tate_o ) )
% 0.21/0.51 => ( B_8 = A_44 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_35_the__elem__eq,axiom,
% 0.21/0.51 ! [X_18: hoare_1262092251_state] :
% 0.21/0.51 ( ( the_el417915516_state @ ( insert81609953_state @ X_18 @ bot_bo113204042tate_o ) )
% 0.21/0.51 = X_18 ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_36_bot__apply,axiom,
% 0.21/0.51 ! [X_17: hoare_1262092251_state] :
% 0.21/0.51 ( ( bot_bo113204042tate_o @ X_17 )
% 0.21/0.51 <=> bot_bot_o ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_37_bot__fun__def,axiom,
% 0.21/0.51 ! [X_2: hoare_1262092251_state] :
% 0.21/0.51 ( ( bot_bo113204042tate_o @ X_2 )
% 0.21/0.51 <=> bot_bot_o ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_38_hoare__derivs_OSkip,axiom,
% 0.21/0.51 ! [G_3: hoare_1262092251_state > $o,P_6: state > state > $o] : ( hoare_930741239_state @ G_3 @ ( insert81609953_state @ ( hoare_951399329_state @ P_6 @ skip @ P_6 ) @ bot_bo113204042tate_o ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_39_Comp,axiom,
% 0.21/0.51 ! [D: com,R: state > state > $o,G_2: hoare_1262092251_state > $o,P_5: state > state > $o,C_3: com,Q_2: state > state > $o] :
% 0.21/0.51 ( ( hoare_930741239_state @ G_2 @ ( insert81609953_state @ ( hoare_951399329_state @ P_5 @ C_3 @ Q_2 ) @ bot_bo113204042tate_o ) )
% 0.21/0.51 => ( ( hoare_930741239_state @ G_2 @ ( insert81609953_state @ ( hoare_951399329_state @ Q_2 @ D @ R ) @ bot_bo113204042tate_o ) )
% 0.21/0.51 => ( hoare_930741239_state @ G_2 @ ( insert81609953_state @ ( hoare_951399329_state @ P_5 @ ( semi @ C_3 @ D ) @ R ) @ bot_bo113204042tate_o ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_40_triple_Oexhaust,axiom,
% 0.21/0.51 ! [Y_2: hoare_1262092251_state] :
% 0.21/0.51 ~ ! [Fun1: state > state > $o,Com: com,Fun2: state > state > $o] :
% 0.21/0.51 ( Y_2
% 0.21/0.51 != ( hoare_951399329_state @ Fun1 @ Com @ Fun2 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_41_Set_Oset__insert,axiom,
% 0.21/0.51 ! [X_16: hoare_1262092251_state,A_43: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( member5164104_state @ X_16 @ A_43 )
% 0.21/0.51 => ~ ! [B_7: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( A_43
% 0.21/0.51 = ( insert81609953_state @ X_16 @ B_7 ) )
% 0.21/0.51 => ( member5164104_state @ X_16 @ B_7 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_42_mk__disjoint__insert,axiom,
% 0.21/0.51 ! [A_42: hoare_1262092251_state,A_41: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( member5164104_state @ A_42 @ A_41 )
% 0.21/0.51 => ? [B_7: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( A_41
% 0.21/0.51 = ( insert81609953_state @ A_42 @ B_7 ) )
% 0.21/0.51 & ~ ( member5164104_state @ A_42 @ B_7 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_43_com_Osimps_I13_J,axiom,
% 0.21/0.51 ! [Com1: com,Com2: com] :
% 0.21/0.51 ( ( semi @ Com1 @ Com2 )
% 0.21/0.51 != skip ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_44_com_Osimps_I12_J,axiom,
% 0.21/0.51 ! [Com1: com,Com2: com] :
% 0.21/0.51 ( skip
% 0.21/0.51 != ( semi @ Com1 @ Com2 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_45_equals0I,axiom,
% 0.21/0.51 ! [A_40: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ! [Y: hoare_1262092251_state] :
% 0.21/0.51 ~ ( member5164104_state @ Y @ A_40 )
% 0.21/0.51 => ( A_40 = bot_bo113204042tate_o ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_46_conseq,axiom,
% 0.21/0.51 ! [Q: state > state > $o,G_1: hoare_1262092251_state > $o,C_2: com,P_3: state > state > $o] :
% 0.21/0.51 ( ! [Z_5: state,S: state] :
% 0.21/0.51 ( ( P_3 @ Z_5 @ S )
% 0.21/0.51 => ? [P_4: state > state > $o,Q_1: state > state > $o] :
% 0.21/0.51 ( ( hoare_930741239_state @ G_1 @ ( insert81609953_state @ ( hoare_951399329_state @ P_4 @ C_2 @ Q_1 ) @ bot_bo113204042tate_o ) )
% 0.21/0.51 & ! [S_1: state] :
% 0.21/0.51 ( ! [Z_6: state] :
% 0.21/0.51 ( ( P_4 @ Z_6 @ S )
% 0.21/0.51 => ( Q_1 @ Z_6 @ S_1 ) )
% 0.21/0.51 => ( Q @ Z_5 @ S_1 ) ) ) )
% 0.21/0.51 => ( hoare_930741239_state @ G_1 @ ( insert81609953_state @ ( hoare_951399329_state @ P_3 @ C_2 @ Q ) @ bot_bo113204042tate_o ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_47_com_Osimps_I3_J,axiom,
% 0.21/0.51 ! [Com1_1: com,Com2_1: com,Com1: com,Com2: com] :
% 0.21/0.51 ( ( ( semi @ Com1_1 @ Com2_1 )
% 0.21/0.51 = ( semi @ Com1 @ Com2 ) )
% 0.21/0.51 <=> ( ( Com1_1 = Com1 )
% 0.21/0.51 & ( Com2_1 = Com2 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_48_nonempty__iff,axiom,
% 0.21/0.51 ! [A_39: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( A_39 != bot_bo113204042tate_o )
% 0.21/0.51 <=> ? [X_2: hoare_1262092251_state,B_7: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( A_39
% 0.21/0.51 = ( insert81609953_state @ X_2 @ B_7 ) )
% 0.21/0.51 & ~ ( member5164104_state @ X_2 @ B_7 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_49_bot__empty__eq,axiom,
% 0.21/0.51 ! [X_2: hoare_1262092251_state] :
% 0.21/0.51 ( ( bot_bo113204042tate_o @ X_2 )
% 0.21/0.51 <=> ( member5164104_state @ X_2 @ bot_bo113204042tate_o ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_50_fold1Set__sing,axiom,
% 0.21/0.51 ! [F_34: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,A_38: hoare_1262092251_state,B_6: hoare_1262092251_state] :
% 0.21/0.51 ( ( finite403475723_state @ F_34 @ ( insert81609953_state @ A_38 @ bot_bo113204042tate_o ) @ B_6 )
% 0.21/0.51 <=> ( A_38 = B_6 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_51_folding__one_Osingleton,axiom,
% 0.21/0.51 ! [X_15: hoare_1262092251_state,F_33: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,F_32: ( hoare_1262092251_state > $o ) > hoare_1262092251_state] :
% 0.21/0.51 ( ( finite1168661790_state @ F_33 @ F_32 )
% 0.21/0.51 => ( ( F_32 @ ( insert81609953_state @ X_15 @ bot_bo113204042tate_o ) )
% 0.21/0.51 = X_15 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_52_fold1__singleton,axiom,
% 0.21/0.51 ! [F_31: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,A_37: hoare_1262092251_state] :
% 0.21/0.51 ( ( finite1740352635_state @ F_31 @ ( insert81609953_state @ A_37 @ bot_bo113204042tate_o ) )
% 0.21/0.51 = A_37 ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_53_fold1__singleton__def,axiom,
% 0.21/0.51 ! [A_36: hoare_1262092251_state,G: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,F_30: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state] :
% 0.21/0.51 ( ( G
% 0.21/0.51 = ( finite1740352635_state @ F_30 ) )
% 0.21/0.51 => ( ( G @ ( insert81609953_state @ A_36 @ bot_bo113204042tate_o ) )
% 0.21/0.51 = A_36 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_54_empty__fold1SetE,axiom,
% 0.21/0.51 ! [F_29: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,X_14: hoare_1262092251_state] :
% 0.21/0.51 ~ ( finite403475723_state @ F_29 @ bot_bo113204042tate_o @ X_14 ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_55_fold1Set__nonempty,axiom,
% 0.21/0.51 ! [F_28: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,A_35: hoare_1262092251_state > $o,X_13: hoare_1262092251_state] :
% 0.21/0.51 ( ( finite403475723_state @ F_28 @ A_35 @ X_13 )
% 0.21/0.51 => ( A_35 != bot_bo113204042tate_o ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_56_fold1Set_Ointros,axiom,
% 0.21/0.51 ! [F_27: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,A_34: hoare_1262092251_state,A_33: hoare_1262092251_state > $o,X_12: hoare_1262092251_state] :
% 0.21/0.51 ( ( finite975744042_state @ F_27 @ A_34 @ A_33 @ X_12 )
% 0.21/0.51 => ( ~ ( member5164104_state @ A_34 @ A_33 )
% 0.21/0.51 => ( finite403475723_state @ F_27 @ ( insert81609953_state @ A_34 @ A_33 ) @ X_12 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_57_folding__one_Oinsert,axiom,
% 0.21/0.51 ! [X_11: hoare_1262092251_state,A_32: hoare_1262092251_state > $o,F_26: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,F_25: ( hoare_1262092251_state > $o ) > hoare_1262092251_state] :
% 0.21/0.51 ( ( finite1168661790_state @ F_26 @ F_25 )
% 0.21/0.51 => ( ( finite1178804552_state @ A_32 )
% 0.21/0.51 => ( ~ ( member5164104_state @ X_11 @ A_32 )
% 0.21/0.51 => ( ( A_32 != bot_bo113204042tate_o )
% 0.21/0.51 => ( ( F_25 @ ( insert81609953_state @ X_11 @ A_32 ) )
% 0.21/0.51 = ( F_26 @ X_11 @ ( F_25 @ A_32 ) ) ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_58_folding__one_Oeq__fold,axiom,
% 0.21/0.51 ! [A_31: hoare_1262092251_state > $o,F_24: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,F_23: ( hoare_1262092251_state > $o ) > hoare_1262092251_state] :
% 0.21/0.51 ( ( finite1168661790_state @ F_24 @ F_23 )
% 0.21/0.51 => ( ( finite1178804552_state @ A_31 )
% 0.21/0.51 => ( ( F_23 @ A_31 )
% 0.21/0.51 = ( finite1740352635_state @ F_24 @ A_31 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_59_finite_OemptyI,axiom,
% 0.21/0.51 finite1178804552_state @ bot_bo113204042tate_o ).
% 0.21/0.51
% 0.21/0.51 thf(fact_60_finite_OinsertI,axiom,
% 0.21/0.51 ! [A_30: hoare_1262092251_state,A_29: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( finite1178804552_state @ A_29 )
% 0.21/0.51 => ( finite1178804552_state @ ( insert81609953_state @ A_30 @ A_29 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_61_fold__graph_OemptyI,axiom,
% 0.21/0.51 ! [F_22: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,Z_4: hoare_1262092251_state] : ( finite975744042_state @ F_22 @ Z_4 @ bot_bo113204042tate_o @ Z_4 ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_62_empty__fold__graphE,axiom,
% 0.21/0.51 ! [F_21: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,Z_3: hoare_1262092251_state,X_10: hoare_1262092251_state] :
% 0.21/0.51 ( ( finite975744042_state @ F_21 @ Z_3 @ bot_bo113204042tate_o @ X_10 )
% 0.21/0.51 => ( X_10 = Z_3 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_63_fold__graph_OinsertI,axiom,
% 0.21/0.51 ! [F_20: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,Z_2: hoare_1262092251_state,Y_1: hoare_1262092251_state,X_9: hoare_1262092251_state,A_28: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ~ ( member5164104_state @ X_9 @ A_28 )
% 0.21/0.51 => ( ( finite975744042_state @ F_20 @ Z_2 @ A_28 @ Y_1 )
% 0.21/0.51 => ( finite975744042_state @ F_20 @ Z_2 @ ( insert81609953_state @ X_9 @ A_28 ) @ ( F_20 @ X_9 @ Y_1 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_64_finite__insert,axiom,
% 0.21/0.51 ! [A_27: hoare_1262092251_state,A_26: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( finite1178804552_state @ ( insert81609953_state @ A_27 @ A_26 ) )
% 0.21/0.51 <=> ( finite1178804552_state @ A_26 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_65_folding__one_Oclosed,axiom,
% 0.21/0.51 ! [A_25: hoare_1262092251_state > $o,F_19: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,F_18: ( hoare_1262092251_state > $o ) > hoare_1262092251_state] :
% 0.21/0.51 ( ( finite1168661790_state @ F_19 @ F_18 )
% 0.21/0.51 => ( ( finite1178804552_state @ A_25 )
% 0.21/0.51 => ( ( A_25 != bot_bo113204042tate_o )
% 0.21/0.51 => ( ! [X_2: hoare_1262092251_state,Y: hoare_1262092251_state] : ( member5164104_state @ ( F_19 @ X_2 @ Y ) @ ( insert81609953_state @ X_2 @ ( insert81609953_state @ Y @ bot_bo113204042tate_o ) ) )
% 0.21/0.51 => ( member5164104_state @ ( F_18 @ A_25 ) @ A_25 ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_66_insert__fold1SetE,axiom,
% 0.21/0.51 ! [F_17: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,A_24: hoare_1262092251_state,X_8: hoare_1262092251_state > $o,X_7: hoare_1262092251_state] :
% 0.21/0.51 ( ( finite403475723_state @ F_17 @ ( insert81609953_state @ A_24 @ X_8 ) @ X_7 )
% 0.21/0.51 => ~ ! [A_19: hoare_1262092251_state,A_18: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( ( insert81609953_state @ A_24 @ X_8 )
% 0.21/0.51 = ( insert81609953_state @ A_19 @ A_18 ) )
% 0.21/0.51 => ( ( finite975744042_state @ F_17 @ A_19 @ A_18 @ X_7 )
% 0.21/0.51 => ( member5164104_state @ A_19 @ A_18 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_67_finite__nonempty__imp__fold1Set,axiom,
% 0.21/0.51 ! [F_16: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,A_23: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( finite1178804552_state @ A_23 )
% 0.21/0.51 => ( ( A_23 != bot_bo113204042tate_o )
% 0.21/0.51 => ( ex @ ( finite403475723_state @ F_16 @ A_23 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_68_finite__induct,axiom,
% 0.21/0.51 ! [P_2: ( hoare_1262092251_state > $o ) > $o,F_15: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( finite1178804552_state @ F_15 )
% 0.21/0.51 => ( ( P_2 @ bot_bo113204042tate_o )
% 0.21/0.51 => ( ! [X_2: hoare_1262092251_state,F_5: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( finite1178804552_state @ F_5 )
% 0.21/0.51 => ( ~ ( member5164104_state @ X_2 @ F_5 )
% 0.21/0.51 => ( ( P_2 @ F_5 )
% 0.21/0.51 => ( P_2 @ ( insert81609953_state @ X_2 @ F_5 ) ) ) ) )
% 0.21/0.51 => ( P_2 @ F_15 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_69_mem__def,axiom,
% 0.21/0.51 ! [X_6: hoare_1262092251_state,A_22: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( member5164104_state @ X_6 @ A_22 )
% 0.21/0.51 <=> ( A_22 @ X_6 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_70_Collect__def,axiom,
% 0.21/0.51 ! [P_1: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( collec1121927558_state @ P_1 )
% 0.21/0.51 = P_1 ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_71_finite_Osimps,axiom,
% 0.21/0.51 ! [A_21: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( finite1178804552_state @ A_21 )
% 0.21/0.51 <=> ( ( A_21 = bot_bo113204042tate_o )
% 0.21/0.51 | ? [A_18: hoare_1262092251_state > $o,A_19: hoare_1262092251_state] :
% 0.21/0.51 ( ( A_21
% 0.21/0.51 = ( insert81609953_state @ A_19 @ A_18 ) )
% 0.21/0.51 & ( finite1178804552_state @ A_18 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_72_finite__imp__fold__graph,axiom,
% 0.21/0.51 ! [F_14: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,Z_1: hoare_1262092251_state,A_20: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( finite1178804552_state @ A_20 )
% 0.21/0.51 => ( ex @ ( finite975744042_state @ F_14 @ Z_1 @ A_20 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_73_fold1Set_Osimps,axiom,
% 0.21/0.51 ! [F_13: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,A1_1: hoare_1262092251_state > $o,A2_1: hoare_1262092251_state] :
% 0.21/0.51 ( ( finite403475723_state @ F_13 @ A1_1 @ A2_1 )
% 0.21/0.51 <=> ? [A_19: hoare_1262092251_state,A_18: hoare_1262092251_state > $o,X_2: hoare_1262092251_state] :
% 0.21/0.51 ( ( A1_1
% 0.21/0.51 = ( insert81609953_state @ A_19 @ A_18 ) )
% 0.21/0.51 & ( A2_1 = X_2 )
% 0.21/0.51 & ( finite975744042_state @ F_13 @ A_19 @ A_18 @ X_2 )
% 0.21/0.51 & ~ ( member5164104_state @ A_19 @ A_18 ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_74_fold__graph_Osimps,axiom,
% 0.21/0.51 ! [F_12: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,Z: hoare_1262092251_state,A1: hoare_1262092251_state > $o,A2: hoare_1262092251_state] :
% 0.21/0.51 ( ( finite975744042_state @ F_12 @ Z @ A1 @ A2 )
% 0.21/0.51 <=> ( ( ( A1 = bot_bo113204042tate_o )
% 0.21/0.51 & ( A2 = Z ) )
% 0.21/0.51 | ? [X_2: hoare_1262092251_state,A_18: hoare_1262092251_state > $o,Y: hoare_1262092251_state] :
% 0.21/0.51 ( ( A1
% 0.21/0.51 = ( insert81609953_state @ X_2 @ A_18 ) )
% 0.21/0.51 & ( A2
% 0.21/0.51 = ( F_12 @ X_2 @ Y ) )
% 0.21/0.51 & ~ ( member5164104_state @ X_2 @ A_18 )
% 0.21/0.51 & ( finite975744042_state @ F_12 @ Z @ A_18 @ Y ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_75_folding__one__idem_Oinsert__idem,axiom,
% 0.21/0.51 ! [X_5: hoare_1262092251_state,A_17: hoare_1262092251_state > $o,F_11: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,F_10: ( hoare_1262092251_state > $o ) > hoare_1262092251_state] :
% 0.21/0.51 ( ( finite900773345_state @ F_11 @ F_10 )
% 0.21/0.51 => ( ( finite1178804552_state @ A_17 )
% 0.21/0.51 => ( ( A_17 != bot_bo113204042tate_o )
% 0.21/0.51 => ( ( F_10 @ ( insert81609953_state @ X_5 @ A_17 ) )
% 0.21/0.51 = ( F_11 @ X_5 @ ( F_10 @ A_17 ) ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_76_folding__one__idem_Oidem,axiom,
% 0.21/0.51 ! [X_4: hoare_1262092251_state,F_9: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,F_8: ( hoare_1262092251_state > $o ) > hoare_1262092251_state] :
% 0.21/0.51 ( ( finite900773345_state @ F_9 @ F_8 )
% 0.21/0.51 => ( ( F_9 @ X_4 @ X_4 )
% 0.21/0.51 = X_4 ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_77_folding__one__idem_Oin__idem,axiom,
% 0.21/0.51 ! [X_3: hoare_1262092251_state,A_16: hoare_1262092251_state > $o,F_7: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,F_6: ( hoare_1262092251_state > $o ) > hoare_1262092251_state] :
% 0.21/0.51 ( ( finite900773345_state @ F_7 @ F_6 )
% 0.21/0.51 => ( ( finite1178804552_state @ A_16 )
% 0.21/0.51 => ( ( member5164104_state @ X_3 @ A_16 )
% 0.21/0.51 => ( ( F_7 @ X_3 @ ( F_6 @ A_16 ) )
% 0.21/0.51 = ( F_6 @ A_16 ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_78_finite__ne__induct,axiom,
% 0.21/0.51 ! [P: ( hoare_1262092251_state > $o ) > $o,F_4: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( finite1178804552_state @ F_4 )
% 0.21/0.51 => ( ( F_4 != bot_bo113204042tate_o )
% 0.21/0.51 => ( ! [X_2: hoare_1262092251_state] : ( P @ ( insert81609953_state @ X_2 @ bot_bo113204042tate_o ) )
% 0.21/0.51 => ( ! [X_2: hoare_1262092251_state,F_5: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( finite1178804552_state @ F_5 )
% 0.21/0.51 => ( ( F_5 != bot_bo113204042tate_o )
% 0.21/0.51 => ( ~ ( member5164104_state @ X_2 @ F_5 )
% 0.21/0.51 => ( ( P @ F_5 )
% 0.21/0.51 => ( P @ ( insert81609953_state @ X_2 @ F_5 ) ) ) ) ) )
% 0.21/0.51 => ( P @ F_4 ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_79_semilattice__big_OF__eq,axiom,
% 0.21/0.51 ! [A_15: hoare_1262092251_state > $o,F_3: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,F_2: ( hoare_1262092251_state > $o ) > hoare_1262092251_state] :
% 0.21/0.51 ( ( big_se1697321605_state @ F_3 @ F_2 )
% 0.21/0.51 => ( ( finite1178804552_state @ A_15 )
% 0.21/0.51 => ( ( F_2 @ A_15 )
% 0.21/0.51 = ( finite1740352635_state @ F_3 @ A_15 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_80_folding__one_Oremove,axiom,
% 0.21/0.51 ! [X_1: hoare_1262092251_state,A_14: hoare_1262092251_state > $o,F_1: hoare_1262092251_state > hoare_1262092251_state > hoare_1262092251_state,F: ( hoare_1262092251_state > $o ) > hoare_1262092251_state] :
% 0.21/0.51 ( ( finite1168661790_state @ F_1 @ F )
% 0.21/0.51 => ( ( finite1178804552_state @ A_14 )
% 0.21/0.51 => ( ( member5164104_state @ X_1 @ A_14 )
% 0.21/0.51 => ( ( ( ( minus_2758725tate_o @ A_14 @ ( insert81609953_state @ X_1 @ bot_bo113204042tate_o ) )
% 0.21/0.51 = bot_bo113204042tate_o )
% 0.21/0.51 => ( ( F @ A_14 )
% 0.21/0.51 = X_1 ) )
% 0.21/0.51 & ( ( ( minus_2758725tate_o @ A_14 @ ( insert81609953_state @ X_1 @ bot_bo113204042tate_o ) )
% 0.21/0.51 != bot_bo113204042tate_o )
% 0.21/0.51 => ( ( F @ A_14 )
% 0.21/0.51 = ( F_1 @ X_1 @ ( F @ ( minus_2758725tate_o @ A_14 @ ( insert81609953_state @ X_1 @ bot_bo113204042tate_o ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_81_DiffI,axiom,
% 0.21/0.51 ! [B_5: hoare_1262092251_state > $o,C_1: hoare_1262092251_state,A_13: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( member5164104_state @ C_1 @ A_13 )
% 0.21/0.51 => ( ~ ( member5164104_state @ C_1 @ B_5 )
% 0.21/0.51 => ( member5164104_state @ C_1 @ ( minus_2758725tate_o @ A_13 @ B_5 ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(fact_82_DiffE,axiom,
% 0.21/0.51 ! [C: hoare_1262092251_state,A_12: hoare_1262092251_state > $o,B_4: hoare_1262092251_state > $o] :
% 0.21/0.51 ( ( member5164104_state @ C @ ( minus_2758725tate_o @ A_12 @ B_4 ) )
% 0.21/0.54 => ~ ( ( member5164104_state @ C @ A_12 )
% 0.21/0.54 => ( member5164104_state @ C @ B_4 ) ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(fact_83_finite__Diff,axiom,
% 0.21/0.54 ! [B_3: hoare_1262092251_state > $o,A_11: hoare_1262092251_state > $o] :
% 0.21/0.54 ( ( finite1178804552_state @ A_11 )
% 0.21/0.54 => ( finite1178804552_state @ ( minus_2758725tate_o @ A_11 @ B_3 ) ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(fact_84_insert__Diff,axiom,
% 0.21/0.54 ! [A_10: hoare_1262092251_state,A_9: hoare_1262092251_state > $o] :
% 0.21/0.54 ( ( member5164104_state @ A_10 @ A_9 )
% 0.21/0.54 => ( ( insert81609953_state @ A_10 @ ( minus_2758725tate_o @ A_9 @ ( insert81609953_state @ A_10 @ bot_bo113204042tate_o ) ) )
% 0.21/0.54 = A_9 ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(fact_85_Diff__insert__absorb,axiom,
% 0.21/0.54 ! [X: hoare_1262092251_state,A_8: hoare_1262092251_state > $o] :
% 0.21/0.54 ( ~ ( member5164104_state @ X @ A_8 )
% 0.21/0.54 => ( ( minus_2758725tate_o @ ( insert81609953_state @ X @ A_8 ) @ ( insert81609953_state @ X @ bot_bo113204042tate_o ) )
% 0.21/0.54 = A_8 ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(fact_86_insert__Diff__single,axiom,
% 0.21/0.54 ! [A_7: hoare_1262092251_state,A_6: hoare_1262092251_state > $o] :
% 0.21/0.54 ( ( insert81609953_state @ A_7 @ ( minus_2758725tate_o @ A_6 @ ( insert81609953_state @ A_7 @ bot_bo113204042tate_o ) ) )
% 0.21/0.54 = ( insert81609953_state @ A_7 @ A_6 ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(fact_87_Diff__insert2,axiom,
% 0.21/0.54 ! [A_5: hoare_1262092251_state > $o,A_4: hoare_1262092251_state,B_2: hoare_1262092251_state > $o] :
% 0.21/0.54 ( ( minus_2758725tate_o @ A_5 @ ( insert81609953_state @ A_4 @ B_2 ) )
% 0.21/0.54 = ( minus_2758725tate_o @ ( minus_2758725tate_o @ A_5 @ ( insert81609953_state @ A_4 @ bot_bo113204042tate_o ) ) @ B_2 ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(fact_88_Diff__insert,axiom,
% 0.21/0.54 ! [A_3: hoare_1262092251_state > $o,A_2: hoare_1262092251_state,B_1: hoare_1262092251_state > $o] :
% 0.21/0.54 ( ( minus_2758725tate_o @ A_3 @ ( insert81609953_state @ A_2 @ B_1 ) )
% 0.21/0.54 = ( minus_2758725tate_o @ ( minus_2758725tate_o @ A_3 @ B_1 ) @ ( insert81609953_state @ A_2 @ bot_bo113204042tate_o ) ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(fact_89_finite__Diff__insert,axiom,
% 0.21/0.54 ! [A_1: hoare_1262092251_state > $o,A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
% 0.21/0.54 ( ( finite1178804552_state @ ( minus_2758725tate_o @ A_1 @ ( insert81609953_state @ A @ B ) ) )
% 0.21/0.54 <=> ( finite1178804552_state @ ( minus_2758725tate_o @ A_1 @ B ) ) ) ).
% 0.21/0.54
% 0.21/0.54 %----Conjectures (3)
% 0.21/0.54 thf(conj_0,hypothesis,
% 0.21/0.54 hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ c ) @ bot_bo113204042tate_o ) ).
% 0.21/0.54
% 0.21/0.54 thf(conj_1,hypothesis,
% 0.21/0.54 hoare_1337152501_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_951399329_state @ p @ c @ q ) @ bot_bo113204042tate_o ) ).
% 0.21/0.54
% 0.21/0.54 thf(conj_2,conjecture,
% 0.21/0.54 hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_951399329_state @ p @ c @ q ) @ bot_bo113204042tate_o ) ).
% 0.21/0.54
% 0.21/0.54 %------------------------------------------------------------------------------
% 0.21/0.54 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.yMaIuB0buH/cvc5---1.0.5_23492.p...
% 0.21/0.54 (declare-sort $$unsorted 0)
% 0.21/0.54 (declare-sort tptp.com 0)
% 0.21/0.54 (declare-sort tptp.state 0)
% 0.21/0.54 (declare-sort tptp.hoare_1262092251_state 0)
% 0.21/0.54 (declare-fun tptp.big_se1697321605_state ((-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state) (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state)) Bool)
% 0.21/0.54 (declare-fun tptp.skip () tptp.com)
% 0.21/0.54 (declare-fun tptp.semi (tptp.com tptp.com) tptp.com)
% 0.21/0.54 (declare-fun tptp.ex ((-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.21/0.54 (declare-fun tptp.finite1178804552_state ((-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.21/0.54 (declare-fun tptp.finite403475723_state ((-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state) (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state) Bool)
% 0.21/0.54 (declare-fun tptp.finite1740352635_state ((-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state) (-> tptp.hoare_1262092251_state Bool)) tptp.hoare_1262092251_state)
% 0.21/0.54 (declare-fun tptp.finite975744042_state ((-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state) tptp.hoare_1262092251_state (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state) Bool)
% 0.21/0.54 (declare-fun tptp.finite1168661790_state ((-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state) (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state)) Bool)
% 0.21/0.54 (declare-fun tptp.finite900773345_state ((-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state) (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state)) Bool)
% 0.21/0.54 (declare-fun tptp.minus_2758725tate_o ((-> tptp.hoare_1262092251_state Bool) (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state) Bool)
% 0.21/0.54 (declare-fun tptp.hoare_Mirabelle_MGT (tptp.com) tptp.hoare_1262092251_state)
% 0.21/0.54 (declare-fun tptp.hoare_930741239_state ((-> tptp.hoare_1262092251_state Bool) (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.21/0.54 (declare-fun tptp.hoare_1337152501_state ((-> tptp.hoare_1262092251_state Bool) (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.21/0.54 (declare-fun tptp.hoare_951399329_state ((-> tptp.state tptp.state Bool) tptp.com (-> tptp.state tptp.state Bool)) tptp.hoare_1262092251_state)
% 0.21/0.54 (declare-fun tptp.bot_bo113204042tate_o (tptp.hoare_1262092251_state) Bool)
% 0.21/0.54 (declare-fun tptp.bot_bot_o () Bool)
% 0.21/0.54 (declare-fun tptp.collec1121927558_state ((-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state) Bool)
% 0.21/0.54 (declare-fun tptp.insert81609953_state (tptp.hoare_1262092251_state (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state) Bool)
% 0.21/0.54 (declare-fun tptp.the_el417915516_state ((-> tptp.hoare_1262092251_state Bool)) tptp.hoare_1262092251_state)
% 0.21/0.54 (declare-fun tptp.member5164104_state (tptp.hoare_1262092251_state (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.21/0.54 (declare-fun tptp.p (tptp.state tptp.state) Bool)
% 0.21/0.54 (declare-fun tptp.q (tptp.state tptp.state) Bool)
% 0.21/0.54 (declare-fun tptp.c () tptp.com)
% 0.21/0.54 (assert (forall ((G_12 (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.hoare_930741239_state G_12) tptp.bot_bo113204042tate_o)))
% 0.21/0.54 (assert (forall ((Fun1_2 (-> tptp.state tptp.state Bool)) (Com_2 tptp.com) (Fun2_2 (-> tptp.state tptp.state Bool)) (Fun1_1 (-> tptp.state tptp.state Bool)) (Com_1 tptp.com) (Fun2_1 (-> tptp.state tptp.state Bool))) (= (= (@ (@ (@ tptp.hoare_951399329_state Fun1_2) Com_2) Fun2_2) (@ (@ (@ tptp.hoare_951399329_state Fun1_1) Com_1) Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_2 Com_1) (= Fun2_2 Fun2_1)))))
% 0.21/0.54 (assert (forall ((G_11 (-> tptp.hoare_1262092251_state Bool)) (Ts_3 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.hoare_930741239_state G_11) Ts_3) (@ (@ tptp.hoare_1337152501_state G_11) Ts_3))))
% 0.21/0.54 (assert (forall ((G_10 (-> tptp.hoare_1262092251_state Bool)) (G_9 (-> tptp.hoare_1262092251_state Bool)) (Ts_2 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.hoare_930741239_state G_10))) (=> (@ (@ tptp.hoare_930741239_state G_9) Ts_2) (=> (@ _let_1 G_9) (@ _let_1 Ts_2))))))
% 0.21/0.54 (assert (forall ((Ts_1 (-> tptp.hoare_1262092251_state Bool)) (G_8 (-> tptp.hoare_1262092251_state Bool)) (T_1 tptp.hoare_1262092251_state)) (let ((_let_1 (@ tptp.insert81609953_state T_1))) (let ((_let_2 (@ tptp.hoare_930741239_state G_8))) (=> (@ _let_2 (@ _let_1 tptp.bot_bo113204042tate_o)) (=> (@ _let_2 Ts_1) (@ _let_2 (@ _let_1 Ts_1))))))))
% 0.21/0.54 (assert (forall ((G_7 (-> tptp.hoare_1262092251_state Bool)) (T tptp.hoare_1262092251_state) (Ts (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.hoare_930741239_state G_7))) (let ((_let_2 (@ tptp.insert81609953_state T))) (=> (@ _let_1 (@ _let_2 Ts)) (and (@ _let_1 (@ _let_2 tptp.bot_bo113204042tate_o)) (@ _let_1 Ts)))))))
% 0.21/0.54 (assert (forall ((Q_7 (-> tptp.state tptp.state Bool)) (G_6 (-> tptp.hoare_1262092251_state Bool)) (P_14 (-> tptp.state tptp.state Bool)) (C_8 tptp.com) (Q_6 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ (@ tptp.hoare_951399329_state P_14) C_8))) (let ((_let_2 (@ tptp.hoare_930741239_state G_6))) (=> (@ _let_2 (@ (@ tptp.insert81609953_state (@ _let_1 Q_6)) tptp.bot_bo113204042tate_o)) (=> (forall ((Z_5 tptp.state) (S tptp.state)) (=> (@ (@ Q_6 Z_5) S) (@ (@ Q_7 Z_5) S))) (@ _let_2 (@ (@ tptp.insert81609953_state (@ _let_1 Q_7)) tptp.bot_bo113204042tate_o))))))))
% 0.21/0.54 (assert (forall ((P_13 (-> tptp.state tptp.state Bool)) (G_5 (-> tptp.hoare_1262092251_state Bool)) (P_12 (-> tptp.state tptp.state Bool)) (C_7 tptp.com) (Q_5 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_930741239_state G_5))) (=> (@ _let_1 (@ (@ tptp.insert81609953_state (@ (@ (@ tptp.hoare_951399329_state P_12) C_7) Q_5)) tptp.bot_bo113204042tate_o)) (=> (forall ((Z_5 tptp.state) (S tptp.state)) (=> (@ (@ P_13 Z_5) S) (@ (@ P_12 Z_5) S))) (@ _let_1 (@ (@ tptp.insert81609953_state (@ (@ (@ tptp.hoare_951399329_state P_13) C_7) Q_5)) tptp.bot_bo113204042tate_o)))))))
% 0.21/0.54 (assert (forall ((A_71 tptp.hoare_1262092251_state) (B_20 tptp.hoare_1262092251_state) (A_70 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_71))) (=> (@ _let_1 (@ (@ tptp.insert81609953_state B_20) A_70)) (=> (not (= A_71 B_20)) (@ _let_1 A_70))))))
% 0.21/0.54 (assert (forall ((B_19 tptp.hoare_1262092251_state) (A_69 tptp.hoare_1262092251_state) (B_18 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_69))) (=> (=> (not (@ _let_1 B_18)) (= A_69 B_19)) (@ _let_1 (@ (@ tptp.insert81609953_state B_19) B_18))))))
% 0.21/0.54 (assert (forall ((Q_4 (-> tptp.state tptp.state Bool)) (P_11 (-> tptp.state tptp.state Bool)) (G_4 (-> tptp.hoare_1262092251_state Bool)) (P_10 (-> tptp.state tptp.state Bool)) (C_6 tptp.com) (Q_3 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_930741239_state G_4))) (=> (@ _let_1 (@ (@ tptp.insert81609953_state (@ (@ (@ tptp.hoare_951399329_state P_10) C_6) Q_3)) tptp.bot_bo113204042tate_o)) (=> (forall ((Z_5 tptp.state) (S tptp.state)) (=> (@ (@ P_11 Z_5) S) (forall ((S_1 tptp.state)) (=> (forall ((Z_6 tptp.state)) (=> (@ (@ P_10 Z_6) S) (@ (@ Q_3 Z_6) S_1))) (@ (@ Q_4 Z_5) S_1))))) (@ _let_1 (@ (@ tptp.insert81609953_state (@ (@ (@ tptp.hoare_951399329_state P_11) C_6) Q_4)) tptp.bot_bo113204042tate_o)))))))
% 0.21/0.54 (assert (forall ((A_68 tptp.hoare_1262092251_state)) (not (@ (@ tptp.member5164104_state A_68) tptp.bot_bo113204042tate_o))))
% 0.21/0.54 (assert (forall ((A_67 tptp.hoare_1262092251_state) (A_66 (-> tptp.hoare_1262092251_state Bool))) (not (= tptp.bot_bo113204042tate_o (@ (@ tptp.insert81609953_state A_67) A_66)))))
% 0.21/0.54 (assert (forall ((A_65 tptp.hoare_1262092251_state) (A_64 (-> tptp.hoare_1262092251_state Bool))) (not (= (@ (@ tptp.insert81609953_state A_65) A_64) tptp.bot_bo113204042tate_o))))
% 0.21/0.54 (assert (forall ((B_17 tptp.hoare_1262092251_state) (A_63 tptp.hoare_1262092251_state)) (= (@ (@ tptp.member5164104_state B_17) (@ (@ tptp.insert81609953_state A_63) tptp.bot_bo113204042tate_o)) (= B_17 A_63))))
% 0.21/0.54 (assert (forall ((A_62 tptp.hoare_1262092251_state) (B_16 tptp.hoare_1262092251_state) (C_5 tptp.hoare_1262092251_state) (D_1 tptp.hoare_1262092251_state)) (= (= (@ (@ tptp.insert81609953_state A_62) (@ (@ tptp.insert81609953_state B_16) tptp.bot_bo113204042tate_o)) (@ (@ tptp.insert81609953_state C_5) (@ (@ tptp.insert81609953_state D_1) tptp.bot_bo113204042tate_o))) (or (and (= A_62 C_5) (= B_16 D_1)) (and (= A_62 D_1) (= B_16 C_5))))))
% 0.21/0.54 (assert (forall ((A_61 tptp.hoare_1262092251_state) (A_60 (-> tptp.hoare_1262092251_state Bool))) (=> (= A_60 tptp.bot_bo113204042tate_o) (not (@ (@ tptp.member5164104_state A_61) A_60)))))
% 0.21/0.54 (assert (forall ((P_9 (-> tptp.hoare_1262092251_state Bool))) (= (= (@ tptp.collec1121927558_state P_9) tptp.bot_bo113204042tate_o) (forall ((X_2 tptp.hoare_1262092251_state)) (not (@ P_9 X_2))))))
% 0.21/0.54 (assert (forall ((C_4 tptp.hoare_1262092251_state)) (not (@ (@ tptp.member5164104_state C_4) tptp.bot_bo113204042tate_o))))
% 0.21/0.54 (assert (forall ((P_8 (-> tptp.hoare_1262092251_state Bool))) (= (= tptp.bot_bo113204042tate_o (@ tptp.collec1121927558_state P_8)) (forall ((X_2 tptp.hoare_1262092251_state)) (not (@ P_8 X_2))))))
% 0.21/0.54 (assert (forall ((A_59 (-> tptp.hoare_1262092251_state Bool))) (= (exists ((X_2 tptp.hoare_1262092251_state)) (@ (@ tptp.member5164104_state X_2) A_59)) (not (= A_59 tptp.bot_bo113204042tate_o)))))
% 0.21/0.54 (assert (forall ((A_58 (-> tptp.hoare_1262092251_state Bool))) (= (forall ((X_2 tptp.hoare_1262092251_state)) (not (@ (@ tptp.member5164104_state X_2) A_58))) (= A_58 tptp.bot_bo113204042tate_o))))
% 0.21/0.54 (assert (= tptp.bot_bo113204042tate_o (@ tptp.collec1121927558_state (lambda ((X_2 tptp.hoare_1262092251_state)) false))))
% 0.21/0.54 (assert (forall ((A_57 tptp.hoare_1262092251_state) (A_56 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.member5164104_state A_57) A_56) (= (@ (@ tptp.insert81609953_state A_57) A_56) A_56))))
% 0.21/0.54 (assert (forall ((B_15 tptp.hoare_1262092251_state) (A_55 tptp.hoare_1262092251_state) (B_14 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_55))) (=> (@ _let_1 B_14) (@ _let_1 (@ (@ tptp.insert81609953_state B_15) B_14))))))
% 0.21/0.54 (assert (forall ((B_13 (-> tptp.hoare_1262092251_state Bool)) (X_22 tptp.hoare_1262092251_state) (A_54 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state X_22))) (let ((_let_2 (@ tptp.member5164104_state X_22))) (=> (not (@ _let_2 A_54)) (=> (not (@ _let_2 B_13)) (= (= (@ _let_1 A_54) (@ _let_1 B_13)) (= A_54 B_13))))))))
% 0.21/0.54 (assert (forall ((Y_4 tptp.hoare_1262092251_state) (A_53 (-> tptp.hoare_1262092251_state Bool)) (X_21 tptp.hoare_1262092251_state)) (= (@ (@ (@ tptp.insert81609953_state Y_4) A_53) X_21) (or (= Y_4 X_21) (@ A_53 X_21)))))
% 0.21/0.54 (assert (forall ((A_52 tptp.hoare_1262092251_state) (B_12 tptp.hoare_1262092251_state) (A_51 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_52))) (= (@ _let_1 (@ (@ tptp.insert81609953_state B_12) A_51)) (or (= A_52 B_12) (@ _let_1 A_51))))))
% 0.21/0.54 (assert (forall ((X_20 tptp.hoare_1262092251_state) (Y_3 tptp.hoare_1262092251_state) (A_50 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state X_20))) (let ((_let_2 (@ tptp.insert81609953_state Y_3))) (= (@ _let_1 (@ _let_2 A_50)) (@ _let_2 (@ _let_1 A_50)))))))
% 0.21/0.54 (assert (forall ((X_19 tptp.hoare_1262092251_state) (A_49 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state X_19))) (let ((_let_2 (@ _let_1 A_49))) (= (@ _let_1 _let_2) _let_2)))))
% 0.21/0.54 (assert (forall ((A_48 tptp.hoare_1262092251_state) (P_7 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.insert81609953_state A_48) (@ tptp.collec1121927558_state P_7)) (@ tptp.collec1121927558_state (lambda ((U tptp.hoare_1262092251_state)) (=> (not (= U A_48)) (@ P_7 U)))))))
% 0.21/0.54 (assert (forall ((A_47 tptp.hoare_1262092251_state) (B_11 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.insert81609953_state A_47) B_11) (@ tptp.collec1121927558_state (lambda ((X_2 tptp.hoare_1262092251_state)) (or (= X_2 A_47) (@ (@ tptp.member5164104_state X_2) B_11)))))))
% 0.21/0.54 (assert (forall ((A_46 tptp.hoare_1262092251_state) (B_10 (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.member5164104_state A_46) (@ (@ tptp.insert81609953_state A_46) B_10))))
% 0.21/0.54 (assert (forall ((A_45 tptp.hoare_1262092251_state) (B_9 tptp.hoare_1262092251_state)) (=> (= (@ (@ tptp.insert81609953_state A_45) tptp.bot_bo113204042tate_o) (@ (@ tptp.insert81609953_state B_9) tptp.bot_bo113204042tate_o)) (= A_45 B_9))))
% 0.21/0.54 (assert (forall ((B_8 tptp.hoare_1262092251_state) (A_44 tptp.hoare_1262092251_state)) (=> (@ (@ tptp.member5164104_state B_8) (@ (@ tptp.insert81609953_state A_44) tptp.bot_bo113204042tate_o)) (= B_8 A_44))))
% 0.21/0.54 (assert (forall ((X_18 tptp.hoare_1262092251_state)) (= (@ tptp.the_el417915516_state (@ (@ tptp.insert81609953_state X_18) tptp.bot_bo113204042tate_o)) X_18)))
% 0.21/0.54 (assert (forall ((X_17 tptp.hoare_1262092251_state)) (= (@ tptp.bot_bo113204042tate_o X_17) tptp.bot_bot_o)))
% 0.21/0.54 (assert (forall ((X_2 tptp.hoare_1262092251_state)) (= (@ tptp.bot_bo113204042tate_o X_2) tptp.bot_bot_o)))
% 0.21/0.54 (assert (forall ((G_3 (-> tptp.hoare_1262092251_state Bool)) (P_6 (-> tptp.state tptp.state Bool))) (@ (@ tptp.hoare_930741239_state G_3) (@ (@ tptp.insert81609953_state (@ (@ (@ tptp.hoare_951399329_state P_6) tptp.skip) P_6)) tptp.bot_bo113204042tate_o))))
% 0.21/0.54 (assert (forall ((D tptp.com) (R (-> tptp.state tptp.state Bool)) (G_2 (-> tptp.hoare_1262092251_state Bool)) (P_5 (-> tptp.state tptp.state Bool)) (C_3 tptp.com) (Q_2 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_951399329_state P_5))) (let ((_let_2 (@ tptp.hoare_930741239_state G_2))) (=> (@ _let_2 (@ (@ tptp.insert81609953_state (@ (@ _let_1 C_3) Q_2)) tptp.bot_bo113204042tate_o)) (=> (@ _let_2 (@ (@ tptp.insert81609953_state (@ (@ (@ tptp.hoare_951399329_state Q_2) D) R)) tptp.bot_bo113204042tate_o)) (@ _let_2 (@ (@ tptp.insert81609953_state (@ (@ _let_1 (@ (@ tptp.semi C_3) D)) R)) tptp.bot_bo113204042tate_o))))))))
% 0.21/0.54 (assert (forall ((Y_2 tptp.hoare_1262092251_state)) (not (forall ((Fun1 (-> tptp.state tptp.state Bool)) (Com tptp.com) (Fun2 (-> tptp.state tptp.state Bool))) (not (= Y_2 (@ (@ (@ tptp.hoare_951399329_state Fun1) Com) Fun2)))))))
% 0.21/0.54 (assert (forall ((X_16 tptp.hoare_1262092251_state) (A_43 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.member5164104_state X_16) A_43) (not (forall ((B_7 (-> tptp.hoare_1262092251_state Bool))) (=> (= A_43 (@ (@ tptp.insert81609953_state X_16) B_7)) (@ (@ tptp.member5164104_state X_16) B_7)))))))
% 0.21/0.54 (assert (forall ((A_42 tptp.hoare_1262092251_state) (A_41 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.member5164104_state A_42) A_41) (exists ((B_7 (-> tptp.hoare_1262092251_state Bool))) (and (= A_41 (@ (@ tptp.insert81609953_state A_42) B_7)) (not (@ (@ tptp.member5164104_state A_42) B_7)))))))
% 0.21/0.54 (assert (forall ((Com1 tptp.com) (Com2 tptp.com)) (not (= (@ (@ tptp.semi Com1) Com2) tptp.skip))))
% 0.21/0.54 (assert (forall ((Com1 tptp.com) (Com2 tptp.com)) (not (= tptp.skip (@ (@ tptp.semi Com1) Com2)))))
% 0.21/0.54 (assert (forall ((A_40 (-> tptp.hoare_1262092251_state Bool))) (=> (forall ((Y tptp.hoare_1262092251_state)) (not (@ (@ tptp.member5164104_state Y) A_40))) (= A_40 tptp.bot_bo113204042tate_o))))
% 0.21/0.54 (assert (forall ((Q (-> tptp.state tptp.state Bool)) (G_1 (-> tptp.hoare_1262092251_state Bool)) (C_2 tptp.com) (P_3 (-> tptp.state tptp.state Bool))) (=> (forall ((Z_5 tptp.state) (S tptp.state)) (=> (@ (@ P_3 Z_5) S) (exists ((P_4 (-> tptp.state tptp.state Bool)) (Q_1 (-> tptp.state tptp.state Bool))) (and (@ (@ tptp.hoare_930741239_state G_1) (@ (@ tptp.insert81609953_state (@ (@ (@ tptp.hoare_951399329_state P_4) C_2) Q_1)) tptp.bot_bo113204042tate_o)) (forall ((S_1 tptp.state)) (=> (forall ((Z_6 tptp.state)) (=> (@ (@ P_4 Z_6) S) (@ (@ Q_1 Z_6) S_1))) (@ (@ Q Z_5) S_1))))))) (@ (@ tptp.hoare_930741239_state G_1) (@ (@ tptp.insert81609953_state (@ (@ (@ tptp.hoare_951399329_state P_3) C_2) Q)) tptp.bot_bo113204042tate_o)))))
% 0.21/0.54 (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)))))
% 0.21/0.54 (assert (forall ((A_39 (-> tptp.hoare_1262092251_state Bool))) (= (not (= A_39 tptp.bot_bo113204042tate_o)) (exists ((X_2 tptp.hoare_1262092251_state) (B_7 (-> tptp.hoare_1262092251_state Bool))) (and (= A_39 (@ (@ tptp.insert81609953_state X_2) B_7)) (not (@ (@ tptp.member5164104_state X_2) B_7)))))))
% 0.21/0.54 (assert (forall ((X_2 tptp.hoare_1262092251_state)) (= (@ tptp.bot_bo113204042tate_o X_2) (@ (@ tptp.member5164104_state X_2) tptp.bot_bo113204042tate_o))))
% 0.21/0.54 (assert (forall ((F_34 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (A_38 tptp.hoare_1262092251_state) (B_6 tptp.hoare_1262092251_state)) (= (@ (@ (@ tptp.finite403475723_state F_34) (@ (@ tptp.insert81609953_state A_38) tptp.bot_bo113204042tate_o)) B_6) (= A_38 B_6))))
% 0.21/0.54 (assert (forall ((X_15 tptp.hoare_1262092251_state) (F_33 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (F_32 (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state))) (=> (@ (@ tptp.finite1168661790_state F_33) F_32) (= (@ F_32 (@ (@ tptp.insert81609953_state X_15) tptp.bot_bo113204042tate_o)) X_15))))
% 0.21/0.54 (assert (forall ((F_31 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (A_37 tptp.hoare_1262092251_state)) (= (@ (@ tptp.finite1740352635_state F_31) (@ (@ tptp.insert81609953_state A_37) tptp.bot_bo113204042tate_o)) A_37)))
% 0.21/0.54 (assert (forall ((A_36 tptp.hoare_1262092251_state) (G (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state)) (F_30 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state))) (=> (= G (@ tptp.finite1740352635_state F_30)) (= (@ G (@ (@ tptp.insert81609953_state A_36) tptp.bot_bo113204042tate_o)) A_36))))
% 0.21/0.54 (assert (forall ((F_29 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (X_14 tptp.hoare_1262092251_state)) (not (@ (@ (@ tptp.finite403475723_state F_29) tptp.bot_bo113204042tate_o) X_14))))
% 0.21/0.54 (assert (forall ((F_28 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (A_35 (-> tptp.hoare_1262092251_state Bool)) (X_13 tptp.hoare_1262092251_state)) (=> (@ (@ (@ tptp.finite403475723_state F_28) A_35) X_13) (not (= A_35 tptp.bot_bo113204042tate_o)))))
% 0.21/0.54 (assert (forall ((F_27 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (A_34 tptp.hoare_1262092251_state) (A_33 (-> tptp.hoare_1262092251_state Bool)) (X_12 tptp.hoare_1262092251_state)) (=> (@ (@ (@ (@ tptp.finite975744042_state F_27) A_34) A_33) X_12) (=> (not (@ (@ tptp.member5164104_state A_34) A_33)) (@ (@ (@ tptp.finite403475723_state F_27) (@ (@ tptp.insert81609953_state A_34) A_33)) X_12)))))
% 0.21/0.54 (assert (forall ((X_11 tptp.hoare_1262092251_state) (A_32 (-> tptp.hoare_1262092251_state Bool)) (F_26 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (F_25 (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state))) (=> (@ (@ tptp.finite1168661790_state F_26) F_25) (=> (@ tptp.finite1178804552_state A_32) (=> (not (@ (@ tptp.member5164104_state X_11) A_32)) (=> (not (= A_32 tptp.bot_bo113204042tate_o)) (= (@ F_25 (@ (@ tptp.insert81609953_state X_11) A_32)) (@ (@ F_26 X_11) (@ F_25 A_32)))))))))
% 0.21/0.54 (assert (forall ((A_31 (-> tptp.hoare_1262092251_state Bool)) (F_24 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (F_23 (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state))) (=> (@ (@ tptp.finite1168661790_state F_24) F_23) (=> (@ tptp.finite1178804552_state A_31) (= (@ F_23 A_31) (@ (@ tptp.finite1740352635_state F_24) A_31))))))
% 0.21/0.54 (assert (@ tptp.finite1178804552_state tptp.bot_bo113204042tate_o))
% 0.21/0.54 (assert (forall ((A_30 tptp.hoare_1262092251_state) (A_29 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_29) (@ tptp.finite1178804552_state (@ (@ tptp.insert81609953_state A_30) A_29)))))
% 0.21/0.54 (assert (forall ((F_22 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (Z_4 tptp.hoare_1262092251_state)) (@ (@ (@ (@ tptp.finite975744042_state F_22) Z_4) tptp.bot_bo113204042tate_o) Z_4)))
% 0.21/0.54 (assert (forall ((F_21 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (Z_3 tptp.hoare_1262092251_state) (X_10 tptp.hoare_1262092251_state)) (=> (@ (@ (@ (@ tptp.finite975744042_state F_21) Z_3) tptp.bot_bo113204042tate_o) X_10) (= X_10 Z_3))))
% 0.21/0.54 (assert (forall ((F_20 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (Z_2 tptp.hoare_1262092251_state) (Y_1 tptp.hoare_1262092251_state) (X_9 tptp.hoare_1262092251_state) (A_28 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ (@ tptp.finite975744042_state F_20) Z_2))) (=> (not (@ (@ tptp.member5164104_state X_9) A_28)) (=> (@ (@ _let_1 A_28) Y_1) (@ (@ _let_1 (@ (@ tptp.insert81609953_state X_9) A_28)) (@ (@ F_20 X_9) Y_1)))))))
% 0.21/0.54 (assert (forall ((A_27 tptp.hoare_1262092251_state) (A_26 (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.finite1178804552_state (@ (@ tptp.insert81609953_state A_27) A_26)) (@ tptp.finite1178804552_state A_26))))
% 0.21/0.54 (assert (forall ((A_25 (-> tptp.hoare_1262092251_state Bool)) (F_19 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (F_18 (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state))) (=> (@ (@ tptp.finite1168661790_state F_19) F_18) (=> (@ tptp.finite1178804552_state A_25) (=> (not (= A_25 tptp.bot_bo113204042tate_o)) (=> (forall ((X_2 tptp.hoare_1262092251_state) (Y tptp.hoare_1262092251_state)) (@ (@ tptp.member5164104_state (@ (@ F_19 X_2) Y)) (@ (@ tptp.insert81609953_state X_2) (@ (@ tptp.insert81609953_state Y) tptp.bot_bo113204042tate_o)))) (@ (@ tptp.member5164104_state (@ F_18 A_25)) A_25)))))))
% 0.21/0.54 (assert (forall ((F_17 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (A_24 tptp.hoare_1262092251_state) (X_8 (-> tptp.hoare_1262092251_state Bool)) (X_7 tptp.hoare_1262092251_state)) (=> (@ (@ (@ tptp.finite403475723_state F_17) (@ (@ tptp.insert81609953_state A_24) X_8)) X_7) (not (forall ((A_19 tptp.hoare_1262092251_state) (A_18 (-> tptp.hoare_1262092251_state Bool))) (=> (= (@ (@ tptp.insert81609953_state A_24) X_8) (@ (@ tptp.insert81609953_state A_19) A_18)) (=> (@ (@ (@ (@ tptp.finite975744042_state F_17) A_19) A_18) X_7) (@ (@ tptp.member5164104_state A_19) A_18))))))))
% 0.21/0.54 (assert (forall ((F_16 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (A_23 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_23) (=> (not (= A_23 tptp.bot_bo113204042tate_o)) (@ tptp.ex (@ (@ tptp.finite403475723_state F_16) A_23))))))
% 0.21/0.54 (assert (forall ((P_2 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (F_15 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_15) (=> (@ P_2 tptp.bot_bo113204042tate_o) (=> (forall ((X_2 tptp.hoare_1262092251_state) (F_5 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_5) (=> (not (@ (@ tptp.member5164104_state X_2) F_5)) (=> (@ P_2 F_5) (@ P_2 (@ (@ tptp.insert81609953_state X_2) F_5)))))) (@ P_2 F_15))))))
% 0.21/0.54 (assert (forall ((X_6 tptp.hoare_1262092251_state) (A_22 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.member5164104_state X_6) A_22) (@ A_22 X_6))))
% 0.21/0.54 (assert (forall ((P_1 (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.collec1121927558_state P_1) P_1)))
% 0.21/0.54 (assert (forall ((A_21 (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.finite1178804552_state A_21) (or (= A_21 tptp.bot_bo113204042tate_o) (exists ((A_18 (-> tptp.hoare_1262092251_state Bool)) (A_19 tptp.hoare_1262092251_state)) (and (= A_21 (@ (@ tptp.insert81609953_state A_19) A_18)) (@ tptp.finite1178804552_state A_18)))))))
% 0.21/0.54 (assert (forall ((F_14 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (Z_1 tptp.hoare_1262092251_state) (A_20 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_20) (@ tptp.ex (@ (@ (@ tptp.finite975744042_state F_14) Z_1) A_20)))))
% 0.21/0.54 (assert (forall ((F_13 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (A1_1 (-> tptp.hoare_1262092251_state Bool)) (A2_1 tptp.hoare_1262092251_state)) (= (@ (@ (@ tptp.finite403475723_state F_13) A1_1) A2_1) (exists ((A_19 tptp.hoare_1262092251_state) (A_18 (-> tptp.hoare_1262092251_state Bool)) (X_2 tptp.hoare_1262092251_state)) (and (= A1_1 (@ (@ tptp.insert81609953_state A_19) A_18)) (= A2_1 X_2) (@ (@ (@ (@ tptp.finite975744042_state F_13) A_19) A_18) X_2) (not (@ (@ tptp.member5164104_state A_19) A_18)))))))
% 0.21/0.54 (assert (forall ((F_12 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (Z tptp.hoare_1262092251_state) (A1 (-> tptp.hoare_1262092251_state Bool)) (A2 tptp.hoare_1262092251_state)) (= (@ (@ (@ (@ tptp.finite975744042_state F_12) Z) A1) A2) (or (and (= A1 tptp.bot_bo113204042tate_o) (= A2 Z)) (exists ((X_2 tptp.hoare_1262092251_state) (A_18 (-> tptp.hoare_1262092251_state Bool)) (Y tptp.hoare_1262092251_state)) (and (= A1 (@ (@ tptp.insert81609953_state X_2) A_18)) (= A2 (@ (@ F_12 X_2) Y)) (not (@ (@ tptp.member5164104_state X_2) A_18)) (@ (@ (@ (@ tptp.finite975744042_state F_12) Z) A_18) Y)))))))
% 0.21/0.54 (assert (forall ((X_5 tptp.hoare_1262092251_state) (A_17 (-> tptp.hoare_1262092251_state Bool)) (F_11 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (F_10 (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state))) (=> (@ (@ tptp.finite900773345_state F_11) F_10) (=> (@ tptp.finite1178804552_state A_17) (=> (not (= A_17 tptp.bot_bo113204042tate_o)) (= (@ F_10 (@ (@ tptp.insert81609953_state X_5) A_17)) (@ (@ F_11 X_5) (@ F_10 A_17))))))))
% 0.21/0.54 (assert (forall ((X_4 tptp.hoare_1262092251_state) (F_9 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (F_8 (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state))) (=> (@ (@ tptp.finite900773345_state F_9) F_8) (= (@ (@ F_9 X_4) X_4) X_4))))
% 0.21/0.54 (assert (forall ((X_3 tptp.hoare_1262092251_state) (A_16 (-> tptp.hoare_1262092251_state Bool)) (F_7 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (F_6 (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state))) (let ((_let_1 (@ F_6 A_16))) (=> (@ (@ tptp.finite900773345_state F_7) F_6) (=> (@ tptp.finite1178804552_state A_16) (=> (@ (@ tptp.member5164104_state X_3) A_16) (= (@ (@ F_7 X_3) _let_1) _let_1)))))))
% 0.21/0.54 (assert (forall ((P (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (F_4 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_4) (=> (not (= F_4 tptp.bot_bo113204042tate_o)) (=> (forall ((X_2 tptp.hoare_1262092251_state)) (@ P (@ (@ tptp.insert81609953_state X_2) tptp.bot_bo113204042tate_o))) (=> (forall ((X_2 tptp.hoare_1262092251_state) (F_5 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_5) (=> (not (= F_5 tptp.bot_bo113204042tate_o)) (=> (not (@ (@ tptp.member5164104_state X_2) F_5)) (=> (@ P F_5) (@ P (@ (@ tptp.insert81609953_state X_2) F_5))))))) (@ P F_4)))))))
% 0.21/0.54 (assert (forall ((A_15 (-> tptp.hoare_1262092251_state Bool)) (F_3 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (F_2 (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state))) (=> (@ (@ tptp.big_se1697321605_state F_3) F_2) (=> (@ tptp.finite1178804552_state A_15) (= (@ F_2 A_15) (@ (@ tptp.finite1740352635_state F_3) A_15))))))
% 0.21/0.54 (assert (forall ((X_1 tptp.hoare_1262092251_state) (A_14 (-> tptp.hoare_1262092251_state Bool)) (F_1 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state tptp.hoare_1262092251_state)) (F (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state))) (let ((_let_1 (@ (@ tptp.minus_2758725tate_o A_14) (@ (@ tptp.insert81609953_state X_1) tptp.bot_bo113204042tate_o)))) (let ((_let_2 (@ F A_14))) (let ((_let_3 (= _let_1 tptp.bot_bo113204042tate_o))) (=> (@ (@ tptp.finite1168661790_state F_1) F) (=> (@ tptp.finite1178804552_state A_14) (=> (@ (@ tptp.member5164104_state X_1) A_14) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (@ (@ F_1 X_1) (@ F _let_1)))))))))))))
% 0.21/0.54 (assert (forall ((B_5 (-> tptp.hoare_1262092251_state Bool)) (C_1 tptp.hoare_1262092251_state) (A_13 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state C_1))) (=> (@ _let_1 A_13) (=> (not (@ _let_1 B_5)) (@ _let_1 (@ (@ tptp.minus_2758725tate_o A_13) B_5)))))))
% 0.21/0.54 (assert (forall ((C tptp.hoare_1262092251_state) (A_12 (-> tptp.hoare_1262092251_state Bool)) (B_4 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state C))) (=> (@ _let_1 (@ (@ tptp.minus_2758725tate_o A_12) B_4)) (not (=> (@ _let_1 A_12) (@ _let_1 B_4)))))))
% 0.21/0.54 (assert (forall ((B_3 (-> tptp.hoare_1262092251_state Bool)) (A_11 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_11) (@ tptp.finite1178804552_state (@ (@ tptp.minus_2758725tate_o A_11) B_3)))))
% 0.21/0.54 (assert (forall ((A_10 tptp.hoare_1262092251_state) (A_9 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state A_10))) (=> (@ (@ tptp.member5164104_state A_10) A_9) (= (@ _let_1 (@ (@ tptp.minus_2758725tate_o A_9) (@ _let_1 tptp.bot_bo113204042tate_o))) A_9)))))
% 0.21/0.54 (assert (forall ((X tptp.hoare_1262092251_state) (A_8 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state X))) (=> (not (@ (@ tptp.member5164104_state X) A_8)) (= (@ (@ tptp.minus_2758725tate_o (@ _let_1 A_8)) (@ _let_1 tptp.bot_bo113204042tat/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 23742 Alarm clock ( read result; case "$result" in
% 299.97/300.21 unsat)
% 299.97/300.21 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.97/300.21 ;;
% 299.97/300.21 sat)
% 299.97/300.21 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.97/300.21 ;;
% 299.97/300.21 esac; exit 1 )
% 299.97/300.22 Alarm clock
% 299.97/300.22 % cvc5---1.0.5 exiting
% 299.97/300.22 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------