TSTP Solution File: SWW474^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW474^1 : 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 00:21:07 EDT 2023
% Result : Theorem 0.83s 1.05s
% Output : Proof 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.18 % Problem : SWW474^1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.19 % Command : do_cvc5 %s %d
% 0.19/0.40 % Computer : n025.cluster.edu
% 0.19/0.40 % Model : x86_64 x86_64
% 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40 % Memory : 8042.1875MB
% 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40 % CPULimit : 300
% 0.19/0.40 % WCLimit : 300
% 0.19/0.40 % DateTime : Sun Aug 27 23:10:24 EDT 2023
% 0.19/0.41 % CPUTime :
% 0.25/0.58 %----Proving TH0
% 0.25/0.59 %------------------------------------------------------------------------------
% 0.25/0.59 % File : SWW474^1 : TPTP v8.1.2. Released v5.3.0.
% 0.25/0.59 % Domain : Software Verification
% 0.25/0.59 % Problem : Hoare's Logic with Procedures line 440, 100 axioms selected
% 0.25/0.59 % Version : Especial.
% 0.25/0.59 % English :
% 0.25/0.59
% 0.25/0.59 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.25/0.59 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.25/0.59 % Source : [Bla11]
% 0.25/0.59 % Names : hoare_100_thf_l440 [Bla11]
% 0.25/0.59
% 0.25/0.59 % Status : Theorem
% 0.25/0.59 % Rating : 0.31 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.56 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% 0.25/0.59 % Syntax : Number of formulae : 396 ( 58 unt; 80 typ; 0 def)
% 0.25/0.59 % Number of atoms : 1340 ( 265 equ; 42 cnn)
% 0.25/0.59 % Maximal formula atoms : 10 ( 4 avg)
% 0.25/0.59 % Number of connectives : 2174 ( 94 ~; 36 |; 58 &;1615 @)
% 0.25/0.59 % ( 53 <=>; 318 =>; 0 <=; 0 <~>)
% 0.25/0.59 % Maximal formula depth : 17 ( 7 avg)
% 0.25/0.59 % Number of types : 5 ( 4 usr)
% 0.25/0.59 % Number of type conns : 1124 (1124 >; 0 *; 0 +; 0 <<)
% 0.25/0.59 % Number of symbols : 82 ( 76 usr; 9 con; 0-3 aty)
% 0.25/0.59 % Number of variables : 776 ( 89 ^; 680 !; 7 ?; 776 :)
% 0.25/0.59 % SPC : TH0_THM_EQU_NAR
% 0.25/0.59
% 0.25/0.59 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.25/0.59 % 2011-08-09 19:26:26
% 0.25/0.59 %------------------------------------------------------------------------------
% 0.25/0.59 %----Should-be-implicit typings (4)
% 0.25/0.59 thf(ty_ty_tc__Com__Ocom,type,
% 0.25/0.59 com: $tType ).
% 0.25/0.59
% 0.25/0.59 thf(ty_ty_tc__Com__Opname,type,
% 0.25/0.59 pname: $tType ).
% 0.25/0.59
% 0.25/0.59 thf(ty_ty_tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J,type,
% 0.25/0.59 hoare_1262092251_state: $tType ).
% 0.25/0.59
% 0.25/0.59 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.25/0.59 option_com: $tType ).
% 0.25/0.59
% 0.25/0.59 %----Explicit typings (76)
% 0.25/0.59 thf(sy_c_Com_OWT,type,
% 0.25/0.59 wt: com > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Com_OWT__bodies,type,
% 0.25/0.59 wT_bodies: $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Com_Obody,type,
% 0.25/0.59 body: pname > option_com ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Com_Ocom_OBODY,type,
% 0.25/0.59 body_1: pname > com ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo,type,
% 0.25/0.59 finite1648353812_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbq,type,
% 0.25/0.59 finite734360985_o_o_o: ( ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.25/0.59 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Ot,type,
% 0.25/0.59 finite1303896758te_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.59 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_,type,
% 0.25/0.59 finite1423311111tate_o: ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 0.25/0.59 finite_finite_pname: ( pname > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__C,type,
% 0.25/0.59 finite1178804552_state: ( hoare_1262092251_state > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_OMGT,type,
% 0.25/0.59 hoare_Mirabelle_MGT: com > hoare_1262092251_state ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ohoare__derivs_000tc__Com__Ostate,type,
% 0.25/0.59 hoare_930741239_state: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ostate__not__singleton,type,
% 0.25/0.59 hoare_1821564147gleton: $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Map_Odom_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Ocom,type,
% 0.25/0.59 dom_pname_o_com: ( ( pname > $o ) > option_com ) > ( pname > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Map_Odom_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__O,type,
% 0.25/0.59 dom_Ho1489634536_o_com: ( ( hoare_1262092251_state > $o ) > option_com ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,type,
% 0.25/0.59 dom_pname_com: ( pname > option_com ) > pname > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Option_Ooption_OSome_000tc__Com__Ocom,type,
% 0.25/0.59 some_com: com > option_com ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
% 0.25/0.59 the_com: option_com > com ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo,type,
% 0.25/0.59 bot_bot_pname_o_o_o: ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_I_062_Itc__Hoare____Mirabelle____g,type,
% 0.25/0.59 bot_bo388435036_o_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.25/0.59 bot_bot_pname_o_o: ( pname > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsb,type,
% 0.25/0.59 bot_bo1962689075te_o_o: ( hoare_1262092251_state > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.59 bot_bot_pname_o: pname > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__O,type,
% 0.25/0.59 bot_bo113204042tate_o: hoare_1262092251_state > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.59 ord_le1828183645_o_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Hoare____Mirabelle,type,
% 0.25/0.59 ord_le1891858320_o_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,
% 0.25/0.59 ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Hoare____Mirabelle____gh,type,
% 0.25/0.59 ord_le2012720639te_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.59 ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____ghhkfsbq,type,
% 0.25/0.59 ord_le870406270tate_o: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.25/0.59 collect_pname_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otr,type,
% 0.25/0.59 collec101077467_o_o_o: ( ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.25/0.59 collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_I,type,
% 0.25/0.59 collec341954548te_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.59 collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Co,type,
% 0.25/0.59 collec313158217tate_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 0.25/0.59 collect_pname: ( pname > $o ) > pname > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost,type,
% 0.25/0.59 collec1121927558_state: ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 0.25/0.59 image_471733107_pname: ( ( ( pname > $o ) > $o ) > pname ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Hoare____Mir,type,
% 0.25/0.59 image_1036078444_state: ( ( ( pname > $o ) > $o ) > hoare_1262092251_state ) > ( ( ( pname > $o ) > $o ) > $o ) > hoare_1262092251_state > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc,type,
% 0.25/0.59 image_893364936_pname: ( ( ( hoare_1262092251_state > $o ) > $o ) > pname ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > pname > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc_001,type,
% 0.25/0.59 image_165349207_state: ( ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > hoare_1262092251_state > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
% 0.25/0.59 image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Hoare____Mirabelle____ghh,type,
% 0.25/0.59 image_1476171975_state: ( ( pname > $o ) > hoare_1262092251_state ) > ( ( pname > $o ) > $o ) > hoare_1262092251_state > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com_,type,
% 0.25/0.59 image_1820530197_pname: ( ( hoare_1262092251_state > $o ) > pname ) > ( ( hoare_1262092251_state > $o ) > $o ) > pname > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__002,type,
% 0.25/0.59 image_234589002_state: ( ( hoare_1262092251_state > $o ) > hoare_1262092251_state ) > ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.25/0.59 image_504089495me_o_o: ( pname > ( pname > $o ) > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Hoare____Mirabelle____ghhk,type,
% 0.25/0.59 image_827868872te_o_o: ( pname > ( hoare_1262092251_state > $o ) > $o ) > ( pname > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.59 image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq,type,
% 0.25/0.59 image_518521461tate_o: ( pname > hoare_1262092251_state > $o ) > ( pname > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.25/0.59 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otri,type,
% 0.25/0.59 image_669833818_state: ( pname > hoare_1262092251_state ) > ( pname > $o ) > hoare_1262092251_state > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat,type,
% 0.25/0.59 image_333245000me_o_o: ( hoare_1262092251_state > ( pname > $o ) > $o ) > ( hoare_1262092251_state > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_003,type,
% 0.25/0.59 image_1731108951te_o_o: ( hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_004,type,
% 0.25/0.59 image_1320925383name_o: ( hoare_1262092251_state > pname > $o ) > ( hoare_1262092251_state > $o ) > ( pname > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_005,type,
% 0.25/0.59 image_1403668518tate_o: ( hoare_1262092251_state > hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_006,type,
% 0.25/0.59 image_202231862_pname: ( hoare_1262092251_state > pname ) > ( hoare_1262092251_state > $o ) > pname > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.25/0.59 insert_pname_o_o: ( ( pname > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It,type,
% 0.25/0.59 insert1691644879te_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.59 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com,type,
% 0.25/0.59 insert1042460334tate_o: ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 0.25/0.59 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Osta,type,
% 0.25/0.59 insert81609953_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.59 fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost,type,
% 0.25/0.59 fequal1529404211tate_o: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_fequal_000tc__Com__Opname,type,
% 0.25/0.59 fequal_pname: pname > pname > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J,type,
% 0.25/0.59 fequal1925511196_state: hoare_1262092251_state > hoare_1262092251_state > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.59 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost,type,
% 0.25/0.59 member907417095tate_o: ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_member_000tc__Com__Opname,type,
% 0.25/0.59 member_pname: pname > ( pname > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_member_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J,type,
% 0.25/0.59 member5164104_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_v_Fa,type,
% 0.25/0.59 fa: hoare_1262092251_state > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_v_pn,type,
% 0.25/0.59 pn: pname ).
% 0.25/0.59
% 0.25/0.59 thf(sy_v_y,type,
% 0.25/0.59 y: com ).
% 0.25/0.59
% 0.25/0.59 %----Relevant facts (300)
% 0.25/0.59 thf(fact_0_empty,axiom,
% 0.25/0.59 ! [G: hoare_1262092251_state > $o] : ( hoare_930741239_state @ G @ bot_bo113204042tate_o ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_1_asm,axiom,
% 0.25/0.59 ! [Ts_6: hoare_1262092251_state > $o,G_8: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( ord_le870406270tate_o @ Ts_6 @ G_8 )
% 0.25/0.59 => ( hoare_930741239_state @ G_8 @ Ts_6 ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_2_weaken,axiom,
% 0.25/0.59 ! [Ts_5: hoare_1262092251_state > $o,G_7: hoare_1262092251_state > $o,Ts_4: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( hoare_930741239_state @ G_7 @ Ts_4 )
% 0.25/0.59 => ( ( ord_le870406270tate_o @ Ts_5 @ Ts_4 )
% 0.25/0.59 => ( hoare_930741239_state @ G_7 @ Ts_5 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_3_thin,axiom,
% 0.25/0.59 ! [G_6: hoare_1262092251_state > $o,G_5: hoare_1262092251_state > $o,Ts_3: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( hoare_930741239_state @ G_5 @ Ts_3 )
% 0.25/0.59 => ( ( ord_le870406270tate_o @ G_5 @ G_6 )
% 0.25/0.59 => ( hoare_930741239_state @ G_6 @ Ts_3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_4_cut,axiom,
% 0.25/0.59 ! [G_4: hoare_1262092251_state > $o,G_3: hoare_1262092251_state > $o,Ts_2: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( hoare_930741239_state @ G_3 @ Ts_2 )
% 0.25/0.59 => ( ( hoare_930741239_state @ G_4 @ G_3 )
% 0.25/0.59 => ( hoare_930741239_state @ G_4 @ Ts_2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_5_hoare__derivs_Oinsert,axiom,
% 0.25/0.59 ! [Ts_1: hoare_1262092251_state > $o,G_2: hoare_1262092251_state > $o,T_1: hoare_1262092251_state] :
% 0.25/0.59 ( ( hoare_930741239_state @ G_2 @ ( insert81609953_state @ T_1 @ bot_bo113204042tate_o ) )
% 0.25/0.59 => ( ( hoare_930741239_state @ G_2 @ Ts_1 )
% 0.25/0.59 => ( hoare_930741239_state @ G_2 @ ( insert81609953_state @ T_1 @ Ts_1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_6_derivs__insertD,axiom,
% 0.25/0.59 ! [G_1: hoare_1262092251_state > $o,T: hoare_1262092251_state,Ts: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( hoare_930741239_state @ G_1 @ ( insert81609953_state @ T @ Ts ) )
% 0.25/0.59 => ( ( hoare_930741239_state @ G_1 @ ( insert81609953_state @ T @ bot_bo113204042tate_o ) )
% 0.25/0.59 & ( hoare_930741239_state @ G_1 @ Ts ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_7_MGT__BodyN,axiom,
% 0.25/0.59 ! [Pn_1: pname,G: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( hoare_930741239_state @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ G ) @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn_1 ) ) ) @ bot_bo113204042tate_o ) )
% 0.25/0.59 => ( hoare_930741239_state @ G @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ bot_bo113204042tate_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_8_finite__Collect__subsets,axiom,
% 0.25/0.59 ! [A_77: pname > $o] :
% 0.25/0.59 ( ( finite_finite_pname @ A_77 )
% 0.25/0.59 => ( finite297249702name_o
% 0.25/0.59 @ ( collect_pname_o
% 0.25/0.59 @ ^ [B_41: pname > $o] : ( ord_less_eq_pname_o @ B_41 @ A_77 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_9_finite__Collect__subsets,axiom,
% 0.25/0.59 ! [A_77: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( finite1178804552_state @ A_77 )
% 0.25/0.59 => ( finite1423311111tate_o
% 0.25/0.59 @ ( collec313158217tate_o
% 0.25/0.59 @ ^ [B_41: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ B_41 @ A_77 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_10_finite__Collect__subsets,axiom,
% 0.25/0.59 ! [A_77: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1066544169me_o_o @ A_77 )
% 0.25/0.59 => ( finite1648353812_o_o_o
% 0.25/0.59 @ ( collect_pname_o_o_o
% 0.25/0.59 @ ^ [B_41: ( ( pname > $o ) > $o ) > $o] : ( ord_le1828183645_o_o_o @ B_41 @ A_77 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_11_finite__Collect__subsets,axiom,
% 0.25/0.59 ! [A_77: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1303896758te_o_o @ A_77 )
% 0.25/0.59 => ( finite734360985_o_o_o
% 0.25/0.59 @ ( collec101077467_o_o_o
% 0.25/0.59 @ ^ [B_41: ( ( hoare_1262092251_state > $o ) > $o ) > $o] : ( ord_le1891858320_o_o_o @ B_41 @ A_77 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_12_finite__Collect__subsets,axiom,
% 0.25/0.59 ! [A_77: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.59 ( ( finite1423311111tate_o @ A_77 )
% 0.25/0.59 => ( finite1303896758te_o_o
% 0.25/0.59 @ ( collec341954548te_o_o
% 0.25/0.59 @ ^ [B_41: ( hoare_1262092251_state > $o ) > $o] : ( ord_le2012720639te_o_o @ B_41 @ A_77 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_13_finite__Collect__subsets,axiom,
% 0.25/0.59 ! [A_77: ( pname > $o ) > $o] :
% 0.25/0.59 ( ( finite297249702name_o @ A_77 )
% 0.25/0.59 => ( finite1066544169me_o_o
% 0.25/0.59 @ ( collect_pname_o_o
% 0.25/0.59 @ ^ [B_41: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_41 @ A_77 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_14_finite__imageI,axiom,
% 0.25/0.59 ! [H: pname > hoare_1262092251_state,F_17: pname > $o] :
% 0.25/0.59 ( ( finite_finite_pname @ F_17 )
% 0.25/0.59 => ( finite1178804552_state @ ( image_669833818_state @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_15_finite__imageI,axiom,
% 0.25/0.59 ! [H: ( ( pname > $o ) > $o ) > pname,F_17: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1066544169me_o_o @ F_17 )
% 0.25/0.59 => ( finite_finite_pname @ ( image_471733107_pname @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_16_finite__imageI,axiom,
% 0.25/0.59 ! [H: ( ( hoare_1262092251_state > $o ) > $o ) > pname,F_17: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1303896758te_o_o @ F_17 )
% 0.25/0.59 => ( finite_finite_pname @ ( image_893364936_pname @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_17_finite__imageI,axiom,
% 0.25/0.59 ! [H: ( hoare_1262092251_state > $o ) > pname,F_17: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.59 ( ( finite1423311111tate_o @ F_17 )
% 0.25/0.59 => ( finite_finite_pname @ ( image_1820530197_pname @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_18_finite__imageI,axiom,
% 0.25/0.59 ! [H: ( pname > $o ) > pname,F_17: ( pname > $o ) > $o] :
% 0.25/0.59 ( ( finite297249702name_o @ F_17 )
% 0.25/0.59 => ( finite_finite_pname @ ( image_pname_o_pname @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_19_finite__imageI,axiom,
% 0.25/0.59 ! [H: ( ( pname > $o ) > $o ) > hoare_1262092251_state,F_17: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1066544169me_o_o @ F_17 )
% 0.25/0.59 => ( finite1178804552_state @ ( image_1036078444_state @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_20_finite__imageI,axiom,
% 0.25/0.59 ! [H: ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state,F_17: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1303896758te_o_o @ F_17 )
% 0.25/0.59 => ( finite1178804552_state @ ( image_165349207_state @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_21_finite__imageI,axiom,
% 0.25/0.59 ! [H: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,F_17: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.59 ( ( finite1423311111tate_o @ F_17 )
% 0.25/0.59 => ( finite1178804552_state @ ( image_234589002_state @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_22_finite__imageI,axiom,
% 0.25/0.59 ! [H: ( pname > $o ) > hoare_1262092251_state,F_17: ( pname > $o ) > $o] :
% 0.25/0.59 ( ( finite297249702name_o @ F_17 )
% 0.25/0.59 => ( finite1178804552_state @ ( image_1476171975_state @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_23_finite__imageI,axiom,
% 0.25/0.59 ! [H: pname > ( pname > $o ) > $o,F_17: pname > $o] :
% 0.25/0.59 ( ( finite_finite_pname @ F_17 )
% 0.25/0.59 => ( finite1066544169me_o_o @ ( image_504089495me_o_o @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_24_finite__imageI,axiom,
% 0.25/0.59 ! [H: pname > ( hoare_1262092251_state > $o ) > $o,F_17: pname > $o] :
% 0.25/0.59 ( ( finite_finite_pname @ F_17 )
% 0.25/0.59 => ( finite1303896758te_o_o @ ( image_827868872te_o_o @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_25_finite__imageI,axiom,
% 0.25/0.59 ! [H: pname > hoare_1262092251_state > $o,F_17: pname > $o] :
% 0.25/0.59 ( ( finite_finite_pname @ F_17 )
% 0.25/0.59 => ( finite1423311111tate_o @ ( image_518521461tate_o @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_26_finite__imageI,axiom,
% 0.25/0.59 ! [H: pname > pname > $o,F_17: pname > $o] :
% 0.25/0.59 ( ( finite_finite_pname @ F_17 )
% 0.25/0.59 => ( finite297249702name_o @ ( image_pname_pname_o @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_27_finite__imageI,axiom,
% 0.25/0.59 ! [H: hoare_1262092251_state > ( pname > $o ) > $o,F_17: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( finite1178804552_state @ F_17 )
% 0.25/0.59 => ( finite1066544169me_o_o @ ( image_333245000me_o_o @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_28_finite__imageI,axiom,
% 0.25/0.59 ! [H: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o,F_17: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( finite1178804552_state @ F_17 )
% 0.25/0.59 => ( finite1303896758te_o_o @ ( image_1731108951te_o_o @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_29_finite__imageI,axiom,
% 0.25/0.59 ! [H: hoare_1262092251_state > hoare_1262092251_state > $o,F_17: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( finite1178804552_state @ F_17 )
% 0.25/0.59 => ( finite1423311111tate_o @ ( image_1403668518tate_o @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_30_finite__imageI,axiom,
% 0.25/0.59 ! [H: hoare_1262092251_state > pname > $o,F_17: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( finite1178804552_state @ F_17 )
% 0.25/0.59 => ( finite297249702name_o @ ( image_1320925383name_o @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_31_finite__imageI,axiom,
% 0.25/0.59 ! [H: hoare_1262092251_state > pname,F_17: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( finite1178804552_state @ F_17 )
% 0.25/0.59 => ( finite_finite_pname @ ( image_202231862_pname @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_32_finite__imageI,axiom,
% 0.25/0.59 ! [H: pname > pname,F_17: pname > $o] :
% 0.25/0.59 ( ( finite_finite_pname @ F_17 )
% 0.25/0.59 => ( finite_finite_pname @ ( image_pname_pname @ H @ F_17 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_33_empty__subsetI,axiom,
% 0.25/0.59 ! [A_76: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ bot_bo113204042tate_o @ A_76 ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_34_empty__subsetI,axiom,
% 0.25/0.59 ! [A_76: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ bot_bot_pname_o_o @ A_76 ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_35_empty__subsetI,axiom,
% 0.25/0.59 ! [A_76: ( hoare_1262092251_state > $o ) > $o] : ( ord_le2012720639te_o_o @ bot_bo1962689075te_o_o @ A_76 ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_36_empty__subsetI,axiom,
% 0.25/0.59 ! [A_76: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_76 ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_37_finite_OinsertI,axiom,
% 0.25/0.59 ! [A_75: hoare_1262092251_state,A_74: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( finite1178804552_state @ A_74 )
% 0.25/0.59 => ( finite1178804552_state @ ( insert81609953_state @ A_75 @ A_74 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_38_finite_OinsertI,axiom,
% 0.25/0.59 ! [A_75: pname,A_74: pname > $o] :
% 0.25/0.59 ( ( finite_finite_pname @ A_74 )
% 0.25/0.59 => ( finite_finite_pname @ ( insert_pname @ A_75 @ A_74 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_39_finite_OinsertI,axiom,
% 0.25/0.59 ! [A_75: ( pname > $o ) > $o,A_74: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1066544169me_o_o @ A_74 )
% 0.25/0.59 => ( finite1066544169me_o_o @ ( insert_pname_o_o @ A_75 @ A_74 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_40_finite_OinsertI,axiom,
% 0.25/0.59 ! [A_75: ( hoare_1262092251_state > $o ) > $o,A_74: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1303896758te_o_o @ A_74 )
% 0.25/0.59 => ( finite1303896758te_o_o @ ( insert1691644879te_o_o @ A_75 @ A_74 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_41_finite_OinsertI,axiom,
% 0.25/0.59 ! [A_75: hoare_1262092251_state > $o,A_74: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.59 ( ( finite1423311111tate_o @ A_74 )
% 0.25/0.59 => ( finite1423311111tate_o @ ( insert1042460334tate_o @ A_75 @ A_74 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_42_finite_OinsertI,axiom,
% 0.25/0.59 ! [A_75: pname > $o,A_74: ( pname > $o ) > $o] :
% 0.25/0.59 ( ( finite297249702name_o @ A_74 )
% 0.25/0.59 => ( finite297249702name_o @ ( insert_pname_o @ A_75 @ A_74 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_43_finite_OemptyI,axiom,
% 0.25/0.59 finite_finite_pname @ bot_bot_pname_o ).
% 0.25/0.59
% 0.25/0.59 thf(fact_44_finite_OemptyI,axiom,
% 0.25/0.59 finite1178804552_state @ bot_bo113204042tate_o ).
% 0.25/0.59
% 0.25/0.59 thf(fact_45_finite_OemptyI,axiom,
% 0.25/0.59 finite1066544169me_o_o @ bot_bot_pname_o_o_o ).
% 0.25/0.59
% 0.25/0.59 thf(fact_46_finite_OemptyI,axiom,
% 0.25/0.59 finite1303896758te_o_o @ bot_bo388435036_o_o_o ).
% 0.25/0.59
% 0.25/0.59 thf(fact_47_finite_OemptyI,axiom,
% 0.25/0.59 finite1423311111tate_o @ bot_bo1962689075te_o_o ).
% 0.25/0.59
% 0.25/0.59 thf(fact_48_finite_OemptyI,axiom,
% 0.25/0.59 finite297249702name_o @ bot_bot_pname_o_o ).
% 0.25/0.59
% 0.25/0.59 thf(fact_49_finite__Collect__conjI,axiom,
% 0.25/0.59 ! [Q_1: pname > $o,P_9: pname > $o] :
% 0.25/0.59 ( ( ( finite_finite_pname @ ( collect_pname @ P_9 ) )
% 0.25/0.59 | ( finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
% 0.25/0.59 => ( finite_finite_pname
% 0.25/0.59 @ ( collect_pname
% 0.25/0.59 @ ^ [X_1: pname] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_50_finite__Collect__conjI,axiom,
% 0.25/0.59 ! [Q_1: hoare_1262092251_state > $o,P_9: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( ( finite1178804552_state @ ( collec1121927558_state @ P_9 ) )
% 0.25/0.59 | ( finite1178804552_state @ ( collec1121927558_state @ Q_1 ) ) )
% 0.25/0.59 => ( finite1178804552_state
% 0.25/0.59 @ ( collec1121927558_state
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_51_finite__Collect__conjI,axiom,
% 0.25/0.59 ! [Q_1: ( ( pname > $o ) > $o ) > $o,P_9: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( ( finite1066544169me_o_o @ ( collect_pname_o_o @ P_9 ) )
% 0.25/0.59 | ( finite1066544169me_o_o @ ( collect_pname_o_o @ Q_1 ) ) )
% 0.25/0.59 => ( finite1066544169me_o_o
% 0.25/0.59 @ ( collect_pname_o_o
% 0.25/0.59 @ ^ [X_1: ( pname > $o ) > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_52_finite__Collect__conjI,axiom,
% 0.25/0.59 ! [Q_1: ( ( hoare_1262092251_state > $o ) > $o ) > $o,P_9: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( ( finite1303896758te_o_o @ ( collec341954548te_o_o @ P_9 ) )
% 0.25/0.59 | ( finite1303896758te_o_o @ ( collec341954548te_o_o @ Q_1 ) ) )
% 0.25/0.59 => ( finite1303896758te_o_o
% 0.25/0.59 @ ( collec341954548te_o_o
% 0.25/0.59 @ ^ [X_1: ( hoare_1262092251_state > $o ) > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_53_finite__Collect__conjI,axiom,
% 0.25/0.59 ! [Q_1: ( hoare_1262092251_state > $o ) > $o,P_9: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.59 ( ( ( finite1423311111tate_o @ ( collec313158217tate_o @ P_9 ) )
% 0.25/0.59 | ( finite1423311111tate_o @ ( collec313158217tate_o @ Q_1 ) ) )
% 0.25/0.59 => ( finite1423311111tate_o
% 0.25/0.59 @ ( collec313158217tate_o
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_54_finite__Collect__conjI,axiom,
% 0.25/0.59 ! [Q_1: ( pname > $o ) > $o,P_9: ( pname > $o ) > $o] :
% 0.25/0.59 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_9 ) )
% 0.25/0.59 | ( finite297249702name_o @ ( collect_pname_o @ Q_1 ) ) )
% 0.25/0.59 => ( finite297249702name_o
% 0.25/0.59 @ ( collect_pname_o
% 0.25/0.59 @ ^ [X_1: pname > $o] : ( (&) @ ( P_9 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_55_image__constant__conv,axiom,
% 0.25/0.59 ! [C_8: hoare_1262092251_state,A_73: pname > $o] :
% 0.25/0.59 ( ( ( A_73 = bot_bot_pname_o )
% 0.25/0.59 => ( ( image_669833818_state
% 0.25/0.59 @ ^ [X_1: pname] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = bot_bo113204042tate_o ) )
% 0.25/0.59 & ( ( A_73 != bot_bot_pname_o )
% 0.25/0.59 => ( ( image_669833818_state
% 0.25/0.59 @ ^ [X_1: pname] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = ( insert81609953_state @ C_8 @ bot_bo113204042tate_o ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_56_image__constant__conv,axiom,
% 0.25/0.59 ! [C_8: pname,A_73: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( ( A_73 = bot_bo113204042tate_o )
% 0.25/0.59 => ( ( image_202231862_pname
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = bot_bot_pname_o ) )
% 0.25/0.59 & ( ( A_73 != bot_bo113204042tate_o )
% 0.25/0.59 => ( ( image_202231862_pname
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_57_image__constant__conv,axiom,
% 0.25/0.59 ! [C_8: pname > $o,A_73: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( ( A_73 = bot_bo113204042tate_o )
% 0.25/0.59 => ( ( image_1320925383name_o
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = bot_bot_pname_o_o ) )
% 0.25/0.59 & ( ( A_73 != bot_bo113204042tate_o )
% 0.25/0.59 => ( ( image_1320925383name_o
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = ( insert_pname_o @ C_8 @ bot_bot_pname_o_o ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_58_image__constant__conv,axiom,
% 0.25/0.59 ! [C_8: hoare_1262092251_state > $o,A_73: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( ( A_73 = bot_bo113204042tate_o )
% 0.25/0.59 => ( ( image_1403668518tate_o
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = bot_bo1962689075te_o_o ) )
% 0.25/0.59 & ( ( A_73 != bot_bo113204042tate_o )
% 0.25/0.59 => ( ( image_1403668518tate_o
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = ( insert1042460334tate_o @ C_8 @ bot_bo1962689075te_o_o ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_59_image__constant__conv,axiom,
% 0.25/0.59 ! [C_8: pname > $o,A_73: pname > $o] :
% 0.25/0.59 ( ( ( A_73 = bot_bot_pname_o )
% 0.25/0.59 => ( ( image_pname_pname_o
% 0.25/0.59 @ ^ [X_1: pname] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = bot_bot_pname_o_o ) )
% 0.25/0.59 & ( ( A_73 != bot_bot_pname_o )
% 0.25/0.59 => ( ( image_pname_pname_o
% 0.25/0.59 @ ^ [X_1: pname] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = ( insert_pname_o @ C_8 @ bot_bot_pname_o_o ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_60_image__constant__conv,axiom,
% 0.25/0.59 ! [C_8: hoare_1262092251_state > $o,A_73: pname > $o] :
% 0.25/0.59 ( ( ( A_73 = bot_bot_pname_o )
% 0.25/0.59 => ( ( image_518521461tate_o
% 0.25/0.59 @ ^ [X_1: pname] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = bot_bo1962689075te_o_o ) )
% 0.25/0.59 & ( ( A_73 != bot_bot_pname_o )
% 0.25/0.59 => ( ( image_518521461tate_o
% 0.25/0.59 @ ^ [X_1: pname] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = ( insert1042460334tate_o @ C_8 @ bot_bo1962689075te_o_o ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_61_image__constant__conv,axiom,
% 0.25/0.59 ! [C_8: pname,A_73: pname > $o] :
% 0.25/0.59 ( ( ( A_73 = bot_bot_pname_o )
% 0.25/0.59 => ( ( image_pname_pname
% 0.25/0.59 @ ^ [X_1: pname] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = bot_bot_pname_o ) )
% 0.25/0.59 & ( ( A_73 != bot_bot_pname_o )
% 0.25/0.59 => ( ( image_pname_pname
% 0.25/0.59 @ ^ [X_1: pname] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_62_image__constant__conv,axiom,
% 0.25/0.59 ! [C_8: hoare_1262092251_state,A_73: ( pname > $o ) > $o] :
% 0.25/0.59 ( ( ( A_73 = bot_bot_pname_o_o )
% 0.25/0.59 => ( ( image_1476171975_state
% 0.25/0.59 @ ^ [X_1: pname > $o] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = bot_bo113204042tate_o ) )
% 0.25/0.59 & ( ( A_73 != bot_bot_pname_o_o )
% 0.25/0.59 => ( ( image_1476171975_state
% 0.25/0.59 @ ^ [X_1: pname > $o] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = ( insert81609953_state @ C_8 @ bot_bo113204042tate_o ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_63_image__constant__conv,axiom,
% 0.25/0.59 ! [C_8: hoare_1262092251_state,A_73: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.59 ( ( ( A_73 = bot_bo1962689075te_o_o )
% 0.25/0.59 => ( ( image_234589002_state
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = bot_bo113204042tate_o ) )
% 0.25/0.59 & ( ( A_73 != bot_bo1962689075te_o_o )
% 0.25/0.59 => ( ( image_234589002_state
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = ( insert81609953_state @ C_8 @ bot_bo113204042tate_o ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_64_image__constant__conv,axiom,
% 0.25/0.59 ! [C_8: pname,A_73: ( pname > $o ) > $o] :
% 0.25/0.59 ( ( ( A_73 = bot_bot_pname_o_o )
% 0.25/0.59 => ( ( image_pname_o_pname
% 0.25/0.59 @ ^ [X_1: pname > $o] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = bot_bot_pname_o ) )
% 0.25/0.59 & ( ( A_73 != bot_bot_pname_o_o )
% 0.25/0.59 => ( ( image_pname_o_pname
% 0.25/0.59 @ ^ [X_1: pname > $o] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_65_image__constant__conv,axiom,
% 0.25/0.59 ! [C_8: pname,A_73: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.59 ( ( ( A_73 = bot_bo1962689075te_o_o )
% 0.25/0.59 => ( ( image_1820530197_pname
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = bot_bot_pname_o ) )
% 0.25/0.59 & ( ( A_73 != bot_bo1962689075te_o_o )
% 0.25/0.59 => ( ( image_1820530197_pname
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state > $o] : C_8
% 0.25/0.59 @ A_73 )
% 0.25/0.59 = ( insert_pname @ C_8 @ bot_bot_pname_o ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_66_image__constant,axiom,
% 0.25/0.59 ! [C_7: hoare_1262092251_state,X_18: pname,A_72: pname > $o] :
% 0.25/0.59 ( ( member_pname @ X_18 @ A_72 )
% 0.25/0.59 => ( ( image_669833818_state
% 0.25/0.59 @ ^ [X_1: pname] : C_7
% 0.25/0.59 @ A_72 )
% 0.25/0.59 = ( insert81609953_state @ C_7 @ bot_bo113204042tate_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_67_image__constant,axiom,
% 0.25/0.59 ! [C_7: pname,X_18: hoare_1262092251_state,A_72: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( member5164104_state @ X_18 @ A_72 )
% 0.25/0.59 => ( ( image_202231862_pname
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state] : C_7
% 0.25/0.59 @ A_72 )
% 0.25/0.59 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_68_image__constant,axiom,
% 0.25/0.59 ! [C_7: pname > $o,X_18: hoare_1262092251_state,A_72: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( member5164104_state @ X_18 @ A_72 )
% 0.25/0.59 => ( ( image_1320925383name_o
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state] : C_7
% 0.25/0.59 @ A_72 )
% 0.25/0.59 = ( insert_pname_o @ C_7 @ bot_bot_pname_o_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_69_image__constant,axiom,
% 0.25/0.59 ! [C_7: hoare_1262092251_state > $o,X_18: hoare_1262092251_state,A_72: hoare_1262092251_state > $o] :
% 0.25/0.59 ( ( member5164104_state @ X_18 @ A_72 )
% 0.25/0.59 => ( ( image_1403668518tate_o
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state] : C_7
% 0.25/0.59 @ A_72 )
% 0.25/0.59 = ( insert1042460334tate_o @ C_7 @ bot_bo1962689075te_o_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_70_image__constant,axiom,
% 0.25/0.59 ! [C_7: pname > $o,X_18: pname,A_72: pname > $o] :
% 0.25/0.59 ( ( member_pname @ X_18 @ A_72 )
% 0.25/0.59 => ( ( image_pname_pname_o
% 0.25/0.59 @ ^ [X_1: pname] : C_7
% 0.25/0.59 @ A_72 )
% 0.25/0.59 = ( insert_pname_o @ C_7 @ bot_bot_pname_o_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_71_image__constant,axiom,
% 0.25/0.59 ! [C_7: hoare_1262092251_state > $o,X_18: pname,A_72: pname > $o] :
% 0.25/0.59 ( ( member_pname @ X_18 @ A_72 )
% 0.25/0.59 => ( ( image_518521461tate_o
% 0.25/0.59 @ ^ [X_1: pname] : C_7
% 0.25/0.59 @ A_72 )
% 0.25/0.59 = ( insert1042460334tate_o @ C_7 @ bot_bo1962689075te_o_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_72_image__constant,axiom,
% 0.25/0.59 ! [C_7: pname,X_18: pname,A_72: pname > $o] :
% 0.25/0.59 ( ( member_pname @ X_18 @ A_72 )
% 0.25/0.59 => ( ( image_pname_pname
% 0.25/0.59 @ ^ [X_1: pname] : C_7
% 0.25/0.59 @ A_72 )
% 0.25/0.59 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_73_image__constant,axiom,
% 0.25/0.59 ! [C_7: hoare_1262092251_state,X_18: pname > $o,A_72: ( pname > $o ) > $o] :
% 0.25/0.59 ( ( member_pname_o @ X_18 @ A_72 )
% 0.25/0.59 => ( ( image_1476171975_state
% 0.25/0.59 @ ^ [X_1: pname > $o] : C_7
% 0.25/0.59 @ A_72 )
% 0.25/0.59 = ( insert81609953_state @ C_7 @ bot_bo113204042tate_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_74_image__constant,axiom,
% 0.25/0.59 ! [C_7: hoare_1262092251_state,X_18: hoare_1262092251_state > $o,A_72: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.59 ( ( member907417095tate_o @ X_18 @ A_72 )
% 0.25/0.59 => ( ( image_234589002_state
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state > $o] : C_7
% 0.25/0.59 @ A_72 )
% 0.25/0.59 = ( insert81609953_state @ C_7 @ bot_bo113204042tate_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_75_image__constant,axiom,
% 0.25/0.59 ! [C_7: pname,X_18: pname > $o,A_72: ( pname > $o ) > $o] :
% 0.25/0.59 ( ( member_pname_o @ X_18 @ A_72 )
% 0.25/0.59 => ( ( image_pname_o_pname
% 0.25/0.59 @ ^ [X_1: pname > $o] : C_7
% 0.25/0.59 @ A_72 )
% 0.25/0.59 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_76_image__constant,axiom,
% 0.25/0.59 ! [C_7: pname,X_18: hoare_1262092251_state > $o,A_72: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.59 ( ( member907417095tate_o @ X_18 @ A_72 )
% 0.25/0.59 => ( ( image_1820530197_pname
% 0.25/0.59 @ ^ [X_1: hoare_1262092251_state > $o] : C_7
% 0.25/0.59 @ A_72 )
% 0.25/0.59 = ( insert_pname @ C_7 @ bot_bot_pname_o ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_77_insert__dom,axiom,
% 0.25/0.59 ! [F_16: pname > option_com,X_17: pname,Y_4: com] :
% 0.25/0.59 ( ( ( F_16 @ X_17 )
% 0.25/0.59 = ( some_com @ Y_4 ) )
% 0.25/0.59 => ( ( insert_pname @ X_17 @ ( dom_pname_com @ F_16 ) )
% 0.25/0.59 = ( dom_pname_com @ F_16 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_78_insert__dom,axiom,
% 0.25/0.59 ! [F_16: ( pname > $o ) > option_com,X_17: pname > $o,Y_4: com] :
% 0.25/0.59 ( ( ( F_16 @ X_17 )
% 0.25/0.59 = ( some_com @ Y_4 ) )
% 0.25/0.59 => ( ( insert_pname_o @ X_17 @ ( dom_pname_o_com @ F_16 ) )
% 0.25/0.59 = ( dom_pname_o_com @ F_16 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_79_insert__dom,axiom,
% 0.25/0.59 ! [F_16: ( hoare_1262092251_state > $o ) > option_com,X_17: hoare_1262092251_state > $o,Y_4: com] :
% 0.25/0.59 ( ( ( F_16 @ X_17 )
% 0.25/0.59 = ( some_com @ Y_4 ) )
% 0.25/0.59 => ( ( insert1042460334tate_o @ X_17 @ ( dom_Ho1489634536_o_com @ F_16 ) )
% 0.25/0.59 = ( dom_Ho1489634536_o_com @ F_16 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_80_finite__surj,axiom,
% 0.25/0.59 ! [B_40: hoare_1262092251_state > $o,F_15: pname > hoare_1262092251_state,A_71: pname > $o] :
% 0.25/0.59 ( ( finite_finite_pname @ A_71 )
% 0.25/0.59 => ( ( ord_le870406270tate_o @ B_40 @ ( image_669833818_state @ F_15 @ A_71 ) )
% 0.25/0.59 => ( finite1178804552_state @ B_40 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_81_finite__surj,axiom,
% 0.25/0.59 ! [B_40: pname > $o,F_15: ( ( pname > $o ) > $o ) > pname,A_71: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1066544169me_o_o @ A_71 )
% 0.25/0.59 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_471733107_pname @ F_15 @ A_71 ) )
% 0.25/0.59 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_82_finite__surj,axiom,
% 0.25/0.59 ! [B_40: pname > $o,F_15: ( ( hoare_1262092251_state > $o ) > $o ) > pname,A_71: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1303896758te_o_o @ A_71 )
% 0.25/0.59 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_893364936_pname @ F_15 @ A_71 ) )
% 0.25/0.59 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_83_finite__surj,axiom,
% 0.25/0.59 ! [B_40: pname > $o,F_15: ( hoare_1262092251_state > $o ) > pname,A_71: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.59 ( ( finite1423311111tate_o @ A_71 )
% 0.25/0.59 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_1820530197_pname @ F_15 @ A_71 ) )
% 0.25/0.59 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_84_finite__surj,axiom,
% 0.25/0.59 ! [B_40: pname > $o,F_15: ( pname > $o ) > pname,A_71: ( pname > $o ) > $o] :
% 0.25/0.59 ( ( finite297249702name_o @ A_71 )
% 0.25/0.59 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_pname_o_pname @ F_15 @ A_71 ) )
% 0.25/0.59 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_85_finite__surj,axiom,
% 0.25/0.59 ! [B_40: hoare_1262092251_state > $o,F_15: ( ( pname > $o ) > $o ) > hoare_1262092251_state,A_71: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1066544169me_o_o @ A_71 )
% 0.25/0.59 => ( ( ord_le870406270tate_o @ B_40 @ ( image_1036078444_state @ F_15 @ A_71 ) )
% 0.25/0.59 => ( finite1178804552_state @ B_40 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_86_finite__surj,axiom,
% 0.25/0.59 ! [B_40: hoare_1262092251_state > $o,F_15: ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state,A_71: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.25/0.59 ( ( finite1303896758te_o_o @ A_71 )
% 0.25/0.59 => ( ( ord_le870406270tate_o @ B_40 @ ( image_165349207_state @ F_15 @ A_71 ) )
% 0.25/0.59 => ( finite1178804552_state @ B_40 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_87_finite__surj,axiom,
% 0.25/0.59 ! [B_40: hoare_1262092251_state > $o,F_15: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,A_71: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.59 ( ( finite1423311111tate_o @ A_71 )
% 0.25/0.59 => ( ( ord_le870406270tate_o @ B_40 @ ( image_234589002_state @ F_15 @ A_71 ) )
% 0.25/0.59 => ( finite1178804552_state @ B_40 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_88_finite__surj,axiom,
% 0.25/0.59 ! [B_40: hoare_1262092251_state > $o,F_15: ( pname > $o ) > hoare_1262092251_state,A_71: ( pname > $o ) > $o] :
% 0.25/0.59 ( ( finite297249702name_o @ A_71 )
% 0.25/0.59 => ( ( ord_le870406270tate_o @ B_40 @ ( image_1476171975_state @ F_15 @ A_71 ) )
% 0.25/0.59 => ( finite1178804552_state @ B_40 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 thf(fact_89_finite__surj,axiom,
% 0.25/0.59 ! [B_40: ( ( pname > $o ) > $o ) > $o,F_15: pname > ( pname > $o ) > $o,A_71: pname > $o] :
% 0.25/0.60 ( ( finite_finite_pname @ A_71 )
% 0.25/0.60 => ( ( ord_le1828183645_o_o_o @ B_40 @ ( image_504089495me_o_o @ F_15 @ A_71 ) )
% 0.25/0.60 => ( finite1066544169me_o_o @ B_40 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_90_finite__surj,axiom,
% 0.25/0.60 ! [B_40: ( ( hoare_1262092251_state > $o ) > $o ) > $o,F_15: pname > ( hoare_1262092251_state > $o ) > $o,A_71: pname > $o] :
% 0.25/0.60 ( ( finite_finite_pname @ A_71 )
% 0.25/0.60 => ( ( ord_le1891858320_o_o_o @ B_40 @ ( image_827868872te_o_o @ F_15 @ A_71 ) )
% 0.25/0.60 => ( finite1303896758te_o_o @ B_40 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_91_finite__surj,axiom,
% 0.25/0.60 ! [B_40: pname > $o,F_15: pname > pname,A_71: pname > $o] :
% 0.25/0.60 ( ( finite_finite_pname @ A_71 )
% 0.25/0.60 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_pname_pname @ F_15 @ A_71 ) )
% 0.25/0.60 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_92_finite__surj,axiom,
% 0.25/0.60 ! [B_40: ( hoare_1262092251_state > $o ) > $o,F_15: pname > hoare_1262092251_state > $o,A_71: pname > $o] :
% 0.25/0.60 ( ( finite_finite_pname @ A_71 )
% 0.25/0.60 => ( ( ord_le2012720639te_o_o @ B_40 @ ( image_518521461tate_o @ F_15 @ A_71 ) )
% 0.25/0.60 => ( finite1423311111tate_o @ B_40 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_93_finite__surj,axiom,
% 0.25/0.60 ! [B_40: ( pname > $o ) > $o,F_15: pname > pname > $o,A_71: pname > $o] :
% 0.25/0.60 ( ( finite_finite_pname @ A_71 )
% 0.25/0.60 => ( ( ord_le1205211808me_o_o @ B_40 @ ( image_pname_pname_o @ F_15 @ A_71 ) )
% 0.25/0.60 => ( finite297249702name_o @ B_40 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_94_finite__surj,axiom,
% 0.25/0.60 ! [B_40: ( ( pname > $o ) > $o ) > $o,F_15: hoare_1262092251_state > ( pname > $o ) > $o,A_71: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( finite1178804552_state @ A_71 )
% 0.25/0.60 => ( ( ord_le1828183645_o_o_o @ B_40 @ ( image_333245000me_o_o @ F_15 @ A_71 ) )
% 0.25/0.60 => ( finite1066544169me_o_o @ B_40 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_95_finite__surj,axiom,
% 0.25/0.60 ! [B_40: ( ( hoare_1262092251_state > $o ) > $o ) > $o,F_15: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o,A_71: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( finite1178804552_state @ A_71 )
% 0.25/0.60 => ( ( ord_le1891858320_o_o_o @ B_40 @ ( image_1731108951te_o_o @ F_15 @ A_71 ) )
% 0.25/0.60 => ( finite1303896758te_o_o @ B_40 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_96_finite__surj,axiom,
% 0.25/0.60 ! [B_40: pname > $o,F_15: hoare_1262092251_state > pname,A_71: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( finite1178804552_state @ A_71 )
% 0.25/0.60 => ( ( ord_less_eq_pname_o @ B_40 @ ( image_202231862_pname @ F_15 @ A_71 ) )
% 0.25/0.60 => ( finite_finite_pname @ B_40 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_97_finite__surj,axiom,
% 0.25/0.60 ! [B_40: ( hoare_1262092251_state > $o ) > $o,F_15: hoare_1262092251_state > hoare_1262092251_state > $o,A_71: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( finite1178804552_state @ A_71 )
% 0.25/0.60 => ( ( ord_le2012720639te_o_o @ B_40 @ ( image_1403668518tate_o @ F_15 @ A_71 ) )
% 0.25/0.60 => ( finite1423311111tate_o @ B_40 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_98_finite__surj,axiom,
% 0.25/0.60 ! [B_40: ( pname > $o ) > $o,F_15: hoare_1262092251_state > pname > $o,A_71: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( finite1178804552_state @ A_71 )
% 0.25/0.60 => ( ( ord_le1205211808me_o_o @ B_40 @ ( image_1320925383name_o @ F_15 @ A_71 ) )
% 0.25/0.60 => ( finite297249702name_o @ B_40 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_99_subset__singletonD,axiom,
% 0.25/0.60 ! [A_70: hoare_1262092251_state > $o,X_16: hoare_1262092251_state] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ A_70 @ ( insert81609953_state @ X_16 @ bot_bo113204042tate_o ) )
% 0.25/0.60 => ( ( A_70 = bot_bo113204042tate_o )
% 0.25/0.60 | ( A_70
% 0.25/0.60 = ( insert81609953_state @ X_16 @ bot_bo113204042tate_o ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_100_subset__singletonD,axiom,
% 0.25/0.60 ! [A_70: ( pname > $o ) > $o,X_16: pname > $o] :
% 0.25/0.60 ( ( ord_le1205211808me_o_o @ A_70 @ ( insert_pname_o @ X_16 @ bot_bot_pname_o_o ) )
% 0.25/0.60 => ( ( A_70 = bot_bot_pname_o_o )
% 0.25/0.60 | ( A_70
% 0.25/0.60 = ( insert_pname_o @ X_16 @ bot_bot_pname_o_o ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_101_subset__singletonD,axiom,
% 0.25/0.60 ! [A_70: ( hoare_1262092251_state > $o ) > $o,X_16: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ord_le2012720639te_o_o @ A_70 @ ( insert1042460334tate_o @ X_16 @ bot_bo1962689075te_o_o ) )
% 0.25/0.60 => ( ( A_70 = bot_bo1962689075te_o_o )
% 0.25/0.60 | ( A_70
% 0.25/0.60 = ( insert1042460334tate_o @ X_16 @ bot_bo1962689075te_o_o ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_102_subset__singletonD,axiom,
% 0.25/0.60 ! [A_70: pname > $o,X_16: pname] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ A_70 @ ( insert_pname @ X_16 @ bot_bot_pname_o ) )
% 0.25/0.60 => ( ( A_70 = bot_bot_pname_o )
% 0.25/0.60 | ( A_70
% 0.25/0.60 = ( insert_pname @ X_16 @ bot_bot_pname_o ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_103_MGF,axiom,
% 0.25/0.60 ! [C_1: com] :
% 0.25/0.60 ( hoare_1821564147gleton
% 0.25/0.60 => ( wT_bodies
% 0.25/0.60 => ( ( wt @ C_1 )
% 0.25/0.60 => ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ C_1 ) @ bot_bo113204042tate_o ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_104_emptyE,axiom,
% 0.25/0.60 ! [A_69: hoare_1262092251_state] :
% 0.25/0.60 ~ ( member5164104_state @ A_69 @ bot_bo113204042tate_o ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_105_emptyE,axiom,
% 0.25/0.60 ! [A_69: pname > $o] :
% 0.25/0.60 ~ ( member_pname_o @ A_69 @ bot_bot_pname_o_o ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_106_emptyE,axiom,
% 0.25/0.60 ! [A_69: hoare_1262092251_state > $o] :
% 0.25/0.60 ~ ( member907417095tate_o @ A_69 @ bot_bo1962689075te_o_o ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_107_emptyE,axiom,
% 0.25/0.60 ! [A_69: pname] :
% 0.25/0.60 ~ ( member_pname @ A_69 @ bot_bot_pname_o ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_108_insertCI,axiom,
% 0.25/0.60 ! [B_39: hoare_1262092251_state,A_68: hoare_1262092251_state,B_38: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ~ ( member5164104_state @ A_68 @ B_38 )
% 0.25/0.60 => ( A_68 = B_39 ) )
% 0.25/0.60 => ( member5164104_state @ A_68 @ ( insert81609953_state @ B_39 @ B_38 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_109_insertCI,axiom,
% 0.25/0.60 ! [B_39: pname > $o,A_68: pname > $o,B_38: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( ~ ( member_pname_o @ A_68 @ B_38 )
% 0.25/0.60 => ( A_68 = B_39 ) )
% 0.25/0.60 => ( member_pname_o @ A_68 @ ( insert_pname_o @ B_39 @ B_38 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_110_insertCI,axiom,
% 0.25/0.60 ! [B_39: hoare_1262092251_state > $o,A_68: hoare_1262092251_state > $o,B_38: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( ~ ( member907417095tate_o @ A_68 @ B_38 )
% 0.25/0.60 => ( A_68 = B_39 ) )
% 0.25/0.60 => ( member907417095tate_o @ A_68 @ ( insert1042460334tate_o @ B_39 @ B_38 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_111_insertCI,axiom,
% 0.25/0.60 ! [B_39: pname,A_68: pname,B_38: pname > $o] :
% 0.25/0.60 ( ( ~ ( member_pname @ A_68 @ B_38 )
% 0.25/0.60 => ( A_68 = B_39 ) )
% 0.25/0.60 => ( member_pname @ A_68 @ ( insert_pname @ B_39 @ B_38 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_112_insertE,axiom,
% 0.25/0.60 ! [A_67: hoare_1262092251_state,B_37: hoare_1262092251_state,A_66: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( member5164104_state @ A_67 @ ( insert81609953_state @ B_37 @ A_66 ) )
% 0.25/0.60 => ( ( A_67 != B_37 )
% 0.25/0.60 => ( member5164104_state @ A_67 @ A_66 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_113_insertE,axiom,
% 0.25/0.60 ! [A_67: pname > $o,B_37: pname > $o,A_66: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( member_pname_o @ A_67 @ ( insert_pname_o @ B_37 @ A_66 ) )
% 0.25/0.60 => ( ( A_67 != B_37 )
% 0.25/0.60 => ( member_pname_o @ A_67 @ A_66 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_114_insertE,axiom,
% 0.25/0.60 ! [A_67: hoare_1262092251_state > $o,B_37: hoare_1262092251_state > $o,A_66: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( member907417095tate_o @ A_67 @ ( insert1042460334tate_o @ B_37 @ A_66 ) )
% 0.25/0.60 => ( ( A_67 != B_37 )
% 0.25/0.60 => ( member907417095tate_o @ A_67 @ A_66 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_115_insertE,axiom,
% 0.25/0.60 ! [A_67: pname,B_37: pname,A_66: pname > $o] :
% 0.25/0.60 ( ( member_pname @ A_67 @ ( insert_pname @ B_37 @ A_66 ) )
% 0.25/0.60 => ( ( A_67 != B_37 )
% 0.25/0.60 => ( member_pname @ A_67 @ A_66 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_116_equalityI,axiom,
% 0.25/0.60 ! [A_65: hoare_1262092251_state > $o,B_36: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ A_65 @ B_36 )
% 0.25/0.60 => ( ( ord_le870406270tate_o @ B_36 @ A_65 )
% 0.25/0.60 => ( A_65 = B_36 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_117_equalityI,axiom,
% 0.25/0.60 ! [A_65: ( pname > $o ) > $o,B_36: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( ord_le1205211808me_o_o @ A_65 @ B_36 )
% 0.25/0.60 => ( ( ord_le1205211808me_o_o @ B_36 @ A_65 )
% 0.25/0.60 => ( A_65 = B_36 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_118_equalityI,axiom,
% 0.25/0.60 ! [A_65: ( hoare_1262092251_state > $o ) > $o,B_36: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( ord_le2012720639te_o_o @ A_65 @ B_36 )
% 0.25/0.60 => ( ( ord_le2012720639te_o_o @ B_36 @ A_65 )
% 0.25/0.60 => ( A_65 = B_36 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_119_equalityI,axiom,
% 0.25/0.60 ! [A_65: pname > $o,B_36: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ A_65 @ B_36 )
% 0.25/0.60 => ( ( ord_less_eq_pname_o @ B_36 @ A_65 )
% 0.25/0.60 => ( A_65 = B_36 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_120_subsetD,axiom,
% 0.25/0.60 ! [C_6: hoare_1262092251_state,A_64: hoare_1262092251_state > $o,B_35: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ A_64 @ B_35 )
% 0.25/0.60 => ( ( member5164104_state @ C_6 @ A_64 )
% 0.25/0.60 => ( member5164104_state @ C_6 @ B_35 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_121_subsetD,axiom,
% 0.25/0.60 ! [C_6: pname > $o,A_64: ( pname > $o ) > $o,B_35: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( ord_le1205211808me_o_o @ A_64 @ B_35 )
% 0.25/0.60 => ( ( member_pname_o @ C_6 @ A_64 )
% 0.25/0.60 => ( member_pname_o @ C_6 @ B_35 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_122_subsetD,axiom,
% 0.25/0.60 ! [C_6: hoare_1262092251_state > $o,A_64: ( hoare_1262092251_state > $o ) > $o,B_35: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( ord_le2012720639te_o_o @ A_64 @ B_35 )
% 0.25/0.60 => ( ( member907417095tate_o @ C_6 @ A_64 )
% 0.25/0.60 => ( member907417095tate_o @ C_6 @ B_35 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_123_subsetD,axiom,
% 0.25/0.60 ! [C_6: pname,A_64: pname > $o,B_35: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ A_64 @ B_35 )
% 0.25/0.60 => ( ( member_pname @ C_6 @ A_64 )
% 0.25/0.60 => ( member_pname @ C_6 @ B_35 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_124_image__eqI,axiom,
% 0.25/0.60 ! [A_63: hoare_1262092251_state > $o,B_34: pname > $o,F_14: hoare_1262092251_state > pname > $o,X_15: hoare_1262092251_state] :
% 0.25/0.60 ( ( B_34
% 0.25/0.60 = ( F_14 @ X_15 ) )
% 0.25/0.60 => ( ( member5164104_state @ X_15 @ A_63 )
% 0.25/0.60 => ( member_pname_o @ B_34 @ ( image_1320925383name_o @ F_14 @ A_63 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_125_image__eqI,axiom,
% 0.25/0.60 ! [A_63: hoare_1262092251_state > $o,B_34: hoare_1262092251_state > $o,F_14: hoare_1262092251_state > hoare_1262092251_state > $o,X_15: hoare_1262092251_state] :
% 0.25/0.60 ( ( B_34
% 0.25/0.60 = ( F_14 @ X_15 ) )
% 0.25/0.60 => ( ( member5164104_state @ X_15 @ A_63 )
% 0.25/0.60 => ( member907417095tate_o @ B_34 @ ( image_1403668518tate_o @ F_14 @ A_63 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_126_image__eqI,axiom,
% 0.25/0.60 ! [A_63: pname > $o,B_34: pname > $o,F_14: pname > pname > $o,X_15: pname] :
% 0.25/0.60 ( ( B_34
% 0.25/0.60 = ( F_14 @ X_15 ) )
% 0.25/0.60 => ( ( member_pname @ X_15 @ A_63 )
% 0.25/0.60 => ( member_pname_o @ B_34 @ ( image_pname_pname_o @ F_14 @ A_63 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_127_image__eqI,axiom,
% 0.25/0.60 ! [A_63: pname > $o,B_34: hoare_1262092251_state > $o,F_14: pname > hoare_1262092251_state > $o,X_15: pname] :
% 0.25/0.60 ( ( B_34
% 0.25/0.60 = ( F_14 @ X_15 ) )
% 0.25/0.60 => ( ( member_pname @ X_15 @ A_63 )
% 0.25/0.60 => ( member907417095tate_o @ B_34 @ ( image_518521461tate_o @ F_14 @ A_63 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_128_image__eqI,axiom,
% 0.25/0.60 ! [A_63: ( pname > $o ) > $o,B_34: hoare_1262092251_state,F_14: ( pname > $o ) > hoare_1262092251_state,X_15: pname > $o] :
% 0.25/0.60 ( ( B_34
% 0.25/0.60 = ( F_14 @ X_15 ) )
% 0.25/0.60 => ( ( member_pname_o @ X_15 @ A_63 )
% 0.25/0.60 => ( member5164104_state @ B_34 @ ( image_1476171975_state @ F_14 @ A_63 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_129_image__eqI,axiom,
% 0.25/0.60 ! [A_63: ( hoare_1262092251_state > $o ) > $o,B_34: hoare_1262092251_state,F_14: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,X_15: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( B_34
% 0.25/0.60 = ( F_14 @ X_15 ) )
% 0.25/0.60 => ( ( member907417095tate_o @ X_15 @ A_63 )
% 0.25/0.60 => ( member5164104_state @ B_34 @ ( image_234589002_state @ F_14 @ A_63 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_130_image__eqI,axiom,
% 0.25/0.60 ! [A_63: hoare_1262092251_state > $o,B_34: pname,F_14: hoare_1262092251_state > pname,X_15: hoare_1262092251_state] :
% 0.25/0.60 ( ( B_34
% 0.25/0.60 = ( F_14 @ X_15 ) )
% 0.25/0.60 => ( ( member5164104_state @ X_15 @ A_63 )
% 0.25/0.60 => ( member_pname @ B_34 @ ( image_202231862_pname @ F_14 @ A_63 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_131_image__eqI,axiom,
% 0.25/0.60 ! [A_63: pname > $o,B_34: pname,F_14: pname > pname,X_15: pname] :
% 0.25/0.60 ( ( B_34
% 0.25/0.60 = ( F_14 @ X_15 ) )
% 0.25/0.60 => ( ( member_pname @ X_15 @ A_63 )
% 0.25/0.60 => ( member_pname @ B_34 @ ( image_pname_pname @ F_14 @ A_63 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_132_image__eqI,axiom,
% 0.25/0.60 ! [A_63: ( pname > $o ) > $o,B_34: pname,F_14: ( pname > $o ) > pname,X_15: pname > $o] :
% 0.25/0.60 ( ( B_34
% 0.25/0.60 = ( F_14 @ X_15 ) )
% 0.25/0.60 => ( ( member_pname_o @ X_15 @ A_63 )
% 0.25/0.60 => ( member_pname @ B_34 @ ( image_pname_o_pname @ F_14 @ A_63 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_133_image__eqI,axiom,
% 0.25/0.60 ! [A_63: ( hoare_1262092251_state > $o ) > $o,B_34: pname,F_14: ( hoare_1262092251_state > $o ) > pname,X_15: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( B_34
% 0.25/0.60 = ( F_14 @ X_15 ) )
% 0.25/0.60 => ( ( member907417095tate_o @ X_15 @ A_63 )
% 0.25/0.60 => ( member_pname @ B_34 @ ( image_1820530197_pname @ F_14 @ A_63 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_134_image__eqI,axiom,
% 0.25/0.60 ! [A_63: pname > $o,B_34: hoare_1262092251_state,F_14: pname > hoare_1262092251_state,X_15: pname] :
% 0.25/0.60 ( ( B_34
% 0.25/0.60 = ( F_14 @ X_15 ) )
% 0.25/0.60 => ( ( member_pname @ X_15 @ A_63 )
% 0.25/0.60 => ( member5164104_state @ B_34 @ ( image_669833818_state @ F_14 @ A_63 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_135_equals0D,axiom,
% 0.25/0.60 ! [A_62: pname > $o,A_61: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( A_61 = bot_bot_pname_o_o )
% 0.25/0.60 => ~ ( member_pname_o @ A_62 @ A_61 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_136_equals0D,axiom,
% 0.25/0.60 ! [A_62: hoare_1262092251_state > $o,A_61: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( A_61 = bot_bo1962689075te_o_o )
% 0.25/0.60 => ~ ( member907417095tate_o @ A_62 @ A_61 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_137_equals0D,axiom,
% 0.25/0.60 ! [A_62: hoare_1262092251_state,A_61: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( A_61 = bot_bo113204042tate_o )
% 0.25/0.60 => ~ ( member5164104_state @ A_62 @ A_61 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_138_equals0D,axiom,
% 0.25/0.60 ! [A_62: pname,A_61: pname > $o] :
% 0.25/0.60 ( ( A_61 = bot_bot_pname_o )
% 0.25/0.60 => ~ ( member_pname @ A_62 @ A_61 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_139_Collect__empty__eq,axiom,
% 0.25/0.60 ! [P_8: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.60 ( ( ( collect_pname_o_o @ P_8 )
% 0.25/0.60 = bot_bot_pname_o_o_o )
% 0.25/0.60 <=> ! [X_1: ( pname > $o ) > $o] :
% 0.25/0.60 ~ ( P_8 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_140_Collect__empty__eq,axiom,
% 0.25/0.60 ! [P_8: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.25/0.60 ( ( ( collec341954548te_o_o @ P_8 )
% 0.25/0.60 = bot_bo388435036_o_o_o )
% 0.25/0.60 <=> ! [X_1: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ~ ( P_8 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_141_Collect__empty__eq,axiom,
% 0.25/0.60 ! [P_8: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( ( collec313158217tate_o @ P_8 )
% 0.25/0.60 = bot_bo1962689075te_o_o )
% 0.25/0.60 <=> ! [X_1: hoare_1262092251_state > $o] :
% 0.25/0.60 ~ ( P_8 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_142_Collect__empty__eq,axiom,
% 0.25/0.60 ! [P_8: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( ( collect_pname_o @ P_8 )
% 0.25/0.60 = bot_bot_pname_o_o )
% 0.25/0.60 <=> ! [X_1: pname > $o] :
% 0.25/0.60 ~ ( P_8 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_143_Collect__empty__eq,axiom,
% 0.25/0.60 ! [P_8: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ( collec1121927558_state @ P_8 )
% 0.25/0.60 = bot_bo113204042tate_o )
% 0.25/0.60 <=> ! [X_1: hoare_1262092251_state] :
% 0.25/0.60 ~ ( P_8 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_144_Collect__empty__eq,axiom,
% 0.25/0.60 ! [P_8: pname > $o] :
% 0.25/0.60 ( ( ( collect_pname @ P_8 )
% 0.25/0.60 = bot_bot_pname_o )
% 0.25/0.60 <=> ! [X_1: pname] :
% 0.25/0.60 ~ ( P_8 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_145_empty__iff,axiom,
% 0.25/0.60 ! [C_5: pname > $o] :
% 0.25/0.60 ~ ( member_pname_o @ C_5 @ bot_bot_pname_o_o ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_146_empty__iff,axiom,
% 0.25/0.60 ! [C_5: hoare_1262092251_state > $o] :
% 0.25/0.60 ~ ( member907417095tate_o @ C_5 @ bot_bo1962689075te_o_o ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_147_empty__iff,axiom,
% 0.25/0.60 ! [C_5: hoare_1262092251_state] :
% 0.25/0.60 ~ ( member5164104_state @ C_5 @ bot_bo113204042tate_o ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_148_empty__iff,axiom,
% 0.25/0.60 ! [C_5: pname] :
% 0.25/0.60 ~ ( member_pname @ C_5 @ bot_bot_pname_o ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_149_empty__Collect__eq,axiom,
% 0.25/0.60 ! [P_7: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.60 ( ( bot_bot_pname_o_o_o
% 0.25/0.60 = ( collect_pname_o_o @ P_7 ) )
% 0.25/0.60 <=> ! [X_1: ( pname > $o ) > $o] :
% 0.25/0.60 ~ ( P_7 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_150_empty__Collect__eq,axiom,
% 0.25/0.60 ! [P_7: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
% 0.25/0.60 ( ( bot_bo388435036_o_o_o
% 0.25/0.60 = ( collec341954548te_o_o @ P_7 ) )
% 0.25/0.60 <=> ! [X_1: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ~ ( P_7 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_151_empty__Collect__eq,axiom,
% 0.25/0.60 ! [P_7: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( bot_bo1962689075te_o_o
% 0.25/0.60 = ( collec313158217tate_o @ P_7 ) )
% 0.25/0.60 <=> ! [X_1: hoare_1262092251_state > $o] :
% 0.25/0.60 ~ ( P_7 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_152_empty__Collect__eq,axiom,
% 0.25/0.60 ! [P_7: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( bot_bot_pname_o_o
% 0.25/0.60 = ( collect_pname_o @ P_7 ) )
% 0.25/0.60 <=> ! [X_1: pname > $o] :
% 0.25/0.60 ~ ( P_7 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_153_empty__Collect__eq,axiom,
% 0.25/0.60 ! [P_7: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( bot_bo113204042tate_o
% 0.25/0.60 = ( collec1121927558_state @ P_7 ) )
% 0.25/0.60 <=> ! [X_1: hoare_1262092251_state] :
% 0.25/0.60 ~ ( P_7 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_154_empty__Collect__eq,axiom,
% 0.25/0.60 ! [P_7: pname > $o] :
% 0.25/0.60 ( ( bot_bot_pname_o
% 0.25/0.60 = ( collect_pname @ P_7 ) )
% 0.25/0.60 <=> ! [X_1: pname] :
% 0.25/0.60 ~ ( P_7 @ X_1 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_155_ex__in__conv,axiom,
% 0.25/0.60 ! [A_60: ( pname > $o ) > $o] :
% 0.25/0.60 ( ? [X_1: pname > $o] : ( member_pname_o @ X_1 @ A_60 )
% 0.25/0.60 <=> ( A_60 != bot_bot_pname_o_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_156_ex__in__conv,axiom,
% 0.25/0.60 ! [A_60: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ? [X_1: hoare_1262092251_state > $o] : ( member907417095tate_o @ X_1 @ A_60 )
% 0.25/0.60 <=> ( A_60 != bot_bo1962689075te_o_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_157_ex__in__conv,axiom,
% 0.25/0.60 ! [A_60: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ? [X_1: hoare_1262092251_state] : ( member5164104_state @ X_1 @ A_60 )
% 0.25/0.60 <=> ( A_60 != bot_bo113204042tate_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_158_ex__in__conv,axiom,
% 0.25/0.60 ! [A_60: pname > $o] :
% 0.25/0.60 ( ? [X_1: pname] : ( member_pname @ X_1 @ A_60 )
% 0.25/0.60 <=> ( A_60 != bot_bot_pname_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_159_all__not__in__conv,axiom,
% 0.25/0.60 ! [A_59: ( pname > $o ) > $o] :
% 0.25/0.60 ( ! [X_1: pname > $o] :
% 0.25/0.60 ~ ( member_pname_o @ X_1 @ A_59 )
% 0.25/0.60 <=> ( A_59 = bot_bot_pname_o_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_160_all__not__in__conv,axiom,
% 0.25/0.60 ! [A_59: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ! [X_1: hoare_1262092251_state > $o] :
% 0.25/0.60 ~ ( member907417095tate_o @ X_1 @ A_59 )
% 0.25/0.60 <=> ( A_59 = bot_bo1962689075te_o_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_161_all__not__in__conv,axiom,
% 0.25/0.60 ! [A_59: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ! [X_1: hoare_1262092251_state] :
% 0.25/0.60 ~ ( member5164104_state @ X_1 @ A_59 )
% 0.25/0.60 <=> ( A_59 = bot_bo113204042tate_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_162_all__not__in__conv,axiom,
% 0.25/0.60 ! [A_59: pname > $o] :
% 0.25/0.60 ( ! [X_1: pname] :
% 0.25/0.60 ~ ( member_pname @ X_1 @ A_59 )
% 0.25/0.60 <=> ( A_59 = bot_bot_pname_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_163_empty__def,axiom,
% 0.25/0.60 ( bot_bo388435036_o_o_o
% 0.25/0.60 = ( collec341954548te_o_o
% 0.25/0.60 @ ^ [X_1: ( hoare_1262092251_state > $o ) > $o] : $false ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_164_empty__def,axiom,
% 0.25/0.60 ( bot_bo1962689075te_o_o
% 0.25/0.60 = ( collec313158217tate_o
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state > $o] : $false ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_165_empty__def,axiom,
% 0.25/0.60 ( bot_bot_pname_o_o
% 0.25/0.60 = ( collect_pname_o
% 0.25/0.60 @ ^ [X_1: pname > $o] : $false ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_166_empty__def,axiom,
% 0.25/0.60 ( bot_bo113204042tate_o
% 0.25/0.60 = ( collec1121927558_state
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state] : $false ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_167_empty__def,axiom,
% 0.25/0.60 ( bot_bot_pname_o
% 0.25/0.60 = ( collect_pname
% 0.25/0.60 @ ^ [X_1: pname] : $false ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_168_insert__absorb,axiom,
% 0.25/0.60 ! [A_58: pname,A_57: pname > $o] :
% 0.25/0.60 ( ( member_pname @ A_58 @ A_57 )
% 0.25/0.60 => ( ( insert_pname @ A_58 @ A_57 )
% 0.25/0.60 = A_57 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_169_insert__absorb,axiom,
% 0.25/0.60 ! [A_58: hoare_1262092251_state,A_57: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( member5164104_state @ A_58 @ A_57 )
% 0.25/0.60 => ( ( insert81609953_state @ A_58 @ A_57 )
% 0.25/0.60 = A_57 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_170_insertI2,axiom,
% 0.25/0.60 ! [B_33: pname,A_56: pname,B_32: pname > $o] :
% 0.25/0.60 ( ( member_pname @ A_56 @ B_32 )
% 0.25/0.60 => ( member_pname @ A_56 @ ( insert_pname @ B_33 @ B_32 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_171_insertI2,axiom,
% 0.25/0.60 ! [B_33: hoare_1262092251_state,A_56: hoare_1262092251_state,B_32: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( member5164104_state @ A_56 @ B_32 )
% 0.25/0.60 => ( member5164104_state @ A_56 @ ( insert81609953_state @ B_33 @ B_32 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_172_insert__ident,axiom,
% 0.25/0.60 ! [B_31: pname > $o,X_14: pname,A_55: pname > $o] :
% 0.25/0.60 ( ~ ( member_pname @ X_14 @ A_55 )
% 0.25/0.60 => ( ~ ( member_pname @ X_14 @ B_31 )
% 0.25/0.60 => ( ( ( insert_pname @ X_14 @ A_55 )
% 0.25/0.60 = ( insert_pname @ X_14 @ B_31 ) )
% 0.25/0.60 <=> ( A_55 = B_31 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_173_insert__ident,axiom,
% 0.25/0.60 ! [B_31: hoare_1262092251_state > $o,X_14: hoare_1262092251_state,A_55: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ~ ( member5164104_state @ X_14 @ A_55 )
% 0.25/0.60 => ( ~ ( member5164104_state @ X_14 @ B_31 )
% 0.25/0.60 => ( ( ( insert81609953_state @ X_14 @ A_55 )
% 0.25/0.60 = ( insert81609953_state @ X_14 @ B_31 ) )
% 0.25/0.60 <=> ( A_55 = B_31 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_174_insert__code,axiom,
% 0.25/0.60 ! [Y_3: pname,A_54: pname > $o,X_13: pname] :
% 0.25/0.60 ( ( insert_pname @ Y_3 @ A_54 @ X_13 )
% 0.25/0.60 <=> ( ( Y_3 = X_13 )
% 0.25/0.60 | ( A_54 @ X_13 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_175_insert__code,axiom,
% 0.25/0.60 ! [Y_3: hoare_1262092251_state,A_54: hoare_1262092251_state > $o,X_13: hoare_1262092251_state] :
% 0.25/0.60 ( ( insert81609953_state @ Y_3 @ A_54 @ X_13 )
% 0.25/0.60 <=> ( ( Y_3 = X_13 )
% 0.25/0.60 | ( A_54 @ X_13 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_176_insert__iff,axiom,
% 0.25/0.60 ! [A_53: pname,B_30: pname,A_52: pname > $o] :
% 0.25/0.60 ( ( member_pname @ A_53 @ ( insert_pname @ B_30 @ A_52 ) )
% 0.25/0.60 <=> ( ( A_53 = B_30 )
% 0.25/0.60 | ( member_pname @ A_53 @ A_52 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_177_insert__iff,axiom,
% 0.25/0.60 ! [A_53: hoare_1262092251_state,B_30: hoare_1262092251_state,A_52: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( member5164104_state @ A_53 @ ( insert81609953_state @ B_30 @ A_52 ) )
% 0.25/0.60 <=> ( ( A_53 = B_30 )
% 0.25/0.60 | ( member5164104_state @ A_53 @ A_52 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_178_insert__commute,axiom,
% 0.25/0.60 ! [X_12: pname,Y_2: pname,A_51: pname > $o] :
% 0.25/0.60 ( ( insert_pname @ X_12 @ ( insert_pname @ Y_2 @ A_51 ) )
% 0.25/0.60 = ( insert_pname @ Y_2 @ ( insert_pname @ X_12 @ A_51 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_179_insert__commute,axiom,
% 0.25/0.60 ! [X_12: hoare_1262092251_state,Y_2: hoare_1262092251_state,A_51: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( insert81609953_state @ X_12 @ ( insert81609953_state @ Y_2 @ A_51 ) )
% 0.25/0.60 = ( insert81609953_state @ Y_2 @ ( insert81609953_state @ X_12 @ A_51 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_180_insert__absorb2,axiom,
% 0.25/0.60 ! [X_11: pname,A_50: pname > $o] :
% 0.25/0.60 ( ( insert_pname @ X_11 @ ( insert_pname @ X_11 @ A_50 ) )
% 0.25/0.60 = ( insert_pname @ X_11 @ A_50 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_181_insert__absorb2,axiom,
% 0.25/0.60 ! [X_11: hoare_1262092251_state,A_50: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( insert81609953_state @ X_11 @ ( insert81609953_state @ X_11 @ A_50 ) )
% 0.25/0.60 = ( insert81609953_state @ X_11 @ A_50 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_182_insert__Collect,axiom,
% 0.25/0.60 ! [A_49: pname,P_6: pname > $o] :
% 0.25/0.60 ( ( insert_pname @ A_49 @ ( collect_pname @ P_6 ) )
% 0.25/0.60 = ( collect_pname
% 0.25/0.60 @ ^ [U: pname] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_183_insert__Collect,axiom,
% 0.25/0.60 ! [A_49: hoare_1262092251_state,P_6: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( insert81609953_state @ A_49 @ ( collec1121927558_state @ P_6 ) )
% 0.25/0.60 = ( collec1121927558_state
% 0.25/0.60 @ ^ [U: hoare_1262092251_state] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_184_insert__Collect,axiom,
% 0.25/0.60 ! [A_49: pname > $o,P_6: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( insert_pname_o @ A_49 @ ( collect_pname_o @ P_6 ) )
% 0.25/0.60 = ( collect_pname_o
% 0.25/0.60 @ ^ [U: pname > $o] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_185_insert__Collect,axiom,
% 0.25/0.60 ! [A_49: hoare_1262092251_state > $o,P_6: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( insert1042460334tate_o @ A_49 @ ( collec313158217tate_o @ P_6 ) )
% 0.25/0.60 = ( collec313158217tate_o
% 0.25/0.60 @ ^ [U: hoare_1262092251_state > $o] : ( (=>) @ ( (~) @ ( U = A_49 ) ) @ ( P_6 @ U ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_186_insert__compr,axiom,
% 0.25/0.60 ! [A_48: pname,B_29: pname > $o] :
% 0.25/0.60 ( ( insert_pname @ A_48 @ B_29 )
% 0.25/0.60 = ( collect_pname
% 0.25/0.60 @ ^ [X_1: pname] : ( (|) @ ( X_1 = A_48 ) @ ( member_pname @ X_1 @ B_29 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_187_insert__compr,axiom,
% 0.25/0.60 ! [A_48: hoare_1262092251_state,B_29: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( insert81609953_state @ A_48 @ B_29 )
% 0.25/0.60 = ( collec1121927558_state
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state] : ( (|) @ ( X_1 = A_48 ) @ ( member5164104_state @ X_1 @ B_29 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_188_insert__compr,axiom,
% 0.25/0.60 ! [A_48: pname > $o,B_29: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( insert_pname_o @ A_48 @ B_29 )
% 0.25/0.60 = ( collect_pname_o
% 0.25/0.60 @ ^ [X_1: pname > $o] : ( (|) @ ( X_1 = A_48 ) @ ( member_pname_o @ X_1 @ B_29 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_189_insert__compr,axiom,
% 0.25/0.60 ! [A_48: hoare_1262092251_state > $o,B_29: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( insert1042460334tate_o @ A_48 @ B_29 )
% 0.25/0.60 = ( collec313158217tate_o
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state > $o] : ( (|) @ ( X_1 = A_48 ) @ ( member907417095tate_o @ X_1 @ B_29 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_190_insertI1,axiom,
% 0.25/0.60 ! [A_47: pname,B_28: pname > $o] : ( member_pname @ A_47 @ ( insert_pname @ A_47 @ B_28 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_191_insertI1,axiom,
% 0.25/0.60 ! [A_47: hoare_1262092251_state,B_28: hoare_1262092251_state > $o] : ( member5164104_state @ A_47 @ ( insert81609953_state @ A_47 @ B_28 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_192_equalityE,axiom,
% 0.25/0.60 ! [A_46: pname > $o,B_27: pname > $o] :
% 0.25/0.60 ( ( A_46 = B_27 )
% 0.25/0.60 => ~ ( ( ord_less_eq_pname_o @ A_46 @ B_27 )
% 0.25/0.60 => ~ ( ord_less_eq_pname_o @ B_27 @ A_46 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_193_equalityE,axiom,
% 0.25/0.60 ! [A_46: hoare_1262092251_state > $o,B_27: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( A_46 = B_27 )
% 0.25/0.60 => ~ ( ( ord_le870406270tate_o @ A_46 @ B_27 )
% 0.25/0.60 => ~ ( ord_le870406270tate_o @ B_27 @ A_46 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_194_subset__trans,axiom,
% 0.25/0.60 ! [C_4: pname > $o,A_45: pname > $o,B_26: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ A_45 @ B_26 )
% 0.25/0.60 => ( ( ord_less_eq_pname_o @ B_26 @ C_4 )
% 0.25/0.60 => ( ord_less_eq_pname_o @ A_45 @ C_4 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_195_subset__trans,axiom,
% 0.25/0.60 ! [C_4: hoare_1262092251_state > $o,A_45: hoare_1262092251_state > $o,B_26: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ A_45 @ B_26 )
% 0.25/0.60 => ( ( ord_le870406270tate_o @ B_26 @ C_4 )
% 0.25/0.60 => ( ord_le870406270tate_o @ A_45 @ C_4 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_196_set__mp,axiom,
% 0.25/0.60 ! [X_10: pname,A_44: pname > $o,B_25: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ A_44 @ B_25 )
% 0.25/0.60 => ( ( member_pname @ X_10 @ A_44 )
% 0.25/0.60 => ( member_pname @ X_10 @ B_25 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_197_set__mp,axiom,
% 0.25/0.60 ! [X_10: hoare_1262092251_state,A_44: hoare_1262092251_state > $o,B_25: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ A_44 @ B_25 )
% 0.25/0.60 => ( ( member5164104_state @ X_10 @ A_44 )
% 0.25/0.60 => ( member5164104_state @ X_10 @ B_25 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_198_set__rev__mp,axiom,
% 0.25/0.60 ! [B_24: pname > $o,X_9: pname,A_43: pname > $o] :
% 0.25/0.60 ( ( member_pname @ X_9 @ A_43 )
% 0.25/0.60 => ( ( ord_less_eq_pname_o @ A_43 @ B_24 )
% 0.25/0.60 => ( member_pname @ X_9 @ B_24 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_199_set__rev__mp,axiom,
% 0.25/0.60 ! [B_24: hoare_1262092251_state > $o,X_9: hoare_1262092251_state,A_43: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( member5164104_state @ X_9 @ A_43 )
% 0.25/0.60 => ( ( ord_le870406270tate_o @ A_43 @ B_24 )
% 0.25/0.60 => ( member5164104_state @ X_9 @ B_24 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_200_in__mono,axiom,
% 0.25/0.60 ! [X_8: pname,A_42: pname > $o,B_23: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ A_42 @ B_23 )
% 0.25/0.60 => ( ( member_pname @ X_8 @ A_42 )
% 0.25/0.60 => ( member_pname @ X_8 @ B_23 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_201_in__mono,axiom,
% 0.25/0.60 ! [X_8: hoare_1262092251_state,A_42: hoare_1262092251_state > $o,B_23: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ A_42 @ B_23 )
% 0.25/0.60 => ( ( member5164104_state @ X_8 @ A_42 )
% 0.25/0.60 => ( member5164104_state @ X_8 @ B_23 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_202_equalityD2,axiom,
% 0.25/0.60 ! [A_41: pname > $o,B_22: pname > $o] :
% 0.25/0.60 ( ( A_41 = B_22 )
% 0.25/0.60 => ( ord_less_eq_pname_o @ B_22 @ A_41 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_203_equalityD2,axiom,
% 0.25/0.60 ! [A_41: hoare_1262092251_state > $o,B_22: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( A_41 = B_22 )
% 0.25/0.60 => ( ord_le870406270tate_o @ B_22 @ A_41 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_204_equalityD1,axiom,
% 0.25/0.60 ! [A_40: pname > $o,B_21: pname > $o] :
% 0.25/0.60 ( ( A_40 = B_21 )
% 0.25/0.60 => ( ord_less_eq_pname_o @ A_40 @ B_21 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_205_equalityD1,axiom,
% 0.25/0.60 ! [A_40: hoare_1262092251_state > $o,B_21: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( A_40 = B_21 )
% 0.25/0.60 => ( ord_le870406270tate_o @ A_40 @ B_21 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_206_set__eq__subset,axiom,
% 0.25/0.60 ! [A_39: pname > $o,B_20: pname > $o] :
% 0.25/0.60 ( ( A_39 = B_20 )
% 0.25/0.60 <=> ( ( ord_less_eq_pname_o @ A_39 @ B_20 )
% 0.25/0.60 & ( ord_less_eq_pname_o @ B_20 @ A_39 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_207_set__eq__subset,axiom,
% 0.25/0.60 ! [A_39: hoare_1262092251_state > $o,B_20: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( A_39 = B_20 )
% 0.25/0.60 <=> ( ( ord_le870406270tate_o @ A_39 @ B_20 )
% 0.25/0.60 & ( ord_le870406270tate_o @ B_20 @ A_39 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_208_subset__refl,axiom,
% 0.25/0.60 ! [A_38: pname > $o] : ( ord_less_eq_pname_o @ A_38 @ A_38 ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_209_subset__refl,axiom,
% 0.25/0.60 ! [A_38: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ A_38 @ A_38 ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_210_rev__image__eqI,axiom,
% 0.25/0.60 ! [B_19: hoare_1262092251_state,F_13: pname > hoare_1262092251_state,X_7: pname,A_37: pname > $o] :
% 0.25/0.60 ( ( member_pname @ X_7 @ A_37 )
% 0.25/0.60 => ( ( B_19
% 0.25/0.60 = ( F_13 @ X_7 ) )
% 0.25/0.60 => ( member5164104_state @ B_19 @ ( image_669833818_state @ F_13 @ A_37 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_211_imageI,axiom,
% 0.25/0.60 ! [F_12: pname > hoare_1262092251_state,X_6: pname,A_36: pname > $o] :
% 0.25/0.60 ( ( member_pname @ X_6 @ A_36 )
% 0.25/0.60 => ( member5164104_state @ ( F_12 @ X_6 ) @ ( image_669833818_state @ F_12 @ A_36 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_212_image__iff,axiom,
% 0.25/0.60 ! [Z: hoare_1262092251_state,F_11: pname > hoare_1262092251_state,A_35: pname > $o] :
% 0.25/0.60 ( ( member5164104_state @ Z @ ( image_669833818_state @ F_11 @ A_35 ) )
% 0.25/0.60 <=> ? [X_1: pname] :
% 0.25/0.60 ( ( member_pname @ X_1 @ A_35 )
% 0.25/0.60 & ( Z
% 0.25/0.60 = ( F_11 @ X_1 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_213_finite__Collect__disjI,axiom,
% 0.25/0.60 ! [P_5: pname > $o,Q: pname > $o] :
% 0.25/0.60 ( ( finite_finite_pname
% 0.25/0.60 @ ( collect_pname
% 0.25/0.60 @ ^ [X_1: pname] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.25/0.60 <=> ( ( finite_finite_pname @ ( collect_pname @ P_5 ) )
% 0.25/0.60 & ( finite_finite_pname @ ( collect_pname @ Q ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_214_finite__Collect__disjI,axiom,
% 0.25/0.60 ! [P_5: hoare_1262092251_state > $o,Q: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( finite1178804552_state
% 0.25/0.60 @ ( collec1121927558_state
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.25/0.60 <=> ( ( finite1178804552_state @ ( collec1121927558_state @ P_5 ) )
% 0.25/0.60 & ( finite1178804552_state @ ( collec1121927558_state @ Q ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_215_finite__Collect__disjI,axiom,
% 0.25/0.60 ! [P_5: ( pname > $o ) > $o,Q: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( finite297249702name_o
% 0.25/0.60 @ ( collect_pname_o
% 0.25/0.60 @ ^ [X_1: pname > $o] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.25/0.60 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_5 ) )
% 0.25/0.60 & ( finite297249702name_o @ ( collect_pname_o @ Q ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_216_finite__Collect__disjI,axiom,
% 0.25/0.60 ! [P_5: ( hoare_1262092251_state > $o ) > $o,Q: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( finite1423311111tate_o
% 0.25/0.60 @ ( collec313158217tate_o
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state > $o] : ( (|) @ ( P_5 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.25/0.60 <=> ( ( finite1423311111tate_o @ ( collec313158217tate_o @ P_5 ) )
% 0.25/0.60 & ( finite1423311111tate_o @ ( collec313158217tate_o @ Q ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_217_insert__compr__raw,axiom,
% 0.25/0.60 ! [X_1: pname,Xa: pname > $o] :
% 0.25/0.60 ( ( insert_pname @ X_1 @ Xa )
% 0.25/0.60 = ( collect_pname
% 0.25/0.60 @ ^ [Y_1: pname] : ( (|) @ ( Y_1 = X_1 ) @ ( member_pname @ Y_1 @ Xa ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_218_insert__compr__raw,axiom,
% 0.25/0.60 ! [X_1: hoare_1262092251_state,Xa: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( insert81609953_state @ X_1 @ Xa )
% 0.25/0.60 = ( collec1121927558_state
% 0.25/0.60 @ ^ [Y_1: hoare_1262092251_state] : ( (|) @ ( Y_1 = X_1 ) @ ( member5164104_state @ Y_1 @ Xa ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_219_insert__compr__raw,axiom,
% 0.25/0.60 ! [X_1: pname > $o,Xa: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( insert_pname_o @ X_1 @ Xa )
% 0.25/0.60 = ( collect_pname_o
% 0.25/0.60 @ ^ [Y_1: pname > $o] : ( (|) @ ( Y_1 = X_1 ) @ ( member_pname_o @ Y_1 @ Xa ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_220_insert__compr__raw,axiom,
% 0.25/0.60 ! [X_1: hoare_1262092251_state > $o,Xa: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( insert1042460334tate_o @ X_1 @ Xa )
% 0.25/0.60 = ( collec313158217tate_o
% 0.25/0.60 @ ^ [Y_1: hoare_1262092251_state > $o] : ( (|) @ ( Y_1 = X_1 ) @ ( member907417095tate_o @ Y_1 @ Xa ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_221_singleton__inject,axiom,
% 0.25/0.60 ! [A_34: pname,B_18: pname] :
% 0.25/0.60 ( ( ( insert_pname @ A_34 @ bot_bot_pname_o )
% 0.25/0.60 = ( insert_pname @ B_18 @ bot_bot_pname_o ) )
% 0.25/0.60 => ( A_34 = B_18 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_222_singleton__inject,axiom,
% 0.25/0.60 ! [A_34: hoare_1262092251_state,B_18: hoare_1262092251_state] :
% 0.25/0.60 ( ( ( insert81609953_state @ A_34 @ bot_bo113204042tate_o )
% 0.25/0.60 = ( insert81609953_state @ B_18 @ bot_bo113204042tate_o ) )
% 0.25/0.60 => ( A_34 = B_18 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_223_singletonE,axiom,
% 0.25/0.60 ! [B_17: pname,A_33: pname] :
% 0.25/0.60 ( ( member_pname @ B_17 @ ( insert_pname @ A_33 @ bot_bot_pname_o ) )
% 0.25/0.60 => ( B_17 = A_33 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_224_singletonE,axiom,
% 0.25/0.60 ! [B_17: hoare_1262092251_state,A_33: hoare_1262092251_state] :
% 0.25/0.60 ( ( member5164104_state @ B_17 @ ( insert81609953_state @ A_33 @ bot_bo113204042tate_o ) )
% 0.25/0.60 => ( B_17 = A_33 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_225_doubleton__eq__iff,axiom,
% 0.25/0.60 ! [A_32: pname,B_16: pname,C_3: pname,D_1: pname] :
% 0.25/0.60 ( ( ( insert_pname @ A_32 @ ( insert_pname @ B_16 @ bot_bot_pname_o ) )
% 0.25/0.60 = ( insert_pname @ C_3 @ ( insert_pname @ D_1 @ bot_bot_pname_o ) ) )
% 0.25/0.60 <=> ( ( ( A_32 = C_3 )
% 0.25/0.60 & ( B_16 = D_1 ) )
% 0.25/0.60 | ( ( A_32 = D_1 )
% 0.25/0.60 & ( B_16 = C_3 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_226_doubleton__eq__iff,axiom,
% 0.25/0.60 ! [A_32: hoare_1262092251_state,B_16: hoare_1262092251_state,C_3: hoare_1262092251_state,D_1: hoare_1262092251_state] :
% 0.25/0.60 ( ( ( insert81609953_state @ A_32 @ ( insert81609953_state @ B_16 @ bot_bo113204042tate_o ) )
% 0.25/0.60 = ( insert81609953_state @ C_3 @ ( insert81609953_state @ D_1 @ bot_bo113204042tate_o ) ) )
% 0.25/0.60 <=> ( ( ( A_32 = C_3 )
% 0.25/0.60 & ( B_16 = D_1 ) )
% 0.25/0.60 | ( ( A_32 = D_1 )
% 0.25/0.60 & ( B_16 = C_3 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_227_singleton__iff,axiom,
% 0.25/0.60 ! [B_15: pname,A_31: pname] :
% 0.25/0.60 ( ( member_pname @ B_15 @ ( insert_pname @ A_31 @ bot_bot_pname_o ) )
% 0.25/0.60 <=> ( B_15 = A_31 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_228_singleton__iff,axiom,
% 0.25/0.60 ! [B_15: hoare_1262092251_state,A_31: hoare_1262092251_state] :
% 0.25/0.60 ( ( member5164104_state @ B_15 @ ( insert81609953_state @ A_31 @ bot_bo113204042tate_o ) )
% 0.25/0.60 <=> ( B_15 = A_31 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_229_insert__not__empty,axiom,
% 0.25/0.60 ! [A_30: pname,A_29: pname > $o] :
% 0.25/0.60 ( ( insert_pname @ A_30 @ A_29 )
% 0.25/0.60 != bot_bot_pname_o ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_230_insert__not__empty,axiom,
% 0.25/0.60 ! [A_30: hoare_1262092251_state,A_29: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( insert81609953_state @ A_30 @ A_29 )
% 0.25/0.60 != bot_bo113204042tate_o ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_231_empty__not__insert,axiom,
% 0.25/0.60 ! [A_28: pname,A_27: pname > $o] :
% 0.25/0.60 ( bot_bot_pname_o
% 0.25/0.60 != ( insert_pname @ A_28 @ A_27 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_232_empty__not__insert,axiom,
% 0.25/0.60 ! [A_28: hoare_1262092251_state,A_27: hoare_1262092251_state > $o] :
% 0.25/0.60 ( bot_bo113204042tate_o
% 0.25/0.60 != ( insert81609953_state @ A_28 @ A_27 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_233_finite__insert,axiom,
% 0.25/0.60 ! [A_26: pname,A_25: pname > $o] :
% 0.25/0.60 ( ( finite_finite_pname @ ( insert_pname @ A_26 @ A_25 ) )
% 0.25/0.60 <=> ( finite_finite_pname @ A_25 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_234_finite__insert,axiom,
% 0.25/0.60 ! [A_26: hoare_1262092251_state,A_25: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( finite1178804552_state @ ( insert81609953_state @ A_26 @ A_25 ) )
% 0.25/0.60 <=> ( finite1178804552_state @ A_25 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_235_finite__insert,axiom,
% 0.25/0.60 ! [A_26: pname > $o,A_25: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( finite297249702name_o @ ( insert_pname_o @ A_26 @ A_25 ) )
% 0.25/0.60 <=> ( finite297249702name_o @ A_25 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_236_finite__insert,axiom,
% 0.25/0.60 ! [A_26: hoare_1262092251_state > $o,A_25: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( finite1423311111tate_o @ ( insert1042460334tate_o @ A_26 @ A_25 ) )
% 0.25/0.60 <=> ( finite1423311111tate_o @ A_25 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_237_subset__empty,axiom,
% 0.25/0.60 ! [A_24: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ A_24 @ bot_bot_pname_o )
% 0.25/0.60 <=> ( A_24 = bot_bot_pname_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_238_subset__empty,axiom,
% 0.25/0.60 ! [A_24: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ A_24 @ bot_bo113204042tate_o )
% 0.25/0.60 <=> ( A_24 = bot_bo113204042tate_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_239_image__is__empty,axiom,
% 0.25/0.60 ! [F_10: pname > hoare_1262092251_state,A_23: pname > $o] :
% 0.25/0.60 ( ( ( image_669833818_state @ F_10 @ A_23 )
% 0.25/0.60 = bot_bo113204042tate_o )
% 0.25/0.60 <=> ( A_23 = bot_bot_pname_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_240_image__empty,axiom,
% 0.25/0.60 ! [F_9: pname > hoare_1262092251_state] :
% 0.25/0.60 ( ( image_669833818_state @ F_9 @ bot_bot_pname_o )
% 0.25/0.60 = bot_bo113204042tate_o ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_241_empty__is__image,axiom,
% 0.25/0.60 ! [F_8: pname > hoare_1262092251_state,A_22: pname > $o] :
% 0.25/0.60 ( ( bot_bo113204042tate_o
% 0.25/0.60 = ( image_669833818_state @ F_8 @ A_22 ) )
% 0.25/0.60 <=> ( A_22 = bot_bot_pname_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_242_finite__subset,axiom,
% 0.25/0.60 ! [A_21: ( pname > $o ) > $o,B_14: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( ord_le1205211808me_o_o @ A_21 @ B_14 )
% 0.25/0.60 => ( ( finite297249702name_o @ B_14 )
% 0.25/0.60 => ( finite297249702name_o @ A_21 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_243_finite__subset,axiom,
% 0.25/0.60 ! [A_21: ( hoare_1262092251_state > $o ) > $o,B_14: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( ord_le2012720639te_o_o @ A_21 @ B_14 )
% 0.25/0.60 => ( ( finite1423311111tate_o @ B_14 )
% 0.25/0.60 => ( finite1423311111tate_o @ A_21 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_244_finite__subset,axiom,
% 0.25/0.60 ! [A_21: pname > $o,B_14: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ A_21 @ B_14 )
% 0.25/0.60 => ( ( finite_finite_pname @ B_14 )
% 0.25/0.60 => ( finite_finite_pname @ A_21 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_245_finite__subset,axiom,
% 0.25/0.60 ! [A_21: hoare_1262092251_state > $o,B_14: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ A_21 @ B_14 )
% 0.25/0.60 => ( ( finite1178804552_state @ B_14 )
% 0.25/0.60 => ( finite1178804552_state @ A_21 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_246_rev__finite__subset,axiom,
% 0.25/0.60 ! [A_20: ( pname > $o ) > $o,B_13: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( finite297249702name_o @ B_13 )
% 0.25/0.60 => ( ( ord_le1205211808me_o_o @ A_20 @ B_13 )
% 0.25/0.60 => ( finite297249702name_o @ A_20 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_247_rev__finite__subset,axiom,
% 0.25/0.60 ! [A_20: ( hoare_1262092251_state > $o ) > $o,B_13: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( finite1423311111tate_o @ B_13 )
% 0.25/0.60 => ( ( ord_le2012720639te_o_o @ A_20 @ B_13 )
% 0.25/0.60 => ( finite1423311111tate_o @ A_20 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_248_rev__finite__subset,axiom,
% 0.25/0.60 ! [A_20: pname > $o,B_13: pname > $o] :
% 0.25/0.60 ( ( finite_finite_pname @ B_13 )
% 0.25/0.60 => ( ( ord_less_eq_pname_o @ A_20 @ B_13 )
% 0.25/0.60 => ( finite_finite_pname @ A_20 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_249_rev__finite__subset,axiom,
% 0.25/0.60 ! [A_20: hoare_1262092251_state > $o,B_13: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( finite1178804552_state @ B_13 )
% 0.25/0.60 => ( ( ord_le870406270tate_o @ A_20 @ B_13 )
% 0.25/0.60 => ( finite1178804552_state @ A_20 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_250_insert__mono,axiom,
% 0.25/0.60 ! [A_19: pname,C_2: pname > $o,D: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ C_2 @ D )
% 0.25/0.60 => ( ord_less_eq_pname_o @ ( insert_pname @ A_19 @ C_2 ) @ ( insert_pname @ A_19 @ D ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_251_insert__mono,axiom,
% 0.25/0.60 ! [A_19: hoare_1262092251_state,C_2: hoare_1262092251_state > $o,D: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ C_2 @ D )
% 0.25/0.60 => ( ord_le870406270tate_o @ ( insert81609953_state @ A_19 @ C_2 ) @ ( insert81609953_state @ A_19 @ D ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_252_mem__def,axiom,
% 0.25/0.60 ! [X_5: pname,A_18: pname > $o] :
% 0.25/0.60 ( ( member_pname @ X_5 @ A_18 )
% 0.25/0.60 <=> ( A_18 @ X_5 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_253_mem__def,axiom,
% 0.25/0.60 ! [X_5: hoare_1262092251_state,A_18: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( member5164104_state @ X_5 @ A_18 )
% 0.25/0.60 <=> ( A_18 @ X_5 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_254_Collect__def,axiom,
% 0.25/0.60 ! [P_4: pname > $o] :
% 0.25/0.60 ( ( collect_pname @ P_4 )
% 0.25/0.60 = P_4 ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_255_Collect__def,axiom,
% 0.25/0.60 ! [P_4: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( collec1121927558_state @ P_4 )
% 0.25/0.60 = P_4 ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_256_Collect__def,axiom,
% 0.25/0.60 ! [P_4: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( collect_pname_o @ P_4 )
% 0.25/0.60 = P_4 ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_257_Collect__def,axiom,
% 0.25/0.60 ! [P_4: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( collec313158217tate_o @ P_4 )
% 0.25/0.60 = P_4 ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_258_subset__insertI2,axiom,
% 0.25/0.60 ! [B_12: pname,A_17: pname > $o,B_11: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ A_17 @ B_11 )
% 0.25/0.60 => ( ord_less_eq_pname_o @ A_17 @ ( insert_pname @ B_12 @ B_11 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_259_subset__insertI2,axiom,
% 0.25/0.60 ! [B_12: hoare_1262092251_state,A_17: hoare_1262092251_state > $o,B_11: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ A_17 @ B_11 )
% 0.25/0.60 => ( ord_le870406270tate_o @ A_17 @ ( insert81609953_state @ B_12 @ B_11 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_260_subset__insert,axiom,
% 0.25/0.60 ! [B_10: pname > $o,X_4: pname,A_16: pname > $o] :
% 0.25/0.60 ( ~ ( member_pname @ X_4 @ A_16 )
% 0.25/0.60 => ( ( ord_less_eq_pname_o @ A_16 @ ( insert_pname @ X_4 @ B_10 ) )
% 0.25/0.60 <=> ( ord_less_eq_pname_o @ A_16 @ B_10 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_261_subset__insert,axiom,
% 0.25/0.60 ! [B_10: hoare_1262092251_state > $o,X_4: hoare_1262092251_state,A_16: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ~ ( member5164104_state @ X_4 @ A_16 )
% 0.25/0.60 => ( ( ord_le870406270tate_o @ A_16 @ ( insert81609953_state @ X_4 @ B_10 ) )
% 0.25/0.60 <=> ( ord_le870406270tate_o @ A_16 @ B_10 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_262_insert__subset,axiom,
% 0.25/0.60 ! [X_3: pname,A_15: pname > $o,B_9: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_3 @ A_15 ) @ B_9 )
% 0.25/0.60 <=> ( ( member_pname @ X_3 @ B_9 )
% 0.25/0.60 & ( ord_less_eq_pname_o @ A_15 @ B_9 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_263_insert__subset,axiom,
% 0.25/0.60 ! [X_3: hoare_1262092251_state,A_15: hoare_1262092251_state > $o,B_9: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ ( insert81609953_state @ X_3 @ A_15 ) @ B_9 )
% 0.25/0.60 <=> ( ( member5164104_state @ X_3 @ B_9 )
% 0.25/0.60 & ( ord_le870406270tate_o @ A_15 @ B_9 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_264_subset__insertI,axiom,
% 0.25/0.60 ! [B_8: pname > $o,A_14: pname] : ( ord_less_eq_pname_o @ B_8 @ ( insert_pname @ A_14 @ B_8 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_265_subset__insertI,axiom,
% 0.25/0.60 ! [B_8: hoare_1262092251_state > $o,A_14: hoare_1262092251_state] : ( ord_le870406270tate_o @ B_8 @ ( insert81609953_state @ A_14 @ B_8 ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_266_insert__image,axiom,
% 0.25/0.60 ! [F_7: pname > hoare_1262092251_state,X_2: pname,A_13: pname > $o] :
% 0.25/0.60 ( ( member_pname @ X_2 @ A_13 )
% 0.25/0.60 => ( ( insert81609953_state @ ( F_7 @ X_2 ) @ ( image_669833818_state @ F_7 @ A_13 ) )
% 0.25/0.60 = ( image_669833818_state @ F_7 @ A_13 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_267_image__insert,axiom,
% 0.25/0.60 ! [F_6: pname > hoare_1262092251_state,A_12: pname,B_7: pname > $o] :
% 0.25/0.60 ( ( image_669833818_state @ F_6 @ ( insert_pname @ A_12 @ B_7 ) )
% 0.25/0.60 = ( insert81609953_state @ ( F_6 @ A_12 ) @ ( image_669833818_state @ F_6 @ B_7 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_268_image__mono,axiom,
% 0.25/0.60 ! [F_5: pname > hoare_1262092251_state,A_11: pname > $o,B_6: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ A_11 @ B_6 )
% 0.25/0.60 => ( ord_le870406270tate_o @ ( image_669833818_state @ F_5 @ A_11 ) @ ( image_669833818_state @ F_5 @ B_6 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_269_subset__image__iff,axiom,
% 0.25/0.60 ! [B_5: hoare_1262092251_state > $o,F_4: pname > hoare_1262092251_state,A_10: pname > $o] :
% 0.25/0.60 ( ( ord_le870406270tate_o @ B_5 @ ( image_669833818_state @ F_4 @ A_10 ) )
% 0.25/0.60 <=> ? [AA: pname > $o] :
% 0.25/0.60 ( ( ord_less_eq_pname_o @ AA @ A_10 )
% 0.25/0.60 & ( B_5
% 0.25/0.60 = ( image_669833818_state @ F_4 @ AA ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_270_domI,axiom,
% 0.25/0.60 ! [M: pname > option_com,A_9: pname,B_4: com] :
% 0.25/0.60 ( ( ( M @ A_9 )
% 0.25/0.60 = ( some_com @ B_4 ) )
% 0.25/0.60 => ( member_pname @ A_9 @ ( dom_pname_com @ M ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_271_Collect__conv__if,axiom,
% 0.25/0.60 ! [P_3: pname > $o,A_8: pname] :
% 0.25/0.60 ( ( ( P_3 @ A_8 )
% 0.25/0.60 => ( ( collect_pname
% 0.25/0.60 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.25/0.60 = ( insert_pname @ A_8 @ bot_bot_pname_o ) ) )
% 0.25/0.60 & ( ~ ( P_3 @ A_8 )
% 0.25/0.60 => ( ( collect_pname
% 0.25/0.60 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.25/0.60 = bot_bot_pname_o ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_272_Collect__conv__if,axiom,
% 0.25/0.60 ! [P_3: hoare_1262092251_state > $o,A_8: hoare_1262092251_state] :
% 0.25/0.60 ( ( ( P_3 @ A_8 )
% 0.25/0.60 => ( ( collec1121927558_state
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.25/0.60 = ( insert81609953_state @ A_8 @ bot_bo113204042tate_o ) ) )
% 0.25/0.60 & ( ~ ( P_3 @ A_8 )
% 0.25/0.60 => ( ( collec1121927558_state
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.25/0.60 = bot_bo113204042tate_o ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_273_Collect__conv__if,axiom,
% 0.25/0.60 ! [P_3: ( pname > $o ) > $o,A_8: pname > $o] :
% 0.25/0.60 ( ( ( P_3 @ A_8 )
% 0.25/0.60 => ( ( collect_pname_o
% 0.25/0.60 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.25/0.60 = ( insert_pname_o @ A_8 @ bot_bot_pname_o_o ) ) )
% 0.25/0.60 & ( ~ ( P_3 @ A_8 )
% 0.25/0.60 => ( ( collect_pname_o
% 0.25/0.60 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.25/0.60 = bot_bot_pname_o_o ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_274_Collect__conv__if,axiom,
% 0.25/0.60 ! [P_3: ( hoare_1262092251_state > $o ) > $o,A_8: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ( P_3 @ A_8 )
% 0.25/0.60 => ( ( collec313158217tate_o
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.25/0.60 = ( insert1042460334tate_o @ A_8 @ bot_bo1962689075te_o_o ) ) )
% 0.25/0.60 & ( ~ ( P_3 @ A_8 )
% 0.25/0.60 => ( ( collec313158217tate_o
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( X_1 = A_8 ) @ ( P_3 @ X_1 ) ) )
% 0.25/0.60 = bot_bo1962689075te_o_o ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_275_Collect__conv__if2,axiom,
% 0.25/0.60 ! [P_2: pname > $o,A_7: pname] :
% 0.25/0.60 ( ( ( P_2 @ A_7 )
% 0.25/0.60 => ( ( collect_pname
% 0.25/0.60 @ ^ [X_1: pname] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.25/0.60 = ( insert_pname @ A_7 @ bot_bot_pname_o ) ) )
% 0.25/0.60 & ( ~ ( P_2 @ A_7 )
% 0.25/0.60 => ( ( collect_pname
% 0.25/0.60 @ ^ [X_1: pname] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.25/0.60 = bot_bot_pname_o ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_276_Collect__conv__if2,axiom,
% 0.25/0.60 ! [P_2: hoare_1262092251_state > $o,A_7: hoare_1262092251_state] :
% 0.25/0.60 ( ( ( P_2 @ A_7 )
% 0.25/0.60 => ( ( collec1121927558_state
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.25/0.60 = ( insert81609953_state @ A_7 @ bot_bo113204042tate_o ) ) )
% 0.25/0.60 & ( ~ ( P_2 @ A_7 )
% 0.25/0.60 => ( ( collec1121927558_state
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.25/0.60 = bot_bo113204042tate_o ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_277_Collect__conv__if2,axiom,
% 0.25/0.60 ! [P_2: ( pname > $o ) > $o,A_7: pname > $o] :
% 0.25/0.60 ( ( ( P_2 @ A_7 )
% 0.25/0.60 => ( ( collect_pname_o
% 0.25/0.60 @ ^ [X_1: pname > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.25/0.60 = ( insert_pname_o @ A_7 @ bot_bot_pname_o_o ) ) )
% 0.25/0.60 & ( ~ ( P_2 @ A_7 )
% 0.25/0.60 => ( ( collect_pname_o
% 0.25/0.60 @ ^ [X_1: pname > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.25/0.60 = bot_bot_pname_o_o ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_278_Collect__conv__if2,axiom,
% 0.25/0.60 ! [P_2: ( hoare_1262092251_state > $o ) > $o,A_7: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( ( P_2 @ A_7 )
% 0.25/0.60 => ( ( collec313158217tate_o
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.25/0.60 = ( insert1042460334tate_o @ A_7 @ bot_bo1962689075te_o_o ) ) )
% 0.25/0.60 & ( ~ ( P_2 @ A_7 )
% 0.25/0.60 => ( ( collec313158217tate_o
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state > $o] : ( (&) @ ( A_7 = X_1 ) @ ( P_2 @ X_1 ) ) )
% 0.25/0.60 = bot_bo1962689075te_o_o ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_279_singleton__conv,axiom,
% 0.25/0.60 ! [A_6: pname] :
% 0.25/0.60 ( ( collect_pname
% 0.25/0.60 @ ^ [X_1: pname] : ( X_1 = A_6 ) )
% 0.25/0.60 = ( insert_pname @ A_6 @ bot_bot_pname_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_280_singleton__conv,axiom,
% 0.25/0.60 ! [A_6: hoare_1262092251_state] :
% 0.25/0.60 ( ( collec1121927558_state
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state] : ( X_1 = A_6 ) )
% 0.25/0.60 = ( insert81609953_state @ A_6 @ bot_bo113204042tate_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_281_singleton__conv,axiom,
% 0.25/0.60 ! [A_6: pname > $o] :
% 0.25/0.60 ( ( collect_pname_o
% 0.25/0.60 @ ^ [X_1: pname > $o] : ( X_1 = A_6 ) )
% 0.25/0.60 = ( insert_pname_o @ A_6 @ bot_bot_pname_o_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_282_singleton__conv,axiom,
% 0.25/0.60 ! [A_6: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( collec313158217tate_o
% 0.25/0.60 @ ^ [X_1: hoare_1262092251_state > $o] : ( X_1 = A_6 ) )
% 0.25/0.60 = ( insert1042460334tate_o @ A_6 @ bot_bo1962689075te_o_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_283_singleton__conv2,axiom,
% 0.25/0.60 ! [A_5: pname] :
% 0.25/0.60 ( ( collect_pname @ ( fequal_pname @ A_5 ) )
% 0.25/0.60 = ( insert_pname @ A_5 @ bot_bot_pname_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_284_singleton__conv2,axiom,
% 0.25/0.60 ! [A_5: hoare_1262092251_state] :
% 0.25/0.60 ( ( collec1121927558_state @ ( fequal1925511196_state @ A_5 ) )
% 0.25/0.60 = ( insert81609953_state @ A_5 @ bot_bo113204042tate_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_285_singleton__conv2,axiom,
% 0.25/0.60 ! [A_5: pname > $o] :
% 0.25/0.60 ( ( collect_pname_o @ ( fequal_pname_o @ A_5 ) )
% 0.25/0.60 = ( insert_pname_o @ A_5 @ bot_bot_pname_o_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_286_singleton__conv2,axiom,
% 0.25/0.60 ! [A_5: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( collec313158217tate_o @ ( fequal1529404211tate_o @ A_5 ) )
% 0.25/0.60 = ( insert1042460334tate_o @ A_5 @ bot_bo1962689075te_o_o ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_287_MGF__lemma1,axiom,
% 0.25/0.60 ! [C_1: com,G: hoare_1262092251_state > $o] :
% 0.25/0.60 ( hoare_1821564147gleton
% 0.25/0.60 => ( ! [X_1: pname] :
% 0.25/0.60 ( ( member_pname @ X_1 @ ( dom_pname_com @ body ) )
% 0.25/0.60 => ( hoare_930741239_state @ G @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ X_1 ) ) @ bot_bo113204042tate_o ) ) )
% 0.25/0.60 => ( ( wt @ C_1 )
% 0.25/0.60 => ( hoare_930741239_state @ G @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ C_1 ) @ bot_bo113204042tate_o ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_288_WT__bodiesD,axiom,
% 0.25/0.60 ! [Pn_1: pname,B_3: com] :
% 0.25/0.60 ( wT_bodies
% 0.25/0.60 => ( ( ( body @ Pn_1 )
% 0.25/0.60 = ( some_com @ B_3 ) )
% 0.25/0.60 => ( wt @ B_3 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_289_imageE,axiom,
% 0.25/0.60 ! [B_2: hoare_1262092251_state,F_3: pname > hoare_1262092251_state,A_4: pname > $o] :
% 0.25/0.60 ( ( member5164104_state @ B_2 @ ( image_669833818_state @ F_3 @ A_4 ) )
% 0.25/0.60 => ~ ! [X_1: pname] :
% 0.25/0.60 ( ( B_2
% 0.25/0.60 = ( F_3 @ X_1 ) )
% 0.25/0.60 => ~ ( member_pname @ X_1 @ A_4 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_290_finite__subset__induct,axiom,
% 0.25/0.60 ! [P_1: ( pname > $o ) > $o,A_2: pname > $o,F_1: pname > $o] :
% 0.25/0.60 ( ( finite_finite_pname @ F_1 )
% 0.25/0.60 => ( ( ord_less_eq_pname_o @ F_1 @ A_2 )
% 0.25/0.60 => ( ( P_1 @ bot_bot_pname_o )
% 0.25/0.60 => ( ! [A_3: pname,F_2: pname > $o] :
% 0.25/0.60 ( ( finite_finite_pname @ F_2 )
% 0.25/0.60 => ( ( member_pname @ A_3 @ A_2 )
% 0.25/0.60 => ( ~ ( member_pname @ A_3 @ F_2 )
% 0.25/0.60 => ( ( P_1 @ F_2 )
% 0.25/0.60 => ( P_1 @ ( insert_pname @ A_3 @ F_2 ) ) ) ) ) )
% 0.25/0.60 => ( P_1 @ F_1 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_291_finite__subset__induct,axiom,
% 0.25/0.60 ! [P_1: ( hoare_1262092251_state > $o ) > $o,A_2: hoare_1262092251_state > $o,F_1: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( finite1178804552_state @ F_1 )
% 0.25/0.60 => ( ( ord_le870406270tate_o @ F_1 @ A_2 )
% 0.25/0.60 => ( ( P_1 @ bot_bo113204042tate_o )
% 0.25/0.60 => ( ! [A_3: hoare_1262092251_state,F_2: hoare_1262092251_state > $o] :
% 0.25/0.60 ( ( finite1178804552_state @ F_2 )
% 0.25/0.60 => ( ( member5164104_state @ A_3 @ A_2 )
% 0.25/0.60 => ( ~ ( member5164104_state @ A_3 @ F_2 )
% 0.25/0.60 => ( ( P_1 @ F_2 )
% 0.25/0.60 => ( P_1 @ ( insert81609953_state @ A_3 @ F_2 ) ) ) ) ) )
% 0.25/0.60 => ( P_1 @ F_1 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_292_finite__subset__induct,axiom,
% 0.25/0.60 ! [P_1: ( ( pname > $o ) > $o ) > $o,A_2: ( pname > $o ) > $o,F_1: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( finite297249702name_o @ F_1 )
% 0.25/0.60 => ( ( ord_le1205211808me_o_o @ F_1 @ A_2 )
% 0.25/0.60 => ( ( P_1 @ bot_bot_pname_o_o )
% 0.25/0.60 => ( ! [A_3: pname > $o,F_2: ( pname > $o ) > $o] :
% 0.25/0.60 ( ( finite297249702name_o @ F_2 )
% 0.25/0.60 => ( ( member_pname_o @ A_3 @ A_2 )
% 0.25/0.60 => ( ~ ( member_pname_o @ A_3 @ F_2 )
% 0.25/0.60 => ( ( P_1 @ F_2 )
% 0.25/0.60 => ( P_1 @ ( insert_pname_o @ A_3 @ F_2 ) ) ) ) ) )
% 0.25/0.60 => ( P_1 @ F_1 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_293_finite__subset__induct,axiom,
% 0.25/0.60 ! [P_1: ( ( hoare_1262092251_state > $o ) > $o ) > $o,A_2: ( hoare_1262092251_state > $o ) > $o,F_1: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( finite1423311111tate_o @ F_1 )
% 0.25/0.60 => ( ( ord_le2012720639te_o_o @ F_1 @ A_2 )
% 0.25/0.60 => ( ( P_1 @ bot_bo1962689075te_o_o )
% 0.25/0.60 => ( ! [A_3: hoare_1262092251_state > $o,F_2: ( hoare_1262092251_state > $o ) > $o] :
% 0.25/0.60 ( ( finite1423311111tate_o @ F_2 )
% 0.25/0.60 => ( ( member907417095tate_o @ A_3 @ A_2 )
% 0.25/0.60 => ( ~ ( member907417095tate_o @ A_3 @ F_2 )
% 0.25/0.60 => ( ( P_1 @ F_2 )
% 0.25/0.60 => ( P_1 @ ( insert1042460334tate_o @ A_3 @ F_2 ) ) ) ) ) )
% 0.25/0.60 => ( P_1 @ F_1 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 thf(fact_294_WTs__elim__cases_I7_J,axiom,
% 0.25/0.60 ! [P: pname] :
% 0.25/0.60 ( ( wt @ ( body_1 @ P ) )
% 0.25/0.67 => ~ ! [Y_1: com] :
% 0.25/0.67 ( ( body @ P )
% 0.25/0.67 != ( some_com @ Y_1 ) ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(fact_295_subsetI,axiom,
% 0.25/0.67 ! [B_1: pname > $o,A_1: pname > $o] :
% 0.25/0.67 ( ! [X_1: pname] :
% 0.25/0.67 ( ( member_pname @ X_1 @ A_1 )
% 0.25/0.67 => ( member_pname @ X_1 @ B_1 ) )
% 0.25/0.67 => ( ord_less_eq_pname_o @ A_1 @ B_1 ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(fact_296_subsetI,axiom,
% 0.25/0.67 ! [B_1: hoare_1262092251_state > $o,A_1: hoare_1262092251_state > $o] :
% 0.25/0.67 ( ! [X_1: hoare_1262092251_state] :
% 0.25/0.67 ( ( member5164104_state @ X_1 @ A_1 )
% 0.25/0.67 => ( member5164104_state @ X_1 @ B_1 ) )
% 0.25/0.67 => ( ord_le870406270tate_o @ A_1 @ B_1 ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(fact_297_finite__subset__image,axiom,
% 0.25/0.67 ! [F: pname > hoare_1262092251_state,A: pname > $o,B: hoare_1262092251_state > $o] :
% 0.25/0.67 ( ( finite1178804552_state @ B )
% 0.25/0.67 => ( ( ord_le870406270tate_o @ B @ ( image_669833818_state @ F @ A ) )
% 0.25/0.67 => ? [C: pname > $o] :
% 0.25/0.67 ( ( ord_less_eq_pname_o @ C @ A )
% 0.25/0.67 & ( finite_finite_pname @ C )
% 0.25/0.67 & ( B
% 0.25/0.67 = ( image_669833818_state @ F @ C ) ) ) ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(fact_298_finite__dom__body,axiom,
% 0.25/0.67 finite_finite_pname @ ( dom_pname_com @ body ) ).
% 0.25/0.67
% 0.25/0.67 thf(fact_299_com_Osimps_I6_J,axiom,
% 0.25/0.67 ! [Pname_1: pname,Pname: pname] :
% 0.25/0.67 ( ( ( body_1 @ Pname_1 )
% 0.25/0.67 = ( body_1 @ Pname ) )
% 0.25/0.67 <=> ( Pname_1 = Pname ) ) ).
% 0.25/0.67
% 0.25/0.67 %----Helper facts (8)
% 0.25/0.67 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 0.25/0.67 ! [X: pname,Y: pname] :
% 0.25/0.67 ( ~ ( fequal_pname @ X @ Y )
% 0.25/0.67 | ( X = Y ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 0.25/0.67 ! [X: pname,Y: pname] :
% 0.25/0.67 ( ( X != Y )
% 0.25/0.67 | ( fequal_pname @ X @ Y ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.25/0.67 ! [X: pname > $o,Y: pname > $o] :
% 0.25/0.67 ( ~ ( fequal_pname_o @ X @ Y )
% 0.25/0.67 | ( X = Y ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.25/0.67 ! [X: pname > $o,Y: pname > $o] :
% 0.25/0.67 ( ( X != Y )
% 0.25/0.67 | ( fequal_pname_o @ X @ Y ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com,axiom,
% 0.25/0.67 ! [X: hoare_1262092251_state,Y: hoare_1262092251_state] :
% 0.25/0.67 ( ~ ( fequal1925511196_state @ X @ Y )
% 0.25/0.67 | ( X = Y ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com,axiom,
% 0.25/0.67 ! [X: hoare_1262092251_state,Y: hoare_1262092251_state] :
% 0.25/0.67 ( ( X != Y )
% 0.25/0.67 | ( fequal1925511196_state @ X @ Y ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It,axiom,
% 0.25/0.67 ! [X: hoare_1262092251_state > $o,Y: hoare_1262092251_state > $o] :
% 0.25/0.67 ( ~ ( fequal1529404211tate_o @ X @ Y )
% 0.25/0.67 | ( X = Y ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It,axiom,
% 0.25/0.67 ! [X: hoare_1262092251_state > $o,Y: hoare_1262092251_state > $o] :
% 0.25/0.67 ( ( X != Y )
% 0.25/0.67 | ( fequal1529404211tate_o @ X @ Y ) ) ).
% 0.25/0.67
% 0.25/0.67 %----Conjectures (8)
% 0.25/0.67 thf(conj_0,hypothesis,
% 0.25/0.67 hoare_1821564147gleton ).
% 0.25/0.67
% 0.25/0.67 thf(conj_1,hypothesis,
% 0.25/0.67 wT_bodies ).
% 0.25/0.67
% 0.25/0.67 thf(conj_2,hypothesis,
% 0.25/0.67 finite1178804552_state @ fa ).
% 0.25/0.67
% 0.25/0.67 thf(conj_3,hypothesis,
% 0.25/0.67 ~ ( member5164104_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ) ).
% 0.25/0.67
% 0.25/0.67 thf(conj_4,hypothesis,
% 0.25/0.67 ( ord_le870406270tate_o @ fa
% 0.25/0.67 @ ( image_669833818_state
% 0.25/0.67 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
% 0.25/0.67 @ ( dom_pname_com @ body ) ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(conj_5,hypothesis,
% 0.25/0.67 ( ( body @ pn )
% 0.25/0.67 = ( some_com @ y ) ) ).
% 0.25/0.67
% 0.25/0.67 thf(conj_6,hypothesis,
% 0.25/0.67 ( hoare_930741239_state
% 0.25/0.67 @ ( image_669833818_state
% 0.25/0.67 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.25/0.67 @ ( dom_pname_com @ body ) )
% 0.25/0.67 @ fa ) ).
% 0.25/0.67
% 0.25/0.67 thf(conj_7,conjecture,
% 0.25/0.67 ( hoare_930741239_state
% 0.25/0.67 @ ( image_669833818_state
% 0.25/0.67 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.25/0.67 @ ( dom_pname_com @ body ) )
% 0.25/0.67 @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ) ).
% 0.25/0.67
% 0.25/0.67 %------------------------------------------------------------------------------
% 0.25/0.67 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.1gQ4w6uOSA/cvc5---1.0.5_12974.p...
% 0.25/0.67 (declare-sort $$unsorted 0)
% 0.25/0.67 (declare-sort tptp.com 0)
% 0.25/0.67 (declare-sort tptp.pname 0)
% 0.25/0.67 (declare-sort tptp.hoare_1262092251_state 0)
% 0.25/0.67 (declare-sort tptp.option_com 0)
% 0.25/0.67 (declare-fun tptp.wt (tptp.com) Bool)
% 0.25/0.67 (declare-fun tptp.wT_bodies () Bool)
% 0.25/0.67 (declare-fun tptp.body (tptp.pname) tptp.option_com)
% 0.25/0.67 (declare-fun tptp.body_1 (tptp.pname) tptp.com)
% 0.25/0.67 (declare-fun tptp.finite1648353812_o_o_o ((-> (-> (-> (-> tptp.pname Bool) Bool) Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.finite734360985_o_o_o ((-> (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.finite1066544169me_o_o ((-> (-> (-> tptp.pname Bool) Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.finite1303896758te_o_o ((-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.finite297249702name_o ((-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.finite1423311111tate_o ((-> (-> tptp.hoare_1262092251_state Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.finite_finite_pname ((-> tptp.pname Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.finite1178804552_state ((-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.hoare_Mirabelle_MGT (tptp.com) tptp.hoare_1262092251_state)
% 0.25/0.67 (declare-fun tptp.hoare_930741239_state ((-> tptp.hoare_1262092251_state Bool) (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.hoare_1821564147gleton () Bool)
% 0.25/0.67 (declare-fun tptp.dom_pname_o_com ((-> (-> tptp.pname Bool) tptp.option_com) (-> tptp.pname Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.dom_Ho1489634536_o_com ((-> (-> tptp.hoare_1262092251_state Bool) tptp.option_com) (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.dom_pname_com ((-> tptp.pname tptp.option_com) tptp.pname) Bool)
% 0.25/0.67 (declare-fun tptp.some_com (tptp.com) tptp.option_com)
% 0.25/0.67 (declare-fun tptp.the_com (tptp.option_com) tptp.com)
% 0.25/0.67 (declare-fun tptp.bot_bot_pname_o_o_o ((-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.bot_bo388435036_o_o_o ((-> (-> tptp.hoare_1262092251_state Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.bot_bot_pname_o_o ((-> tptp.pname Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.bot_bo1962689075te_o_o ((-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.bot_bot_pname_o (tptp.pname) Bool)
% 0.25/0.67 (declare-fun tptp.bot_bo113204042tate_o (tptp.hoare_1262092251_state) Bool)
% 0.25/0.67 (declare-fun tptp.ord_le1828183645_o_o_o ((-> (-> (-> tptp.pname Bool) Bool) Bool) (-> (-> (-> tptp.pname Bool) Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.ord_le1891858320_o_o_o ((-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool) (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.ord_le1205211808me_o_o ((-> (-> tptp.pname Bool) Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.ord_le2012720639te_o_o ((-> (-> tptp.hoare_1262092251_state Bool) Bool) (-> (-> tptp.hoare_1262092251_state Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.ord_less_eq_pname_o ((-> tptp.pname Bool) (-> tptp.pname Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.ord_le870406270tate_o ((-> tptp.hoare_1262092251_state Bool) (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.collect_pname_o_o_o ((-> (-> (-> (-> tptp.pname Bool) Bool) Bool) Bool) (-> (-> (-> tptp.pname Bool) Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.collec101077467_o_o_o ((-> (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool) Bool) (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.collect_pname_o_o ((-> (-> (-> tptp.pname Bool) Bool) Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.collec341954548te_o_o ((-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool) (-> (-> tptp.hoare_1262092251_state Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.collect_pname_o ((-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.collec313158217tate_o ((-> (-> tptp.hoare_1262092251_state Bool) Bool) (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.collect_pname ((-> tptp.pname Bool) tptp.pname) Bool)
% 0.25/0.67 (declare-fun tptp.collec1121927558_state ((-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state) Bool)
% 0.25/0.67 (declare-fun tptp.image_471733107_pname ((-> (-> (-> tptp.pname Bool) Bool) tptp.pname) (-> (-> (-> tptp.pname Bool) Bool) Bool) tptp.pname) Bool)
% 0.25/0.67 (declare-fun tptp.image_1036078444_state ((-> (-> (-> tptp.pname Bool) Bool) tptp.hoare_1262092251_state) (-> (-> (-> tptp.pname Bool) Bool) Bool) tptp.hoare_1262092251_state) Bool)
% 0.25/0.67 (declare-fun tptp.image_893364936_pname ((-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.pname) (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool) tptp.pname) Bool)
% 0.25/0.67 (declare-fun tptp.image_165349207_state ((-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.hoare_1262092251_state) (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool) tptp.hoare_1262092251_state) Bool)
% 0.25/0.67 (declare-fun tptp.image_pname_o_pname ((-> (-> tptp.pname Bool) tptp.pname) (-> (-> tptp.pname Bool) Bool) tptp.pname) Bool)
% 0.25/0.67 (declare-fun tptp.image_1476171975_state ((-> (-> tptp.pname Bool) tptp.hoare_1262092251_state) (-> (-> tptp.pname Bool) Bool) tptp.hoare_1262092251_state) Bool)
% 0.25/0.67 (declare-fun tptp.image_1820530197_pname ((-> (-> tptp.hoare_1262092251_state Bool) tptp.pname) (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.pname) Bool)
% 0.25/0.67 (declare-fun tptp.image_234589002_state ((-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state) (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.hoare_1262092251_state) Bool)
% 0.25/0.67 (declare-fun tptp.image_504089495me_o_o ((-> tptp.pname (-> tptp.pname Bool) Bool) (-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.image_827868872te_o_o ((-> tptp.pname (-> tptp.hoare_1262092251_state Bool) Bool) (-> tptp.pname Bool) (-> (-> tptp.hoare_1262092251_state Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.image_pname_pname_o ((-> tptp.pname tptp.pname Bool) (-> tptp.pname Bool) (-> tptp.pname Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.image_518521461tate_o ((-> tptp.pname tptp.hoare_1262092251_state Bool) (-> tptp.pname Bool) (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.image_pname_pname ((-> tptp.pname tptp.pname) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.25/0.67 (declare-fun tptp.image_669833818_state ((-> tptp.pname tptp.hoare_1262092251_state) (-> tptp.pname Bool) tptp.hoare_1262092251_state) Bool)
% 0.25/0.67 (declare-fun tptp.image_333245000me_o_o ((-> tptp.hoare_1262092251_state (-> tptp.pname Bool) Bool) (-> tptp.hoare_1262092251_state Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.image_1731108951te_o_o ((-> tptp.hoare_1262092251_state (-> tptp.hoare_1262092251_state Bool) Bool) (-> tptp.hoare_1262092251_state Bool) (-> (-> tptp.hoare_1262092251_state Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.image_1320925383name_o ((-> tptp.hoare_1262092251_state tptp.pname Bool) (-> tptp.hoare_1262092251_state Bool) (-> tptp.pname Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.image_1403668518tate_o ((-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool) (-> tptp.hoare_1262092251_state Bool) (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.image_202231862_pname ((-> tptp.hoare_1262092251_state tptp.pname) (-> tptp.hoare_1262092251_state Bool) tptp.pname) Bool)
% 0.25/0.67 (declare-fun tptp.insert_pname_o_o ((-> (-> tptp.pname Bool) Bool) (-> (-> (-> tptp.pname Bool) Bool) Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.insert1691644879te_o_o ((-> (-> tptp.hoare_1262092251_state Bool) Bool) (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool) (-> (-> tptp.hoare_1262092251_state Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.insert_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.insert1042460334tate_o ((-> tptp.hoare_1262092251_state Bool) (-> (-> tptp.hoare_1262092251_state Bool) Bool) (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.insert_pname (tptp.pname (-> tptp.pname Bool) tptp.pname) Bool)
% 0.25/0.67 (declare-fun tptp.insert81609953_state (tptp.hoare_1262092251_state (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state) Bool)
% 0.25/0.67 (declare-fun tptp.fequal_pname_o ((-> tptp.pname Bool) (-> tptp.pname Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.fequal1529404211tate_o ((-> tptp.hoare_1262092251_state Bool) (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.fequal_pname (tptp.pname tptp.pname) Bool)
% 0.25/0.67 (declare-fun tptp.fequal1925511196_state (tptp.hoare_1262092251_state tptp.hoare_1262092251_state) Bool)
% 0.25/0.67 (declare-fun tptp.member_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.member907417095tate_o ((-> tptp.hoare_1262092251_state Bool) (-> (-> tptp.hoare_1262092251_state Bool) Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.member_pname (tptp.pname (-> tptp.pname Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.member5164104_state (tptp.hoare_1262092251_state (-> tptp.hoare_1262092251_state Bool)) Bool)
% 0.25/0.67 (declare-fun tptp.fa (tptp.hoare_1262092251_state) Bool)
% 0.25/0.67 (declare-fun tptp.pn () tptp.pname)
% 0.25/0.67 (declare-fun tptp.y () tptp.com)
% 0.25/0.67 (assert (forall ((G (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.hoare_930741239_state G) tptp.bot_bo113204042tate_o)))
% 0.25/0.67 (assert (forall ((Ts_6 (-> tptp.hoare_1262092251_state Bool)) (G_8 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.ord_le870406270tate_o Ts_6) G_8) (@ (@ tptp.hoare_930741239_state G_8) Ts_6))))
% 0.25/0.67 (assert (forall ((Ts_5 (-> tptp.hoare_1262092251_state Bool)) (G_7 (-> tptp.hoare_1262092251_state Bool)) (Ts_4 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.hoare_930741239_state G_7))) (=> (@ _let_1 Ts_4) (=> (@ (@ tptp.ord_le870406270tate_o Ts_5) Ts_4) (@ _let_1 Ts_5))))))
% 0.25/0.67 (assert (forall ((G_6 (-> tptp.hoare_1262092251_state Bool)) (G_5 (-> tptp.hoare_1262092251_state Bool)) (Ts_3 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.hoare_930741239_state G_5) Ts_3) (=> (@ (@ tptp.ord_le870406270tate_o G_5) G_6) (@ (@ tptp.hoare_930741239_state G_6) Ts_3)))))
% 0.25/0.67 (assert (forall ((G_4 (-> tptp.hoare_1262092251_state Bool)) (G_3 (-> tptp.hoare_1262092251_state Bool)) (Ts_2 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.hoare_930741239_state G_4))) (=> (@ (@ tptp.hoare_930741239_state G_3) Ts_2) (=> (@ _let_1 G_3) (@ _let_1 Ts_2))))))
% 0.25/0.67 (assert (forall ((Ts_1 (-> tptp.hoare_1262092251_state Bool)) (G_2 (-> tptp.hoare_1262092251_state Bool)) (T_1 tptp.hoare_1262092251_state)) (let ((_let_1 (@ tptp.insert81609953_state T_1))) (let ((_let_2 (@ tptp.hoare_930741239_state G_2))) (=> (@ _let_2 (@ _let_1 tptp.bot_bo113204042tate_o)) (=> (@ _let_2 Ts_1) (@ _let_2 (@ _let_1 Ts_1))))))))
% 0.25/0.67 (assert (forall ((G_1 (-> tptp.hoare_1262092251_state Bool)) (T tptp.hoare_1262092251_state) (Ts (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.hoare_930741239_state G_1))) (let ((_let_2 (@ tptp.insert81609953_state T))) (=> (@ _let_1 (@ _let_2 Ts)) (and (@ _let_1 (@ _let_2 tptp.bot_bo113204042tate_o)) (@ _let_1 Ts)))))))
% 0.25/0.67 (assert (forall ((Pn_1 tptp.pname) (G (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT (@ tptp.body_1 Pn_1))))) (=> (@ (@ tptp.hoare_930741239_state (@ _let_1 G)) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT (@ tptp.the_com (@ tptp.body Pn_1)))) tptp.bot_bo113204042tate_o)) (@ (@ tptp.hoare_930741239_state G) (@ _let_1 tptp.bot_bo113204042tate_o))))))
% 0.25/0.67 (assert (forall ((A_77 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_77) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((B_41 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o B_41) A_77)))))))
% 0.25/0.67 (assert (forall ((A_77 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_77) (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o (lambda ((B_41 (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.ord_le870406270tate_o B_41) A_77)))))))
% 0.25/0.67 (assert (forall ((A_77 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_77) (@ tptp.finite1648353812_o_o_o (@ tptp.collect_pname_o_o_o (lambda ((B_41 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (@ (@ tptp.ord_le1828183645_o_o_o B_41) A_77)))))))
% 0.25/0.67 (assert (forall ((A_77 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o A_77) (@ tptp.finite734360985_o_o_o (@ tptp.collec101077467_o_o_o (lambda ((B_41 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (@ (@ tptp.ord_le1891858320_o_o_o B_41) A_77)))))))
% 0.25/0.67 (assert (forall ((A_77 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o A_77) (@ tptp.finite1303896758te_o_o (@ tptp.collec341954548te_o_o (lambda ((B_41 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (@ (@ tptp.ord_le2012720639te_o_o B_41) A_77)))))))
% 0.25/0.67 (assert (forall ((A_77 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_77) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o (lambda ((B_41 (-> (-> tptp.pname Bool) Bool))) (@ (@ tptp.ord_le1205211808me_o_o B_41) A_77)))))))
% 0.25/0.67 (assert (forall ((H (-> tptp.pname tptp.hoare_1262092251_state)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite1178804552_state (@ (@ tptp.image_669833818_state H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> (-> (-> tptp.pname Bool) Bool) tptp.pname)) (F_17 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_471733107_pname H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.pname)) (F_17 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_893364936_pname H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> (-> tptp.hoare_1262092251_state Bool) tptp.pname)) (F_17 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_1820530197_pname H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> (-> tptp.pname Bool) tptp.pname)) (F_17 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_o_pname H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> (-> (-> tptp.pname Bool) Bool) tptp.hoare_1262092251_state)) (F_17 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o F_17) (@ tptp.finite1178804552_state (@ (@ tptp.image_1036078444_state H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.hoare_1262092251_state)) (F_17 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o F_17) (@ tptp.finite1178804552_state (@ (@ tptp.image_165349207_state H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state)) (F_17 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o F_17) (@ tptp.finite1178804552_state (@ (@ tptp.image_234589002_state H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> (-> tptp.pname Bool) tptp.hoare_1262092251_state)) (F_17 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_17) (@ tptp.finite1178804552_state (@ (@ tptp.image_1476171975_state H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> tptp.pname (-> tptp.pname Bool) Bool)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite1066544169me_o_o (@ (@ tptp.image_504089495me_o_o H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> tptp.pname (-> tptp.hoare_1262092251_state Bool) Bool)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite1303896758te_o_o (@ (@ tptp.image_827868872te_o_o H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> tptp.pname tptp.hoare_1262092251_state Bool)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite1423311111tate_o (@ (@ tptp.image_518521461tate_o H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> tptp.pname tptp.pname Bool)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite297249702name_o (@ (@ tptp.image_pname_pname_o H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> tptp.hoare_1262092251_state (-> tptp.pname Bool) Bool)) (F_17 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_17) (@ tptp.finite1066544169me_o_o (@ (@ tptp.image_333245000me_o_o H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> tptp.hoare_1262092251_state (-> tptp.hoare_1262092251_state Bool) Bool)) (F_17 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_17) (@ tptp.finite1303896758te_o_o (@ (@ tptp.image_1731108951te_o_o H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)) (F_17 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_17) (@ tptp.finite1423311111tate_o (@ (@ tptp.image_1403668518tate_o H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> tptp.hoare_1262092251_state tptp.pname Bool)) (F_17 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_17) (@ tptp.finite297249702name_o (@ (@ tptp.image_1320925383name_o H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> tptp.hoare_1262092251_state tptp.pname)) (F_17 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_202231862_pname H) F_17)))))
% 0.25/0.67 (assert (forall ((H (-> tptp.pname tptp.pname)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_pname H) F_17)))))
% 0.25/0.67 (assert (forall ((A_76 (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.ord_le870406270tate_o tptp.bot_bo113204042tate_o) A_76)))
% 0.25/0.67 (assert (forall ((A_76 (-> (-> tptp.pname Bool) Bool))) (@ (@ tptp.ord_le1205211808me_o_o tptp.bot_bot_pname_o_o) A_76)))
% 0.25/0.67 (assert (forall ((A_76 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (@ (@ tptp.ord_le2012720639te_o_o tptp.bot_bo1962689075te_o_o) A_76)))
% 0.25/0.67 (assert (forall ((A_76 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o tptp.bot_bot_pname_o) A_76)))
% 0.25/0.67 (assert (forall ((A_75 tptp.hoare_1262092251_state) (A_74 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_74) (@ tptp.finite1178804552_state (@ (@ tptp.insert81609953_state A_75) A_74)))))
% 0.25/0.67 (assert (forall ((A_75 tptp.pname) (A_74 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_74) (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_75) A_74)))))
% 0.25/0.67 (assert (forall ((A_75 (-> (-> tptp.pname Bool) Bool)) (A_74 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_74) (@ tptp.finite1066544169me_o_o (@ (@ tptp.insert_pname_o_o A_75) A_74)))))
% 0.25/0.67 (assert (forall ((A_75 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (A_74 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o A_74) (@ tptp.finite1303896758te_o_o (@ (@ tptp.insert1691644879te_o_o A_75) A_74)))))
% 0.25/0.67 (assert (forall ((A_75 (-> tptp.hoare_1262092251_state Bool)) (A_74 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o A_74) (@ tptp.finite1423311111tate_o (@ (@ tptp.insert1042460334tate_o A_75) A_74)))))
% 0.25/0.67 (assert (forall ((A_75 (-> tptp.pname Bool)) (A_74 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_74) (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_75) A_74)))))
% 0.25/0.67 (assert (@ tptp.finite_finite_pname tptp.bot_bot_pname_o))
% 0.25/0.67 (assert (@ tptp.finite1178804552_state tptp.bot_bo113204042tate_o))
% 0.25/0.67 (assert (@ tptp.finite1066544169me_o_o tptp.bot_bot_pname_o_o_o))
% 0.25/0.67 (assert (@ tptp.finite1303896758te_o_o tptp.bot_bo388435036_o_o_o))
% 0.25/0.67 (assert (@ tptp.finite1423311111tate_o tptp.bot_bo1962689075te_o_o))
% 0.25/0.67 (assert (@ tptp.finite297249702name_o tptp.bot_bot_pname_o_o))
% 0.25/0.67 (assert (forall ((Q_1 (-> tptp.pname Bool)) (P_9 (-> tptp.pname Bool))) (=> (or (@ tptp.finite_finite_pname (@ tptp.collect_pname P_9)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_1))) (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (@ P_9 X_1) (@ Q_1 X_1))))))))
% 0.25/0.67 (assert (forall ((Q_1 (-> tptp.hoare_1262092251_state Bool)) (P_9 (-> tptp.hoare_1262092251_state Bool))) (=> (or (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state P_9)) (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state Q_1))) (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (and (@ P_9 X_1) (@ Q_1 X_1))))))))
% 0.25/0.67 (assert (forall ((Q_1 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (P_9 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (or (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o P_9)) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o Q_1))) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o (lambda ((X_1 (-> (-> tptp.pname Bool) Bool))) (and (@ P_9 X_1) (@ Q_1 X_1))))))))
% 0.25/0.67 (assert (forall ((Q_1 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) (P_9 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (or (@ tptp.finite1303896758te_o_o (@ tptp.collec341954548te_o_o P_9)) (@ tptp.finite1303896758te_o_o (@ tptp.collec341954548te_o_o Q_1))) (@ tptp.finite1303896758te_o_o (@ tptp.collec341954548te_o_o (lambda ((X_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (and (@ P_9 X_1) (@ Q_1 X_1))))))))
% 0.25/0.67 (assert (forall ((Q_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (P_9 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (or (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o P_9)) (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o Q_1))) (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (and (@ P_9 X_1) (@ Q_1 X_1))))))))
% 0.25/0.67 (assert (forall ((Q_1 (-> (-> tptp.pname Bool) Bool)) (P_9 (-> (-> tptp.pname Bool) Bool))) (=> (or (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_9)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q_1))) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (@ P_9 X_1) (@ Q_1 X_1))))))))
% 0.25/0.67 (assert (forall ((C_8 tptp.hoare_1262092251_state) (A_73 (-> tptp.pname Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_669833818_state (lambda ((X_1 tptp.pname)) C_8)) A_73) tptp.bot_bo113204042tate_o)) (=> (not _let_1) (= (@ (@ tptp.image_669833818_state (lambda ((X_1 tptp.pname)) C_8)) A_73) (@ (@ tptp.insert81609953_state C_8) tptp.bot_bo113204042tate_o)))))))
% 0.25/0.67 (assert (forall ((C_8 tptp.pname) (A_73 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (= A_73 tptp.bot_bo113204042tate_o))) (and (=> _let_1 (= (@ (@ tptp.image_202231862_pname (lambda ((X_1 tptp.hoare_1262092251_state)) C_8)) A_73) tptp.bot_bot_pname_o)) (=> (not _let_1) (= (@ (@ tptp.image_202231862_pname (lambda ((X_1 tptp.hoare_1262092251_state)) C_8)) A_73) (@ (@ tptp.insert_pname C_8) tptp.bot_bot_pname_o)))))))
% 0.25/0.67 (assert (forall ((C_8 (-> tptp.pname Bool)) (A_73 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (= A_73 tptp.bot_bo113204042tate_o))) (and (=> _let_1 (= (@ (@ tptp.image_1320925383name_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.pname)) (@ C_8 __flatten_var_0))) A_73) tptp.bot_bot_pname_o_o)) (=> (not _let_1) (= (@ (@ tptp.image_1320925383name_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.pname)) (@ C_8 __flatten_var_0))) A_73) (@ (@ tptp.insert_pname_o C_8) tptp.bot_bot_pname_o_o)))))))
% 0.25/0.67 (assert (forall ((C_8 (-> tptp.hoare_1262092251_state Bool)) (A_73 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (= A_73 tptp.bot_bo113204042tate_o))) (and (=> _let_1 (= (@ (@ tptp.image_1403668518tate_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_8 __flatten_var_0))) A_73) tptp.bot_bo1962689075te_o_o)) (=> (not _let_1) (= (@ (@ tptp.image_1403668518tate_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_8 __flatten_var_0))) A_73) (@ (@ tptp.insert1042460334tate_o C_8) tptp.bot_bo1962689075te_o_o)))))))
% 0.25/0.67 (assert (forall ((C_8 (-> tptp.pname Bool)) (A_73 (-> tptp.pname Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_pname_pname_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.pname)) (@ C_8 __flatten_var_0))) A_73) tptp.bot_bot_pname_o_o)) (=> (not _let_1) (= (@ (@ tptp.image_pname_pname_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.pname)) (@ C_8 __flatten_var_0))) A_73) (@ (@ tptp.insert_pname_o C_8) tptp.bot_bot_pname_o_o)))))))
% 0.25/0.67 (assert (forall ((C_8 (-> tptp.hoare_1262092251_state Bool)) (A_73 (-> tptp.pname Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_518521461tate_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_8 __flatten_var_0))) A_73) tptp.bot_bo1962689075te_o_o)) (=> (not _let_1) (= (@ (@ tptp.image_518521461tate_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_8 __flatten_var_0))) A_73) (@ (@ tptp.insert1042460334tate_o C_8) tptp.bot_bo1962689075te_o_o)))))))
% 0.25/0.67 (assert (forall ((C_8 tptp.pname) (A_73 (-> tptp.pname Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_pname_pname (lambda ((X_1 tptp.pname)) C_8)) A_73) tptp.bot_bot_pname_o)) (=> (not _let_1) (= (@ (@ tptp.image_pname_pname (lambda ((X_1 tptp.pname)) C_8)) A_73) (@ (@ tptp.insert_pname C_8) tptp.bot_bot_pname_o)))))))
% 0.25/0.67 (assert (forall ((C_8 tptp.hoare_1262092251_state) (A_73 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o_o))) (and (=> _let_1 (= (@ (@ tptp.image_1476171975_state (lambda ((X_1 (-> tptp.pname Bool))) C_8)) A_73) tptp.bot_bo113204042tate_o)) (=> (not _let_1) (= (@ (@ tptp.image_1476171975_state (lambda ((X_1 (-> tptp.pname Bool))) C_8)) A_73) (@ (@ tptp.insert81609953_state C_8) tptp.bot_bo113204042tate_o)))))))
% 0.25/0.67 (assert (forall ((C_8 tptp.hoare_1262092251_state) (A_73 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (= A_73 tptp.bot_bo1962689075te_o_o))) (and (=> _let_1 (= (@ (@ tptp.image_234589002_state (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_8)) A_73) tptp.bot_bo113204042tate_o)) (=> (not _let_1) (= (@ (@ tptp.image_234589002_state (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_8)) A_73) (@ (@ tptp.insert81609953_state C_8) tptp.bot_bo113204042tate_o)))))))
% 0.25/0.67 (assert (forall ((C_8 tptp.pname) (A_73 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o_o))) (and (=> _let_1 (= (@ (@ tptp.image_pname_o_pname (lambda ((X_1 (-> tptp.pname Bool))) C_8)) A_73) tptp.bot_bot_pname_o)) (=> (not _let_1) (= (@ (@ tptp.image_pname_o_pname (lambda ((X_1 (-> tptp.pname Bool))) C_8)) A_73) (@ (@ tptp.insert_pname C_8) tptp.bot_bot_pname_o)))))))
% 0.25/0.67 (assert (forall ((C_8 tptp.pname) (A_73 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (= A_73 tptp.bot_bo1962689075te_o_o))) (and (=> _let_1 (= (@ (@ tptp.image_1820530197_pname (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_8)) A_73) tptp.bot_bot_pname_o)) (=> (not _let_1) (= (@ (@ tptp.image_1820530197_pname (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_8)) A_73) (@ (@ tptp.insert_pname C_8) tptp.bot_bot_pname_o)))))))
% 0.25/0.67 (assert (forall ((C_7 tptp.hoare_1262092251_state) (X_18 tptp.pname) (A_72 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_18) A_72) (= (@ (@ tptp.image_669833818_state (lambda ((X_1 tptp.pname)) C_7)) A_72) (@ (@ tptp.insert81609953_state C_7) tptp.bot_bo113204042tate_o)))))
% 0.25/0.67 (assert (forall ((C_7 tptp.pname) (X_18 tptp.hoare_1262092251_state) (A_72 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.member5164104_state X_18) A_72) (= (@ (@ tptp.image_202231862_pname (lambda ((X_1 tptp.hoare_1262092251_state)) C_7)) A_72) (@ (@ tptp.insert_pname C_7) tptp.bot_bot_pname_o)))))
% 0.25/0.67 (assert (forall ((C_7 (-> tptp.pname Bool)) (X_18 tptp.hoare_1262092251_state) (A_72 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.member5164104_state X_18) A_72) (= (@ (@ tptp.image_1320925383name_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.pname)) (@ C_7 __flatten_var_0))) A_72) (@ (@ tptp.insert_pname_o C_7) tptp.bot_bot_pname_o_o)))))
% 0.25/0.67 (assert (forall ((C_7 (-> tptp.hoare_1262092251_state Bool)) (X_18 tptp.hoare_1262092251_state) (A_72 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.member5164104_state X_18) A_72) (= (@ (@ tptp.image_1403668518tate_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_7 __flatten_var_0))) A_72) (@ (@ tptp.insert1042460334tate_o C_7) tptp.bot_bo1962689075te_o_o)))))
% 0.25/0.67 (assert (forall ((C_7 (-> tptp.pname Bool)) (X_18 tptp.pname) (A_72 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_18) A_72) (= (@ (@ tptp.image_pname_pname_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.pname)) (@ C_7 __flatten_var_0))) A_72) (@ (@ tptp.insert_pname_o C_7) tptp.bot_bot_pname_o_o)))))
% 0.25/0.67 (assert (forall ((C_7 (-> tptp.hoare_1262092251_state Bool)) (X_18 tptp.pname) (A_72 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_18) A_72) (= (@ (@ tptp.image_518521461tate_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_7 __flatten_var_0))) A_72) (@ (@ tptp.insert1042460334tate_o C_7) tptp.bot_bo1962689075te_o_o)))))
% 0.25/0.67 (assert (forall ((C_7 tptp.pname) (X_18 tptp.pname) (A_72 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_18) A_72) (= (@ (@ tptp.image_pname_pname (lambda ((X_1 tptp.pname)) C_7)) A_72) (@ (@ tptp.insert_pname C_7) tptp.bot_bot_pname_o)))))
% 0.25/0.67 (assert (forall ((C_7 tptp.hoare_1262092251_state) (X_18 (-> tptp.pname Bool)) (A_72 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.member_pname_o X_18) A_72) (= (@ (@ tptp.image_1476171975_state (lambda ((X_1 (-> tptp.pname Bool))) C_7)) A_72) (@ (@ tptp.insert81609953_state C_7) tptp.bot_bo113204042tate_o)))))
% 0.25/0.67 (assert (forall ((C_7 tptp.hoare_1262092251_state) (X_18 (-> tptp.hoare_1262092251_state Bool)) (A_72 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ (@ tptp.member907417095tate_o X_18) A_72) (= (@ (@ tptp.image_234589002_state (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_7)) A_72) (@ (@ tptp.insert81609953_state C_7) tptp.bot_bo113204042tate_o)))))
% 0.25/0.67 (assert (forall ((C_7 tptp.pname) (X_18 (-> tptp.pname Bool)) (A_72 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.member_pname_o X_18) A_72) (= (@ (@ tptp.image_pname_o_pname (lambda ((X_1 (-> tptp.pname Bool))) C_7)) A_72) (@ (@ tptp.insert_pname C_7) tptp.bot_bot_pname_o)))))
% 0.25/0.67 (assert (forall ((C_7 tptp.pname) (X_18 (-> tptp.hoare_1262092251_state Bool)) (A_72 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ (@ tptp.member907417095tate_o X_18) A_72) (= (@ (@ tptp.image_1820530197_pname (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_7)) A_72) (@ (@ tptp.insert_pname C_7) tptp.bot_bot_pname_o)))))
% 0.25/0.67 (assert (forall ((F_16 (-> tptp.pname tptp.option_com)) (X_17 tptp.pname) (Y_4 tptp.com)) (let ((_let_1 (@ tptp.dom_pname_com F_16))) (=> (= (@ F_16 X_17) (@ tptp.some_com Y_4)) (= (@ (@ tptp.insert_pname X_17) _let_1) _let_1)))))
% 0.25/0.67 (assert (forall ((F_16 (-> (-> tptp.pname Bool) tptp.option_com)) (X_17 (-> tptp.pname Bool)) (Y_4 tptp.com)) (let ((_let_1 (@ tptp.dom_pname_o_com F_16))) (=> (= (@ F_16 X_17) (@ tptp.some_com Y_4)) (= (@ (@ tptp.insert_pname_o X_17) _let_1) _let_1)))))
% 0.25/0.67 (assert (forall ((F_16 (-> (-> tptp.hoare_1262092251_state Bool) tptp.option_com)) (X_17 (-> tptp.hoare_1262092251_state Bool)) (Y_4 tptp.com)) (let ((_let_1 (@ tptp.dom_Ho1489634536_o_com F_16))) (=> (= (@ F_16 X_17) (@ tptp.some_com Y_4)) (= (@ (@ tptp.insert1042460334tate_o X_17) _let_1) _let_1)))))
% 0.25/0.67 (assert (forall ((B_40 (-> tptp.hoare_1262092251_state Bool)) (F_15 (-> tptp.pname tptp.hoare_1262092251_state)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_le870406270tate_o B_40) (@ (@ tptp.image_669833818_state F_15) A_71)) (@ tptp.finite1178804552_state B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> (-> (-> tptp.pname Bool) Bool) tptp.pname)) (A_71 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_471733107_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.pname)) (A_71 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_893364936_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> (-> tptp.hoare_1262092251_state Bool) tptp.pname)) (A_71 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_1820530197_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> (-> tptp.pname Bool) tptp.pname)) (A_71 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_pname_o_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> tptp.hoare_1262092251_state Bool)) (F_15 (-> (-> (-> tptp.pname Bool) Bool) tptp.hoare_1262092251_state)) (A_71 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_71) (=> (@ (@ tptp.ord_le870406270tate_o B_40) (@ (@ tptp.image_1036078444_state F_15) A_71)) (@ tptp.finite1178804552_state B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> tptp.hoare_1262092251_state Bool)) (F_15 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.hoare_1262092251_state)) (A_71 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o A_71) (=> (@ (@ tptp.ord_le870406270tate_o B_40) (@ (@ tptp.image_165349207_state F_15) A_71)) (@ tptp.finite1178804552_state B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> tptp.hoare_1262092251_state Bool)) (F_15 (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state)) (A_71 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o A_71) (=> (@ (@ tptp.ord_le870406270tate_o B_40) (@ (@ tptp.image_234589002_state F_15) A_71)) (@ tptp.finite1178804552_state B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> tptp.hoare_1262092251_state Bool)) (F_15 (-> (-> tptp.pname Bool) tptp.hoare_1262092251_state)) (A_71 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_71) (=> (@ (@ tptp.ord_le870406270tate_o B_40) (@ (@ tptp.image_1476171975_state F_15) A_71)) (@ tptp.finite1178804552_state B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (F_15 (-> tptp.pname (-> tptp.pname Bool) Bool)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_le1828183645_o_o_o B_40) (@ (@ tptp.image_504089495me_o_o F_15) A_71)) (@ tptp.finite1066544169me_o_o B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) (F_15 (-> tptp.pname (-> tptp.hoare_1262092251_state Bool) Bool)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_le1891858320_o_o_o B_40) (@ (@ tptp.image_827868872te_o_o F_15) A_71)) (@ tptp.finite1303896758te_o_o B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> tptp.pname tptp.pname)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_pname_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (F_15 (-> tptp.pname tptp.hoare_1262092251_state Bool)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_le2012720639te_o_o B_40) (@ (@ tptp.image_518521461tate_o F_15) A_71)) (@ tptp.finite1423311111tate_o B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> (-> tptp.pname Bool) Bool)) (F_15 (-> tptp.pname tptp.pname Bool)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_le1205211808me_o_o B_40) (@ (@ tptp.image_pname_pname_o F_15) A_71)) (@ tptp.finite297249702name_o B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (F_15 (-> tptp.hoare_1262092251_state (-> tptp.pname Bool) Bool)) (A_71 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_71) (=> (@ (@ tptp.ord_le1828183645_o_o_o B_40) (@ (@ tptp.image_333245000me_o_o F_15) A_71)) (@ tptp.finite1066544169me_o_o B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) (F_15 (-> tptp.hoare_1262092251_state (-> tptp.hoare_1262092251_state Bool) Bool)) (A_71 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_71) (=> (@ (@ tptp.ord_le1891858320_o_o_o B_40) (@ (@ tptp.image_1731108951te_o_o F_15) A_71)) (@ tptp.finite1303896758te_o_o B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> tptp.hoare_1262092251_state tptp.pname)) (A_71 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_202231862_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (F_15 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)) (A_71 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_71) (=> (@ (@ tptp.ord_le2012720639te_o_o B_40) (@ (@ tptp.image_1403668518tate_o F_15) A_71)) (@ tptp.finite1423311111tate_o B_40)))))
% 0.25/0.67 (assert (forall ((B_40 (-> (-> tptp.pname Bool) Bool)) (F_15 (-> tptp.hoare_1262092251_state tptp.pname Bool)) (A_71 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_71) (=> (@ (@ tptp.ord_le1205211808me_o_o B_40) (@ (@ tptp.image_1320925383name_o F_15) A_71)) (@ tptp.finite297249702name_o B_40)))))
% 0.25/0.67 (assert (forall ((A_70 (-> tptp.hoare_1262092251_state Bool)) (X_16 tptp.hoare_1262092251_state)) (let ((_let_1 (@ (@ tptp.insert81609953_state X_16) tptp.bot_bo113204042tate_o))) (=> (@ (@ tptp.ord_le870406270tate_o A_70) _let_1) (or (= A_70 tptp.bot_bo113204042tate_o) (= A_70 _let_1))))))
% 0.25/0.67 (assert (forall ((A_70 (-> (-> tptp.pname Bool) Bool)) (X_16 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.insert_pname_o X_16) tptp.bot_bot_pname_o_o))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_70) _let_1) (or (= A_70 tptp.bot_bot_pname_o_o) (= A_70 _let_1))))))
% 0.25/0.67 (assert (forall ((A_70 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (X_16 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ (@ tptp.insert1042460334tate_o X_16) tptp.bot_bo1962689075te_o_o))) (=> (@ (@ tptp.ord_le2012720639te_o_o A_70) _let_1) (or (= A_70 tptp.bot_bo1962689075te_o_o) (= A_70 _let_1))))))
% 0.25/0.67 (assert (forall ((A_70 (-> tptp.pname Bool)) (X_16 tptp.pname)) (let ((_let_1 (@ (@ tptp.insert_pname X_16) tptp.bot_bot_pname_o))) (=> (@ (@ tptp.ord_less_eq_pname_o A_70) _let_1) (or (= A_70 tptp.bot_bot_pname_o) (= A_70 _let_1))))))
% 0.25/0.67 (assert (forall ((C_1 tptp.com)) (=> tptp.hoare_1821564147gleton (=> tptp.wT_bodies (=> (@ tptp.wt C_1) (@ (@ tptp.hoare_930741239_state tptp.bot_bo113204042tate_o) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT C_1)) tptp.bot_bo113204042tate_o)))))))
% 0.25/0.67 (assert (forall ((A_69 tptp.hoare_1262092251_state)) (not (@ (@ tptp.member5164104_state A_69) tptp.bot_bo113204042tate_o))))
% 0.25/0.67 (assert (forall ((A_69 (-> tptp.pname Bool))) (not (@ (@ tptp.member_pname_o A_69) tptp.bot_bot_pname_o_o))))
% 0.25/0.67 (assert (forall ((A_69 (-> tptp.hoare_1262092251_state Bool))) (not (@ (@ tptp.member907417095tate_o A_69) tptp.bot_bo1962689075te_o_o))))
% 0.25/0.67 (assert (forall ((A_69 tptp.pname)) (not (@ (@ tptp.member_pname A_69) tptp.bot_bot_pname_o))))
% 0.25/0.67 (assert (forall ((B_39 tptp.hoare_1262092251_state) (A_68 tptp.hoare_1262092251_state) (B_38 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_68))) (=> (=> (not (@ _let_1 B_38)) (= A_68 B_39)) (@ _let_1 (@ (@ tptp.insert81609953_state B_39) B_38))))))
% 0.25/0.67 (assert (forall ((B_39 (-> tptp.pname Bool)) (A_68 (-> tptp.pname Bool)) (B_38 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.member_pname_o A_68))) (=> (=> (not (@ _let_1 B_38)) (= A_68 B_39)) (@ _let_1 (@ (@ tptp.insert_pname_o B_39) B_38))))))
% 0.25/0.67 (assert (forall ((B_39 (-> tptp.hoare_1262092251_state Bool)) (A_68 (-> tptp.hoare_1262092251_state Bool)) (B_38 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (@ tptp.member907417095tate_o A_68))) (=> (=> (not (@ _let_1 B_38)) (= A_68 B_39)) (@ _let_1 (@ (@ tptp.insert1042460334tate_o B_39) B_38))))))
% 0.25/0.67 (assert (forall ((B_39 tptp.pname) (A_68 tptp.pname) (B_38 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_68))) (=> (=> (not (@ _let_1 B_38)) (= A_68 B_39)) (@ _let_1 (@ (@ tptp.insert_pname B_39) B_38))))))
% 0.25/0.67 (assert (forall ((A_67 tptp.hoare_1262092251_state) (B_37 tptp.hoare_1262092251_state) (A_66 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_67))) (=> (@ _let_1 (@ (@ tptp.insert81609953_state B_37) A_66)) (=> (not (= A_67 B_37)) (@ _let_1 A_66))))))
% 0.25/0.67 (assert (forall ((A_67 (-> tptp.pname Bool)) (B_37 (-> tptp.pname Bool)) (A_66 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.member_pname_o A_67))) (=> (@ _let_1 (@ (@ tptp.insert_pname_o B_37) A_66)) (=> (not (= A_67 B_37)) (@ _let_1 A_66))))))
% 0.25/0.67 (assert (forall ((A_67 (-> tptp.hoare_1262092251_state Bool)) (B_37 (-> tptp.hoare_1262092251_state Bool)) (A_66 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (@ tptp.member907417095tate_o A_67))) (=> (@ _let_1 (@ (@ tptp.insert1042460334tate_o B_37) A_66)) (=> (not (= A_67 B_37)) (@ _let_1 A_66))))))
% 0.25/0.67 (assert (forall ((A_67 tptp.pname) (B_37 tptp.pname) (A_66 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_67))) (=> (@ _let_1 (@ (@ tptp.insert_pname B_37) A_66)) (=> (not (= A_67 B_37)) (@ _let_1 A_66))))))
% 0.25/0.67 (assert (forall ((A_65 (-> tptp.hoare_1262092251_state Bool)) (B_36 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.ord_le870406270tate_o A_65) B_36) (=> (@ (@ tptp.ord_le870406270tate_o B_36) A_65) (= A_65 B_36)))))
% 0.25/0.67 (assert (forall ((A_65 (-> (-> tptp.pname Bool) Bool)) (B_36 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_65) B_36) (=> (@ (@ tptp.ord_le1205211808me_o_o B_36) A_65) (= A_65 B_36)))))
% 0.25/0.67 (assert (forall ((A_65 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (B_36 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ (@ tptp.ord_le2012720639te_o_o A_65) B_36) (=> (@ (@ tptp.ord_le2012720639te_o_o B_36) A_65) (= A_65 B_36)))))
% 0.25/0.67 (assert (forall ((A_65 (-> tptp.pname Bool)) (B_36 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_65) B_36) (=> (@ (@ tptp.ord_less_eq_pname_o B_36) A_65) (= A_65 B_36)))))
% 0.25/0.67 (assert (forall ((C_6 tptp.hoare_1262092251_state) (A_64 (-> tptp.hoare_1262092251_state Bool)) (B_35 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state C_6))) (=> (@ (@ tptp.ord_le870406270tate_o A_64) B_35) (=> (@ _let_1 A_64) (@ _let_1 B_35))))))
% 0.25/0.67 (assert (forall ((C_6 (-> tptp.pname Bool)) (A_64 (-> (-> tptp.pname Bool) Bool)) (B_35 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.member_pname_o C_6))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_64) B_35) (=> (@ _let_1 A_64) (@ _let_1 B_35))))))
% 0.25/0.67 (assert (forall ((C_6 (-> tptp.hoare_1262092251_state Bool)) (A_64 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (B_35 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (@ tptp.member907417095tate_o C_6))) (=> (@ (@ tptp.ord_le2012720639te_o_o A_64) B_35) (=> (@ _let_1 A_64) (@ _let_1 B_35))))))
% 0.25/0.67 (assert (forall ((C_6 tptp.pname) (A_64 (-> tptp.pname Bool)) (B_35 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_6))) (=> (@ (@ tptp.ord_less_eq_pname_o A_64) B_35) (=> (@ _let_1 A_64) (@ _let_1 B_35))))))
% 0.25/0.67 (assert (forall ((A_63 (-> tptp.hoare_1262092251_state Bool)) (B_34 (-> tptp.pname Bool)) (F_14 (-> tptp.hoare_1262092251_state tptp.pname Bool)) (X_15 tptp.hoare_1262092251_state)) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member5164104_state X_15) A_63) (@ (@ tptp.member_pname_o B_34) (@ (@ tptp.image_1320925383name_o F_14) A_63))))))
% 0.25/0.67 (assert (forall ((A_63 (-> tptp.hoare_1262092251_state Bool)) (B_34 (-> tptp.hoare_1262092251_state Bool)) (F_14 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)) (X_15 tptp.hoare_1262092251_state)) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member5164104_state X_15) A_63) (@ (@ tptp.member907417095tate_o B_34) (@ (@ tptp.image_1403668518tate_o F_14) A_63))))))
% 0.25/0.67 (assert (forall ((A_63 (-> tptp.pname Bool)) (B_34 (-> tptp.pname Bool)) (F_14 (-> tptp.pname tptp.pname Bool)) (X_15 tptp.pname)) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member_pname X_15) A_63) (@ (@ tptp.member_pname_o B_34) (@ (@ tptp.image_pname_pname_o F_14) A_63))))))
% 0.25/0.67 (assert (forall ((A_63 (-> tptp.pname Bool)) (B_34 (-> tptp.hoare_1262092251_state Bool)) (F_14 (-> tptp.pname tptp.hoare_1262092251_state Bool)) (X_15 tptp.pname)) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member_pname X_15) A_63) (@ (@ tptp.member907417095tate_o B_34) (@ (@ tptp.image_518521461tate_o F_14) A_63))))))
% 0.25/0.67 (assert (forall ((A_63 (-> (-> tptp.pname Bool) Bool)) (B_34 tptp.hoare_1262092251_state) (F_14 (-> (-> tptp.pname Bool) tptp.hoare_1262092251_state)) (X_15 (-> tptp.pname Bool))) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member_pname_o X_15) A_63) (@ (@ tptp.member5164104_state B_34) (@ (@ tptp.image_1476171975_state F_14) A_63))))))
% 0.25/0.67 (assert (forall ((A_63 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (B_34 tptp.hoare_1262092251_state) (F_14 (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state)) (X_15 (-> tptp.hoare_1262092251_state Bool))) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member907417095tate_o X_15) A_63) (@ (@ tptp.member5164104_state B_34) (@ (@ tptp.image_234589002_state F_14) A_63))))))
% 0.25/0.67 (assert (forall ((A_63 (-> tptp.hoare_1262092251_state Bool)) (B_34 tptp.pname) (F_14 (-> tptp.hoare_1262092251_state tptp.pname)) (X_15 tptp.hoare_1262092251_state)) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member5164104_state X_15) A_63) (@ (@ tptp.member_pname B_34) (@ (@ tptp.image_202231862_pname F_14) A_63))))))
% 0.25/0.67 (assert (forall ((A_63 (-> tptp.pname Bool)) (B_34 tptp.pname) (F_14 (-> tptp.pname tptp.pname)) (X_15 tptp.pname)) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member_pname X_15) A_63) (@ (@ tptp.member_pname B_34) (@ (@ tptp.image_pname_pname F_14) A_63))))))
% 0.25/0.67 (assert (forall ((A_63 (-> (-> tptp.pname Bool) Bool)) (B_34 tptp.pname) (F_14 (-> (-> tptp.pname Bool) tptp.pname)) (X_15 (-> tptp.pname Bool))) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member_pname_o X_15) A_63) (@ (@ tptp.member_pname B_34) (@ (@ tptp.image_pname_o_pname F_14) A_63))))))
% 0.25/0.67 (assert (forall ((A_63 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (B_34 tptp.pname) (F_14 (-> (-> tptp.hoare_1262092251_state Bool) tptp.pname)) (X_15 (-> tptp.hoare_1262092251_state Bool))) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member907417095tate_o X_15) A_63) (@ (@ tptp.member_pname B_34) (@ (@ tptp.image_1820530197_pname F_14) A_63))))))
% 0.25/0.67 (assert (forall ((A_63 (-> tptp.pname Bool)) (B_34 tptp.hoare_1262092251_state) (F_14 (-> tptp.pname tptp.hoare_1262092251_state)) (X_15 tptp.pname)) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member_pname X_15) A_63) (@ (@ tptp.member5164104_state B_34) (@ (@ tptp.image_669833818_state F_14) A_63))))))
% 0.25/0.67 (assert (forall ((A_62 (-> tptp.pname Bool)) (A_61 (-> (-> tptp.pname Bool) Bool))) (=> (= A_61 tptp.bot_bot_pname_o_o) (not (@ (@ tptp.member_pname_o A_62) A_61)))))
% 0.25/0.67 (assert (forall ((A_62 (-> tptp.hoare_1262092251_state Bool)) (A_61 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (= A_61 tptp.bot_bo1962689075te_o_o) (not (@ (@ tptp.member907417095tate_o A_62) A_61)))))
% 0.25/0.67 (assert (forall ((A_62 tptp.hoare_1262092251_state) (A_61 (-> tptp.hoare_1262092251_state Bool))) (=> (= A_61 tptp.bot_bo113204042tate_o) (not (@ (@ tptp.member5164104_state A_62) A_61)))))
% 0.25/0.67 (assert (forall ((A_62 tptp.pname) (A_61 (-> tptp.pname Bool))) (=> (= A_61 tptp.bot_bot_pname_o) (not (@ (@ tptp.member_pname A_62) A_61)))))
% 0.25/0.67 (assert (forall ((P_8 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (= (= (@ tptp.collect_pname_o_o P_8) tptp.bot_bot_pname_o_o_o) (forall ((X_1 (-> (-> tptp.pname Bool) Bool))) (not (@ P_8 X_1))))))
% 0.25/0.67 (assert (forall ((P_8 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (= (= (@ tptp.collec341954548te_o_o P_8) tptp.bot_bo388435036_o_o_o) (forall ((X_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (not (@ P_8 X_1))))))
% 0.25/0.67 (assert (forall ((P_8 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (= (@ tptp.collec313158217tate_o P_8) tptp.bot_bo1962689075te_o_o) (forall ((X_1 (-> tptp.hoare_1262092251_state Bool))) (not (@ P_8 X_1))))))
% 0.25/0.67 (assert (forall ((P_8 (-> (-> tptp.pname Bool) Bool))) (= (= (@ tptp.collect_pname_o P_8) tptp.bot_bot_pname_o_o) (forall ((X_1 (-> tptp.pname Bool))) (not (@ P_8 X_1))))))
% 0.25/0.67 (assert (forall ((P_8 (-> tptp.hoare_1262092251_state Bool))) (= (= (@ tptp.collec1121927558_state P_8) tptp.bot_bo113204042tate_o) (forall ((X_1 tptp.hoare_1262092251_state)) (not (@ P_8 X_1))))))
% 0.25/0.67 (assert (forall ((P_8 (-> tptp.pname Bool))) (= (= (@ tptp.collect_pname P_8) tptp.bot_bot_pname_o) (forall ((X_1 tptp.pname)) (not (@ P_8 X_1))))))
% 0.25/0.67 (assert (forall ((C_5 (-> tptp.pname Bool))) (not (@ (@ tptp.member_pname_o C_5) tptp.bot_bot_pname_o_o))))
% 0.25/0.67 (assert (forall ((C_5 (-> tptp.hoare_1262092251_state Bool))) (not (@ (@ tptp.member907417095tate_o C_5) tptp.bot_bo1962689075te_o_o))))
% 0.25/0.67 (assert (forall ((C_5 tptp.hoare_1262092251_state)) (not (@ (@ tptp.member5164104_state C_5) tptp.bot_bo113204042tate_o))))
% 0.25/0.67 (assert (forall ((C_5 tptp.pname)) (not (@ (@ tptp.member_pname C_5) tptp.bot_bot_pname_o))))
% 0.25/0.67 (assert (forall ((P_7 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (= (= tptp.bot_bot_pname_o_o_o (@ tptp.collect_pname_o_o P_7)) (forall ((X_1 (-> (-> tptp.pname Bool) Bool))) (not (@ P_7 X_1))))))
% 0.25/0.67 (assert (forall ((P_7 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (= (= tptp.bot_bo388435036_o_o_o (@ tptp.collec341954548te_o_o P_7)) (forall ((X_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (not (@ P_7 X_1))))))
% 0.25/0.67 (assert (forall ((P_7 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (= tptp.bot_bo1962689075te_o_o (@ tptp.collec313158217tate_o P_7)) (forall ((X_1 (-> tptp.hoare_1262092251_state Bool))) (not (@ P_7 X_1))))))
% 0.25/0.67 (assert (forall ((P_7 (-> (-> tptp.pname Bool) Bool))) (= (= tptp.bot_bot_pname_o_o (@ tptp.collect_pname_o P_7)) (forall ((X_1 (-> tptp.pname Bool))) (not (@ P_7 X_1))))))
% 0.25/0.67 (assert (forall ((P_7 (-> tptp.hoare_1262092251_state Bool))) (= (= tptp.bot_bo113204042tate_o (@ tptp.collec1121927558_state P_7)) (forall ((X_1 tptp.hoare_1262092251_state)) (not (@ P_7 X_1))))))
% 0.25/0.67 (assert (forall ((P_7 (-> tptp.pname Bool))) (= (= tptp.bot_bot_pname_o (@ tptp.collect_pname P_7)) (forall ((X_1 tptp.pname)) (not (@ P_7 X_1))))))
% 0.25/0.67 (assert (forall ((A_60 (-> (-> tptp.pname Bool) Bool))) (= (exists ((X_1 (-> tptp.pname Bool))) (@ (@ tptp.member_pname_o X_1) A_60)) (not (= A_60 tptp.bot_bot_pname_o_o)))))
% 0.25/0.67 (assert (forall ((A_60 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (exists ((X_1 (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.member907417095tate_o X_1) A_60)) (not (= A_60 tptp.bot_bo1962689075te_o_o)))))
% 0.25/0.67 (assert (forall ((A_60 (-> tptp.hoare_1262092251_state Bool))) (= (exists ((X_1 tptp.hoare_1262092251_state)) (@ (@ tptp.member5164104_state X_1) A_60)) (not (= A_60 tptp.bot_bo113204042tate_o)))))
% 0.25/0.67 (assert (forall ((A_60 (-> tptp.pname Bool))) (= (exists ((X_1 tptp.pname)) (@ (@ tptp.member_pname X_1) A_60)) (not (= A_60 tptp.bot_bot_pname_o)))))
% 0.25/0.67 (assert (forall ((A_59 (-> (-> tptp.pname Bool) Bool))) (= (forall ((X_1 (-> tptp.pname Bool))) (not (@ (@ tptp.member_pname_o X_1) A_59))) (= A_59 tptp.bot_bot_pname_o_o))))
% 0.25/0.67 (assert (forall ((A_59 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (forall ((X_1 (-> tptp.hoare_1262092251_state Bool))) (not (@ (@ tptp.member907417095tate_o X_1) A_59))) (= A_59 tptp.bot_bo1962689075te_o_o))))
% 0.25/0.67 (assert (forall ((A_59 (-> tptp.hoare_1262092251_state Bool))) (= (forall ((X_1 tptp.hoare_1262092251_state)) (not (@ (@ tptp.member5164104_state X_1) A_59))) (= A_59 tptp.bot_bo113204042tate_o))))
% 0.25/0.67 (assert (forall ((A_59 (-> tptp.pname Bool))) (= (forall ((X_1 tptp.pname)) (not (@ (@ tptp.member_pname X_1) A_59))) (= A_59 tptp.bot_bot_pname_o))))
% 0.25/0.67 (assert (= tptp.bot_bo388435036_o_o_o (@ tptp.collec341954548te_o_o (lambda ((X_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) false))))
% 0.25/0.67 (assert (= tptp.bot_bo1962689075te_o_o (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) false))))
% 0.25/0.67 (assert (= tptp.bot_bot_pname_o_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) false))))
% 0.25/0.67 (assert (= tptp.bot_bo113204042tate_o (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) false))))
% 0.25/0.67 (assert (= tptp.bot_bot_pname_o (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) false))))
% 0.25/0.67 (assert (forall ((A_58 tptp.pname) (A_57 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname A_58) A_57) (= (@ (@ tptp.insert_pname A_58) A_57) A_57))))
% 0.25/0.67 (assert (forall ((A_58 tptp.hoare_1262092251_state) (A_57 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.member5164104_state A_58) A_57) (= (@ (@ tptp.insert81609953_state A_58) A_57) A_57))))
% 0.25/0.67 (assert (forall ((B_33 tptp.pname) (A_56 tptp.pname) (B_32 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_56))) (=> (@ _let_1 B_32) (@ _let_1 (@ (@ tptp.insert_pname B_33) B_32))))))
% 0.25/0.67 (assert (forall ((B_33 tptp.hoare_1262092251_state) (A_56 tptp.hoare_1262092251_state) (B_32 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_56))) (=> (@ _let_1 B_32) (@ _let_1 (@ (@ tptp.insert81609953_state B_33) B_32))))))
% 0.25/0.67 (assert (forall ((B_31 (-> tptp.pname Bool)) (X_14 tptp.pname) (A_55 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_14))) (let ((_let_2 (@ tptp.member_pname X_14))) (=> (not (@ _let_2 A_55)) (=> (not (@ _let_2 B_31)) (= (= (@ _let_1 A_55) (@ _let_1 B_31)) (= A_55 B_31))))))))
% 0.25/0.67 (assert (forall ((B_31 (-> tptp.hoare_1262092251_state Bool)) (X_14 tptp.hoare_1262092251_state) (A_55 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state X_14))) (let ((_let_2 (@ tptp.member5164104_state X_14))) (=> (not (@ _let_2 A_55)) (=> (not (@ _let_2 B_31)) (= (= (@ _let_1 A_55) (@ _let_1 B_31)) (= A_55 B_31))))))))
% 0.25/0.67 (assert (forall ((Y_3 tptp.pname) (A_54 (-> tptp.pname Bool)) (X_13 tptp.pname)) (= (@ (@ (@ tptp.insert_pname Y_3) A_54) X_13) (or (= Y_3 X_13) (@ A_54 X_13)))))
% 0.25/0.67 (assert (forall ((Y_3 tptp.hoare_1262092251_state) (A_54 (-> tptp.hoare_1262092251_state Bool)) (X_13 tptp.hoare_1262092251_state)) (= (@ (@ (@ tptp.insert81609953_state Y_3) A_54) X_13) (or (= Y_3 X_13) (@ A_54 X_13)))))
% 0.25/0.67 (assert (forall ((A_53 tptp.pname) (B_30 tptp.pname) (A_52 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_53))) (= (@ _let_1 (@ (@ tptp.insert_pname B_30) A_52)) (or (= A_53 B_30) (@ _let_1 A_52))))))
% 0.25/0.67 (assert (forall ((A_53 tptp.hoare_1262092251_state) (B_30 tptp.hoare_1262092251_state) (A_52 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_53))) (= (@ _let_1 (@ (@ tptp.insert81609953_state B_30) A_52)) (or (= A_53 B_30) (@ _let_1 A_52))))))
% 0.25/0.67 (assert (forall ((X_12 tptp.pname) (Y_2 tptp.pname) (A_51 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_12))) (let ((_let_2 (@ tptp.insert_pname Y_2))) (= (@ _let_1 (@ _let_2 A_51)) (@ _let_2 (@ _let_1 A_51)))))))
% 0.25/0.67 (assert (forall ((X_12 tptp.hoare_1262092251_state) (Y_2 tptp.hoare_1262092251_state) (A_51 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state X_12))) (let ((_let_2 (@ tptp.insert81609953_state Y_2))) (= (@ _let_1 (@ _let_2 A_51)) (@ _let_2 (@ _let_1 A_51)))))))
% 0.25/0.67 (assert (forall ((X_11 tptp.pname) (A_50 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_11))) (let ((_let_2 (@ _let_1 A_50))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.67 (assert (forall ((X_11 tptp.hoare_1262092251_state) (A_50 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state X_11))) (let ((_let_2 (@ _let_1 A_50))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.67 (assert (forall ((A_49 tptp.pname) (P_6 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_49) (@ tptp.collect_pname P_6)) (@ tptp.collect_pname (lambda ((U tptp.pname)) (=> (not (= U A_49)) (@ P_6 U)))))))
% 0.25/0.67 (assert (forall ((A_49 tptp.hoare_1262092251_state) (P_6 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.insert81609953_state A_49) (@ tptp.collec1121927558_state P_6)) (@ tptp.collec1121927558_state (lambda ((U tptp.hoare_1262092251_state)) (=> (not (= U A_49)) (@ P_6 U)))))))
% 0.25/0.67 (assert (forall ((A_49 (-> tptp.pname Bool)) (P_6 (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o A_49) (@ tptp.collect_pname_o P_6)) (@ tptp.collect_pname_o (lambda ((U (-> tptp.pname Bool))) (=> (not (= U A_49)) (@ P_6 U)))))))
% 0.25/0.67 (assert (forall ((A_49 (-> tptp.hoare_1262092251_state Bool)) (P_6 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ (@ tptp.insert1042460334tate_o A_49) (@ tptp.collec313158217tate_o P_6)) (@ tptp.collec313158217tate_o (lambda ((U (-> tptp.hoare_1262092251_state Bool))) (=> (not (= U A_49)) (@ P_6 U)))))))
% 0.25/0.67 (assert (forall ((A_48 tptp.pname) (B_29 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_48) B_29) (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (or (= X_1 A_48) (@ (@ tptp.member_pname X_1) B_29)))))))
% 0.25/0.67 (assert (forall ((A_48 tptp.hoare_1262092251_state) (B_29 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.insert81609953_state A_48) B_29) (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (or (= X_1 A_48) (@ (@ tptp.member5164104_state X_1) B_29)))))))
% 0.25/0.67 (assert (forall ((A_48 (-> tptp.pname Bool)) (B_29 (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o A_48) B_29) (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (or (= X_1 A_48) (@ (@ tptp.member_pname_o X_1) B_29)))))))
% 0.25/0.67 (assert (forall ((A_48 (-> tptp.hoare_1262092251_state Bool)) (B_29 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ (@ tptp.insert1042460334tate_o A_48) B_29) (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (or (= X_1 A_48) (@ (@ tptp.member907417095tate_o X_1) B_29)))))))
% 0.25/0.67 (assert (forall ((A_47 tptp.pname) (B_28 (-> tptp.pname Bool))) (@ (@ tptp.member_pname A_47) (@ (@ tptp.insert_pname A_47) B_28))))
% 0.25/0.67 (assert (forall ((A_47 tptp.hoare_1262092251_state) (B_28 (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.member5164104_state A_47) (@ (@ tptp.insert81609953_state A_47) B_28))))
% 0.25/0.67 (assert (forall ((A_46 (-> tptp.pname Bool)) (B_27 (-> tptp.pname Bool))) (=> (= A_46 B_27) (not (=> (@ (@ tptp.ord_less_eq_pname_o A_46) B_27) (not (@ (@ tptp.ord_less_eq_pname_o B_27) A_46)))))))
% 0.25/0.67 (assert (forall ((A_46 (-> tptp.hoare_1262092251_state Bool)) (B_27 (-> tptp.hoare_1262092251_state Bool))) (=> (= A_46 B_27) (not (=> (@ (@ tptp.ord_le870406270tate_o A_46) B_27) (not (@ (@ tptp.ord_le870406270tate_o B_27) A_46)))))))
% 0.25/0.67 (assert (forall ((C_4 (-> tptp.pname Bool)) (A_45 (-> tptp.pname Bool)) (B_26 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_45))) (=> (@ _let_1 B_26) (=> (@ (@ tptp.ord_less_eq_pname_o B_26) C_4) (@ _let_1 C_4))))))
% 0.25/0.67 (assert (forall ((C_4 (-> tptp.hoare_1262092251_state Bool)) (A_45 (-> tptp.hoare_1262092251_state Bool)) (B_26 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.ord_le870406270tate_o A_45))) (=> (@ _let_1 B_26) (=> (@ (@ tptp.ord_le870406270tate_o B_26) C_4) (@ _let_1 C_4))))))
% 0.25/0.67 (assert (forall ((X_10 tptp.pname) (A_44 (-> tptp.pname Bool)) (B_25 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_10))) (=> (@ (@ tptp.ord_less_eq_pname_o A_44) B_25) (=> (@ _let_1 A_44) (@ _let_1 B_25))))))
% 0.25/0.67 (assert (forall ((X_10 tptp.hoare_1262092251_state) (A_44 (-> tptp.hoare_1262092251_state Bool)) (B_25 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state X_10))) (=> (@ (@ tptp.ord_le870406270tate_o A_44) B_25) (=> (@ _let_1 A_44) (@ _let_1 B_25))))))
% 0.25/0.67 (assert (forall ((B_24 (-> tptp.pname Bool)) (X_9 tptp.pname) (A_43 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_9))) (=> (@ _let_1 A_43) (=> (@ (@ tptp.ord_less_eq_pname_o A_43) B_24) (@ _let_1 B_24))))))
% 0.25/0.67 (assert (forall ((B_24 (-> tptp.hoare_1262092251_state Bool)) (X_9 tptp.hoare_1262092251_state) (A_43 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state X_9))) (=> (@ _let_1 A_43) (=> (@ (@ tptp.ord_le870406270tate_o A_43) B_24) (@ _let_1 B_24))))))
% 0.25/0.67 (assert (forall ((X_8 tptp.pname) (A_42 (-> tptp.pname Bool)) (B_23 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_8))) (=> (@ (@ tptp.ord_less_eq_pname_o A_42) B_23) (=> (@ _let_1 A_42) (@ _let_1 B_23))))))
% 0.25/0.67 (assert (forall ((X_8 tptp.hoare_1262092251_state) (A_42 (-> tptp.hoare_1262092251_state Bool)) (B_23 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state X_8))) (=> (@ (@ tptp.ord_le870406270tate_o A_42) B_23) (=> (@ _let_1 A_42) (@ _let_1 B_23))))))
% 0.25/0.67 (assert (forall ((A_41 (-> tptp.pname Bool)) (B_22 (-> tptp.pname Bool))) (=> (= A_41 B_22) (@ (@ tptp.ord_less_eq_pname_o B_22) A_41))))
% 0.25/0.67 (assert (forall ((A_41 (-> tptp.hoare_1262092251_state Bool)) (B_22 (-> tptp.hoare_1262092251_state Bool))) (=> (= A_41 B_22) (@ (@ tptp.ord_le870406270tate_o B_22) A_41))))
% 0.25/0.67 (assert (forall ((A_40 (-> tptp.pname Bool)) (B_21 (-> tptp.pname Bool))) (=> (= A_40 B_21) (@ (@ tptp.ord_less_eq_pname_o A_40) B_21))))
% 0.25/0.67 (assert (forall ((A_40 (-> tptp.hoare_1262092251_state Bool)) (B_21 (-> tptp.hoare_1262092251_state Bool))) (=> (= A_40 B_21) (@ (@ tptp.ord_le870406270tate_o A_40) B_21))))
% 0.25/0.67 (assert (forall ((A_39 (-> tptp.pname Bool)) (B_20 (-> tptp.pname Bool))) (= (= A_39 B_20) (and (@ (@ tptp.ord_less_eq_pname_o A_39) B_20) (@ (@ tptp.ord_less_eq_pname_o B_20) A_39)))))
% 0.25/0.67 (assert (forall ((A_39 (-> tptp.hoare_1262092251_state Bool)) (B_20 (-> tptp.hoare_1262092251_state Bool))) (= (= A_39 B_20) (and (@ (@ tptp.ord_le870406270tate_o A_39) B_20) (@ (@ tptp.ord_le870406270tate_o B_20) A_39)))))
% 0.25/0.67 (assert (forall ((A_38 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o A_38) A_38)))
% 0.25/0.67 (assert (forall ((A_38 (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.ord_le870406270tate_o A_38) A_38)))
% 0.25/0.67 (assert (forall ((B_19 tptp.hoare_1262092251_state) (F_13 (-> tptp.pname tptp.hoare_1262092251_state)) (X_7 tptp.pname) (A_37 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_7) A_37) (=> (= B_19 (@ F_13 X_7)) (@ (@ tptp.member5164104_state B_19) (@ (@ tptp.image_669833818_state F_13) A_37))))))
% 0.25/0.67 (assert (forall ((F_12 (-> tptp.pname tptp.hoare_1262092251_state)) (X_6 tptp.pname) (A_36 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_6) A_36) (@ (@ tptp.member5164104_state (@ F_12 X_6)) (@ (@ tptp.image_669833818_state F_12) A_36)))))
% 0.25/0.67 (assert (forall ((Z tptp.hoare_1262092251_state) (F_11 (-> tptp.pname tptp.hoare_1262092251_state)) (A_35 (-> tptp.pname Bool))) (= (@ (@ tptp.member5164104_state Z) (@ (@ tptp.image_669833818_state F_11) A_35)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_35) (= Z (@ F_11 X_1)))))))
% 0.25/0.67 (assert (forall ((P_5 (-> tptp.pname Bool)) (Q (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (or (@ P_5 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_pname (@ tptp.collect_pname P_5)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q))))))
% 0.25/0.67 (assert (forall ((P_5 (-> tptp.hoare_1262092251_state Bool)) (Q (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (or (@ P_5 X_1) (@ Q X_1))))) (and (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state P_5)) (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state Q))))))
% 0.25/0.67 (assert (forall ((P_5 (-> (-> tptp.pname Bool) Bool)) (Q (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (or (@ P_5 X_1) (@ Q X_1))))) (and (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_5)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q))))))
% 0.25/0.67 (assert (forall ((P_5 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (Q (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (or (@ P_5 X_1) (@ Q X_1))))) (and (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o P_5)) (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o Q))))))
% 0.25/0.67 (assert (forall ((X_1 tptp.pname) (Xa (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname X_1) Xa) (@ tptp.collect_pname (lambda ((Y_1 tptp.pname)) (or (= Y_1 X_1) (@ (@ tptp.member_pname Y_1) Xa)))))))
% 0.25/0.67 (assert (forall ((X_1 tptp.hoare_1262092251_state) (Xa (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.insert81609953_state X_1) Xa) (@ tptp.collec1121927558_state (lambda ((Y_1 tptp.hoare_1262092251_state)) (or (= Y_1 X_1) (@ (@ tptp.member5164104_state Y_1) Xa)))))))
% 0.25/0.67 (assert (forall ((X_1 (-> tptp.pname Bool)) (Xa (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o X_1) Xa) (@ tptp.collect_pname_o (lambda ((Y_1 (-> tptp.pname Bool))) (or (= Y_1 X_1) (@ (@ tptp.member_pname_o Y_1) Xa)))))))
% 0.25/0.67 (assert (forall ((X_1 (-> tptp.hoare_1262092251_state Bool)) (Xa (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ (@ tptp.insert1042460334tate_o X_1) Xa) (@ tptp.collec313158217tate_o (lambda ((Y_1 (-> tptp.hoare_1262092251_state Bool))) (or (= Y_1 X_1) (@ (@ tptp.member907417095tate_o Y_1) Xa)))))))
% 0.25/0.67 (assert (forall ((A_34 tptp.pname) (B_18 tptp.pname)) (=> (= (@ (@ tptp.insert_pname A_34) tptp.bot_bot_pname_o) (@ (@ tptp.insert_pname B_18) tptp.bot_bot_pname_o)) (= A_34 B_18))))
% 0.25/0.67 (assert (forall ((A_34 tptp.hoare_1262092251_state) (B_18 tptp.hoare_1262092251_state)) (=> (= (@ (@ tptp.insert81609953_state A_34) tptp.bot_bo113204042tate_o) (@ (@ tptp.insert81609953_state B_18) tptp.bot_bo113204042tate_o)) (= A_34 B_18))))
% 0.25/0.67 (assert (forall ((B_17 tptp.pname) (A_33 tptp.pname)) (=> (@ (@ tptp.member_pname B_17) (@ (@ tptp.insert_pname A_33) tptp.bot_bot_pname_o)) (= B_17 A_33))))
% 0.25/0.67 (assert (forall ((B_17 tptp.hoare_1262092251_state) (A_33 tptp.hoare_1262092251_state)) (=> (@ (@ tptp.member5164104_state B_17) (@ (@ tptp.insert81609953_state A_33) tptp.bot_bo113204042tate_o)) (= B_17 A_33))))
% 0.25/0.67 (assert (forall ((A_32 tptp.pname) (B_16 tptp.pname) (C_3 tptp.pname) (D_1 tptp.pname)) (= (= (@ (@ tptp.insert_pname A_32) (@ (@ tptp.insert_pname B_16) tptp.bot_bot_pname_o)) (@ (@ tptp.insert_pname C_3) (@ (@ tptp.insert_pname D_1) tptp.bot_bot_pname_o))) (or (and (= A_32 C_3) (= B_16 D_1)) (and (= A_32 D_1) (= B_16 C_3))))))
% 0.25/0.67 (assert (forall ((A_32 tptp.hoare_1262092251_state) (B_16 tptp.hoare_1262092251_state) (C_3 tptp.hoare_1262092251_state) (D_1 tptp.hoare_1262092251_state)) (= (= (@ (@ tptp.insert81609953_state A_32) (@ (@ tptp.insert81609953_state B_16) tptp.bot_bo113204042tate_o)) (@ (@ tptp.insert81609953_state C_3) (@ (@ tptp.insert81609953_state D_1) tptp.bot_bo113204042tate_o))) (or (and (= A_32 C_3) (= B_16 D_1)) (and (= A_32 D_1) (= B_16 C_3))))))
% 0.25/0.67 (assert (forall ((B_15 tptp.pname) (A_31 tptp.pname)) (= (@ (@ tptp.member_pname B_15) (@ (@ tptp.insert_pname A_31) tptp.bot_bot_pname_o)) (= B_15 A_31))))
% 0.25/0.67 (assert (forall ((B_15 tptp.hoare_1262092251_state) (A_31 tptp.hoare_1262092251_state)) (= (@ (@ tptp.member5164104_state B_15) (@ (@ tptp.insert81609953_state A_31) tptp.bot_bo113204042tate_o)) (= B_15 A_31))))
% 0.25/0.67 (assert (forall ((A_30 tptp.pname) (A_29 (-> tptp.pname Bool))) (not (= (@ (@ tptp.insert_pname A_30) A_29) tptp.bot_bot_pname_o))))
% 0.25/0.67 (assert (forall ((A_30 tptp.hoare_1262092251_state) (A_29 (-> tptp.hoare_1262092251_state Bool))) (not (= (@ (@ tptp.insert81609953_state A_30) A_29) tptp.bot_bo113204042tate_o))))
% 0.25/0.67 (assert (forall ((A_28 tptp.pname) (A_27 (-> tptp.pname Bool))) (not (= tptp.bot_bot_pname_o (@ (@ tptp.insert_pname A_28) A_27)))))
% 0.25/0.67 (assert (forall ((A_28 tptp.hoare_1262092251_state) (A_27 (-> tptp.hoare_1262092251_state Bool))) (not (= tptp.bot_bo113204042tate_o (@ (@ tptp.insert81609953_state A_28) A_27)))))
% 0.25/0.67 (assert (forall ((A_26 tptp.pname) (A_25 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_26) A_25)) (@ tptp.finite_finite_pname A_25))))
% 0.25/0.67 (assert (forall ((A_26 tptp.hoare_1262092251_state) (A_25 (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.finite1178804552_state (@ (@ tptp.insert81609953_state A_26) A_25)) (@ tptp.finite1178804552_state A_25))))
% 0.25/0.67 (assert (forall ((A_26 (-> tptp.pname Bool)) (A_25 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_26) A_25)) (@ tptp.finite297249702name_o A_25))))
% 0.25/0.67 (assert (forall ((A_26 (-> tptp.hoare_1262092251_state Bool)) (A_25 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ tptp.finite1423311111tate_o (@ (@ tptp.insert1042460334tate_o A_26) A_25)) (@ tptp.finite1423311111tate_o A_25))))
% 0.25/0.67 (assert (forall ((A_24 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o A_24) tptp.bot_bot_pname_o) (= A_24 tptp.bot_bot_pname_o))))
% 0.25/0.67 (assert (forall ((A_24 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.ord_le870406270tate_o A_24) tptp.bot_bo113204042tate_o) (= A_24 tptp.bot_bo113204042tate_o))))
% 0.25/0.67 (assert (forall ((F_10 (-> tptp.pname tptp.hoare_1262092251_state)) (A_23 (-> tptp.pname Bool))) (= (= (@ (@ tptp.image_669833818_state F_10) A_23) tptp.bot_bo113204042tate_o) (= A_23 tptp.bot_bot_pname_o))))
% 0.25/0.67 (assert (forall ((F_9 (-> tptp.pname tptp.hoare_1262092251_state))) (= (@ (@ tptp.image_669833818_state F_9) tptp.bot_bot_pname_o) tptp.bot_bo113204042tate_o)))
% 0.25/0.67 (assert (forall ((F_8 (-> tptp.pname tptp.hoare_1262092251_state)) (A_22 (-> tptp.pname Bool))) (= (= tptp.bot_bo113204042tate_o (@ (@ tptp.image_669833818_state F_8) A_22)) (= A_22 tptp.bot_bot_pname_o))))
% 0.25/0.67 (assert (forall ((A_21 (-> (-> tptp.pname Bool) Bool)) (B_14 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_21) B_14) (=> (@ tptp.finite297249702name_o B_14) (@ tptp.finite297249702name_o A_21)))))
% 0.25/0.67 (assert (forall ((A_21 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (B_14 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ (@ tptp.ord_le2012720639te_o_o A_21) B_14) (=> (@ tptp.finite1423311111tate_o B_14) (@ tptp.finite1423311111tate_o A_21)))))
% 0.25/0.67 (assert (forall ((A_21 (-> tptp.pname Bool)) (B_14 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_21) B_14) (=> (@ tptp.finite_finite_pname B_14) (@ tptp.finite_finite_pname A_21)))))
% 0.25/0.67 (assert (forall ((A_21 (-> tptp.hoare_1262092251_state Bool)) (B_14 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.ord_le870406270tate_o A_21) B_14) (=> (@ tptp.finite1178804552_state B_14) (@ tptp.finite1178804552_state A_21)))))
% 0.25/0.67 (assert (forall ((A_20 (-> (-> tptp.pname Bool) Bool)) (B_13 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_13) (=> (@ (@ tptp.ord_le1205211808me_o_o A_20) B_13) (@ tptp.finite297249702name_o A_20)))))
% 0.25/0.67 (assert (forall ((A_20 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (B_13 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o B_13) (=> (@ (@ tptp.ord_le2012720639te_o_o A_20) B_13) (@ tptp.finite1423311111tate_o A_20)))))
% 0.25/0.67 (assert (forall ((A_20 (-> tptp.pname Bool)) (B_13 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_13) (=> (@ (@ tptp.ord_less_eq_pname_o A_20) B_13) (@ tptp.finite_finite_pname A_20)))))
% 0.25/0.67 (assert (forall ((A_20 (-> tptp.hoare_1262092251_state Bool)) (B_13 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state B_13) (=> (@ (@ tptp.ord_le870406270tate_o A_20) B_13) (@ tptp.finite1178804552_state A_20)))))
% 0.25/0.67 (assert (forall ((A_19 tptp.pname) (C_2 (-> tptp.pname Bool)) (D (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_19))) (=> (@ (@ tptp.ord_less_eq_pname_o C_2) D) (@ (@ tptp.ord_less_eq_pname_o (@ _let_1 C_2)) (@ _let_1 D))))))
% 0.25/0.67 (assert (forall ((A_19 tptp.hoare_1262092251_state) (C_2 (-> tptp.hoare_1262092251_state Bool)) (D (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state A_19))) (=> (@ (@ tptp.ord_le870406270tate_o C_2) D) (@ (@ tptp.ord_le870406270tate_o (@ _let_1 C_2)) (@ _let_1 D))))))
% 0.25/0.67 (assert (forall ((X_5 tptp.pname) (A_18 (-> tptp.pname Bool))) (= (@ (@ tptp.member_pname X_5) A_18) (@ A_18 X_5))))
% 0.25/0.67 (assert (forall ((X_5 tptp.hoare_1262092251_state) (A_18 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.member5164104_state X_5) A_18) (@ A_18 X_5))))
% 0.25/0.67 (assert (forall ((P_4 (-> tptp.pname Bool))) (= (@ tptp.collect_pname P_4) P_4)))
% 0.25/0.67 (assert (forall ((P_4 (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.collec1121927558_state P_4) P_4)))
% 0.25/0.67 (assert (forall ((P_4 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.collect_pname_o P_4) P_4)))
% 0.25/0.67 (assert (forall ((P_4 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ tptp.collec313158217tate_o P_4) P_4)))
% 0.25/0.67 (assert (forall ((B_12 tptp.pname) (A_17 (-> tptp.pname Bool)) (B_11 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_17))) (=> (@ _let_1 B_11) (@ _let_1 (@ (@ tptp.insert_pname B_12) B_11))))))
% 0.25/0.67 (assert (forall ((B_12 tptp.hoare_1262092251_state) (A_17 (-> tptp.hoare_1262092251_state Bool)) (B_11 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.ord_le870406270tate_o A_17))) (=> (@ _let_1 B_11) (@ _let_1 (@ (@ tptp.insert81609953_state B_12) B_11))))))
% 0.25/0.67 (assert (forall ((B_10 (-> tptp.pname Bool)) (X_4 tptp.pname) (A_16 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_16))) (=> (not (@ (@ tptp.member_pname X_4) A_16)) (= (@ _let_1 (@ (@ tptp.insert_pname X_4) B_10)) (@ _let_1 B_10))))))
% 0.25/0.67 (assert (forall ((B_10 (-> tptp.hoare_1262092251_state Bool)) (X_4 tptp.hoare_1262092251_state) (A_16 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.ord_le870406270tate_o A_16))) (=> (not (@ (@ tptp.member5164104_state X_4) A_16)) (= (@ _let_1 (@ (@ tptp.insert81609953_state X_4) B_10)) (@ _let_1 B_10))))))
% 0.25/0.67 (assert (forall ((X_3 tptp.pname) (A_15 (-> tptp.pname Bool)) (B_9 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.insert_pname X_3) A_15)) B_9) (and (@ (@ tptp.member_pname X_3) B_9) (@ (@ tptp.ord_less_eq_pname_o A_15) B_9)))))
% 0.25/0.67 (assert (forall ((X_3 tptp.hoare_1262092251_state) (A_15 (-> tptp.hoare_1262092251_state Bool)) (B_9 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.ord_le870406270tate_o (@ (@ tptp.insert81609953_state X_3) A_15)) B_9) (and (@ (@ tptp.member5164104_state X_3) B_9) (@ (@ tptp.ord_le870406270tate_o A_15) B_9)))))
% 0.25/0.67 (assert (forall ((B_8 (-> tptp.pname Bool)) (A_14 tptp.pname)) (@ (@ tptp.ord_less_eq_pname_o B_8) (@ (@ tptp.insert_pname A_14) B_8))))
% 0.25/0.67 (assert (forall ((B_8 (-> tptp.hoare_1262092251_state Bool)) (A_14 tptp.hoare_1262092251_state)) (@ (@ tptp.ord_le870406270tate_o B_8) (@ (@ tptp.insert81609953_state A_14) B_8))))
% 0.25/0.67 (assert (forall ((F_7 (-> tptp.pname tptp.hoare_1262092251_state)) (X_2 tptp.pname) (A_13 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_669833818_state F_7) A_13))) (=> (@ (@ tptp.member_pname X_2) A_13) (= (@ (@ tptp.insert81609953_state (@ F_7 X_2)) _let_1) _let_1)))))
% 0.25/0.67 (assert (forall ((F_6 (-> tptp.pname tptp.hoare_1262092251_state)) (A_12 tptp.pname) (B_7 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_669833818_state F_6))) (= (@ _let_1 (@ (@ tptp.insert_pname A_12) B_7)) (@ (@ tptp.insert81609953_state (@ F_6 A_12)) (@ _let_1 B_7))))))
% 0.25/0.67 (assert (forall ((F_5 (-> tptp.pname tptp.hoare_1262092251_state)) (A_11 (-> tptp.pname Bool)) (B_6 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_669833818_state F_5))) (=> (@ (@ tptp.ord_less_eq_pname_o A_11) B_6) (@ (@ tptp.ord_le870406270tate_o (@ _let_1 A_11)) (@ _let_1 B_6))))))
% 0.25/0.67 (assert (forall ((B_5 (-> tptp.hoare_1262092251_state Bool)) (F_4 (-> tptp.pname tptp.hoare_1262092251_state)) (A_10 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_le870406270tate_o B_5) (@ (@ tptp.image_669833818_state F_4) A_10)) (exists ((AA (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o AA) A_10) (= B_5 (@ (@ tptp.image_669833818_state F_4) AA)))))))
% 0.25/0.67 (assert (forall ((M (-> tptp.pname tptp.option_com)) (A_9 tptp.pname) (B_4 tptp.com)) (=> (= (@ M A_9) (@ tptp.some_com B_4)) (@ (@ tptp.member_pname A_9) (@ tptp.dom_pname_com M)))))
% 0.25/0.67 (assert (forall ((P_3 (-> tptp.pname Bool)) (A_8 tptp.pname)) (let ((_let_1 (@ P_3 A_8))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= X_1 A_8) (@ P_3 X_1)))) (@ (@ tptp.insert_pname A_8) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= X_1 A_8) (@ P_3 X_1)))) tptp.bot_bot_pname_o))))))
% 0.25/0.67 (assert (forall ((P_3 (-> tptp.hoare_1262092251_state Bool)) (A_8 tptp.hoare_1262092251_state)) (let ((_let_1 (@ P_3 A_8))) (and (=> _let_1 (= (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (and (= X_1 A_8) (@ P_3 X_1)))) (@ (@ tptp.insert81609953_state A_8) tptp.bot_bo113204042tate_o))) (=> (not _let_1) (= (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (and (= X_1 A_8) (@ P_3 X_1)))) tptp.bot_bo113204042tate_o))))))
% 0.25/0.67 (assert (forall ((P_3 (-> (-> tptp.pname Bool) Bool)) (A_8 (-> tptp.pname Bool))) (let ((_let_1 (@ P_3 A_8))) (and (=> _let_1 (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= X_1 A_8) (@ P_3 X_1)))) (@ (@ tptp.insert_pname_o A_8) tptp.bot_bot_pname_o_o))) (=> (not _let_1) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= X_1 A_8) (@ P_3 X_1)))) tptp.bot_bot_pname_o_o))))))
% 0.25/0.67 (assert (forall ((P_3 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (A_8 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ P_3 A_8))) (and (=> _let_1 (= (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (and (= X_1 A_8) (@ P_3 X_1)))) (@ (@ tptp.insert1042460334tate_o A_8) tptp.bot_bo1962689075te_o_o))) (=> (not _let_1) (= (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (and (= X_1 A_8) (@ P_3 X_1)))) tptp.bot_bo1962689075te_o_o))))))
% 0.25/0.67 (assert (forall ((P_2 (-> tptp.pname Bool)) (A_7 tptp.pname)) (let ((_let_1 (@ P_2 A_7))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= A_7 X_1) (@ P_2 X_1)))) (@ (@ tptp.insert_pname A_7) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= A_7 X_1) (@ P_2 X_1)))) tptp.bot_bot_pname_o))))))
% 0.25/0.67 (assert (forall ((P_2 (-> tptp.hoare_1262092251_state Bool)) (A_7 tptp.hoare_1262092251_state)) (let ((_let_1 (@ P_2 A_7))) (and (=> _let_1 (= (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (and (= A_7 X_1) (@ P_2 X_1)))) (@ (@ tptp.insert81609953_state A_7) tptp.bot_bo113204042tate_o))) (=> (not _let_1) (= (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (and (= A_7 X_1) (@ P_2 X_1)))) tptp.bot_bo113204042tate_o))))))
% 0.25/0.67 (assert (forall ((P_2 (-> (-> tptp.pname Bool) Bool)) (A_7 (-> tptp.pname Bool))) (let ((_let_1 (@ P_2 A_7))) (and (=> _let_1 (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= A_7 X_1) (@ P_2 X_1)))) (@ (@ tptp.insert_pname_o A_7) tptp.bot_bot_pname_o_o))) (=> (not _let_1) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= A_7 X_1) (@ P_2 X_1)))) tptp.bot_bot_pname_o_o))))))
% 0.25/0.67 (assert (forall ((P_2 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (A_7 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ P_2 A_7))) (and (=> _let_1 (= (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (and (= A_7 X_1) (@ P_2 X_1)))) (@ (@ tptp.insert1042460334tate_o A_7) tptp.bot_bo1962689075te_o_o))) (=> (not _let_1) (= (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (and (= A_7 X_1) (@ P_2 X_1)))) tptp.bot_bo1962689075te_o_o))))))
% 0.25/0.67 (assert (forall ((A_6 tptp.pname)) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (= X_1 A_6))) (@ (@ tptp.insert_pname A_6) tptp.bot_bot_pname_o))))
% 0.25/0.67 (assert (forall ((A_6 tptp.hoare_1262092251_state)) (= (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (= X_1 A_6))) (@ (@ tptp.insert81609953_state A_6) tptp.bot_bo113204042tate_o))))
% 0.25/0.67 (assert (forall ((A_6 (-> tptp.pname Bool))) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (= X_1 A_6))) (@ (@ tptp.insert_pname_o A_6) tptp.bot_bot_pname_o_o))))
% 0.25/0.67 (assert (forall ((A_6 (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (= X_1 A_6))) (@ (@ tptp.insert1042460334tate_o A_6) tptp.bot_bo1962689075te_o_o))))
% 0.25/0.67 (assert (forall ((A_5 tptp.pname)) (= (@ tptp.collect_pname (@ tptp.fequal_pname A_5)) (@ (@ tptp.insert_pname A_5) tptp.bot_bot_pname_o))))
% 0.25/0.67 (assert (forall ((A_5 tptp.hoare_1262092251_state)) (= (@ tptp.collec1121927558_state (@ tptp.fequal1925511196_state A_5)) (@ (@ tptp.insert81609953_state A_5) tptp.bot_bo113204042tate_o))))
% 0.25/0.67 (assert (forall ((A_5 (-> tptp.pname Bool))) (= (@ tptp.collect_pname_o (@ tptp.fequal_pname_o A_5)) (@ (@ tptp.insert_pname_o A_5) tptp.bot_bot_pname_o_o))))
% 0.25/0.67 (assert (forall ((A_5 (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.collec313158217tate_o (@ tptp.fequal1529404211tate_o A_5)) (@ (@ tptp.insert1042460334tate_o A_5) tptp.bot_bo1962689075te_o_o))))
% 0.25/0.67 (assert (forall ((C_1 tptp.com) (G (-> tptp.hoare_1262092251_state Bool))) (=> tptp.hoare_1821564147gleton (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) (@ tptp.dom_pname_com tptp.body)) (@ (@ tptp.hoare_930741239_state G) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT (@ tptp.body_1 X_1))) tptp.bot_bo113204042tate_o)))) (=> (@ tptp.wt C_1) (@ (@ tptp.hoare_930741239_state G) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT C_1)) tptp.bot_bo113204042tate_o)))))))
% 0.25/0.67 (assert (forall ((Pn_1 tptp.pname) (B_3 tptp.com)) (=> tptp.wT_bodies (=> (= (@ tptp.body Pn_1) (@ tptp.some_com B_3)) (@ tptp.wt B_3)))))
% 0.25/0.67 (assert (forall ((B_2 tptp.hoare_1262092251_state) (F_3 (-> tptp.pname tptp.hoare_1262092251_state)) (A_4 (-> tptp.pname Bool))) (=> (@ (@ tptp.member5164104_state B_2) (@ (@ tptp.image_669833818_state F_3) A_4)) (not (forall ((X_1 tptp.pname)) (=> (= B_2 (@ F_3 X_1)) (not (@ (@ tptp.member_pname X_1) A_4))))))))
% 0.25/0.67 (assert (forall ((P_1 (-> (-> tptp.pname Bool) Bool)) (A_2 (-> tptp.pname Bool)) (F_1 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_1) (=> (@ (@ tptp.ord_less_eq_pname_o F_1) A_2) (=> (@ P_1 tptp.bot_bot_pname_o) (=> (forall ((A_3 tptp.pname) (F_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_3))) (=> (@ tptp.finite_finite_pname F_2) (=> (@ _let_1 A_2) (=> (not (@ _let_1 F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert_pname A_3) F_2)))))))) (@ P_1 F_1)))))))
% 0.25/0.67 (assert (forall ((P_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (A_2 (-> tptp.hoare_1262092251_state Bool)) (F_1 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_1) (=> (@ (@ tptp.ord_le870406270tate_o F_1) A_2) (=> (@ P_1 tptp.bot_bo113204042tate_o) (=> (forall ((A_3 tptp.hoare_1262092251_state) (F_2 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_3))) (=> (@ tptp.finite1178804552_state F_2) (=> (@ _let_1 A_2) (=> (not (@ _let_1 F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert81609953_state A_3) F_2)))))))) (@ P_1 F_1)))))))
% 0.25/0.67 (assert (forall ((P_1 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (A_2 (-> (-> tptp.pname Bool) Bool)) (F_1 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_1) (=> (@ (@ tptp.ord_le1205211808me_o_o F_1) A_2) (=> (@ P_1 tptp.bot_bot_pname_o_o) (=> (forall ((A_3 (-> tptp.pname Bool)) (F_2 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.member_pname_o A_3))) (=> (@ tptp.finite297249702name_o F_2) (=> (@ _let_1 A_2) (=> (not (@ _let_1 F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert_pname_o A_3) F_2)))))))) (@ P_1 F_1)))))))
% 0.25/0.67 (assert (forall ((P_1 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) (A_2 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (F_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o F_1) (=> (@ (@ tptp.ord_le2012720639te_o_o F_1) A_2) (=> (@ P_1 tptp.bot_bo1962689075te_o_o) (=> (forall ((A_3 (-> tptp.hoare_1262092251_state Bool)) (F_2 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (@ tptp.member907417095tate_o A_3))) (=> (@ tptp.finite1423311111tate_o F_2) (=> (@ _let_1 A_2) (=> (not (@ _let_1 F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert1042460334tate_o A_3) F_2)))))))) (@ P_1 F_1)))))))
% 0.25/0.67 (assert (forall ((P tptp.pname)) (=> (@ tptp.wt (@ tptp.body_1 P)) (not (forall ((Y_1 tptp.com)) (not (= (@ tptp.body P) (@ tptp.some_com Y_1))))))))
% 0.25/0.67 (assert (forall ((B_1 (-> tptp.pname Bool)) (A_1 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (let ((_let_1 (@ tptp.member_pname X_1))) (=> (@ _let_1 A_1) (@ _let_1 B_1)))) (@ (@ tptp.ord_less_eq_pname_o A_1) B_1))))
% 0.25/0.67 (assert (forall ((B_1 (-> tptp.hoare_1262092251_state Bool)) (A_1 (-> tptp.hoare_1262092251_state Bool))) (=> (forall ((X_1 tptp.hoare_1262092251_state)) (let ((_let_1 (@ tptp.member5164104_state X_1))) (=> (@ _let_1 A_1) (@ _let_1 B_1)))) (@ (@ tptp.ord_le870406270tate_o A_1) B_1))))
% 0.25/0.67 (assert (forall ((F (-> tptp.pname tptp.hoare_1262092251_state)) (A (-> tptp.pname Bool)) (B (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state B) (=> (@ (@ tptp.ord_le870406270tate_o B) (@ (@ tptp.image_669833818_state F) A)) (exists ((C (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C) A) (@ tptp.finite_finite_pname C) (= B (@ (@ tptp.image_669833818_state F) C))))))))
% 0.25/0.67 (assert (@ tptp.finite_finite_pname (@ tptp.dom_pname_com tptp.body)))
% 0.25/0.67 (assert (forall ((Pname_1 tptp.pname) (Pname tptp.pname)) (= (= (@ tptp.body_1 Pname_1) (@ tptp.body_1 Pname)) (= Pname_1 Pname))))
% 0.25/0.67 (assert (forall ((X tptp.pname) (Y tptp.pname)) (or (not (@ (@ tptp.fequal_pname X) Y)) (= X Y))))
% 0.25/0.67 (assert (forall ((X tptp.pname) (Y tptp.pname)) (or (not (= X Y)) (@ (@ tptp.fequal_pname X) Y))))
% 0.25/0.67 (assert (forall ((X (-> tptp.pname Bool)) (Y (-> tptp.pname Bool))) (or (not (@ (@ tptp.fequal_pname_o X) Y)) (= X Y))))
% 0.83/1.05 (assert (forall ((X (-> tptp.pname Bool)) (Y (-> tptp.pname Bool))) (or (not (= X Y)) (@ (@ tptp.fequal_pname_o X) Y))))
% 0.83/1.05 (assert (forall ((X tptp.hoare_1262092251_state) (Y tptp.hoare_1262092251_state)) (or (not (@ (@ tptp.fequal1925511196_state X) Y)) (= X Y))))
% 0.83/1.05 (assert (forall ((X tptp.hoare_1262092251_state) (Y tptp.hoare_1262092251_state)) (or (not (= X Y)) (@ (@ tptp.fequal1925511196_state X) Y))))
% 0.83/1.05 (assert (forall ((X (-> tptp.hoare_1262092251_state Bool)) (Y (-> tptp.hoare_1262092251_state Bool))) (or (not (@ (@ tptp.fequal1529404211tate_o X) Y)) (= X Y))))
% 0.83/1.05 (assert (forall ((X (-> tptp.hoare_1262092251_state Bool)) (Y (-> tptp.hoare_1262092251_state Bool))) (or (not (= X Y)) (@ (@ tptp.fequal1529404211tate_o X) Y))))
% 0.83/1.05 (assert tptp.hoare_1821564147gleton)
% 0.83/1.05 (assert tptp.wT_bodies)
% 0.83/1.05 (assert (@ tptp.finite1178804552_state tptp.fa))
% 0.83/1.05 (assert (not (@ (@ tptp.member5164104_state (@ tptp.hoare_Mirabelle_MGT tptp.y)) tptp.fa)))
% 0.83/1.05 (assert (@ (@ tptp.ord_le870406270tate_o tptp.fa) (@ (@ tptp.image_669833818_state (lambda ((Pn tptp.pname)) (@ tptp.hoare_Mirabelle_MGT (@ tptp.the_com (@ tptp.body Pn))))) (@ tptp.dom_pname_com tptp.body))))
% 0.83/1.05 (assert (= (@ tptp.body tptp.pn) (@ tptp.some_com tptp.y)))
% 0.83/1.05 (assert (@ (@ tptp.hoare_930741239_state (@ (@ tptp.image_669833818_state (lambda ((Pn tptp.pname)) (@ tptp.hoare_Mirabelle_MGT (@ tptp.body_1 Pn)))) (@ tptp.dom_pname_com tptp.body))) tptp.fa))
% 0.83/1.05 (assert (not (@ (@ tptp.hoare_930741239_state (@ (@ tptp.image_669833818_state (lambda ((Pn tptp.pname)) (@ tptp.hoare_Mirabelle_MGT (@ tptp.body_1 Pn)))) (@ tptp.dom_pname_com tptp.body))) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT tptp.y)) tptp.bot_bo113204042tate_o))))
% 0.83/1.05 (set-info :filename cvc5---1.0.5_12974)
% 0.83/1.05 (check-sat-assuming ( true ))
% 0.83/1.05 ------- get file name : TPTP file name is SWW474^1
% 0.83/1.05 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12974.smt2...
% 0.83/1.05 --- Run --ho-elim --full-saturate-quant at 10...
% 0.83/1.05 % SZS status Theorem for SWW474^1
% 0.83/1.05 % SZS output start Proof for SWW474^1
% 0.83/1.05 (
% 0.83/1.05 (let ((_let_1 (@ tptp.hoare_Mirabelle_MGT tptp.y))) (let ((_let_2 (@ tptp.insert81609953_state _let_1))) (let ((_let_3 (@ tptp.dom_pname_com tptp.body))) (let ((_let_4 (@ tptp.hoare_930741239_state (@ (@ tptp.image_669833818_state (lambda ((Pn tptp.pname)) (@ tptp.hoare_Mirabelle_MGT (@ tptp.body_1 Pn)))) _let_3)))) (let ((_let_5 (not (@ _let_4 (@ _let_2 tptp.bot_bo113204042tate_o))))) (let ((_let_6 (= (@ tptp.body tptp.pn) (@ tptp.some_com tptp.y)))) (let ((_let_7 (forall ((Pn_1 tptp.pname) (B_3 tptp.com)) (=> tptp.wT_bodies (=> (= (@ tptp.body Pn_1) (@ tptp.some_com B_3)) (@ tptp.wt B_3)))))) (let ((_let_8 (= tptp.bot_bot_pname_o (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) false))))) (let ((_let_9 (= tptp.bot_bo113204042tate_o (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) false))))) (let ((_let_10 (= tptp.bot_bot_pname_o_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) false))))) (let ((_let_11 (= tptp.bot_bo1962689075te_o_o (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) false))))) (let ((_let_12 (= tptp.bot_bo388435036_o_o_o (@ tptp.collec341954548te_o_o (lambda ((X_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) false))))) (let ((_let_13 (forall ((C_1 tptp.com)) (=> tptp.hoare_1821564147gleton (=> tptp.wT_bodies (=> (@ tptp.wt C_1) (@ (@ tptp.hoare_930741239_state tptp.bot_bo113204042tate_o) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT C_1)) tptp.bot_bo113204042tate_o)))))))) (let ((_let_14 (forall ((G_4 (-> tptp.hoare_1262092251_state Bool)) (G_3 (-> tptp.hoare_1262092251_state Bool)) (Ts_2 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.hoare_930741239_state G_4))) (=> (@ (@ tptp.hoare_930741239_state G_3) Ts_2) (=> (@ _let_1 G_3) (@ _let_1 Ts_2))))))) (let ((_let_15 (forall ((G (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.hoare_930741239_state G) tptp.bot_bo113204042tate_o)))) (let ((_let_16 (forall ((BOUND_VARIABLE_12483 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_12486 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_12482 |u_(-> tptp.hoare_1262092251_state Bool)|)) (let ((_let_1 (ho_105 k_255 BOUND_VARIABLE_12483))) (or (not (ho_106 (ho_105 k_255 BOUND_VARIABLE_12486) BOUND_VARIABLE_12482)) (not (ho_106 _let_1 BOUND_VARIABLE_12486)) (ho_106 _let_1 BOUND_VARIABLE_12482)))))) (let ((_let_17 (ho_125 k_254 k_253))) (let ((_let_18 (ho_125 (ho_124 k_256 (ho_96 k_95 tptp.y)) _let_17))) (let ((_let_19 (ho_277 (ho_276 k_275 k_91) (ho_343 k_342 k_99)))) (let ((_let_20 (ho_105 k_255 _let_19))) (let ((_let_21 (ho_106 _let_20 _let_18))) (let ((_let_22 (ho_106 _let_20 _let_17))) (let ((_let_23 (not _let_22))) (let ((_let_24 (ho_106 (ho_105 k_255 _let_17) _let_18))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_21))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((G_4 (-> tptp.hoare_1262092251_state Bool)) (G_3 (-> tptp.hoare_1262092251_state Bool)) (Ts_2 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.hoare_930741239_state G_4))) (or (not (@ (@ tptp.hoare_930741239_state G_3) Ts_2)) (not (@ _let_1 G_3)) (@ _let_1 Ts_2)))) _let_16))))))) (let ((_let_28 (not _let_26))) (let ((_let_29 (ho_353 k_352 tptp.y))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_24))) (let ((_let_32 (forall ((C_1 tptp.com)) (let ((_let_1 (ho_125 k_254 k_253))) (or (not (ho_353 k_352 C_1)) (ho_106 (ho_105 k_255 _let_1) (ho_125 (ho_124 k_256 (ho_96 k_95 C_1)) _let_1))))))) (let ((_let_33 (forall ((C_1 tptp.com)) (let ((_let_1 (@ tptp.collec1121927558_state ll_2))) (or (not (@ tptp.wt C_1)) (@ (@ tptp.hoare_930741239_state _let_1) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT C_1)) _let_1))))))) (let ((_let_34 (not tptp.wT_bodies))) (let ((_let_35 (AND_INTRO (MACRO_SR_PRED_TRANSFORM (ASSUME :args (tptp.wT_bodies)) :args ((= tptp.wT_bodies true))) (MACRO_SR_PRED_TRANSFORM (ASSUME :args (tptp.hoare_1821564147gleton)) :args ((= tptp.hoare_1821564147gleton true))) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_13)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_35 :args ((or (not tptp.hoare_1821564147gleton) _let_34 (forall ((C_1 tptp.com)) (or (not (@ tptp.wt C_1)) (@ (@ tptp.hoare_930741239_state tptp.bot_bo113204042tate_o) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT C_1)) tptp.bot_bo113204042tate_o))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((C_1 tptp.com)) (let ((_let_1 (@ tptp.collec1121927558_state (lambda ((BOUND_VARIABLE_8331 tptp.hoare_1262092251_state)) false)))) (or (not (@ tptp.wt C_1)) (@ (@ tptp.hoare_930741239_state _let_1) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT C_1)) _let_1))))) _let_33))) (PREPROCESS :args ((= _let_33 _let_32))))))) (let ((_let_37 (= (ho_345 k_344 tptp.y) (ho_100 k_99 tptp.pn)))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_29))) (let ((_let_40 (forall ((Pn_1 tptp.pname) (B_3 tptp.com)) (or (not (= (ho_345 k_344 B_3) (ho_100 k_99 Pn_1))) (ho_353 k_352 B_3))))) (let ((_let_41 (forall ((Pn_1 tptp.pname) (B_3 tptp.com)) (or (not (= (@ tptp.body Pn_1) (@ tptp.some_com B_3))) (@ tptp.wt B_3))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_35 :args ((or _let_34 _let_41) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= _let_41 _let_40))))))) (let ((_let_43 (forall ((BOUND_VARIABLE_12255 |u_(-> tptp.hoare_1262092251_state Bool)|)) (ho_106 (ho_105 k_255 BOUND_VARIABLE_12255) (ho_125 k_254 k_253))))) (let ((_let_44 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_242 v ii) (ite (= i ii) e (ho_242 u ii)))))))))) (let ((_let_45 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_242 x z) (ho_242 y z)))) (= x y))))) (let ((_let_46 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|) (e Bool) (i |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_243 v ii) (ite (= i ii) e (ho_243 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_243 x z) (ho_243 y z)))) (= x y))))) (let ((_let_48 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_239 v ii) (ite (= i ii) e (ho_239 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_239 x z) (ho_239 y z)))) (= x y))))) (let ((_let_50 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_228 v ii) (ite (= i ii) e (ho_228 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_228 x z) (ho_228 y z)))) (= x y))))) (let ((_let_52 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_320 v ii) (ite (= i ii) e (ho_320 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_320 x z) (ho_320 y z)))) (= x y))))) (let ((_let_54 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_224 v ii) (ite (= i ii) e (ho_224 u ii)))))))))) (let ((_let_55 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_224 x z) (ho_224 y z)))) (= x y))))) (let ((_let_56 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_225 v ii) (ite (= i ii) e (ho_225 u ii)))))))))) (let ((_let_57 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_225 x z) (ho_225 y z)))) (= x y))))) (let ((_let_58 (forall ((u |u_(-> tptp.hoare_1262092251_state tptp.pname)|) (e tptp.pname) (i tptp.hoare_1262092251_state)) (not (forall ((v |u_(-> tptp.hoare_1262092251_state tptp.pname)|)) (not (forall ((ii tptp.hoare_1262092251_state)) (= (ho_196 v ii) (ite (= i ii) e (ho_196 u ii)))))))))) (let ((_let_59 (forall ((x |u_(-> tptp.hoare_1262092251_state tptp.pname)|) (y |u_(-> tptp.hoare_1262092251_state tptp.pname)|)) (or (not (forall ((z tptp.hoare_1262092251_state)) (= (ho_196 x z) (ho_196 y z)))) (= x y))))) (let ((_let_60 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_227 v ii) (ite (= i ii) e (ho_227 u ii)))))))))) (let ((_let_61 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_227 x z) (ho_227 y z)))) (= x y))))) (let ((_let_62 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state tptp.pname Bool)|) (e |u_(-> tptp.hoare_1262092251_state tptp.pname Bool)|) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state tptp.pname Bool)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_192 v ii) (ite (= i ii) e (ho_192 u ii)))))))))) (let ((_let_63 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state tptp.pname Bool)|) (y |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state tptp.pname Bool)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_192 x z) (ho_192 y z)))) (= x y))))) (let ((_let_64 (forall ((u |u_(-> tptp.option_com tptp.com)|) (e tptp.com) (i tptp.option_com)) (not (forall ((v |u_(-> tptp.option_com tptp.com)|)) (not (forall ((ii tptp.option_com)) (= (ho_102 v ii) (ite (= i ii) e (ho_102 u ii)))))))))) (let ((_let_65 (forall ((x |u_(-> tptp.option_com tptp.com)|) (y |u_(-> tptp.option_com tptp.com)|)) (or (not (forall ((z tptp.option_com)) (= (ho_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_66 (forall ((u |u_(-> tptp.pname tptp.hoare_1262092251_state tptp.pname)|) (e |u_(-> tptp.hoare_1262092251_state tptp.pname)|) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname tptp.hoare_1262092251_state tptp.pname)|)) (not (forall ((ii tptp.pname)) (= (ho_195 v ii) (ite (= i ii) e (ho_195 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> tptp.pname tptp.hoare_1262092251_state tptp.pname)|) (y |u_(-> tptp.pname tptp.hoare_1262092251_state tptp.pname)|)) (or (not (forall ((z tptp.pname)) (= (ho_195 x z) (ho_195 y z)))) (= x y))))) (let ((_let_68 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_116 v ii) (ite (= i ii) e (ho_116 u ii)))))))))) (let ((_let_69 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_70 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)_ Bool)|) (e Bool) (i |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (= (ho_266 v ii) (ite (= i ii) e (ho_266 u ii)))))))))) (let ((_let_71 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (= (ho_266 x z) (ho_266 y z)))) (= x y))))) (let ((_let_72 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|) (e |u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_190 v ii) (ite (= i ii) e (ho_190 u ii)))))))))) (let ((_let_73 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_190 x z) (ho_190 y z)))) (= x y))))) (let ((_let_74 (forall ((u |u_(-> tptp.pname tptp.hoare_1262092251_state Bool)|) (e |u_(-> tptp.hoare_1262092251_state Bool)|) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii tptp.pname)) (= (ho_186 v ii) (ite (= i ii) e (ho_186 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> tptp.pname tptp.hoare_1262092251_state Bool)|) (y |u_(-> tptp.pname tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z tptp.pname)) (= (ho_186 x z) (ho_186 y z)))) (= x y))))) (let ((_let_76 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname tptp.pname Bool)|) (e |u_(-> tptp.pname tptp.pname Bool)|) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname tptp.pname Bool)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_188 v ii) (ite (= i ii) e (ho_188 u ii)))))))))) (let ((_let_77 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname tptp.pname Bool)|) (y |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname tptp.pname Bool)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_188 x z) (ho_188 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> _u_(-> tptp.pname _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (i |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_307 v ii) (ite (= i ii) e (ho_307 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> _u_(-> tptp.pname _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.pname _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_307 x z) (ho_307 y z)))) (= x y))))) (let ((_let_80 (forall ((u |u_(-> tptp.pname tptp.pname tptp.pname)|) (e |u_(-> tptp.pname tptp.pname)|) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname tptp.pname tptp.pname)|)) (not (forall ((ii tptp.pname)) (= (ho_182 v ii) (ite (= i ii) e (ho_182 u ii)))))))))) (let ((_let_81 (forall ((x |u_(-> tptp.pname tptp.pname tptp.pname)|) (y |u_(-> tptp.pname tptp.pname tptp.pname)|)) (or (not (forall ((z tptp.pname)) (= (ho_182 x z) (ho_182 y z)))) (= x y))))) (let ((_let_82 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_236 v ii) (ite (= i ii) e (ho_236 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_236 x z) (ho_236 y z)))) (= x y))))) (let ((_let_84 (forall ((u |u_(-> tptp.pname tptp.pname)|) (e tptp.pname) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname tptp.pname)|)) (not (forall ((ii tptp.pname)) (= (ho_183 v ii) (ite (= i ii) e (ho_183 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> tptp.pname tptp.pname)|) (y |u_(-> tptp.pname tptp.pname)|)) (or (not (forall ((z tptp.pname)) (= (ho_183 x z) (ho_183 y z)))) (= x y))))) (let ((_let_86 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|) (e tptp.hoare_1262092251_state) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_180 v ii) (ite (= i ii) e (ho_180 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|) (y |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_180 x z) (ho_180 y z)))) (= x y))))) (let ((_let_88 (forall ((u |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|) (i tptp.hoare_1262092251_state)) (not (forall ((v |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|)) (not (forall ((ii tptp.hoare_1262092251_state)) (= (ho_176 v ii) (ite (= i ii) e (ho_176 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|) (y |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|)) (or (not (forall ((z tptp.hoare_1262092251_state)) (= (ho_176 x z) (ho_176 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname Bool)|) (i |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)|)) (= (ho_290 v ii) (ite (= i ii) e (ho_290 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)|)) (= (ho_290 x z) (ho_290 y z)))) (= x y))))) (let ((_let_92 (forall ((u |u_(-> tptp.hoare_1262092251_state tptp.pname tptp.hoare_1262092251_state)|) (e |u_(-> tptp.pname tptp.hoare_1262092251_state)|) (i tptp.hoare_1262092251_state)) (not (forall ((v |u_(-> tptp.hoare_1262092251_state tptp.pname tptp.hoare_1262092251_state)|)) (not (forall ((ii tptp.hoare_1262092251_state)) (= (ho_198 v ii) (ite (= i ii) e (ho_198 u ii)))))))))) (let ((_let_93 (forall ((x |u_(-> tptp.hoare_1262092251_state tptp.pname tptp.hoare_1262092251_state)|) (y |u_(-> tptp.hoare_1262092251_state tptp.pname tptp.hoare_1262092251_state)|)) (or (not (forall ((z tptp.hoare_1262092251_state)) (= (ho_198 x z) (ho_198 y z)))) (= x y))))) (let ((_let_94 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|) (e tptp.hoare_1262092251_state) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_177 v ii) (ite (= i ii) e (ho_177 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_177 x z) (ho_177 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)|) (e tptp.pname) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_174 v ii) (ite (= i ii) e (ho_174 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)|) (y |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_174 x z) (ho_174 y z)))) (= x y))))) (let ((_let_98 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|) (e tptp.pname) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_171 v ii) (ite (= i ii) e (ho_171 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_171 x z) (ho_171 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_158 v ii) (ite (= i ii) e (ho_158 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_158 x z) (ho_158 y z)))) (= x y))))) (let ((_let_102 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.option_com)|) (e tptp.option_com) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.option_com)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_349 v ii) (ite (= i ii) e (ho_349 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.option_com)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.option_com)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_349 x z) (ho_349 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_109 v ii) (ite (= i ii) e (ho_109 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_109 x z) (ho_109 y z)))) (= x y))))) (let ((_let_106 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_105 v ii) (ite (= i ii) e (ho_105 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_105 x z) (ho_105 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> tptp.pname tptp.hoare_1262092251_state)|) (e tptp.hoare_1262092251_state) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname tptp.hoare_1262092251_state)|)) (not (forall ((ii tptp.pname)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> tptp.pname tptp.hoare_1262092251_state)|) (y |u_(-> tptp.pname tptp.hoare_1262092251_state)|)) (or (not (forall ((z tptp.pname)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_110 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname tptp.hoare_1262092251_state Bool)|) (e |u_(-> tptp.pname tptp.hoare_1262092251_state Bool)|) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_185 v ii) (ite (= i ii) e (ho_185 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_185 x z) (ho_185 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> tptp.pname tptp.option_com)|) (e tptp.option_com) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname tptp.option_com)|)) (not (forall ((ii tptp.pname)) (= (ho_100 v ii) (ite (= i ii) e (ho_100 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> tptp.pname tptp.option_com)|) (y |u_(-> tptp.pname tptp.option_com)|)) (or (not (forall ((z tptp.pname)) (= (ho_100 x z) (ho_100 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.pname)_ _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname Bool)|) (i |u_(-> tptp.hoare_1262092251_state tptp.pname)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.pname)_ _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state tptp.pname)|)) (= (ho_329 v ii) (ite (= i ii) e (ho_329 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.pname)_ _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.pname)_ _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state tptp.pname)|)) (= (ho_329 x z) (ho_329 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> tptp.pname Bool)|) (e Bool) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname Bool)|)) (not (forall ((ii tptp.pname)) (= (ho_107 v ii) (ite (= i ii) e (ho_107 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> tptp.pname Bool)|) (y |u_(-> tptp.pname Bool)|)) (or (not (forall ((z tptp.pname)) (= (ho_107 x z) (ho_107 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_338 v ii) (ite (= i ii) e (ho_338 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_338 x z) (ho_338 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> tptp.hoare_1262092251_state Bool)|) (e Bool) (i tptp.hoare_1262092251_state)) (not (forall ((v |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii tptp.hoare_1262092251_state)) (= (ho_103 v ii) (ite (= i ii) e (ho_103 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> tptp.hoare_1262092251_state Bool)|) (y |u_(-> tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z tptp.hoare_1262092251_state)) (= (ho_103 x z) (ho_103 y z)))) (= x y))))) (let ((_let_122 (forall ((u |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ tptp.pname Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname Bool)|) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ tptp.pname Bool)|)) (not (forall ((ii tptp.pname)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_123 (forall ((x |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ tptp.pname Bool)|) (y |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ tptp.pname Bool)|)) (or (not (forall ((z tptp.pname)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_124 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname Bool)|) (e |u_(-> tptp.pname Bool)|) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_129 v ii) (ite (= i ii) e (ho_129 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_129 x z) (ho_129 y z)))) (= x y))))) (let ((_let_126 (forall ((u |u_(-> tptp.pname tptp.pname Bool)|) (e |u_(-> tptp.pname Bool)|) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname tptp.pname Bool)|)) (not (forall ((ii tptp.pname)) (= (ho_114 v ii) (ite (= i ii) e (ho_114 u ii)))))))))) (let ((_let_127 (forall ((x |u_(-> tptp.pname tptp.pname Bool)|) (y |u_(-> tptp.pname tptp.pname Bool)|)) (or (not (forall ((z tptp.pname)) (= (ho_114 x z) (ho_114 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|) (e Bool) (i |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_247 v ii) (ite (= i ii) e (ho_247 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_247 x z) (ho_247 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_117 v ii) (ite (= i ii) e (ho_117 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_117 x z) (ho_117 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ tptp.pname Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname Bool)|) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_160 v ii) (ite (= i ii) e (ho_160 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_160 x z) (ho_160 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|)) (not (forall ((ii tptp.pname)) (= (ho_170 v ii) (ite (= i ii) e (ho_170 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|) (y |u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|)) (or (not (forall ((z tptp.pname)) (= (ho_170 x z) (ho_170 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)_ Bool)|) (e Bool) (i |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (= (ho_271 v ii) (ite (= i ii) e (ho_271 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (= (ho_271 x z) (ho_271 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_145 v ii) (ite (= i ii) e (ho_145 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_145 x z) (ho_145 y z)))) (= x y))))) (let ((_let_140 (forall ((u |u_(-> tptp.com tptp.hoare_1262092251_state)|) (e tptp.hoare_1262092251_state) (i tptp.com)) (not (forall ((v |u_(-> tptp.com tptp.hoare_1262092251_state)|)) (not (forall ((ii tptp.com)) (= (ho_96 v ii) (ite (= i ii) e (ho_96 u ii)))))))))) (let ((_let_141 (forall ((x |u_(-> tptp.com tptp.hoare_1262092251_state)|) (y |u_(-> tptp.com tptp.hoare_1262092251_state)|)) (or (not (forall ((z tptp.com)) (= (ho_96 x z) (ho_96 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> tptp.hoare_1262092251_state tptp.pname Bool)|) (e |u_(-> tptp.pname Bool)|) (i tptp.hoare_1262092251_state)) (not (forall ((v |u_(-> tptp.hoare_1262092251_state tptp.pname Bool)|)) (not (forall ((ii tptp.hoare_1262092251_state)) (= (ho_193 v ii) (ite (= i ii) e (ho_193 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> tptp.hoare_1262092251_state tptp.pname Bool)|) (y |u_(-> tptp.hoare_1262092251_state tptp.pname Bool)|)) (or (not (forall ((z tptp.hoare_1262092251_state)) (= (ho_193 x z) (ho_193 y z)))) (= x y))))) (let ((_let_144 (forall ((u |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|) (e |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|) (i tptp.hoare_1262092251_state)) (not (forall ((v |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|)) (not (forall ((ii tptp.hoare_1262092251_state)) (= (ho_179 v ii) (ite (= i ii) e (ho_179 u ii)))))))))) (let ((_let_145 (forall ((x |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|) (y |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|)) (or (not (forall ((z tptp.hoare_1262092251_state)) (= (ho_179 x z) (ho_179 y z)))) (= x y))))) (let ((_let_146 (forall ((u |u_(-> tptp.pname tptp.com)|) (e tptp.com) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname tptp.com)|)) (not (forall ((ii tptp.pname)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_147 (forall ((x |u_(-> tptp.pname tptp.com)|) (y |u_(-> tptp.pname tptp.com)|)) (or (not (forall ((z tptp.pname)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_148 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> tptp.hoare_1262092251_state Bool)|) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_302 v ii) (ite (= i ii) e (ho_302 u ii)))))))))) (let ((_let_149 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_302 x z) (ho_302 y z)))) (= x y))))) (let ((_let_150 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_336 v ii) (ite (= i ii) e (ho_336 u ii)))))))))) (let ((_let_151 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_336 x z) (ho_336 y z)))) (= x y))))) (let ((_let_152 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_141 v ii) (ite (= i ii) e (ho_141 u ii)))))))))) (let ((_let_153 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_141 x z) (ho_141 y z)))) (= x y))))) (let ((_let_154 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (e Bool) (i |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_146 v ii) (ite (= i ii) e (ho_146 u ii)))))))))) (let ((_let_155 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_146 x z) (ho_146 y z)))) (= x y))))) (let ((_let_156 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_120 v ii) (ite (= i ii) e (ho_120 u ii)))))))))) (let ((_let_157 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_158 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 v ii) (ite (= i ii) e (ho_106 u ii)))))))))) (let ((_let_159 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 x z) (ho_106 y z)))) (= x y))))) (let ((_let_160 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> tptp.hoare_1262092251_state Bool)|) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_125 v ii) (ite (= i ii) e (ho_125 u ii)))))))))) (let ((_let_161 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_162 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (e Bool) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_142 v ii) (ite (= i ii) e (ho_142 u ii)))))))))) (let ((_let_163 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_142 x z) (ho_142 y z)))) (= x y))))) (let ((_let_164 (forall ((u |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|) (i tptp.hoare_1262092251_state)) (not (forall ((v |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii tptp.hoare_1262092251_state)) (= (ho_124 v ii) (ite (= i ii) e (ho_124 u ii)))))))))) (let ((_let_165 (forall ((x |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z tptp.hoare_1262092251_state)) (= (ho_124 x z) (ho_124 y z)))) (= x y))))) (let ((_let_166 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> tptp.hoare_1262092251_state Bool)|) (i |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_305 v ii) (ite (= i ii) e (ho_305 u ii)))))))))) (let ((_let_167 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_305 x z) (ho_305 y z)))) (= x y))))) (let ((_let_168 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (i |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_156 v ii) (ite (= i ii) e (ho_156 u ii)))))))))) (let ((_let_169 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_156 x z) (ho_156 y z)))) (= x y))))) (let ((_let_170 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|)) (= (ho_301 v ii) (ite (= i ii) e (ho_301 u ii)))))))))) (let ((_let_171 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.hoare_1262092251_state)|)) (= (ho_301 x z) (ho_301 y z)))) (= x y))))) (let ((_let_172 (forall ((u |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ tptp.pname)|) (e |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname)|) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ tptp.pname)|)) (not (forall ((ii tptp.pname)) (= (ho_173 v ii) (ite (= i ii) e (ho_173 u ii)))))))))) (let ((_let_173 (forall ((x |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ tptp.pname)|) (y |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ tptp.pname)|)) (or (not (forall ((z tptp.pname)) (= (ho_173 x z) (ho_173 y z)))) (= x y))))) (let ((_let_174 (forall ((u |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (i tptp.hoare_1262092251_state)) (not (forall ((v |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((ii tptp.hoare_1262092251_state)) (= (ho_149 v ii) (ite (= i ii) e (ho_149 u ii)))))))))) (let ((_let_175 (forall ((x |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (y |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (or (not (forall ((z tptp.hoare_1262092251_state)) (= (ho_149 x z) (ho_149 y z)))) (= x y))))) (let ((_let_176 (forall ((u |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((ii tptp.pname)) (= (ho_152 v ii) (ite (= i ii) e (ho_152 u ii)))))))))) (let ((_let_177 (forall ((x |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ Bool)|) (y |u_(-> tptp.pname _u_(-> tptp.pname Bool)_ Bool)|)) (or (not (forall ((z tptp.pname)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_178 (forall ((u |u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|) (e |u_(-> tptp.hoare_1262092251_state Bool)|) (i tptp.hoare_1262092251_state)) (not (forall ((v |u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii tptp.hoare_1262092251_state)) (= (ho_112 v ii) (ite (= i ii) e (ho_112 u ii)))))))))) (let ((_let_179 (forall ((x |u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|) (y |u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z tptp.hoare_1262092251_state)) (= (ho_112 x z) (ho_112 y z)))) (= x y))))) (let ((_let_180 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_110 v ii) (ite (= i ii) e (ho_110 u ii)))))))))) (let ((_let_181 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_110 x z) (ho_110 y z)))) (= x y))))) (let ((_let_182 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (i |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_121 v ii) (ite (= i ii) e (ho_121 u ii)))))))))) (let ((_let_183 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_121 x z) (ho_121 y z)))) (= x y))))) (let ((_let_184 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_154 v ii) (ite (= i ii) e (ho_154 u ii)))))))))) (let ((_let_185 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_186 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname)|) (e tptp.pname) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_282 v ii) (ite (= i ii) e (ho_282 u ii)))))))))) (let ((_let_187 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_282 x z) (ho_282 y z)))) (= x y))))) (let ((_let_188 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_246 v ii) (ite (= i ii) e (ho_246 u ii)))))))))) (let ((_let_189 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_246 x z) (ho_246 y z)))) (= x y))))) (let ((_let_190 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (= (ho_264 v ii) (ite (= i ii) e (ho_264 u ii)))))))))) (let ((_let_191 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ Bool)|)) (= (ho_264 x z) (ho_264 y z)))) (= x y))))) (let ((_let_192 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|) (i |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (= (ho_269 v ii) (ite (= i ii) e (ho_269 u ii)))))))))) (let ((_let_193 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ Bool)|)) (= (ho_269 x z) (ho_269 y z)))) (= x y))))) (let ((_let_194 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> tptp.hoare_1262092251_state Bool)|) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_277 v ii) (ite (= i ii) e (ho_277 u ii)))))))))) (let ((_let_195 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_277 x z) (ho_277 y z)))) (= x y))))) (let ((_let_196 (forall ((u |u_(-> _u_(-> tptp.pname tptp.hoare_1262092251_state)_ _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state Bool)|) (i |u_(-> tptp.pname tptp.hoare_1262092251_state)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname tptp.hoare_1262092251_state)_ _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> tptp.pname tptp.hoare_1262092251_state)|)) (= (ho_276 v ii) (ite (= i ii) e (ho_276 u ii)))))))))) (let ((_let_197 (forall ((x |u_(-> _u_(-> tptp.pname tptp.hoare_1262092251_state)_ _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> tptp.pname tptp.hoare_1262092251_state)_ _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> tptp.pname tptp.hoare_1262092251_state)|)) (= (ho_276 x z) (ho_276 y z)))) (= x y))))) (let ((_let_198 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.pname Bool)|) (e |u_(-> tptp.pname Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_281 v ii) (ite (= i ii) e (ho_281 u ii)))))))))) (let ((_let_199 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_281 x z) (ho_281 y z)))) (= x y))))) (let ((_let_200 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname)|) (e tptp.pname) (i |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_278 v ii) (ite (= i ii) e (ho_278 u ii)))))))))) (let ((_let_201 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_278 x z) (ho_278 y z)))) (= x y))))) (let ((_let_202 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.pname Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.pname Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname)|)) (= (ho_280 v ii) (ite (= i ii) e (ho_280 u ii)))))))))) (let ((_let_203 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname)|)) (= (ho_280 x z) (ho_280 y z)))) (= x y))))) (let ((_let_204 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.pname Bool)|) (e |u_(-> tptp.pname Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_285 v ii) (ite (= i ii) e (ho_285 u ii)))))))))) (let ((_let_205 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_285 x z) (ho_285 y z)))) (= x y))))) (let ((_let_206 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.pname Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.pname Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname)|)) (= (ho_284 v ii) (ite (= i ii) e (ho_284 u ii)))))))))) (let ((_let_207 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname)|)) (= (ho_284 x z) (ho_284 y z)))) (= x y))))) (let ((_let_208 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname Bool)|) (e |u_(-> tptp.pname Bool)|) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_288 v ii) (ite (= i ii) e (ho_288 u ii)))))))))) (let ((_let_209 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_288 x z) (ho_288 y z)))) (= x y))))) (let ((_let_210 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname Bool)|) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|)) (= (ho_287 v ii) (ite (= i ii) e (ho_287 u ii)))))))))) (let ((_let_211 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname)|)) (= (ho_287 x z) (ho_287 y z)))) (= x y))))) (let ((_let_212 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname Bool)|) (e |u_(-> tptp.pname Bool)|) (i |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_291 v ii) (ite (= i ii) e (ho_291 u ii)))))))))) (let ((_let_213 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_291 x z) (ho_291 y z)))) (= x y))))) (let ((_let_214 (forall ((u |u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (i tptp.pname)) (not (forall ((v |u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((ii tptp.pname)) (= (ho_308 v ii) (ite (= i ii) e (ho_308 u ii)))))))))) (let ((_let_215 (forall ((x |u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (y |u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (or (not (forall ((z tptp.pname)) (= (ho_308 x z) (ho_308 y z)))) (= x y))))) (let ((_let_216 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> tptp.hoare_1262092251_state Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_295 v ii) (ite (= i ii) e (ho_295 u ii)))))))))) (let ((_let_217 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_295 x z) (ho_295 y z)))) (= x y))))) (let ((_let_218 (forall ((u |u_(-> _u_(-> tptp.pname tptp.pname)_ _u_(-> tptp.pname Bool)_ tptp.pname Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ tptp.pname Bool)|) (i |u_(-> tptp.pname tptp.pname)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname tptp.pname)_ _u_(-> tptp.pname Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> tptp.pname tptp.pname)|)) (= (ho_332 v ii) (ite (= i ii) e (ho_332 u ii)))))))))) (let ((_let_219 (forall ((x |u_(-> _u_(-> tptp.pname tptp.pname)_ _u_(-> tptp.pname Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> tptp.pname tptp.pname)_ _u_(-> tptp.pname Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> tptp.pname tptp.pname)|)) (= (ho_332 x z) (ho_332 y z)))) (= x y))))) (let ((_let_220 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state)|) (e tptp.hoare_1262092251_state) (i |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_292 v ii) (ite (= i ii) e (ho_292 u ii)))))))))) (let ((_let_221 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_292 x z) (ho_292 y z)))) (= x y))))) (let ((_let_222 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state)|)) (= (ho_294 v ii) (ite (= i ii) e (ho_294 u ii)))))))))) (let ((_let_223 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state)|)) (= (ho_294 x z) (ho_294 y z)))) (= x y))))) (let ((_let_224 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> tptp.hoare_1262092251_state Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_299 v ii) (ite (= i ii) e (ho_299 u ii)))))))))) (let ((_let_225 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_299 x z) (ho_299 y z)))) (= x y))))) (let ((_let_226 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state)|) (e tptp.hoare_1262092251_state) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_296 v ii) (ite (= i ii) e (ho_296 u ii)))))))))) (let ((_let_227 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_296 x z) (ho_296 y z)))) (= x y))))) (let ((_let_228 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (i |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state)|)) (= (ho_298 v ii) (ite (= i ii) e (ho_298 u ii)))))))))) (let ((_let_229 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ tptp.hoare_1262092251_state)|)) (= (ho_298 x z) (ho_298 y z)))) (= x y))))) (let ((_let_230 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (i |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|)) (= (ho_304 v ii) (ite (= i ii) e (ho_304 u ii)))))))))) (let ((_let_231 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ tptp.hoare_1262092251_state Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ tptp.hoare_1262092251_state)|)) (= (ho_304 x z) (ho_304 y z)))) (= x y))))) (let ((_let_232 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_327 v ii) (ite (= i ii) e (ho_327 u ii)))))))))) (let ((_let_233 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_327 x z) (ho_327 y z)))) (= x y))))) (let ((_let_234 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_311 v ii) (ite (= i ii) e (ho_311 u ii)))))))))) (let ((_let_235 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_311 x z) (ho_311 y z)))) (= x y))))) (let ((_let_236 (forall ((u |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.option_com)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (i |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.option_com)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.option_com)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.option_com)|)) (= (ho_351 v ii) (ite (= i ii) e (ho_351 u ii)))))))))) (let ((_let_237 (forall ((x |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.option_com)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.option_com)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.option_com)|)) (= (ho_351 x z) (ho_351 y z)))) (= x y))))) (let ((_let_238 (forall ((u |u_(-> _u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (i |u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_310 v ii) (ite (= i ii) e (ho_310 u ii)))))))))) (let ((_let_239 (forall ((x |u_(-> _u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.pname _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_310 x z) (ho_310 y z)))) (= x y))))) (let ((_let_240 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_314 v ii) (ite (= i ii) e (ho_314 u ii)))))))))) (let ((_let_241 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_314 x z) (ho_314 y z)))) (= x y))))) (let ((_let_242 (forall ((u |u_(-> _u_(-> tptp.pname tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (i |u_(-> tptp.pname tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.pname tptp.hoare_1262092251_state Bool)|)) (= (ho_313 v ii) (ite (= i ii) e (ho_313 u ii)))))))))) (let ((_let_243 (forall ((x |u_(-> _u_(-> tptp.pname tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.pname tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.pname tptp.hoare_1262092251_state Bool)|)) (= (ho_313 x z) (ho_313 y z)))) (= x y))))) (let ((_let_244 (forall ((u |u_(-> _u_(-> tptp.pname tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (i |u_(-> tptp.pname tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.pname tptp.pname Bool)|)) (= (ho_316 v ii) (ite (= i ii) e (ho_316 u ii)))))))))) (let ((_let_245 (forall ((x |u_(-> _u_(-> tptp.pname tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.pname tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.pname tptp.pname Bool)|)) (= (ho_316 x z) (ho_316 y z)))) (= x y))))) (let ((_let_246 (forall ((u |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (i tptp.hoare_1262092251_state)) (not (forall ((v |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((ii tptp.hoare_1262092251_state)) (= (ho_317 v ii) (ite (= i ii) e (ho_317 u ii)))))))))) (let ((_let_247 (forall ((x |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ Bool)|) (y |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ Bool)|)) (or (not (forall ((z tptp.hoare_1262092251_state)) (= (ho_317 x z) (ho_317 y z)))) (= x y))))) (let ((_let_248 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (i |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_319 v ii) (ite (= i ii) e (ho_319 u ii)))))))))) (let ((_let_249 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_319 x z) (ho_319 y z)))) (= x y))))) (let ((_let_250 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (i |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_322 v ii) (ite (= i ii) e (ho_322 u ii)))))))))) (let ((_let_251 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_322 x z) (ho_322 y z)))) (= x y))))) (let ((_let_252 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (i |u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|)) (= (ho_324 v ii) (ite (= i ii) e (ho_324 u ii)))))))))) (let ((_let_253 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)|)) (= (ho_324 x z) (ho_324 y z)))) (= x y))))) (let ((_let_254 (forall ((u |u_(-> tptp.com Bool)|) (e Bool) (i tptp.com)) (not (forall ((v |u_(-> tptp.com Bool)|)) (not (forall ((ii tptp.com)) (= (ho_353 v ii) (ite (= i ii) e (ho_353 u ii)))))))))) (let ((_let_255 (forall ((x |u_(-> tptp.com Bool)|) (y |u_(-> tptp.com Bool)|)) (or (not (forall ((z tptp.com)) (= (ho_353 x z) (ho_353 y z)))) (= x y))))) (let ((_let_256 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (i |u_(-> tptp.hoare_1262092251_state tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state tptp.pname Bool)|)) (= (ho_326 v ii) (ite (= i ii) e (ho_326 u ii)))))))))) (let ((_let_257 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state tptp.pname Bool)_ _u_(-> tptp.hoare_1262092251_state Bool)_ _u_(-> tptp.pname Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state tptp.pname Bool)|)) (= (ho_326 x z) (ho_326 y z)))) (= x y))))) (let ((_let_258 (forall ((u |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname Bool)|) (e |u_(-> tptp.pname Bool)|) (i |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_330 v ii) (ite (= i ii) e (ho_330 u ii)))))))))) (let ((_let_259 (forall ((x |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname Bool)|) (y |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_330 x z) (ho_330 y z)))) (= x y))))) (let ((_let_260 (forall ((u |u_(-> _u_(-> tptp.pname tptp.option_com)_ tptp.pname Bool)|) (e |u_(-> tptp.pname Bool)|) (i |u_(-> tptp.pname tptp.option_com)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname tptp.option_com)_ tptp.pname Bool)|)) (not (forall ((ii |u_(-> tptp.pname tptp.option_com)|)) (= (ho_343 v ii) (ite (= i ii) e (ho_343 u ii)))))))))) (let ((_let_261 (forall ((x |u_(-> _u_(-> tptp.pname tptp.option_com)_ tptp.pname Bool)|) (y |u_(-> _u_(-> tptp.pname tptp.option_com)_ tptp.pname Bool)|)) (or (not (forall ((z |u_(-> tptp.pname tptp.option_com)|)) (= (ho_343 x z) (ho_343 y z)))) (= x y))))) (let ((_let_262 (forall ((u |u_(-> tptp.com tptp.option_com)|) (e tptp.option_com) (i tptp.com)) (not (forall ((v |u_(-> tptp.com tptp.option_com)|)) (not (forall ((ii tptp.com)) (= (ho_345 v ii) (ite (= i ii) e (ho_345 u ii)))))))))) (let ((_let_263 (forall ((x |u_(-> tptp.com tptp.option_com)|) (y |u_(-> tptp.com tptp.option_com)|)) (or (not (forall ((z tptp.com)) (= (ho_345 x z) (ho_345 y z)))) (= x y))))) (let ((_let_264 (forall ((u |u_(-> _u_(-> tptp.pname Bool)_ tptp.option_com)|) (e tptp.option_com) (i |u_(-> tptp.pname Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.pname Bool)_ tptp.option_com)|)) (not (forall ((ii |u_(-> tptp.pname Bool)|)) (= (ho_346 v ii) (ite (= i ii) e (ho_346 u ii)))))))))) (let ((_let_265 (forall ((x |u_(-> _u_(-> tptp.pname Bool)_ tptp.option_com)|) (y |u_(-> _u_(-> tptp.pname Bool)_ tptp.option_com)|)) (or (not (forall ((z |u_(-> tptp.pname Bool)|)) (= (ho_346 x z) (ho_346 y z)))) (= x y))))) (let ((_let_266 (forall ((u |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.option_com)_ _u_(-> tptp.pname Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (i |u_(-> _u_(-> tptp.pname Bool)_ tptp.option_com)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.option_com)_ _u_(-> tptp.pname Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> tptp.pname Bool)_ tptp.option_com)|)) (= (ho_348 v ii) (ite (= i ii) e (ho_348 u ii)))))))))) (let ((_let_267 (forall ((x |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.option_com)_ _u_(-> tptp.pname Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ tptp.option_com)_ _u_(-> tptp.pname Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.pname Bool)_ tptp.option_com)|)) (= (ho_348 x z) (ho_348 y z)))) (= x y))))) (let ((_let_268 (forall ((BOUND_VARIABLE_10702 tptp.pname)) (= (ho_92 k_91 BOUND_VARIABLE_10702) (ho_96 k_95 (ho_94 k_93 BOUND_VARIABLE_10702)))))) (let ((_let_269 (forall ((BOUND_VARIABLE_10695 tptp.pname)) (= (ho_92 k_97 BOUND_VARIABLE_10695) (ho_96 k_95 (ho_94 k_93 BOUND_VARIABLE_10695)))))) (let ((_let_270 (forall ((BOUND_VARIABLE_10687 tptp.pname)) (= (ho_92 k_98 BOUND_VARIABLE_10687) (ho_96 k_95 (ho_102 k_101 (ho_100 k_99 BOUND_VARIABLE_10687))))))) (let ((_let_271 (forall ((BOUND_VARIABLE_11022 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_11019 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 (ho_105 k_104 BOUND_VARIABLE_11022) BOUND_VARIABLE_11019) (= BOUND_VARIABLE_11019 BOUND_VARIABLE_11022))))) (let ((_let_272 (forall ((BOUND_VARIABLE_11044 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_11041 |u_(-> tptp.pname Bool)|)) (= (ho_110 (ho_109 k_108 BOUND_VARIABLE_11044) BOUND_VARIABLE_11041) (= BOUND_VARIABLE_11041 BOUND_VARIABLE_11044))))) (let ((_let_273 (forall ((BOUND_VARIABLE_10666 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10667 tptp.hoare_1262092251_state)) (= (= BOUND_VARIABLE_10666 BOUND_VARIABLE_10667) (ho_103 (ho_112 k_111 BOUND_VARIABLE_10666) BOUND_VARIABLE_10667))))) (let ((_let_274 (forall ((BOUND_VARIABLE_10659 tptp.pname) (BOUND_VARIABLE_10660 tptp.pname)) (= (= BOUND_VARIABLE_10659 BOUND_VARIABLE_10660) (ho_107 (ho_114 k_113 BOUND_VARIABLE_10659) BOUND_VARIABLE_10660))))) (let ((_let_275 (forall ((BOUND_VARIABLE_11083 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_11081 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_11080 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 (ho_117 (ho_116 k_115 BOUND_VARIABLE_11083) BOUND_VARIABLE_11081) BOUND_VARIABLE_11080) (and (= BOUND_VARIABLE_11080 BOUND_VARIABLE_11083) (ho_106 BOUND_VARIABLE_11081 BOUND_VARIABLE_11080)))))) (let ((_let_276 (forall ((BOUND_VARIABLE_11106 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_11104 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_11103 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 (ho_117 (ho_116 k_118 BOUND_VARIABLE_11106) BOUND_VARIABLE_11104) BOUND_VARIABLE_11103) (and (= BOUND_VARIABLE_11103 BOUND_VARIABLE_11106) (ho_106 BOUND_VARIABLE_11104 BOUND_VARIABLE_11103)))))) (let ((_let_277 (forall ((BOUND_VARIABLE_11122 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_11120 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_11119 |u_(-> tptp.pname Bool)|)) (= (ho_110 (ho_121 (ho_120 k_119 BOUND_VARIABLE_11122) BOUND_VARIABLE_11120) BOUND_VARIABLE_11119) (and (= BOUND_VARIABLE_11119 BOUND_VARIABLE_11122) (ho_110 BOUND_VARIABLE_11120 BOUND_VARIABLE_11119)))))) (let ((_let_278 (forall ((BOUND_VARIABLE_11145 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_11143 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_11142 |u_(-> tptp.pname Bool)|)) (= (ho_110 (ho_121 (ho_120 k_122 BOUND_VARIABLE_11145) BOUND_VARIABLE_11143) BOUND_VARIABLE_11142) (and (= BOUND_VARIABLE_11142 BOUND_VARIABLE_11145) (ho_110 BOUND_VARIABLE_11143 BOUND_VARIABLE_11142)))))) (let ((_let_279 (forall ((BOUND_VARIABLE_10609 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11158 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10611 tptp.hoare_1262092251_state)) (= (and (= BOUND_VARIABLE_10609 BOUND_VARIABLE_10611) (ho_103 BOUND_VARIABLE_11158 BOUND_VARIABLE_10611)) (ho_103 (ho_125 (ho_124 k_123 BOUND_VARIABLE_10609) BOUND_VARIABLE_11158) BOUND_VARIABLE_10611))))) (let ((_let_280 (forall ((BOUND_VARIABLE_10599 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11178 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10601 tptp.hoare_1262092251_state)) (= (and (= BOUND_VARIABLE_10599 BOUND_VARIABLE_10601) (ho_103 BOUND_VARIABLE_11178 BOUND_VARIABLE_10601)) (ho_103 (ho_125 (ho_124 k_126 BOUND_VARIABLE_10599) BOUND_VARIABLE_11178) BOUND_VARIABLE_10601))))) (let ((_let_281 (forall ((BOUND_VARIABLE_10589 tptp.pname) (BOUND_VARIABLE_11191 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10591 tptp.pname)) (= (and (= BOUND_VARIABLE_10589 BOUND_VARIABLE_10591) (ho_107 BOUND_VARIABLE_11191 BOUND_VARIABLE_10591)) (ho_107 (ho_129 (ho_128 k_127 BOUND_VARIABLE_10589) BOUND_VARIABLE_11191) BOUND_VARIABLE_10591))))) (let ((_let_282 (forall ((BOUND_VARIABLE_10579 tptp.pname) (BOUND_VARIABLE_11211 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10581 tptp.pname)) (= (and (= BOUND_VARIABLE_10579 BOUND_VARIABLE_10581) (ho_107 BOUND_VARIABLE_11211 BOUND_VARIABLE_10581)) (ho_107 (ho_129 (ho_128 k_130 BOUND_VARIABLE_10579) BOUND_VARIABLE_11211) BOUND_VARIABLE_10581))))) (let ((_let_283 (forall ((BOUND_VARIABLE_11227 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_11225 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_11224 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 (ho_117 (ho_116 k_131 BOUND_VARIABLE_11227) BOUND_VARIABLE_11225) BOUND_VARIABLE_11224) (and (= BOUND_VARIABLE_11224 BOUND_VARIABLE_11227) (ho_106 BOUND_VARIABLE_11225 BOUND_VARIABLE_11224)))))) (let ((_let_284 (forall ((BOUND_VARIABLE_11243 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_11241 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_11240 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 (ho_117 (ho_116 k_132 BOUND_VARIABLE_11243) BOUND_VARIABLE_11241) BOUND_VARIABLE_11240) (and (= BOUND_VARIABLE_11240 BOUND_VARIABLE_11243) (ho_106 BOUND_VARIABLE_11241 BOUND_VARIABLE_11240)))))) (let ((_let_285 (forall ((BOUND_VARIABLE_11259 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_11257 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_11256 |u_(-> tptp.pname Bool)|)) (= (ho_110 (ho_121 (ho_120 k_133 BOUND_VARIABLE_11259) BOUND_VARIABLE_11257) BOUND_VARIABLE_11256) (and (= BOUND_VARIABLE_11256 BOUND_VARIABLE_11259) (ho_110 BOUND_VARIABLE_11257 BOUND_VARIABLE_11256)))))) (let ((_let_286 (forall ((BOUND_VARIABLE_11275 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_11273 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_11272 |u_(-> tptp.pname Bool)|)) (= (ho_110 (ho_121 (ho_120 k_134 BOUND_VARIABLE_11275) BOUND_VARIABLE_11273) BOUND_VARIABLE_11272) (and (= BOUND_VARIABLE_11272 BOUND_VARIABLE_11275) (ho_110 BOUND_VARIABLE_11273 BOUND_VARIABLE_11272)))))) (let ((_let_287 (forall ((BOUND_VARIABLE_10529 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11288 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10531 tptp.hoare_1262092251_state)) (= (and (= BOUND_VARIABLE_10529 BOUND_VARIABLE_10531) (ho_103 BOUND_VARIABLE_11288 BOUND_VARIABLE_10531)) (ho_103 (ho_125 (ho_124 k_135 BOUND_VARIABLE_10529) BOUND_VARIABLE_11288) BOUND_VARIABLE_10531))))) (let ((_let_288 (forall ((BOUND_VARIABLE_10519 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11301 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10521 tptp.hoare_1262092251_state)) (= (and (= BOUND_VARIABLE_10519 BOUND_VARIABLE_10521) (ho_103 BOUND_VARIABLE_11301 BOUND_VARIABLE_10521)) (ho_103 (ho_125 (ho_124 k_136 BOUND_VARIABLE_10519) BOUND_VARIABLE_11301) BOUND_VARIABLE_10521))))) (let ((_let_289 (forall ((BOUND_VARIABLE_10509 tptp.pname) (BOUND_VARIABLE_11314 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10511 tptp.pname)) (= (and (= BOUND_VARIABLE_10509 BOUND_VARIABLE_10511) (ho_107 BOUND_VARIABLE_11314 BOUND_VARIABLE_10511)) (ho_107 (ho_129 (ho_128 k_137 BOUND_VARIABLE_10509) BOUND_VARIABLE_11314) BOUND_VARIABLE_10511))))) (let ((_let_290 (forall ((BOUND_VARIABLE_10499 tptp.pname) (BOUND_VARIABLE_11327 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10501 tptp.pname)) (= (and (= BOUND_VARIABLE_10499 BOUND_VARIABLE_10501) (ho_107 BOUND_VARIABLE_11327 BOUND_VARIABLE_10501)) (ho_107 (ho_129 (ho_128 k_138 BOUND_VARIABLE_10499) BOUND_VARIABLE_11327) BOUND_VARIABLE_10501))))) (let ((_let_291 (forall ((BOUND_VARIABLE_11345 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_11344 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_11343 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 (ho_117 (ho_116 k_139 BOUND_VARIABLE_11345) BOUND_VARIABLE_11344) BOUND_VARIABLE_11343) (or (= BOUND_VARIABLE_11343 BOUND_VARIABLE_11345) (ho_142 (ho_141 k_140 BOUND_VARIABLE_11343) BOUND_VARIABLE_11344)))))) (let ((_let_292 (forall ((BOUND_VARIABLE_11371 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_11370 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_11369 |u_(-> tptp.pname Bool)|)) (= (ho_110 (ho_121 (ho_120 k_143 BOUND_VARIABLE_11371) BOUND_VARIABLE_11370) BOUND_VARIABLE_11369) (or (= BOUND_VARIABLE_11369 BOUND_VARIABLE_11371) (ho_146 (ho_145 k_144 BOUND_VARIABLE_11369) BOUND_VARIABLE_11370)))))) (let ((_let_293 (forall ((BOUND_VARIABLE_10466 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11395 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10468 tptp.hoare_1262092251_state)) (= (ho_103 (ho_125 (ho_124 k_147 BOUND_VARIABLE_10466) BOUND_VARIABLE_11395) BOUND_VARIABLE_10468) (or (= BOUND_VARIABLE_10466 BOUND_VARIABLE_10468) (ho_106 (ho_149 k_148 BOUND_VARIABLE_10468) BOUND_VARIABLE_11395)))))) (let ((_let_294 (forall ((BOUND_VARIABLE_10455 tptp.pname) (BOUND_VARIABLE_11414 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10457 tptp.pname)) (= (ho_107 (ho_129 (ho_128 k_150 BOUND_VARIABLE_10455) BOUND_VARIABLE_11414) BOUND_VARIABLE_10457) (or (= BOUND_VARIABLE_10455 BOUND_VARIABLE_10457) (ho_110 (ho_152 k_151 BOUND_VARIABLE_10457) BOUND_VARIABLE_11414)))))) (let ((_let_295 (forall ((BOUND_VARIABLE_11435 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_11434 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_11433 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 (ho_117 (ho_154 k_153 BOUND_VARIABLE_11435) BOUND_VARIABLE_11434) BOUND_VARIABLE_11433) (or (ho_106 BOUND_VARIABLE_11435 BOUND_VARIABLE_11433) (ho_106 BOUND_VARIABLE_11434 BOUND_VARIABLE_11433)))))) (let ((_let_296 (forall ((BOUND_VARIABLE_11455 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_11454 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_11453 |u_(-> tptp.pname Bool)|)) (= (ho_110 (ho_121 (ho_156 k_155 BOUND_VARIABLE_11455) BOUND_VARIABLE_11454) BOUND_VARIABLE_11453) (or (ho_110 BOUND_VARIABLE_11455 BOUND_VARIABLE_11453) (ho_110 BOUND_VARIABLE_11454 BOUND_VARIABLE_11453)))))) (let ((_let_297 (forall ((BOUND_VARIABLE_11474 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_11473 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10427 tptp.hoare_1262092251_state)) (= (ho_103 (ho_125 (ho_158 k_157 BOUND_VARIABLE_11474) BOUND_VARIABLE_11473) BOUND_VARIABLE_10427) (or (ho_103 BOUND_VARIABLE_11474 BOUND_VARIABLE_10427) (ho_103 BOUND_VARIABLE_11473 BOUND_VARIABLE_10427)))))) (let ((_let_298 (forall ((BOUND_VARIABLE_11493 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_11492 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10417 tptp.pname)) (= (ho_107 (ho_129 (ho_160 k_159 BOUND_VARIABLE_11493) BOUND_VARIABLE_11492) BOUND_VARIABLE_10417) (or (ho_107 BOUND_VARIABLE_11493 BOUND_VARIABLE_10417) (ho_107 BOUND_VARIABLE_11492 BOUND_VARIABLE_10417)))))) (let ((_let_299 (forall ((BOUND_VARIABLE_11513 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_11512 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_11511 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 (ho_117 (ho_116 k_161 BOUND_VARIABLE_11513) BOUND_VARIABLE_11512) BOUND_VARIABLE_11511) (or (= BOUND_VARIABLE_11511 BOUND_VARIABLE_11513) (ho_142 (ho_141 k_140 BOUND_VARIABLE_11511) BOUND_VARIABLE_11512)))))) (let ((_let_300 (forall ((BOUND_VARIABLE_11530 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_11529 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_11528 |u_(-> tptp.pname Bool)|)) (= (ho_110 (ho_121 (ho_120 k_162 BOUND_VARIABLE_11530) BOUND_VARIABLE_11529) BOUND_VARIABLE_11528) (or (= BOUND_VARIABLE_11528 BOUND_VARIABLE_11530) (ho_146 (ho_145 k_144 BOUND_VARIABLE_11528) BOUND_VARIABLE_11529)))))) (let ((_let_301 (forall ((BOUND_VARIABLE_10382 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11545 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10384 tptp.hoare_1262092251_state)) (= (ho_103 (ho_125 (ho_124 k_163 BOUND_VARIABLE_10382) BOUND_VARIABLE_11545) BOUND_VARIABLE_10384) (or (= BOUND_VARIABLE_10382 BOUND_VARIABLE_10384) (ho_106 (ho_149 k_148 BOUND_VARIABLE_10384) BOUND_VARIABLE_11545)))))) (let ((_let_302 (forall ((BOUND_VARIABLE_10371 tptp.pname) (BOUND_VARIABLE_11559 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10373 tptp.pname)) (= (ho_107 (ho_129 (ho_128 k_164 BOUND_VARIABLE_10371) BOUND_VARIABLE_11559) BOUND_VARIABLE_10373) (or (= BOUND_VARIABLE_10371 BOUND_VARIABLE_10373) (ho_110 (ho_152 k_151 BOUND_VARIABLE_10373) BOUND_VARIABLE_11559)))))) (let ((_let_303 (forall ((BOUND_VARIABLE_11573 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_11571 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_11570 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 (ho_117 (ho_116 k_165 BOUND_VARIABLE_11573) BOUND_VARIABLE_11571) BOUND_VARIABLE_11570) (or (= BOUND_VARIABLE_11570 BOUND_VARIABLE_11573) (ho_106 BOUND_VARIABLE_11571 BOUND_VARIABLE_11570)))))) (let ((_let_304 (forall ((BOUND_VARIABLE_11589 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_11587 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_11586 |u_(-> tptp.pname Bool)|)) (= (ho_110 (ho_121 (ho_120 k_166 BOUND_VARIABLE_11589) BOUND_VARIABLE_11587) BOUND_VARIABLE_11586) (or (= BOUND_VARIABLE_11586 BOUND_VARIABLE_11589) (ho_110 BOUND_VARIABLE_11587 BOUND_VARIABLE_11586)))))) (let ((_let_305 (forall ((BOUND_VARIABLE_10338 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11602 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10340 tptp.hoare_1262092251_state)) (= (or (= BOUND_VARIABLE_10338 BOUND_VARIABLE_10340) (ho_103 BOUND_VARIABLE_11602 BOUND_VARIABLE_10340)) (ho_103 (ho_125 (ho_124 k_167 BOUND_VARIABLE_10338) BOUND_VARIABLE_11602) BOUND_VARIABLE_10340))))) (let ((_let_306 (forall ((BOUND_VARIABLE_10327 tptp.pname) (BOUND_VARIABLE_11615 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10329 tptp.pname)) (= (or (= BOUND_VARIABLE_10327 BOUND_VARIABLE_10329) (ho_107 BOUND_VARIABLE_11615 BOUND_VARIABLE_10329)) (ho_107 (ho_129 (ho_128 k_168 BOUND_VARIABLE_10327) BOUND_VARIABLE_11615) BOUND_VARIABLE_10329))))) (let ((_let_307 (forall ((BOUND_VARIABLE_10321 tptp.pname) (BOUND_VARIABLE_11630 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= BOUND_VARIABLE_10321 (ho_171 (ho_170 k_169 BOUND_VARIABLE_10321) BOUND_VARIABLE_11630))))) (let ((_let_308 (forall ((BOUND_VARIABLE_10315 tptp.pname) (BOUND_VARIABLE_11647 |u_(-> tptp.pname Bool)|)) (= BOUND_VARIABLE_10315 (ho_174 (ho_173 k_172 BOUND_VARIABLE_10315) BOUND_VARIABLE_11647))))) (let ((_let_309 (forall ((BOUND_VARIABLE_10309 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11664 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= BOUND_VARIABLE_10309 (ho_177 (ho_176 k_175 BOUND_VARIABLE_10309) BOUND_VARIABLE_11664))))) (let ((_let_310 (forall ((BOUND_VARIABLE_10303 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11681 |u_(-> tptp.pname Bool)|)) (= BOUND_VARIABLE_10303 (ho_180 (ho_179 k_178 BOUND_VARIABLE_10303) BOUND_VARIABLE_11681))))) (let ((_let_311 (forall ((BOUND_VARIABLE_10297 tptp.pname) (BOUND_VARIABLE_10298 tptp.pname)) (= BOUND_VARIABLE_10297 (ho_183 (ho_182 k_181 BOUND_VARIABLE_10297) BOUND_VARIABLE_10298))))) (let ((_let_312 (forall ((BOUND_VARIABLE_11712 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10290 tptp.pname) (BOUND_VARIABLE_10291 tptp.hoare_1262092251_state)) (= (ho_103 (ho_186 (ho_185 k_184 BOUND_VARIABLE_11712) BOUND_VARIABLE_10290) BOUND_VARIABLE_10291) (ho_103 BOUND_VARIABLE_11712 BOUND_VARIABLE_10291))))) (let ((_let_313 (forall ((BOUND_VARIABLE_11731 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10282 tptp.pname) (BOUND_VARIABLE_10283 tptp.pname)) (= (ho_107 (ho_114 (ho_188 k_187 BOUND_VARIABLE_11731) BOUND_VARIABLE_10282) BOUND_VARIABLE_10283) (ho_107 BOUND_VARIABLE_11731 BOUND_VARIABLE_10283))))) (let ((_let_314 (forall ((BOUND_VARIABLE_11747 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10274 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10275 tptp.hoare_1262092251_state)) (= (ho_103 (ho_112 (ho_190 k_189 BOUND_VARIABLE_11747) BOUND_VARIABLE_10274) BOUND_VARIABLE_10275) (ho_103 BOUND_VARIABLE_11747 BOUND_VARIABLE_10275))))) (let ((_let_315 (forall ((BOUND_VARIABLE_11763 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10266 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10267 tptp.pname)) (= (ho_107 (ho_193 (ho_192 k_191 BOUND_VARIABLE_11763) BOUND_VARIABLE_10266) BOUND_VARIABLE_10267) (ho_107 BOUND_VARIABLE_11763 BOUND_VARIABLE_10267))))) (let ((_let_316 (forall ((BOUND_VARIABLE_10259 tptp.pname) (BOUND_VARIABLE_10260 tptp.hoare_1262092251_state)) (= BOUND_VARIABLE_10259 (ho_196 (ho_195 k_194 BOUND_VARIABLE_10259) BOUND_VARIABLE_10260))))) (let ((_let_317 (forall ((BOUND_VARIABLE_10253 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10254 tptp.pname)) (= BOUND_VARIABLE_10253 (ho_92 (ho_198 k_197 BOUND_VARIABLE_10253) BOUND_VARIABLE_10254))))) (let ((_let_318 (forall ((BOUND_VARIABLE_10247 tptp.pname) (BOUND_VARIABLE_11804 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= BOUND_VARIABLE_10247 (ho_171 (ho_170 k_199 BOUND_VARIABLE_10247) BOUND_VARIABLE_11804))))) (let ((_let_319 (forall ((BOUND_VARIABLE_10241 tptp.pname) (BOUND_VARIABLE_11813 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= BOUND_VARIABLE_10241 (ho_171 (ho_170 k_200 BOUND_VARIABLE_10241) BOUND_VARIABLE_11813))))) (let ((_let_320 (forall ((BOUND_VARIABLE_10235 tptp.pname) (BOUND_VARIABLE_11822 |u_(-> tptp.pname Bool)|)) (= BOUND_VARIABLE_10235 (ho_174 (ho_173 k_201 BOUND_VARIABLE_10235) BOUND_VARIABLE_11822))))) (let ((_let_321 (forall ((BOUND_VARIABLE_10229 tptp.pname) (BOUND_VARIABLE_11831 |u_(-> tptp.pname Bool)|)) (= BOUND_VARIABLE_10229 (ho_174 (ho_173 k_202 BOUND_VARIABLE_10229) BOUND_VARIABLE_11831))))) (let ((_let_322 (forall ((BOUND_VARIABLE_10223 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11840 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= BOUND_VARIABLE_10223 (ho_177 (ho_176 k_203 BOUND_VARIABLE_10223) BOUND_VARIABLE_11840))))) (let ((_let_323 (forall ((BOUND_VARIABLE_10217 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11849 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= BOUND_VARIABLE_10217 (ho_177 (ho_176 k_204 BOUND_VARIABLE_10217) BOUND_VARIABLE_11849))))) (let ((_let_324 (forall ((BOUND_VARIABLE_10211 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11858 |u_(-> tptp.pname Bool)|)) (= BOUND_VARIABLE_10211 (ho_180 (ho_179 k_205 BOUND_VARIABLE_10211) BOUND_VARIABLE_11858))))) (let ((_let_325 (forall ((BOUND_VARIABLE_10205 tptp.hoare_1262092251_state) (BOUND_VARIABLE_11867 |u_(-> tptp.pname Bool)|)) (= BOUND_VARIABLE_10205 (ho_180 (ho_179 k_206 BOUND_VARIABLE_10205) BOUND_VARIABLE_11867))))) (let ((_let_326 (forall ((BOUND_VARIABLE_10199 tptp.pname) (BOUND_VARIABLE_10200 tptp.pname)) (= BOUND_VARIABLE_10199 (ho_183 (ho_182 k_207 BOUND_VARIABLE_10199) BOUND_VARIABLE_10200))))) (let ((_let_327 (forall ((BOUND_VARIABLE_10193 tptp.pname) (BOUND_VARIABLE_10194 tptp.pname)) (= BOUND_VARIABLE_10193 (ho_183 (ho_182 k_208 BOUND_VARIABLE_10193) BOUND_VARIABLE_10194))))) (let ((_let_328 (forall ((BOUND_VARIABLE_11891 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10186 tptp.pname) (BOUND_VARIABLE_10187 tptp.hoare_1262092251_state)) (= (ho_103 (ho_186 (ho_185 k_209 BOUND_VARIABLE_11891) BOUND_VARIABLE_10186) BOUND_VARIABLE_10187) (ho_103 BOUND_VARIABLE_11891 BOUND_VARIABLE_10187))))) (let ((_let_329 (forall ((BOUND_VARIABLE_11903 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10178 tptp.pname) (BOUND_VARIABLE_10179 tptp.hoare_1262092251_state)) (= (ho_103 (ho_186 (ho_185 k_210 BOUND_VARIABLE_11903) BOUND_VARIABLE_10178) BOUND_VARIABLE_10179) (ho_103 BOUND_VARIABLE_11903 BOUND_VARIABLE_10179))))) (let ((_let_330 (forall ((BOUND_VARIABLE_11915 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10170 tptp.pname) (BOUND_VARIABLE_10171 tptp.pname)) (= (ho_107 (ho_114 (ho_188 k_211 BOUND_VARIABLE_11915) BOUND_VARIABLE_10170) BOUND_VARIABLE_10171) (ho_107 BOUND_VARIABLE_11915 BOUND_VARIABLE_10171))))) (let ((_let_331 (forall ((BOUND_VARIABLE_11927 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10162 tptp.pname) (BOUND_VARIABLE_10163 tptp.pname)) (= (ho_107 (ho_114 (ho_188 k_212 BOUND_VARIABLE_11927) BOUND_VARIABLE_10162) BOUND_VARIABLE_10163) (ho_107 BOUND_VARIABLE_11927 BOUND_VARIABLE_10163))))) (let ((_let_332 (forall ((BOUND_VARIABLE_11939 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10154 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10155 tptp.hoare_1262092251_state)) (= (ho_103 (ho_112 (ho_190 k_213 BOUND_VARIABLE_11939) BOUND_VARIABLE_10154) BOUND_VARIABLE_10155) (ho_103 BOUND_VARIABLE_11939 BOUND_VARIABLE_10155))))) (let ((_let_333 (forall ((BOUND_VARIABLE_11951 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10146 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10147 tptp.hoare_1262092251_state)) (= (ho_103 (ho_112 (ho_190 k_214 BOUND_VARIABLE_11951) BOUND_VARIABLE_10146) BOUND_VARIABLE_10147) (ho_103 BOUND_VARIABLE_11951 BOUND_VARIABLE_10147))))) (let ((_let_334 (forall ((BOUND_VARIABLE_11963 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10138 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10139 tptp.pname)) (= (ho_107 (ho_193 (ho_192 k_215 BOUND_VARIABLE_11963) BOUND_VARIABLE_10138) BOUND_VARIABLE_10139) (ho_107 BOUND_VARIABLE_11963 BOUND_VARIABLE_10139))))) (let ((_let_335 (forall ((BOUND_VARIABLE_11975 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10130 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10131 tptp.pname)) (= (ho_107 (ho_193 (ho_192 k_216 BOUND_VARIABLE_11975) BOUND_VARIABLE_10130) BOUND_VARIABLE_10131) (ho_107 BOUND_VARIABLE_11975 BOUND_VARIABLE_10131))))) (let ((_let_336 (forall ((BOUND_VARIABLE_10123 tptp.pname) (BOUND_VARIABLE_10124 tptp.hoare_1262092251_state)) (= BOUND_VARIABLE_10123 (ho_196 (ho_195 k_217 BOUND_VARIABLE_10123) BOUND_VARIABLE_10124))))) (let ((_let_337 (forall ((BOUND_VARIABLE_10117 tptp.pname) (BOUND_VARIABLE_10118 tptp.hoare_1262092251_state)) (= BOUND_VARIABLE_10117 (ho_196 (ho_195 k_218 BOUND_VARIABLE_10117) BOUND_VARIABLE_10118))))) (let ((_let_338 (forall ((BOUND_VARIABLE_10111 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10112 tptp.pname)) (= BOUND_VARIABLE_10111 (ho_92 (ho_198 k_219 BOUND_VARIABLE_10111) BOUND_VARIABLE_10112))))) (let ((_let_339 (forall ((BOUND_VARIABLE_10105 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10106 tptp.pname)) (= BOUND_VARIABLE_10105 (ho_92 (ho_198 k_220 BOUND_VARIABLE_10105) BOUND_VARIABLE_10106))))) (let ((_let_340 (forall ((BOUND_VARIABLE_12017 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_12016 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_12015 |u_(-> tptp.pname Bool)|)) (= (ho_110 (ho_121 (ho_156 k_221 BOUND_VARIABLE_12017) BOUND_VARIABLE_12016) BOUND_VARIABLE_12015) (and (ho_110 BOUND_VARIABLE_12017 BOUND_VARIABLE_12015) (ho_110 BOUND_VARIABLE_12016 BOUND_VARIABLE_12015)))))) (let ((_let_341 (forall ((BOUND_VARIABLE_12033 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_12032 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_12031 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 (ho_117 (ho_154 k_222 BOUND_VARIABLE_12033) BOUND_VARIABLE_12032) BOUND_VARIABLE_12031) (and (ho_106 BOUND_VARIABLE_12033 BOUND_VARIABLE_12031) (ho_106 BOUND_VARIABLE_12032 BOUND_VARIABLE_12031)))))) (let ((_let_342 (forall ((BOUND_VARIABLE_12049 |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (BOUND_VARIABLE_12048 |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (BOUND_VARIABLE_12047 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_142 (ho_225 (ho_224 k_223 BOUND_VARIABLE_12049) BOUND_VARIABLE_12048) BOUND_VARIABLE_12047) (and (ho_142 BOUND_VARIABLE_12049 BOUND_VARIABLE_12047) (ho_142 BOUND_VARIABLE_12048 BOUND_VARIABLE_12047)))))) (let ((_let_343 (forall ((BOUND_VARIABLE_12072 |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (BOUND_VARIABLE_12071 |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (BOUND_VARIABLE_12070 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_146 (ho_228 (ho_227 k_226 BOUND_VARIABLE_12072) BOUND_VARIABLE_12071) BOUND_VARIABLE_12070) (and (ho_146 BOUND_VARIABLE_12072 BOUND_VARIABLE_12070) (ho_146 BOUND_VARIABLE_12071 BOUND_VARIABLE_12070)))))) (let ((_let_344 (forall ((BOUND_VARIABLE_12094 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_12093 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_10057 tptp.hoare_1262092251_state)) (= (ho_103 (ho_125 (ho_158 k_229 BOUND_VARIABLE_12094) BOUND_VARIABLE_12093) BOUND_VARIABLE_10057) (and (ho_103 BOUND_VARIABLE_12094 BOUND_VARIABLE_10057) (ho_103 BOUND_VARIABLE_12093 BOUND_VARIABLE_10057)))))) (let ((_let_345 (forall ((BOUND_VARIABLE_12109 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_12108 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_10047 tptp.pname)) (= (ho_107 (ho_129 (ho_160 k_230 BOUND_VARIABLE_12109) BOUND_VARIABLE_12108) BOUND_VARIABLE_10047) (and (ho_107 BOUND_VARIABLE_12109 BOUND_VARIABLE_10047) (ho_107 BOUND_VARIABLE_12108 BOUND_VARIABLE_10047)))))) (let ((_let_346 (forall ((BOUND_VARIABLE_12121 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (not (ho_142 k_231 BOUND_VARIABLE_12121))))) (let ((_let_347 (forall ((BOUND_VARIABLE_10035 tptp.pname)) (not (ho_107 k_232 BOUND_VARIABLE_10035))))) (let ((_let_348 (forall ((BOUND_VARIABLE_12133 |u_(-> tptp.hoare_1262092251_state Bool)|)) (not (ho_106 k_233 BOUND_VARIABLE_12133))))) (let ((_let_349 (forall ((BOUND_VARIABLE_12140 |u_(-> tptp.pname Bool)|)) (not (ho_110 k_234 BOUND_VARIABLE_12140))))) (let ((_let_350 (forall ((BOUND_VARIABLE_12149 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|) (BOUND_VARIABLE_12148 |u_(-> _u_(-> tptp.pname Bool)_ Bool)|)) (= (ho_146 (ho_236 k_235 BOUND_VARIABLE_12149) BOUND_VARIABLE_12148) (ho_146 (ho_236 k_237 BOUND_VARIABLE_12148) BOUND_VARIABLE_12149))))) (let ((_let_351 (forall ((BOUND_VARIABLE_12166 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|) (BOUND_VARIABLE_12165 |u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)|)) (= (ho_142 (ho_239 k_238 BOUND_VARIABLE_12166) BOUND_VARIABLE_12165) (ho_142 (ho_239 k_240 BOUND_VARIABLE_12165) BOUND_VARIABLE_12166))))) (let ((_let_352 (forall ((BOUND_VARIABLE_12183 |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|) (BOUND_VARIABLE_12182 |u_(-> _u_(-> _u_(-> tptp.hoare_1262092251_state Bool)_ Bool)_ Bool)|)) (= (ho_243 (ho_242 k_241 BOUND_VARIABLE_12183) BOUND_VARIABLE_12182) (ho_243 (ho_242 k_244 BOUND_VARIABLE_12182) BOUND_VARIABLE_12183))))) (let ((_let_353 (forall ((BOUND_VARIABLE_12204 |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|) (BOUND_VARIABLE_12203 |u_(-> _u_(-> _u_(-> tptp.pname Bool)_ Bool)_ Bool)|)) (= (ho_247 (ho_246 k_245 BOUND_VARIABLE_12204) BOUND_VARIABLE_12203) (ho_247 (ho_246 k_248 BOUND_VARIABLE_12203) BOUND_VARIABLE_12204))))) (let ((_let_354 (forall ((BOUND_VARIABLE_12225 |u_(-> tptp.hoare_1262092251_state Bool)|) (BOUND_VARIABLE_12224 |u_(-> tptp.hoare_1262092251_state Bool)|)) (= (ho_106 (ho_105 k_249 BOUND_VARIABLE_12225) BOUND_VARIABLE_12224) (ho_106 (ho_105 k_250 BOUND_VARIABLE_12224) BOUND_VARIABLE_12225))))) (let ((_let_355 (forall ((BOUND_VARIABLE_12238 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_12237 |u_(-> tptp.pname Bool)|)) (= (ho_110 (ho_109 k_251 BOUND_VARIABLE_12238) BOUND_VARIABLE_12237) (ho_110 (ho_109 k_252 BOUND_VARIABLE_12237) BOUND_VARIABLE_12238))))) (let ((_let_356 (forall ((BOUND_VARIABLE_9972 tptp.hoare_1262092251_state)) (not (ho_103 k_253 BOUND_VARIABLE_9972))))) (let ((_let_357 (forall ((BOUND_VARIABLE_10702 tptp.pname)) (= (@ tptp.hoare_Mirabelle_MGT (@ tptp.body_1 BOUND_VARIABLE_10702)) (ll_90 BOUND_VARIABLE_10702))))) (let ((_let_358 (forall ((BOUND_VARIABLE_10695 tptp.pname)) (= (@ tptp.hoare_Mirabelle_MGT (@ tptp.body_1 BOUND_VARIABLE_10695)) (ll_89 BOUND_VARIABLE_10695))))) (let ((_let_359 (forall ((BOUND_VARIABLE_10687 tptp.pname)) (= (@ tptp.hoare_Mirabelle_MGT (@ tptp.the_com (@ tptp.body BOUND_VARIABLE_10687))) (ll_88 BOUND_VARIABLE_10687))))) (let ((_let_360 (forall ((BOUND_VARIABLE_10680 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10681 (-> tptp.hoare_1262092251_state Bool))) (= (= BOUND_VARIABLE_10680 BOUND_VARIABLE_10681) (ll_87 BOUND_VARIABLE_10680 BOUND_VARIABLE_10681))))) (let ((_let_361 (forall ((BOUND_VARIABLE_10673 (-> tptp.pname Bool)) (BOUND_VARIABLE_10674 (-> tptp.pname Bool))) (= (= BOUND_VARIABLE_10673 BOUND_VARIABLE_10674) (ll_86 BOUND_VARIABLE_10673 BOUND_VARIABLE_10674))))) (let ((_let_362 (forall ((BOUND_VARIABLE_10666 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10667 tptp.hoare_1262092251_state)) (= (= BOUND_VARIABLE_10666 BOUND_VARIABLE_10667) (ll_85 BOUND_VARIABLE_10666 BOUND_VARIABLE_10667))))) (let ((_let_363 (forall ((BOUND_VARIABLE_10659 tptp.pname) (BOUND_VARIABLE_10660 tptp.pname)) (= (= BOUND_VARIABLE_10659 BOUND_VARIABLE_10660) (ll_84 BOUND_VARIABLE_10659 BOUND_VARIABLE_10660))))) (let ((_let_364 (forall ((BOUND_VARIABLE_10649 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10650 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10651 (-> tptp.hoare_1262092251_state Bool))) (= (ll_83 BOUND_VARIABLE_10649 BOUND_VARIABLE_10650 BOUND_VARIABLE_10651) (and (= BOUND_VARIABLE_10649 BOUND_VARIABLE_10651) (@ BOUND_VARIABLE_10650 BOUND_VARIABLE_10651)))))) (let ((_let_365 (forall ((BOUND_VARIABLE_10639 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10640 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10641 (-> tptp.hoare_1262092251_state Bool))) (= (ll_82 BOUND_VARIABLE_10639 BOUND_VARIABLE_10640 BOUND_VARIABLE_10641) (and (= BOUND_VARIABLE_10639 BOUND_VARIABLE_10641) (@ BOUND_VARIABLE_10640 BOUND_VARIABLE_10641)))))) (let ((_let_366 (forall ((BOUND_VARIABLE_10629 (-> tptp.pname Bool)) (BOUND_VARIABLE_10630 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10631 (-> tptp.pname Bool))) (= (ll_81 BOUND_VARIABLE_10629 BOUND_VARIABLE_10630 BOUND_VARIABLE_10631) (and (= BOUND_VARIABLE_10629 BOUND_VARIABLE_10631) (@ BOUND_VARIABLE_10630 BOUND_VARIABLE_10631)))))) (let ((_let_367 (forall ((BOUND_VARIABLE_10619 (-> tptp.pname Bool)) (BOUND_VARIABLE_10620 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10621 (-> tptp.pname Bool))) (= (ll_80 BOUND_VARIABLE_10619 BOUND_VARIABLE_10620 BOUND_VARIABLE_10621) (and (= BOUND_VARIABLE_10619 BOUND_VARIABLE_10621) (@ BOUND_VARIABLE_10620 BOUND_VARIABLE_10621)))))) (let ((_let_368 (forall ((BOUND_VARIABLE_10609 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10610 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10611 tptp.hoare_1262092251_state)) (= (ll_79 BOUND_VARIABLE_10609 BOUND_VARIABLE_10610 BOUND_VARIABLE_10611) (and (= BOUND_VARIABLE_10609 BOUND_VARIABLE_10611) (@ BOUND_VARIABLE_10610 BOUND_VARIABLE_10611)))))) (let ((_let_369 (forall ((BOUND_VARIABLE_10599 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10600 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10601 tptp.hoare_1262092251_state)) (= (ll_78 BOUND_VARIABLE_10599 BOUND_VARIABLE_10600 BOUND_VARIABLE_10601) (and (= BOUND_VARIABLE_10599 BOUND_VARIABLE_10601) (@ BOUND_VARIABLE_10600 BOUND_VARIABLE_10601)))))) (let ((_let_370 (forall ((BOUND_VARIABLE_10589 tptp.pname) (BOUND_VARIABLE_10590 (-> tptp.pname Bool)) (BOUND_VARIABLE_10591 tptp.pname)) (= (ll_77 BOUND_VARIABLE_10589 BOUND_VARIABLE_10590 BOUND_VARIABLE_10591) (and (= BOUND_VARIABLE_10589 BOUND_VARIABLE_10591) (@ BOUND_VARIABLE_10590 BOUND_VARIABLE_10591)))))) (let ((_let_371 (forall ((BOUND_VARIABLE_10579 tptp.pname) (BOUND_VARIABLE_10580 (-> tptp.pname Bool)) (BOUND_VARIABLE_10581 tptp.pname)) (= (ll_76 BOUND_VARIABLE_10579 BOUND_VARIABLE_10580 BOUND_VARIABLE_10581) (and (= BOUND_VARIABLE_10579 BOUND_VARIABLE_10581) (@ BOUND_VARIABLE_10580 BOUND_VARIABLE_10581)))))) (let ((_let_372 (forall ((BOUND_VARIABLE_10569 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10570 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10571 (-> tptp.hoare_1262092251_state Bool))) (= (ll_75 BOUND_VARIABLE_10569 BOUND_VARIABLE_10570 BOUND_VARIABLE_10571) (and (= BOUND_VARIABLE_10569 BOUND_VARIABLE_10571) (@ BOUND_VARIABLE_10570 BOUND_VARIABLE_10571)))))) (let ((_let_373 (forall ((BOUND_VARIABLE_10559 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10560 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10561 (-> tptp.hoare_1262092251_state Bool))) (= (ll_74 BOUND_VARIABLE_10559 BOUND_VARIABLE_10560 BOUND_VARIABLE_10561) (and (= BOUND_VARIABLE_10559 BOUND_VARIABLE_10561) (@ BOUND_VARIABLE_10560 BOUND_VARIABLE_10561)))))) (let ((_let_374 (forall ((BOUND_VARIABLE_10549 (-> tptp.pname Bool)) (BOUND_VARIABLE_10550 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10551 (-> tptp.pname Bool))) (= (ll_73 BOUND_VARIABLE_10549 BOUND_VARIABLE_10550 BOUND_VARIABLE_10551) (and (= BOUND_VARIABLE_10549 BOUND_VARIABLE_10551) (@ BOUND_VARIABLE_10550 BOUND_VARIABLE_10551)))))) (let ((_let_375 (forall ((BOUND_VARIABLE_10539 (-> tptp.pname Bool)) (BOUND_VARIABLE_10540 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10541 (-> tptp.pname Bool))) (= (ll_72 BOUND_VARIABLE_10539 BOUND_VARIABLE_10540 BOUND_VARIABLE_10541) (and (= BOUND_VARIABLE_10539 BOUND_VARIABLE_10541) (@ BOUND_VARIABLE_10540 BOUND_VARIABLE_10541)))))) (let ((_let_376 (forall ((BOUND_VARIABLE_10529 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10530 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10531 tptp.hoare_1262092251_state)) (= (ll_71 BOUND_VARIABLE_10529 BOUND_VARIABLE_10530 BOUND_VARIABLE_10531) (and (= BOUND_VARIABLE_10529 BOUND_VARIABLE_10531) (@ BOUND_VARIABLE_10530 BOUND_VARIABLE_10531)))))) (let ((_let_377 (forall ((BOUND_VARIABLE_10519 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10520 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10521 tptp.hoare_1262092251_state)) (= (ll_70 BOUND_VARIABLE_10519 BOUND_VARIABLE_10520 BOUND_VARIABLE_10521) (and (= BOUND_VARIABLE_10519 BOUND_VARIABLE_10521) (@ BOUND_VARIABLE_10520 BOUND_VARIABLE_10521)))))) (let ((_let_378 (forall ((BOUND_VARIABLE_10509 tptp.pname) (BOUND_VARIABLE_10510 (-> tptp.pname Bool)) (BOUND_VARIABLE_10511 tptp.pname)) (= (ll_69 BOUND_VARIABLE_10509 BOUND_VARIABLE_10510 BOUND_VARIABLE_10511) (and (= BOUND_VARIABLE_10509 BOUND_VARIABLE_10511) (@ BOUND_VARIABLE_10510 BOUND_VARIABLE_10511)))))) (let ((_let_379 (forall ((BOUND_VARIABLE_10499 tptp.pname) (BOUND_VARIABLE_10500 (-> tptp.pname Bool)) (BOUND_VARIABLE_10501 tptp.pname)) (= (ll_68 BOUND_VARIABLE_10499 BOUND_VARIABLE_10500 BOUND_VARIABLE_10501) (and (= BOUND_VARIABLE_10499 BOUND_VARIABLE_10501) (@ BOUND_VARIABLE_10500 BOUND_VARIABLE_10501)))))) (let ((_let_380 (forall ((BOUND_VARIABLE_10488 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10489 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10490 (-> tptp.hoare_1262092251_state Bool))) (= (or (= BOUND_VARIABLE_10488 BOUND_VARIABLE_10490) (@ (@ tptp.member907417095tate_o BOUND_VARIABLE_10490) BOUND_VARIABLE_10489)) (ll_67 BOUND_VARIABLE_10488 BOUND_VARIABLE_10489 BOUND_VARIABLE_10490))))) (let ((_let_381 (forall ((BOUND_VARIABLE_10477 (-> tptp.pname Bool)) (BOUND_VARIABLE_10478 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10479 (-> tptp.pname Bool))) (= (or (= BOUND_VARIABLE_10477 BOUND_VARIABLE_10479) (@ (@ tptp.member_pname_o BOUND_VARIABLE_10479) BOUND_VARIABLE_10478)) (ll_66 BOUND_VARIABLE_10477 BOUND_VARIABLE_10478 BOUND_VARIABLE_10479))))) (let ((_let_382 (forall ((BOUND_VARIABLE_10466 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10467 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10468 tptp.hoare_1262092251_state)) (= (or (= BOUND_VARIABLE_10466 BOUND_VARIABLE_10468) (@ (@ tptp.member5164104_state BOUND_VARIABLE_10468) BOUND_VARIABLE_10467)) (ll_65 BOUND_VARIABLE_10466 BOUND_VARIABLE_10467 BOUND_VARIABLE_10468))))) (let ((_let_383 (forall ((BOUND_VARIABLE_10455 tptp.pname) (BOUND_VARIABLE_10456 (-> tptp.pname Bool)) (BOUND_VARIABLE_10457 tptp.pname)) (= (or (= BOUND_VARIABLE_10455 BOUND_VARIABLE_10457) (@ (@ tptp.member_pname BOUND_VARIABLE_10457) BOUND_VARIABLE_10456)) (ll_64 BOUND_VARIABLE_10455 BOUND_VARIABLE_10456 BOUND_VARIABLE_10457))))) (let ((_let_384 (forall ((BOUND_VARIABLE_10445 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10446 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10447 (-> tptp.hoare_1262092251_state Bool))) (= (or (@ BOUND_VARIABLE_10445 BOUND_VARIABLE_10447) (@ BOUND_VARIABLE_10446 BOUND_VARIABLE_10447)) (ll_63 BOUND_VARIABLE_10445 BOUND_VARIABLE_10446 BOUND_VARIABLE_10447))))) (let ((_let_385 (forall ((BOUND_VARIABLE_10435 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10436 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10437 (-> tptp.pname Bool))) (= (or (@ BOUND_VARIABLE_10435 BOUND_VARIABLE_10437) (@ BOUND_VARIABLE_10436 BOUND_VARIABLE_10437)) (ll_62 BOUND_VARIABLE_10435 BOUND_VARIABLE_10436 BOUND_VARIABLE_10437))))) (let ((_let_386 (forall ((BOUND_VARIABLE_10425 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10426 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10427 tptp.hoare_1262092251_state)) (= (or (@ BOUND_VARIABLE_10425 BOUND_VARIABLE_10427) (@ BOUND_VARIABLE_10426 BOUND_VARIABLE_10427)) (ll_61 BOUND_VARIABLE_10425 BOUND_VARIABLE_10426 BOUND_VARIABLE_10427))))) (let ((_let_387 (forall ((BOUND_VARIABLE_10415 (-> tptp.pname Bool)) (BOUND_VARIABLE_10416 (-> tptp.pname Bool)) (BOUND_VARIABLE_10417 tptp.pname)) (= (or (@ BOUND_VARIABLE_10415 BOUND_VARIABLE_10417) (@ BOUND_VARIABLE_10416 BOUND_VARIABLE_10417)) (ll_60 BOUND_VARIABLE_10415 BOUND_VARIABLE_10416 BOUND_VARIABLE_10417))))) (let ((_let_388 (forall ((BOUND_VARIABLE_10404 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10405 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10406 (-> tptp.hoare_1262092251_state Bool))) (= (or (= BOUND_VARIABLE_10404 BOUND_VARIABLE_10406) (@ (@ tptp.member907417095tate_o BOUND_VARIABLE_10406) BOUND_VARIABLE_10405)) (ll_59 BOUND_VARIABLE_10404 BOUND_VARIABLE_10405 BOUND_VARIABLE_10406))))) (let ((_let_389 (forall ((BOUND_VARIABLE_10393 (-> tptp.pname Bool)) (BOUND_VARIABLE_10394 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10395 (-> tptp.pname Bool))) (= (or (= BOUND_VARIABLE_10393 BOUND_VARIABLE_10395) (@ (@ tptp.member_pname_o BOUND_VARIABLE_10395) BOUND_VARIABLE_10394)) (ll_58 BOUND_VARIABLE_10393 BOUND_VARIABLE_10394 BOUND_VARIABLE_10395))))) (let ((_let_390 (forall ((BOUND_VARIABLE_10382 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10383 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10384 tptp.hoare_1262092251_state)) (= (or (= BOUND_VARIABLE_10382 BOUND_VARIABLE_10384) (@ (@ tptp.member5164104_state BOUND_VARIABLE_10384) BOUND_VARIABLE_10383)) (ll_57 BOUND_VARIABLE_10382 BOUND_VARIABLE_10383 BOUND_VARIABLE_10384))))) (let ((_let_391 (forall ((BOUND_VARIABLE_10371 tptp.pname) (BOUND_VARIABLE_10372 (-> tptp.pname Bool)) (BOUND_VARIABLE_10373 tptp.pname)) (= (or (= BOUND_VARIABLE_10371 BOUND_VARIABLE_10373) (@ (@ tptp.member_pname BOUND_VARIABLE_10373) BOUND_VARIABLE_10372)) (ll_56 BOUND_VARIABLE_10371 BOUND_VARIABLE_10372 BOUND_VARIABLE_10373))))) (let ((_let_392 (forall ((BOUND_VARIABLE_10360 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10361 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10362 (-> tptp.hoare_1262092251_state Bool))) (= (ll_55 BOUND_VARIABLE_10360 BOUND_VARIABLE_10361 BOUND_VARIABLE_10362) (or (= BOUND_VARIABLE_10360 BOUND_VARIABLE_10362) (@ BOUND_VARIABLE_10361 BOUND_VARIABLE_10362)))))) (let ((_let_393 (forall ((BOUND_VARIABLE_10349 (-> tptp.pname Bool)) (BOUND_VARIABLE_10350 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10351 (-> tptp.pname Bool))) (= (ll_54 BOUND_VARIABLE_10349 BOUND_VARIABLE_10350 BOUND_VARIABLE_10351) (or (= BOUND_VARIABLE_10349 BOUND_VARIABLE_10351) (@ BOUND_VARIABLE_10350 BOUND_VARIABLE_10351)))))) (let ((_let_394 (forall ((BOUND_VARIABLE_10338 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10339 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10340 tptp.hoare_1262092251_state)) (= (ll_53 BOUND_VARIABLE_10338 BOUND_VARIABLE_10339 BOUND_VARIABLE_10340) (or (= BOUND_VARIABLE_10338 BOUND_VARIABLE_10340) (@ BOUND_VARIABLE_10339 BOUND_VARIABLE_10340)))))) (let ((_let_395 (forall ((BOUND_VARIABLE_10327 tptp.pname) (BOUND_VARIABLE_10328 (-> tptp.pname Bool)) (BOUND_VARIABLE_10329 tptp.pname)) (= (ll_52 BOUND_VARIABLE_10327 BOUND_VARIABLE_10328 BOUND_VARIABLE_10329) (or (= BOUND_VARIABLE_10327 BOUND_VARIABLE_10329) (@ BOUND_VARIABLE_10328 BOUND_VARIABLE_10329)))))) (let ((_let_396 (forall ((BOUND_VARIABLE_10321 tptp.pname) (BOUND_VARIABLE_10322 (-> tptp.hoare_1262092251_state Bool))) (= BOUND_VARIABLE_10321 (ll_51 BOUND_VARIABLE_10321 BOUND_VARIABLE_10322))))) (let ((_let_397 (forall ((BOUND_VARIABLE_10315 tptp.pname) (BOUND_VARIABLE_10316 (-> tptp.pname Bool))) (= BOUND_VARIABLE_10315 (ll_50 BOUND_VARIABLE_10315 BOUND_VARIABLE_10316))))) (let ((_let_398 (forall ((BOUND_VARIABLE_10309 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10310 (-> tptp.hoare_1262092251_state Bool))) (= BOUND_VARIABLE_10309 (ll_49 BOUND_VARIABLE_10309 BOUND_VARIABLE_10310))))) (let ((_let_399 (forall ((BOUND_VARIABLE_10303 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10304 (-> tptp.pname Bool))) (= BOUND_VARIABLE_10303 (ll_48 BOUND_VARIABLE_10303 BOUND_VARIABLE_10304))))) (let ((_let_400 (forall ((BOUND_VARIABLE_10297 tptp.pname) (BOUND_VARIABLE_10298 tptp.pname)) (= BOUND_VARIABLE_10297 (ll_47 BOUND_VARIABLE_10297 BOUND_VARIABLE_10298))))) (let ((_let_401 (forall ((BOUND_VARIABLE_10289 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10290 tptp.pname) (BOUND_VARIABLE_10291 tptp.hoare_1262092251_state)) (= (@ BOUND_VARIABLE_10289 BOUND_VARIABLE_10291) (ll_46 BOUND_VARIABLE_10289 BOUND_VARIABLE_10290 BOUND_VARIABLE_10291))))) (let ((_let_402 (forall ((BOUND_VARIABLE_10281 (-> tptp.pname Bool)) (BOUND_VARIABLE_10282 tptp.pname) (BOUND_VARIABLE_10283 tptp.pname)) (= (@ BOUND_VARIABLE_10281 BOUND_VARIABLE_10283) (ll_45 BOUND_VARIABLE_10281 BOUND_VARIABLE_10282 BOUND_VARIABLE_10283))))) (let ((_let_403 (forall ((BOUND_VARIABLE_10273 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10274 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10275 tptp.hoare_1262092251_state)) (= (@ BOUND_VARIABLE_10273 BOUND_VARIABLE_10275) (ll_44 BOUND_VARIABLE_10273 BOUND_VARIABLE_10274 BOUND_VARIABLE_10275))))) (let ((_let_404 (forall ((BOUND_VARIABLE_10265 (-> tptp.pname Bool)) (BOUND_VARIABLE_10266 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10267 tptp.pname)) (= (@ BOUND_VARIABLE_10265 BOUND_VARIABLE_10267) (ll_43 BOUND_VARIABLE_10265 BOUND_VARIABLE_10266 BOUND_VARIABLE_10267))))) (let ((_let_405 (forall ((BOUND_VARIABLE_10259 tptp.pname) (BOUND_VARIABLE_10260 tptp.hoare_1262092251_state)) (= BOUND_VARIABLE_10259 (ll_42 BOUND_VARIABLE_10259 BOUND_VARIABLE_10260))))) (let ((_let_406 (forall ((BOUND_VARIABLE_10253 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10254 tptp.pname)) (= BOUND_VARIABLE_10253 (ll_41 BOUND_VARIABLE_10253 BOUND_VARIABLE_10254))))) (let ((_let_407 (forall ((BOUND_VARIABLE_10247 tptp.pname) (BOUND_VARIABLE_10248 (-> tptp.hoare_1262092251_state Bool))) (= BOUND_VARIABLE_10247 (ll_40 BOUND_VARIABLE_10247 BOUND_VARIABLE_10248))))) (let ((_let_408 (forall ((BOUND_VARIABLE_10241 tptp.pname) (BOUND_VARIABLE_10242 (-> tptp.hoare_1262092251_state Bool))) (= BOUND_VARIABLE_10241 (ll_39 BOUND_VARIABLE_10241 BOUND_VARIABLE_10242))))) (let ((_let_409 (forall ((BOUND_VARIABLE_10235 tptp.pname) (BOUND_VARIABLE_10236 (-> tptp.pname Bool))) (= BOUND_VARIABLE_10235 (ll_38 BOUND_VARIABLE_10235 BOUND_VARIABLE_10236))))) (let ((_let_410 (forall ((BOUND_VARIABLE_10229 tptp.pname) (BOUND_VARIABLE_10230 (-> tptp.pname Bool))) (= BOUND_VARIABLE_10229 (ll_37 BOUND_VARIABLE_10229 BOUND_VARIABLE_10230))))) (let ((_let_411 (forall ((BOUND_VARIABLE_10223 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10224 (-> tptp.hoare_1262092251_state Bool))) (= BOUND_VARIABLE_10223 (ll_36 BOUND_VARIABLE_10223 BOUND_VARIABLE_10224))))) (let ((_let_412 (forall ((BOUND_VARIABLE_10217 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10218 (-> tptp.hoare_1262092251_state Bool))) (= BOUND_VARIABLE_10217 (ll_35 BOUND_VARIABLE_10217 BOUND_VARIABLE_10218))))) (let ((_let_413 (forall ((BOUND_VARIABLE_10211 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10212 (-> tptp.pname Bool))) (= BOUND_VARIABLE_10211 (ll_34 BOUND_VARIABLE_10211 BOUND_VARIABLE_10212))))) (let ((_let_414 (forall ((BOUND_VARIABLE_10205 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10206 (-> tptp.pname Bool))) (= BOUND_VARIABLE_10205 (ll_33 BOUND_VARIABLE_10205 BOUND_VARIABLE_10206))))) (let ((_let_415 (forall ((BOUND_VARIABLE_10199 tptp.pname) (BOUND_VARIABLE_10200 tptp.pname)) (= BOUND_VARIABLE_10199 (ll_32 BOUND_VARIABLE_10199 BOUND_VARIABLE_10200))))) (let ((_let_416 (forall ((BOUND_VARIABLE_10193 tptp.pname) (BOUND_VARIABLE_10194 tptp.pname)) (= BOUND_VARIABLE_10193 (ll_31 BOUND_VARIABLE_10193 BOUND_VARIABLE_10194))))) (let ((_let_417 (forall ((BOUND_VARIABLE_10185 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10186 tptp.pname) (BOUND_VARIABLE_10187 tptp.hoare_1262092251_state)) (= (@ BOUND_VARIABLE_10185 BOUND_VARIABLE_10187) (ll_30 BOUND_VARIABLE_10185 BOUND_VARIABLE_10186 BOUND_VARIABLE_10187))))) (let ((_let_418 (forall ((BOUND_VARIABLE_10177 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10178 tptp.pname) (BOUND_VARIABLE_10179 tptp.hoare_1262092251_state)) (= (@ BOUND_VARIABLE_10177 BOUND_VARIABLE_10179) (ll_29 BOUND_VARIABLE_10177 BOUND_VARIABLE_10178 BOUND_VARIABLE_10179))))) (let ((_let_419 (forall ((BOUND_VARIABLE_10169 (-> tptp.pname Bool)) (BOUND_VARIABLE_10170 tptp.pname) (BOUND_VARIABLE_10171 tptp.pname)) (= (@ BOUND_VARIABLE_10169 BOUND_VARIABLE_10171) (ll_28 BOUND_VARIABLE_10169 BOUND_VARIABLE_10170 BOUND_VARIABLE_10171))))) (let ((_let_420 (forall ((BOUND_VARIABLE_10161 (-> tptp.pname Bool)) (BOUND_VARIABLE_10162 tptp.pname) (BOUND_VARIABLE_10163 tptp.pname)) (= (@ BOUND_VARIABLE_10161 BOUND_VARIABLE_10163) (ll_27 BOUND_VARIABLE_10161 BOUND_VARIABLE_10162 BOUND_VARIABLE_10163))))) (let ((_let_421 (forall ((BOUND_VARIABLE_10153 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10154 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10155 tptp.hoare_1262092251_state)) (= (@ BOUND_VARIABLE_10153 BOUND_VARIABLE_10155) (ll_26 BOUND_VARIABLE_10153 BOUND_VARIABLE_10154 BOUND_VARIABLE_10155))))) (let ((_let_422 (forall ((BOUND_VARIABLE_10145 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10146 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10147 tptp.hoare_1262092251_state)) (= (@ BOUND_VARIABLE_10145 BOUND_VARIABLE_10147) (ll_25 BOUND_VARIABLE_10145 BOUND_VARIABLE_10146 BOUND_VARIABLE_10147))))) (let ((_let_423 (forall ((BOUND_VARIABLE_10137 (-> tptp.pname Bool)) (BOUND_VARIABLE_10138 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10139 tptp.pname)) (= (@ BOUND_VARIABLE_10137 BOUND_VARIABLE_10139) (ll_24 BOUND_VARIABLE_10137 BOUND_VARIABLE_10138 BOUND_VARIABLE_10139))))) (let ((_let_424 (forall ((BOUND_VARIABLE_10129 (-> tptp.pname Bool)) (BOUND_VARIABLE_10130 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10131 tptp.pname)) (= (@ BOUND_VARIABLE_10129 BOUND_VARIABLE_10131) (ll_23 BOUND_VARIABLE_10129 BOUND_VARIABLE_10130 BOUND_VARIABLE_10131))))) (let ((_let_425 (forall ((BOUND_VARIABLE_10123 tptp.pname) (BOUND_VARIABLE_10124 tptp.hoare_1262092251_state)) (= BOUND_VARIABLE_10123 (ll_22 BOUND_VARIABLE_10123 BOUND_VARIABLE_10124))))) (let ((_let_426 (forall ((BOUND_VARIABLE_10117 tptp.pname) (BOUND_VARIABLE_10118 tptp.hoare_1262092251_state)) (= BOUND_VARIABLE_10117 (ll_21 BOUND_VARIABLE_10117 BOUND_VARIABLE_10118))))) (let ((_let_427 (forall ((BOUND_VARIABLE_10111 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10112 tptp.pname)) (= BOUND_VARIABLE_10111 (ll_20 BOUND_VARIABLE_10111 BOUND_VARIABLE_10112))))) (let ((_let_428 (forall ((BOUND_VARIABLE_10105 tptp.hoare_1262092251_state) (BOUND_VARIABLE_10106 tptp.pname)) (= BOUND_VARIABLE_10105 (ll_19 BOUND_VARIABLE_10105 BOUND_VARIABLE_10106))))) (let ((_let_429 (forall ((BOUND_VARIABLE_10095 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10096 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10097 (-> tptp.pname Bool))) (= (and (@ BOUND_VARIABLE_10095 BOUND_VARIABLE_10097) (@ BOUND_VARIABLE_10096 BOUND_VARIABLE_10097)) (ll_18 BOUND_VARIABLE_10095 BOUND_VARIABLE_10096 BOUND_VARIABLE_10097))))) (let ((_let_430 (forall ((BOUND_VARIABLE_10085 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10086 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10087 (-> tptp.hoare_1262092251_state Bool))) (= (and (@ BOUND_VARIABLE_10085 BOUND_VARIABLE_10087) (@ BOUND_VARIABLE_10086 BOUND_VARIABLE_10087)) (ll_17 BOUND_VARIABLE_10085 BOUND_VARIABLE_10086 BOUND_VARIABLE_10087))))) (let ((_let_431 (forall ((BOUND_VARIABLE_10075 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) (BOUND_VARIABLE_10076 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) (BOUND_VARIABLE_10077 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (and (@ BOUND_VARIABLE_10075 BOUND_VARIABLE_10077) (@ BOUND_VARIABLE_10076 BOUND_VARIABLE_10077)) (ll_16 BOUND_VARIABLE_10075 BOUND_VARIABLE_10076 BOUND_VARIABLE_10077))))) (let ((_let_432 (forall ((BOUND_VARIABLE_10065 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (BOUND_VARIABLE_10066 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (BOUND_VARIABLE_10067 (-> (-> tptp.pname Bool) Bool))) (= (and (@ BOUND_VARIABLE_10065 BOUND_VARIABLE_10067) (@ BOUND_VARIABLE_10066 BOUND_VARIABLE_10067)) (ll_15 BOUND_VARIABLE_10065 BOUND_VARIABLE_10066 BOUND_VARIABLE_10067))))) (let ((_let_433 (forall ((BOUND_VARIABLE_10055 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10056 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_10057 tptp.hoare_1262092251_state)) (= (and (@ BOUND_VARIABLE_10055 BOUND_VARIABLE_10057) (@ BOUND_VARIABLE_10056 BOUND_VARIABLE_10057)) (ll_14 BOUND_VARIABLE_10055 BOUND_VARIABLE_10056 BOUND_VARIABLE_10057))))) (let ((_let_434 (forall ((BOUND_VARIABLE_10045 (-> tptp.pname Bool)) (BOUND_VARIABLE_10046 (-> tptp.pname Bool)) (BOUND_VARIABLE_10047 tptp.pname)) (= (and (@ BOUND_VARIABLE_10045 BOUND_VARIABLE_10047) (@ BOUND_VARIABLE_10046 BOUND_VARIABLE_10047)) (ll_13 BOUND_VARIABLE_10045 BOUND_VARIABLE_10046 BOUND_VARIABLE_10047))))) (let ((_let_435 (forall ((BOUND_VARIABLE_10040 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (not (ll_12 BOUND_VARIABLE_10040))))) (let ((_let_436 (forall ((BOUND_VARIABLE_10035 tptp.pname)) (not (ll_11 BOUND_VARIABLE_10035))))) (let ((_let_437 (forall ((BOUND_VARIABLE_10030 (-> tptp.hoare_1262092251_state Bool))) (not (ll_10 BOUND_VARIABLE_10030))))) (let ((_let_438 (forall ((BOUND_VARIABLE_10025 (-> tptp.pname Bool))) (not (ll_9 BOUND_VARIABLE_10025))))) (let ((_let_439 (forall ((BOUND_VARIABLE_10017 (-> (-> tptp.pname Bool) Bool)) (BOUND_VARIABLE_10018 (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.ord_le1205211808me_o_o BOUND_VARIABLE_10018) BOUND_VARIABLE_10017) (ll_8 BOUND_VARIABLE_10017 BOUND_VARIABLE_10018))))) (let ((_let_440 (forall ((BOUND_VARIABLE_10009 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (BOUND_VARIABLE_10010 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ (@ tptp.ord_le2012720639te_o_o BOUND_VARIABLE_10010) BOUND_VARIABLE_10009) (ll_7 BOUND_VARIABLE_10009 BOUND_VARIABLE_10010))))) (let ((_let_441 (forall ((BOUND_VARIABLE_10001 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) (BOUND_VARIABLE_10002 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (= (@ (@ tptp.ord_le1891858320_o_o_o BOUND_VARIABLE_10002) BOUND_VARIABLE_10001) (ll_6 BOUND_VARIABLE_10001 BOUND_VARIABLE_10002))))) (let ((_let_442 (forall ((BOUND_VARIABLE_9993 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (BOUND_VARIABLE_9994 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (= (@ (@ tptp.ord_le1828183645_o_o_o BOUND_VARIABLE_9994) BOUND_VARIABLE_9993) (ll_5 BOUND_VARIABLE_9993 BOUND_VARIABLE_9994))))) (let ((_let_443 (forall ((BOUND_VARIABLE_9985 (-> tptp.hoare_1262092251_state Bool)) (BOUND_VARIABLE_9986 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.ord_le870406270tate_o BOUND_VARIABLE_9986) BOUND_VARIABLE_9985) (ll_4 BOUND_VARIABLE_9985 BOUND_VARIABLE_9986))))) (let ((_let_444 (forall ((BOUND_VARIABLE_9977 (-> tptp.pname Bool)) (BOUND_VARIABLE_9978 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o BOUND_VARIABLE_9978) BOUND_VARIABLE_9977) (ll_3 BOUND_VARIABLE_9977 BOUND_VARIABLE_9978))))) (let ((_let_445 (forall ((BOUND_VARIABLE_9972 tptp.hoare_1262092251_state)) (not (ll_2 BOUND_VARIABLE_9972))))) (let ((_let_446 (forall ((G (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.hoare_930741239_state G) (@ tptp.collec1121927558_state ll_2))))) (let ((_let_447 (and _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357))) (let ((_let_448 (_let_43))) (let ((_let_449 (not (@ (@ tptp.hoare_930741239_state (@ (@ tptp.image_669833818_state ll_90) _let_3)) (@ _let_2 (@ tptp.collec1121927558_state ll_2)))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (_let_19 _let_17 _let_18 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_16))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_21 _let_23 _let_25 _let_28))) (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO _let_35 :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (@ _let_4 (@ _let_2 (@ tptp.collec1121927558_state (lambda ((BOUND_VARIABLE_8331 tptp.hoare_1262092251_state)) false))))) _let_449))) (PREPROCESS :args ((= _let_449 (not _let_21)))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_448) :args (_let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_105 k_255 BOUND_VARIABLE_12255)))) :args _let_448)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_15)) (TRANS (MACRO_SR_EQ_INTRO _let_35 :args (_let_15 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((G (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.hoare_930741239_state G) (@ tptp.collec1121927558_state (lambda ((BOUND_VARIABLE_8331 tptp.hoare_1262092251_state)) false)))) _let_446))))) (PREPROCESS :args ((and _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357)))) :args (_let_447)) (PREPROCESS :args ((= _let_447 (and _let_43 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268))))) (PREPROCESS :args ((and _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44)))) :args ((and _let_43 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44))) :args (0)) :args (_let_22 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_24 (not _let_31)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_29 (not _let_39)))) (EQ_RESOLVE (ASSUME :args (_let_6)) (PREPROCESS :args ((= _let_6 _let_37)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.pn tptp.y QUANTIFIERS_INST_E_MATCHING ((ho_345 k_344 B_3) (ho_100 k_99 Pn_1)))) :args (_let_40))) _let_42 :args (_let_39 false _let_40)) :args (_let_29 false _let_37 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_96 k_95 C_1)))) :args (_let_32))) _let_36 :args (_let_31 false _let_32)) :args (_let_24 false _let_29 false _let_31)) :args (_let_28 true _let_21 false _let_22 false _let_24)) _let_27 :args (false true _let_26 false _let_16)) :args (_let_15 (forall ((Ts_6 (-> tptp.hoare_1262092251_state Bool)) (G_8 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.ord_le870406270tate_o Ts_6) G_8) (@ (@ tptp.hoare_930741239_state G_8) Ts_6))) (forall ((Ts_5 (-> tptp.hoare_1262092251_state Bool)) (G_7 (-> tptp.hoare_1262092251_state Bool)) (Ts_4 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.hoare_930741239_state G_7))) (=> (@ _let_1 Ts_4) (=> (@ (@ tptp.ord_le870406270tate_o Ts_5) Ts_4) (@ _let_1 Ts_5))))) (forall ((G_6 (-> tptp.hoare_1262092251_state Bool)) (G_5 (-> tptp.hoare_1262092251_state Bool)) (Ts_3 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.hoare_930741239_state G_5) Ts_3) (=> (@ (@ tptp.ord_le870406270tate_o G_5) G_6) (@ (@ tptp.hoare_930741239_state G_6) Ts_3)))) _let_14 (forall ((Ts_1 (-> tptp.hoare_1262092251_state Bool)) (G_2 (-> tptp.hoare_1262092251_state Bool)) (T_1 tptp.hoare_1262092251_state)) (let ((_let_1 (@ tptp.insert81609953_state T_1))) (let ((_let_2 (@ tptp.hoare_930741239_state G_2))) (=> (@ _let_2 (@ _let_1 tptp.bot_bo113204042tate_o)) (=> (@ _let_2 Ts_1) (@ _let_2 (@ _let_1 Ts_1))))))) (forall ((G_1 (-> tptp.hoare_1262092251_state Bool)) (T tptp.hoare_1262092251_state) (Ts (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.hoare_930741239_state G_1))) (let ((_let_2 (@ tptp.insert81609953_state T))) (=> (@ _let_1 (@ _let_2 Ts)) (and (@ _let_1 (@ _let_2 tptp.bot_bo113204042tate_o)) (@ _let_1 Ts)))))) (forall ((Pn_1 tptp.pname) (G (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT (@ tptp.body_1 Pn_1))))) (=> (@ (@ tptp.hoare_930741239_state (@ _let_1 G)) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT (@ tptp.the_com (@ tptp.body Pn_1)))) tptp.bot_bo113204042tate_o)) (@ (@ tptp.hoare_930741239_state G) (@ _let_1 tptp.bot_bo113204042tate_o))))) (forall ((A_77 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_77) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((B_41 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o B_41) A_77)))))) (forall ((A_77 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_77) (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o (lambda ((B_41 (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.ord_le870406270tate_o B_41) A_77)))))) (forall ((A_77 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_77) (@ tptp.finite1648353812_o_o_o (@ tptp.collect_pname_o_o_o (lambda ((B_41 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (@ (@ tptp.ord_le1828183645_o_o_o B_41) A_77)))))) (forall ((A_77 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o A_77) (@ tptp.finite734360985_o_o_o (@ tptp.collec101077467_o_o_o (lambda ((B_41 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (@ (@ tptp.ord_le1891858320_o_o_o B_41) A_77)))))) (forall ((A_77 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o A_77) (@ tptp.finite1303896758te_o_o (@ tptp.collec341954548te_o_o (lambda ((B_41 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (@ (@ tptp.ord_le2012720639te_o_o B_41) A_77)))))) (forall ((A_77 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_77) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o (lambda ((B_41 (-> (-> tptp.pname Bool) Bool))) (@ (@ tptp.ord_le1205211808me_o_o B_41) A_77)))))) (forall ((H (-> tptp.pname tptp.hoare_1262092251_state)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite1178804552_state (@ (@ tptp.image_669833818_state H) F_17)))) (forall ((H (-> (-> (-> tptp.pname Bool) Bool) tptp.pname)) (F_17 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_471733107_pname H) F_17)))) (forall ((H (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.pname)) (F_17 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_893364936_pname H) F_17)))) (forall ((H (-> (-> tptp.hoare_1262092251_state Bool) tptp.pname)) (F_17 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_1820530197_pname H) F_17)))) (forall ((H (-> (-> tptp.pname Bool) tptp.pname)) (F_17 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_o_pname H) F_17)))) (forall ((H (-> (-> (-> tptp.pname Bool) Bool) tptp.hoare_1262092251_state)) (F_17 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o F_17) (@ tptp.finite1178804552_state (@ (@ tptp.image_1036078444_state H) F_17)))) (forall ((H (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.hoare_1262092251_state)) (F_17 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o F_17) (@ tptp.finite1178804552_state (@ (@ tptp.image_165349207_state H) F_17)))) (forall ((H (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state)) (F_17 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o F_17) (@ tptp.finite1178804552_state (@ (@ tptp.image_234589002_state H) F_17)))) (forall ((H (-> (-> tptp.pname Bool) tptp.hoare_1262092251_state)) (F_17 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_17) (@ tptp.finite1178804552_state (@ (@ tptp.image_1476171975_state H) F_17)))) (forall ((H (-> tptp.pname (-> tptp.pname Bool) Bool)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite1066544169me_o_o (@ (@ tptp.image_504089495me_o_o H) F_17)))) (forall ((H (-> tptp.pname (-> tptp.hoare_1262092251_state Bool) Bool)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite1303896758te_o_o (@ (@ tptp.image_827868872te_o_o H) F_17)))) (forall ((H (-> tptp.pname tptp.hoare_1262092251_state Bool)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite1423311111tate_o (@ (@ tptp.image_518521461tate_o H) F_17)))) (forall ((H (-> tptp.pname tptp.pname Bool)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite297249702name_o (@ (@ tptp.image_pname_pname_o H) F_17)))) (forall ((H (-> tptp.hoare_1262092251_state (-> tptp.pname Bool) Bool)) (F_17 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_17) (@ tptp.finite1066544169me_o_o (@ (@ tptp.image_333245000me_o_o H) F_17)))) (forall ((H (-> tptp.hoare_1262092251_state (-> tptp.hoare_1262092251_state Bool) Bool)) (F_17 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_17) (@ tptp.finite1303896758te_o_o (@ (@ tptp.image_1731108951te_o_o H) F_17)))) (forall ((H (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)) (F_17 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_17) (@ tptp.finite1423311111tate_o (@ (@ tptp.image_1403668518tate_o H) F_17)))) (forall ((H (-> tptp.hoare_1262092251_state tptp.pname Bool)) (F_17 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_17) (@ tptp.finite297249702name_o (@ (@ tptp.image_1320925383name_o H) F_17)))) (forall ((H (-> tptp.hoare_1262092251_state tptp.pname)) (F_17 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_202231862_pname H) F_17)))) (forall ((H (-> tptp.pname tptp.pname)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_pname H) F_17)))) (forall ((A_76 (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.ord_le870406270tate_o tptp.bot_bo113204042tate_o) A_76)) (forall ((A_76 (-> (-> tptp.pname Bool) Bool))) (@ (@ tptp.ord_le1205211808me_o_o tptp.bot_bot_pname_o_o) A_76)) (forall ((A_76 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (@ (@ tptp.ord_le2012720639te_o_o tptp.bot_bo1962689075te_o_o) A_76)) (forall ((A_76 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o tptp.bot_bot_pname_o) A_76)) (forall ((A_75 tptp.hoare_1262092251_state) (A_74 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_74) (@ tptp.finite1178804552_state (@ (@ tptp.insert81609953_state A_75) A_74)))) (forall ((A_75 tptp.pname) (A_74 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_74) (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_75) A_74)))) (forall ((A_75 (-> (-> tptp.pname Bool) Bool)) (A_74 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_74) (@ tptp.finite1066544169me_o_o (@ (@ tptp.insert_pname_o_o A_75) A_74)))) (forall ((A_75 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (A_74 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o A_74) (@ tptp.finite1303896758te_o_o (@ (@ tptp.insert1691644879te_o_o A_75) A_74)))) (forall ((A_75 (-> tptp.hoare_1262092251_state Bool)) (A_74 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o A_74) (@ tptp.finite1423311111tate_o (@ (@ tptp.insert1042460334tate_o A_75) A_74)))) (forall ((A_75 (-> tptp.pname Bool)) (A_74 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_74) (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_75) A_74)))) (@ tptp.finite_finite_pname tptp.bot_bot_pname_o) (@ tptp.finite1178804552_state tptp.bot_bo113204042tate_o) (@ tptp.finite1066544169me_o_o tptp.bot_bot_pname_o_o_o) (@ tptp.finite1303896758te_o_o tptp.bot_bo388435036_o_o_o) (@ tptp.finite1423311111tate_o tptp.bot_bo1962689075te_o_o) (@ tptp.finite297249702name_o tptp.bot_bot_pname_o_o) (forall ((Q_1 (-> tptp.pname Bool)) (P_9 (-> tptp.pname Bool))) (=> (or (@ tptp.finite_finite_pname (@ tptp.collect_pname P_9)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_1))) (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (@ P_9 X_1) (@ Q_1 X_1))))))) (forall ((Q_1 (-> tptp.hoare_1262092251_state Bool)) (P_9 (-> tptp.hoare_1262092251_state Bool))) (=> (or (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state P_9)) (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state Q_1))) (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (and (@ P_9 X_1) (@ Q_1 X_1))))))) (forall ((Q_1 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (P_9 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (or (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o P_9)) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o Q_1))) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o (lambda ((X_1 (-> (-> tptp.pname Bool) Bool))) (and (@ P_9 X_1) (@ Q_1 X_1))))))) (forall ((Q_1 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) (P_9 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (or (@ tptp.finite1303896758te_o_o (@ tptp.collec341954548te_o_o P_9)) (@ tptp.finite1303896758te_o_o (@ tptp.collec341954548te_o_o Q_1))) (@ tptp.finite1303896758te_o_o (@ tptp.collec341954548te_o_o (lambda ((X_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (and (@ P_9 X_1) (@ Q_1 X_1))))))) (forall ((Q_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (P_9 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (or (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o P_9)) (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o Q_1))) (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (and (@ P_9 X_1) (@ Q_1 X_1))))))) (forall ((Q_1 (-> (-> tptp.pname Bool) Bool)) (P_9 (-> (-> tptp.pname Bool) Bool))) (=> (or (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_9)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q_1))) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (@ P_9 X_1) (@ Q_1 X_1))))))) (forall ((C_8 tptp.hoare_1262092251_state) (A_73 (-> tptp.pname Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_669833818_state (lambda ((X_1 tptp.pname)) C_8)) A_73) tptp.bot_bo113204042tate_o)) (=> (not _let_1) (= (@ (@ tptp.image_669833818_state (lambda ((X_1 tptp.pname)) C_8)) A_73) (@ (@ tptp.insert81609953_state C_8) tptp.bot_bo113204042tate_o)))))) (forall ((C_8 tptp.pname) (A_73 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (= A_73 tptp.bot_bo113204042tate_o))) (and (=> _let_1 (= (@ (@ tptp.image_202231862_pname (lambda ((X_1 tptp.hoare_1262092251_state)) C_8)) A_73) tptp.bot_bot_pname_o)) (=> (not _let_1) (= (@ (@ tptp.image_202231862_pname (lambda ((X_1 tptp.hoare_1262092251_state)) C_8)) A_73) (@ (@ tptp.insert_pname C_8) tptp.bot_bot_pname_o)))))) (forall ((C_8 (-> tptp.pname Bool)) (A_73 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (= A_73 tptp.bot_bo113204042tate_o))) (and (=> _let_1 (= (@ (@ tptp.image_1320925383name_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.pname)) (@ C_8 __flatten_var_0))) A_73) tptp.bot_bot_pname_o_o)) (=> (not _let_1) (= (@ (@ tptp.image_1320925383name_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.pname)) (@ C_8 __flatten_var_0))) A_73) (@ (@ tptp.insert_pname_o C_8) tptp.bot_bot_pname_o_o)))))) (forall ((C_8 (-> tptp.hoare_1262092251_state Bool)) (A_73 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (= A_73 tptp.bot_bo113204042tate_o))) (and (=> _let_1 (= (@ (@ tptp.image_1403668518tate_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_8 __flatten_var_0))) A_73) tptp.bot_bo1962689075te_o_o)) (=> (not _let_1) (= (@ (@ tptp.image_1403668518tate_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_8 __flatten_var_0))) A_73) (@ (@ tptp.insert1042460334tate_o C_8) tptp.bot_bo1962689075te_o_o)))))) (forall ((C_8 (-> tptp.pname Bool)) (A_73 (-> tptp.pname Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_pname_pname_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.pname)) (@ C_8 __flatten_var_0))) A_73) tptp.bot_bot_pname_o_o)) (=> (not _let_1) (= (@ (@ tptp.image_pname_pname_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.pname)) (@ C_8 __flatten_var_0))) A_73) (@ (@ tptp.insert_pname_o C_8) tptp.bot_bot_pname_o_o)))))) (forall ((C_8 (-> tptp.hoare_1262092251_state Bool)) (A_73 (-> tptp.pname Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_518521461tate_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_8 __flatten_var_0))) A_73) tptp.bot_bo1962689075te_o_o)) (=> (not _let_1) (= (@ (@ tptp.image_518521461tate_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_8 __flatten_var_0))) A_73) (@ (@ tptp.insert1042460334tate_o C_8) tptp.bot_bo1962689075te_o_o)))))) (forall ((C_8 tptp.pname) (A_73 (-> tptp.pname Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_pname_pname (lambda ((X_1 tptp.pname)) C_8)) A_73) tptp.bot_bot_pname_o)) (=> (not _let_1) (= (@ (@ tptp.image_pname_pname (lambda ((X_1 tptp.pname)) C_8)) A_73) (@ (@ tptp.insert_pname C_8) tptp.bot_bot_pname_o)))))) (forall ((C_8 tptp.hoare_1262092251_state) (A_73 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o_o))) (and (=> _let_1 (= (@ (@ tptp.image_1476171975_state (lambda ((X_1 (-> tptp.pname Bool))) C_8)) A_73) tptp.bot_bo113204042tate_o)) (=> (not _let_1) (= (@ (@ tptp.image_1476171975_state (lambda ((X_1 (-> tptp.pname Bool))) C_8)) A_73) (@ (@ tptp.insert81609953_state C_8) tptp.bot_bo113204042tate_o)))))) (forall ((C_8 tptp.hoare_1262092251_state) (A_73 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (= A_73 tptp.bot_bo1962689075te_o_o))) (and (=> _let_1 (= (@ (@ tptp.image_234589002_state (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_8)) A_73) tptp.bot_bo113204042tate_o)) (=> (not _let_1) (= (@ (@ tptp.image_234589002_state (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_8)) A_73) (@ (@ tptp.insert81609953_state C_8) tptp.bot_bo113204042tate_o)))))) (forall ((C_8 tptp.pname) (A_73 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (= A_73 tptp.bot_bot_pname_o_o))) (and (=> _let_1 (= (@ (@ tptp.image_pname_o_pname (lambda ((X_1 (-> tptp.pname Bool))) C_8)) A_73) tptp.bot_bot_pname_o)) (=> (not _let_1) (= (@ (@ tptp.image_pname_o_pname (lambda ((X_1 (-> tptp.pname Bool))) C_8)) A_73) (@ (@ tptp.insert_pname C_8) tptp.bot_bot_pname_o)))))) (forall ((C_8 tptp.pname) (A_73 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (= A_73 tptp.bot_bo1962689075te_o_o))) (and (=> _let_1 (= (@ (@ tptp.image_1820530197_pname (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_8)) A_73) tptp.bot_bot_pname_o)) (=> (not _let_1) (= (@ (@ tptp.image_1820530197_pname (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_8)) A_73) (@ (@ tptp.insert_pname C_8) tptp.bot_bot_pname_o)))))) (forall ((C_7 tptp.hoare_1262092251_state) (X_18 tptp.pname) (A_72 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_18) A_72) (= (@ (@ tptp.image_669833818_state (lambda ((X_1 tptp.pname)) C_7)) A_72) (@ (@ tptp.insert81609953_state C_7) tptp.bot_bo113204042tate_o)))) (forall ((C_7 tptp.pname) (X_18 tptp.hoare_1262092251_state) (A_72 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.member5164104_state X_18) A_72) (= (@ (@ tptp.image_202231862_pname (lambda ((X_1 tptp.hoare_1262092251_state)) C_7)) A_72) (@ (@ tptp.insert_pname C_7) tptp.bot_bot_pname_o)))) (forall ((C_7 (-> tptp.pname Bool)) (X_18 tptp.hoare_1262092251_state) (A_72 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.member5164104_state X_18) A_72) (= (@ (@ tptp.image_1320925383name_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.pname)) (@ C_7 __flatten_var_0))) A_72) (@ (@ tptp.insert_pname_o C_7) tptp.bot_bot_pname_o_o)))) (forall ((C_7 (-> tptp.hoare_1262092251_state Bool)) (X_18 tptp.hoare_1262092251_state) (A_72 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.member5164104_state X_18) A_72) (= (@ (@ tptp.image_1403668518tate_o (lambda ((X_1 tptp.hoare_1262092251_state) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_7 __flatten_var_0))) A_72) (@ (@ tptp.insert1042460334tate_o C_7) tptp.bot_bo1962689075te_o_o)))) (forall ((C_7 (-> tptp.pname Bool)) (X_18 tptp.pname) (A_72 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_18) A_72) (= (@ (@ tptp.image_pname_pname_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.pname)) (@ C_7 __flatten_var_0))) A_72) (@ (@ tptp.insert_pname_o C_7) tptp.bot_bot_pname_o_o)))) (forall ((C_7 (-> tptp.hoare_1262092251_state Bool)) (X_18 tptp.pname) (A_72 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_18) A_72) (= (@ (@ tptp.image_518521461tate_o (lambda ((X_1 tptp.pname) (__flatten_var_0 tptp.hoare_1262092251_state)) (@ C_7 __flatten_var_0))) A_72) (@ (@ tptp.insert1042460334tate_o C_7) tptp.bot_bo1962689075te_o_o)))) (forall ((C_7 tptp.pname) (X_18 tptp.pname) (A_72 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_18) A_72) (= (@ (@ tptp.image_pname_pname (lambda ((X_1 tptp.pname)) C_7)) A_72) (@ (@ tptp.insert_pname C_7) tptp.bot_bot_pname_o)))) (forall ((C_7 tptp.hoare_1262092251_state) (X_18 (-> tptp.pname Bool)) (A_72 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.member_pname_o X_18) A_72) (= (@ (@ tptp.image_1476171975_state (lambda ((X_1 (-> tptp.pname Bool))) C_7)) A_72) (@ (@ tptp.insert81609953_state C_7) tptp.bot_bo113204042tate_o)))) (forall ((C_7 tptp.hoare_1262092251_state) (X_18 (-> tptp.hoare_1262092251_state Bool)) (A_72 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ (@ tptp.member907417095tate_o X_18) A_72) (= (@ (@ tptp.image_234589002_state (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_7)) A_72) (@ (@ tptp.insert81609953_state C_7) tptp.bot_bo113204042tate_o)))) (forall ((C_7 tptp.pname) (X_18 (-> tptp.pname Bool)) (A_72 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.member_pname_o X_18) A_72) (= (@ (@ tptp.image_pname_o_pname (lambda ((X_1 (-> tptp.pname Bool))) C_7)) A_72) (@ (@ tptp.insert_pname C_7) tptp.bot_bot_pname_o)))) (forall ((C_7 tptp.pname) (X_18 (-> tptp.hoare_1262092251_state Bool)) (A_72 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ (@ tptp.member907417095tate_o X_18) A_72) (= (@ (@ tptp.image_1820530197_pname (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) C_7)) A_72) (@ (@ tptp.insert_pname C_7) tptp.bot_bot_pname_o)))) (forall ((F_16 (-> tptp.pname tptp.option_com)) (X_17 tptp.pname) (Y_4 tptp.com)) (let ((_let_1 (@ tptp.dom_pname_com F_16))) (=> (= (@ F_16 X_17) (@ tptp.some_com Y_4)) (= (@ (@ tptp.insert_pname X_17) _let_1) _let_1)))) (forall ((F_16 (-> (-> tptp.pname Bool) tptp.option_com)) (X_17 (-> tptp.pname Bool)) (Y_4 tptp.com)) (let ((_let_1 (@ tptp.dom_pname_o_com F_16))) (=> (= (@ F_16 X_17) (@ tptp.some_com Y_4)) (= (@ (@ tptp.insert_pname_o X_17) _let_1) _let_1)))) (forall ((F_16 (-> (-> tptp.hoare_1262092251_state Bool) tptp.option_com)) (X_17 (-> tptp.hoare_1262092251_state Bool)) (Y_4 tptp.com)) (let ((_let_1 (@ tptp.dom_Ho1489634536_o_com F_16))) (=> (= (@ F_16 X_17) (@ tptp.some_com Y_4)) (= (@ (@ tptp.insert1042460334tate_o X_17) _let_1) _let_1)))) (forall ((B_40 (-> tptp.hoare_1262092251_state Bool)) (F_15 (-> tptp.pname tptp.hoare_1262092251_state)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_le870406270tate_o B_40) (@ (@ tptp.image_669833818_state F_15) A_71)) (@ tptp.finite1178804552_state B_40)))) (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> (-> (-> tptp.pname Bool) Bool) tptp.pname)) (A_71 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_471733107_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))) (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.pname)) (A_71 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_893364936_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))) (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> (-> tptp.hoare_1262092251_state Bool) tptp.pname)) (A_71 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_1820530197_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))) (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> (-> tptp.pname Bool) tptp.pname)) (A_71 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_pname_o_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))) (forall ((B_40 (-> tptp.hoare_1262092251_state Bool)) (F_15 (-> (-> (-> tptp.pname Bool) Bool) tptp.hoare_1262092251_state)) (A_71 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_71) (=> (@ (@ tptp.ord_le870406270tate_o B_40) (@ (@ tptp.image_1036078444_state F_15) A_71)) (@ tptp.finite1178804552_state B_40)))) (forall ((B_40 (-> tptp.hoare_1262092251_state Bool)) (F_15 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) tptp.hoare_1262092251_state)) (A_71 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (=> (@ tptp.finite1303896758te_o_o A_71) (=> (@ (@ tptp.ord_le870406270tate_o B_40) (@ (@ tptp.image_165349207_state F_15) A_71)) (@ tptp.finite1178804552_state B_40)))) (forall ((B_40 (-> tptp.hoare_1262092251_state Bool)) (F_15 (-> (-> tptp.hoare_1262092251_state Bool) tptp.hoare_1262092251_state)) (A_71 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o A_71) (=> (@ (@ tptp.ord_le870406270tate_o B_40) (@ (@ tptp.image_234589002_state F_15) A_71)) (@ tptp.finite1178804552_state B_40)))) (forall ((B_40 (-> tptp.hoare_1262092251_state Bool)) (F_15 (-> (-> tptp.pname Bool) tptp.hoare_1262092251_state)) (A_71 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_71) (=> (@ (@ tptp.ord_le870406270tate_o B_40) (@ (@ tptp.image_1476171975_state F_15) A_71)) (@ tptp.finite1178804552_state B_40)))) (forall ((B_40 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (F_15 (-> tptp.pname (-> tptp.pname Bool) Bool)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_le1828183645_o_o_o B_40) (@ (@ tptp.image_504089495me_o_o F_15) A_71)) (@ tptp.finite1066544169me_o_o B_40)))) (forall ((B_40 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) (F_15 (-> tptp.pname (-> tptp.hoare_1262092251_state Bool) Bool)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_le1891858320_o_o_o B_40) (@ (@ tptp.image_827868872te_o_o F_15) A_71)) (@ tptp.finite1303896758te_o_o B_40)))) (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> tptp.pname tptp.pname)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_pname_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))) (forall ((B_40 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (F_15 (-> tptp.pname tptp.hoare_1262092251_state Bool)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_le2012720639te_o_o B_40) (@ (@ tptp.image_518521461tate_o F_15) A_71)) (@ tptp.finite1423311111tate_o B_40)))) (forall ((B_40 (-> (-> tptp.pname Bool) Bool)) (F_15 (-> tptp.pname tptp.pname Bool)) (A_71 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_71) (=> (@ (@ tptp.ord_le1205211808me_o_o B_40) (@ (@ tptp.image_pname_pname_o F_15) A_71)) (@ tptp.finite297249702name_o B_40)))) (forall ((B_40 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (F_15 (-> tptp.hoare_1262092251_state (-> tptp.pname Bool) Bool)) (A_71 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_71) (=> (@ (@ tptp.ord_le1828183645_o_o_o B_40) (@ (@ tptp.image_333245000me_o_o F_15) A_71)) (@ tptp.finite1066544169me_o_o B_40)))) (forall ((B_40 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) (F_15 (-> tptp.hoare_1262092251_state (-> tptp.hoare_1262092251_state Bool) Bool)) (A_71 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_71) (=> (@ (@ tptp.ord_le1891858320_o_o_o B_40) (@ (@ tptp.image_1731108951te_o_o F_15) A_71)) (@ tptp.finite1303896758te_o_o B_40)))) (forall ((B_40 (-> tptp.pname Bool)) (F_15 (-> tptp.hoare_1262092251_state tptp.pname)) (A_71 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_71) (=> (@ (@ tptp.ord_less_eq_pname_o B_40) (@ (@ tptp.image_202231862_pname F_15) A_71)) (@ tptp.finite_finite_pname B_40)))) (forall ((B_40 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (F_15 (-> tptp.hoare_1262092251_state tptp.hoare_1262092251_state Bool)) (A_71 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_71) (=> (@ (@ tptp.ord_le2012720639te_o_o B_40) (@ (@ tptp.image_1403668518tate_o F_15) A_71)) (@ tptp.finite1423311111tate_o B_40)))) (forall ((B_40 (-> (-> tptp.pname Bool) Bool)) (F_15 (-> tptp.hoare_1262092251_state tptp.pname Bool)) (A_71 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state A_71) (=> (@ (@ tptp.ord_le1205211808me_o_o B_40) (@ (@ tptp.image_1320925383name_o F_15) A_71)) (@ tptp.finite297249702name_o B_40)))) (forall ((A_70 (-> tptp.hoare_1262092251_state Bool)) (X_16 tptp.hoare_1262092251_state)) (let ((_let_1 (@ (@ tptp.insert81609953_state X_16) tptp.bot_bo113204042tate_o))) (=> (@ (@ tptp.ord_le870406270tate_o A_70) _let_1) (or (= A_70 tptp.bot_bo113204042tate_o) (= A_70 _let_1))))) (forall ((A_70 (-> (-> tptp.pname Bool) Bool)) (X_16 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.insert_pname_o X_16) tptp.bot_bot_pname_o_o))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_70) _let_1) (or (= A_70 tptp.bot_bot_pname_o_o) (= A_70 _let_1))))) (forall ((A_70 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (X_16 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ (@ tptp.insert1042460334tate_o X_16) tptp.bot_bo1962689075te_o_o))) (=> (@ (@ tptp.ord_le2012720639te_o_o A_70) _let_1) (or (= A_70 tptp.bot_bo1962689075te_o_o) (= A_70 _let_1))))) (forall ((A_70 (-> tptp.pname Bool)) (X_16 tptp.pname)) (let ((_let_1 (@ (@ tptp.insert_pname X_16) tptp.bot_bot_pname_o))) (=> (@ (@ tptp.ord_less_eq_pname_o A_70) _let_1) (or (= A_70 tptp.bot_bot_pname_o) (= A_70 _let_1))))) _let_13 (forall ((A_69 tptp.hoare_1262092251_state)) (not (@ (@ tptp.member5164104_state A_69) tptp.bot_bo113204042tate_o))) (forall ((A_69 (-> tptp.pname Bool))) (not (@ (@ tptp.member_pname_o A_69) tptp.bot_bot_pname_o_o))) (forall ((A_69 (-> tptp.hoare_1262092251_state Bool))) (not (@ (@ tptp.member907417095tate_o A_69) tptp.bot_bo1962689075te_o_o))) (forall ((A_69 tptp.pname)) (not (@ (@ tptp.member_pname A_69) tptp.bot_bot_pname_o))) (forall ((B_39 tptp.hoare_1262092251_state) (A_68 tptp.hoare_1262092251_state) (B_38 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_68))) (=> (=> (not (@ _let_1 B_38)) (= A_68 B_39)) (@ _let_1 (@ (@ tptp.insert81609953_state B_39) B_38))))) (forall ((B_39 (-> tptp.pname Bool)) (A_68 (-> tptp.pname Bool)) (B_38 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.member_pname_o A_68))) (=> (=> (not (@ _let_1 B_38)) (= A_68 B_39)) (@ _let_1 (@ (@ tptp.insert_pname_o B_39) B_38))))) (forall ((B_39 (-> tptp.hoare_1262092251_state Bool)) (A_68 (-> tptp.hoare_1262092251_state Bool)) (B_38 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (@ tptp.member907417095tate_o A_68))) (=> (=> (not (@ _let_1 B_38)) (= A_68 B_39)) (@ _let_1 (@ (@ tptp.insert1042460334tate_o B_39) B_38))))) (forall ((B_39 tptp.pname) (A_68 tptp.pname) (B_38 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_68))) (=> (=> (not (@ _let_1 B_38)) (= A_68 B_39)) (@ _let_1 (@ (@ tptp.insert_pname B_39) B_38))))) (forall ((A_67 tptp.hoare_1262092251_state) (B_37 tptp.hoare_1262092251_state) (A_66 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_67))) (=> (@ _let_1 (@ (@ tptp.insert81609953_state B_37) A_66)) (=> (not (= A_67 B_37)) (@ _let_1 A_66))))) (forall ((A_67 (-> tptp.pname Bool)) (B_37 (-> tptp.pname Bool)) (A_66 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.member_pname_o A_67))) (=> (@ _let_1 (@ (@ tptp.insert_pname_o B_37) A_66)) (=> (not (= A_67 B_37)) (@ _let_1 A_66))))) (forall ((A_67 (-> tptp.hoare_1262092251_state Bool)) (B_37 (-> tptp.hoare_1262092251_state Bool)) (A_66 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (@ tptp.member907417095tate_o A_67))) (=> (@ _let_1 (@ (@ tptp.insert1042460334tate_o B_37) A_66)) (=> (not (= A_67 B_37)) (@ _let_1 A_66))))) (forall ((A_67 tptp.pname) (B_37 tptp.pname) (A_66 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_67))) (=> (@ _let_1 (@ (@ tptp.insert_pname B_37) A_66)) (=> (not (= A_67 B_37)) (@ _let_1 A_66))))) (forall ((A_65 (-> tptp.hoare_1262092251_state Bool)) (B_36 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.ord_le870406270tate_o A_65) B_36) (=> (@ (@ tptp.ord_le870406270tate_o B_36) A_65) (= A_65 B_36)))) (forall ((A_65 (-> (-> tptp.pname Bool) Bool)) (B_36 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_65) B_36) (=> (@ (@ tptp.ord_le1205211808me_o_o B_36) A_65) (= A_65 B_36)))) (forall ((A_65 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (B_36 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ (@ tptp.ord_le2012720639te_o_o A_65) B_36) (=> (@ (@ tptp.ord_le2012720639te_o_o B_36) A_65) (= A_65 B_36)))) (forall ((A_65 (-> tptp.pname Bool)) (B_36 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_65) B_36) (=> (@ (@ tptp.ord_less_eq_pname_o B_36) A_65) (= A_65 B_36)))) (forall ((C_6 tptp.hoare_1262092251_state) (A_64 (-> tptp.hoare_1262092251_state Bool)) (B_35 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state C_6))) (=> (@ (@ tptp.ord_le870406270tate_o A_64) B_35) (=> (@ _let_1 A_64) (@ _let_1 B_35))))) (forall ((C_6 (-> tptp.pname Bool)) (A_64 (-> (-> tptp.pname Bool) Bool)) (B_35 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.member_pname_o C_6))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_64) B_35) (=> (@ _let_1 A_64) (@ _let_1 B_35))))) (forall ((C_6 (-> tptp.hoare_1262092251_state Bool)) (A_64 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (B_35 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (@ 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tptp.image_1403668518tate_o F_14) A_63))))) (forall ((A_63 (-> tptp.pname Bool)) (B_34 (-> tptp.pname Bool)) (F_14 (-> tptp.pname tptp.pname Bool)) (X_15 tptp.pname)) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member_pname X_15) A_63) (@ (@ tptp.member_pname_o B_34) (@ (@ tptp.image_pname_pname_o F_14) A_63))))) (forall ((A_63 (-> tptp.pname Bool)) (B_34 (-> tptp.hoare_1262092251_state Bool)) (F_14 (-> tptp.pname tptp.hoare_1262092251_state Bool)) (X_15 tptp.pname)) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member_pname X_15) A_63) (@ (@ tptp.member907417095tate_o B_34) (@ (@ tptp.image_518521461tate_o F_14) A_63))))) (forall ((A_63 (-> (-> tptp.pname Bool) Bool)) (B_34 tptp.hoare_1262092251_state) (F_14 (-> (-> tptp.pname Bool) tptp.hoare_1262092251_state)) (X_15 (-> tptp.pname Bool))) (=> (= B_34 (@ F_14 X_15)) (=> (@ (@ tptp.member_pname_o X_15) A_63) (@ (@ tptp.member5164104_state B_34) (@ (@ tptp.image_1476171975_state F_14) A_63))))) (forall ((A_63 (-> (-> 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A_61)))) (forall ((A_62 (-> tptp.hoare_1262092251_state Bool)) (A_61 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (= A_61 tptp.bot_bo1962689075te_o_o) (not (@ (@ tptp.member907417095tate_o A_62) A_61)))) (forall ((A_62 tptp.hoare_1262092251_state) (A_61 (-> tptp.hoare_1262092251_state Bool))) (=> (= A_61 tptp.bot_bo113204042tate_o) (not (@ (@ tptp.member5164104_state A_62) A_61)))) (forall ((A_62 tptp.pname) (A_61 (-> tptp.pname Bool))) (=> (= A_61 tptp.bot_bot_pname_o) (not (@ (@ tptp.member_pname A_62) A_61)))) (forall ((P_8 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (= (= (@ tptp.collect_pname_o_o P_8) tptp.bot_bot_pname_o_o_o) (forall ((X_1 (-> (-> tptp.pname Bool) Bool))) (not (@ P_8 X_1))))) (forall ((P_8 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool))) (= (= (@ tptp.collec341954548te_o_o P_8) tptp.bot_bo388435036_o_o_o) (forall ((X_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (not (@ P_8 X_1))))) (forall ((P_8 (-> (-> tptp.hoare_1262092251_state Bool) 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B_29)))))) (forall ((A_48 tptp.hoare_1262092251_state) (B_29 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.insert81609953_state A_48) B_29) (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (or (= X_1 A_48) (@ (@ tptp.member5164104_state X_1) B_29)))))) (forall ((A_48 (-> tptp.pname Bool)) (B_29 (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o A_48) B_29) (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (or (= X_1 A_48) (@ (@ tptp.member_pname_o X_1) B_29)))))) (forall ((A_48 (-> tptp.hoare_1262092251_state Bool)) (B_29 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ (@ tptp.insert1042460334tate_o A_48) B_29) (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (or (= X_1 A_48) (@ (@ tptp.member907417095tate_o X_1) B_29)))))) (forall ((A_47 tptp.pname) (B_28 (-> tptp.pname Bool))) (@ (@ tptp.member_pname A_47) (@ (@ tptp.insert_pname A_47) B_28))) (forall ((A_47 tptp.hoare_1262092251_state) (B_28 (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.member5164104_state A_47) (@ (@ tptp.insert81609953_state A_47) B_28))) (forall ((A_46 (-> tptp.pname Bool)) (B_27 (-> tptp.pname Bool))) (=> (= A_46 B_27) (not (=> (@ (@ tptp.ord_less_eq_pname_o A_46) B_27) (not (@ (@ tptp.ord_less_eq_pname_o B_27) A_46)))))) (forall ((A_46 (-> tptp.hoare_1262092251_state Bool)) (B_27 (-> tptp.hoare_1262092251_state Bool))) (=> (= A_46 B_27) (not (=> (@ (@ tptp.ord_le870406270tate_o A_46) B_27) (not (@ (@ tptp.ord_le870406270tate_o B_27) A_46)))))) (forall ((C_4 (-> tptp.pname Bool)) (A_45 (-> tptp.pname Bool)) (B_26 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_45))) (=> (@ _let_1 B_26) (=> (@ (@ tptp.ord_less_eq_pname_o B_26) C_4) (@ _let_1 C_4))))) (forall ((C_4 (-> tptp.hoare_1262092251_state Bool)) (A_45 (-> tptp.hoare_1262092251_state Bool)) (B_26 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.ord_le870406270tate_o A_45))) (=> (@ _let_1 B_26) (=> (@ (@ tptp.ord_le870406270tate_o B_26) C_4) (@ _let_1 C_4))))) (forall ((X_10 tptp.pname) (A_44 (-> tptp.pname Bool)) (B_25 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_10))) (=> (@ (@ tptp.ord_less_eq_pname_o A_44) B_25) (=> (@ _let_1 A_44) (@ _let_1 B_25))))) (forall ((X_10 tptp.hoare_1262092251_state) (A_44 (-> tptp.hoare_1262092251_state Bool)) (B_25 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state X_10))) (=> (@ (@ tptp.ord_le870406270tate_o A_44) B_25) (=> (@ _let_1 A_44) (@ _let_1 B_25))))) (forall ((B_24 (-> tptp.pname Bool)) (X_9 tptp.pname) (A_43 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_9))) (=> (@ _let_1 A_43) (=> (@ (@ tptp.ord_less_eq_pname_o A_43) B_24) (@ _let_1 B_24))))) (forall ((B_24 (-> tptp.hoare_1262092251_state Bool)) (X_9 tptp.hoare_1262092251_state) (A_43 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state X_9))) (=> (@ _let_1 A_43) (=> (@ (@ tptp.ord_le870406270tate_o A_43) B_24) (@ _let_1 B_24))))) (forall ((X_8 tptp.pname) (A_42 (-> tptp.pname Bool)) (B_23 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_8))) (=> (@ (@ tptp.ord_less_eq_pname_o A_42) B_23) (=> (@ _let_1 A_42) (@ _let_1 B_23))))) (forall ((X_8 tptp.hoare_1262092251_state) (A_42 (-> tptp.hoare_1262092251_state Bool)) (B_23 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state X_8))) (=> (@ (@ tptp.ord_le870406270tate_o A_42) B_23) (=> (@ _let_1 A_42) (@ _let_1 B_23))))) (forall ((A_41 (-> tptp.pname Bool)) (B_22 (-> tptp.pname Bool))) (=> (= A_41 B_22) (@ (@ tptp.ord_less_eq_pname_o B_22) A_41))) (forall ((A_41 (-> tptp.hoare_1262092251_state Bool)) (B_22 (-> tptp.hoare_1262092251_state Bool))) (=> (= A_41 B_22) (@ (@ tptp.ord_le870406270tate_o B_22) A_41))) (forall ((A_40 (-> tptp.pname Bool)) (B_21 (-> tptp.pname Bool))) (=> (= A_40 B_21) (@ (@ tptp.ord_less_eq_pname_o A_40) B_21))) (forall ((A_40 (-> tptp.hoare_1262092251_state Bool)) (B_21 (-> tptp.hoare_1262092251_state Bool))) (=> (= A_40 B_21) (@ (@ tptp.ord_le870406270tate_o A_40) B_21))) (forall ((A_39 (-> tptp.pname Bool)) (B_20 (-> tptp.pname Bool))) (= (= A_39 B_20) (and (@ (@ tptp.ord_less_eq_pname_o A_39) B_20) (@ (@ tptp.ord_less_eq_pname_o B_20) A_39)))) (forall ((A_39 (-> tptp.hoare_1262092251_state Bool)) (B_20 (-> tptp.hoare_1262092251_state Bool))) (= (= A_39 B_20) (and (@ (@ tptp.ord_le870406270tate_o A_39) B_20) (@ (@ tptp.ord_le870406270tate_o B_20) A_39)))) (forall ((A_38 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o A_38) A_38)) (forall ((A_38 (-> tptp.hoare_1262092251_state Bool))) (@ (@ tptp.ord_le870406270tate_o A_38) A_38)) (forall ((B_19 tptp.hoare_1262092251_state) (F_13 (-> tptp.pname tptp.hoare_1262092251_state)) (X_7 tptp.pname) (A_37 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_7) A_37) (=> (= B_19 (@ F_13 X_7)) (@ (@ tptp.member5164104_state B_19) (@ (@ tptp.image_669833818_state F_13) A_37))))) (forall ((F_12 (-> tptp.pname tptp.hoare_1262092251_state)) (X_6 tptp.pname) (A_36 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_6) A_36) (@ (@ tptp.member5164104_state (@ F_12 X_6)) (@ (@ tptp.image_669833818_state F_12) A_36)))) (forall ((Z tptp.hoare_1262092251_state) (F_11 (-> tptp.pname tptp.hoare_1262092251_state)) (A_35 (-> tptp.pname Bool))) (= (@ (@ tptp.member5164104_state Z) (@ (@ tptp.image_669833818_state F_11) A_35)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_35) (= Z (@ F_11 X_1)))))) (forall ((P_5 (-> tptp.pname Bool)) (Q (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (or (@ P_5 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_pname (@ tptp.collect_pname P_5)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q))))) (forall ((P_5 (-> tptp.hoare_1262092251_state Bool)) (Q (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (or (@ P_5 X_1) (@ Q X_1))))) (and (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state P_5)) (@ tptp.finite1178804552_state (@ tptp.collec1121927558_state Q))))) (forall ((P_5 (-> (-> tptp.pname Bool) Bool)) (Q (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (or (@ P_5 X_1) (@ Q X_1))))) (and (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_5)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q))))) (forall ((P_5 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (Q (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (or (@ P_5 X_1) (@ Q X_1))))) (and (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o P_5)) (@ tptp.finite1423311111tate_o (@ tptp.collec313158217tate_o Q))))) (forall ((X_1 tptp.pname) (Xa (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname X_1) Xa) (@ tptp.collect_pname (lambda ((Y_1 tptp.pname)) (or (= Y_1 X_1) (@ (@ tptp.member_pname Y_1) Xa)))))) (forall ((X_1 tptp.hoare_1262092251_state) (Xa (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.insert81609953_state X_1) Xa) (@ tptp.collec1121927558_state (lambda ((Y_1 tptp.hoare_1262092251_state)) (or (= Y_1 X_1) (@ (@ tptp.member5164104_state Y_1) Xa)))))) (forall ((X_1 (-> tptp.pname Bool)) (Xa (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o X_1) Xa) (@ tptp.collect_pname_o (lambda ((Y_1 (-> tptp.pname Bool))) (or (= Y_1 X_1) (@ (@ tptp.member_pname_o Y_1) Xa)))))) (forall ((X_1 (-> tptp.hoare_1262092251_state Bool)) (Xa (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ (@ tptp.insert1042460334tate_o X_1) Xa) (@ tptp.collec313158217tate_o (lambda ((Y_1 (-> tptp.hoare_1262092251_state Bool))) (or (= Y_1 X_1) (@ (@ tptp.member907417095tate_o Y_1) Xa)))))) (forall ((A_34 tptp.pname) (B_18 tptp.pname)) (=> (= (@ (@ tptp.insert_pname A_34) tptp.bot_bot_pname_o) (@ (@ tptp.insert_pname B_18) tptp.bot_bot_pname_o)) (= A_34 B_18))) (forall ((A_34 tptp.hoare_1262092251_state) (B_18 tptp.hoare_1262092251_state)) (=> (= (@ (@ tptp.insert81609953_state A_34) tptp.bot_bo113204042tate_o) (@ (@ tptp.insert81609953_state B_18) tptp.bot_bo113204042tate_o)) (= A_34 B_18))) (forall ((B_17 tptp.pname) (A_33 tptp.pname)) (=> (@ (@ tptp.member_pname B_17) (@ (@ tptp.insert_pname A_33) tptp.bot_bot_pname_o)) (= B_17 A_33))) (forall ((B_17 tptp.hoare_1262092251_state) (A_33 tptp.hoare_1262092251_state)) (=> (@ (@ tptp.member5164104_state B_17) (@ (@ tptp.insert81609953_state A_33) tptp.bot_bo113204042tate_o)) (= B_17 A_33))) (forall ((A_32 tptp.pname) (B_16 tptp.pname) (C_3 tptp.pname) (D_1 tptp.pname)) (= (= (@ (@ tptp.insert_pname A_32) (@ (@ tptp.insert_pname B_16) tptp.bot_bot_pname_o)) (@ (@ tptp.insert_pname C_3) (@ (@ tptp.insert_pname D_1) tptp.bot_bot_pname_o))) (or (and (= A_32 C_3) (= B_16 D_1)) (and (= A_32 D_1) (= B_16 C_3))))) (forall ((A_32 tptp.hoare_1262092251_state) (B_16 tptp.hoare_1262092251_state) (C_3 tptp.hoare_1262092251_state) (D_1 tptp.hoare_1262092251_state)) (= (= (@ (@ tptp.insert81609953_state A_32) (@ (@ tptp.insert81609953_state B_16) tptp.bot_bo113204042tate_o)) (@ (@ tptp.insert81609953_state C_3) (@ (@ tptp.insert81609953_state D_1) tptp.bot_bo113204042tate_o))) (or (and (= A_32 C_3) (= B_16 D_1)) (and (= A_32 D_1) (= B_16 C_3))))) (forall ((B_15 tptp.pname) (A_31 tptp.pname)) (= (@ (@ tptp.member_pname B_15) (@ (@ tptp.insert_pname A_31) tptp.bot_bot_pname_o)) (= B_15 A_31))) (forall ((B_15 tptp.hoare_1262092251_state) (A_31 tptp.hoare_1262092251_state)) (= (@ (@ tptp.member5164104_state B_15) (@ (@ tptp.insert81609953_state A_31) tptp.bot_bo113204042tate_o)) (= B_15 A_31))) (forall ((A_30 tptp.pname) (A_29 (-> tptp.pname Bool))) (not (= (@ (@ tptp.insert_pname A_30) A_29) tptp.bot_bot_pname_o))) (forall ((A_30 tptp.hoare_1262092251_state) (A_29 (-> tptp.hoare_1262092251_state Bool))) (not (= (@ (@ tptp.insert81609953_state A_30) A_29) tptp.bot_bo113204042tate_o))) (forall ((A_28 tptp.pname) (A_27 (-> tptp.pname Bool))) (not (= tptp.bot_bot_pname_o (@ (@ tptp.insert_pname A_28) A_27)))) (forall ((A_28 tptp.hoare_1262092251_state) (A_27 (-> tptp.hoare_1262092251_state Bool))) (not (= tptp.bot_bo113204042tate_o (@ (@ tptp.insert81609953_state A_28) A_27)))) (forall ((A_26 tptp.pname) (A_25 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_26) A_25)) (@ tptp.finite_finite_pname A_25))) (forall ((A_26 tptp.hoare_1262092251_state) (A_25 (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.finite1178804552_state (@ (@ tptp.insert81609953_state A_26) A_25)) (@ tptp.finite1178804552_state A_25))) (forall ((A_26 (-> tptp.pname Bool)) (A_25 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_26) A_25)) (@ tptp.finite297249702name_o A_25))) (forall ((A_26 (-> tptp.hoare_1262092251_state Bool)) (A_25 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ tptp.finite1423311111tate_o (@ (@ tptp.insert1042460334tate_o A_26) A_25)) (@ tptp.finite1423311111tate_o A_25))) (forall ((A_24 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o A_24) tptp.bot_bot_pname_o) (= A_24 tptp.bot_bot_pname_o))) (forall ((A_24 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.ord_le870406270tate_o A_24) tptp.bot_bo113204042tate_o) (= A_24 tptp.bot_bo113204042tate_o))) (forall ((F_10 (-> tptp.pname tptp.hoare_1262092251_state)) (A_23 (-> tptp.pname Bool))) (= (= (@ (@ tptp.image_669833818_state F_10) A_23) tptp.bot_bo113204042tate_o) (= A_23 tptp.bot_bot_pname_o))) (forall ((F_9 (-> tptp.pname tptp.hoare_1262092251_state))) (= (@ (@ tptp.image_669833818_state F_9) tptp.bot_bot_pname_o) tptp.bot_bo113204042tate_o)) (forall ((F_8 (-> tptp.pname tptp.hoare_1262092251_state)) (A_22 (-> tptp.pname Bool))) (= (= tptp.bot_bo113204042tate_o (@ (@ tptp.image_669833818_state F_8) A_22)) (= A_22 tptp.bot_bot_pname_o))) (forall ((A_21 (-> (-> tptp.pname Bool) Bool)) (B_14 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_21) B_14) (=> (@ tptp.finite297249702name_o B_14) (@ tptp.finite297249702name_o A_21)))) (forall ((A_21 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (B_14 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ (@ tptp.ord_le2012720639te_o_o A_21) B_14) (=> (@ tptp.finite1423311111tate_o B_14) (@ tptp.finite1423311111tate_o A_21)))) (forall ((A_21 (-> tptp.pname Bool)) (B_14 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_21) B_14) (=> (@ tptp.finite_finite_pname B_14) (@ tptp.finite_finite_pname A_21)))) (forall ((A_21 (-> tptp.hoare_1262092251_state Bool)) (B_14 (-> tptp.hoare_1262092251_state Bool))) (=> (@ (@ tptp.ord_le870406270tate_o A_21) B_14) (=> (@ tptp.finite1178804552_state B_14) (@ tptp.finite1178804552_state A_21)))) (forall ((A_20 (-> (-> tptp.pname Bool) Bool)) (B_13 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_13) (=> (@ (@ tptp.ord_le1205211808me_o_o A_20) B_13) (@ tptp.finite297249702name_o A_20)))) (forall ((A_20 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (B_13 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o B_13) (=> (@ (@ tptp.ord_le2012720639te_o_o A_20) B_13) (@ tptp.finite1423311111tate_o A_20)))) (forall ((A_20 (-> tptp.pname Bool)) (B_13 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_13) (=> (@ (@ tptp.ord_less_eq_pname_o A_20) B_13) (@ tptp.finite_finite_pname A_20)))) (forall ((A_20 (-> tptp.hoare_1262092251_state Bool)) (B_13 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state B_13) (=> (@ (@ tptp.ord_le870406270tate_o A_20) B_13) (@ tptp.finite1178804552_state A_20)))) (forall ((A_19 tptp.pname) (C_2 (-> tptp.pname Bool)) (D (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_19))) (=> (@ (@ tptp.ord_less_eq_pname_o C_2) D) (@ (@ tptp.ord_less_eq_pname_o (@ _let_1 C_2)) (@ _let_1 D))))) (forall ((A_19 tptp.hoare_1262092251_state) (C_2 (-> tptp.hoare_1262092251_state Bool)) (D (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.insert81609953_state A_19))) (=> (@ (@ tptp.ord_le870406270tate_o C_2) D) (@ (@ tptp.ord_le870406270tate_o (@ _let_1 C_2)) (@ _let_1 D))))) (forall ((X_5 tptp.pname) (A_18 (-> tptp.pname Bool))) (= (@ (@ tptp.member_pname X_5) A_18) (@ A_18 X_5))) (forall ((X_5 tptp.hoare_1262092251_state) (A_18 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.member5164104_state X_5) A_18) (@ A_18 X_5))) (forall ((P_4 (-> tptp.pname Bool))) (= (@ tptp.collect_pname P_4) P_4)) (forall ((P_4 (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.collec1121927558_state P_4) P_4)) (forall ((P_4 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.collect_pname_o P_4) P_4)) (forall ((P_4 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (= (@ tptp.collec313158217tate_o P_4) P_4)) (forall ((B_12 tptp.pname) (A_17 (-> tptp.pname Bool)) (B_11 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_17))) (=> (@ _let_1 B_11) (@ _let_1 (@ (@ tptp.insert_pname B_12) B_11))))) (forall ((B_12 tptp.hoare_1262092251_state) (A_17 (-> tptp.hoare_1262092251_state Bool)) (B_11 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.ord_le870406270tate_o A_17))) (=> (@ _let_1 B_11) (@ _let_1 (@ (@ tptp.insert81609953_state B_12) B_11))))) (forall ((B_10 (-> tptp.pname Bool)) (X_4 tptp.pname) (A_16 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_16))) (=> (not (@ (@ tptp.member_pname X_4) A_16)) (= (@ _let_1 (@ (@ tptp.insert_pname X_4) B_10)) (@ _let_1 B_10))))) (forall ((B_10 (-> tptp.hoare_1262092251_state Bool)) (X_4 tptp.hoare_1262092251_state) (A_16 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.ord_le870406270tate_o A_16))) (=> (not (@ (@ tptp.member5164104_state X_4) A_16)) (= (@ _let_1 (@ (@ tptp.insert81609953_state X_4) B_10)) (@ _let_1 B_10))))) (forall ((X_3 tptp.pname) (A_15 (-> tptp.pname Bool)) (B_9 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.insert_pname X_3) A_15)) B_9) (and (@ (@ tptp.member_pname X_3) B_9) (@ (@ tptp.ord_less_eq_pname_o A_15) B_9)))) (forall ((X_3 tptp.hoare_1262092251_state) (A_15 (-> tptp.hoare_1262092251_state Bool)) (B_9 (-> tptp.hoare_1262092251_state Bool))) (= (@ (@ tptp.ord_le870406270tate_o (@ (@ tptp.insert81609953_state X_3) A_15)) B_9) (and (@ (@ tptp.member5164104_state X_3) B_9) (@ (@ tptp.ord_le870406270tate_o A_15) B_9)))) (forall ((B_8 (-> tptp.pname Bool)) (A_14 tptp.pname)) (@ (@ tptp.ord_less_eq_pname_o B_8) (@ (@ tptp.insert_pname A_14) B_8))) (forall ((B_8 (-> tptp.hoare_1262092251_state Bool)) (A_14 tptp.hoare_1262092251_state)) (@ (@ tptp.ord_le870406270tate_o B_8) (@ (@ tptp.insert81609953_state A_14) B_8))) (forall ((F_7 (-> tptp.pname tptp.hoare_1262092251_state)) (X_2 tptp.pname) (A_13 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_669833818_state F_7) A_13))) (=> (@ (@ tptp.member_pname X_2) A_13) (= (@ (@ tptp.insert81609953_state (@ F_7 X_2)) _let_1) _let_1)))) (forall ((F_6 (-> tptp.pname tptp.hoare_1262092251_state)) (A_12 tptp.pname) (B_7 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_669833818_state F_6))) (= (@ _let_1 (@ (@ tptp.insert_pname A_12) B_7)) (@ (@ tptp.insert81609953_state (@ F_6 A_12)) (@ _let_1 B_7))))) (forall ((F_5 (-> tptp.pname tptp.hoare_1262092251_state)) (A_11 (-> tptp.pname Bool)) (B_6 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_669833818_state F_5))) (=> (@ (@ tptp.ord_less_eq_pname_o A_11) B_6) (@ (@ tptp.ord_le870406270tate_o (@ _let_1 A_11)) (@ _let_1 B_6))))) (forall ((B_5 (-> tptp.hoare_1262092251_state Bool)) (F_4 (-> tptp.pname tptp.hoare_1262092251_state)) (A_10 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_le870406270tate_o B_5) (@ (@ tptp.image_669833818_state F_4) A_10)) (exists ((AA (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o AA) A_10) (= B_5 (@ (@ tptp.image_669833818_state F_4) AA)))))) (forall ((M (-> tptp.pname tptp.option_com)) (A_9 tptp.pname) (B_4 tptp.com)) (=> (= (@ M A_9) (@ tptp.some_com B_4)) (@ (@ tptp.member_pname A_9) (@ tptp.dom_pname_com M)))) (forall ((P_3 (-> tptp.pname Bool)) (A_8 tptp.pname)) (let ((_let_1 (@ P_3 A_8))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= X_1 A_8) (@ P_3 X_1)))) (@ (@ tptp.insert_pname A_8) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= X_1 A_8) (@ P_3 X_1)))) tptp.bot_bot_pname_o))))) (forall ((P_3 (-> tptp.hoare_1262092251_state Bool)) (A_8 tptp.hoare_1262092251_state)) (let ((_let_1 (@ P_3 A_8))) (and (=> _let_1 (= (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (and (= X_1 A_8) (@ P_3 X_1)))) (@ (@ tptp.insert81609953_state A_8) tptp.bot_bo113204042tate_o))) (=> (not _let_1) (= (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (and (= X_1 A_8) (@ P_3 X_1)))) tptp.bot_bo113204042tate_o))))) (forall ((P_3 (-> (-> tptp.pname Bool) Bool)) (A_8 (-> tptp.pname Bool))) (let ((_let_1 (@ P_3 A_8))) (and (=> _let_1 (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= X_1 A_8) (@ P_3 X_1)))) (@ (@ tptp.insert_pname_o A_8) tptp.bot_bot_pname_o_o))) (=> (not _let_1) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= X_1 A_8) (@ P_3 X_1)))) tptp.bot_bot_pname_o_o))))) (forall ((P_3 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (A_8 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ P_3 A_8))) (and (=> _let_1 (= (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (and (= X_1 A_8) (@ P_3 X_1)))) (@ (@ tptp.insert1042460334tate_o A_8) tptp.bot_bo1962689075te_o_o))) (=> (not _let_1) (= (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (and (= X_1 A_8) (@ P_3 X_1)))) tptp.bot_bo1962689075te_o_o))))) (forall ((P_2 (-> tptp.pname Bool)) (A_7 tptp.pname)) (let ((_let_1 (@ P_2 A_7))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= A_7 X_1) (@ P_2 X_1)))) (@ (@ tptp.insert_pname A_7) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= A_7 X_1) (@ P_2 X_1)))) tptp.bot_bot_pname_o))))) (forall ((P_2 (-> tptp.hoare_1262092251_state Bool)) (A_7 tptp.hoare_1262092251_state)) (let ((_let_1 (@ P_2 A_7))) (and (=> _let_1 (= (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (and (= A_7 X_1) (@ P_2 X_1)))) (@ (@ tptp.insert81609953_state A_7) tptp.bot_bo113204042tate_o))) (=> (not _let_1) (= (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (and (= A_7 X_1) (@ P_2 X_1)))) tptp.bot_bo113204042tate_o))))) (forall ((P_2 (-> (-> tptp.pname Bool) Bool)) (A_7 (-> tptp.pname Bool))) (let ((_let_1 (@ P_2 A_7))) (and (=> _let_1 (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= A_7 X_1) (@ P_2 X_1)))) (@ (@ tptp.insert_pname_o A_7) tptp.bot_bot_pname_o_o))) (=> (not _let_1) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= A_7 X_1) (@ P_2 X_1)))) tptp.bot_bot_pname_o_o))))) (forall ((P_2 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (A_7 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ P_2 A_7))) (and (=> _let_1 (= (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (and (= A_7 X_1) (@ P_2 X_1)))) (@ (@ tptp.insert1042460334tate_o A_7) tptp.bot_bo1962689075te_o_o))) (=> (not _let_1) (= (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (and (= A_7 X_1) (@ P_2 X_1)))) tptp.bot_bo1962689075te_o_o))))) (forall ((A_6 tptp.pname)) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (= X_1 A_6))) (@ (@ tptp.insert_pname A_6) tptp.bot_bot_pname_o))) (forall ((A_6 tptp.hoare_1262092251_state)) (= (@ tptp.collec1121927558_state (lambda ((X_1 tptp.hoare_1262092251_state)) (= X_1 A_6))) (@ (@ tptp.insert81609953_state A_6) tptp.bot_bo113204042tate_o))) (forall ((A_6 (-> tptp.pname Bool))) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (= X_1 A_6))) (@ (@ tptp.insert_pname_o A_6) tptp.bot_bot_pname_o_o))) (forall ((A_6 (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.collec313158217tate_o (lambda ((X_1 (-> tptp.hoare_1262092251_state Bool))) (= X_1 A_6))) (@ (@ tptp.insert1042460334tate_o A_6) tptp.bot_bo1962689075te_o_o))) (forall ((A_5 tptp.pname)) (= (@ tptp.collect_pname (@ tptp.fequal_pname A_5)) (@ (@ tptp.insert_pname A_5) tptp.bot_bot_pname_o))) (forall ((A_5 tptp.hoare_1262092251_state)) (= (@ tptp.collec1121927558_state (@ tptp.fequal1925511196_state A_5)) (@ (@ tptp.insert81609953_state A_5) tptp.bot_bo113204042tate_o))) (forall ((A_5 (-> tptp.pname Bool))) (= (@ tptp.collect_pname_o (@ tptp.fequal_pname_o A_5)) (@ (@ tptp.insert_pname_o A_5) tptp.bot_bot_pname_o_o))) (forall ((A_5 (-> tptp.hoare_1262092251_state Bool))) (= (@ tptp.collec313158217tate_o (@ tptp.fequal1529404211tate_o A_5)) (@ (@ tptp.insert1042460334tate_o A_5) tptp.bot_bo1962689075te_o_o))) (forall ((C_1 tptp.com) (G (-> tptp.hoare_1262092251_state Bool))) (=> tptp.hoare_1821564147gleton (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) (@ tptp.dom_pname_com tptp.body)) (@ (@ tptp.hoare_930741239_state G) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT (@ tptp.body_1 X_1))) tptp.bot_bo113204042tate_o)))) (=> (@ tptp.wt C_1) (@ (@ tptp.hoare_930741239_state G) (@ (@ tptp.insert81609953_state (@ tptp.hoare_Mirabelle_MGT C_1)) tptp.bot_bo113204042tate_o)))))) _let_7 (forall ((B_2 tptp.hoare_1262092251_state) (F_3 (-> tptp.pname tptp.hoare_1262092251_state)) (A_4 (-> tptp.pname Bool))) (=> (@ (@ tptp.member5164104_state B_2) (@ (@ tptp.image_669833818_state F_3) A_4)) (not (forall ((X_1 tptp.pname)) (=> (= B_2 (@ F_3 X_1)) (not (@ (@ tptp.member_pname X_1) A_4))))))) (forall ((P_1 (-> (-> tptp.pname Bool) Bool)) (A_2 (-> tptp.pname Bool)) (F_1 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_1) (=> (@ (@ tptp.ord_less_eq_pname_o F_1) A_2) (=> (@ P_1 tptp.bot_bot_pname_o) (=> (forall ((A_3 tptp.pname) (F_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_3))) (=> (@ tptp.finite_finite_pname F_2) (=> (@ _let_1 A_2) (=> (not (@ _let_1 F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert_pname A_3) F_2)))))))) (@ P_1 F_1)))))) (forall ((P_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (A_2 (-> tptp.hoare_1262092251_state Bool)) (F_1 (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state F_1) (=> (@ (@ tptp.ord_le870406270tate_o F_1) A_2) (=> (@ P_1 tptp.bot_bo113204042tate_o) (=> (forall ((A_3 tptp.hoare_1262092251_state) (F_2 (-> tptp.hoare_1262092251_state Bool))) (let ((_let_1 (@ tptp.member5164104_state A_3))) (=> (@ tptp.finite1178804552_state F_2) (=> (@ _let_1 A_2) (=> (not (@ _let_1 F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert81609953_state A_3) F_2)))))))) (@ P_1 F_1)))))) (forall ((P_1 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (A_2 (-> (-> tptp.pname Bool) Bool)) (F_1 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_1) (=> (@ (@ tptp.ord_le1205211808me_o_o F_1) A_2) (=> (@ P_1 tptp.bot_bot_pname_o_o) (=> (forall ((A_3 (-> tptp.pname Bool)) (F_2 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.member_pname_o A_3))) (=> (@ tptp.finite297249702name_o F_2) (=> (@ _let_1 A_2) (=> (not (@ _let_1 F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert_pname_o A_3) F_2)))))))) (@ P_1 F_1)))))) (forall ((P_1 (-> (-> (-> tptp.hoare_1262092251_state Bool) Bool) Bool)) (A_2 (-> (-> tptp.hoare_1262092251_state Bool) Bool)) (F_1 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (=> (@ tptp.finite1423311111tate_o F_1) (=> (@ (@ tptp.ord_le2012720639te_o_o F_1) A_2) (=> (@ P_1 tptp.bot_bo1962689075te_o_o) (=> (forall ((A_3 (-> tptp.hoare_1262092251_state Bool)) (F_2 (-> (-> tptp.hoare_1262092251_state Bool) Bool))) (let ((_let_1 (@ tptp.member907417095tate_o A_3))) (=> (@ tptp.finite1423311111tate_o F_2) (=> (@ _let_1 A_2) (=> (not (@ _let_1 F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert1042460334tate_o A_3) F_2)))))))) (@ P_1 F_1)))))) (forall ((P tptp.pname)) (=> (@ tptp.wt (@ tptp.body_1 P)) (not (forall ((Y_1 tptp.com)) (not (= (@ tptp.body P) (@ tptp.some_com Y_1))))))) (forall ((B_1 (-> tptp.pname Bool)) (A_1 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (let ((_let_1 (@ tptp.member_pname X_1))) (=> (@ _let_1 A_1) (@ _let_1 B_1)))) (@ (@ tptp.ord_less_eq_pname_o A_1) B_1))) (forall ((B_1 (-> tptp.hoare_1262092251_state Bool)) (A_1 (-> tptp.hoare_1262092251_state Bool))) (=> (forall ((X_1 tptp.hoare_1262092251_state)) (let ((_let_1 (@ tptp.member5164104_state X_1))) (=> (@ _let_1 A_1) (@ _let_1 B_1)))) (@ (@ tptp.ord_le870406270tate_o A_1) B_1))) (forall ((F (-> tptp.pname tptp.hoare_1262092251_state)) (A (-> tptp.pname Bool)) (B (-> tptp.hoare_1262092251_state Bool))) (=> (@ tptp.finite1178804552_state B) (=> (@ (@ tptp.ord_le870406270tate_o B) (@ (@ tptp.image_669833818_state F) A)) (exists ((C (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C) A) (@ tptp.finite_finite_pname C) (= B (@ (@ tptp.image_669833818_state F) C))))))) (@ tptp.finite_finite_pname _let_3) (forall ((Pname_1 tptp.pname) (Pname tptp.pname)) (= (= (@ tptp.body_1 Pname_1) (@ tptp.body_1 Pname)) (= Pname_1 Pname))) (forall ((X tptp.pname) (Y tptp.pname)) (or (not (@ (@ tptp.fequal_pname X) Y)) (= X Y))) (forall ((X tptp.pname) (Y tptp.pname)) (or (not (= X Y)) (@ (@ tptp.fequal_pname X) Y))) (forall ((X (-> tptp.pname Bool)) (Y (-> tptp.pname Bool))) (or (not (@ (@ tptp.fequal_pname_o X) Y)) (= X Y))) (forall ((X (-> tptp.pname Bool)) (Y (-> tptp.pname Bool))) (or (not (= X Y)) (@ (@ tptp.fequal_pname_o X) Y))) (forall ((X tptp.hoare_1262092251_state) (Y tptp.hoare_1262092251_state)) (or (not (@ (@ tptp.fequal1925511196_state X) Y)) (= X Y))) (forall ((X tptp.hoare_1262092251_state) (Y tptp.hoare_1262092251_state)) (or (not (= X Y)) (@ (@ tptp.fequal1925511196_state X) Y))) (forall ((X (-> tptp.hoare_1262092251_state Bool)) (Y (-> tptp.hoare_1262092251_state Bool))) (or (not (@ (@ tptp.fequal1529404211tate_o X) Y)) (= X Y))) (forall ((X (-> tptp.hoare_1262092251_state Bool)) (Y (-> tptp.hoare_1262092251_state Bool))) (or (not (= X Y)) (@ (@ tptp.fequal1529404211tate_o X) Y))) tptp.hoare_1821564147gleton tptp.wT_bodies (@ tptp.finite1178804552_state tptp.fa) (not (@ (@ tptp.member5164104_state _let_1) tptp.fa)) (@ (@ tptp.ord_le870406270tate_o tptp.fa) (@ (@ tptp.image_669833818_state (lambda ((Pn tptp.pname)) (@ tptp.hoare_Mirabelle_MGT (@ tptp.the_com (@ tptp.body Pn))))) _let_3)) _let_6 (@ (@ tptp.hoare_930741239_state (@ (@ tptp.image_669833818_state (lambda ((Pn tptp.pname)) (@ tptp.hoare_Mirabelle_MGT (@ tptp.body_1 Pn)))) _let_3)) tptp.fa) _let_5 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.83/1.05 )
% 0.83/1.05 % SZS output end Proof for SWW474^1
% 0.83/1.06 % cvc5---1.0.5 exiting
% 0.83/1.06 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------