TSTP Solution File: SWW472^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW472^2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 299.85s 300.21s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.17 % Problem : SWW472^2 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.18 % Command : do_cvc5 %s %d
% 0.18/0.39 % Computer : n025.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Sun Aug 27 20:53:39 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.24/0.57 %----Proving TH0
% 0.24/0.58 %------------------------------------------------------------------------------
% 0.24/0.58 % File : SWW472^2 : TPTP v8.1.2. Released v5.3.0.
% 0.24/0.58 % Domain : Software Verification
% 0.24/0.58 % Problem : Hoare's Logic with Procedures line 327, 500 axioms selected
% 0.24/0.58 % Version : Especial.
% 0.24/0.58 % English :
% 0.24/0.58
% 0.24/0.58 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.24/0.58 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.24/0.58 % Source : [Bla11]
% 0.24/0.58 % Names : hoare_500_thf_l327 [Bla11]
% 0.24/0.58
% 0.24/0.58 % Status : Theorem
% 0.24/0.58 % Rating : 1.00 v5.3.0
% 0.24/0.58 % Syntax : Number of formulae : 370 ( 41 unt; 52 typ; 0 def)
% 0.24/0.58 % Number of atoms : 1185 ( 184 equ; 5 cnn)
% 0.24/0.58 % Maximal formula atoms : 12 ( 3 avg)
% 0.24/0.58 % Number of connectives : 2830 ( 103 ~; 12 |; 37 &;2115 @)
% 0.24/0.58 % ( 84 <=>; 479 =>; 0 <=; 0 <~>)
% 0.24/0.58 % Maximal formula depth : 18 ( 8 avg)
% 0.24/0.58 % Number of types : 5 ( 4 usr)
% 0.24/0.58 % Number of type conns : 847 ( 847 >; 0 *; 0 +; 0 <<)
% 0.24/0.58 % Number of symbols : 54 ( 48 usr; 8 con; 0-4 aty)
% 0.24/0.58 % Number of variables : 924 ( 4 ^; 904 !; 16 ?; 924 :)
% 0.24/0.58 % SPC : TH0_THM_EQU_NAR
% 0.24/0.58
% 0.24/0.58 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.24/0.58 % 2011-08-09 19:32:32
% 0.24/0.58 %------------------------------------------------------------------------------
% 0.24/0.58 %----Should-be-implicit typings (4)
% 0.24/0.58 thf(ty_ty_tc__Com__Ocom,type,
% 0.24/0.58 com: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_ty_tc__Com__Ostate,type,
% 0.24/0.58 state: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_ty_tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 0.24/0.58 hoare_1167836817_state: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_ty_tc__Nat__Onat,type,
% 0.24/0.58 nat: $tType ).
% 0.24/0.58
% 0.24/0.58 %----Explicit typings (48)
% 0.24/0.58 thf(sy_c_All2,type,
% 0.24/0.58 all2: ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_All1,type,
% 0.24/0.58 all1: ( $o > $o ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_000tc__Hoare____Mirabelle_,type,
% 0.24/0.58 big_co337839062te_nat: ( hoare_1167836817_state > nat ) > ( hoare_1167836817_state > $o ) > nat ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Big__Operators_Osemilattice__big_000tc__Hoare____Mirabelle____srushsumbx__O,type,
% 0.24/0.58 big_se1603066171_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Com_Ocom_OSKIP,type,
% 0.24/0.58 skip: com ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Com_Ocom_OSemi,type,
% 0.24/0.58 semi: com > com > com ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Ex,type,
% 0.24/0.58 ex: ( hoare_1167836817_state > $o ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ocomp__fun__commute_000tc__Hoare____Mirabelle____srushsumbx__Ot,type,
% 0.24/0.58 finite1091222817_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____srushsumbx__Otrip,type,
% 0.24/0.58 finite856902323tate_o: ( hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____srushsumbx__Otrip_001,type,
% 0.24/0.58 finite1900754844_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__C,type,
% 0.24/0.58 finite1084549118_state: ( hoare_1167836817_state > $o ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ofold1Set_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc_,type,
% 0.24/0.58 finite309220289_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ofold1_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Co,type,
% 0.24/0.58 finite1646097201_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,type,
% 0.24/0.58 finite291020855tate_o: ( hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com_002,type,
% 0.24/0.58 finite1731015960_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ofold__graph_000tc__Hoare____Mirabelle____srushsumbx__Otriple_I,type,
% 0.24/0.58 finite1316643734_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____srushsumbx__Otriple_,type,
% 0.24/0.58 finite1074406356_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____srushsumbx__Ot,type,
% 0.24/0.58 finite806517911_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____srushsumbx__,type,
% 0.24/0.58 minus_2107060239tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Groups_Ominus__class_Ominus_000_Eo,type,
% 0.24/0.58 minus_minus_o: $o > $o > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 0.24/0.58 minus_minus_nat: nat > nat > nat ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
% 0.24/0.58 plus_plus_nat: nat > nat > nat ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Hoare__Mirabelle__srushsumbx_OMGT,type,
% 0.24/0.58 hoare_Mirabelle_MGT: com > hoare_1167836817_state ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__derivs_000tc__Com__Ostate,type,
% 0.24/0.58 hoare_123228589_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__valids_000tc__Com__Ostate,type,
% 0.24/0.58 hoare_529639851_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple_000tc__Com__Ostate,type,
% 0.24/0.58 hoare_908217195_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1167836817_state ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____srushsumbx__O,type,
% 0.24/0.58 bot_bo70021908tate_o: hoare_1167836817_state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 0.24/0.58 bot_bot_o: $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord_Omax_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_,type,
% 0.24/0.58 max_Ho421493569tate_o: ( ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord_Omax_000_Eo,type,
% 0.24/0.58 max_o: ( $o > $o > $o ) > $o > $o > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord_Omin_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_,type,
% 0.24/0.58 min_Ho1955171539tate_o: ( ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord_Omin_000_Eo,type,
% 0.24/0.58 min_o: ( $o > $o > $o ) > $o > $o > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__Hoare____Mirabelle____srushsumbx__,type,
% 0.24/0.58 ord_le65125204tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord__class_Oless_000_Eo,type,
% 0.24/0.58 ord_less_o: $o > $o > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
% 0.24/0.58 ord_less_nat: nat > nat > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____srushsum,type,
% 0.24/0.58 ord_le827224136tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord__class_Oless__eq_000_Eo,type,
% 0.24/0.58 ord_less_eq_o: $o > $o > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord__class_Omax_000_062_Itc__Hoare____Mirabelle____srushsumbx__O,type,
% 0.24/0.58 ord_ma164008317tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord__class_Omax_000_Eo,type,
% 0.24/0.58 ord_max_o: $o > $o > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord__class_Omin_000_062_Itc__Hoare____Mirabelle____srushsumbx__O,type,
% 0.24/0.58 ord_mi1697686287tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord__class_Omin_000_Eo,type,
% 0.24/0.58 ord_min_o: $o > $o > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,
% 0.24/0.58 collec1027672124_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Osta,type,
% 0.24/0.58 insert2134838167_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__O,type,
% 0.24/0.58 the_el323660082_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_member_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,
% 0.24/0.58 member2058392318_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_P,type,
% 0.24/0.58 p: state > state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_Q,type,
% 0.24/0.58 q: state > state > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_c,type,
% 0.24/0.58 c: com ).
% 0.24/0.58
% 0.24/0.58 %----Relevant facts (315)
% 0.24/0.58 thf(fact_0_empty,axiom,
% 0.24/0.58 ! [G_29: hoare_1167836817_state > $o] : ( hoare_123228589_state @ G_29 @ bot_bo70021908tate_o ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_1_triple_Oinject,axiom,
% 0.24/0.58 ! [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] :
% 0.24/0.58 ( ( ( hoare_908217195_state @ Fun1_2 @ Com_2 @ Fun2_2 )
% 0.24/0.58 = ( hoare_908217195_state @ Fun1_1 @ Com_1 @ Fun2_1 ) )
% 0.24/0.58 <=> ( ( Fun1_2 = Fun1_1 )
% 0.24/0.58 & ( Com_2 = Com_1 )
% 0.24/0.58 & ( Fun2_2 = Fun2_1 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_2_hoare__sound,axiom,
% 0.24/0.58 ! [G_28: hoare_1167836817_state > $o,Ts_7: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( hoare_123228589_state @ G_28 @ Ts_7 )
% 0.24/0.58 => ( hoare_529639851_state @ G_28 @ Ts_7 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_3_cut,axiom,
% 0.24/0.58 ! [G_27: hoare_1167836817_state > $o,G_26: hoare_1167836817_state > $o,Ts_6: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( hoare_123228589_state @ G_26 @ Ts_6 )
% 0.24/0.58 => ( ( hoare_123228589_state @ G_27 @ G_26 )
% 0.24/0.58 => ( hoare_123228589_state @ G_27 @ Ts_6 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_4_hoare__derivs_Oinsert,axiom,
% 0.24/0.58 ! [Ts_5: hoare_1167836817_state > $o,G_25: hoare_1167836817_state > $o,T_1: hoare_1167836817_state] :
% 0.24/0.58 ( ( hoare_123228589_state @ G_25 @ ( insert2134838167_state @ T_1 @ bot_bo70021908tate_o ) )
% 0.24/0.58 => ( ( hoare_123228589_state @ G_25 @ Ts_5 )
% 0.24/0.58 => ( hoare_123228589_state @ G_25 @ ( insert2134838167_state @ T_1 @ Ts_5 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_5_derivs__insertD,axiom,
% 0.24/0.58 ! [G_24: hoare_1167836817_state > $o,T: hoare_1167836817_state,Ts_4: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( hoare_123228589_state @ G_24 @ ( insert2134838167_state @ T @ Ts_4 ) )
% 0.24/0.58 => ( ( hoare_123228589_state @ G_24 @ ( insert2134838167_state @ T @ bot_bo70021908tate_o ) )
% 0.24/0.58 & ( hoare_123228589_state @ G_24 @ Ts_4 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_6_conseq2,axiom,
% 0.24/0.58 ! [Q_11: state > state > $o,G_23: hoare_1167836817_state > $o,P_21: state > state > $o,C_39: com,Q_10: state > state > $o] :
% 0.24/0.58 ( ( hoare_123228589_state @ G_23 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_21 @ C_39 @ Q_10 ) @ bot_bo70021908tate_o ) )
% 0.24/0.58 => ( ! [Z_28: state,S: state] :
% 0.24/0.58 ( ( Q_10 @ Z_28 @ S )
% 0.24/0.58 => ( Q_11 @ Z_28 @ S ) )
% 0.24/0.58 => ( hoare_123228589_state @ G_23 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_21 @ C_39 @ Q_11 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_7_conseq1,axiom,
% 0.24/0.58 ! [P_20: state > state > $o,G_22: hoare_1167836817_state > $o,P_19: state > state > $o,C_38: com,Q_9: state > state > $o] :
% 0.24/0.58 ( ( hoare_123228589_state @ G_22 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_19 @ C_38 @ Q_9 ) @ bot_bo70021908tate_o ) )
% 0.24/0.58 => ( ! [Z_28: state,S: state] :
% 0.24/0.58 ( ( P_20 @ Z_28 @ S )
% 0.24/0.58 => ( P_19 @ Z_28 @ S ) )
% 0.24/0.58 => ( hoare_123228589_state @ G_22 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_20 @ C_38 @ Q_9 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_8_insertE,axiom,
% 0.24/0.58 ! [A_185: hoare_1167836817_state,B_92: hoare_1167836817_state,A_184: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ A_185 @ ( insert2134838167_state @ B_92 @ A_184 ) )
% 0.24/0.58 => ( ( A_185 != B_92 )
% 0.24/0.58 => ( member2058392318_state @ A_185 @ A_184 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_9_insertCI,axiom,
% 0.24/0.58 ! [B_91: hoare_1167836817_state,A_183: hoare_1167836817_state,B_90: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ~ ( member2058392318_state @ A_183 @ B_90 )
% 0.24/0.58 => ( A_183 = B_91 ) )
% 0.24/0.58 => ( member2058392318_state @ A_183 @ ( insert2134838167_state @ B_91 @ B_90 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_10_conseq12,axiom,
% 0.24/0.58 ! [Q_8: state > state > $o,P_18: state > state > $o,G_21: hoare_1167836817_state > $o,P_17: state > state > $o,C_37: com,Q_7: state > state > $o] :
% 0.24/0.58 ( ( hoare_123228589_state @ G_21 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_17 @ C_37 @ Q_7 ) @ bot_bo70021908tate_o ) )
% 0.24/0.58 => ( ! [Z_28: state,S: state] :
% 0.24/0.58 ( ( P_18 @ Z_28 @ S )
% 0.24/0.58 => ! [S_1: state] :
% 0.24/0.58 ( ! [Z_29: state] :
% 0.24/0.58 ( ( P_17 @ Z_29 @ S )
% 0.24/0.58 => ( Q_7 @ Z_29 @ S_1 ) )
% 0.24/0.58 => ( Q_8 @ Z_28 @ S_1 ) ) )
% 0.24/0.58 => ( hoare_123228589_state @ G_21 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_18 @ C_37 @ Q_8 ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_11_emptyE,axiom,
% 0.24/0.58 ! [A_182: hoare_1167836817_state] :
% 0.24/0.58 ~ ( member2058392318_state @ A_182 @ bot_bo70021908tate_o ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_12_empty__not__insert,axiom,
% 0.24/0.58 ! [A_181: hoare_1167836817_state,A_180: hoare_1167836817_state > $o] :
% 0.24/0.58 ( bot_bo70021908tate_o
% 0.24/0.58 != ( insert2134838167_state @ A_181 @ A_180 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_13_insert__not__empty,axiom,
% 0.24/0.58 ! [A_179: hoare_1167836817_state,A_178: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( insert2134838167_state @ A_179 @ A_178 )
% 0.24/0.58 != bot_bo70021908tate_o ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_14_singleton__iff,axiom,
% 0.24/0.58 ! [B_89: hoare_1167836817_state,A_177: hoare_1167836817_state] :
% 0.24/0.58 ( ( member2058392318_state @ B_89 @ ( insert2134838167_state @ A_177 @ bot_bo70021908tate_o ) )
% 0.24/0.58 <=> ( B_89 = A_177 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_15_doubleton__eq__iff,axiom,
% 0.24/0.58 ! [A_176: hoare_1167836817_state,B_88: hoare_1167836817_state,C_36: hoare_1167836817_state,D_3: hoare_1167836817_state] :
% 0.24/0.58 ( ( ( insert2134838167_state @ A_176 @ ( insert2134838167_state @ B_88 @ bot_bo70021908tate_o ) )
% 0.24/0.58 = ( insert2134838167_state @ C_36 @ ( insert2134838167_state @ D_3 @ bot_bo70021908tate_o ) ) )
% 0.24/0.58 <=> ( ( ( A_176 = C_36 )
% 0.24/0.58 & ( B_88 = D_3 ) )
% 0.24/0.58 | ( ( A_176 = D_3 )
% 0.24/0.58 & ( B_88 = C_36 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_16_equals0D,axiom,
% 0.24/0.58 ! [A_175: hoare_1167836817_state,A_174: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_174 = bot_bo70021908tate_o )
% 0.24/0.58 => ~ ( member2058392318_state @ A_175 @ A_174 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_17_Collect__empty__eq,axiom,
% 0.24/0.58 ! [P_16: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ( collec1027672124_state @ P_16 )
% 0.24/0.58 = bot_bo70021908tate_o )
% 0.24/0.58 <=> ! [X: hoare_1167836817_state] :
% 0.24/0.58 ~ ( P_16 @ X ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_18_empty__iff,axiom,
% 0.24/0.58 ! [C_35: hoare_1167836817_state] :
% 0.24/0.58 ~ ( member2058392318_state @ C_35 @ bot_bo70021908tate_o ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_19_empty__Collect__eq,axiom,
% 0.24/0.58 ! [P_15: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( bot_bo70021908tate_o
% 0.24/0.58 = ( collec1027672124_state @ P_15 ) )
% 0.24/0.58 <=> ! [X: hoare_1167836817_state] :
% 0.24/0.58 ~ ( P_15 @ X ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_20_ex__in__conv,axiom,
% 0.24/0.58 ! [A_173: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ? [X: hoare_1167836817_state] : ( member2058392318_state @ X @ A_173 )
% 0.24/0.58 <=> ( A_173 != bot_bo70021908tate_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_21_all__not__in__conv,axiom,
% 0.24/0.58 ! [A_172: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ! [X: hoare_1167836817_state] :
% 0.24/0.58 ~ ( member2058392318_state @ X @ A_172 )
% 0.24/0.58 <=> ( A_172 = bot_bo70021908tate_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_22_empty__def,axiom,
% 0.24/0.58 ( bot_bo70021908tate_o
% 0.24/0.58 = ( collec1027672124_state
% 0.24/0.58 @ ^ [X: hoare_1167836817_state] : $false ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_23_insert__absorb,axiom,
% 0.24/0.58 ! [A_171: hoare_1167836817_state,A_170: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ A_171 @ A_170 )
% 0.24/0.58 => ( ( insert2134838167_state @ A_171 @ A_170 )
% 0.24/0.58 = A_170 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_24_insertI2,axiom,
% 0.24/0.58 ! [B_87: hoare_1167836817_state,A_169: hoare_1167836817_state,B_86: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ A_169 @ B_86 )
% 0.24/0.58 => ( member2058392318_state @ A_169 @ ( insert2134838167_state @ B_87 @ B_86 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_25_insert__ident,axiom,
% 0.24/0.58 ! [B_85: hoare_1167836817_state > $o,X_85: hoare_1167836817_state,A_168: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ~ ( member2058392318_state @ X_85 @ A_168 )
% 0.24/0.58 => ( ~ ( member2058392318_state @ X_85 @ B_85 )
% 0.24/0.58 => ( ( ( insert2134838167_state @ X_85 @ A_168 )
% 0.24/0.58 = ( insert2134838167_state @ X_85 @ B_85 ) )
% 0.24/0.58 <=> ( A_168 = B_85 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_26_insert__code,axiom,
% 0.24/0.58 ! [Y_34: hoare_1167836817_state,A_167: hoare_1167836817_state > $o,X_84: hoare_1167836817_state] :
% 0.24/0.58 ( ( insert2134838167_state @ Y_34 @ A_167 @ X_84 )
% 0.24/0.58 <=> ( ( Y_34 = X_84 )
% 0.24/0.58 | ( A_167 @ X_84 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_27_insert__iff,axiom,
% 0.24/0.58 ! [A_166: hoare_1167836817_state,B_84: hoare_1167836817_state,A_165: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ A_166 @ ( insert2134838167_state @ B_84 @ A_165 ) )
% 0.24/0.58 <=> ( ( A_166 = B_84 )
% 0.24/0.58 | ( member2058392318_state @ A_166 @ A_165 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_28_insert__commute,axiom,
% 0.24/0.58 ! [X_83: hoare_1167836817_state,Y_33: hoare_1167836817_state,A_164: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( insert2134838167_state @ X_83 @ ( insert2134838167_state @ Y_33 @ A_164 ) )
% 0.24/0.58 = ( insert2134838167_state @ Y_33 @ ( insert2134838167_state @ X_83 @ A_164 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_29_insert__absorb2,axiom,
% 0.24/0.58 ! [X_82: hoare_1167836817_state,A_163: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( insert2134838167_state @ X_82 @ ( insert2134838167_state @ X_82 @ A_163 ) )
% 0.24/0.58 = ( insert2134838167_state @ X_82 @ A_163 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_30_insert__Collect,axiom,
% 0.24/0.58 ! [A_162: hoare_1167836817_state,P_14: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( insert2134838167_state @ A_162 @ ( collec1027672124_state @ P_14 ) )
% 0.24/0.58 = ( collec1027672124_state
% 0.24/0.58 @ ^ [U: hoare_1167836817_state] : ( (=>) @ ( (~) @ ( U = A_162 ) ) @ ( P_14 @ U ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_31_insert__compr,axiom,
% 0.24/0.58 ! [A_161: hoare_1167836817_state,B_83: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( insert2134838167_state @ A_161 @ B_83 )
% 0.24/0.58 = ( collec1027672124_state
% 0.24/0.58 @ ^ [X: hoare_1167836817_state] : ( (|) @ ( X = A_161 ) @ ( member2058392318_state @ X @ B_83 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_32_insertI1,axiom,
% 0.24/0.58 ! [A_160: hoare_1167836817_state,B_82: hoare_1167836817_state > $o] : ( member2058392318_state @ A_160 @ ( insert2134838167_state @ A_160 @ B_82 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_33_singleton__inject,axiom,
% 0.24/0.58 ! [A_159: hoare_1167836817_state,B_81: hoare_1167836817_state] :
% 0.24/0.58 ( ( ( insert2134838167_state @ A_159 @ bot_bo70021908tate_o )
% 0.24/0.58 = ( insert2134838167_state @ B_81 @ bot_bo70021908tate_o ) )
% 0.24/0.58 => ( A_159 = B_81 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_34_singletonE,axiom,
% 0.24/0.58 ! [B_80: hoare_1167836817_state,A_158: hoare_1167836817_state] :
% 0.24/0.58 ( ( member2058392318_state @ B_80 @ ( insert2134838167_state @ A_158 @ bot_bo70021908tate_o ) )
% 0.24/0.58 => ( B_80 = A_158 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_35_the__elem__eq,axiom,
% 0.24/0.58 ! [X_81: hoare_1167836817_state] :
% 0.24/0.58 ( ( the_el323660082_state @ ( insert2134838167_state @ X_81 @ bot_bo70021908tate_o ) )
% 0.24/0.58 = X_81 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_36_bot__apply,axiom,
% 0.24/0.58 ! [X_80: hoare_1167836817_state] :
% 0.24/0.58 ( ( bot_bo70021908tate_o @ X_80 )
% 0.24/0.58 <=> bot_bot_o ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_37_bot__fun__def,axiom,
% 0.24/0.58 ! [X: hoare_1167836817_state] :
% 0.24/0.58 ( ( bot_bo70021908tate_o @ X )
% 0.24/0.58 <=> bot_bot_o ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_38_hoare__derivs_OSkip,axiom,
% 0.24/0.58 ! [G_20: hoare_1167836817_state > $o,P_13: state > state > $o] : ( hoare_123228589_state @ G_20 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_13 @ skip @ P_13 ) @ bot_bo70021908tate_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_39_Comp,axiom,
% 0.24/0.58 ! [D_2: com,R: state > state > $o,G_19: hoare_1167836817_state > $o,P_12: state > state > $o,C_34: com,Q_6: state > state > $o] :
% 0.24/0.58 ( ( hoare_123228589_state @ G_19 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_12 @ C_34 @ Q_6 ) @ bot_bo70021908tate_o ) )
% 0.24/0.58 => ( ( hoare_123228589_state @ G_19 @ ( insert2134838167_state @ ( hoare_908217195_state @ Q_6 @ D_2 @ R ) @ bot_bo70021908tate_o ) )
% 0.24/0.58 => ( hoare_123228589_state @ G_19 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_12 @ ( semi @ C_34 @ D_2 ) @ R ) @ bot_bo70021908tate_o ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_40_triple_Oexhaust,axiom,
% 0.24/0.58 ! [Y_32: hoare_1167836817_state] :
% 0.24/0.58 ~ ! [Fun1: state > state > $o,Com: com,Fun2: state > state > $o] :
% 0.24/0.58 ( Y_32
% 0.24/0.58 != ( hoare_908217195_state @ Fun1 @ Com @ Fun2 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_41_Set_Oset__insert,axiom,
% 0.24/0.58 ! [X_79: hoare_1167836817_state,A_157: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ X_79 @ A_157 )
% 0.24/0.58 => ~ ! [B_79: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_157
% 0.24/0.58 = ( insert2134838167_state @ X_79 @ B_79 ) )
% 0.24/0.58 => ( member2058392318_state @ X_79 @ B_79 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_42_mk__disjoint__insert,axiom,
% 0.24/0.58 ! [A_156: hoare_1167836817_state,A_155: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ A_156 @ A_155 )
% 0.24/0.58 => ? [B_79: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_155
% 0.24/0.58 = ( insert2134838167_state @ A_156 @ B_79 ) )
% 0.24/0.58 & ~ ( member2058392318_state @ A_156 @ B_79 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_43_equals0I,axiom,
% 0.24/0.58 ! [A_154: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ! [Y: hoare_1167836817_state] :
% 0.24/0.58 ~ ( member2058392318_state @ Y @ A_154 )
% 0.24/0.58 => ( A_154 = bot_bo70021908tate_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_44_conseq,axiom,
% 0.24/0.58 ! [Q_4: state > state > $o,G_18: hoare_1167836817_state > $o,C_33: com,P_10: state > state > $o] :
% 0.24/0.58 ( ! [Z_28: state,S: state] :
% 0.24/0.58 ( ( P_10 @ Z_28 @ S )
% 0.24/0.58 => ? [P_11: state > state > $o,Q_5: state > state > $o] :
% 0.24/0.58 ( ( hoare_123228589_state @ G_18 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_11 @ C_33 @ Q_5 ) @ bot_bo70021908tate_o ) )
% 0.24/0.58 & ! [S_1: state] :
% 0.24/0.58 ( ! [Z_29: state] :
% 0.24/0.58 ( ( P_11 @ Z_29 @ S )
% 0.24/0.58 => ( Q_5 @ Z_29 @ S_1 ) )
% 0.24/0.58 => ( Q_4 @ Z_28 @ S_1 ) ) ) )
% 0.24/0.58 => ( hoare_123228589_state @ G_18 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_10 @ C_33 @ Q_4 ) @ bot_bo70021908tate_o ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_45_nonempty__iff,axiom,
% 0.24/0.58 ! [A_153: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_153 != bot_bo70021908tate_o )
% 0.24/0.58 <=> ? [X: hoare_1167836817_state,B_79: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_153
% 0.24/0.58 = ( insert2134838167_state @ X @ B_79 ) )
% 0.24/0.58 & ~ ( member2058392318_state @ X @ B_79 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_46_com_Osimps_I13_J,axiom,
% 0.24/0.58 ! [Com1: com,Com2: com] :
% 0.24/0.58 ( ( semi @ Com1 @ Com2 )
% 0.24/0.58 != skip ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_47_com_Osimps_I12_J,axiom,
% 0.24/0.58 ! [Com1: com,Com2: com] :
% 0.24/0.58 ( skip
% 0.24/0.58 != ( semi @ Com1 @ Com2 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_48_com_Osimps_I3_J,axiom,
% 0.24/0.58 ! [Com1_1: com,Com2_1: com,Com1: com,Com2: com] :
% 0.24/0.58 ( ( ( semi @ Com1_1 @ Com2_1 )
% 0.24/0.58 = ( semi @ Com1 @ Com2 ) )
% 0.24/0.58 <=> ( ( Com1_1 = Com1 )
% 0.24/0.58 & ( Com2_1 = Com2 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_49_fold1Set__sing,axiom,
% 0.24/0.58 ! [F_82: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,A_152: hoare_1167836817_state,B_78: hoare_1167836817_state] :
% 0.24/0.58 ( ( finite309220289_state @ F_82 @ ( insert2134838167_state @ A_152 @ bot_bo70021908tate_o ) @ B_78 )
% 0.24/0.58 <=> ( A_152 = B_78 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_50_folding__one_Osingleton,axiom,
% 0.24/0.58 ! [X_78: hoare_1167836817_state,F_81: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_80: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1074406356_state @ F_81 @ F_80 )
% 0.24/0.58 => ( ( F_80 @ ( insert2134838167_state @ X_78 @ bot_bo70021908tate_o ) )
% 0.24/0.58 = X_78 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_51_bot__empty__eq,axiom,
% 0.24/0.58 ! [X: hoare_1167836817_state] :
% 0.24/0.58 ( ( bot_bo70021908tate_o @ X )
% 0.24/0.58 <=> ( member2058392318_state @ X @ bot_bo70021908tate_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_52_fold1__singleton,axiom,
% 0.24/0.58 ! [F_79: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,A_151: hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1646097201_state @ F_79 @ ( insert2134838167_state @ A_151 @ bot_bo70021908tate_o ) )
% 0.24/0.58 = A_151 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_53_fold1__singleton__def,axiom,
% 0.24/0.58 ! [A_150: hoare_1167836817_state,G_17: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,F_78: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( G_17
% 0.24/0.58 = ( finite1646097201_state @ F_78 ) )
% 0.24/0.58 => ( ( G_17 @ ( insert2134838167_state @ A_150 @ bot_bo70021908tate_o ) )
% 0.24/0.58 = A_150 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_54_empty__fold1SetE,axiom,
% 0.24/0.58 ! [F_77: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,X_77: hoare_1167836817_state] :
% 0.24/0.58 ~ ( finite309220289_state @ F_77 @ bot_bo70021908tate_o @ X_77 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_55_fold1Set__nonempty,axiom,
% 0.24/0.58 ! [F_76: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,A_149: hoare_1167836817_state > $o,X_76: hoare_1167836817_state] :
% 0.24/0.58 ( ( finite309220289_state @ F_76 @ A_149 @ X_76 )
% 0.24/0.58 => ( A_149 != bot_bo70021908tate_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_56_fold1Set_Ointros,axiom,
% 0.24/0.58 ! [F_75: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,A_148: hoare_1167836817_state,A_147: hoare_1167836817_state > $o,X_75: hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1316643734_state @ F_75 @ A_148 @ A_147 @ X_75 )
% 0.24/0.58 => ( ~ ( member2058392318_state @ A_148 @ A_147 )
% 0.24/0.58 => ( finite309220289_state @ F_75 @ ( insert2134838167_state @ A_148 @ A_147 ) @ X_75 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_57_folding__one_Oinsert,axiom,
% 0.24/0.58 ! [X_74: hoare_1167836817_state,A_146: hoare_1167836817_state > $o,F_74: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_73: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1074406356_state @ F_74 @ F_73 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_146 )
% 0.24/0.58 => ( ~ ( member2058392318_state @ X_74 @ A_146 )
% 0.24/0.58 => ( ( A_146 != bot_bo70021908tate_o )
% 0.24/0.58 => ( ( F_73 @ ( insert2134838167_state @ X_74 @ A_146 ) )
% 0.24/0.58 = ( F_74 @ X_74 @ ( F_73 @ A_146 ) ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_58_folding__one_Oeq__fold,axiom,
% 0.24/0.58 ! [A_145: hoare_1167836817_state > $o,F_72: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_71: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1074406356_state @ F_72 @ F_71 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_145 )
% 0.24/0.58 => ( ( F_71 @ A_145 )
% 0.24/0.58 = ( finite1646097201_state @ F_72 @ A_145 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_59_folding__one_Oclosed,axiom,
% 0.24/0.58 ! [A_144: hoare_1167836817_state > $o,F_70: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_69: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1074406356_state @ F_70 @ F_69 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_144 )
% 0.24/0.58 => ( ( A_144 != bot_bo70021908tate_o )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] : ( member2058392318_state @ ( F_70 @ X @ Y ) @ ( insert2134838167_state @ X @ ( insert2134838167_state @ Y @ bot_bo70021908tate_o ) ) )
% 0.24/0.58 => ( member2058392318_state @ ( F_69 @ A_144 ) @ A_144 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_60_insert__fold1SetE,axiom,
% 0.24/0.58 ! [F_68: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,A_143: hoare_1167836817_state,X_73: hoare_1167836817_state > $o,X_72: hoare_1167836817_state] :
% 0.24/0.58 ( ( finite309220289_state @ F_68 @ ( insert2134838167_state @ A_143 @ X_73 ) @ X_72 )
% 0.24/0.58 => ~ ! [A_59: hoare_1167836817_state,A_58: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ( insert2134838167_state @ A_143 @ X_73 )
% 0.24/0.58 = ( insert2134838167_state @ A_59 @ A_58 ) )
% 0.24/0.58 => ( ( finite1316643734_state @ F_68 @ A_59 @ A_58 @ X_72 )
% 0.24/0.58 => ( member2058392318_state @ A_59 @ A_58 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_61_subset__singletonD,axiom,
% 0.24/0.58 ! [A_142: hoare_1167836817_state > $o,X_71: hoare_1167836817_state] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_142 @ ( insert2134838167_state @ X_71 @ bot_bo70021908tate_o ) )
% 0.24/0.58 => ( ( A_142 = bot_bo70021908tate_o )
% 0.24/0.58 | ( A_142
% 0.24/0.58 = ( insert2134838167_state @ X_71 @ bot_bo70021908tate_o ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_62_order__refl,axiom,
% 0.24/0.58 ! [X_70: $o] : ( ord_less_eq_o @ X_70 @ X_70 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_63_order__refl,axiom,
% 0.24/0.58 ! [X_70: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ X_70 @ X_70 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_64_subsetD,axiom,
% 0.24/0.58 ! [C_32: hoare_1167836817_state,A_141: hoare_1167836817_state > $o,B_77: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_141 @ B_77 )
% 0.24/0.58 => ( ( member2058392318_state @ C_32 @ A_141 )
% 0.24/0.58 => ( member2058392318_state @ C_32 @ B_77 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_65_equalityI,axiom,
% 0.24/0.58 ! [A_140: hoare_1167836817_state > $o,B_76: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_140 @ B_76 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ B_76 @ A_140 )
% 0.24/0.58 => ( A_140 = B_76 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_66_finite_OemptyI,axiom,
% 0.24/0.58 finite1084549118_state @ bot_bo70021908tate_o ).
% 0.24/0.58
% 0.24/0.58 thf(fact_67_finite_OinsertI,axiom,
% 0.24/0.58 ! [A_139: hoare_1167836817_state,A_138: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_138 )
% 0.24/0.58 => ( finite1084549118_state @ ( insert2134838167_state @ A_139 @ A_138 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_68_empty__subsetI,axiom,
% 0.24/0.58 ! [A_137: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A_137 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_69_rev__predicate1D,axiom,
% 0.24/0.58 ! [Q_3: hoare_1167836817_state > $o,P_9: hoare_1167836817_state > $o,X_69: hoare_1167836817_state] :
% 0.24/0.58 ( ( P_9 @ X_69 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ P_9 @ Q_3 )
% 0.24/0.58 => ( Q_3 @ X_69 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_70_predicate1D,axiom,
% 0.24/0.58 ! [X_68: hoare_1167836817_state,P_8: hoare_1167836817_state > $o,Q_2: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ P_8 @ Q_2 )
% 0.24/0.58 => ( ( P_8 @ X_68 )
% 0.24/0.58 => ( Q_2 @ X_68 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_71_mem__def,axiom,
% 0.24/0.58 ! [X_67: hoare_1167836817_state,A_136: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ X_67 @ A_136 )
% 0.24/0.58 <=> ( A_136 @ X_67 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_72_Collect__def,axiom,
% 0.24/0.58 ! [P_7: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( collec1027672124_state @ P_7 )
% 0.24/0.58 = P_7 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_73_subset__refl,axiom,
% 0.24/0.58 ! [A_135: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A_135 @ A_135 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_74_set__eq__subset,axiom,
% 0.24/0.58 ! [A_134: hoare_1167836817_state > $o,B_75: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_134 = B_75 )
% 0.24/0.58 <=> ( ( ord_le827224136tate_o @ A_134 @ B_75 )
% 0.24/0.58 & ( ord_le827224136tate_o @ B_75 @ A_134 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_75_equalityD1,axiom,
% 0.24/0.58 ! [A_133: hoare_1167836817_state > $o,B_74: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_133 = B_74 )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_133 @ B_74 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_76_equalityD2,axiom,
% 0.24/0.58 ! [A_132: hoare_1167836817_state > $o,B_73: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_132 = B_73 )
% 0.24/0.58 => ( ord_le827224136tate_o @ B_73 @ A_132 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_77_in__mono,axiom,
% 0.24/0.58 ! [X_66: hoare_1167836817_state,A_131: hoare_1167836817_state > $o,B_72: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_131 @ B_72 )
% 0.24/0.58 => ( ( member2058392318_state @ X_66 @ A_131 )
% 0.24/0.58 => ( member2058392318_state @ X_66 @ B_72 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_78_set__rev__mp,axiom,
% 0.24/0.58 ! [B_71: hoare_1167836817_state > $o,X_65: hoare_1167836817_state,A_130: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ X_65 @ A_130 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ A_130 @ B_71 )
% 0.24/0.58 => ( member2058392318_state @ X_65 @ B_71 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_79_set__mp,axiom,
% 0.24/0.58 ! [X_64: hoare_1167836817_state,A_129: hoare_1167836817_state > $o,B_70: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_129 @ B_70 )
% 0.24/0.58 => ( ( member2058392318_state @ X_64 @ A_129 )
% 0.24/0.58 => ( member2058392318_state @ X_64 @ B_70 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_80_subset__trans,axiom,
% 0.24/0.58 ! [C_31: hoare_1167836817_state > $o,A_128: hoare_1167836817_state > $o,B_69: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_128 @ B_69 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ B_69 @ C_31 )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_128 @ C_31 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_81_equalityE,axiom,
% 0.24/0.58 ! [A_127: hoare_1167836817_state > $o,B_68: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_127 = B_68 )
% 0.24/0.58 => ~ ( ( ord_le827224136tate_o @ A_127 @ B_68 )
% 0.24/0.58 => ~ ( ord_le827224136tate_o @ B_68 @ A_127 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_82_le__fun__def,axiom,
% 0.24/0.58 ! [F_67: hoare_1167836817_state > $o,G_16: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ F_67 @ G_16 )
% 0.24/0.58 <=> ! [X: hoare_1167836817_state] : ( ord_less_eq_o @ ( F_67 @ X ) @ ( G_16 @ X ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_83_order__eq__iff,axiom,
% 0.24/0.58 ! [Y_31: $o,X_63: $o] :
% 0.24/0.58 ( ( X_63
% 0.24/0.58 <=> Y_31 )
% 0.24/0.58 <=> ( ( ord_less_eq_o @ X_63 @ Y_31 )
% 0.24/0.58 & ( ord_less_eq_o @ Y_31 @ X_63 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_84_order__eq__iff,axiom,
% 0.24/0.58 ! [X_63: hoare_1167836817_state > $o,Y_31: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( X_63 = Y_31 )
% 0.24/0.58 <=> ( ( ord_le827224136tate_o @ X_63 @ Y_31 )
% 0.24/0.58 & ( ord_le827224136tate_o @ Y_31 @ X_63 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_85_rev__finite__subset,axiom,
% 0.24/0.58 ! [A_126: hoare_1167836817_state > $o,B_67: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ B_67 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ A_126 @ B_67 )
% 0.24/0.58 => ( finite1084549118_state @ A_126 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_86_order__eq__refl,axiom,
% 0.24/0.58 ! [Y_30: $o,X_62: $o] :
% 0.24/0.58 ( ( X_62
% 0.24/0.58 <=> Y_30 )
% 0.24/0.58 => ( ord_less_eq_o @ X_62 @ Y_30 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_87_order__eq__refl,axiom,
% 0.24/0.58 ! [X_62: hoare_1167836817_state > $o,Y_30: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( X_62 = Y_30 )
% 0.24/0.58 => ( ord_le827224136tate_o @ X_62 @ Y_30 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_88_le__funD,axiom,
% 0.24/0.58 ! [X_61: hoare_1167836817_state,F_66: hoare_1167836817_state > $o,G_15: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ F_66 @ G_15 )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_66 @ X_61 ) @ ( G_15 @ X_61 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_89_order__antisym__conv,axiom,
% 0.24/0.58 ! [Y_29: $o,X_60: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ Y_29 @ X_60 )
% 0.24/0.58 => ( ( ord_less_eq_o @ X_60 @ Y_29 )
% 0.24/0.58 <=> ( X_60
% 0.24/0.58 <=> Y_29 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_90_order__antisym__conv,axiom,
% 0.24/0.58 ! [Y_29: hoare_1167836817_state > $o,X_60: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ Y_29 @ X_60 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ X_60 @ Y_29 )
% 0.24/0.58 <=> ( X_60 = Y_29 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_91_finite__subset,axiom,
% 0.24/0.58 ! [A_125: hoare_1167836817_state > $o,B_66: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_125 @ B_66 )
% 0.24/0.58 => ( ( finite1084549118_state @ B_66 )
% 0.24/0.58 => ( finite1084549118_state @ A_125 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_92_ord__eq__le__trans,axiom,
% 0.24/0.58 ! [C_30: $o,B_65: $o,A_124: $o] :
% 0.24/0.58 ( ( A_124
% 0.24/0.58 <=> B_65 )
% 0.24/0.58 => ( ( ord_less_eq_o @ B_65 @ C_30 )
% 0.24/0.58 => ( ord_less_eq_o @ A_124 @ C_30 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_93_ord__eq__le__trans,axiom,
% 0.24/0.58 ! [C_30: hoare_1167836817_state > $o,A_124: hoare_1167836817_state > $o,B_65: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_124 = B_65 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ B_65 @ C_30 )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_124 @ C_30 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_94_xt1_I3_J,axiom,
% 0.24/0.58 ! [C_29: $o,B_64: $o,A_123: $o] :
% 0.24/0.58 ( ( A_123
% 0.24/0.58 <=> B_64 )
% 0.24/0.58 => ( ( ord_less_eq_o @ C_29 @ B_64 )
% 0.24/0.58 => ( ord_less_eq_o @ C_29 @ A_123 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_95_xt1_I3_J,axiom,
% 0.24/0.58 ! [C_29: hoare_1167836817_state > $o,A_123: hoare_1167836817_state > $o,B_64: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_123 = B_64 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ C_29 @ B_64 )
% 0.24/0.58 => ( ord_le827224136tate_o @ C_29 @ A_123 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_96_ord__le__eq__trans,axiom,
% 0.24/0.58 ! [C_28: $o,A_122: $o,B_63: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ A_122 @ B_63 )
% 0.24/0.58 => ( ( B_63
% 0.24/0.58 <=> C_28 )
% 0.24/0.58 => ( ord_less_eq_o @ A_122 @ C_28 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_97_ord__le__eq__trans,axiom,
% 0.24/0.58 ! [C_28: hoare_1167836817_state > $o,A_122: hoare_1167836817_state > $o,B_63: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_122 @ B_63 )
% 0.24/0.58 => ( ( B_63 = C_28 )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_122 @ C_28 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_98_xt1_I4_J,axiom,
% 0.24/0.58 ! [C_27: $o,B_62: $o,A_121: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ B_62 @ A_121 )
% 0.24/0.58 => ( ( B_62
% 0.24/0.58 <=> C_27 )
% 0.24/0.58 => ( ord_less_eq_o @ C_27 @ A_121 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_99_xt1_I4_J,axiom,
% 0.24/0.58 ! [C_27: hoare_1167836817_state > $o,B_62: hoare_1167836817_state > $o,A_121: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ B_62 @ A_121 )
% 0.24/0.58 => ( ( B_62 = C_27 )
% 0.24/0.58 => ( ord_le827224136tate_o @ C_27 @ A_121 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_100_order__antisym,axiom,
% 0.24/0.58 ! [X_59: $o,Y_28: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ X_59 @ Y_28 )
% 0.24/0.58 => ( ( ord_less_eq_o @ Y_28 @ X_59 )
% 0.24/0.58 => ( X_59
% 0.24/0.58 <=> Y_28 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_101_order__antisym,axiom,
% 0.24/0.58 ! [X_59: hoare_1167836817_state > $o,Y_28: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ X_59 @ Y_28 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ Y_28 @ X_59 )
% 0.24/0.58 => ( X_59 = Y_28 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_102_order__trans,axiom,
% 0.24/0.58 ! [Z_27: $o,X_58: $o,Y_27: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ X_58 @ Y_27 )
% 0.24/0.58 => ( ( ord_less_eq_o @ Y_27 @ Z_27 )
% 0.24/0.58 => ( ord_less_eq_o @ X_58 @ Z_27 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_103_order__trans,axiom,
% 0.24/0.58 ! [Z_27: hoare_1167836817_state > $o,X_58: hoare_1167836817_state > $o,Y_27: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ X_58 @ Y_27 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ Y_27 @ Z_27 )
% 0.24/0.58 => ( ord_le827224136tate_o @ X_58 @ Z_27 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_104_xt1_I5_J,axiom,
% 0.24/0.58 ! [Y_26: $o,X_57: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ Y_26 @ X_57 )
% 0.24/0.58 => ( ( ord_less_eq_o @ X_57 @ Y_26 )
% 0.24/0.58 => ( X_57
% 0.24/0.58 <=> Y_26 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_105_xt1_I5_J,axiom,
% 0.24/0.58 ! [Y_26: hoare_1167836817_state > $o,X_57: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ Y_26 @ X_57 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ X_57 @ Y_26 )
% 0.24/0.58 => ( X_57 = Y_26 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_106_xt1_I6_J,axiom,
% 0.24/0.58 ! [Z_26: $o,Y_25: $o,X_56: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ Y_25 @ X_56 )
% 0.24/0.58 => ( ( ord_less_eq_o @ Z_26 @ Y_25 )
% 0.24/0.58 => ( ord_less_eq_o @ Z_26 @ X_56 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_107_xt1_I6_J,axiom,
% 0.24/0.58 ! [Z_26: hoare_1167836817_state > $o,Y_25: hoare_1167836817_state > $o,X_56: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ Y_25 @ X_56 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ Z_26 @ Y_25 )
% 0.24/0.58 => ( ord_le827224136tate_o @ Z_26 @ X_56 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_108_le__funE,axiom,
% 0.24/0.58 ! [X_55: hoare_1167836817_state,F_65: hoare_1167836817_state > $o,G_14: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ F_65 @ G_14 )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_65 @ X_55 ) @ ( G_14 @ X_55 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_109_bot__least,axiom,
% 0.24/0.58 ! [A_120: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A_120 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_110_bot__least,axiom,
% 0.24/0.58 ! [A_120: $o] : ( ord_less_eq_o @ bot_bot_o @ A_120 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_111_bot__unique,axiom,
% 0.24/0.58 ! [A_119: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_119 @ bot_bo70021908tate_o )
% 0.24/0.58 <=> ( A_119 = bot_bo70021908tate_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_112_bot__unique,axiom,
% 0.24/0.58 ! [A_119: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ A_119 @ bot_bot_o )
% 0.24/0.58 <=> ( A_119
% 0.24/0.58 <=> bot_bot_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_113_le__bot,axiom,
% 0.24/0.58 ! [A_118: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_118 @ bot_bo70021908tate_o )
% 0.24/0.58 => ( A_118 = bot_bo70021908tate_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_114_le__bot,axiom,
% 0.24/0.58 ! [A_118: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ A_118 @ bot_bot_o )
% 0.24/0.58 => ( A_118
% 0.24/0.58 <=> bot_bot_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_115_subset__empty,axiom,
% 0.24/0.58 ! [A_117: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_117 @ bot_bo70021908tate_o )
% 0.24/0.58 <=> ( A_117 = bot_bo70021908tate_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_116_subset__insertI,axiom,
% 0.24/0.58 ! [B_61: hoare_1167836817_state > $o,A_116: hoare_1167836817_state] : ( ord_le827224136tate_o @ B_61 @ ( insert2134838167_state @ A_116 @ B_61 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_117_insert__subset,axiom,
% 0.24/0.58 ! [X_54: hoare_1167836817_state,A_115: hoare_1167836817_state > $o,B_60: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ ( insert2134838167_state @ X_54 @ A_115 ) @ B_60 )
% 0.24/0.58 <=> ( ( member2058392318_state @ X_54 @ B_60 )
% 0.24/0.58 & ( ord_le827224136tate_o @ A_115 @ B_60 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_118_subset__insert,axiom,
% 0.24/0.58 ! [B_59: hoare_1167836817_state > $o,X_53: hoare_1167836817_state,A_114: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ~ ( member2058392318_state @ X_53 @ A_114 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ A_114 @ ( insert2134838167_state @ X_53 @ B_59 ) )
% 0.24/0.58 <=> ( ord_le827224136tate_o @ A_114 @ B_59 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_119_subset__insertI2,axiom,
% 0.24/0.58 ! [B_58: hoare_1167836817_state,A_113: hoare_1167836817_state > $o,B_57: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_113 @ B_57 )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_113 @ ( insert2134838167_state @ B_58 @ B_57 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_120_insert__mono,axiom,
% 0.24/0.58 ! [A_112: hoare_1167836817_state,C_26: hoare_1167836817_state > $o,D_1: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ C_26 @ D_1 )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( insert2134838167_state @ A_112 @ C_26 ) @ ( insert2134838167_state @ A_112 @ D_1 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_121_finite__insert,axiom,
% 0.24/0.58 ! [A_111: hoare_1167836817_state,A_110: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ ( insert2134838167_state @ A_111 @ A_110 ) )
% 0.24/0.58 <=> ( finite1084549118_state @ A_110 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_122_asm,axiom,
% 0.24/0.58 ! [Ts_3: hoare_1167836817_state > $o,G_13: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ Ts_3 @ G_13 )
% 0.24/0.58 => ( hoare_123228589_state @ G_13 @ Ts_3 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_123_weaken,axiom,
% 0.24/0.58 ! [Ts_2: hoare_1167836817_state > $o,G_12: hoare_1167836817_state > $o,Ts_1: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( hoare_123228589_state @ G_12 @ Ts_1 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ Ts_2 @ Ts_1 )
% 0.24/0.58 => ( hoare_123228589_state @ G_12 @ Ts_2 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_124_thin,axiom,
% 0.24/0.58 ! [G_11: hoare_1167836817_state > $o,G_10: hoare_1167836817_state > $o,Ts: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( hoare_123228589_state @ G_10 @ Ts )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ G_10 @ G_11 )
% 0.24/0.58 => ( hoare_123228589_state @ G_11 @ Ts ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_125_fold__graph_OemptyI,axiom,
% 0.24/0.58 ! [F_64: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,Z_25: hoare_1167836817_state] : ( finite1316643734_state @ F_64 @ Z_25 @ bot_bo70021908tate_o @ Z_25 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_126_empty__fold__graphE,axiom,
% 0.24/0.58 ! [F_63: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,Z_24: hoare_1167836817_state,X_52: hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1316643734_state @ F_63 @ Z_24 @ bot_bo70021908tate_o @ X_52 )
% 0.24/0.58 => ( X_52 = Z_24 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_127_fold__graph_OinsertI,axiom,
% 0.24/0.58 ! [F_62: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,Z_23: hoare_1167836817_state,Y_24: hoare_1167836817_state,X_51: hoare_1167836817_state,A_109: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ~ ( member2058392318_state @ X_51 @ A_109 )
% 0.24/0.58 => ( ( finite1316643734_state @ F_62 @ Z_23 @ A_109 @ Y_24 )
% 0.24/0.58 => ( finite1316643734_state @ F_62 @ Z_23 @ ( insert2134838167_state @ X_51 @ A_109 ) @ ( F_62 @ X_51 @ Y_24 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_128_finite__subset__induct,axiom,
% 0.24/0.58 ! [P_6: ( hoare_1167836817_state > $o ) > $o,A_108: hoare_1167836817_state > $o,F_61: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ F_61 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ F_61 @ A_108 )
% 0.24/0.58 => ( ( P_6 @ bot_bo70021908tate_o )
% 0.24/0.58 => ( ! [A_59: hoare_1167836817_state,F_50: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ F_50 )
% 0.24/0.58 => ( ( member2058392318_state @ A_59 @ A_108 )
% 0.24/0.58 => ( ~ ( member2058392318_state @ A_59 @ F_50 )
% 0.24/0.58 => ( ( P_6 @ F_50 )
% 0.24/0.58 => ( P_6 @ ( insert2134838167_state @ A_59 @ F_50 ) ) ) ) ) )
% 0.24/0.58 => ( P_6 @ F_61 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_129_finite__nonempty__imp__fold1Set,axiom,
% 0.24/0.58 ! [F_60: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,A_107: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_107 )
% 0.24/0.58 => ( ( A_107 != bot_bo70021908tate_o )
% 0.24/0.58 => ( ex @ ( finite309220289_state @ F_60 @ A_107 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_130_subsetI,axiom,
% 0.24/0.58 ! [B_56: hoare_1167836817_state > $o,A_106: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ! [X: hoare_1167836817_state] :
% 0.24/0.58 ( ( member2058392318_state @ X @ A_106 )
% 0.24/0.58 => ( member2058392318_state @ X @ B_56 ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_106 @ B_56 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_131_finite_Osimps,axiom,
% 0.24/0.58 ! [A_105: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_105 )
% 0.24/0.58 <=> ( ( A_105 = bot_bo70021908tate_o )
% 0.24/0.58 | ? [A_58: hoare_1167836817_state > $o,A_59: hoare_1167836817_state] :
% 0.24/0.58 ( ( A_105
% 0.24/0.58 = ( insert2134838167_state @ A_59 @ A_58 ) )
% 0.24/0.58 & ( finite1084549118_state @ A_58 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_132_finite__induct,axiom,
% 0.24/0.58 ! [P_5: ( hoare_1167836817_state > $o ) > $o,F_59: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ F_59 )
% 0.24/0.58 => ( ( P_5 @ bot_bo70021908tate_o )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state,F_50: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ F_50 )
% 0.24/0.58 => ( ~ ( member2058392318_state @ X @ F_50 )
% 0.24/0.58 => ( ( P_5 @ F_50 )
% 0.24/0.58 => ( P_5 @ ( insert2134838167_state @ X @ F_50 ) ) ) ) )
% 0.24/0.58 => ( P_5 @ F_59 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_133_finite__imp__fold__graph,axiom,
% 0.24/0.58 ! [F_58: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,Z_22: hoare_1167836817_state,A_104: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_104 )
% 0.24/0.58 => ( ex @ ( finite1316643734_state @ F_58 @ Z_22 @ A_104 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_134_le__funI,axiom,
% 0.24/0.58 ! [F_57: hoare_1167836817_state > $o,G_9: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ! [X: hoare_1167836817_state] : ( ord_less_eq_o @ ( F_57 @ X ) @ ( G_9 @ X ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ F_57 @ G_9 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_135_fold1Set_Osimps,axiom,
% 0.24/0.58 ! [F_56: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,A1_1: hoare_1167836817_state > $o,A2_1: hoare_1167836817_state] :
% 0.24/0.58 ( ( finite309220289_state @ F_56 @ A1_1 @ A2_1 )
% 0.24/0.58 <=> ? [A_59: hoare_1167836817_state,A_58: hoare_1167836817_state > $o,X: hoare_1167836817_state] :
% 0.24/0.58 ( ( A1_1
% 0.24/0.58 = ( insert2134838167_state @ A_59 @ A_58 ) )
% 0.24/0.58 & ( A2_1 = X )
% 0.24/0.58 & ( finite1316643734_state @ F_56 @ A_59 @ A_58 @ X )
% 0.24/0.58 & ~ ( member2058392318_state @ A_59 @ A_58 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_136_fold__graph_Osimps,axiom,
% 0.24/0.58 ! [F_55: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,Z_21: hoare_1167836817_state,A1: hoare_1167836817_state > $o,A2: hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1316643734_state @ F_55 @ Z_21 @ A1 @ A2 )
% 0.24/0.58 <=> ( ( ( A1 = bot_bo70021908tate_o )
% 0.24/0.58 & ( A2 = Z_21 ) )
% 0.24/0.58 | ? [X: hoare_1167836817_state,A_58: hoare_1167836817_state > $o,Y: hoare_1167836817_state] :
% 0.24/0.58 ( ( A1
% 0.24/0.58 = ( insert2134838167_state @ X @ A_58 ) )
% 0.24/0.58 & ( A2
% 0.24/0.58 = ( F_55 @ X @ Y ) )
% 0.24/0.58 & ~ ( member2058392318_state @ X @ A_58 )
% 0.24/0.58 & ( finite1316643734_state @ F_55 @ Z_21 @ A_58 @ Y ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_137_folding__one__idem_Osubset__idem,axiom,
% 0.24/0.58 ! [B_55: hoare_1167836817_state > $o,A_103: hoare_1167836817_state > $o,F_54: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_53: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite806517911_state @ F_54 @ F_53 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_103 )
% 0.24/0.58 => ( ( B_55 != bot_bo70021908tate_o )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ B_55 @ A_103 )
% 0.24/0.58 => ( ( F_54 @ ( F_53 @ B_55 ) @ ( F_53 @ A_103 ) )
% 0.24/0.58 = ( F_53 @ A_103 ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_138_folding__one__idem_Oinsert__idem,axiom,
% 0.24/0.58 ! [X_50: hoare_1167836817_state,A_102: hoare_1167836817_state > $o,F_52: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_51: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite806517911_state @ F_52 @ F_51 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_102 )
% 0.24/0.58 => ( ( A_102 != bot_bo70021908tate_o )
% 0.24/0.58 => ( ( F_51 @ ( insert2134838167_state @ X_50 @ A_102 ) )
% 0.24/0.58 = ( F_52 @ X_50 @ ( F_51 @ A_102 ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_139_finite__ne__induct,axiom,
% 0.24/0.58 ! [P_4: ( hoare_1167836817_state > $o ) > $o,F_49: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ F_49 )
% 0.24/0.58 => ( ( F_49 != bot_bo70021908tate_o )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state] : ( P_4 @ ( insert2134838167_state @ X @ bot_bo70021908tate_o ) )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state,F_50: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ F_50 )
% 0.24/0.58 => ( ( F_50 != bot_bo70021908tate_o )
% 0.24/0.58 => ( ~ ( member2058392318_state @ X @ F_50 )
% 0.24/0.58 => ( ( P_4 @ F_50 )
% 0.24/0.58 => ( P_4 @ ( insert2134838167_state @ X @ F_50 ) ) ) ) ) )
% 0.24/0.58 => ( P_4 @ F_49 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_140_Collect__mono,axiom,
% 0.24/0.58 ! [Q_1: hoare_1167836817_state > $o,P_3: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ! [X: hoare_1167836817_state] :
% 0.24/0.58 ( ( P_3 @ X )
% 0.24/0.58 => ( Q_1 @ X ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( collec1027672124_state @ P_3 ) @ ( collec1027672124_state @ Q_1 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_141_folding__one__idem_Oidem,axiom,
% 0.24/0.58 ! [X_49: hoare_1167836817_state,F_48: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_47: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite806517911_state @ F_48 @ F_47 )
% 0.24/0.58 => ( ( F_48 @ X_49 @ X_49 )
% 0.24/0.58 = X_49 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_142_folding__one__idem_Oin__idem,axiom,
% 0.24/0.58 ! [X_48: hoare_1167836817_state,A_101: hoare_1167836817_state > $o,F_46: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_45: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite806517911_state @ F_46 @ F_45 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_101 )
% 0.24/0.58 => ( ( member2058392318_state @ X_48 @ A_101 )
% 0.24/0.58 => ( ( F_46 @ X_48 @ ( F_45 @ A_101 ) )
% 0.24/0.58 = ( F_45 @ A_101 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_143_predicate1I,axiom,
% 0.24/0.58 ! [Q: hoare_1167836817_state > $o,P_2: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ! [X: hoare_1167836817_state] :
% 0.24/0.58 ( ( P_2 @ X )
% 0.24/0.58 => ( Q @ X ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ P_2 @ Q ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_144_xt3,axiom,
% 0.24/0.58 ! [C_25: $o,F_44: ( hoare_1167836817_state > $o ) > $o,B_54: hoare_1167836817_state > $o,A_100: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ B_54 @ A_100 )
% 0.24/0.58 => ( ( ord_less_eq_o @ C_25 @ ( F_44 @ B_54 ) )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ Y @ X )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_44 @ Y ) @ ( F_44 @ X ) ) )
% 0.24/0.58 => ( ord_less_eq_o @ C_25 @ ( F_44 @ A_100 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_145_xt3,axiom,
% 0.24/0.58 ! [C_25: hoare_1167836817_state > $o,F_44: $o > hoare_1167836817_state > $o,B_54: $o,A_100: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ B_54 @ A_100 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ C_25 @ ( F_44 @ B_54 ) )
% 0.24/0.58 => ( ! [X: $o,Y: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ Y @ X )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_44 @ Y ) @ ( F_44 @ X ) ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ C_25 @ ( F_44 @ A_100 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_146_xt1_I16_J,axiom,
% 0.24/0.58 ! [C_24: $o,F_43: $o > $o,B_53: $o,A_99: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ B_53 @ A_99 )
% 0.24/0.58 => ( ( ( F_43 @ B_53 )
% 0.24/0.58 <=> C_24 )
% 0.24/0.58 => ( ! [X: $o,Y: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ Y @ X )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_43 @ Y ) @ ( F_43 @ X ) ) )
% 0.24/0.58 => ( ord_less_eq_o @ C_24 @ ( F_43 @ A_99 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_147_xt1_I16_J,axiom,
% 0.24/0.58 ! [F_43: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,C_24: hoare_1167836817_state > $o,B_53: hoare_1167836817_state > $o,A_99: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ B_53 @ A_99 )
% 0.24/0.58 => ( ( ( F_43 @ B_53 )
% 0.24/0.58 = C_24 )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ Y @ X )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_43 @ Y ) @ ( F_43 @ X ) ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ C_24 @ ( F_43 @ A_99 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_148_ord__le__eq__subst,axiom,
% 0.24/0.58 ! [C_23: $o,F_42: ( hoare_1167836817_state > $o ) > $o,A_98: hoare_1167836817_state > $o,B_52: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_98 @ B_52 )
% 0.24/0.58 => ( ( ( F_42 @ B_52 )
% 0.24/0.58 <=> C_23 )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ X @ Y )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_42 @ X ) @ ( F_42 @ Y ) ) )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_42 @ A_98 ) @ C_23 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_149_ord__le__eq__subst,axiom,
% 0.24/0.58 ! [F_42: $o > hoare_1167836817_state > $o,C_23: hoare_1167836817_state > $o,A_98: $o,B_52: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ A_98 @ B_52 )
% 0.24/0.58 => ( ( ( F_42 @ B_52 )
% 0.24/0.58 = C_23 )
% 0.24/0.58 => ( ! [X: $o,Y: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ X @ Y )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_42 @ X ) @ ( F_42 @ Y ) ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_42 @ A_98 ) @ C_23 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_150_order__subst2,axiom,
% 0.24/0.58 ! [F_41: ( hoare_1167836817_state > $o ) > $o,C_22: $o,A_97: hoare_1167836817_state > $o,B_51: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_97 @ B_51 )
% 0.24/0.58 => ( ( ord_less_eq_o @ ( F_41 @ B_51 ) @ C_22 )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ X @ Y )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_41 @ X ) @ ( F_41 @ Y ) ) )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_41 @ A_97 ) @ C_22 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_151_order__subst2,axiom,
% 0.24/0.58 ! [F_41: $o > hoare_1167836817_state > $o,C_22: hoare_1167836817_state > $o,A_97: $o,B_51: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ A_97 @ B_51 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ ( F_41 @ B_51 ) @ C_22 )
% 0.24/0.58 => ( ! [X: $o,Y: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ X @ Y )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_41 @ X ) @ ( F_41 @ Y ) ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_41 @ A_97 ) @ C_22 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_152_ord__eq__le__subst,axiom,
% 0.24/0.58 ! [C_21: hoare_1167836817_state > $o,F_40: ( hoare_1167836817_state > $o ) > $o,B_50: hoare_1167836817_state > $o,A_96: $o] :
% 0.24/0.58 ( ( A_96
% 0.24/0.58 <=> ( F_40 @ B_50 ) )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ B_50 @ C_21 )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ X @ Y )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_40 @ X ) @ ( F_40 @ Y ) ) )
% 0.24/0.58 => ( ord_less_eq_o @ A_96 @ ( F_40 @ C_21 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_153_ord__eq__le__subst,axiom,
% 0.24/0.58 ! [C_21: $o,A_96: hoare_1167836817_state > $o,F_40: $o > hoare_1167836817_state > $o,B_50: $o] :
% 0.24/0.58 ( ( A_96
% 0.24/0.58 = ( F_40 @ B_50 ) )
% 0.24/0.58 => ( ( ord_less_eq_o @ B_50 @ C_21 )
% 0.24/0.58 => ( ! [X: $o,Y: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ X @ Y )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_40 @ X ) @ ( F_40 @ Y ) ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_96 @ ( F_40 @ C_21 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_154_xt2,axiom,
% 0.24/0.58 ! [C_20: $o,F_39: $o > hoare_1167836817_state > $o,B_49: $o,A_95: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ ( F_39 @ B_49 ) @ A_95 )
% 0.24/0.58 => ( ( ord_less_eq_o @ C_20 @ B_49 )
% 0.24/0.58 => ( ! [X: $o,Y: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ Y @ X )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_39 @ Y ) @ ( F_39 @ X ) ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_39 @ C_20 ) @ A_95 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_155_xt2,axiom,
% 0.24/0.58 ! [C_20: hoare_1167836817_state > $o,F_39: ( hoare_1167836817_state > $o ) > $o,B_49: hoare_1167836817_state > $o,A_95: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ ( F_39 @ B_49 ) @ A_95 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ C_20 @ B_49 )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ Y @ X )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_39 @ Y ) @ ( F_39 @ X ) ) )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_39 @ C_20 ) @ A_95 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_156_xt1_I15_J,axiom,
% 0.24/0.58 ! [C_19: $o,F_38: $o > $o,B_48: $o,A_94: $o] :
% 0.24/0.58 ( ( A_94
% 0.24/0.58 <=> ( F_38 @ B_48 ) )
% 0.24/0.58 => ( ( ord_less_eq_o @ C_19 @ B_48 )
% 0.24/0.58 => ( ! [X: $o,Y: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ Y @ X )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_38 @ Y ) @ ( F_38 @ X ) ) )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_38 @ C_19 ) @ A_94 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_157_xt1_I15_J,axiom,
% 0.24/0.58 ! [C_19: hoare_1167836817_state > $o,A_94: hoare_1167836817_state > $o,F_38: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,B_48: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_94
% 0.24/0.58 = ( F_38 @ B_48 ) )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ C_19 @ B_48 )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ Y @ X )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_38 @ Y ) @ ( F_38 @ X ) ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_38 @ C_19 ) @ A_94 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_158_order__subst1,axiom,
% 0.24/0.58 ! [C_18: $o,A_93: hoare_1167836817_state > $o,F_37: $o > hoare_1167836817_state > $o,B_47: $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_93 @ ( F_37 @ B_47 ) )
% 0.24/0.58 => ( ( ord_less_eq_o @ B_47 @ C_18 )
% 0.24/0.58 => ( ! [X: $o,Y: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ X @ Y )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F_37 @ X ) @ ( F_37 @ Y ) ) )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_93 @ ( F_37 @ C_18 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_159_order__subst1,axiom,
% 0.24/0.58 ! [C_18: hoare_1167836817_state > $o,A_93: $o,F_37: ( hoare_1167836817_state > $o ) > $o,B_47: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ A_93 @ ( F_37 @ B_47 ) )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ B_47 @ C_18 )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ X @ Y )
% 0.24/0.58 => ( ord_less_eq_o @ ( F_37 @ X ) @ ( F_37 @ Y ) ) )
% 0.24/0.58 => ( ord_less_eq_o @ A_93 @ ( F_37 @ C_18 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_160_semilattice__big_OF__eq,axiom,
% 0.24/0.58 ! [A_92: hoare_1167836817_state > $o,F_36: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_35: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( big_se1603066171_state @ F_36 @ F_35 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_92 )
% 0.24/0.58 => ( ( F_35 @ A_92 )
% 0.24/0.58 = ( finite1646097201_state @ F_36 @ A_92 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_161_folding__one_Oremove,axiom,
% 0.24/0.58 ! [X_47: hoare_1167836817_state,A_91: hoare_1167836817_state > $o,F_34: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_33: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1074406356_state @ F_34 @ F_33 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_91 )
% 0.24/0.58 => ( ( member2058392318_state @ X_47 @ A_91 )
% 0.24/0.58 => ( ( ( ( minus_2107060239tate_o @ A_91 @ ( insert2134838167_state @ X_47 @ bot_bo70021908tate_o ) )
% 0.24/0.58 = bot_bo70021908tate_o )
% 0.24/0.58 => ( ( F_33 @ A_91 )
% 0.24/0.58 = X_47 ) )
% 0.24/0.58 & ( ( ( minus_2107060239tate_o @ A_91 @ ( insert2134838167_state @ X_47 @ bot_bo70021908tate_o ) )
% 0.24/0.58 != bot_bo70021908tate_o )
% 0.24/0.58 => ( ( F_33 @ A_91 )
% 0.24/0.58 = ( F_34 @ X_47 @ ( F_33 @ ( minus_2107060239tate_o @ A_91 @ ( insert2134838167_state @ X_47 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_162_folding__one_Oinsert__remove,axiom,
% 0.24/0.58 ! [X_46: hoare_1167836817_state,A_90: hoare_1167836817_state > $o,F_32: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_31: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1074406356_state @ F_32 @ F_31 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_90 )
% 0.24/0.58 => ( ( ( ( minus_2107060239tate_o @ A_90 @ ( insert2134838167_state @ X_46 @ bot_bo70021908tate_o ) )
% 0.24/0.58 = bot_bo70021908tate_o )
% 0.24/0.58 => ( ( F_31 @ ( insert2134838167_state @ X_46 @ A_90 ) )
% 0.24/0.58 = X_46 ) )
% 0.24/0.58 & ( ( ( minus_2107060239tate_o @ A_90 @ ( insert2134838167_state @ X_46 @ bot_bo70021908tate_o ) )
% 0.24/0.58 != bot_bo70021908tate_o )
% 0.24/0.58 => ( ( F_31 @ ( insert2134838167_state @ X_46 @ A_90 ) )
% 0.24/0.58 = ( F_32 @ X_46 @ ( F_31 @ ( minus_2107060239tate_o @ A_90 @ ( insert2134838167_state @ X_46 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_163_DiffI,axiom,
% 0.24/0.58 ! [B_46: hoare_1167836817_state > $o,C_17: hoare_1167836817_state,A_89: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ C_17 @ A_89 )
% 0.24/0.58 => ( ~ ( member2058392318_state @ C_17 @ B_46 )
% 0.24/0.58 => ( member2058392318_state @ C_17 @ ( minus_2107060239tate_o @ A_89 @ B_46 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_164_DiffE,axiom,
% 0.24/0.58 ! [C_16: hoare_1167836817_state,A_88: hoare_1167836817_state > $o,B_45: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ C_16 @ ( minus_2107060239tate_o @ A_88 @ B_45 ) )
% 0.24/0.58 => ~ ( ( member2058392318_state @ C_16 @ A_88 )
% 0.24/0.58 => ( member2058392318_state @ C_16 @ B_45 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_165_finite__Diff,axiom,
% 0.24/0.58 ! [B_44: hoare_1167836817_state > $o,A_87: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_87 )
% 0.24/0.58 => ( finite1084549118_state @ ( minus_2107060239tate_o @ A_87 @ B_44 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_166_set__diff__eq,axiom,
% 0.24/0.58 ! [A_86: hoare_1167836817_state > $o,B_43: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( minus_2107060239tate_o @ A_86 @ B_43 )
% 0.24/0.58 = ( collec1027672124_state
% 0.24/0.58 @ ^ [X: hoare_1167836817_state] : ( (&) @ ( member2058392318_state @ X @ A_86 ) @ ( (~) @ ( member2058392318_state @ X @ B_43 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_167_Diff__iff,axiom,
% 0.24/0.58 ! [C_15: hoare_1167836817_state,A_85: hoare_1167836817_state > $o,B_42: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ C_15 @ ( minus_2107060239tate_o @ A_85 @ B_42 ) )
% 0.24/0.58 <=> ( ( member2058392318_state @ C_15 @ A_85 )
% 0.24/0.58 & ~ ( member2058392318_state @ C_15 @ B_42 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_168_Diff__idemp,axiom,
% 0.24/0.58 ! [A_84: hoare_1167836817_state > $o,B_41: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A_84 @ B_41 ) @ B_41 )
% 0.24/0.58 = ( minus_2107060239tate_o @ A_84 @ B_41 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_169_DiffD1,axiom,
% 0.24/0.58 ! [C_14: hoare_1167836817_state,A_83: hoare_1167836817_state > $o,B_40: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ C_14 @ ( minus_2107060239tate_o @ A_83 @ B_40 ) )
% 0.24/0.58 => ( member2058392318_state @ C_14 @ A_83 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_170_DiffD2,axiom,
% 0.24/0.58 ! [C_13: hoare_1167836817_state,A_82: hoare_1167836817_state > $o,B_39: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ C_13 @ ( minus_2107060239tate_o @ A_82 @ B_39 ) )
% 0.24/0.58 => ~ ( member2058392318_state @ C_13 @ B_39 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_171_empty__Diff,axiom,
% 0.24/0.58 ! [A_81: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( minus_2107060239tate_o @ bot_bo70021908tate_o @ A_81 )
% 0.24/0.58 = bot_bo70021908tate_o ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_172_Diff__empty,axiom,
% 0.24/0.58 ! [A_80: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( minus_2107060239tate_o @ A_80 @ bot_bo70021908tate_o )
% 0.24/0.58 = A_80 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_173_Diff__cancel,axiom,
% 0.24/0.58 ! [A_79: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( minus_2107060239tate_o @ A_79 @ A_79 )
% 0.24/0.58 = bot_bo70021908tate_o ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_174_finite__Diff2,axiom,
% 0.24/0.58 ! [A_78: hoare_1167836817_state > $o,B_38: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ B_38 )
% 0.24/0.58 => ( ( finite1084549118_state @ ( minus_2107060239tate_o @ A_78 @ B_38 ) )
% 0.24/0.58 <=> ( finite1084549118_state @ A_78 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_175_insert__Diff__if,axiom,
% 0.24/0.58 ! [A_77: hoare_1167836817_state > $o,X_45: hoare_1167836817_state,B_37: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ( member2058392318_state @ X_45 @ B_37 )
% 0.24/0.58 => ( ( minus_2107060239tate_o @ ( insert2134838167_state @ X_45 @ A_77 ) @ B_37 )
% 0.24/0.58 = ( minus_2107060239tate_o @ A_77 @ B_37 ) ) )
% 0.24/0.58 & ( ~ ( member2058392318_state @ X_45 @ B_37 )
% 0.24/0.58 => ( ( minus_2107060239tate_o @ ( insert2134838167_state @ X_45 @ A_77 ) @ B_37 )
% 0.24/0.58 = ( insert2134838167_state @ X_45 @ ( minus_2107060239tate_o @ A_77 @ B_37 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_176_insert__Diff1,axiom,
% 0.24/0.58 ! [A_76: hoare_1167836817_state > $o,X_44: hoare_1167836817_state,B_36: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ X_44 @ B_36 )
% 0.24/0.58 => ( ( minus_2107060239tate_o @ ( insert2134838167_state @ X_44 @ A_76 ) @ B_36 )
% 0.24/0.58 = ( minus_2107060239tate_o @ A_76 @ B_36 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_177_Diff__subset,axiom,
% 0.24/0.58 ! [A_75: hoare_1167836817_state > $o,B_35: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( minus_2107060239tate_o @ A_75 @ B_35 ) @ A_75 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_178_Diff__mono,axiom,
% 0.24/0.58 ! [D: hoare_1167836817_state > $o,B_34: hoare_1167836817_state > $o,A_74: hoare_1167836817_state > $o,C_12: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_74 @ C_12 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ D @ B_34 )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( minus_2107060239tate_o @ A_74 @ B_34 ) @ ( minus_2107060239tate_o @ C_12 @ D ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_179_double__diff,axiom,
% 0.24/0.58 ! [C_11: hoare_1167836817_state > $o,A_73: hoare_1167836817_state > $o,B_33: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_73 @ B_33 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ B_33 @ C_11 )
% 0.24/0.58 => ( ( minus_2107060239tate_o @ B_33 @ ( minus_2107060239tate_o @ C_11 @ A_73 ) )
% 0.24/0.58 = A_73 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_180_Diff__insert,axiom,
% 0.24/0.58 ! [A_72: hoare_1167836817_state > $o,A_71: hoare_1167836817_state,B_32: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( minus_2107060239tate_o @ A_72 @ ( insert2134838167_state @ A_71 @ B_32 ) )
% 0.24/0.58 = ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A_72 @ B_32 ) @ ( insert2134838167_state @ A_71 @ bot_bo70021908tate_o ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_181_Diff__insert2,axiom,
% 0.24/0.58 ! [A_70: hoare_1167836817_state > $o,A_69: hoare_1167836817_state,B_31: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( minus_2107060239tate_o @ A_70 @ ( insert2134838167_state @ A_69 @ B_31 ) )
% 0.24/0.58 = ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A_70 @ ( insert2134838167_state @ A_69 @ bot_bo70021908tate_o ) ) @ B_31 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_182_insert__Diff__single,axiom,
% 0.24/0.58 ! [A_68: hoare_1167836817_state,A_67: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( insert2134838167_state @ A_68 @ ( minus_2107060239tate_o @ A_67 @ ( insert2134838167_state @ A_68 @ bot_bo70021908tate_o ) ) )
% 0.24/0.58 = ( insert2134838167_state @ A_68 @ A_67 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_183_Diff__insert__absorb,axiom,
% 0.24/0.58 ! [X_43: hoare_1167836817_state,A_66: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ~ ( member2058392318_state @ X_43 @ A_66 )
% 0.24/0.58 => ( ( minus_2107060239tate_o @ ( insert2134838167_state @ X_43 @ A_66 ) @ ( insert2134838167_state @ X_43 @ bot_bo70021908tate_o ) )
% 0.24/0.58 = A_66 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_184_insert__Diff,axiom,
% 0.24/0.58 ! [A_65: hoare_1167836817_state,A_64: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( member2058392318_state @ A_65 @ A_64 )
% 0.24/0.58 => ( ( insert2134838167_state @ A_65 @ ( minus_2107060239tate_o @ A_64 @ ( insert2134838167_state @ A_65 @ bot_bo70021908tate_o ) ) )
% 0.24/0.58 = A_64 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_185_finite__Diff__insert,axiom,
% 0.24/0.58 ! [A_63: hoare_1167836817_state > $o,A_62: hoare_1167836817_state,B_30: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ ( minus_2107060239tate_o @ A_63 @ ( insert2134838167_state @ A_62 @ B_30 ) ) )
% 0.24/0.58 <=> ( finite1084549118_state @ ( minus_2107060239tate_o @ A_63 @ B_30 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_186_subset__insert__iff,axiom,
% 0.24/0.58 ! [A_61: hoare_1167836817_state > $o,X_42: hoare_1167836817_state,B_29: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_61 @ ( insert2134838167_state @ X_42 @ B_29 ) )
% 0.24/0.58 <=> ( ( ( member2058392318_state @ X_42 @ A_61 )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( minus_2107060239tate_o @ A_61 @ ( insert2134838167_state @ X_42 @ bot_bo70021908tate_o ) ) @ B_29 ) )
% 0.24/0.58 & ( ~ ( member2058392318_state @ X_42 @ A_61 )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_61 @ B_29 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_187_diff__single__insert,axiom,
% 0.24/0.58 ! [A_60: hoare_1167836817_state > $o,X_41: hoare_1167836817_state,B_28: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ ( minus_2107060239tate_o @ A_60 @ ( insert2134838167_state @ X_41 @ bot_bo70021908tate_o ) ) @ B_28 )
% 0.24/0.58 => ( ( member2058392318_state @ X_41 @ A_60 )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_60 @ ( insert2134838167_state @ X_41 @ B_28 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_188_finite__empty__induct,axiom,
% 0.24/0.58 ! [P_1: ( hoare_1167836817_state > $o ) > $o,A_57: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_57 )
% 0.24/0.58 => ( ( P_1 @ A_57 )
% 0.24/0.58 => ( ! [A_59: hoare_1167836817_state,A_58: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_58 )
% 0.24/0.58 => ( ( member2058392318_state @ A_59 @ A_58 )
% 0.24/0.58 => ( ( P_1 @ A_58 )
% 0.24/0.58 => ( P_1 @ ( minus_2107060239tate_o @ A_58 @ ( insert2134838167_state @ A_59 @ bot_bo70021908tate_o ) ) ) ) ) )
% 0.24/0.58 => ( P_1 @ bot_bo70021908tate_o ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_189_minus__apply,axiom,
% 0.24/0.58 ! [A_56: hoare_1167836817_state > $o,B_27: hoare_1167836817_state > $o,X_40: hoare_1167836817_state] :
% 0.24/0.58 ( ( minus_2107060239tate_o @ A_56 @ B_27 @ X_40 )
% 0.24/0.58 <=> ( minus_minus_o @ ( A_56 @ X_40 ) @ ( B_27 @ X_40 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_190_fun__diff__def,axiom,
% 0.24/0.58 ! [A_55: hoare_1167836817_state > $o,B_26: hoare_1167836817_state > $o,X: hoare_1167836817_state] :
% 0.24/0.58 ( ( minus_2107060239tate_o @ A_55 @ B_26 @ X )
% 0.24/0.58 <=> ( minus_minus_o @ ( A_55 @ X ) @ ( B_26 @ X ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_191_comp__fun__commute_Ofold__graph__insertE__aux,axiom,
% 0.24/0.58 ! [A_54: hoare_1167836817_state,Z_20: hoare_1167836817_state,A_53: hoare_1167836817_state > $o,Y_22: hoare_1167836817_state,F_30: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1091222817_state @ F_30 )
% 0.24/0.58 => ( ( finite1316643734_state @ F_30 @ Z_20 @ A_53 @ Y_22 )
% 0.24/0.58 => ( ( member2058392318_state @ A_54 @ A_53 )
% 0.24/0.58 => ? [Y_23: hoare_1167836817_state] :
% 0.24/0.58 ( ( Y_22
% 0.24/0.58 = ( F_30 @ A_54 @ Y_23 ) )
% 0.24/0.58 & ( finite1316643734_state @ F_30 @ Z_20 @ ( minus_2107060239tate_o @ A_53 @ ( insert2134838167_state @ A_54 @ bot_bo70021908tate_o ) ) @ Y_23 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_192_comp__fun__commute_Ofun__left__comm,axiom,
% 0.24/0.58 ! [X_39: hoare_1167836817_state,Y_21: hoare_1167836817_state,Z_19: hoare_1167836817_state,F_29: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1091222817_state @ F_29 )
% 0.24/0.58 => ( ( F_29 @ X_39 @ ( F_29 @ Y_21 @ Z_19 ) )
% 0.24/0.58 = ( F_29 @ Y_21 @ ( F_29 @ X_39 @ Z_19 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_193_comp__fun__commute_Ofold__graph__determ,axiom,
% 0.24/0.58 ! [Y_20: hoare_1167836817_state,Z_18: hoare_1167836817_state,A_52: hoare_1167836817_state > $o,X_38: hoare_1167836817_state,F_28: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1091222817_state @ F_28 )
% 0.24/0.58 => ( ( finite1316643734_state @ F_28 @ Z_18 @ A_52 @ X_38 )
% 0.24/0.58 => ( ( finite1316643734_state @ F_28 @ Z_18 @ A_52 @ Y_20 )
% 0.24/0.58 => ( Y_20 = X_38 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_194_comp__fun__commute_Ofold__graph__insertE,axiom,
% 0.24/0.58 ! [Z_17: hoare_1167836817_state,X_37: hoare_1167836817_state,A_51: hoare_1167836817_state > $o,V: hoare_1167836817_state,F_27: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1091222817_state @ F_27 )
% 0.24/0.58 => ( ( finite1316643734_state @ F_27 @ Z_17 @ ( insert2134838167_state @ X_37 @ A_51 ) @ V )
% 0.24/0.58 => ( ~ ( member2058392318_state @ X_37 @ A_51 )
% 0.24/0.58 => ~ ! [Y: hoare_1167836817_state] :
% 0.24/0.58 ( ( V
% 0.24/0.58 = ( F_27 @ X_37 @ Y ) )
% 0.24/0.58 => ~ ( finite1316643734_state @ F_27 @ Z_17 @ A_51 @ Y ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_195_min__leastR,axiom,
% 0.24/0.58 ! [X_36: $o,Least_3: $o] :
% 0.24/0.58 ( ( all1 @ ( ord_less_eq_o @ Least_3 ) )
% 0.24/0.58 => ( ( ord_min_o @ X_36 @ Least_3 )
% 0.24/0.58 <=> Least_3 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_196_min__leastR,axiom,
% 0.24/0.58 ! [X_36: hoare_1167836817_state > $o,Least_3: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( all2 @ ( ord_le827224136tate_o @ Least_3 ) )
% 0.24/0.58 => ( ( ord_mi1697686287tate_o @ X_36 @ Least_3 )
% 0.24/0.58 = Least_3 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_197_min__leastL,axiom,
% 0.24/0.58 ! [X_35: $o,Least_2: $o] :
% 0.24/0.58 ( ( all1 @ ( ord_less_eq_o @ Least_2 ) )
% 0.24/0.58 => ( ( ord_min_o @ Least_2 @ X_35 )
% 0.24/0.58 <=> Least_2 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_198_min__leastL,axiom,
% 0.24/0.58 ! [X_35: hoare_1167836817_state > $o,Least_2: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( all2 @ ( ord_le827224136tate_o @ Least_2 ) )
% 0.24/0.58 => ( ( ord_mi1697686287tate_o @ Least_2 @ X_35 )
% 0.24/0.58 = Least_2 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_199_min__ord__min,axiom,
% 0.24/0.58 ( ord_min_o
% 0.24/0.58 = ( min_o @ ord_less_eq_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_200_min__ord__min,axiom,
% 0.24/0.58 ( ord_mi1697686287tate_o
% 0.24/0.58 = ( min_Ho1955171539tate_o @ ord_le827224136tate_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_201_comp__fun__commute_Ofold__insert__remove,axiom,
% 0.24/0.58 ! [Z_16: hoare_1167836817_state,X_34: hoare_1167836817_state,A_50: hoare_1167836817_state > $o,F_26: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1091222817_state @ F_26 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_50 )
% 0.24/0.58 => ( ( finite1731015960_state @ F_26 @ Z_16 @ ( insert2134838167_state @ X_34 @ A_50 ) )
% 0.24/0.58 = ( F_26 @ X_34 @ ( finite1731015960_state @ F_26 @ Z_16 @ ( minus_2107060239tate_o @ A_50 @ ( insert2134838167_state @ X_34 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_202_comp__fun__commute_Ofold__rec,axiom,
% 0.24/0.58 ! [Z_15: hoare_1167836817_state,X_33: hoare_1167836817_state,A_49: hoare_1167836817_state > $o,F_25: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1091222817_state @ F_25 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_49 )
% 0.24/0.58 => ( ( member2058392318_state @ X_33 @ A_49 )
% 0.24/0.58 => ( ( finite1731015960_state @ F_25 @ Z_15 @ A_49 )
% 0.24/0.58 = ( F_25 @ X_33 @ ( finite1731015960_state @ F_25 @ Z_15 @ ( minus_2107060239tate_o @ A_49 @ ( insert2134838167_state @ X_33 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_203_fold__empty,axiom,
% 0.24/0.58 ! [F_24: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,Z_14: hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1731015960_state @ F_24 @ Z_14 @ bot_bo70021908tate_o )
% 0.24/0.58 = Z_14 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_204_comp__fun__commute_Ofold__fun__comm,axiom,
% 0.24/0.58 ! [X_32: hoare_1167836817_state,Z_13: hoare_1167836817_state,A_48: hoare_1167836817_state > $o,F_23: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1091222817_state @ F_23 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_48 )
% 0.24/0.58 => ( ( F_23 @ X_32 @ ( finite1731015960_state @ F_23 @ Z_13 @ A_48 ) )
% 0.24/0.58 = ( finite1731015960_state @ F_23 @ ( F_23 @ X_32 @ Z_13 ) @ A_48 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_205_comp__fun__commute_Ofold__equality,axiom,
% 0.24/0.58 ! [Z_12: hoare_1167836817_state,A_47: hoare_1167836817_state > $o,Y_19: hoare_1167836817_state,F_22: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1091222817_state @ F_22 )
% 0.24/0.58 => ( ( finite1316643734_state @ F_22 @ Z_12 @ A_47 @ Y_19 )
% 0.24/0.58 => ( ( finite1731015960_state @ F_22 @ Z_12 @ A_47 )
% 0.24/0.58 = Y_19 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_206_comp__fun__commute_Ofold__insert2,axiom,
% 0.24/0.58 ! [Z_11: hoare_1167836817_state,X_31: hoare_1167836817_state,A_46: hoare_1167836817_state > $o,F_21: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1091222817_state @ F_21 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_46 )
% 0.24/0.58 => ( ~ ( member2058392318_state @ X_31 @ A_46 )
% 0.24/0.58 => ( ( finite1731015960_state @ F_21 @ Z_11 @ ( insert2134838167_state @ X_31 @ A_46 ) )
% 0.24/0.58 = ( finite1731015960_state @ F_21 @ ( F_21 @ X_31 @ Z_11 ) @ A_46 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_207_comp__fun__commute_Ofold__insert,axiom,
% 0.24/0.58 ! [Z_10: hoare_1167836817_state,X_30: hoare_1167836817_state,A_45: hoare_1167836817_state > $o,F_20: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1091222817_state @ F_20 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_45 )
% 0.24/0.58 => ( ~ ( member2058392318_state @ X_30 @ A_45 )
% 0.24/0.58 => ( ( finite1731015960_state @ F_20 @ Z_10 @ ( insert2134838167_state @ X_30 @ A_45 ) )
% 0.24/0.58 = ( F_20 @ X_30 @ ( finite1731015960_state @ F_20 @ Z_10 @ A_45 ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_208_folding__one_Oeq__fold_H,axiom,
% 0.24/0.58 ! [X_29: hoare_1167836817_state,A_44: hoare_1167836817_state > $o,F_19: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_18: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1074406356_state @ F_19 @ F_18 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_44 )
% 0.24/0.58 => ( ~ ( member2058392318_state @ X_29 @ A_44 )
% 0.24/0.58 => ( ( F_18 @ ( insert2134838167_state @ X_29 @ A_44 ) )
% 0.24/0.58 = ( finite1731015960_state @ F_19 @ X_29 @ A_44 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_209_folding__one__idem_Oeq__fold__idem_H,axiom,
% 0.24/0.58 ! [A_43: hoare_1167836817_state,A_42: hoare_1167836817_state > $o,F_17: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_16: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite806517911_state @ F_17 @ F_16 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_42 )
% 0.24/0.58 => ( ( F_16 @ ( insert2134838167_state @ A_43 @ A_42 ) )
% 0.24/0.58 = ( finite1731015960_state @ F_17 @ A_43 @ A_42 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_210_comp__fun__commute_Ofold__graph__fold,axiom,
% 0.24/0.58 ! [Z_9: hoare_1167836817_state,A_41: hoare_1167836817_state > $o,F_15: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1091222817_state @ F_15 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_41 )
% 0.24/0.58 => ( finite1316643734_state @ F_15 @ Z_9 @ A_41 @ ( finite1731015960_state @ F_15 @ Z_9 @ A_41 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_211_comp__fun__idem_Ofold__insert__idem,axiom,
% 0.24/0.58 ! [Z_8: hoare_1167836817_state,X_28: hoare_1167836817_state,A_40: hoare_1167836817_state > $o,F_14: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1900754844_state @ F_14 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_40 )
% 0.24/0.58 => ( ( finite1731015960_state @ F_14 @ Z_8 @ ( insert2134838167_state @ X_28 @ A_40 ) )
% 0.24/0.58 = ( F_14 @ X_28 @ ( finite1731015960_state @ F_14 @ Z_8 @ A_40 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_212_comp__fun__idem_Ofold__insert__idem,axiom,
% 0.24/0.58 ! [Z_8: hoare_1167836817_state > $o,X_28: hoare_1167836817_state,A_40: hoare_1167836817_state > $o,F_14: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite856902323tate_o @ F_14 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_40 )
% 0.24/0.58 => ( ( finite291020855tate_o @ F_14 @ Z_8 @ ( insert2134838167_state @ X_28 @ A_40 ) )
% 0.24/0.58 = ( F_14 @ X_28 @ ( finite291020855tate_o @ F_14 @ Z_8 @ A_40 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_213_comp__fun__idem_Ofold__insert__idem2,axiom,
% 0.24/0.58 ! [Z_7: hoare_1167836817_state,X_27: hoare_1167836817_state,A_39: hoare_1167836817_state > $o,F_13: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
% 0.24/0.58 ( ( finite1900754844_state @ F_13 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_39 )
% 0.24/0.58 => ( ( finite1731015960_state @ F_13 @ Z_7 @ ( insert2134838167_state @ X_27 @ A_39 ) )
% 0.24/0.58 = ( finite1731015960_state @ F_13 @ ( F_13 @ X_27 @ Z_7 ) @ A_39 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_214_comp__fun__idem_Ofold__insert__idem2,axiom,
% 0.24/0.58 ! [Z_7: hoare_1167836817_state > $o,X_27: hoare_1167836817_state,A_39: hoare_1167836817_state > $o,F_13: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite856902323tate_o @ F_13 )
% 0.24/0.58 => ( ( finite1084549118_state @ A_39 )
% 0.24/0.58 => ( ( finite291020855tate_o @ F_13 @ Z_7 @ ( insert2134838167_state @ X_27 @ A_39 ) )
% 0.24/0.58 = ( finite291020855tate_o @ F_13 @ ( F_13 @ X_27 @ Z_7 ) @ A_39 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_215_comp__fun__idem_Ofun__left__idem,axiom,
% 0.24/0.58 ! [X_26: hoare_1167836817_state,Z_6: hoare_1167836817_state > $o,F_12: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite856902323tate_o @ F_12 )
% 0.24/0.58 => ( ( F_12 @ X_26 @ ( F_12 @ X_26 @ Z_6 ) )
% 0.24/0.58 = ( F_12 @ X_26 @ Z_6 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_216_comp__fun__idem__insert,axiom,
% 0.24/0.58 finite856902323tate_o @ insert2134838167_state ).
% 0.24/0.58
% 0.24/0.58 thf(fact_217_setsum__diff1__nat,axiom,
% 0.24/0.58 ! [F_11: hoare_1167836817_state > nat,A_38: hoare_1167836817_state,A_37: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ( member2058392318_state @ A_38 @ A_37 )
% 0.24/0.58 => ( ( big_co337839062te_nat @ F_11 @ ( minus_2107060239tate_o @ A_37 @ ( insert2134838167_state @ A_38 @ bot_bo70021908tate_o ) ) )
% 0.24/0.58 = ( minus_minus_nat @ ( big_co337839062te_nat @ F_11 @ A_37 ) @ ( F_11 @ A_38 ) ) ) )
% 0.24/0.58 & ( ~ ( member2058392318_state @ A_38 @ A_37 )
% 0.24/0.58 => ( ( big_co337839062te_nat @ F_11 @ ( minus_2107060239tate_o @ A_37 @ ( insert2134838167_state @ A_38 @ bot_bo70021908tate_o ) ) )
% 0.24/0.58 = ( big_co337839062te_nat @ F_11 @ A_37 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_218_setsum__diff__nat,axiom,
% 0.24/0.58 ! [F_10: hoare_1167836817_state > nat,A_36: hoare_1167836817_state > $o,B_25: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ B_25 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ B_25 @ A_36 )
% 0.24/0.58 => ( ( big_co337839062te_nat @ F_10 @ ( minus_2107060239tate_o @ A_36 @ B_25 ) )
% 0.24/0.58 = ( minus_minus_nat @ ( big_co337839062te_nat @ F_10 @ A_36 ) @ ( big_co337839062te_nat @ F_10 @ B_25 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_219_setsum_Ocong,axiom,
% 0.24/0.58 ! [G_8: hoare_1167836817_state > nat,H_1: hoare_1167836817_state > nat,A_35: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_35 )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state] :
% 0.24/0.58 ( ( member2058392318_state @ X @ A_35 )
% 0.24/0.58 => ( ( G_8 @ X )
% 0.24/0.58 = ( H_1 @ X ) ) )
% 0.24/0.58 => ( ( big_co337839062te_nat @ G_8 @ A_35 )
% 0.24/0.58 = ( big_co337839062te_nat @ H_1 @ A_35 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_220_max__leastR,axiom,
% 0.24/0.58 ! [X_25: $o,Least_1: $o] :
% 0.24/0.58 ( ( all1 @ ( ord_less_eq_o @ Least_1 ) )
% 0.24/0.58 => ( ( ord_max_o @ X_25 @ Least_1 )
% 0.24/0.58 <=> X_25 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_221_max__leastR,axiom,
% 0.24/0.58 ! [X_25: hoare_1167836817_state > $o,Least_1: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( all2 @ ( ord_le827224136tate_o @ Least_1 ) )
% 0.24/0.58 => ( ( ord_ma164008317tate_o @ X_25 @ Least_1 )
% 0.24/0.58 = X_25 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_222_max__leastL,axiom,
% 0.24/0.58 ! [X_24: $o,Least: $o] :
% 0.24/0.58 ( ( all1 @ ( ord_less_eq_o @ Least ) )
% 0.24/0.58 => ( ( ord_max_o @ Least @ X_24 )
% 0.24/0.58 <=> X_24 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_223_max__leastL,axiom,
% 0.24/0.58 ! [X_24: hoare_1167836817_state > $o,Least: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( all2 @ ( ord_le827224136tate_o @ Least ) )
% 0.24/0.58 => ( ( ord_ma164008317tate_o @ Least @ X_24 )
% 0.24/0.58 = X_24 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_224_max__ord__max,axiom,
% 0.24/0.58 ( ord_max_o
% 0.24/0.58 = ( max_o @ ord_less_eq_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_225_max__ord__max,axiom,
% 0.24/0.58 ( ord_ma164008317tate_o
% 0.24/0.58 = ( max_Ho421493569tate_o @ ord_le827224136tate_o ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_226_setsum_Oremove,axiom,
% 0.24/0.58 ! [G_7: hoare_1167836817_state > nat,X_23: hoare_1167836817_state,A_34: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_34 )
% 0.24/0.58 => ( ( member2058392318_state @ X_23 @ A_34 )
% 0.24/0.58 => ( ( big_co337839062te_nat @ G_7 @ A_34 )
% 0.24/0.58 = ( plus_plus_nat @ ( G_7 @ X_23 ) @ ( big_co337839062te_nat @ G_7 @ ( minus_2107060239tate_o @ A_34 @ ( insert2134838167_state @ X_23 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_227_setsum__diff1_H,axiom,
% 0.24/0.58 ! [F_9: hoare_1167836817_state > nat,A_33: hoare_1167836817_state,A_32: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_32 )
% 0.24/0.58 => ( ( member2058392318_state @ A_33 @ A_32 )
% 0.24/0.58 => ( ( big_co337839062te_nat @ F_9 @ A_32 )
% 0.24/0.58 = ( plus_plus_nat @ ( F_9 @ A_33 ) @ ( big_co337839062te_nat @ F_9 @ ( minus_2107060239tate_o @ A_32 @ ( insert2134838167_state @ A_33 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_228_setsum_Oinsert,axiom,
% 0.24/0.58 ! [G_6: hoare_1167836817_state > nat,X_22: hoare_1167836817_state,A_31: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_31 )
% 0.24/0.58 => ( ~ ( member2058392318_state @ X_22 @ A_31 )
% 0.24/0.58 => ( ( big_co337839062te_nat @ G_6 @ ( insert2134838167_state @ X_22 @ A_31 ) )
% 0.24/0.58 = ( plus_plus_nat @ ( G_6 @ X_22 ) @ ( big_co337839062te_nat @ G_6 @ A_31 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_229_setsum__insert,axiom,
% 0.24/0.58 ! [F_8: hoare_1167836817_state > nat,A_30: hoare_1167836817_state,F_7: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ F_7 )
% 0.24/0.58 => ( ~ ( member2058392318_state @ A_30 @ F_7 )
% 0.24/0.58 => ( ( big_co337839062te_nat @ F_8 @ ( insert2134838167_state @ A_30 @ F_7 ) )
% 0.24/0.58 = ( plus_plus_nat @ ( F_8 @ A_30 ) @ ( big_co337839062te_nat @ F_8 @ F_7 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_230_setsum_Oinsert__remove,axiom,
% 0.24/0.58 ! [G_5: hoare_1167836817_state > nat,X_21: hoare_1167836817_state,A_29: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_29 )
% 0.24/0.58 => ( ( big_co337839062te_nat @ G_5 @ ( insert2134838167_state @ X_21 @ A_29 ) )
% 0.24/0.58 = ( plus_plus_nat @ ( G_5 @ X_21 ) @ ( big_co337839062te_nat @ G_5 @ ( minus_2107060239tate_o @ A_29 @ ( insert2134838167_state @ X_21 @ bot_bo70021908tate_o ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_231_setsum__cong2,axiom,
% 0.24/0.58 ! [F_6: hoare_1167836817_state > nat,G_4: hoare_1167836817_state > nat,A_28: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ! [X: hoare_1167836817_state] :
% 0.24/0.58 ( ( member2058392318_state @ X @ A_28 )
% 0.24/0.58 => ( ( F_6 @ X )
% 0.24/0.58 = ( G_4 @ X ) ) )
% 0.24/0.58 => ( ( big_co337839062te_nat @ F_6 @ A_28 )
% 0.24/0.58 = ( big_co337839062te_nat @ G_4 @ A_28 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_232_setsum__cong,axiom,
% 0.24/0.58 ! [F_5: hoare_1167836817_state > nat,G_3: hoare_1167836817_state > nat,A_27: hoare_1167836817_state > $o,B_24: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_27 = B_24 )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state] :
% 0.24/0.58 ( ( member2058392318_state @ X @ B_24 )
% 0.24/0.58 => ( ( F_5 @ X )
% 0.24/0.58 = ( G_3 @ X ) ) )
% 0.24/0.58 => ( ( big_co337839062te_nat @ F_5 @ A_27 )
% 0.24/0.58 = ( big_co337839062te_nat @ G_3 @ B_24 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_233_setsum_OF__cong,axiom,
% 0.24/0.58 ! [H: hoare_1167836817_state > nat,G_2: hoare_1167836817_state > nat,A_26: hoare_1167836817_state > $o,B_23: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_26 = B_23 )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state] :
% 0.24/0.58 ( ( member2058392318_state @ X @ B_23 )
% 0.24/0.58 => ( ( H @ X )
% 0.24/0.58 = ( G_2 @ X ) ) )
% 0.24/0.58 => ( ( big_co337839062te_nat @ H @ A_26 )
% 0.24/0.58 = ( big_co337839062te_nat @ G_2 @ B_23 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_234_not__less__bot,axiom,
% 0.24/0.58 ! [A_25: hoare_1167836817_state > $o] :
% 0.24/0.58 ~ ( ord_le65125204tate_o @ A_25 @ bot_bo70021908tate_o ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_235_not__less__bot,axiom,
% 0.24/0.58 ! [A_25: $o] :
% 0.24/0.58 ~ ( ord_less_o @ A_25 @ bot_bot_o ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_236_bot__less,axiom,
% 0.24/0.58 ! [A_24: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_24 != bot_bo70021908tate_o )
% 0.24/0.58 <=> ( ord_le65125204tate_o @ bot_bo70021908tate_o @ A_24 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_237_bot__less,axiom,
% 0.24/0.58 ! [A_24: $o] :
% 0.24/0.58 ( ~ ( A_24
% 0.24/0.58 <=> bot_bot_o )
% 0.24/0.58 <=> ( ord_less_o @ bot_bot_o @ A_24 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_238_not__psubset__empty,axiom,
% 0.24/0.58 ! [A_23: hoare_1167836817_state > $o] :
% 0.24/0.58 ~ ( ord_le65125204tate_o @ A_23 @ bot_bo70021908tate_o ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_239_psubset__eq,axiom,
% 0.24/0.58 ! [A_22: hoare_1167836817_state > $o,B_22: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ A_22 @ B_22 )
% 0.24/0.58 <=> ( ( ord_le827224136tate_o @ A_22 @ B_22 )
% 0.24/0.58 & ( A_22 != B_22 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_240_subset__iff__psubset__eq,axiom,
% 0.24/0.58 ! [A_21: hoare_1167836817_state > $o,B_21: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_21 @ B_21 )
% 0.24/0.58 <=> ( ( ord_le65125204tate_o @ A_21 @ B_21 )
% 0.24/0.58 | ( A_21 = B_21 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_241_psubset__imp__subset,axiom,
% 0.24/0.58 ! [A_20: hoare_1167836817_state > $o,B_20: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ A_20 @ B_20 )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_20 @ B_20 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_242_psubset__subset__trans,axiom,
% 0.24/0.58 ! [C_10: hoare_1167836817_state > $o,A_19: hoare_1167836817_state > $o,B_19: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ A_19 @ B_19 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ B_19 @ C_10 )
% 0.24/0.58 => ( ord_le65125204tate_o @ A_19 @ C_10 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_243_subset__psubset__trans,axiom,
% 0.24/0.58 ! [C_9: hoare_1167836817_state > $o,A_18: hoare_1167836817_state > $o,B_18: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_18 @ B_18 )
% 0.24/0.58 => ( ( ord_le65125204tate_o @ B_18 @ C_9 )
% 0.24/0.58 => ( ord_le65125204tate_o @ A_18 @ C_9 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_244_order__less__asym,axiom,
% 0.24/0.58 ! [X_20: hoare_1167836817_state > $o,Y_18: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_20 @ Y_18 )
% 0.24/0.58 => ~ ( ord_le65125204tate_o @ Y_18 @ X_20 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_245_order__less__asym,axiom,
% 0.24/0.58 ! [X_20: $o,Y_18: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_20 @ Y_18 )
% 0.24/0.58 => ~ ( ord_less_o @ Y_18 @ X_20 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_246_xt1_I10_J,axiom,
% 0.24/0.58 ! [Z_5: hoare_1167836817_state > $o,Y_17: hoare_1167836817_state > $o,X_19: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ Y_17 @ X_19 )
% 0.24/0.58 => ( ( ord_le65125204tate_o @ Z_5 @ Y_17 )
% 0.24/0.58 => ( ord_le65125204tate_o @ Z_5 @ X_19 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_247_xt1_I10_J,axiom,
% 0.24/0.58 ! [Z_5: $o,Y_17: $o,X_19: $o] :
% 0.24/0.58 ( ( ord_less_o @ Y_17 @ X_19 )
% 0.24/0.58 => ( ( ord_less_o @ Z_5 @ Y_17 )
% 0.24/0.58 => ( ord_less_o @ Z_5 @ X_19 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_248_order__less__trans,axiom,
% 0.24/0.58 ! [Z_4: hoare_1167836817_state > $o,X_18: hoare_1167836817_state > $o,Y_16: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_18 @ Y_16 )
% 0.24/0.58 => ( ( ord_le65125204tate_o @ Y_16 @ Z_4 )
% 0.24/0.58 => ( ord_le65125204tate_o @ X_18 @ Z_4 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_249_order__less__trans,axiom,
% 0.24/0.58 ! [Z_4: $o,X_18: $o,Y_16: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_18 @ Y_16 )
% 0.24/0.58 => ( ( ord_less_o @ Y_16 @ Z_4 )
% 0.24/0.58 => ( ord_less_o @ X_18 @ Z_4 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_250_xt1_I2_J,axiom,
% 0.24/0.58 ! [C_8: hoare_1167836817_state > $o,B_17: hoare_1167836817_state > $o,A_17: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ B_17 @ A_17 )
% 0.24/0.58 => ( ( B_17 = C_8 )
% 0.24/0.58 => ( ord_le65125204tate_o @ C_8 @ A_17 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_251_xt1_I2_J,axiom,
% 0.24/0.58 ! [C_8: $o,B_17: $o,A_17: $o] :
% 0.24/0.58 ( ( ord_less_o @ B_17 @ A_17 )
% 0.24/0.58 => ( ( B_17
% 0.24/0.58 <=> C_8 )
% 0.24/0.58 => ( ord_less_o @ C_8 @ A_17 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_252_ord__less__eq__trans,axiom,
% 0.24/0.58 ! [C_7: hoare_1167836817_state > $o,A_16: hoare_1167836817_state > $o,B_16: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ A_16 @ B_16 )
% 0.24/0.58 => ( ( B_16 = C_7 )
% 0.24/0.58 => ( ord_le65125204tate_o @ A_16 @ C_7 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_253_ord__less__eq__trans,axiom,
% 0.24/0.58 ! [C_7: $o,A_16: $o,B_16: $o] :
% 0.24/0.58 ( ( ord_less_o @ A_16 @ B_16 )
% 0.24/0.58 => ( ( B_16
% 0.24/0.58 <=> C_7 )
% 0.24/0.58 => ( ord_less_o @ A_16 @ C_7 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_254_xt1_I1_J,axiom,
% 0.24/0.58 ! [C_6: hoare_1167836817_state > $o,A_15: hoare_1167836817_state > $o,B_15: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_15 = B_15 )
% 0.24/0.58 => ( ( ord_le65125204tate_o @ C_6 @ B_15 )
% 0.24/0.58 => ( ord_le65125204tate_o @ C_6 @ A_15 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_255_xt1_I1_J,axiom,
% 0.24/0.58 ! [C_6: $o,B_15: $o,A_15: $o] :
% 0.24/0.58 ( ( A_15
% 0.24/0.58 <=> B_15 )
% 0.24/0.58 => ( ( ord_less_o @ C_6 @ B_15 )
% 0.24/0.58 => ( ord_less_o @ C_6 @ A_15 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_256_ord__eq__less__trans,axiom,
% 0.24/0.58 ! [C_5: hoare_1167836817_state > $o,A_14: hoare_1167836817_state > $o,B_14: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_14 = B_14 )
% 0.24/0.58 => ( ( ord_le65125204tate_o @ B_14 @ C_5 )
% 0.24/0.58 => ( ord_le65125204tate_o @ A_14 @ C_5 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_257_ord__eq__less__trans,axiom,
% 0.24/0.58 ! [C_5: $o,B_14: $o,A_14: $o] :
% 0.24/0.58 ( ( A_14
% 0.24/0.58 <=> B_14 )
% 0.24/0.58 => ( ( ord_less_o @ B_14 @ C_5 )
% 0.24/0.58 => ( ord_less_o @ A_14 @ C_5 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_258_xt1_I9_J,axiom,
% 0.24/0.58 ! [B_13: hoare_1167836817_state > $o,A_13: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ B_13 @ A_13 )
% 0.24/0.58 => ~ ( ord_le65125204tate_o @ A_13 @ B_13 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_259_xt1_I9_J,axiom,
% 0.24/0.58 ! [B_13: $o,A_13: $o] :
% 0.24/0.58 ( ( ord_less_o @ B_13 @ A_13 )
% 0.24/0.58 => ~ ( ord_less_o @ A_13 @ B_13 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_260_order__less__asym_H,axiom,
% 0.24/0.58 ! [A_12: hoare_1167836817_state > $o,B_12: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ A_12 @ B_12 )
% 0.24/0.58 => ~ ( ord_le65125204tate_o @ B_12 @ A_12 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_261_order__less__asym_H,axiom,
% 0.24/0.58 ! [A_12: $o,B_12: $o] :
% 0.24/0.58 ( ( ord_less_o @ A_12 @ B_12 )
% 0.24/0.58 => ~ ( ord_less_o @ B_12 @ A_12 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_262_order__less__imp__triv,axiom,
% 0.24/0.58 ! [P: $o,X_17: hoare_1167836817_state > $o,Y_15: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_17 @ Y_15 )
% 0.24/0.58 => ( ( ord_le65125204tate_o @ Y_15 @ X_17 )
% 0.24/0.58 => P ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_263_order__less__imp__triv,axiom,
% 0.24/0.58 ! [P: $o,X_17: $o,Y_15: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_17 @ Y_15 )
% 0.24/0.58 => ( ( ord_less_o @ Y_15 @ X_17 )
% 0.24/0.58 => P ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_264_order__less__imp__not__eq2,axiom,
% 0.24/0.58 ! [X_16: hoare_1167836817_state > $o,Y_14: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_16 @ Y_14 )
% 0.24/0.58 => ( Y_14 != X_16 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_265_order__less__imp__not__eq2,axiom,
% 0.24/0.58 ! [X_16: $o,Y_14: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_16 @ Y_14 )
% 0.24/0.58 => ( Y_14
% 0.24/0.58 <=> ~ X_16 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_266_order__less__imp__not__eq,axiom,
% 0.24/0.58 ! [X_15: hoare_1167836817_state > $o,Y_13: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_15 @ Y_13 )
% 0.24/0.58 => ( X_15 != Y_13 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_267_order__less__imp__not__eq,axiom,
% 0.24/0.58 ! [X_15: $o,Y_13: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_15 @ Y_13 )
% 0.24/0.58 => ( X_15
% 0.24/0.58 <=> ~ Y_13 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_268_order__less__imp__not__less,axiom,
% 0.24/0.58 ! [X_14: hoare_1167836817_state > $o,Y_12: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_14 @ Y_12 )
% 0.24/0.58 => ~ ( ord_le65125204tate_o @ Y_12 @ X_14 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_269_order__less__imp__not__less,axiom,
% 0.24/0.58 ! [X_14: $o,Y_12: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_14 @ Y_12 )
% 0.24/0.58 => ~ ( ord_less_o @ Y_12 @ X_14 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_270_order__less__not__sym,axiom,
% 0.24/0.58 ! [X_13: hoare_1167836817_state > $o,Y_11: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_13 @ Y_11 )
% 0.24/0.58 => ~ ( ord_le65125204tate_o @ Y_11 @ X_13 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_271_order__less__not__sym,axiom,
% 0.24/0.58 ! [X_13: $o,Y_11: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_13 @ Y_11 )
% 0.24/0.58 => ~ ( ord_less_o @ Y_11 @ X_13 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_272_less__imp__neq,axiom,
% 0.24/0.58 ! [X_12: hoare_1167836817_state > $o,Y_10: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_12 @ Y_10 )
% 0.24/0.58 => ( X_12 != Y_10 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_273_less__imp__neq,axiom,
% 0.24/0.58 ! [X_12: $o,Y_10: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_12 @ Y_10 )
% 0.24/0.58 => ~ ( X_12
% 0.24/0.58 <=> Y_10 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_274_order__less__irrefl,axiom,
% 0.24/0.58 ! [X_11: hoare_1167836817_state > $o] :
% 0.24/0.58 ~ ( ord_le65125204tate_o @ X_11 @ X_11 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_275_order__less__irrefl,axiom,
% 0.24/0.58 ! [X_11: $o] :
% 0.24/0.58 ~ ( ord_less_o @ X_11 @ X_11 ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_276_order__less__le,axiom,
% 0.24/0.58 ! [X_10: $o,Y_9: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_10 @ Y_9 )
% 0.24/0.58 <=> ( ( ord_less_eq_o @ X_10 @ Y_9 )
% 0.24/0.58 & ~ ( X_10
% 0.24/0.58 <=> Y_9 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_277_order__less__le,axiom,
% 0.24/0.58 ! [X_10: hoare_1167836817_state > $o,Y_9: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_10 @ Y_9 )
% 0.24/0.58 <=> ( ( ord_le827224136tate_o @ X_10 @ Y_9 )
% 0.24/0.58 & ( X_10 != Y_9 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_278_less__le__not__le,axiom,
% 0.24/0.58 ! [X_9: $o,Y_8: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_9 @ Y_8 )
% 0.24/0.58 <=> ( ( ord_less_eq_o @ X_9 @ Y_8 )
% 0.24/0.58 & ~ ( ord_less_eq_o @ Y_8 @ X_9 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_279_less__le__not__le,axiom,
% 0.24/0.58 ! [X_9: hoare_1167836817_state > $o,Y_8: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_9 @ Y_8 )
% 0.24/0.58 <=> ( ( ord_le827224136tate_o @ X_9 @ Y_8 )
% 0.24/0.58 & ~ ( ord_le827224136tate_o @ Y_8 @ X_9 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_280_order__le__less,axiom,
% 0.24/0.58 ! [X_8: $o,Y_7: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ X_8 @ Y_7 )
% 0.24/0.58 <=> ( ( ord_less_o @ X_8 @ Y_7 )
% 0.24/0.58 | ( X_8
% 0.24/0.58 <=> Y_7 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_281_order__le__less,axiom,
% 0.24/0.58 ! [X_8: hoare_1167836817_state > $o,Y_7: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ X_8 @ Y_7 )
% 0.24/0.58 <=> ( ( ord_le65125204tate_o @ X_8 @ Y_7 )
% 0.24/0.58 | ( X_8 = Y_7 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_282_order__neq__le__trans,axiom,
% 0.24/0.58 ! [B_11: $o,A_11: $o] :
% 0.24/0.58 ( ~ ( A_11
% 0.24/0.58 <=> B_11 )
% 0.24/0.58 => ( ( ord_less_eq_o @ A_11 @ B_11 )
% 0.24/0.58 => ( ord_less_o @ A_11 @ B_11 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_283_order__neq__le__trans,axiom,
% 0.24/0.58 ! [A_11: hoare_1167836817_state > $o,B_11: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_11 != B_11 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ A_11 @ B_11 )
% 0.24/0.58 => ( ord_le65125204tate_o @ A_11 @ B_11 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_284_xt1_I12_J,axiom,
% 0.24/0.58 ! [B_10: $o,A_10: $o] :
% 0.24/0.58 ( ~ ( A_10
% 0.24/0.58 <=> B_10 )
% 0.24/0.58 => ( ( ord_less_eq_o @ B_10 @ A_10 )
% 0.24/0.58 => ( ord_less_o @ B_10 @ A_10 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_285_xt1_I12_J,axiom,
% 0.24/0.58 ! [A_10: hoare_1167836817_state > $o,B_10: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( A_10 != B_10 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ B_10 @ A_10 )
% 0.24/0.58 => ( ord_le65125204tate_o @ B_10 @ A_10 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_286_order__less__imp__le,axiom,
% 0.24/0.58 ! [X_7: $o,Y_6: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_7 @ Y_6 )
% 0.24/0.58 => ( ord_less_eq_o @ X_7 @ Y_6 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_287_order__less__imp__le,axiom,
% 0.24/0.58 ! [X_7: hoare_1167836817_state > $o,Y_6: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_7 @ Y_6 )
% 0.24/0.58 => ( ord_le827224136tate_o @ X_7 @ Y_6 ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_288_order__le__imp__less__or__eq,axiom,
% 0.24/0.58 ! [X_6: $o,Y_5: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ X_6 @ Y_5 )
% 0.24/0.58 => ( ( ord_less_o @ X_6 @ Y_5 )
% 0.24/0.58 | ( X_6
% 0.24/0.58 <=> Y_5 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_289_order__le__imp__less__or__eq,axiom,
% 0.24/0.58 ! [X_6: hoare_1167836817_state > $o,Y_5: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ X_6 @ Y_5 )
% 0.24/0.58 => ( ( ord_le65125204tate_o @ X_6 @ Y_5 )
% 0.24/0.58 | ( X_6 = Y_5 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_290_order__le__neq__trans,axiom,
% 0.24/0.58 ! [A_9: $o,B_9: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ A_9 @ B_9 )
% 0.24/0.58 => ( ~ ( A_9
% 0.24/0.58 <=> B_9 )
% 0.24/0.58 => ( ord_less_o @ A_9 @ B_9 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_291_order__le__neq__trans,axiom,
% 0.24/0.58 ! [A_9: hoare_1167836817_state > $o,B_9: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ A_9 @ B_9 )
% 0.24/0.58 => ( ( A_9 != B_9 )
% 0.24/0.58 => ( ord_le65125204tate_o @ A_9 @ B_9 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_292_xt1_I11_J,axiom,
% 0.24/0.58 ! [B_8: $o,A_8: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ B_8 @ A_8 )
% 0.24/0.58 => ( ~ ( A_8
% 0.24/0.58 <=> B_8 )
% 0.24/0.58 => ( ord_less_o @ B_8 @ A_8 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_293_xt1_I11_J,axiom,
% 0.24/0.58 ! [B_8: hoare_1167836817_state > $o,A_8: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ B_8 @ A_8 )
% 0.24/0.58 => ( ( A_8 != B_8 )
% 0.24/0.58 => ( ord_le65125204tate_o @ B_8 @ A_8 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_294_order__less__le__trans,axiom,
% 0.24/0.58 ! [Z_3: $o,X_5: $o,Y_4: $o] :
% 0.24/0.58 ( ( ord_less_o @ X_5 @ Y_4 )
% 0.24/0.58 => ( ( ord_less_eq_o @ Y_4 @ Z_3 )
% 0.24/0.58 => ( ord_less_o @ X_5 @ Z_3 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_295_order__less__le__trans,axiom,
% 0.24/0.58 ! [Z_3: hoare_1167836817_state > $o,X_5: hoare_1167836817_state > $o,Y_4: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ X_5 @ Y_4 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ Y_4 @ Z_3 )
% 0.24/0.58 => ( ord_le65125204tate_o @ X_5 @ Z_3 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_296_xt1_I7_J,axiom,
% 0.24/0.58 ! [Z_2: $o,Y_3: $o,X_4: $o] :
% 0.24/0.58 ( ( ord_less_o @ Y_3 @ X_4 )
% 0.24/0.58 => ( ( ord_less_eq_o @ Z_2 @ Y_3 )
% 0.24/0.58 => ( ord_less_o @ Z_2 @ X_4 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_297_xt1_I7_J,axiom,
% 0.24/0.58 ! [Z_2: hoare_1167836817_state > $o,Y_3: hoare_1167836817_state > $o,X_4: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ Y_3 @ X_4 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ Z_2 @ Y_3 )
% 0.24/0.58 => ( ord_le65125204tate_o @ Z_2 @ X_4 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_298_order__le__less__trans,axiom,
% 0.24/0.58 ! [Z_1: $o,X_3: $o,Y_2: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ X_3 @ Y_2 )
% 0.24/0.58 => ( ( ord_less_o @ Y_2 @ Z_1 )
% 0.24/0.58 => ( ord_less_o @ X_3 @ Z_1 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_299_order__le__less__trans,axiom,
% 0.24/0.58 ! [Z_1: hoare_1167836817_state > $o,X_3: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ X_3 @ Y_2 )
% 0.24/0.58 => ( ( ord_le65125204tate_o @ Y_2 @ Z_1 )
% 0.24/0.58 => ( ord_le65125204tate_o @ X_3 @ Z_1 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_300_xt1_I8_J,axiom,
% 0.24/0.58 ! [Z: $o,Y_1: $o,X_2: $o] :
% 0.24/0.58 ( ( ord_less_eq_o @ Y_1 @ X_2 )
% 0.24/0.58 => ( ( ord_less_o @ Z @ Y_1 )
% 0.24/0.58 => ( ord_less_o @ Z @ X_2 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_301_xt1_I8_J,axiom,
% 0.24/0.58 ! [Z: hoare_1167836817_state > $o,Y_1: hoare_1167836817_state > $o,X_2: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ Y_1 @ X_2 )
% 0.24/0.58 => ( ( ord_le65125204tate_o @ Z @ Y_1 )
% 0.24/0.58 => ( ord_le65125204tate_o @ Z @ X_2 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_302_less__fun__def,axiom,
% 0.24/0.58 ! [F_4: hoare_1167836817_state > $o,G_1: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ F_4 @ G_1 )
% 0.24/0.58 <=> ( ( ord_le827224136tate_o @ F_4 @ G_1 )
% 0.24/0.58 & ~ ( ord_le827224136tate_o @ G_1 @ F_4 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_303_psubset__insert__iff,axiom,
% 0.24/0.58 ! [A_7: hoare_1167836817_state > $o,X_1: hoare_1167836817_state,B_7: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ A_7 @ ( insert2134838167_state @ X_1 @ B_7 ) )
% 0.24/0.58 <=> ( ( ( member2058392318_state @ X_1 @ B_7 )
% 0.24/0.58 => ( ord_le65125204tate_o @ A_7 @ B_7 ) )
% 0.24/0.58 & ( ~ ( member2058392318_state @ X_1 @ B_7 )
% 0.24/0.58 => ( ( ( member2058392318_state @ X_1 @ A_7 )
% 0.24/0.58 => ( ord_le65125204tate_o @ ( minus_2107060239tate_o @ A_7 @ ( insert2134838167_state @ X_1 @ bot_bo70021908tate_o ) ) @ B_7 ) )
% 0.24/0.58 & ( ~ ( member2058392318_state @ X_1 @ A_7 )
% 0.24/0.58 => ( ord_le827224136tate_o @ A_7 @ B_7 ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_304_setsum__strict__mono,axiom,
% 0.24/0.58 ! [F_3: hoare_1167836817_state > nat,G: hoare_1167836817_state > nat,A_6: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( finite1084549118_state @ A_6 )
% 0.24/0.58 => ( ( A_6 != bot_bo70021908tate_o )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state] :
% 0.24/0.58 ( ( member2058392318_state @ X @ A_6 )
% 0.24/0.58 => ( ord_less_nat @ ( F_3 @ X ) @ ( G @ X ) ) )
% 0.24/0.58 => ( ord_less_nat @ ( big_co337839062te_nat @ F_3 @ A_6 ) @ ( big_co337839062te_nat @ G @ A_6 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_305_psubset__trans,axiom,
% 0.24/0.58 ! [C_4: hoare_1167836817_state > $o,A_5: hoare_1167836817_state > $o,B_6: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ A_5 @ B_6 )
% 0.24/0.58 => ( ( ord_le65125204tate_o @ B_6 @ C_4 )
% 0.24/0.58 => ( ord_le65125204tate_o @ A_5 @ C_4 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_306_psubsetD,axiom,
% 0.24/0.58 ! [C_3: hoare_1167836817_state,A_4: hoare_1167836817_state > $o,B_5: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ A_4 @ B_5 )
% 0.24/0.58 => ( ( member2058392318_state @ C_3 @ A_4 )
% 0.24/0.58 => ( member2058392318_state @ C_3 @ B_5 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_307_psubset__imp__ex__mem,axiom,
% 0.24/0.58 ! [A_3: hoare_1167836817_state > $o,B_3: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ A_3 @ B_3 )
% 0.24/0.58 => ? [B_4: hoare_1167836817_state] : ( member2058392318_state @ B_4 @ ( minus_2107060239tate_o @ B_3 @ A_3 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_308_xt6,axiom,
% 0.24/0.58 ! [C_2: hoare_1167836817_state > $o,F_2: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,B_2: hoare_1167836817_state > $o,A_2: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ ( F_2 @ B_2 ) @ A_2 )
% 0.24/0.58 => ( ( ord_le65125204tate_o @ C_2 @ B_2 )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ Y @ X )
% 0.24/0.58 => ( ord_le65125204tate_o @ ( F_2 @ Y ) @ ( F_2 @ X ) ) )
% 0.24/0.58 => ( ord_le65125204tate_o @ ( F_2 @ C_2 ) @ A_2 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_309_xt6,axiom,
% 0.24/0.58 ! [C_2: $o,F_2: $o > hoare_1167836817_state > $o,B_2: $o,A_2: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ ( F_2 @ B_2 ) @ A_2 )
% 0.24/0.58 => ( ( ord_less_o @ C_2 @ B_2 )
% 0.24/0.58 => ( ! [X: $o,Y: $o] :
% 0.24/0.58 ( ( ord_less_o @ Y @ X )
% 0.24/0.58 => ( ord_le65125204tate_o @ ( F_2 @ Y ) @ ( F_2 @ X ) ) )
% 0.24/0.58 => ( ord_le65125204tate_o @ ( F_2 @ C_2 ) @ A_2 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_310_xt5,axiom,
% 0.24/0.58 ! [C_1: hoare_1167836817_state > $o,F_1: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,B_1: hoare_1167836817_state > $o,A_1: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ B_1 @ A_1 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ C_1 @ ( F_1 @ B_1 ) )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ Y @ X )
% 0.24/0.58 => ( ord_le65125204tate_o @ ( F_1 @ Y ) @ ( F_1 @ X ) ) )
% 0.24/0.58 => ( ord_le65125204tate_o @ C_1 @ ( F_1 @ A_1 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_311_xt5,axiom,
% 0.24/0.58 ! [C_1: hoare_1167836817_state > $o,F_1: $o > hoare_1167836817_state > $o,B_1: $o,A_1: $o] :
% 0.24/0.58 ( ( ord_less_o @ B_1 @ A_1 )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ C_1 @ ( F_1 @ B_1 ) )
% 0.24/0.58 => ( ! [X: $o,Y: $o] :
% 0.24/0.58 ( ( ord_less_o @ Y @ X )
% 0.24/0.58 => ( ord_le65125204tate_o @ ( F_1 @ Y ) @ ( F_1 @ X ) ) )
% 0.24/0.58 => ( ord_le65125204tate_o @ C_1 @ ( F_1 @ A_1 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 thf(fact_312_xt4,axiom,
% 0.24/0.58 ! [C: hoare_1167836817_state > $o,F: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,A: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le65125204tate_o @ ( F @ B ) @ A )
% 0.24/0.58 => ( ( ord_le827224136tate_o @ C @ B )
% 0.24/0.58 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.58 ( ( ord_le827224136tate_o @ Y @ X )
% 0.24/0.58 => ( ord_le827224136tate_o @ ( F @ Y ) @ ( F @ X ) ) )
% 0.24/0.66 => ( ord_le65125204tate_o @ ( F @ C ) @ A ) ) ) ) ).
% 0.24/0.66
% 0.24/0.66 thf(fact_313_xt4,axiom,
% 0.24/0.66 ! [C: hoare_1167836817_state > $o,F: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o,A: $o] :
% 0.24/0.66 ( ( ord_less_o @ ( F @ B ) @ A )
% 0.24/0.66 => ( ( ord_le827224136tate_o @ C @ B )
% 0.24/0.66 => ( ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
% 0.24/0.66 ( ( ord_le827224136tate_o @ Y @ X )
% 0.24/0.66 => ( ord_less_eq_o @ ( F @ Y ) @ ( F @ X ) ) )
% 0.24/0.66 => ( ord_less_o @ ( F @ C ) @ A ) ) ) ) ).
% 0.24/0.66
% 0.24/0.66 thf(fact_314_xt4,axiom,
% 0.24/0.66 ! [C: $o,F: $o > hoare_1167836817_state > $o,B: $o,A: hoare_1167836817_state > $o] :
% 0.24/0.66 ( ( ord_le65125204tate_o @ ( F @ B ) @ A )
% 0.24/0.66 => ( ( ord_less_eq_o @ C @ B )
% 0.24/0.66 => ( ! [X: $o,Y: $o] :
% 0.24/0.66 ( ( ord_less_eq_o @ Y @ X )
% 0.24/0.66 => ( ord_le827224136tate_o @ ( F @ Y ) @ ( F @ X ) ) )
% 0.24/0.66 => ( ord_le65125204tate_o @ ( F @ C ) @ A ) ) ) ) ).
% 0.24/0.66
% 0.24/0.66 %----Conjectures (3)
% 0.24/0.66 thf(conj_0,hypothesis,
% 0.24/0.66 hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ c ) @ bot_bo70021908tate_o ) ).
% 0.24/0.66
% 0.24/0.66 thf(conj_1,hypothesis,
% 0.24/0.66 hoare_529639851_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ p @ c @ q ) @ bot_bo70021908tate_o ) ).
% 0.24/0.66
% 0.24/0.66 thf(conj_2,conjecture,
% 0.24/0.66 hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ p @ c @ q ) @ bot_bo70021908tate_o ) ).
% 0.24/0.66
% 0.24/0.66 %------------------------------------------------------------------------------
% 0.24/0.66 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.7TUmV8VPDV/cvc5---1.0.5_1568.p...
% 0.24/0.66 (declare-sort $$unsorted 0)
% 0.24/0.66 (declare-sort tptp.com 0)
% 0.24/0.66 (declare-sort tptp.state 0)
% 0.24/0.66 (declare-sort tptp.hoare_1167836817_state 0)
% 0.24/0.66 (declare-sort tptp.nat 0)
% 0.24/0.66 (declare-fun tptp.all2 ((-> (-> tptp.hoare_1167836817_state Bool) Bool)) Bool)
% 0.24/0.66 (declare-fun tptp.all1 ((-> Bool Bool)) Bool)
% 0.24/0.66 (declare-fun tptp.big_co337839062te_nat ((-> tptp.hoare_1167836817_state tptp.nat) (-> tptp.hoare_1167836817_state Bool)) tptp.nat)
% 0.24/0.66 (declare-fun tptp.big_se1603066171_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state) (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state)) Bool)
% 0.24/0.66 (declare-fun tptp.skip () tptp.com)
% 0.24/0.66 (declare-fun tptp.semi (tptp.com tptp.com) tptp.com)
% 0.24/0.66 (declare-fun tptp.ex ((-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.24/0.66 (declare-fun tptp.finite1091222817_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) Bool)
% 0.24/0.66 (declare-fun tptp.finite856902323tate_o ((-> tptp.hoare_1167836817_state (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool)) Bool)
% 0.24/0.66 (declare-fun tptp.finite1900754844_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) Bool)
% 0.24/0.66 (declare-fun tptp.finite1084549118_state ((-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.24/0.66 (declare-fun tptp.finite309220289_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.24/0.66 (declare-fun tptp.finite1646097201_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state) (-> tptp.hoare_1167836817_state Bool)) tptp.hoare_1167836817_state)
% 0.24/0.66 (declare-fun tptp.finite291020855tate_o ((-> tptp.hoare_1167836817_state (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.24/0.66 (declare-fun tptp.finite1731015960_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state) tptp.hoare_1167836817_state (-> tptp.hoare_1167836817_state Bool)) tptp.hoare_1167836817_state)
% 0.24/0.66 (declare-fun tptp.finite1316643734_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state) tptp.hoare_1167836817_state (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.24/0.66 (declare-fun tptp.finite1074406356_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state) (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state)) Bool)
% 0.24/0.66 (declare-fun tptp.finite806517911_state ((-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state) (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state)) Bool)
% 0.24/0.66 (declare-fun tptp.minus_2107060239tate_o ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.24/0.66 (declare-fun tptp.minus_minus_o (Bool Bool) Bool)
% 0.24/0.66 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.24/0.66 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.24/0.66 (declare-fun tptp.hoare_Mirabelle_MGT (tptp.com) tptp.hoare_1167836817_state)
% 0.24/0.66 (declare-fun tptp.hoare_123228589_state ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.24/0.66 (declare-fun tptp.hoare_529639851_state ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.24/0.66 (declare-fun tptp.hoare_908217195_state ((-> tptp.state tptp.state Bool) tptp.com (-> tptp.state tptp.state Bool)) tptp.hoare_1167836817_state)
% 0.24/0.66 (declare-fun tptp.bot_bo70021908tate_o (tptp.hoare_1167836817_state) Bool)
% 0.24/0.66 (declare-fun tptp.bot_bot_o () Bool)
% 0.24/0.66 (declare-fun tptp.max_Ho421493569tate_o ((-> (-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) Bool) (-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.24/0.66 (declare-fun tptp.max_o ((-> Bool Bool Bool) Bool Bool) Bool)
% 0.24/0.66 (declare-fun tptp.min_Ho1955171539tate_o ((-> (-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) Bool) (-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.24/0.66 (declare-fun tptp.min_o ((-> Bool Bool Bool) Bool Bool) Bool)
% 0.24/0.66 (declare-fun tptp.ord_le65125204tate_o ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.24/0.66 (declare-fun tptp.ord_less_o (Bool Bool) Bool)
% 0.24/0.66 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.24/0.66 (declare-fun tptp.ord_le827224136tate_o ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.24/0.66 (declare-fun tptp.ord_less_eq_o (Bool Bool) Bool)
% 0.24/0.66 (declare-fun tptp.ord_ma164008317tate_o ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.24/0.66 (declare-fun tptp.ord_max_o (Bool Bool) Bool)
% 0.24/0.66 (declare-fun tptp.ord_mi1697686287tate_o ((-> tptp.hoare_1167836817_state Bool) (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.24/0.66 (declare-fun tptp.ord_min_o (Bool Bool) Bool)
% 0.24/0.66 (declare-fun tptp.collec1027672124_state ((-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.24/0.66 (declare-fun tptp.insert2134838167_state (tptp.hoare_1167836817_state (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state) Bool)
% 0.24/0.66 (declare-fun tptp.the_el323660082_state ((-> tptp.hoare_1167836817_state Bool)) tptp.hoare_1167836817_state)
% 0.24/0.66 (declare-fun tptp.member2058392318_state (tptp.hoare_1167836817_state (-> tptp.hoare_1167836817_state Bool)) Bool)
% 0.24/0.66 (declare-fun tptp.p (tptp.state tptp.state) Bool)
% 0.24/0.66 (declare-fun tptp.q (tptp.state tptp.state) Bool)
% 0.24/0.66 (declare-fun tptp.c () tptp.com)
% 0.24/0.66 (assert (forall ((G_29 (-> tptp.hoare_1167836817_state Bool))) (@ (@ tptp.hoare_123228589_state G_29) tptp.bot_bo70021908tate_o)))
% 0.24/0.66 (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_908217195_state Fun1_2) Com_2) Fun2_2) (@ (@ (@ tptp.hoare_908217195_state Fun1_1) Com_1) Fun2_1)) (and (= Fun1_2 Fun1_1) (= Com_2 Com_1) (= Fun2_2 Fun2_1)))))
% 0.24/0.66 (assert (forall ((G_28 (-> tptp.hoare_1167836817_state Bool)) (Ts_7 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.hoare_123228589_state G_28) Ts_7) (@ (@ tptp.hoare_529639851_state G_28) Ts_7))))
% 0.24/0.66 (assert (forall ((G_27 (-> tptp.hoare_1167836817_state Bool)) (G_26 (-> tptp.hoare_1167836817_state Bool)) (Ts_6 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.hoare_123228589_state G_27))) (=> (@ (@ tptp.hoare_123228589_state G_26) Ts_6) (=> (@ _let_1 G_26) (@ _let_1 Ts_6))))))
% 0.24/0.66 (assert (forall ((Ts_5 (-> tptp.hoare_1167836817_state Bool)) (G_25 (-> tptp.hoare_1167836817_state Bool)) (T_1 tptp.hoare_1167836817_state)) (let ((_let_1 (@ tptp.insert2134838167_state T_1))) (let ((_let_2 (@ tptp.hoare_123228589_state G_25))) (=> (@ _let_2 (@ _let_1 tptp.bot_bo70021908tate_o)) (=> (@ _let_2 Ts_5) (@ _let_2 (@ _let_1 Ts_5))))))))
% 0.24/0.66 (assert (forall ((G_24 (-> tptp.hoare_1167836817_state Bool)) (T tptp.hoare_1167836817_state) (Ts_4 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.hoare_123228589_state G_24))) (let ((_let_2 (@ tptp.insert2134838167_state T))) (=> (@ _let_1 (@ _let_2 Ts_4)) (and (@ _let_1 (@ _let_2 tptp.bot_bo70021908tate_o)) (@ _let_1 Ts_4)))))))
% 0.24/0.66 (assert (forall ((Q_11 (-> tptp.state tptp.state Bool)) (G_23 (-> tptp.hoare_1167836817_state Bool)) (P_21 (-> tptp.state tptp.state Bool)) (C_39 tptp.com) (Q_10 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ (@ tptp.hoare_908217195_state P_21) C_39))) (let ((_let_2 (@ tptp.hoare_123228589_state G_23))) (=> (@ _let_2 (@ (@ tptp.insert2134838167_state (@ _let_1 Q_10)) tptp.bot_bo70021908tate_o)) (=> (forall ((Z_28 tptp.state) (S tptp.state)) (=> (@ (@ Q_10 Z_28) S) (@ (@ Q_11 Z_28) S))) (@ _let_2 (@ (@ tptp.insert2134838167_state (@ _let_1 Q_11)) tptp.bot_bo70021908tate_o))))))))
% 0.24/0.66 (assert (forall ((P_20 (-> tptp.state tptp.state Bool)) (G_22 (-> tptp.hoare_1167836817_state Bool)) (P_19 (-> tptp.state tptp.state Bool)) (C_38 tptp.com) (Q_9 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_123228589_state G_22))) (=> (@ _let_1 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_19) C_38) Q_9)) tptp.bot_bo70021908tate_o)) (=> (forall ((Z_28 tptp.state) (S tptp.state)) (=> (@ (@ P_20 Z_28) S) (@ (@ P_19 Z_28) S))) (@ _let_1 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_20) C_38) Q_9)) tptp.bot_bo70021908tate_o)))))))
% 0.24/0.66 (assert (forall ((A_185 tptp.hoare_1167836817_state) (B_92 tptp.hoare_1167836817_state) (A_184 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state A_185))) (=> (@ _let_1 (@ (@ tptp.insert2134838167_state B_92) A_184)) (=> (not (= A_185 B_92)) (@ _let_1 A_184))))))
% 0.24/0.66 (assert (forall ((B_91 tptp.hoare_1167836817_state) (A_183 tptp.hoare_1167836817_state) (B_90 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state A_183))) (=> (=> (not (@ _let_1 B_90)) (= A_183 B_91)) (@ _let_1 (@ (@ tptp.insert2134838167_state B_91) B_90))))))
% 0.24/0.66 (assert (forall ((Q_8 (-> tptp.state tptp.state Bool)) (P_18 (-> tptp.state tptp.state Bool)) (G_21 (-> tptp.hoare_1167836817_state Bool)) (P_17 (-> tptp.state tptp.state Bool)) (C_37 tptp.com) (Q_7 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_123228589_state G_21))) (=> (@ _let_1 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_17) C_37) Q_7)) tptp.bot_bo70021908tate_o)) (=> (forall ((Z_28 tptp.state) (S tptp.state)) (=> (@ (@ P_18 Z_28) S) (forall ((S_1 tptp.state)) (=> (forall ((Z_29 tptp.state)) (=> (@ (@ P_17 Z_29) S) (@ (@ Q_7 Z_29) S_1))) (@ (@ Q_8 Z_28) S_1))))) (@ _let_1 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_18) C_37) Q_8)) tptp.bot_bo70021908tate_o)))))))
% 0.24/0.66 (assert (forall ((A_182 tptp.hoare_1167836817_state)) (not (@ (@ tptp.member2058392318_state A_182) tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (forall ((A_181 tptp.hoare_1167836817_state) (A_180 (-> tptp.hoare_1167836817_state Bool))) (not (= tptp.bot_bo70021908tate_o (@ (@ tptp.insert2134838167_state A_181) A_180)))))
% 0.24/0.66 (assert (forall ((A_179 tptp.hoare_1167836817_state) (A_178 (-> tptp.hoare_1167836817_state Bool))) (not (= (@ (@ tptp.insert2134838167_state A_179) A_178) tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (forall ((B_89 tptp.hoare_1167836817_state) (A_177 tptp.hoare_1167836817_state)) (= (@ (@ tptp.member2058392318_state B_89) (@ (@ tptp.insert2134838167_state A_177) tptp.bot_bo70021908tate_o)) (= B_89 A_177))))
% 0.24/0.66 (assert (forall ((A_176 tptp.hoare_1167836817_state) (B_88 tptp.hoare_1167836817_state) (C_36 tptp.hoare_1167836817_state) (D_3 tptp.hoare_1167836817_state)) (= (= (@ (@ tptp.insert2134838167_state A_176) (@ (@ tptp.insert2134838167_state B_88) tptp.bot_bo70021908tate_o)) (@ (@ tptp.insert2134838167_state C_36) (@ (@ tptp.insert2134838167_state D_3) tptp.bot_bo70021908tate_o))) (or (and (= A_176 C_36) (= B_88 D_3)) (and (= A_176 D_3) (= B_88 C_36))))))
% 0.24/0.66 (assert (forall ((A_175 tptp.hoare_1167836817_state) (A_174 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_174 tptp.bot_bo70021908tate_o) (not (@ (@ tptp.member2058392318_state A_175) A_174)))))
% 0.24/0.66 (assert (forall ((P_16 (-> tptp.hoare_1167836817_state Bool))) (= (= (@ tptp.collec1027672124_state P_16) tptp.bot_bo70021908tate_o) (forall ((X tptp.hoare_1167836817_state)) (not (@ P_16 X))))))
% 0.24/0.66 (assert (forall ((C_35 tptp.hoare_1167836817_state)) (not (@ (@ tptp.member2058392318_state C_35) tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (forall ((P_15 (-> tptp.hoare_1167836817_state Bool))) (= (= tptp.bot_bo70021908tate_o (@ tptp.collec1027672124_state P_15)) (forall ((X tptp.hoare_1167836817_state)) (not (@ P_15 X))))))
% 0.24/0.66 (assert (forall ((A_173 (-> tptp.hoare_1167836817_state Bool))) (= (exists ((X tptp.hoare_1167836817_state)) (@ (@ tptp.member2058392318_state X) A_173)) (not (= A_173 tptp.bot_bo70021908tate_o)))))
% 0.24/0.66 (assert (forall ((A_172 (-> tptp.hoare_1167836817_state Bool))) (= (forall ((X tptp.hoare_1167836817_state)) (not (@ (@ tptp.member2058392318_state X) A_172))) (= A_172 tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (= tptp.bot_bo70021908tate_o (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) false))))
% 0.24/0.66 (assert (forall ((A_171 tptp.hoare_1167836817_state) (A_170 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.member2058392318_state A_171) A_170) (= (@ (@ tptp.insert2134838167_state A_171) A_170) A_170))))
% 0.24/0.66 (assert (forall ((B_87 tptp.hoare_1167836817_state) (A_169 tptp.hoare_1167836817_state) (B_86 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state A_169))) (=> (@ _let_1 B_86) (@ _let_1 (@ (@ tptp.insert2134838167_state B_87) B_86))))))
% 0.24/0.66 (assert (forall ((B_85 (-> tptp.hoare_1167836817_state Bool)) (X_85 tptp.hoare_1167836817_state) (A_168 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state X_85))) (let ((_let_2 (@ tptp.member2058392318_state X_85))) (=> (not (@ _let_2 A_168)) (=> (not (@ _let_2 B_85)) (= (= (@ _let_1 A_168) (@ _let_1 B_85)) (= A_168 B_85))))))))
% 0.24/0.66 (assert (forall ((Y_34 tptp.hoare_1167836817_state) (A_167 (-> tptp.hoare_1167836817_state Bool)) (X_84 tptp.hoare_1167836817_state)) (= (@ (@ (@ tptp.insert2134838167_state Y_34) A_167) X_84) (or (= Y_34 X_84) (@ A_167 X_84)))))
% 0.24/0.66 (assert (forall ((A_166 tptp.hoare_1167836817_state) (B_84 tptp.hoare_1167836817_state) (A_165 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state A_166))) (= (@ _let_1 (@ (@ tptp.insert2134838167_state B_84) A_165)) (or (= A_166 B_84) (@ _let_1 A_165))))))
% 0.24/0.66 (assert (forall ((X_83 tptp.hoare_1167836817_state) (Y_33 tptp.hoare_1167836817_state) (A_164 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state X_83))) (let ((_let_2 (@ tptp.insert2134838167_state Y_33))) (= (@ _let_1 (@ _let_2 A_164)) (@ _let_2 (@ _let_1 A_164)))))))
% 0.24/0.66 (assert (forall ((X_82 tptp.hoare_1167836817_state) (A_163 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state X_82))) (let ((_let_2 (@ _let_1 A_163))) (= (@ _let_1 _let_2) _let_2)))))
% 0.24/0.66 (assert (forall ((A_162 tptp.hoare_1167836817_state) (P_14 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.insert2134838167_state A_162) (@ tptp.collec1027672124_state P_14)) (@ tptp.collec1027672124_state (lambda ((U tptp.hoare_1167836817_state)) (=> (not (= U A_162)) (@ P_14 U)))))))
% 0.24/0.66 (assert (forall ((A_161 tptp.hoare_1167836817_state) (B_83 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.insert2134838167_state A_161) B_83) (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) (or (= X A_161) (@ (@ tptp.member2058392318_state X) B_83)))))))
% 0.24/0.66 (assert (forall ((A_160 tptp.hoare_1167836817_state) (B_82 (-> tptp.hoare_1167836817_state Bool))) (@ (@ tptp.member2058392318_state A_160) (@ (@ tptp.insert2134838167_state A_160) B_82))))
% 0.24/0.66 (assert (forall ((A_159 tptp.hoare_1167836817_state) (B_81 tptp.hoare_1167836817_state)) (=> (= (@ (@ tptp.insert2134838167_state A_159) tptp.bot_bo70021908tate_o) (@ (@ tptp.insert2134838167_state B_81) tptp.bot_bo70021908tate_o)) (= A_159 B_81))))
% 0.24/0.66 (assert (forall ((B_80 tptp.hoare_1167836817_state) (A_158 tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state B_80) (@ (@ tptp.insert2134838167_state A_158) tptp.bot_bo70021908tate_o)) (= B_80 A_158))))
% 0.24/0.66 (assert (forall ((X_81 tptp.hoare_1167836817_state)) (= (@ tptp.the_el323660082_state (@ (@ tptp.insert2134838167_state X_81) tptp.bot_bo70021908tate_o)) X_81)))
% 0.24/0.66 (assert (forall ((X_80 tptp.hoare_1167836817_state)) (= (@ tptp.bot_bo70021908tate_o X_80) tptp.bot_bot_o)))
% 0.24/0.66 (assert (forall ((X tptp.hoare_1167836817_state)) (= (@ tptp.bot_bo70021908tate_o X) tptp.bot_bot_o)))
% 0.24/0.66 (assert (forall ((G_20 (-> tptp.hoare_1167836817_state Bool)) (P_13 (-> tptp.state tptp.state Bool))) (@ (@ tptp.hoare_123228589_state G_20) (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_13) tptp.skip) P_13)) tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (forall ((D_2 tptp.com) (R (-> tptp.state tptp.state Bool)) (G_19 (-> tptp.hoare_1167836817_state Bool)) (P_12 (-> tptp.state tptp.state Bool)) (C_34 tptp.com) (Q_6 (-> tptp.state tptp.state Bool))) (let ((_let_1 (@ tptp.hoare_908217195_state P_12))) (let ((_let_2 (@ tptp.hoare_123228589_state G_19))) (=> (@ _let_2 (@ (@ tptp.insert2134838167_state (@ (@ _let_1 C_34) Q_6)) tptp.bot_bo70021908tate_o)) (=> (@ _let_2 (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state Q_6) D_2) R)) tptp.bot_bo70021908tate_o)) (@ _let_2 (@ (@ tptp.insert2134838167_state (@ (@ _let_1 (@ (@ tptp.semi C_34) D_2)) R)) tptp.bot_bo70021908tate_o))))))))
% 0.24/0.66 (assert (forall ((Y_32 tptp.hoare_1167836817_state)) (not (forall ((Fun1 (-> tptp.state tptp.state Bool)) (Com tptp.com) (Fun2 (-> tptp.state tptp.state Bool))) (not (= Y_32 (@ (@ (@ tptp.hoare_908217195_state Fun1) Com) Fun2)))))))
% 0.24/0.66 (assert (forall ((X_79 tptp.hoare_1167836817_state) (A_157 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.member2058392318_state X_79) A_157) (not (forall ((B_79 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_157 (@ (@ tptp.insert2134838167_state X_79) B_79)) (@ (@ tptp.member2058392318_state X_79) B_79)))))))
% 0.24/0.66 (assert (forall ((A_156 tptp.hoare_1167836817_state) (A_155 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.member2058392318_state A_156) A_155) (exists ((B_79 (-> tptp.hoare_1167836817_state Bool))) (and (= A_155 (@ (@ tptp.insert2134838167_state A_156) B_79)) (not (@ (@ tptp.member2058392318_state A_156) B_79)))))))
% 0.24/0.66 (assert (forall ((A_154 (-> tptp.hoare_1167836817_state Bool))) (=> (forall ((Y tptp.hoare_1167836817_state)) (not (@ (@ tptp.member2058392318_state Y) A_154))) (= A_154 tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (forall ((Q_4 (-> tptp.state tptp.state Bool)) (G_18 (-> tptp.hoare_1167836817_state Bool)) (C_33 tptp.com) (P_10 (-> tptp.state tptp.state Bool))) (=> (forall ((Z_28 tptp.state) (S tptp.state)) (=> (@ (@ P_10 Z_28) S) (exists ((P_11 (-> tptp.state tptp.state Bool)) (Q_5 (-> tptp.state tptp.state Bool))) (and (@ (@ tptp.hoare_123228589_state G_18) (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_11) C_33) Q_5)) tptp.bot_bo70021908tate_o)) (forall ((S_1 tptp.state)) (=> (forall ((Z_29 tptp.state)) (=> (@ (@ P_11 Z_29) S) (@ (@ Q_5 Z_29) S_1))) (@ (@ Q_4 Z_28) S_1))))))) (@ (@ tptp.hoare_123228589_state G_18) (@ (@ tptp.insert2134838167_state (@ (@ (@ tptp.hoare_908217195_state P_10) C_33) Q_4)) tptp.bot_bo70021908tate_o)))))
% 0.24/0.66 (assert (forall ((A_153 (-> tptp.hoare_1167836817_state Bool))) (= (not (= A_153 tptp.bot_bo70021908tate_o)) (exists ((X tptp.hoare_1167836817_state) (B_79 (-> tptp.hoare_1167836817_state Bool))) (and (= A_153 (@ (@ tptp.insert2134838167_state X) B_79)) (not (@ (@ tptp.member2058392318_state X) B_79)))))))
% 0.24/0.66 (assert (forall ((Com1 tptp.com) (Com2 tptp.com)) (not (= (@ (@ tptp.semi Com1) Com2) tptp.skip))))
% 0.24/0.66 (assert (forall ((Com1 tptp.com) (Com2 tptp.com)) (not (= tptp.skip (@ (@ tptp.semi Com1) Com2)))))
% 0.24/0.66 (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)))))
% 0.24/0.66 (assert (forall ((F_82 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (A_152 tptp.hoare_1167836817_state) (B_78 tptp.hoare_1167836817_state)) (= (@ (@ (@ tptp.finite309220289_state F_82) (@ (@ tptp.insert2134838167_state A_152) tptp.bot_bo70021908tate_o)) B_78) (= A_152 B_78))))
% 0.24/0.66 (assert (forall ((X_78 tptp.hoare_1167836817_state) (F_81 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_80 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite1074406356_state F_81) F_80) (= (@ F_80 (@ (@ tptp.insert2134838167_state X_78) tptp.bot_bo70021908tate_o)) X_78))))
% 0.24/0.66 (assert (forall ((X tptp.hoare_1167836817_state)) (= (@ tptp.bot_bo70021908tate_o X) (@ (@ tptp.member2058392318_state X) tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (forall ((F_79 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (A_151 tptp.hoare_1167836817_state)) (= (@ (@ tptp.finite1646097201_state F_79) (@ (@ tptp.insert2134838167_state A_151) tptp.bot_bo70021908tate_o)) A_151)))
% 0.24/0.66 (assert (forall ((A_150 tptp.hoare_1167836817_state) (G_17 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state)) (F_78 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (=> (= G_17 (@ tptp.finite1646097201_state F_78)) (= (@ G_17 (@ (@ tptp.insert2134838167_state A_150) tptp.bot_bo70021908tate_o)) A_150))))
% 0.24/0.66 (assert (forall ((F_77 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (X_77 tptp.hoare_1167836817_state)) (not (@ (@ (@ tptp.finite309220289_state F_77) tptp.bot_bo70021908tate_o) X_77))))
% 0.24/0.66 (assert (forall ((F_76 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (A_149 (-> tptp.hoare_1167836817_state Bool)) (X_76 tptp.hoare_1167836817_state)) (=> (@ (@ (@ tptp.finite309220289_state F_76) A_149) X_76) (not (= A_149 tptp.bot_bo70021908tate_o)))))
% 0.24/0.66 (assert (forall ((F_75 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (A_148 tptp.hoare_1167836817_state) (A_147 (-> tptp.hoare_1167836817_state Bool)) (X_75 tptp.hoare_1167836817_state)) (=> (@ (@ (@ (@ tptp.finite1316643734_state F_75) A_148) A_147) X_75) (=> (not (@ (@ tptp.member2058392318_state A_148) A_147)) (@ (@ (@ tptp.finite309220289_state F_75) (@ (@ tptp.insert2134838167_state A_148) A_147)) X_75)))))
% 0.24/0.66 (assert (forall ((X_74 tptp.hoare_1167836817_state) (A_146 (-> tptp.hoare_1167836817_state Bool)) (F_74 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_73 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite1074406356_state F_74) F_73) (=> (@ tptp.finite1084549118_state A_146) (=> (not (@ (@ tptp.member2058392318_state X_74) A_146)) (=> (not (= A_146 tptp.bot_bo70021908tate_o)) (= (@ F_73 (@ (@ tptp.insert2134838167_state X_74) A_146)) (@ (@ F_74 X_74) (@ F_73 A_146)))))))))
% 0.24/0.66 (assert (forall ((A_145 (-> tptp.hoare_1167836817_state Bool)) (F_72 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_71 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite1074406356_state F_72) F_71) (=> (@ tptp.finite1084549118_state A_145) (= (@ F_71 A_145) (@ (@ tptp.finite1646097201_state F_72) A_145))))))
% 0.24/0.66 (assert (forall ((A_144 (-> tptp.hoare_1167836817_state Bool)) (F_70 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_69 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite1074406356_state F_70) F_69) (=> (@ tptp.finite1084549118_state A_144) (=> (not (= A_144 tptp.bot_bo70021908tate_o)) (=> (forall ((X tptp.hoare_1167836817_state) (Y tptp.hoare_1167836817_state)) (@ (@ tptp.member2058392318_state (@ (@ F_70 X) Y)) (@ (@ tptp.insert2134838167_state X) (@ (@ tptp.insert2134838167_state Y) tptp.bot_bo70021908tate_o)))) (@ (@ tptp.member2058392318_state (@ F_69 A_144)) A_144)))))))
% 0.24/0.66 (assert (forall ((F_68 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (A_143 tptp.hoare_1167836817_state) (X_73 (-> tptp.hoare_1167836817_state Bool)) (X_72 tptp.hoare_1167836817_state)) (=> (@ (@ (@ tptp.finite309220289_state F_68) (@ (@ tptp.insert2134838167_state A_143) X_73)) X_72) (not (forall ((A_59 tptp.hoare_1167836817_state) (A_58 (-> tptp.hoare_1167836817_state Bool))) (=> (= (@ (@ tptp.insert2134838167_state A_143) X_73) (@ (@ tptp.insert2134838167_state A_59) A_58)) (=> (@ (@ (@ (@ tptp.finite1316643734_state F_68) A_59) A_58) X_72) (@ (@ tptp.member2058392318_state A_59) A_58))))))))
% 0.24/0.66 (assert (forall ((A_142 (-> tptp.hoare_1167836817_state Bool)) (X_71 tptp.hoare_1167836817_state)) (let ((_let_1 (@ (@ tptp.insert2134838167_state X_71) tptp.bot_bo70021908tate_o))) (=> (@ (@ tptp.ord_le827224136tate_o A_142) _let_1) (or (= A_142 tptp.bot_bo70021908tate_o) (= A_142 _let_1))))))
% 0.24/0.66 (assert (forall ((X_70 Bool)) (@ (@ tptp.ord_less_eq_o X_70) X_70)))
% 0.24/0.66 (assert (forall ((X_70 (-> tptp.hoare_1167836817_state Bool))) (@ (@ tptp.ord_le827224136tate_o X_70) X_70)))
% 0.24/0.66 (assert (forall ((C_32 tptp.hoare_1167836817_state) (A_141 (-> tptp.hoare_1167836817_state Bool)) (B_77 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_32))) (=> (@ (@ tptp.ord_le827224136tate_o A_141) B_77) (=> (@ _let_1 A_141) (@ _let_1 B_77))))))
% 0.24/0.66 (assert (forall ((A_140 (-> tptp.hoare_1167836817_state Bool)) (B_76 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o A_140) B_76) (=> (@ (@ tptp.ord_le827224136tate_o B_76) A_140) (= A_140 B_76)))))
% 0.24/0.66 (assert (@ tptp.finite1084549118_state tptp.bot_bo70021908tate_o))
% 0.24/0.66 (assert (forall ((A_139 tptp.hoare_1167836817_state) (A_138 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state A_138) (@ tptp.finite1084549118_state (@ (@ tptp.insert2134838167_state A_139) A_138)))))
% 0.24/0.66 (assert (forall ((A_137 (-> tptp.hoare_1167836817_state Bool))) (@ (@ tptp.ord_le827224136tate_o tptp.bot_bo70021908tate_o) A_137)))
% 0.24/0.66 (assert (forall ((Q_3 (-> tptp.hoare_1167836817_state Bool)) (P_9 (-> tptp.hoare_1167836817_state Bool)) (X_69 tptp.hoare_1167836817_state)) (=> (@ P_9 X_69) (=> (@ (@ tptp.ord_le827224136tate_o P_9) Q_3) (@ Q_3 X_69)))))
% 0.24/0.66 (assert (forall ((X_68 tptp.hoare_1167836817_state) (P_8 (-> tptp.hoare_1167836817_state Bool)) (Q_2 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o P_8) Q_2) (=> (@ P_8 X_68) (@ Q_2 X_68)))))
% 0.24/0.66 (assert (forall ((X_67 tptp.hoare_1167836817_state) (A_136 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.member2058392318_state X_67) A_136) (@ A_136 X_67))))
% 0.24/0.66 (assert (forall ((P_7 (-> tptp.hoare_1167836817_state Bool))) (= (@ tptp.collec1027672124_state P_7) P_7)))
% 0.24/0.66 (assert (forall ((A_135 (-> tptp.hoare_1167836817_state Bool))) (@ (@ tptp.ord_le827224136tate_o A_135) A_135)))
% 0.24/0.66 (assert (forall ((A_134 (-> tptp.hoare_1167836817_state Bool)) (B_75 (-> tptp.hoare_1167836817_state Bool))) (= (= A_134 B_75) (and (@ (@ tptp.ord_le827224136tate_o A_134) B_75) (@ (@ tptp.ord_le827224136tate_o B_75) A_134)))))
% 0.24/0.66 (assert (forall ((A_133 (-> tptp.hoare_1167836817_state Bool)) (B_74 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_133 B_74) (@ (@ tptp.ord_le827224136tate_o A_133) B_74))))
% 0.24/0.66 (assert (forall ((A_132 (-> tptp.hoare_1167836817_state Bool)) (B_73 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_132 B_73) (@ (@ tptp.ord_le827224136tate_o B_73) A_132))))
% 0.24/0.66 (assert (forall ((X_66 tptp.hoare_1167836817_state) (A_131 (-> tptp.hoare_1167836817_state Bool)) (B_72 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state X_66))) (=> (@ (@ tptp.ord_le827224136tate_o A_131) B_72) (=> (@ _let_1 A_131) (@ _let_1 B_72))))))
% 0.24/0.66 (assert (forall ((B_71 (-> tptp.hoare_1167836817_state Bool)) (X_65 tptp.hoare_1167836817_state) (A_130 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state X_65))) (=> (@ _let_1 A_130) (=> (@ (@ tptp.ord_le827224136tate_o A_130) B_71) (@ _let_1 B_71))))))
% 0.24/0.66 (assert (forall ((X_64 tptp.hoare_1167836817_state) (A_129 (-> tptp.hoare_1167836817_state Bool)) (B_70 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state X_64))) (=> (@ (@ tptp.ord_le827224136tate_o A_129) B_70) (=> (@ _let_1 A_129) (@ _let_1 B_70))))))
% 0.24/0.66 (assert (forall ((C_31 (-> tptp.hoare_1167836817_state Bool)) (A_128 (-> tptp.hoare_1167836817_state Bool)) (B_69 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le827224136tate_o A_128))) (=> (@ _let_1 B_69) (=> (@ (@ tptp.ord_le827224136tate_o B_69) C_31) (@ _let_1 C_31))))))
% 0.24/0.66 (assert (forall ((A_127 (-> tptp.hoare_1167836817_state Bool)) (B_68 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_127 B_68) (not (=> (@ (@ tptp.ord_le827224136tate_o A_127) B_68) (not (@ (@ tptp.ord_le827224136tate_o B_68) A_127)))))))
% 0.24/0.66 (assert (forall ((F_67 (-> tptp.hoare_1167836817_state Bool)) (G_16 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.ord_le827224136tate_o F_67) G_16) (forall ((X tptp.hoare_1167836817_state)) (@ (@ tptp.ord_less_eq_o (@ F_67 X)) (@ G_16 X))))))
% 0.24/0.66 (assert (forall ((Y_31 Bool) (X_63 Bool)) (= (= X_63 Y_31) (and (@ (@ tptp.ord_less_eq_o X_63) Y_31) (@ (@ tptp.ord_less_eq_o Y_31) X_63)))))
% 0.24/0.66 (assert (forall ((X_63 (-> tptp.hoare_1167836817_state Bool)) (Y_31 (-> tptp.hoare_1167836817_state Bool))) (= (= X_63 Y_31) (and (@ (@ tptp.ord_le827224136tate_o X_63) Y_31) (@ (@ tptp.ord_le827224136tate_o Y_31) X_63)))))
% 0.24/0.66 (assert (forall ((A_126 (-> tptp.hoare_1167836817_state Bool)) (B_67 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state B_67) (=> (@ (@ tptp.ord_le827224136tate_o A_126) B_67) (@ tptp.finite1084549118_state A_126)))))
% 0.24/0.66 (assert (forall ((Y_30 Bool) (X_62 Bool)) (=> (= X_62 Y_30) (@ (@ tptp.ord_less_eq_o X_62) Y_30))))
% 0.24/0.66 (assert (forall ((X_62 (-> tptp.hoare_1167836817_state Bool)) (Y_30 (-> tptp.hoare_1167836817_state Bool))) (=> (= X_62 Y_30) (@ (@ tptp.ord_le827224136tate_o X_62) Y_30))))
% 0.24/0.66 (assert (forall ((X_61 tptp.hoare_1167836817_state) (F_66 (-> tptp.hoare_1167836817_state Bool)) (G_15 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o F_66) G_15) (@ (@ tptp.ord_less_eq_o (@ F_66 X_61)) (@ G_15 X_61)))))
% 0.24/0.66 (assert (forall ((Y_29 Bool) (X_60 Bool)) (=> (@ (@ tptp.ord_less_eq_o Y_29) X_60) (= (@ (@ tptp.ord_less_eq_o X_60) Y_29) (= X_60 Y_29)))))
% 0.24/0.66 (assert (forall ((Y_29 (-> tptp.hoare_1167836817_state Bool)) (X_60 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o Y_29) X_60) (= (@ (@ tptp.ord_le827224136tate_o X_60) Y_29) (= X_60 Y_29)))))
% 0.24/0.66 (assert (forall ((A_125 (-> tptp.hoare_1167836817_state Bool)) (B_66 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o A_125) B_66) (=> (@ tptp.finite1084549118_state B_66) (@ tptp.finite1084549118_state A_125)))))
% 0.24/0.66 (assert (forall ((C_30 Bool) (B_65 Bool) (A_124 Bool)) (=> (= A_124 B_65) (=> (@ (@ tptp.ord_less_eq_o B_65) C_30) (@ (@ tptp.ord_less_eq_o A_124) C_30)))))
% 0.24/0.66 (assert (forall ((C_30 (-> tptp.hoare_1167836817_state Bool)) (A_124 (-> tptp.hoare_1167836817_state Bool)) (B_65 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_124 B_65) (=> (@ (@ tptp.ord_le827224136tate_o B_65) C_30) (@ (@ tptp.ord_le827224136tate_o A_124) C_30)))))
% 0.24/0.66 (assert (forall ((C_29 Bool) (B_64 Bool) (A_123 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_o C_29))) (=> (= A_123 B_64) (=> (@ _let_1 B_64) (@ _let_1 A_123))))))
% 0.24/0.66 (assert (forall ((C_29 (-> tptp.hoare_1167836817_state Bool)) (A_123 (-> tptp.hoare_1167836817_state Bool)) (B_64 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le827224136tate_o C_29))) (=> (= A_123 B_64) (=> (@ _let_1 B_64) (@ _let_1 A_123))))))
% 0.24/0.66 (assert (forall ((C_28 Bool) (A_122 Bool) (B_63 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_o A_122))) (=> (@ _let_1 B_63) (=> (= B_63 C_28) (@ _let_1 C_28))))))
% 0.24/0.66 (assert (forall ((C_28 (-> tptp.hoare_1167836817_state Bool)) (A_122 (-> tptp.hoare_1167836817_state Bool)) (B_63 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le827224136tate_o A_122))) (=> (@ _let_1 B_63) (=> (= B_63 C_28) (@ _let_1 C_28))))))
% 0.24/0.66 (assert (forall ((C_27 Bool) (B_62 Bool) (A_121 Bool)) (=> (@ (@ tptp.ord_less_eq_o B_62) A_121) (=> (= B_62 C_27) (@ (@ tptp.ord_less_eq_o C_27) A_121)))))
% 0.24/0.66 (assert (forall ((C_27 (-> tptp.hoare_1167836817_state Bool)) (B_62 (-> tptp.hoare_1167836817_state Bool)) (A_121 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o B_62) A_121) (=> (= B_62 C_27) (@ (@ tptp.ord_le827224136tate_o C_27) A_121)))))
% 0.24/0.66 (assert (forall ((X_59 Bool) (Y_28 Bool)) (=> (@ (@ tptp.ord_less_eq_o X_59) Y_28) (=> (@ (@ tptp.ord_less_eq_o Y_28) X_59) (= X_59 Y_28)))))
% 0.24/0.66 (assert (forall ((X_59 (-> tptp.hoare_1167836817_state Bool)) (Y_28 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o X_59) Y_28) (=> (@ (@ tptp.ord_le827224136tate_o Y_28) X_59) (= X_59 Y_28)))))
% 0.24/0.66 (assert (forall ((Z_27 Bool) (X_58 Bool) (Y_27 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_o X_58))) (=> (@ _let_1 Y_27) (=> (@ (@ tptp.ord_less_eq_o Y_27) Z_27) (@ _let_1 Z_27))))))
% 0.24/0.66 (assert (forall ((Z_27 (-> tptp.hoare_1167836817_state Bool)) (X_58 (-> tptp.hoare_1167836817_state Bool)) (Y_27 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le827224136tate_o X_58))) (=> (@ _let_1 Y_27) (=> (@ (@ tptp.ord_le827224136tate_o Y_27) Z_27) (@ _let_1 Z_27))))))
% 0.24/0.66 (assert (forall ((Y_26 Bool) (X_57 Bool)) (=> (@ (@ tptp.ord_less_eq_o Y_26) X_57) (=> (@ (@ tptp.ord_less_eq_o X_57) Y_26) (= X_57 Y_26)))))
% 0.24/0.66 (assert (forall ((Y_26 (-> tptp.hoare_1167836817_state Bool)) (X_57 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o Y_26) X_57) (=> (@ (@ tptp.ord_le827224136tate_o X_57) Y_26) (= X_57 Y_26)))))
% 0.24/0.66 (assert (forall ((Z_26 Bool) (Y_25 Bool) (X_56 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_o Z_26))) (=> (@ (@ tptp.ord_less_eq_o Y_25) X_56) (=> (@ _let_1 Y_25) (@ _let_1 X_56))))))
% 0.24/0.66 (assert (forall ((Z_26 (-> tptp.hoare_1167836817_state Bool)) (Y_25 (-> tptp.hoare_1167836817_state Bool)) (X_56 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le827224136tate_o Z_26))) (=> (@ (@ tptp.ord_le827224136tate_o Y_25) X_56) (=> (@ _let_1 Y_25) (@ _let_1 X_56))))))
% 0.24/0.66 (assert (forall ((X_55 tptp.hoare_1167836817_state) (F_65 (-> tptp.hoare_1167836817_state Bool)) (G_14 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o F_65) G_14) (@ (@ tptp.ord_less_eq_o (@ F_65 X_55)) (@ G_14 X_55)))))
% 0.24/0.66 (assert (forall ((A_120 (-> tptp.hoare_1167836817_state Bool))) (@ (@ tptp.ord_le827224136tate_o tptp.bot_bo70021908tate_o) A_120)))
% 0.24/0.66 (assert (forall ((A_120 Bool)) (@ (@ tptp.ord_less_eq_o tptp.bot_bot_o) A_120)))
% 0.24/0.66 (assert (forall ((A_119 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.ord_le827224136tate_o A_119) tptp.bot_bo70021908tate_o) (= A_119 tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (forall ((A_119 Bool)) (= (@ (@ tptp.ord_less_eq_o A_119) tptp.bot_bot_o) (= A_119 tptp.bot_bot_o))))
% 0.24/0.66 (assert (forall ((A_118 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o A_118) tptp.bot_bo70021908tate_o) (= A_118 tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (forall ((A_118 Bool)) (=> (@ (@ tptp.ord_less_eq_o A_118) tptp.bot_bot_o) (= A_118 tptp.bot_bot_o))))
% 0.24/0.66 (assert (forall ((A_117 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.ord_le827224136tate_o A_117) tptp.bot_bo70021908tate_o) (= A_117 tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (forall ((B_61 (-> tptp.hoare_1167836817_state Bool)) (A_116 tptp.hoare_1167836817_state)) (@ (@ tptp.ord_le827224136tate_o B_61) (@ (@ tptp.insert2134838167_state A_116) B_61))))
% 0.24/0.66 (assert (forall ((X_54 tptp.hoare_1167836817_state) (A_115 (-> tptp.hoare_1167836817_state Bool)) (B_60 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.ord_le827224136tate_o (@ (@ tptp.insert2134838167_state X_54) A_115)) B_60) (and (@ (@ tptp.member2058392318_state X_54) B_60) (@ (@ tptp.ord_le827224136tate_o A_115) B_60)))))
% 0.24/0.66 (assert (forall ((B_59 (-> tptp.hoare_1167836817_state Bool)) (X_53 tptp.hoare_1167836817_state) (A_114 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le827224136tate_o A_114))) (=> (not (@ (@ tptp.member2058392318_state X_53) A_114)) (= (@ _let_1 (@ (@ tptp.insert2134838167_state X_53) B_59)) (@ _let_1 B_59))))))
% 0.24/0.66 (assert (forall ((B_58 tptp.hoare_1167836817_state) (A_113 (-> tptp.hoare_1167836817_state Bool)) (B_57 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le827224136tate_o A_113))) (=> (@ _let_1 B_57) (@ _let_1 (@ (@ tptp.insert2134838167_state B_58) B_57))))))
% 0.24/0.66 (assert (forall ((A_112 tptp.hoare_1167836817_state) (C_26 (-> tptp.hoare_1167836817_state Bool)) (D_1 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state A_112))) (=> (@ (@ tptp.ord_le827224136tate_o C_26) D_1) (@ (@ tptp.ord_le827224136tate_o (@ _let_1 C_26)) (@ _let_1 D_1))))))
% 0.24/0.66 (assert (forall ((A_111 tptp.hoare_1167836817_state) (A_110 (-> tptp.hoare_1167836817_state Bool))) (= (@ tptp.finite1084549118_state (@ (@ tptp.insert2134838167_state A_111) A_110)) (@ tptp.finite1084549118_state A_110))))
% 0.24/0.66 (assert (forall ((Ts_3 (-> tptp.hoare_1167836817_state Bool)) (G_13 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o Ts_3) G_13) (@ (@ tptp.hoare_123228589_state G_13) Ts_3))))
% 0.24/0.66 (assert (forall ((Ts_2 (-> tptp.hoare_1167836817_state Bool)) (G_12 (-> tptp.hoare_1167836817_state Bool)) (Ts_1 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.hoare_123228589_state G_12))) (=> (@ _let_1 Ts_1) (=> (@ (@ tptp.ord_le827224136tate_o Ts_2) Ts_1) (@ _let_1 Ts_2))))))
% 0.24/0.66 (assert (forall ((G_11 (-> tptp.hoare_1167836817_state Bool)) (G_10 (-> tptp.hoare_1167836817_state Bool)) (Ts (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.hoare_123228589_state G_10) Ts) (=> (@ (@ tptp.ord_le827224136tate_o G_10) G_11) (@ (@ tptp.hoare_123228589_state G_11) Ts)))))
% 0.24/0.66 (assert (forall ((F_64 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (Z_25 tptp.hoare_1167836817_state)) (@ (@ (@ (@ tptp.finite1316643734_state F_64) Z_25) tptp.bot_bo70021908tate_o) Z_25)))
% 0.24/0.66 (assert (forall ((F_63 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (Z_24 tptp.hoare_1167836817_state) (X_52 tptp.hoare_1167836817_state)) (=> (@ (@ (@ (@ tptp.finite1316643734_state F_63) Z_24) tptp.bot_bo70021908tate_o) X_52) (= X_52 Z_24))))
% 0.24/0.66 (assert (forall ((F_62 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (Z_23 tptp.hoare_1167836817_state) (Y_24 tptp.hoare_1167836817_state) (X_51 tptp.hoare_1167836817_state) (A_109 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ (@ tptp.finite1316643734_state F_62) Z_23))) (=> (not (@ (@ tptp.member2058392318_state X_51) A_109)) (=> (@ (@ _let_1 A_109) Y_24) (@ (@ _let_1 (@ (@ tptp.insert2134838167_state X_51) A_109)) (@ (@ F_62 X_51) Y_24)))))))
% 0.24/0.66 (assert (forall ((P_6 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (A_108 (-> tptp.hoare_1167836817_state Bool)) (F_61 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state F_61) (=> (@ (@ tptp.ord_le827224136tate_o F_61) A_108) (=> (@ P_6 tptp.bot_bo70021908tate_o) (=> (forall ((A_59 tptp.hoare_1167836817_state) (F_50 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state A_59))) (=> (@ tptp.finite1084549118_state F_50) (=> (@ _let_1 A_108) (=> (not (@ _let_1 F_50)) (=> (@ P_6 F_50) (@ P_6 (@ (@ tptp.insert2134838167_state A_59) F_50)))))))) (@ P_6 F_61)))))))
% 0.24/0.66 (assert (forall ((F_60 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (A_107 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state A_107) (=> (not (= A_107 tptp.bot_bo70021908tate_o)) (@ tptp.ex (@ (@ tptp.finite309220289_state F_60) A_107))))))
% 0.24/0.66 (assert (forall ((B_56 (-> tptp.hoare_1167836817_state Bool)) (A_106 (-> tptp.hoare_1167836817_state Bool))) (=> (forall ((X tptp.hoare_1167836817_state)) (let ((_let_1 (@ tptp.member2058392318_state X))) (=> (@ _let_1 A_106) (@ _let_1 B_56)))) (@ (@ tptp.ord_le827224136tate_o A_106) B_56))))
% 0.24/0.66 (assert (forall ((A_105 (-> tptp.hoare_1167836817_state Bool))) (= (@ tptp.finite1084549118_state A_105) (or (= A_105 tptp.bot_bo70021908tate_o) (exists ((A_58 (-> tptp.hoare_1167836817_state Bool)) (A_59 tptp.hoare_1167836817_state)) (and (= A_105 (@ (@ tptp.insert2134838167_state A_59) A_58)) (@ tptp.finite1084549118_state A_58)))))))
% 0.24/0.66 (assert (forall ((P_5 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (F_59 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state F_59) (=> (@ P_5 tptp.bot_bo70021908tate_o) (=> (forall ((X tptp.hoare_1167836817_state) (F_50 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state F_50) (=> (not (@ (@ tptp.member2058392318_state X) F_50)) (=> (@ P_5 F_50) (@ P_5 (@ (@ tptp.insert2134838167_state X) F_50)))))) (@ P_5 F_59))))))
% 0.24/0.66 (assert (forall ((F_58 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (Z_22 tptp.hoare_1167836817_state) (A_104 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state A_104) (@ tptp.ex (@ (@ (@ tptp.finite1316643734_state F_58) Z_22) A_104)))))
% 0.24/0.66 (assert (forall ((F_57 (-> tptp.hoare_1167836817_state Bool)) (G_9 (-> tptp.hoare_1167836817_state Bool))) (=> (forall ((X tptp.hoare_1167836817_state)) (@ (@ tptp.ord_less_eq_o (@ F_57 X)) (@ G_9 X))) (@ (@ tptp.ord_le827224136tate_o F_57) G_9))))
% 0.24/0.66 (assert (forall ((F_56 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (A1_1 (-> tptp.hoare_1167836817_state Bool)) (A2_1 tptp.hoare_1167836817_state)) (= (@ (@ (@ tptp.finite309220289_state F_56) A1_1) A2_1) (exists ((A_59 tptp.hoare_1167836817_state) (A_58 (-> tptp.hoare_1167836817_state Bool)) (X tptp.hoare_1167836817_state)) (and (= A1_1 (@ (@ tptp.insert2134838167_state A_59) A_58)) (= A2_1 X) (@ (@ (@ (@ tptp.finite1316643734_state F_56) A_59) A_58) X) (not (@ (@ tptp.member2058392318_state A_59) A_58)))))))
% 0.24/0.66 (assert (forall ((F_55 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (Z_21 tptp.hoare_1167836817_state) (A1 (-> tptp.hoare_1167836817_state Bool)) (A2 tptp.hoare_1167836817_state)) (= (@ (@ (@ (@ tptp.finite1316643734_state F_55) Z_21) A1) A2) (or (and (= A1 tptp.bot_bo70021908tate_o) (= A2 Z_21)) (exists ((X tptp.hoare_1167836817_state) (A_58 (-> tptp.hoare_1167836817_state Bool)) (Y tptp.hoare_1167836817_state)) (and (= A1 (@ (@ tptp.insert2134838167_state X) A_58)) (= A2 (@ (@ F_55 X) Y)) (not (@ (@ tptp.member2058392318_state X) A_58)) (@ (@ (@ (@ tptp.finite1316643734_state F_55) Z_21) A_58) Y)))))))
% 0.24/0.66 (assert (forall ((B_55 (-> tptp.hoare_1167836817_state Bool)) (A_103 (-> tptp.hoare_1167836817_state Bool)) (F_54 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_53 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (let ((_let_1 (@ F_53 A_103))) (=> (@ (@ tptp.finite806517911_state F_54) F_53) (=> (@ tptp.finite1084549118_state A_103) (=> (not (= B_55 tptp.bot_bo70021908tate_o)) (=> (@ (@ tptp.ord_le827224136tate_o B_55) A_103) (= (@ (@ F_54 (@ F_53 B_55)) _let_1) _let_1))))))))
% 0.24/0.66 (assert (forall ((X_50 tptp.hoare_1167836817_state) (A_102 (-> tptp.hoare_1167836817_state Bool)) (F_52 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_51 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite806517911_state F_52) F_51) (=> (@ tptp.finite1084549118_state A_102) (=> (not (= A_102 tptp.bot_bo70021908tate_o)) (= (@ F_51 (@ (@ tptp.insert2134838167_state X_50) A_102)) (@ (@ F_52 X_50) (@ F_51 A_102))))))))
% 0.24/0.66 (assert (forall ((P_4 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (F_49 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state F_49) (=> (not (= F_49 tptp.bot_bo70021908tate_o)) (=> (forall ((X tptp.hoare_1167836817_state)) (@ P_4 (@ (@ tptp.insert2134838167_state X) tptp.bot_bo70021908tate_o))) (=> (forall ((X tptp.hoare_1167836817_state) (F_50 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state F_50) (=> (not (= F_50 tptp.bot_bo70021908tate_o)) (=> (not (@ (@ tptp.member2058392318_state X) F_50)) (=> (@ P_4 F_50) (@ P_4 (@ (@ tptp.insert2134838167_state X) F_50))))))) (@ P_4 F_49)))))))
% 0.24/0.66 (assert (forall ((Q_1 (-> tptp.hoare_1167836817_state Bool)) (P_3 (-> tptp.hoare_1167836817_state Bool))) (=> (forall ((X tptp.hoare_1167836817_state)) (=> (@ P_3 X) (@ Q_1 X))) (@ (@ tptp.ord_le827224136tate_o (@ tptp.collec1027672124_state P_3)) (@ tptp.collec1027672124_state Q_1)))))
% 0.24/0.66 (assert (forall ((X_49 tptp.hoare_1167836817_state) (F_48 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_47 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite806517911_state F_48) F_47) (= (@ (@ F_48 X_49) X_49) X_49))))
% 0.24/0.66 (assert (forall ((X_48 tptp.hoare_1167836817_state) (A_101 (-> tptp.hoare_1167836817_state Bool)) (F_46 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_45 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (let ((_let_1 (@ F_45 A_101))) (=> (@ (@ tptp.finite806517911_state F_46) F_45) (=> (@ tptp.finite1084549118_state A_101) (=> (@ (@ tptp.member2058392318_state X_48) A_101) (= (@ (@ F_46 X_48) _let_1) _let_1)))))))
% 0.24/0.66 (assert (forall ((Q (-> tptp.hoare_1167836817_state Bool)) (P_2 (-> tptp.hoare_1167836817_state Bool))) (=> (forall ((X tptp.hoare_1167836817_state)) (=> (@ P_2 X) (@ Q X))) (@ (@ tptp.ord_le827224136tate_o P_2) Q))))
% 0.24/0.66 (assert (forall ((C_25 Bool) (F_44 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (B_54 (-> tptp.hoare_1167836817_state Bool)) (A_100 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_less_eq_o C_25))) (=> (@ (@ tptp.ord_le827224136tate_o B_54) A_100) (=> (@ _let_1 (@ F_44 B_54)) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o Y) X) (@ (@ tptp.ord_less_eq_o (@ F_44 Y)) (@ F_44 X)))) (@ _let_1 (@ F_44 A_100))))))))
% 0.24/0.66 (assert (forall ((C_25 (-> tptp.hoare_1167836817_state Bool)) (F_44 (-> Bool tptp.hoare_1167836817_state Bool)) (B_54 Bool) (A_100 Bool)) (let ((_let_1 (@ tptp.ord_le827224136tate_o C_25))) (=> (@ (@ tptp.ord_less_eq_o B_54) A_100) (=> (@ _let_1 (@ F_44 B_54)) (=> (forall ((X Bool) (Y Bool)) (=> (@ (@ tptp.ord_less_eq_o Y) X) (@ (@ tptp.ord_le827224136tate_o (@ F_44 Y)) (@ F_44 X)))) (@ _let_1 (@ F_44 A_100))))))))
% 0.24/0.66 (assert (forall ((C_24 Bool) (F_43 (-> Bool Bool)) (B_53 Bool) (A_99 Bool)) (=> (@ (@ tptp.ord_less_eq_o B_53) A_99) (=> (= (@ F_43 B_53) C_24) (=> (forall ((X Bool) (Y Bool)) (=> (@ (@ tptp.ord_less_eq_o Y) X) (@ (@ tptp.ord_less_eq_o (@ F_43 Y)) (@ F_43 X)))) (@ (@ tptp.ord_less_eq_o C_24) (@ F_43 A_99)))))))
% 0.24/0.66 (assert (forall ((F_43 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool)) (C_24 (-> tptp.hoare_1167836817_state Bool)) (B_53 (-> tptp.hoare_1167836817_state Bool)) (A_99 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o B_53) A_99) (=> (= (@ F_43 B_53) C_24) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o Y) X) (@ (@ tptp.ord_le827224136tate_o (@ F_43 Y)) (@ F_43 X)))) (@ (@ tptp.ord_le827224136tate_o C_24) (@ F_43 A_99)))))))
% 0.24/0.66 (assert (forall ((C_23 Bool) (F_42 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (A_98 (-> tptp.hoare_1167836817_state Bool)) (B_52 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o A_98) B_52) (=> (= (@ F_42 B_52) C_23) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o X) Y) (@ (@ tptp.ord_less_eq_o (@ F_42 X)) (@ F_42 Y)))) (@ (@ tptp.ord_less_eq_o (@ F_42 A_98)) C_23))))))
% 0.24/0.66 (assert (forall ((F_42 (-> Bool tptp.hoare_1167836817_state Bool)) (C_23 (-> tptp.hoare_1167836817_state Bool)) (A_98 Bool) (B_52 Bool)) (=> (@ (@ tptp.ord_less_eq_o A_98) B_52) (=> (= (@ F_42 B_52) C_23) (=> (forall ((X Bool) (Y Bool)) (=> (@ (@ tptp.ord_less_eq_o X) Y) (@ (@ tptp.ord_le827224136tate_o (@ F_42 X)) (@ F_42 Y)))) (@ (@ tptp.ord_le827224136tate_o (@ F_42 A_98)) C_23))))))
% 0.24/0.66 (assert (forall ((F_41 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (C_22 Bool) (A_97 (-> tptp.hoare_1167836817_state Bool)) (B_51 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o A_97) B_51) (=> (@ (@ tptp.ord_less_eq_o (@ F_41 B_51)) C_22) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o X) Y) (@ (@ tptp.ord_less_eq_o (@ F_41 X)) (@ F_41 Y)))) (@ (@ tptp.ord_less_eq_o (@ F_41 A_97)) C_22))))))
% 0.24/0.66 (assert (forall ((F_41 (-> Bool tptp.hoare_1167836817_state Bool)) (C_22 (-> tptp.hoare_1167836817_state Bool)) (A_97 Bool) (B_51 Bool)) (=> (@ (@ tptp.ord_less_eq_o A_97) B_51) (=> (@ (@ tptp.ord_le827224136tate_o (@ F_41 B_51)) C_22) (=> (forall ((X Bool) (Y Bool)) (=> (@ (@ tptp.ord_less_eq_o X) Y) (@ (@ tptp.ord_le827224136tate_o (@ F_41 X)) (@ F_41 Y)))) (@ (@ tptp.ord_le827224136tate_o (@ F_41 A_97)) C_22))))))
% 0.24/0.66 (assert (forall ((C_21 (-> tptp.hoare_1167836817_state Bool)) (F_40 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (B_50 (-> tptp.hoare_1167836817_state Bool)) (A_96 Bool)) (=> (= A_96 (@ F_40 B_50)) (=> (@ (@ tptp.ord_le827224136tate_o B_50) C_21) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o X) Y) (@ (@ tptp.ord_less_eq_o (@ F_40 X)) (@ F_40 Y)))) (@ (@ tptp.ord_less_eq_o A_96) (@ F_40 C_21)))))))
% 0.24/0.66 (assert (forall ((C_21 Bool) (A_96 (-> tptp.hoare_1167836817_state Bool)) (F_40 (-> Bool tptp.hoare_1167836817_state Bool)) (B_50 Bool)) (=> (= A_96 (@ F_40 B_50)) (=> (@ (@ tptp.ord_less_eq_o B_50) C_21) (=> (forall ((X Bool) (Y Bool)) (=> (@ (@ tptp.ord_less_eq_o X) Y) (@ (@ tptp.ord_le827224136tate_o (@ F_40 X)) (@ F_40 Y)))) (@ (@ tptp.ord_le827224136tate_o A_96) (@ F_40 C_21)))))))
% 0.24/0.66 (assert (forall ((C_20 Bool) (F_39 (-> Bool tptp.hoare_1167836817_state Bool)) (B_49 Bool) (A_95 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o (@ F_39 B_49)) A_95) (=> (@ (@ tptp.ord_less_eq_o C_20) B_49) (=> (forall ((X Bool) (Y Bool)) (=> (@ (@ tptp.ord_less_eq_o Y) X) (@ (@ tptp.ord_le827224136tate_o (@ F_39 Y)) (@ F_39 X)))) (@ (@ tptp.ord_le827224136tate_o (@ F_39 C_20)) A_95))))))
% 0.24/0.66 (assert (forall ((C_20 (-> tptp.hoare_1167836817_state Bool)) (F_39 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (B_49 (-> tptp.hoare_1167836817_state Bool)) (A_95 Bool)) (=> (@ (@ tptp.ord_less_eq_o (@ F_39 B_49)) A_95) (=> (@ (@ tptp.ord_le827224136tate_o C_20) B_49) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o Y) X) (@ (@ tptp.ord_less_eq_o (@ F_39 Y)) (@ F_39 X)))) (@ (@ tptp.ord_less_eq_o (@ F_39 C_20)) A_95))))))
% 0.24/0.66 (assert (forall ((C_19 Bool) (F_38 (-> Bool Bool)) (B_48 Bool) (A_94 Bool)) (=> (= A_94 (@ F_38 B_48)) (=> (@ (@ tptp.ord_less_eq_o C_19) B_48) (=> (forall ((X Bool) (Y Bool)) (=> (@ (@ tptp.ord_less_eq_o Y) X) (@ (@ tptp.ord_less_eq_o (@ F_38 Y)) (@ F_38 X)))) (@ (@ tptp.ord_less_eq_o (@ F_38 C_19)) A_94))))))
% 0.24/0.66 (assert (forall ((C_19 (-> tptp.hoare_1167836817_state Bool)) (A_94 (-> tptp.hoare_1167836817_state Bool)) (F_38 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool)) (B_48 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_94 (@ F_38 B_48)) (=> (@ (@ tptp.ord_le827224136tate_o C_19) B_48) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o Y) X) (@ (@ tptp.ord_le827224136tate_o (@ F_38 Y)) (@ F_38 X)))) (@ (@ tptp.ord_le827224136tate_o (@ F_38 C_19)) A_94))))))
% 0.24/0.66 (assert (forall ((C_18 Bool) (A_93 (-> tptp.hoare_1167836817_state Bool)) (F_37 (-> Bool tptp.hoare_1167836817_state Bool)) (B_47 Bool)) (let ((_let_1 (@ tptp.ord_le827224136tate_o A_93))) (=> (@ _let_1 (@ F_37 B_47)) (=> (@ (@ tptp.ord_less_eq_o B_47) C_18) (=> (forall ((X Bool) (Y Bool)) (=> (@ (@ tptp.ord_less_eq_o X) Y) (@ (@ tptp.ord_le827224136tate_o (@ F_37 X)) (@ F_37 Y)))) (@ _let_1 (@ F_37 C_18))))))))
% 0.24/0.66 (assert (forall ((C_18 (-> tptp.hoare_1167836817_state Bool)) (A_93 Bool) (F_37 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (B_47 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_less_eq_o A_93))) (=> (@ _let_1 (@ F_37 B_47)) (=> (@ (@ tptp.ord_le827224136tate_o B_47) C_18) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o X) Y) (@ (@ tptp.ord_less_eq_o (@ F_37 X)) (@ F_37 Y)))) (@ _let_1 (@ F_37 C_18))))))))
% 0.24/0.66 (assert (forall ((A_92 (-> tptp.hoare_1167836817_state Bool)) (F_36 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_35 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.big_se1603066171_state F_36) F_35) (=> (@ tptp.finite1084549118_state A_92) (= (@ F_35 A_92) (@ (@ tptp.finite1646097201_state F_36) A_92))))))
% 0.24/0.66 (assert (forall ((X_47 tptp.hoare_1167836817_state) (A_91 (-> tptp.hoare_1167836817_state Bool)) (F_34 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_33 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (let ((_let_1 (@ (@ tptp.minus_2107060239tate_o A_91) (@ (@ tptp.insert2134838167_state X_47) tptp.bot_bo70021908tate_o)))) (let ((_let_2 (@ F_33 A_91))) (let ((_let_3 (= _let_1 tptp.bot_bo70021908tate_o))) (=> (@ (@ tptp.finite1074406356_state F_34) F_33) (=> (@ tptp.finite1084549118_state A_91) (=> (@ (@ tptp.member2058392318_state X_47) A_91) (and (=> _let_3 (= _let_2 X_47)) (=> (not _let_3) (= _let_2 (@ (@ F_34 X_47) (@ F_33 _let_1)))))))))))))
% 0.24/0.66 (assert (forall ((X_46 tptp.hoare_1167836817_state) (A_90 (-> tptp.hoare_1167836817_state Bool)) (F_32 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_31 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (let ((_let_1 (@ tptp.insert2134838167_state X_46))) (let ((_let_2 (@ (@ tptp.minus_2107060239tate_o A_90) (@ _let_1 tptp.bot_bo70021908tate_o)))) (let ((_let_3 (@ F_31 (@ _let_1 A_90)))) (let ((_let_4 (= _let_2 tptp.bot_bo70021908tate_o))) (=> (@ (@ tptp.finite1074406356_state F_32) F_31) (=> (@ tptp.finite1084549118_state A_90) (and (=> _let_4 (= _let_3 X_46)) (=> (not _let_4) (= _let_3 (@ (@ F_32 X_46) (@ F_31 _let_2)))))))))))))
% 0.24/0.66 (assert (forall ((B_46 (-> tptp.hoare_1167836817_state Bool)) (C_17 tptp.hoare_1167836817_state) (A_89 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_17))) (=> (@ _let_1 A_89) (=> (not (@ _let_1 B_46)) (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_89) B_46)))))))
% 0.24/0.66 (assert (forall ((C_16 tptp.hoare_1167836817_state) (A_88 (-> tptp.hoare_1167836817_state Bool)) (B_45 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_16))) (=> (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_88) B_45)) (not (=> (@ _let_1 A_88) (@ _let_1 B_45)))))))
% 0.24/0.66 (assert (forall ((B_44 (-> tptp.hoare_1167836817_state Bool)) (A_87 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state A_87) (@ tptp.finite1084549118_state (@ (@ tptp.minus_2107060239tate_o A_87) B_44)))))
% 0.24/0.66 (assert (forall ((A_86 (-> tptp.hoare_1167836817_state Bool)) (B_43 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.minus_2107060239tate_o A_86) B_43) (@ tptp.collec1027672124_state (lambda ((X tptp.hoare_1167836817_state)) (let ((_let_1 (@ tptp.member2058392318_state X))) (and (@ _let_1 A_86) (not (@ _let_1 B_43)))))))))
% 0.24/0.66 (assert (forall ((C_15 tptp.hoare_1167836817_state) (A_85 (-> tptp.hoare_1167836817_state Bool)) (B_42 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_15))) (= (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_85) B_42)) (and (@ _let_1 A_85) (not (@ _let_1 B_42)))))))
% 0.24/0.66 (assert (forall ((A_84 (-> tptp.hoare_1167836817_state Bool)) (B_41 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ (@ tptp.minus_2107060239tate_o A_84) B_41))) (= (@ (@ tptp.minus_2107060239tate_o _let_1) B_41) _let_1))))
% 0.24/0.66 (assert (forall ((C_14 tptp.hoare_1167836817_state) (A_83 (-> tptp.hoare_1167836817_state Bool)) (B_40 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_14))) (=> (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_83) B_40)) (@ _let_1 A_83)))))
% 0.24/0.66 (assert (forall ((C_13 tptp.hoare_1167836817_state) (A_82 (-> tptp.hoare_1167836817_state Bool)) (B_39 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_13))) (=> (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_82) B_39)) (not (@ _let_1 B_39))))))
% 0.24/0.66 (assert (forall ((A_81 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.minus_2107060239tate_o tptp.bot_bo70021908tate_o) A_81) tptp.bot_bo70021908tate_o)))
% 0.24/0.66 (assert (forall ((A_80 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.minus_2107060239tate_o A_80) tptp.bot_bo70021908tate_o) A_80)))
% 0.24/0.66 (assert (forall ((A_79 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.minus_2107060239tate_o A_79) A_79) tptp.bot_bo70021908tate_o)))
% 0.24/0.66 (assert (forall ((A_78 (-> tptp.hoare_1167836817_state Bool)) (B_38 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state B_38) (= (@ tptp.finite1084549118_state (@ (@ tptp.minus_2107060239tate_o A_78) B_38)) (@ tptp.finite1084549118_state A_78)))))
% 0.24/0.66 (assert (forall ((A_77 (-> tptp.hoare_1167836817_state Bool)) (X_45 tptp.hoare_1167836817_state) (B_37 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ (@ tptp.minus_2107060239tate_o A_77) B_37))) (let ((_let_2 (@ tptp.insert2134838167_state X_45))) (let ((_let_3 (@ (@ tptp.minus_2107060239tate_o (@ _let_2 A_77)) B_37))) (let ((_let_4 (@ (@ tptp.member2058392318_state X_45) B_37))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 0.24/0.66 (assert (forall ((A_76 (-> tptp.hoare_1167836817_state Bool)) (X_44 tptp.hoare_1167836817_state) (B_36 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.member2058392318_state X_44) B_36) (= (@ (@ tptp.minus_2107060239tate_o (@ (@ tptp.insert2134838167_state X_44) A_76)) B_36) (@ (@ tptp.minus_2107060239tate_o A_76) B_36)))))
% 0.24/0.66 (assert (forall ((A_75 (-> tptp.hoare_1167836817_state Bool)) (B_35 (-> tptp.hoare_1167836817_state Bool))) (@ (@ tptp.ord_le827224136tate_o (@ (@ tptp.minus_2107060239tate_o A_75) B_35)) A_75)))
% 0.24/0.66 (assert (forall ((D (-> tptp.hoare_1167836817_state Bool)) (B_34 (-> tptp.hoare_1167836817_state Bool)) (A_74 (-> tptp.hoare_1167836817_state Bool)) (C_12 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o A_74) C_12) (=> (@ (@ tptp.ord_le827224136tate_o D) B_34) (@ (@ tptp.ord_le827224136tate_o (@ (@ tptp.minus_2107060239tate_o A_74) B_34)) (@ (@ tptp.minus_2107060239tate_o C_12) D))))))
% 0.24/0.66 (assert (forall ((C_11 (-> tptp.hoare_1167836817_state Bool)) (A_73 (-> tptp.hoare_1167836817_state Bool)) (B_33 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o A_73) B_33) (=> (@ (@ tptp.ord_le827224136tate_o B_33) C_11) (= (@ (@ tptp.minus_2107060239tate_o B_33) (@ (@ tptp.minus_2107060239tate_o C_11) A_73)) A_73)))))
% 0.24/0.66 (assert (forall ((A_72 (-> tptp.hoare_1167836817_state Bool)) (A_71 tptp.hoare_1167836817_state) (B_32 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state A_71))) (let ((_let_2 (@ tptp.minus_2107060239tate_o A_72))) (= (@ _let_2 (@ _let_1 B_32)) (@ (@ tptp.minus_2107060239tate_o (@ _let_2 B_32)) (@ _let_1 tptp.bot_bo70021908tate_o)))))))
% 0.24/0.66 (assert (forall ((A_70 (-> tptp.hoare_1167836817_state Bool)) (A_69 tptp.hoare_1167836817_state) (B_31 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state A_69))) (let ((_let_2 (@ tptp.minus_2107060239tate_o A_70))) (= (@ _let_2 (@ _let_1 B_31)) (@ (@ tptp.minus_2107060239tate_o (@ _let_2 (@ _let_1 tptp.bot_bo70021908tate_o))) B_31))))))
% 0.24/0.66 (assert (forall ((A_68 tptp.hoare_1167836817_state) (A_67 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state A_68))) (= (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_67) (@ _let_1 tptp.bot_bo70021908tate_o))) (@ _let_1 A_67)))))
% 0.24/0.66 (assert (forall ((X_43 tptp.hoare_1167836817_state) (A_66 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state X_43))) (=> (not (@ (@ tptp.member2058392318_state X_43) A_66)) (= (@ (@ tptp.minus_2107060239tate_o (@ _let_1 A_66)) (@ _let_1 tptp.bot_bo70021908tate_o)) A_66)))))
% 0.24/0.66 (assert (forall ((A_65 tptp.hoare_1167836817_state) (A_64 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state A_65))) (=> (@ (@ tptp.member2058392318_state A_65) A_64) (= (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_64) (@ _let_1 tptp.bot_bo70021908tate_o))) A_64)))))
% 0.24/0.66 (assert (forall ((A_63 (-> tptp.hoare_1167836817_state Bool)) (A_62 tptp.hoare_1167836817_state) (B_30 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.minus_2107060239tate_o A_63))) (= (@ tptp.finite1084549118_state (@ _let_1 (@ (@ tptp.insert2134838167_state A_62) B_30))) (@ tptp.finite1084549118_state (@ _let_1 B_30))))))
% 0.24/0.66 (assert (forall ((A_61 (-> tptp.hoare_1167836817_state Bool)) (X_42 tptp.hoare_1167836817_state) (B_29 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le827224136tate_o A_61))) (let ((_let_2 (@ (@ tptp.member2058392318_state X_42) A_61))) (let ((_let_3 (@ tptp.insert2134838167_state X_42))) (= (@ _let_1 (@ _let_3 B_29)) (and (=> _let_2 (@ (@ tptp.ord_le827224136tate_o (@ (@ tptp.minus_2107060239tate_o A_61) (@ _let_3 tptp.bot_bo70021908tate_o))) B_29)) (=> (not _let_2) (@ _let_1 B_29)))))))))
% 0.24/0.66 (assert (forall ((A_60 (-> tptp.hoare_1167836817_state Bool)) (X_41 tptp.hoare_1167836817_state) (B_28 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state X_41))) (=> (@ (@ tptp.ord_le827224136tate_o (@ (@ tptp.minus_2107060239tate_o A_60) (@ _let_1 tptp.bot_bo70021908tate_o))) B_28) (=> (@ (@ tptp.member2058392318_state X_41) A_60) (@ (@ tptp.ord_le827224136tate_o A_60) (@ _let_1 B_28)))))))
% 0.24/0.66 (assert (forall ((P_1 (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (A_57 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state A_57) (=> (@ P_1 A_57) (=> (forall ((A_59 tptp.hoare_1167836817_state) (A_58 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state A_58) (=> (@ (@ tptp.member2058392318_state A_59) A_58) (=> (@ P_1 A_58) (@ P_1 (@ (@ tptp.minus_2107060239tate_o A_58) (@ (@ tptp.insert2134838167_state A_59) tptp.bot_bo70021908tate_o))))))) (@ P_1 tptp.bot_bo70021908tate_o))))))
% 0.24/0.66 (assert (forall ((A_56 (-> tptp.hoare_1167836817_state Bool)) (B_27 (-> tptp.hoare_1167836817_state Bool)) (X_40 tptp.hoare_1167836817_state)) (= (@ (@ (@ tptp.minus_2107060239tate_o A_56) B_27) X_40) (@ (@ tptp.minus_minus_o (@ A_56 X_40)) (@ B_27 X_40)))))
% 0.24/0.66 (assert (forall ((A_55 (-> tptp.hoare_1167836817_state Bool)) (B_26 (-> tptp.hoare_1167836817_state Bool)) (X tptp.hoare_1167836817_state)) (= (@ (@ (@ tptp.minus_2107060239tate_o A_55) B_26) X) (@ (@ tptp.minus_minus_o (@ A_55 X)) (@ B_26 X)))))
% 0.24/0.66 (assert (forall ((A_54 tptp.hoare_1167836817_state) (Z_20 tptp.hoare_1167836817_state) (A_53 (-> tptp.hoare_1167836817_state Bool)) (Y_22 tptp.hoare_1167836817_state) (F_30 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (=> (@ tptp.finite1091222817_state F_30) (=> (@ (@ (@ (@ tptp.finite1316643734_state F_30) Z_20) A_53) Y_22) (=> (@ (@ tptp.member2058392318_state A_54) A_53) (exists ((Y_23 tptp.hoare_1167836817_state)) (and (= Y_22 (@ (@ F_30 A_54) Y_23)) (@ (@ (@ (@ tptp.finite1316643734_state F_30) Z_20) (@ (@ tptp.minus_2107060239tate_o A_53) (@ (@ tptp.insert2134838167_state A_54) tptp.bot_bo70021908tate_o))) Y_23))))))))
% 0.24/0.66 (assert (forall ((X_39 tptp.hoare_1167836817_state) (Y_21 tptp.hoare_1167836817_state) (Z_19 tptp.hoare_1167836817_state) (F_29 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (let ((_let_1 (@ F_29 X_39))) (let ((_let_2 (@ F_29 Y_21))) (=> (@ tptp.finite1091222817_state F_29) (= (@ _let_1 (@ _let_2 Z_19)) (@ _let_2 (@ _let_1 Z_19))))))))
% 0.24/0.66 (assert (forall ((Y_20 tptp.hoare_1167836817_state) (Z_18 tptp.hoare_1167836817_state) (A_52 (-> tptp.hoare_1167836817_state Bool)) (X_38 tptp.hoare_1167836817_state) (F_28 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (let ((_let_1 (@ (@ (@ tptp.finite1316643734_state F_28) Z_18) A_52))) (=> (@ tptp.finite1091222817_state F_28) (=> (@ _let_1 X_38) (=> (@ _let_1 Y_20) (= Y_20 X_38)))))))
% 0.24/0.66 (assert (forall ((Z_17 tptp.hoare_1167836817_state) (X_37 tptp.hoare_1167836817_state) (A_51 (-> tptp.hoare_1167836817_state Bool)) (V tptp.hoare_1167836817_state) (F_27 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (=> (@ tptp.finite1091222817_state F_27) (=> (@ (@ (@ (@ tptp.finite1316643734_state F_27) Z_17) (@ (@ tptp.insert2134838167_state X_37) A_51)) V) (=> (not (@ (@ tptp.member2058392318_state X_37) A_51)) (not (forall ((Y tptp.hoare_1167836817_state)) (=> (= V (@ (@ F_27 X_37) Y)) (not (@ (@ (@ (@ tptp.finite1316643734_state F_27) Z_17) A_51) Y))))))))))
% 0.24/0.66 (assert (forall ((X_36 Bool) (Least_3 Bool)) (=> (@ tptp.all1 (@ tptp.ord_less_eq_o Least_3)) (= (@ (@ tptp.ord_min_o X_36) Least_3) Least_3))))
% 0.24/0.66 (assert (forall ((X_36 (-> tptp.hoare_1167836817_state Bool)) (Least_3 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.all2 (@ tptp.ord_le827224136tate_o Least_3)) (= (@ (@ tptp.ord_mi1697686287tate_o X_36) Least_3) Least_3))))
% 0.24/0.66 (assert (forall ((X_35 Bool) (Least_2 Bool)) (=> (@ tptp.all1 (@ tptp.ord_less_eq_o Least_2)) (= (@ (@ tptp.ord_min_o Least_2) X_35) Least_2))))
% 0.24/0.66 (assert (forall ((X_35 (-> tptp.hoare_1167836817_state Bool)) (Least_2 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.all2 (@ tptp.ord_le827224136tate_o Least_2)) (= (@ (@ tptp.ord_mi1697686287tate_o Least_2) X_35) Least_2))))
% 0.24/0.66 (assert (= tptp.ord_min_o (@ tptp.min_o tptp.ord_less_eq_o)))
% 0.24/0.66 (assert (= tptp.ord_mi1697686287tate_o (@ tptp.min_Ho1955171539tate_o tptp.ord_le827224136tate_o)))
% 0.24/0.66 (assert (forall ((Z_16 tptp.hoare_1167836817_state) (X_34 tptp.hoare_1167836817_state) (A_50 (-> tptp.hoare_1167836817_state Bool)) (F_26 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (let ((_let_1 (@ tptp.insert2134838167_state X_34))) (let ((_let_2 (@ (@ tptp.finite1731015960_state F_26) Z_16))) (=> (@ tptp.finite1091222817_state F_26) (=> (@ tptp.finite1084549118_state A_50) (= (@ _let_2 (@ _let_1 A_50)) (@ (@ F_26 X_34) (@ _let_2 (@ (@ tptp.minus_2107060239tate_o A_50) (@ _let_1 tptp.bot_bo70021908tate_o)))))))))))
% 0.24/0.66 (assert (forall ((Z_15 tptp.hoare_1167836817_state) (X_33 tptp.hoare_1167836817_state) (A_49 (-> tptp.hoare_1167836817_state Bool)) (F_25 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (let ((_let_1 (@ (@ tptp.finite1731015960_state F_25) Z_15))) (=> (@ tptp.finite1091222817_state F_25) (=> (@ tptp.finite1084549118_state A_49) (=> (@ (@ tptp.member2058392318_state X_33) A_49) (= (@ _let_1 A_49) (@ (@ F_25 X_33) (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_49) (@ (@ tptp.insert2134838167_state X_33) tptp.bot_bo70021908tate_o)))))))))))
% 0.24/0.66 (assert (forall ((F_24 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (Z_14 tptp.hoare_1167836817_state)) (= (@ (@ (@ tptp.finite1731015960_state F_24) Z_14) tptp.bot_bo70021908tate_o) Z_14)))
% 0.24/0.66 (assert (forall ((X_32 tptp.hoare_1167836817_state) (Z_13 tptp.hoare_1167836817_state) (A_48 (-> tptp.hoare_1167836817_state Bool)) (F_23 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (let ((_let_1 (@ F_23 X_32))) (let ((_let_2 (@ tptp.finite1731015960_state F_23))) (=> (@ tptp.finite1091222817_state F_23) (=> (@ tptp.finite1084549118_state A_48) (= (@ _let_1 (@ (@ _let_2 Z_13) A_48)) (@ (@ _let_2 (@ _let_1 Z_13)) A_48))))))))
% 0.24/0.66 (assert (forall ((Z_12 tptp.hoare_1167836817_state) (A_47 (-> tptp.hoare_1167836817_state Bool)) (Y_19 tptp.hoare_1167836817_state) (F_22 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (=> (@ tptp.finite1091222817_state F_22) (=> (@ (@ (@ (@ tptp.finite1316643734_state F_22) Z_12) A_47) Y_19) (= (@ (@ (@ tptp.finite1731015960_state F_22) Z_12) A_47) Y_19)))))
% 0.24/0.66 (assert (forall ((Z_11 tptp.hoare_1167836817_state) (X_31 tptp.hoare_1167836817_state) (A_46 (-> tptp.hoare_1167836817_state Bool)) (F_21 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (let ((_let_1 (@ tptp.finite1731015960_state F_21))) (=> (@ tptp.finite1091222817_state F_21) (=> (@ tptp.finite1084549118_state A_46) (=> (not (@ (@ tptp.member2058392318_state X_31) A_46)) (= (@ (@ _let_1 Z_11) (@ (@ tptp.insert2134838167_state X_31) A_46)) (@ (@ _let_1 (@ (@ F_21 X_31) Z_11)) A_46))))))))
% 0.24/0.66 (assert (forall ((Z_10 tptp.hoare_1167836817_state) (X_30 tptp.hoare_1167836817_state) (A_45 (-> tptp.hoare_1167836817_state Bool)) (F_20 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (let ((_let_1 (@ (@ tptp.finite1731015960_state F_20) Z_10))) (=> (@ tptp.finite1091222817_state F_20) (=> (@ tptp.finite1084549118_state A_45) (=> (not (@ (@ tptp.member2058392318_state X_30) A_45)) (= (@ _let_1 (@ (@ tptp.insert2134838167_state X_30) A_45)) (@ (@ F_20 X_30) (@ _let_1 A_45)))))))))
% 0.24/0.66 (assert (forall ((X_29 tptp.hoare_1167836817_state) (A_44 (-> tptp.hoare_1167836817_state Bool)) (F_19 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_18 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite1074406356_state F_19) F_18) (=> (@ tptp.finite1084549118_state A_44) (=> (not (@ (@ tptp.member2058392318_state X_29) A_44)) (= (@ F_18 (@ (@ tptp.insert2134838167_state X_29) A_44)) (@ (@ (@ tptp.finite1731015960_state F_19) X_29) A_44)))))))
% 0.24/0.66 (assert (forall ((A_43 tptp.hoare_1167836817_state) (A_42 (-> tptp.hoare_1167836817_state Bool)) (F_17 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state)) (F_16 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state))) (=> (@ (@ tptp.finite806517911_state F_17) F_16) (=> (@ tptp.finite1084549118_state A_42) (= (@ F_16 (@ (@ tptp.insert2134838167_state A_43) A_42)) (@ (@ (@ tptp.finite1731015960_state F_17) A_43) A_42))))))
% 0.24/0.66 (assert (forall ((Z_9 tptp.hoare_1167836817_state) (A_41 (-> tptp.hoare_1167836817_state Bool)) (F_15 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (=> (@ tptp.finite1091222817_state F_15) (=> (@ tptp.finite1084549118_state A_41) (@ (@ (@ (@ tptp.finite1316643734_state F_15) Z_9) A_41) (@ (@ (@ tptp.finite1731015960_state F_15) Z_9) A_41))))))
% 0.24/0.66 (assert (forall ((Z_8 tptp.hoare_1167836817_state) (X_28 tptp.hoare_1167836817_state) (A_40 (-> tptp.hoare_1167836817_state Bool)) (F_14 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (let ((_let_1 (@ (@ tptp.finite1731015960_state F_14) Z_8))) (=> (@ tptp.finite1900754844_state F_14) (=> (@ tptp.finite1084549118_state A_40) (= (@ _let_1 (@ (@ tptp.insert2134838167_state X_28) A_40)) (@ (@ F_14 X_28) (@ _let_1 A_40))))))))
% 0.24/0.66 (assert (forall ((Z_8 (-> tptp.hoare_1167836817_state Bool)) (X_28 tptp.hoare_1167836817_state) (A_40 (-> tptp.hoare_1167836817_state Bool)) (F_14 (-> tptp.hoare_1167836817_state (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ (@ tptp.finite291020855tate_o F_14) Z_8))) (=> (@ tptp.finite856902323tate_o F_14) (=> (@ tptp.finite1084549118_state A_40) (= (@ _let_1 (@ (@ tptp.insert2134838167_state X_28) A_40)) (@ (@ F_14 X_28) (@ _let_1 A_40))))))))
% 0.24/0.66 (assert (forall ((Z_7 tptp.hoare_1167836817_state) (X_27 tptp.hoare_1167836817_state) (A_39 (-> tptp.hoare_1167836817_state Bool)) (F_13 (-> tptp.hoare_1167836817_state tptp.hoare_1167836817_state tptp.hoare_1167836817_state))) (let ((_let_1 (@ tptp.finite1731015960_state F_13))) (=> (@ tptp.finite1900754844_state F_13) (=> (@ tptp.finite1084549118_state A_39) (= (@ (@ _let_1 Z_7) (@ (@ tptp.insert2134838167_state X_27) A_39)) (@ (@ _let_1 (@ (@ F_13 X_27) Z_7)) A_39)))))))
% 0.24/0.66 (assert (forall ((Z_7 (-> tptp.hoare_1167836817_state Bool)) (X_27 tptp.hoare_1167836817_state) (A_39 (-> tptp.hoare_1167836817_state Bool)) (F_13 (-> tptp.hoare_1167836817_state (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.finite291020855tate_o F_13))) (=> (@ tptp.finite856902323tate_o F_13) (=> (@ tptp.finite1084549118_state A_39) (= (@ (@ _let_1 Z_7) (@ (@ tptp.insert2134838167_state X_27) A_39)) (@ (@ _let_1 (@ (@ F_13 X_27) Z_7)) A_39)))))))
% 0.24/0.66 (assert (forall ((X_26 tptp.hoare_1167836817_state) (Z_6 (-> tptp.hoare_1167836817_state Bool)) (F_12 (-> tptp.hoare_1167836817_state (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ F_12 X_26))) (let ((_let_2 (@ _let_1 Z_6))) (=> (@ tptp.finite856902323tate_o F_12) (= (@ _let_1 _let_2) _let_2))))))
% 0.24/0.66 (assert (@ tptp.finite856902323tate_o tptp.insert2134838167_state))
% 0.24/0.66 (assert (forall ((F_11 (-> tptp.hoare_1167836817_state tptp.nat)) (A_38 tptp.hoare_1167836817_state) (A_37 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.big_co337839062te_nat F_11))) (let ((_let_2 (@ _let_1 A_37))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_37) (@ (@ tptp.insert2134838167_state A_38) tptp.bot_bo70021908tate_o))))) (let ((_let_4 (@ (@ tptp.member2058392318_state A_38) A_37))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F_11 A_38)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 0.24/0.66 (assert (forall ((F_10 (-> tptp.hoare_1167836817_state tptp.nat)) (A_36 (-> tptp.hoare_1167836817_state Bool)) (B_25 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.big_co337839062te_nat F_10))) (=> (@ tptp.finite1084549118_state B_25) (=> (@ (@ tptp.ord_le827224136tate_o B_25) A_36) (= (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_36) B_25)) (@ (@ tptp.minus_minus_nat (@ _let_1 A_36)) (@ _let_1 B_25))))))))
% 0.24/0.66 (assert (forall ((G_8 (-> tptp.hoare_1167836817_state tptp.nat)) (H_1 (-> tptp.hoare_1167836817_state tptp.nat)) (A_35 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state A_35) (=> (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) A_35) (= (@ G_8 X) (@ H_1 X)))) (= (@ (@ tptp.big_co337839062te_nat G_8) A_35) (@ (@ tptp.big_co337839062te_nat H_1) A_35))))))
% 0.24/0.66 (assert (forall ((X_25 Bool) (Least_1 Bool)) (=> (@ tptp.all1 (@ tptp.ord_less_eq_o Least_1)) (= (@ (@ tptp.ord_max_o X_25) Least_1) X_25))))
% 0.24/0.66 (assert (forall ((X_25 (-> tptp.hoare_1167836817_state Bool)) (Least_1 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.all2 (@ tptp.ord_le827224136tate_o Least_1)) (= (@ (@ tptp.ord_ma164008317tate_o X_25) Least_1) X_25))))
% 0.24/0.66 (assert (forall ((X_24 Bool) (Least Bool)) (=> (@ tptp.all1 (@ tptp.ord_less_eq_o Least)) (= (@ (@ tptp.ord_max_o Least) X_24) X_24))))
% 0.24/0.66 (assert (forall ((X_24 (-> tptp.hoare_1167836817_state Bool)) (Least (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.all2 (@ tptp.ord_le827224136tate_o Least)) (= (@ (@ tptp.ord_ma164008317tate_o Least) X_24) X_24))))
% 0.24/0.66 (assert (= tptp.ord_max_o (@ tptp.max_o tptp.ord_less_eq_o)))
% 0.24/0.66 (assert (= tptp.ord_ma164008317tate_o (@ tptp.max_Ho421493569tate_o tptp.ord_le827224136tate_o)))
% 0.24/0.66 (assert (forall ((G_7 (-> tptp.hoare_1167836817_state tptp.nat)) (X_23 tptp.hoare_1167836817_state) (A_34 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.big_co337839062te_nat G_7))) (=> (@ tptp.finite1084549118_state A_34) (=> (@ (@ tptp.member2058392318_state X_23) A_34) (= (@ _let_1 A_34) (@ (@ tptp.plus_plus_nat (@ G_7 X_23)) (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_34) (@ (@ tptp.insert2134838167_state X_23) tptp.bot_bo70021908tate_o))))))))))
% 0.24/0.66 (assert (forall ((F_9 (-> tptp.hoare_1167836817_state tptp.nat)) (A_33 tptp.hoare_1167836817_state) (A_32 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.big_co337839062te_nat F_9))) (=> (@ tptp.finite1084549118_state A_32) (=> (@ (@ tptp.member2058392318_state A_33) A_32) (= (@ _let_1 A_32) (@ (@ tptp.plus_plus_nat (@ F_9 A_33)) (@ _let_1 (@ (@ tptp.minus_2107060239tate_o A_32) (@ (@ tptp.insert2134838167_state A_33) tptp.bot_bo70021908tate_o))))))))))
% 0.24/0.66 (assert (forall ((G_6 (-> tptp.hoare_1167836817_state tptp.nat)) (X_22 tptp.hoare_1167836817_state) (A_31 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.big_co337839062te_nat G_6))) (=> (@ tptp.finite1084549118_state A_31) (=> (not (@ (@ tptp.member2058392318_state X_22) A_31)) (= (@ _let_1 (@ (@ tptp.insert2134838167_state X_22) A_31)) (@ (@ tptp.plus_plus_nat (@ G_6 X_22)) (@ _let_1 A_31))))))))
% 0.24/0.66 (assert (forall ((F_8 (-> tptp.hoare_1167836817_state tptp.nat)) (A_30 tptp.hoare_1167836817_state) (F_7 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.big_co337839062te_nat F_8))) (=> (@ tptp.finite1084549118_state F_7) (=> (not (@ (@ tptp.member2058392318_state A_30) F_7)) (= (@ _let_1 (@ (@ tptp.insert2134838167_state A_30) F_7)) (@ (@ tptp.plus_plus_nat (@ F_8 A_30)) (@ _let_1 F_7))))))))
% 0.24/0.66 (assert (forall ((G_5 (-> tptp.hoare_1167836817_state tptp.nat)) (X_21 tptp.hoare_1167836817_state) (A_29 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.insert2134838167_state X_21))) (let ((_let_2 (@ tptp.big_co337839062te_nat G_5))) (=> (@ tptp.finite1084549118_state A_29) (= (@ _let_2 (@ _let_1 A_29)) (@ (@ tptp.plus_plus_nat (@ G_5 X_21)) (@ _let_2 (@ (@ tptp.minus_2107060239tate_o A_29) (@ _let_1 tptp.bot_bo70021908tate_o))))))))))
% 0.24/0.66 (assert (forall ((F_6 (-> tptp.hoare_1167836817_state tptp.nat)) (G_4 (-> tptp.hoare_1167836817_state tptp.nat)) (A_28 (-> tptp.hoare_1167836817_state Bool))) (=> (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) A_28) (= (@ F_6 X) (@ G_4 X)))) (= (@ (@ tptp.big_co337839062te_nat F_6) A_28) (@ (@ tptp.big_co337839062te_nat G_4) A_28)))))
% 0.24/0.66 (assert (forall ((F_5 (-> tptp.hoare_1167836817_state tptp.nat)) (G_3 (-> tptp.hoare_1167836817_state tptp.nat)) (A_27 (-> tptp.hoare_1167836817_state Bool)) (B_24 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_27 B_24) (=> (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) B_24) (= (@ F_5 X) (@ G_3 X)))) (= (@ (@ tptp.big_co337839062te_nat F_5) A_27) (@ (@ tptp.big_co337839062te_nat G_3) B_24))))))
% 0.24/0.66 (assert (forall ((H (-> tptp.hoare_1167836817_state tptp.nat)) (G_2 (-> tptp.hoare_1167836817_state tptp.nat)) (A_26 (-> tptp.hoare_1167836817_state Bool)) (B_23 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_26 B_23) (=> (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) B_23) (= (@ H X) (@ G_2 X)))) (= (@ (@ tptp.big_co337839062te_nat H) A_26) (@ (@ tptp.big_co337839062te_nat G_2) B_23))))))
% 0.24/0.66 (assert (forall ((A_25 (-> tptp.hoare_1167836817_state Bool))) (not (@ (@ tptp.ord_le65125204tate_o A_25) tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (forall ((A_25 Bool)) (not (@ (@ tptp.ord_less_o A_25) tptp.bot_bot_o))))
% 0.24/0.66 (assert (forall ((A_24 (-> tptp.hoare_1167836817_state Bool))) (= (not (= A_24 tptp.bot_bo70021908tate_o)) (@ (@ tptp.ord_le65125204tate_o tptp.bot_bo70021908tate_o) A_24))))
% 0.24/0.66 (assert (forall ((A_24 Bool)) (= (not (= A_24 tptp.bot_bot_o)) (@ (@ tptp.ord_less_o tptp.bot_bot_o) A_24))))
% 0.24/0.66 (assert (forall ((A_23 (-> tptp.hoare_1167836817_state Bool))) (not (@ (@ tptp.ord_le65125204tate_o A_23) tptp.bot_bo70021908tate_o))))
% 0.24/0.66 (assert (forall ((A_22 (-> tptp.hoare_1167836817_state Bool)) (B_22 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.ord_le65125204tate_o A_22) B_22) (and (@ (@ tptp.ord_le827224136tate_o A_22) B_22) (not (= A_22 B_22))))))
% 0.24/0.66 (assert (forall ((A_21 (-> tptp.hoare_1167836817_state Bool)) (B_21 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.ord_le827224136tate_o A_21) B_21) (or (@ (@ tptp.ord_le65125204tate_o A_21) B_21) (= A_21 B_21)))))
% 0.24/0.66 (assert (forall ((A_20 (-> tptp.hoare_1167836817_state Bool)) (B_20 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o A_20) B_20) (@ (@ tptp.ord_le827224136tate_o A_20) B_20))))
% 0.24/0.66 (assert (forall ((C_10 (-> tptp.hoare_1167836817_state Bool)) (A_19 (-> tptp.hoare_1167836817_state Bool)) (B_19 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le65125204tate_o A_19))) (=> (@ _let_1 B_19) (=> (@ (@ tptp.ord_le827224136tate_o B_19) C_10) (@ _let_1 C_10))))))
% 0.24/0.66 (assert (forall ((C_9 (-> tptp.hoare_1167836817_state Bool)) (A_18 (-> tptp.hoare_1167836817_state Bool)) (B_18 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o A_18) B_18) (=> (@ (@ tptp.ord_le65125204tate_o B_18) C_9) (@ (@ tptp.ord_le65125204tate_o A_18) C_9)))))
% 0.24/0.66 (assert (forall ((X_20 (-> tptp.hoare_1167836817_state Bool)) (Y_18 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o X_20) Y_18) (not (@ (@ tptp.ord_le65125204tate_o Y_18) X_20)))))
% 0.24/0.66 (assert (forall ((X_20 Bool) (Y_18 Bool)) (=> (@ (@ tptp.ord_less_o X_20) Y_18) (not (@ (@ tptp.ord_less_o Y_18) X_20)))))
% 0.24/0.66 (assert (forall ((Z_5 (-> tptp.hoare_1167836817_state Bool)) (Y_17 (-> tptp.hoare_1167836817_state Bool)) (X_19 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le65125204tate_o Z_5))) (=> (@ (@ tptp.ord_le65125204tate_o Y_17) X_19) (=> (@ _let_1 Y_17) (@ _let_1 X_19))))))
% 0.24/0.66 (assert (forall ((Z_5 Bool) (Y_17 Bool) (X_19 Bool)) (let ((_let_1 (@ tptp.ord_less_o Z_5))) (=> (@ (@ tptp.ord_less_o Y_17) X_19) (=> (@ _let_1 Y_17) (@ _let_1 X_19))))))
% 0.24/0.66 (assert (forall ((Z_4 (-> tptp.hoare_1167836817_state Bool)) (X_18 (-> tptp.hoare_1167836817_state Bool)) (Y_16 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le65125204tate_o X_18))) (=> (@ _let_1 Y_16) (=> (@ (@ tptp.ord_le65125204tate_o Y_16) Z_4) (@ _let_1 Z_4))))))
% 0.24/0.66 (assert (forall ((Z_4 Bool) (X_18 Bool) (Y_16 Bool)) (let ((_let_1 (@ tptp.ord_less_o X_18))) (=> (@ _let_1 Y_16) (=> (@ (@ tptp.ord_less_o Y_16) Z_4) (@ _let_1 Z_4))))))
% 0.24/0.66 (assert (forall ((C_8 (-> tptp.hoare_1167836817_state Bool)) (B_17 (-> tptp.hoare_1167836817_state Bool)) (A_17 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o B_17) A_17) (=> (= B_17 C_8) (@ (@ tptp.ord_le65125204tate_o C_8) A_17)))))
% 0.24/0.66 (assert (forall ((C_8 Bool) (B_17 Bool) (A_17 Bool)) (=> (@ (@ tptp.ord_less_o B_17) A_17) (=> (= B_17 C_8) (@ (@ tptp.ord_less_o C_8) A_17)))))
% 0.24/0.66 (assert (forall ((C_7 (-> tptp.hoare_1167836817_state Bool)) (A_16 (-> tptp.hoare_1167836817_state Bool)) (B_16 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le65125204tate_o A_16))) (=> (@ _let_1 B_16) (=> (= B_16 C_7) (@ _let_1 C_7))))))
% 0.24/0.66 (assert (forall ((C_7 Bool) (A_16 Bool) (B_16 Bool)) (let ((_let_1 (@ tptp.ord_less_o A_16))) (=> (@ _let_1 B_16) (=> (= B_16 C_7) (@ _let_1 C_7))))))
% 0.24/0.66 (assert (forall ((C_6 (-> tptp.hoare_1167836817_state Bool)) (A_15 (-> tptp.hoare_1167836817_state Bool)) (B_15 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le65125204tate_o C_6))) (=> (= A_15 B_15) (=> (@ _let_1 B_15) (@ _let_1 A_15))))))
% 0.24/0.66 (assert (forall ((C_6 Bool) (B_15 Bool) (A_15 Bool)) (let ((_let_1 (@ tptp.ord_less_o C_6))) (=> (= A_15 B_15) (=> (@ _let_1 B_15) (@ _let_1 A_15))))))
% 0.24/0.66 (assert (forall ((C_5 (-> tptp.hoare_1167836817_state Bool)) (A_14 (-> tptp.hoare_1167836817_state Bool)) (B_14 (-> tptp.hoare_1167836817_state Bool))) (=> (= A_14 B_14) (=> (@ (@ tptp.ord_le65125204tate_o B_14) C_5) (@ (@ tptp.ord_le65125204tate_o A_14) C_5)))))
% 0.24/0.66 (assert (forall ((C_5 Bool) (B_14 Bool) (A_14 Bool)) (=> (= A_14 B_14) (=> (@ (@ tptp.ord_less_o B_14) C_5) (@ (@ tptp.ord_less_o A_14) C_5)))))
% 0.24/0.66 (assert (forall ((B_13 (-> tptp.hoare_1167836817_state Bool)) (A_13 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o B_13) A_13) (not (@ (@ tptp.ord_le65125204tate_o A_13) B_13)))))
% 0.24/0.66 (assert (forall ((B_13 Bool) (A_13 Bool)) (=> (@ (@ tptp.ord_less_o B_13) A_13) (not (@ (@ tptp.ord_less_o A_13) B_13)))))
% 0.24/0.66 (assert (forall ((A_12 (-> tptp.hoare_1167836817_state Bool)) (B_12 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o A_12) B_12) (not (@ (@ tptp.ord_le65125204tate_o B_12) A_12)))))
% 0.24/0.66 (assert (forall ((A_12 Bool) (B_12 Bool)) (=> (@ (@ tptp.ord_less_o A_12) B_12) (not (@ (@ tptp.ord_less_o B_12) A_12)))))
% 0.24/0.66 (assert (forall ((P Bool) (X_17 (-> tptp.hoare_1167836817_state Bool)) (Y_15 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o X_17) Y_15) (=> (@ (@ tptp.ord_le65125204tate_o Y_15) X_17) P))))
% 0.24/0.66 (assert (forall ((P Bool) (X_17 Bool) (Y_15 Bool)) (=> (@ (@ tptp.ord_less_o X_17) Y_15) (=> (@ (@ tptp.ord_less_o Y_15) X_17) P))))
% 0.24/0.66 (assert (forall ((X_16 (-> tptp.hoare_1167836817_state Bool)) (Y_14 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o X_16) Y_14) (not (= Y_14 X_16)))))
% 0.24/0.66 (assert (forall ((X_16 Bool) (Y_14 Bool)) (=> (@ (@ tptp.ord_less_o X_16) Y_14) (= Y_14 (not X_16)))))
% 0.24/0.66 (assert (forall ((X_15 (-> tptp.hoare_1167836817_state Bool)) (Y_13 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o X_15) Y_13) (not (= X_15 Y_13)))))
% 0.24/0.66 (assert (forall ((X_15 Bool) (Y_13 Bool)) (=> (@ (@ tptp.ord_less_o X_15) Y_13) (= X_15 (not Y_13)))))
% 0.24/0.66 (assert (forall ((X_14 (-> tptp.hoare_1167836817_state Bool)) (Y_12 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o X_14) Y_12) (not (@ (@ tptp.ord_le65125204tate_o Y_12) X_14)))))
% 0.24/0.66 (assert (forall ((X_14 Bool) (Y_12 Bool)) (=> (@ (@ tptp.ord_less_o X_14) Y_12) (not (@ (@ tptp.ord_less_o Y_12) X_14)))))
% 0.24/0.66 (assert (forall ((X_13 (-> tptp.hoare_1167836817_state Bool)) (Y_11 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o X_13) Y_11) (not (@ (@ tptp.ord_le65125204tate_o Y_11) X_13)))))
% 0.24/0.66 (assert (forall ((X_13 Bool) (Y_11 Bool)) (=> (@ (@ tptp.ord_less_o X_13) Y_11) (not (@ (@ tptp.ord_less_o Y_11) X_13)))))
% 0.24/0.66 (assert (forall ((X_12 (-> tptp.hoare_1167836817_state Bool)) (Y_10 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o X_12) Y_10) (not (= X_12 Y_10)))))
% 0.24/0.66 (assert (forall ((X_12 Bool) (Y_10 Bool)) (=> (@ (@ tptp.ord_less_o X_12) Y_10) (not (= X_12 Y_10)))))
% 0.24/0.66 (assert (forall ((X_11 (-> tptp.hoare_1167836817_state Bool))) (not (@ (@ tptp.ord_le65125204tate_o X_11) X_11))))
% 0.24/0.66 (assert (forall ((X_11 Bool)) (not (@ (@ tptp.ord_less_o X_11) X_11))))
% 0.24/0.66 (assert (forall ((X_10 Bool) (Y_9 Bool)) (= (@ (@ tptp.ord_less_o X_10) Y_9) (and (@ (@ tptp.ord_less_eq_o X_10) Y_9) (not (= X_10 Y_9))))))
% 0.24/0.66 (assert (forall ((X_10 (-> tptp.hoare_1167836817_state Bool)) (Y_9 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.ord_le65125204tate_o X_10) Y_9) (and (@ (@ tptp.ord_le827224136tate_o X_10) Y_9) (not (= X_10 Y_9))))))
% 0.24/0.66 (assert (forall ((X_9 Bool) (Y_8 Bool)) (= (@ (@ tptp.ord_less_o X_9) Y_8) (and (@ (@ tptp.ord_less_eq_o X_9) Y_8) (not (@ (@ tptp.ord_less_eq_o Y_8) X_9))))))
% 0.24/0.66 (assert (forall ((X_9 (-> tptp.hoare_1167836817_state Bool)) (Y_8 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.ord_le65125204tate_o X_9) Y_8) (and (@ (@ tptp.ord_le827224136tate_o X_9) Y_8) (not (@ (@ tptp.ord_le827224136tate_o Y_8) X_9))))))
% 0.24/0.66 (assert (forall ((X_8 Bool) (Y_7 Bool)) (= (@ (@ tptp.ord_less_eq_o X_8) Y_7) (or (@ (@ tptp.ord_less_o X_8) Y_7) (= X_8 Y_7)))))
% 0.24/0.66 (assert (forall ((X_8 (-> tptp.hoare_1167836817_state Bool)) (Y_7 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.ord_le827224136tate_o X_8) Y_7) (or (@ (@ tptp.ord_le65125204tate_o X_8) Y_7) (= X_8 Y_7)))))
% 0.24/0.66 (assert (forall ((B_11 Bool) (A_11 Bool)) (=> (not (= A_11 B_11)) (=> (@ (@ tptp.ord_less_eq_o A_11) B_11) (@ (@ tptp.ord_less_o A_11) B_11)))))
% 0.24/0.66 (assert (forall ((A_11 (-> tptp.hoare_1167836817_state Bool)) (B_11 (-> tptp.hoare_1167836817_state Bool))) (=> (not (= A_11 B_11)) (=> (@ (@ tptp.ord_le827224136tate_o A_11) B_11) (@ (@ tptp.ord_le65125204tate_o A_11) B_11)))))
% 0.24/0.66 (assert (forall ((B_10 Bool) (A_10 Bool)) (=> (not (= A_10 B_10)) (=> (@ (@ tptp.ord_less_eq_o B_10) A_10) (@ (@ tptp.ord_less_o B_10) A_10)))))
% 0.24/0.66 (assert (forall ((A_10 (-> tptp.hoare_1167836817_state Bool)) (B_10 (-> tptp.hoare_1167836817_state Bool))) (=> (not (= A_10 B_10)) (=> (@ (@ tptp.ord_le827224136tate_o B_10) A_10) (@ (@ tptp.ord_le65125204tate_o B_10) A_10)))))
% 0.24/0.66 (assert (forall ((X_7 Bool) (Y_6 Bool)) (=> (@ (@ tptp.ord_less_o X_7) Y_6) (@ (@ tptp.ord_less_eq_o X_7) Y_6))))
% 0.24/0.66 (assert (forall ((X_7 (-> tptp.hoare_1167836817_state Bool)) (Y_6 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o X_7) Y_6) (@ (@ tptp.ord_le827224136tate_o X_7) Y_6))))
% 0.24/0.66 (assert (forall ((X_6 Bool) (Y_5 Bool)) (=> (@ (@ tptp.ord_less_eq_o X_6) Y_5) (or (@ (@ tptp.ord_less_o X_6) Y_5) (= X_6 Y_5)))))
% 0.24/0.66 (assert (forall ((X_6 (-> tptp.hoare_1167836817_state Bool)) (Y_5 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o X_6) Y_5) (or (@ (@ tptp.ord_le65125204tate_o X_6) Y_5) (= X_6 Y_5)))))
% 0.24/0.66 (assert (forall ((A_9 Bool) (B_9 Bool)) (=> (@ (@ tptp.ord_less_eq_o A_9) B_9) (=> (not (= A_9 B_9)) (@ (@ tptp.ord_less_o A_9) B_9)))))
% 0.24/0.66 (assert (forall ((A_9 (-> tptp.hoare_1167836817_state Bool)) (B_9 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o A_9) B_9) (=> (not (= A_9 B_9)) (@ (@ tptp.ord_le65125204tate_o A_9) B_9)))))
% 0.24/0.66 (assert (forall ((B_8 Bool) (A_8 Bool)) (=> (@ (@ tptp.ord_less_eq_o B_8) A_8) (=> (not (= A_8 B_8)) (@ (@ tptp.ord_less_o B_8) A_8)))))
% 0.24/0.66 (assert (forall ((B_8 (-> tptp.hoare_1167836817_state Bool)) (A_8 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o B_8) A_8) (=> (not (= A_8 B_8)) (@ (@ tptp.ord_le65125204tate_o B_8) A_8)))))
% 0.24/0.66 (assert (forall ((Z_3 Bool) (X_5 Bool) (Y_4 Bool)) (let ((_let_1 (@ tptp.ord_less_o X_5))) (=> (@ _let_1 Y_4) (=> (@ (@ tptp.ord_less_eq_o Y_4) Z_3) (@ _let_1 Z_3))))))
% 0.24/0.66 (assert (forall ((Z_3 (-> tptp.hoare_1167836817_state Bool)) (X_5 (-> tptp.hoare_1167836817_state Bool)) (Y_4 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le65125204tate_o X_5))) (=> (@ _let_1 Y_4) (=> (@ (@ tptp.ord_le827224136tate_o Y_4) Z_3) (@ _let_1 Z_3))))))
% 0.24/0.66 (assert (forall ((Z_2 Bool) (Y_3 Bool) (X_4 Bool)) (=> (@ (@ tptp.ord_less_o Y_3) X_4) (=> (@ (@ tptp.ord_less_eq_o Z_2) Y_3) (@ (@ tptp.ord_less_o Z_2) X_4)))))
% 0.24/0.66 (assert (forall ((Z_2 (-> tptp.hoare_1167836817_state Bool)) (Y_3 (-> tptp.hoare_1167836817_state Bool)) (X_4 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o Y_3) X_4) (=> (@ (@ tptp.ord_le827224136tate_o Z_2) Y_3) (@ (@ tptp.ord_le65125204tate_o Z_2) X_4)))))
% 0.24/0.66 (assert (forall ((Z_1 Bool) (X_3 Bool) (Y_2 Bool)) (=> (@ (@ tptp.ord_less_eq_o X_3) Y_2) (=> (@ (@ tptp.ord_less_o Y_2) Z_1) (@ (@ tptp.ord_less_o X_3) Z_1)))))
% 0.24/0.66 (assert (forall ((Z_1 (-> tptp.hoare_1167836817_state Bool)) (X_3 (-> tptp.hoare_1167836817_state Bool)) (Y_2 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o X_3) Y_2) (=> (@ (@ tptp.ord_le65125204tate_o Y_2) Z_1) (@ (@ tptp.ord_le65125204tate_o X_3) Z_1)))))
% 0.24/0.66 (assert (forall ((Z Bool) (Y_1 Bool) (X_2 Bool)) (let ((_let_1 (@ tptp.ord_less_o Z))) (=> (@ (@ tptp.ord_less_eq_o Y_1) X_2) (=> (@ _let_1 Y_1) (@ _let_1 X_2))))))
% 0.24/0.66 (assert (forall ((Z (-> tptp.hoare_1167836817_state Bool)) (Y_1 (-> tptp.hoare_1167836817_state Bool)) (X_2 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le65125204tate_o Z))) (=> (@ (@ tptp.ord_le827224136tate_o Y_1) X_2) (=> (@ _let_1 Y_1) (@ _let_1 X_2))))))
% 0.24/0.66 (assert (forall ((F_4 (-> tptp.hoare_1167836817_state Bool)) (G_1 (-> tptp.hoare_1167836817_state Bool))) (= (@ (@ tptp.ord_le65125204tate_o F_4) G_1) (and (@ (@ tptp.ord_le827224136tate_o F_4) G_1) (not (@ (@ tptp.ord_le827224136tate_o G_1) F_4))))))
% 0.24/0.66 (assert (forall ((A_7 (-> tptp.hoare_1167836817_state Bool)) (X_1 tptp.hoare_1167836817_state) (B_7 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state X_1))) (let ((_let_2 (@ _let_1 A_7))) (let ((_let_3 (@ tptp.insert2134838167_state X_1))) (let ((_let_4 (@ _let_1 B_7))) (let ((_let_5 (@ tptp.ord_le65125204tate_o A_7))) (= (@ _let_5 (@ _let_3 B_7)) (and (=> _let_4 (@ _let_5 B_7)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le65125204tate_o (@ (@ tptp.minus_2107060239tate_o A_7) (@ _let_3 tptp.bot_bo70021908tate_o))) B_7)) (=> (not _let_2) (@ (@ tptp.ord_le827224136tate_o A_7) B_7)))))))))))))
% 0.24/0.66 (assert (forall ((F_3 (-> tptp.hoare_1167836817_state tptp.nat)) (G (-> tptp.hoare_1167836817_state tptp.nat)) (A_6 (-> tptp.hoare_1167836817_state Bool))) (=> (@ tptp.finite1084549118_state A_6) (=> (not (= A_6 tptp.bot_bo70021908tate_o)) (=> (forall ((X tptp.hoare_1167836817_state)) (=> (@ (@ tptp.member2058392318_state X) A_6) (@ (@ tptp.ord_less_nat (@ F_3 X)) (@ G X)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.big_co337839062te_nat F_3) A_6)) (@ (@ tptp.big_co337839062te_nat G) A_6)))))))
% 0.24/0.66 (assert (forall ((C_4 (-> tptp.hoare_1167836817_state Bool)) (A_5 (-> tptp.hoare_1167836817_state Bool)) (B_6 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.ord_le65125204tate_o A_5))) (=> (@ _let_1 B_6) (=> (@ (@ tptp.ord_le65125204tate_o B_6) C_4) (@ _let_1 C_4))))))
% 0.24/0.66 (assert (forall ((C_3 tptp.hoare_1167836817_state) (A_4 (-> tptp.hoare_1167836817_state Bool)) (B_5 (-> tptp.hoare_1167836817_state Bool))) (let ((_let_1 (@ tptp.member2058392318_state C_3))) (=> (@ (@ tptp.ord_le65125204tate_o A_4) B_5) (=> (@ _let_1 A_4) (@ _let_1 B_5))))))
% 0.24/0.66 (assert (forall ((A_3 (-> tptp.hoare_1167836817_state Bool)) (B_3 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o A_3) B_3) (exists ((B_4 tptp.hoare_1167836817_state)) (@ (@ tptp.member2058392318_state B_4) (@ (@ tptp.minus_2107060239tate_o B_3) A_3))))))
% 0.24/0.66 (assert (forall ((C_2 (-> tptp.hoare_1167836817_state Bool)) (F_2 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool)) (B_2 (-> tptp.hoare_1167836817_state Bool)) (A_2 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o (@ F_2 B_2)) A_2) (=> (@ (@ tptp.ord_le65125204tate_o C_2) B_2) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o Y) X) (@ (@ tptp.ord_le65125204tate_o (@ F_2 Y)) (@ F_2 X)))) (@ (@ tptp.ord_le65125204tate_o (@ F_2 C_2)) A_2))))))
% 0.24/0.66 (assert (forall ((C_2 Bool) (F_2 (-> Bool tptp.hoare_1167836817_state Bool)) (B_2 Bool) (A_2 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o (@ F_2 B_2)) A_2) (=> (@ (@ tptp.ord_less_o C_2) B_2) (=> (forall ((X Bool) (Y Bool)) (=> (@ (@ tptp.ord_less_o Y) X) (@ (@ tptp.ord_le65125204tate_o (@ F_2 Y)) (@ F_2 X)))) (@ (@ tptp.ord_le65125204tate_o (@ F_2 C_2)) A_2))))))
% 0.24/0.66 (assert (forall ((C_1 (-> tptp.hoare_1167836817_state Bool)) (F_1 (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool)) (B_1 (-> tptp.hoare_1167836817_state Bool)) (A_1 (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o B_1) A_1) (=> (@ (@ tptp.ord_le827224136tate_o C_1) (@ F_1 B_1)) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o Y) X) (@ (@ tptp.ord_le65125204tate_o (@ F_1 Y)) (@ F_1 X)))) (@ (@ tptp.ord_le65125204tate_o C_1) (@ F_1 A_1)))))))
% 0.24/0.66 (assert (forall ((C_1 (-> tptp.hoare_1167836817_state Bool)) (F_1 (-> Bool tptp.hoare_1167836817_state Bool)) (B_1 Bool) (A_1 Bool)) (=> (@ (@ tptp.ord_less_o B_1) A_1) (=> (@ (@ tptp.ord_le827224136tate_o C_1) (@ F_1 B_1)) (=> (forall ((X Bool) (Y Bool)) (=> (@ (@ tptp.ord_less_o Y) X) (@ (@ tptp.ord_le65125204tate_o (@ F_1 Y)) (@ F_1 X)))) (@ (@ tptp.ord_le65125204tate_o C_1) (@ F_1 A_1)))))))
% 0.24/0.66 (assert (forall ((C (-> tptp.hoare_1167836817_state Bool)) (F (-> (-> tptp.hoare_1167836817_state Bool) tptp.hoare_1167836817_state Bool)) (B (-> tptp.hoare_1167836817_state Bool)) (A (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le65125204tate_o (@ F B)) A) (=> (@ (@ tptp.ord_le827224136tate_o C) B) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_le827224136tate_o Y) X) (@ (@ tptp.ord_le827224136tate_o (@ F Y)) (@ F X)))) (@ (@ tptp.ord_le65125204tate_o (@ F C)) A))))))
% 0.24/0.66 (assert (forall ((C (-> tptp.hoare_1167836817_state Bool)) (F (-> (-> tptp.hoare_1167836817_state Bool) Bool)) (B (-> tptp.hoare_1167836817_state Bool)) (A Bool)) (=> (@ (@ tptp.ord_less_o (@ F B)) A) (=> (@ (@ tptp.ord_le827224136tate_o C) B) (=> (forall ((X (-> tptp.hoare_1167836817_state Bool)) (Y (-> tptp.hoare_1167836817_state Bool))) (=> (@ (@ tptp.ord_l/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 1869 Alarm clock ( read result; case "$result" in
% 299.85/300.21 unsat)
% 299.85/300.21 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.85/300.21 ;;
% 299.85/300.21 sat)
% 299.85/300.21 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.85/300.21 ;;
% 299.85/300.21 esac; exit 1 )
% 299.85/300.21 Alarm clock
% 299.85/300.21 % cvc5---1.0.5 exiting
% 299.85/300.22 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------