%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWW474^3 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Wed Feb 25 09:48:12 AM UTC 2026
% Result : Theorem 22.77s 4.74s
% Output : Refutation 22.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 20 unt; 0 typ; 2 def)
% Number of atoms : 335 ( 84 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 350 ( 55 ~; 41 |; 0 &; 231 @)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 282 ( 279 usr; 14 con; 0-6 aty)
% Number of variables : 60 ( 8 ^; 52 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
pname: $tType ).
thf(type_def_7,type,
hoare_1708887482_state: $tType ).
thf(type_def_8,type,
com: $tType ).
thf(type_def_9,type,
option_com: $tType ).
thf(type_def_10,type,
state: $tType ).
thf(type_def_11,type,
option_pname: $tType ).
thf(type_def_12,type,
option1624383643_state: $tType ).
thf(func_def_0,type,
com: $tType ).
thf(func_def_1,type,
pname: $tType ).
thf(func_def_2,type,
state: $tType ).
thf(func_def_3,type,
hoare_1708887482_state: $tType ).
thf(func_def_4,type,
option_com: $tType ).
thf(func_def_5,type,
option_pname: $tType ).
thf(func_def_6,type,
option1624383643_state: $tType ).
thf(func_def_7,type,
big_la1126801287name_o: ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_8,type,
big_la781588935tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
thf(func_def_9,type,
wt: com > $o ).
thf(func_def_11,type,
body: pname > option_com ).
thf(func_def_12,type,
body_1: pname > com ).
thf(func_def_13,type,
skip: com ).
thf(func_def_14,type,
semi: com > com > com ).
thf(func_def_15,type,
while: ( state > $o ) > com > com ).
thf(func_def_16,type,
finite138924780name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > $o ).
thf(func_def_17,type,
finite2034616076tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > $o ).
thf(func_def_18,type,
finite2048025996em_o_o: ( $o > $o > $o ) > $o ).
thf(func_def_19,type,
finite567462577_com_o: ( com > ( com > $o ) > com > $o ) > $o ).
thf(func_def_20,type,
finite1123817265name_o: ( pname > ( pname > $o ) > pname > $o ) > $o ).
thf(func_def_21,type,
finite662762081tate_o: ( hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > $o ).
thf(func_def_22,type,
finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(func_def_23,type,
finite1019950101te_o_o: ( ( ( hoare_1708887482_state > $o ) > $o ) > $o ) > $o ).
thf(func_def_24,type,
finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
thf(func_def_25,type,
finite1329924456tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
thf(func_def_26,type,
finite_finite_o: ( $o > $o ) > $o ).
thf(func_def_27,type,
finite_finite_com: ( com > $o ) > $o ).
thf(func_def_28,type,
finite_finite_pname: ( pname > $o ) > $o ).
thf(func_def_29,type,
finite1625599783_state: ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_30,type,
finite1849951719me_o_o: ( ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_31,type,
finite472615016name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_32,type,
finite463603445te_o_o: ( ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_33,type,
finite822533768tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
thf(func_def_34,type,
finite_fold_o_o: ( $o > $o > $o ) > $o > ( $o > $o ) > $o ).
thf(func_def_35,type,
finite504235573_com_o: ( com > ( com > $o ) > com > $o ) > ( com > $o ) > ( com > $o ) > com > $o ).
thf(func_def_36,type,
finite_fold_com_com: ( com > com > com ) > com > ( com > $o ) > com ).
thf(func_def_37,type,
finite603803317name_o: ( pname > ( pname > $o ) > pname > $o ) > ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_38,type,
finite1657623752_pname: ( pname > pname > pname ) > pname > ( pname > $o ) > pname ).
thf(func_def_39,type,
finite96880613tate_o: ( hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_40,type,
finite309095018_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_41,type,
finite2139561282_pname: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( pname > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( pname > $o ) > hoare_1708887482_state > $o ).
thf(func_def_42,type,
finite349908348name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
thf(func_def_43,type,
finite928843026tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ) > $o ).
thf(func_def_44,type,
finite860057415ne_com: ( com > com > com ) > ( ( com > $o ) > com ) > $o ).
thf(func_def_45,type,
finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
thf(func_def_46,type,
finite1615457021_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o ).
thf(func_def_47,type,
finite697516351name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
thf(func_def_48,type,
finite621643279tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ) > $o ).
thf(func_def_49,type,
finite666746948em_com: ( com > com > com ) > ( ( com > $o ) > com ) > $o ).
thf(func_def_50,type,
finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
thf(func_def_51,type,
finite1347568576_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o ).
thf(func_def_52,type,
fun_up1986763201_state: ( pname > hoare_1708887482_state ) > pname > hoare_1708887482_state > pname > hoare_1708887482_state ).
thf(func_def_53,type,
fun_up879233478on_com: ( pname > option_com ) > pname > option_com > pname > option_com ).
thf(func_def_54,type,
inj_on691924881name_o: ( ( pname > $o ) > pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_55,type,
inj_on176908593tate_o: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
thf(func_def_56,type,
inj_on11367768on_com: ( com > option_com ) > ( com > $o ) > $o ).
thf(func_def_57,type,
inj_on_pname_pname: ( pname > pname ) > ( pname > $o ) > $o ).
thf(func_def_58,type,
inj_on1553129421_state: ( pname > hoare_1708887482_state ) > ( pname > $o ) > $o ).
thf(func_def_59,type,
inj_on737724108_pname: ( pname > option_pname ) > ( pname > $o ) > $o ).
thf(func_def_60,type,
inj_on1945914667_pname: ( hoare_1708887482_state > pname ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_61,type,
inj_on632008595_state: ( hoare_1708887482_state > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_62,type,
inj_on945311362_state: ( hoare_1708887482_state > option1624383643_state ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_63,type,
overri1496249029on_com: ( pname > option_com ) > ( pname > option_com ) > ( pname > $o ) > pname > option_com ).
thf(func_def_64,type,
minus_1480864103me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_65,type,
minus_548038231te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_66,type,
minus_minus_com_o: ( com > $o ) > ( com > $o ) > com > $o ).
thf(func_def_67,type,
minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_68,type,
minus_2056855718tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_69,type,
the_com_1: ( com > $o ) > com ).
thf(func_def_70,type,
the_pname: ( pname > $o ) > pname ).
thf(func_def_71,type,
the_Ho851197897_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_72,type,
hoare_Mirabelle_MGT: com > hoare_1708887482_state ).
thf(func_def_73,type,
hoare_90032982_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_74,type,
hoare_496444244_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_76,type,
hoare_858012674_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1708887482_state ).
thf(func_def_77,type,
if_Hoa1374726218_state: $o > hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ).
thf(func_def_78,type,
if_option_com: $o > option_com > option_com > option_com ).
thf(func_def_79,type,
semila2013987940me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_80,type,
semila598060698te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_81,type,
semila513601829_com_o: ( com > $o ) > ( com > $o ) > com > $o ).
thf(func_def_82,type,
semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_83,type,
semila129691299tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_84,type,
semila854092349_inf_o: $o > $o > $o ).
thf(func_def_85,type,
semila181081674me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_86,type,
semila1853742644te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_87,type,
semila1562558655_com_o: ( com > $o ) > ( com > $o ) > com > $o ).
thf(func_def_88,type,
semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_89,type,
semila1122118281tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_90,type,
semila10642723_sup_o: $o > $o > $o ).
thf(func_def_91,type,
dom_com_com: ( com > option_com ) > com > $o ).
thf(func_def_92,type,
dom_pname_com: ( pname > option_com ) > pname > $o ).
thf(func_def_93,type,
dom_pname_pname: ( pname > option_pname ) > pname > $o ).
thf(func_def_94,type,
dom_pn1412407212_state: ( pname > option1624383643_state ) > pname > $o ).
thf(func_def_95,type,
dom_Ho1805192458_pname: ( hoare_1708887482_state > option_pname ) > hoare_1708887482_state > $o ).
thf(func_def_96,type,
dom_Ho1703271284_state: ( hoare_1708887482_state > option1624383643_state ) > hoare_1708887482_state > $o ).
thf(func_def_97,type,
restri1382200118me_com: ( pname > option_com ) > ( pname > $o ) > pname > option_com ).
thf(func_def_98,type,
evalc: com > state > state > $o ).
thf(func_def_99,type,
is_none_com: option_com > $o ).
thf(func_def_100,type,
is_none_pname: option_pname > $o ).
thf(func_def_101,type,
is_non163157940_state: option1624383643_state > $o ).
thf(func_def_102,type,
none_com: option_com ).
thf(func_def_103,type,
none_pname: option_pname ).
thf(func_def_104,type,
none_H1106584047_state: option1624383643_state ).
thf(func_def_105,type,
some_com: com > option_com ).
thf(func_def_106,type,
some_pname: pname > option_pname ).
thf(func_def_107,type,
some_H1974565227_state: hoare_1708887482_state > option1624383643_state ).
thf(func_def_108,type,
set_com: option_com > com > $o ).
thf(func_def_109,type,
set_pname: option_pname > pname > $o ).
thf(func_def_110,type,
set_Ho525251890_state: option1624383643_state > hoare_1708887482_state > $o ).
thf(func_def_111,type,
the_com: option_com > com ).
thf(func_def_112,type,
the_pname_1: option_pname > pname ).
thf(func_def_113,type,
the_Ho963921505_state: option1624383643_state > hoare_1708887482_state ).
thf(func_def_114,type,
bot_bot_pname_o_o: ( pname > $o ) > $o ).
thf(func_def_115,type,
bot_bo1678742418te_o_o: ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_116,type,
bot_bot_com_o: com > $o ).
thf(func_def_117,type,
bot_bot_pname_o: pname > $o ).
thf(func_def_118,type,
bot_bo19817387tate_o: hoare_1708887482_state > $o ).
thf(func_def_120,type,
ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_121,type,
ord_le1728773982te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
thf(func_def_122,type,
ord_less_eq_com_o: ( com > $o ) > ( com > $o ) > $o ).
thf(func_def_123,type,
ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_124,type,
ord_le777019615tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_125,type,
ord_less_eq_o: $o > $o > $o ).
thf(func_def_126,type,
top_top_com_o: com > $o ).
thf(func_def_127,type,
top_top_pname_o: pname > $o ).
thf(func_def_128,type,
top_to832624271tate_o: hoare_1708887482_state > $o ).
thf(func_def_129,type,
partial_flat_lub_com: com > ( com > $o ) > com ).
thf(func_def_130,type,
partia752020666_pname: pname > ( pname > $o ) > pname ).
thf(func_def_131,type,
partia1256728516_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_132,type,
collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_133,type,
collec58007891te_o_o: ( ( ( hoare_1708887482_state > $o ) > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
thf(func_def_134,type,
collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_135,type,
collec219771562tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_136,type,
collect_com: ( com > $o ) > com > $o ).
thf(func_def_137,type,
collect_pname: ( pname > $o ) > pname > $o ).
thf(func_def_138,type,
collec1568722789_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_139,type,
image_1085733413name_o: ( ( pname > $o ) > pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_140,type,
image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_141,type,
image_1922967206_state: ( ( pname > $o ) > hoare_1708887482_state ) > ( ( pname > $o ) > $o ) > hoare_1708887482_state > $o ).
thf(func_def_142,type,
image_909543877tate_o: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_143,type,
image_2051418740_pname: ( ( hoare_1708887482_state > $o ) > pname ) > ( ( hoare_1708887482_state > $o ) > $o ) > pname > $o ).
thf(func_def_144,type,
image_27005066_state: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
thf(func_def_145,type,
image_com_com: ( com > com ) > ( com > $o ) > com > $o ).
thf(func_def_146,type,
image_com_pname: ( com > pname ) > ( com > $o ) > pname > $o ).
thf(func_def_147,type,
image_934102463_state: ( com > hoare_1708887482_state ) > ( com > $o ) > hoare_1708887482_state > $o ).
thf(func_def_148,type,
image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_149,type,
image_425134806tate_o: ( pname > hoare_1708887482_state > $o ) > ( pname > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_150,type,
image_pname_com: ( pname > com ) > ( pname > $o ) > com > $o ).
thf(func_def_151,type,
image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(func_def_152,type,
image_1116629049_state: ( pname > hoare_1708887482_state ) > ( pname > $o ) > hoare_1708887482_state > $o ).
thf(func_def_153,type,
image_1552895654name_o: ( hoare_1708887482_state > pname > $o ) > ( hoare_1708887482_state > $o ) > ( pname > $o ) > $o ).
thf(func_def_154,type,
image_1551509096tate_o: ( hoare_1708887482_state > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_155,type,
image_1604448413te_com: ( hoare_1708887482_state > com ) > ( hoare_1708887482_state > $o ) > com > $o ).
thf(func_def_156,type,
image_1509414295_pname: ( hoare_1708887482_state > pname ) > ( hoare_1708887482_state > $o ) > pname > $o ).
thf(func_def_157,type,
image_757158439_state: ( hoare_1708887482_state > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_158,type,
insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(func_def_159,type,
insert949073679tate_o: ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_160,type,
insert_o: $o > ( $o > $o ) > $o > $o ).
thf(func_def_161,type,
insert_com: com > ( com > $o ) > com > $o ).
thf(func_def_162,type,
insert_pname: pname > ( pname > $o ) > pname > $o ).
thf(func_def_163,type,
insert528405184_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_164,type,
the_elem_com: ( com > $o ) > com ).
thf(func_def_165,type,
the_elem_pname: ( pname > $o ) > pname ).
thf(func_def_166,type,
the_el864710747_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_167,type,
vimage1943311875_state: ( pname > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > pname > $o ).
thf(func_def_168,type,
fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(func_def_169,type,
fequal1436017556tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_170,type,
fequal_com: com > com > $o ).
thf(func_def_171,type,
fequal_pname: pname > pname > $o ).
thf(func_def_172,type,
fequal_state: state > state > $o ).
thf(func_def_173,type,
fequal224822779_state: hoare_1708887482_state > hoare_1708887482_state > $o ).
thf(func_def_174,type,
member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(func_def_175,type,
member814030440tate_o: ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
thf(func_def_176,type,
member_o: $o > ( $o > $o ) > $o ).
thf(func_def_177,type,
member_com: com > ( com > $o ) > $o ).
thf(func_def_178,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(func_def_179,type,
member451959335_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > $o ).
thf(func_def_180,type,
fa: hoare_1708887482_state > $o ).
thf(func_def_181,type,
pn: pname ).
thf(func_def_182,type,
y: com ).
thf(func_def_196,type,
sK0: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_197,type,
sK1: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_198,type,
sK2: ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state ).
thf(func_def_199,type,
sK3: ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
thf(func_def_200,type,
sK4: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_201,type,
sK5: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_202,type,
sK6: ( pname > $o ) > pname ).
thf(func_def_203,type,
sK7: ( pname > $o ) > pname > $o ).
thf(func_def_204,type,
sK8: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_205,type,
sK9: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_206,type,
sK10: ( pname > $o ) > ( pname > hoare_1708887482_state ) > ( pname > hoare_1708887482_state ) > pname ).
thf(func_def_207,type,
sK11: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_208,type,
sK12: hoare_1708887482_state > $o ).
thf(func_def_209,type,
sK13: hoare_1708887482_state > $o ).
thf(func_def_210,type,
sK14: hoare_1708887482_state > $o ).
thf(func_def_211,type,
sK15: ( state > $o ) > state > com > state > state ).
thf(func_def_212,type,
sK16: ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_213,type,
sK17: ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_214,type,
sK18: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state ).
thf(func_def_215,type,
sK19: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
thf(func_def_216,type,
sK20: ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_217,type,
sK21: ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_218,type,
sK22: ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_219,type,
sK23: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_220,type,
sK24: ( hoare_1708887482_state > $o ) > ( pname > state > state > $o ) > ( pname > state > state > $o ) > ( pname > com ) > ( pname > state > state > $o ) > ( pname > state > state > $o ) > pname ).
thf(func_def_221,type,
sK25: state > state ).
thf(func_def_222,type,
sK26: ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_223,type,
sK27: ( state > state > $o ) > ( state > state > $o ) > state ).
thf(func_def_224,type,
sK28: ( ( pname > $o ) > $o ) > pname ).
thf(func_def_225,type,
sK29: ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_226,type,
sK30: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_227,type,
sK31: ( state > state > $o ) > ( state > state > $o ) > com > ( hoare_1708887482_state > $o ) > state ).
thf(func_def_228,type,
sK32: ( state > state > $o ) > ( state > state > $o ) > com > ( hoare_1708887482_state > $o ) > state ).
thf(func_def_229,type,
sK33: ( ( pname > $o ) > $o ) > pname ).
thf(func_def_230,type,
sK34: ( ( pname > $o ) > $o ) > pname > $o ).
thf(func_def_231,type,
sK35: ( ( pname > $o ) > $o ) > pname ).
thf(func_def_232,type,
sK36: ( pname > $o ) > ( hoare_1708887482_state > $o ) > ( pname > hoare_1708887482_state ) > pname ).
thf(func_def_233,type,
sK37: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_234,type,
sK38: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_235,type,
sK39: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_236,type,
sK40: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_237,type,
sK41: ( pname > $o ) > ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_238,type,
sK42: ( pname > $o ) > pname > pname > $o ).
thf(func_def_239,type,
sK43: ( pname > option_com ) > pname > com ).
thf(func_def_240,type,
sK44: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_241,type,
sK45: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_242,type,
sK46: ( pname > $o ) > pname > $o ).
thf(func_def_243,type,
sK47: ( pname > $o ) > pname ).
thf(func_def_244,type,
sK48: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_245,type,
sK49: ( pname > $o ) > pname ).
thf(func_def_246,type,
sK50: ( pname > $o ) > ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_247,type,
sK51: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_248,type,
sK52: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_249,type,
sK53: hoare_1708887482_state > state > state > $o ).
thf(func_def_250,type,
sK54: hoare_1708887482_state > state > state > $o ).
thf(func_def_251,type,
sK55: hoare_1708887482_state > com ).
thf(func_def_252,type,
sK56: ( pname > $o ) > pname > pname > $o ).
thf(func_def_253,type,
sK57: hoare_1708887482_state > ( pname > hoare_1708887482_state ) > ( pname > $o ) > pname ).
thf(func_def_254,type,
sK58: ( hoare_1708887482_state > $o ) > pname ).
thf(func_def_255,type,
sK59: ( ( pname > $o ) > pname > $o ) > pname > $o ).
thf(func_def_256,type,
sK60: ( ( pname > $o ) > pname > $o ) > pname > $o ).
thf(func_def_257,type,
sK61: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_258,type,
sK62: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_259,type,
sK63: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_260,type,
sK64: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_261,type,
sK65: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_262,type,
sK66: pname > $o ).
thf(func_def_263,type,
sK67: pname > $o ).
thf(func_def_264,type,
sK68: pname > $o ).
thf(func_def_265,type,
sK69: hoare_1708887482_state > $o ).
thf(func_def_266,type,
sK70: hoare_1708887482_state > $o ).
thf(func_def_267,type,
sK71: hoare_1708887482_state > $o ).
thf(func_def_268,type,
sK72: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_269,type,
sK73: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_270,type,
sK74: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_271,type,
sK75: pname > com ).
thf(func_def_272,type,
sK76: ( pname > $o ) > ( pname > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > pname > $o ).
thf(func_def_273,type,
sK77: pname > $o ).
thf(func_def_274,type,
sK78: pname > $o ).
thf(func_def_275,type,
sK79: pname > $o ).
thf(func_def_276,type,
sK80: ( pname > hoare_1708887482_state ) > hoare_1708887482_state > ( pname > $o ) > pname ).
thf(func_def_277,type,
sK81: ( ( pname > $o ) > pname > $o ) > pname > $o ).
thf(func_def_278,type,
sK82: ( ( pname > $o ) > pname > $o ) > pname > $o ).
thf(func_def_279,type,
sK83: ( pname > hoare_1708887482_state ) > ( pname > $o ) > ( hoare_1708887482_state > $o ) > pname > $o ).
thf(func_def_280,type,
sK84: state ).
thf(func_def_281,type,
sK85: state ).
thf(func_def_282,type,
sK86: ( pname > $o ) > ( pname > $o ) > pname ).
thf(func_def_283,type,
sK87: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_284,type,
sK88: ( pname > $o ) > pname ).
thf(func_def_285,type,
sK89: ( ( pname > $o ) > $o ) > ( pname > $o ) > pname > $o ).
thf(func_def_286,type,
sK90: ( ( pname > $o ) > $o ) > ( pname > $o ) > pname ).
thf(func_def_287,type,
sK91: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(func_def_288,type,
sK92: ( hoare_1708887482_state > $o ) > ( state > state > $o ) > ( state > state > $o ) > com > state ).
thf(func_def_289,type,
sK93: ( hoare_1708887482_state > $o ) > ( state > state > $o ) > ( state > state > $o ) > com > state ).
thf(func_def_290,type,
sK94: ( state > state > $o ) > ( state > state > $o ) > ( hoare_1708887482_state > $o ) > ( state > state > $o ) > ( state > state > $o ) > com > state ).
thf(func_def_291,type,
sK95: ( pname > $o ) > pname ).
thf(func_def_292,type,
sK96: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_293,type,
sK97: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(func_def_294,type,
sK98: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
thf(func_def_295,type,
sK99: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state ).
thf(func_def_296,type,
sK100: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state ).
thf(func_def_298,type,
ph102:
!>[X0: $tType] : X0 ).
thf(f5295,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f4758,f5269,f5294]) ).
thf(f5294,plain,
~ spl101_1,
inference(avatar_contradiction_clause,[status(thm)],[f5293]) ).
thf(f5293,plain,
( $false
| ~ spl101_1 ),
inference(equality_resolution,[status(thm)],[f4753]) ).
thf(f4753,plain,
( ! [X0: pname] :
( ( body @ pn )
!= ( body @ X0 ) )
| ~ spl101_1 ),
inference(avatar_component_clause,[status(thm)],[f4752]) ).
thf(f4752,definition,
( spl101_1
<=> ! [X0: pname] :
( ( body @ pn )
!= ( body @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl101_1])],[avatar_definition]) ).
thf(f5269,plain,
~ spl101_2,
inference(avatar_contradiction_clause,[status(thm)],[f5268]) ).
thf(f5268,plain,
( $false
| ~ spl101_2 ),
inference(subsumption_resolution,[status(thm)],[f5262,f4757]) ).
thf(f4757,plain,
( ( ( wt @ y )
= $true )
| ~ spl101_2 ),
inference(avatar_component_clause,[status(thm)],[f4755]) ).
thf(f4755,definition,
( spl101_2
<=> ( ( wt @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl101_2])],[avatar_definition]) ).
thf(f5262,plain,
( ( wt @ y )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f5259]) ).
thf(f5259,plain,
( ( $true != $true )
| ( ( wt @ y )
!= $true ) ),
inference(superposition,[status(thm)],[f5178,f4739]) ).
thf(f4739,plain,
! [X0: com] :
( ( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo19817387tate_o ) )
= $true )
| ( ( wt @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4738]) ).
thf(f4738,plain,
! [X0: com] :
( ( ( wt @ X0 )
!= $true )
| ( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo19817387tate_o ) )
= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f4628]) ).
thf(f4628,plain,
! [X0: com] :
( ( $true != $true )
| ( ( wt @ X0 )
!= $true )
| ( $true != $true )
| ( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo19817387tate_o ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f4210,f4615,f4083]) ).
thf(f4083,plain,
hoare_1160767572gleton = $true,
inference(cnf_transformation,[status(thm)],[f2897]) ).
thf(f2897,plain,
hoare_1160767572gleton = $true,
inference(fool_elimination,[status(thm)],[f2896]) ).
thf(f2896,plain,
hoare_1160767572gleton,
inference(rectify,[status(thm)],[f1218]) ).
thf(f1218,axiom,
hoare_1160767572gleton,
file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',conj_0) ).
thf(f4615,plain,
wT_bodies = $true,
inference(cnf_transformation,[status(thm)],[f2103]) ).
thf(f2103,plain,
wT_bodies = $true,
inference(fool_elimination,[status(thm)],[f2102]) ).
thf(f2102,plain,
wT_bodies,
inference(rectify,[status(thm)],[f1219]) ).
thf(f1219,axiom,
wT_bodies,
file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',conj_1) ).
thf(f4210,plain,
! [X0: com] :
( ( wT_bodies != $true )
| ( ( wt @ X0 )
!= $true )
| ( hoare_1160767572gleton != $true )
| ( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo19817387tate_o ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f3602]) ).
thf(f3602,plain,
! [X0: com] :
( ( wT_bodies != $true )
| ( ( wt @ X0 )
!= $true )
| ( hoare_1160767572gleton != $true )
| ( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo19817387tate_o ) )
= $true ) ),
inference(flattening,[status(thm)],[f3601]) ).
thf(f3601,plain,
! [X0: com] :
( ( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo19817387tate_o ) )
= $true )
| ( ( wt @ X0 )
!= $true )
| ( wT_bodies != $true )
| ( hoare_1160767572gleton != $true ) ),
inference(ennf_transformation,[status(thm)],[f2867]) ).
thf(f2867,plain,
! [X0: com] :
( ( hoare_1160767572gleton = $true )
=> ( ( wT_bodies = $true )
=> ( ( ( wt @ X0 )
= $true )
=> ( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo19817387tate_o ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f2866]) ).
thf(f2866,plain,
! [X0: com] :
( hoare_1160767572gleton
=> ( wT_bodies
=> ( ( wt @ X0 )
=> ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ X0 ) @ bot_bo19817387tate_o ) ) ) ) ),
inference(rectify,[status(thm)],[f67]) ).
thf(f67,axiom,
! [X42: com] :
( hoare_1160767572gleton
=> ( wT_bodies
=> ( ( wt @ X42 )
=> ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ X42 ) @ bot_bo19817387tate_o ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',fact_66_MGF) ).
thf(f5178,plain,
( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f5156]) ).
thf(f5156,plain,
( ( $true != $true )
| ( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )
!= $true ) ),
inference(superposition,[status(thm)],[f4861,f4366]) ).
thf(f4366,plain,
! [X0: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ bot_bo19817387tate_o @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f1971]) ).
thf(f1971,plain,
! [X0: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ bot_bo19817387tate_o @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f1970]) ).
thf(f1970,plain,
! [X0: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ bot_bo19817387tate_o @ X0 ),
inference(rectify,[status(thm)],[f515]) ).
thf(f515,axiom,
! [X366: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ bot_bo19817387tate_o @ X366 ),
file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',fact_514_bot__least) ).
thf(f4861,plain,
! [X0: hoare_1708887482_state > $o] :
( ( ( ord_le777019615tate_o @ X0
@ ( image_1116629049_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) ) )
!= $true )
| ( ( hoare_90032982_state @ X0 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4858]) ).
thf(f4858,plain,
! [X0: hoare_1708887482_state > $o] :
( ( $true != $true )
| ( ( hoare_90032982_state @ X0 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )
!= $true )
| ( ( ord_le777019615tate_o @ X0
@ ( image_1116629049_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f4541,f4320]) ).
thf(f4320,plain,
! [X2: hoare_1708887482_state > $o,X0: hoare_1708887482_state > $o,X1: hoare_1708887482_state > $o] :
( ( ( hoare_90032982_state @ X2 @ X0 )
= $true )
| ( ( ord_le777019615tate_o @ X1 @ X2 )
!= $true )
| ( ( hoare_90032982_state @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f3553]) ).
thf(f3553,plain,
! [X0: hoare_1708887482_state > $o,X1: hoare_1708887482_state > $o,X2: hoare_1708887482_state > $o] :
( ( ( ord_le777019615tate_o @ X1 @ X2 )
!= $true )
| ( ( hoare_90032982_state @ X2 @ X0 )
= $true )
| ( ( hoare_90032982_state @ X1 @ X0 )
!= $true ) ),
inference(flattening,[status(thm)],[f3552]) ).
thf(f3552,plain,
! [X0: hoare_1708887482_state > $o,X1: hoare_1708887482_state > $o,X2: hoare_1708887482_state > $o] :
( ( ( hoare_90032982_state @ X2 @ X0 )
= $true )
| ( ( ord_le777019615tate_o @ X1 @ X2 )
!= $true )
| ( ( hoare_90032982_state @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f1645]) ).
thf(f1645,plain,
! [X0: hoare_1708887482_state > $o,X1: hoare_1708887482_state > $o,X2: hoare_1708887482_state > $o] :
( ( ( hoare_90032982_state @ X1 @ X0 )
= $true )
=> ( ( ( ord_le777019615tate_o @ X1 @ X2 )
= $true )
=> ( ( hoare_90032982_state @ X2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f1644]) ).
thf(f1644,plain,
! [X0: hoare_1708887482_state > $o,X1: hoare_1708887482_state > $o,X2: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ X1 @ X0 )
=> ( ( ord_le777019615tate_o @ X1 @ X2 )
=> ( hoare_90032982_state @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X8: hoare_1708887482_state > $o,X7: hoare_1708887482_state > $o,X6: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ X7 @ X8 )
=> ( ( ord_le777019615tate_o @ X7 @ X6 )
=> ( hoare_90032982_state @ X6 @ X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',fact_3_thin) ).
thf(f4541,plain,
( ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f3181]) ).
thf(f3181,plain,
( ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )
!= $true ),
inference(flattening,[status(thm)],[f2017]) ).
thf(f2017,plain,
( ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [Y0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Y0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f2016]) ).
thf(f2016,plain,
~ ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [X0: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X0 ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) ),
inference(rectify,[status(thm)],[f1226]) ).
thf(f1226,negated_conjecture,
~ ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [X217: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X217 ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) ),
inference(negated_conjecture,[status(cth)],[f1225]) ).
thf(f1225,conjecture,
( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [X217: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ X217 ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',conj_7) ).
thf(f4758,plain,
( spl101_1
| spl101_2 ),
inference(avatar_split_clause,[status(thm)],[f4750,f4755,f4752]) ).
thf(f4750,plain,
! [X0: pname] :
( ( ( wt @ y )
= $true )
| ( ( body @ pn )
!= ( body @ X0 ) ) ),
inference(superposition,[status(thm)],[f4734,f4200]) ).
thf(f4200,plain,
( ( body @ pn )
= ( some_com @ y ) ),
inference(cnf_transformation,[status(thm)],[f1223]) ).
thf(f1223,axiom,
( ( body @ pn )
= ( some_com @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',conj_5) ).
thf(f4734,plain,
! [X0: pname,X1: com] :
( ( ( some_com @ X1 )
!= ( body @ X0 ) )
| ( ( wt @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4631]) ).
thf(f4631,plain,
! [X0: pname,X1: com] :
( ( $true != $true )
| ( ( some_com @ X1 )
!= ( body @ X0 ) )
| ( ( wt @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f4480,f4615]) ).
thf(f4480,plain,
! [X0: pname,X1: com] :
( ( wT_bodies != $true )
| ( ( some_com @ X1 )
!= ( body @ X0 ) )
| ( ( wt @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f3454]) ).
thf(f3454,plain,
! [X0: pname,X1: com] :
( ( wT_bodies != $true )
| ( ( some_com @ X1 )
!= ( body @ X0 ) )
| ( ( wt @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f3453]) ).
thf(f3453,plain,
! [X0: pname,X1: com] :
( ( ( wt @ X1 )
= $true )
| ( ( some_com @ X1 )
!= ( body @ X0 ) )
| ( wT_bodies != $true ) ),
inference(ennf_transformation,[status(thm)],[f1457]) ).
thf(f1457,plain,
! [X0: pname,X1: com] :
( ( wT_bodies = $true )
=> ( ( ( some_com @ X1 )
= ( body @ X0 ) )
=> ( ( wt @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f1456]) ).
thf(f1456,plain,
! [X0: pname,X1: com] :
( wT_bodies
=> ( ( ( some_com @ X1 )
= ( body @ X0 ) )
=> ( wt @ X1 ) ) ),
inference(rectify,[status(thm)],[f298]) ).
thf(f298,axiom,
! [X18: pname,X192: com] :
( wT_bodies
=> ( ( ( body @ X18 )
= ( some_com @ X192 ) )
=> ( wt @ X192 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',fact_297_WT__bodiesD) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW474^3 : TPTP v9.2.1. Released v5.3.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n025.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 13:41:12 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.24/0.45 ---- Original DTF file ---
% 0.24/0.45 thf(spec,logic,$$dhol).
% 0.24/0.45 %------------------------------------------------------------------------------
% 0.24/0.45 % File : SWW474^3 : TPTP v9.2.1. Released v5.3.0.
% 0.24/0.45 % Domain : Software Verification
% 0.24/0.45 % Problem : Hoare's Logic with Procedures line 440, 1000 axioms selected
% 0.24/0.45 % Version : Especial.
% 0.24/0.45 % English :
% 0.24/0.45
% 0.24/0.45 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.24/0.45 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.24/0.45 % Source : [Bla11]
% 0.24/0.45 % Names : hoare_1000_thf_l440 [Bla11]
% 0.24/0.45
% 0.24/0.45 % Status : Theorem
% 0.24/0.45 % Rating : 0.44 v9.1.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v5.3.0
% 0.24/0.45 % Syntax : Number of formulae : 1408 ( 309 unt; 183 typ; 0 def)
% 0.24/0.45 % Number of atoms : 5625 ( 988 equ; 98 cnn)
% 0.24/0.45 % Maximal formula atoms : 14 ( 4 avg)
% 0.24/0.45 % Number of connectives : 10844 ( 371 ~; 67 |; 218 &;8598 @)
% 0.24/0.45 % ( 250 <=>;1340 =>; 0 <=; 0 <~>)
% 0.24/0.45 % Maximal formula depth : 19 ( 7 avg)
% 0.24/0.45 % Number of types : 8 ( 7 usr)
% 0.24/0.45 % Number of type conns : 3712 (3712 >; 0 *; 0 +; 0 <<)
% 0.24/0.45 % Number of symbols : 183 ( 176 usr; 15 con; 0-5 aty)
% 0.24/0.45 % Number of variables : 3382 ( 194 ^;3110 !; 78 ?;3382 :)
% 0.24/0.45 % SPC : TH0_THM_EQU_NAR
% 0.24/0.45
% 0.24/0.45 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.24/0.45 % 2011-08-09 20:06:01
% 0.24/0.45 %------------------------------------------------------------------------------
% 0.24/0.45 %----Should-be-implicit typings (7)
% 0.24/0.45 thf(ty_ty_tc__Com__Ocom,type,
% 0.24/0.45 com: $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_ty_tc__Com__Opname,type,
% 0.24/0.45 pname: $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_ty_tc__Com__Ostate,type,
% 0.24/0.45 state: $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_ty_tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,
% 0.24/0.45 hoare_1708887482_state: $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.24/0.45 option_com: $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_ty_tc__Option__Ooption_Itc__Com__Opname_J,type,
% 0.24/0.45 option_pname: $tType ).
% 0.24/0.45
% 0.24/0.45 thf(ty_ty_tc__Option__Ooption_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Co,type,
% 0.24/0.45 option1624383643_state: $tType ).
% 0.24/0.45
% 0.24/0.45 %----Explicit typings (176)
% 0.24/0.45 thf(sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.24/0.45 big_la1126801287name_o: ( ( pname > $o ) > $o ) > pname > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Hoare____Mirabelle___,type,
% 0.24/0.45 big_la781588935tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Com_OWT,type,
% 0.24/0.45 wt: com > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Com_OWT__bodies,type,
% 0.24/0.45 wT_bodies: $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Com_Obody,type,
% 0.24/0.45 body: pname > option_com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Com_Ocom_OBODY,type,
% 0.24/0.45 body_1: pname > com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Com_Ocom_OSKIP,type,
% 0.24/0.45 skip: com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Com_Ocom_OSemi,type,
% 0.24/0.45 semi: com > com > com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Com_Ocom_OWhile,type,
% 0.24/0.45 while: ( state > $o ) > com > com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ocomp__fun__idem_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__C,type,
% 0.24/0.45 finite138924780name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ocomp__fun__idem_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv_,type,
% 0.24/0.45 finite2034616076tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ocomp__fun__idem_000_Eo_000_Eo,type,
% 0.24/0.45 finite2048025996em_o_o: ( $o > $o > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Ocom_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 0.24/0.45 finite567462577_com_o: ( com > ( com > $o ) > com > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Opname_000_062_Itc__Com__Opname_M_,type,
% 0.24/0.45 finite1123817265name_o: ( pname > ( pname > $o ) > pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otrip,type,
% 0.24/0.45 finite662762081tate_o: ( hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.24/0.45 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,
% 0.24/0.45 finite1019950101te_o_o: ( ( ( hoare_1708887482_state > $o ) > $o ) > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.24/0.45 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_,type,
% 0.24/0.45 finite1329924456tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofinite_000_Eo,type,
% 0.24/0.45 finite_finite_o: ( $o > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Ocom,type,
% 0.24/0.45 finite_finite_com: ( com > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 0.24/0.45 finite_finite_pname: ( pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__C,type,
% 0.24/0.45 finite1625599783_state: ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold_000_062_Itc__Com__Opname_M_Eo_J_000_062_I_062_Itc__Com__O,type,
% 0.24/0.45 finite1849951719me_o_o: ( ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_,type,
% 0.24/0.45 finite472615016name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,type,
% 0.24/0.45 finite463603445te_o_o: ( ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It_001,type,
% 0.24/0.45 finite822533768tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold_000_Eo_000_Eo,type,
% 0.24/0.45 finite_fold_o_o: ( $o > $o > $o ) > $o > ( $o > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold_000tc__Com__Ocom_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 0.24/0.45 finite504235573_com_o: ( com > ( com > $o ) > com > $o ) > ( com > $o ) > ( com > $o ) > com > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold_000tc__Com__Ocom_000tc__Com__Ocom,type,
% 0.24/0.45 finite_fold_com_com: ( com > com > com ) > com > ( com > $o ) > com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.24/0.45 finite603803317name_o: ( pname > ( pname > $o ) > pname > $o ) > ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.24/0.45 finite1657623752_pname: ( pname > pname > pname ) > pname > ( pname > $o ) > pname ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,type,
% 0.24/0.45 finite96880613tate_o: ( hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com_002,type,
% 0.24/0.45 finite309095018_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr,type,
% 0.24/0.45 finite2139561282_pname: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( pname > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( pname > $o ) > hoare_1708887482_state > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.24/0.45 finite349908348name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,
% 0.24/0.45 finite928843026tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Ocom,type,
% 0.24/0.45 finite860057415ne_com: ( com > com > com ) > ( ( com > $o ) > com ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,type,
% 0.24/0.45 finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_,type,
% 0.24/0.45 finite1615457021_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.24/0.45 finite697516351name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Hoare____Mirabelle____nqhfsdfv,type,
% 0.24/0.45 finite621643279tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Ocom,type,
% 0.24/0.45 finite666746948em_com: ( com > com > com ) > ( ( com > $o ) > com ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,type,
% 0.24/0.45 finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,
% 0.24/0.45 finite1347568576_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Ofun__upd_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__O,type,
% 0.24/0.45 fun_up1986763201_state: ( pname > hoare_1708887482_state ) > pname > hoare_1708887482_state > pname > hoare_1708887482_state ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Ofun__upd_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.24/0.45 fun_up879233478on_com: ( pname > option_com ) > pname > option_com > pname > option_com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Oinj__on_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_M_Eo_,type,
% 0.24/0.45 inj_on691924881name_o: ( ( pname > $o ) > pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Oinj__on_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Co,type,
% 0.24/0.45 inj_on176908593tate_o: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Oinj__on_000tc__Com__Ocom_000tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.24/0.45 inj_on11367768on_com: ( com > option_com ) > ( com > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.24/0.45 inj_on_pname_pname: ( pname > pname ) > ( pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,
% 0.24/0.45 inj_on1553129421_state: ( pname > hoare_1708887482_state ) > ( pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Opname_J,type,
% 0.24/0.45 inj_on737724108_pname: ( pname > option_pname ) > ( pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost,type,
% 0.24/0.45 inj_on1945914667_pname: ( hoare_1708887482_state > pname ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost_003,type,
% 0.24/0.45 inj_on632008595_state: ( hoare_1708887482_state > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost_004,type,
% 0.24/0.45 inj_on945311362_state: ( hoare_1708887482_state > option1624383643_state ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Fun_Ooverride__on_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_,type,
% 0.24/0.45 overri1496249029on_com: ( pname > option_com ) > ( pname > option_com ) > ( pname > $o ) > pname > option_com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.24/0.45 minus_1480864103me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsd,type,
% 0.24/0.45 minus_548038231te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 0.24/0.45 minus_minus_com_o: ( com > $o ) > ( com > $o ) > com > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.24/0.45 minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__,type,
% 0.24/0.45 minus_2056855718tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_HOL_OThe_000tc__Com__Ocom,type,
% 0.24/0.45 the_com_1: ( com > $o ) > com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_HOL_OThe_000tc__Com__Opname,type,
% 0.24/0.45 the_pname: ( pname > $o ) > pname ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_,type,
% 0.24/0.45 the_Ho851197897_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_OMGT,type,
% 0.24/0.45 hoare_Mirabelle_MGT: com > hoare_1708887482_state ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__derivs_000tc__Com__Ostate,type,
% 0.24/0.45 hoare_90032982_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__valids_000tc__Com__Ostate,type,
% 0.24/0.45 hoare_496444244_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ostate__not__singleton,type,
% 0.24/0.45 hoare_1160767572gleton: $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple_000tc__Com__Ostate,type,
% 0.24/0.45 hoare_858012674_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1708887482_state ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,
% 0.24/0.45 if_Hoa1374726218_state: $o > hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_If_000tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.24/0.45 if_option_com: $o > option_com > option_com > option_com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Com__Opname_M_Eo_,type,
% 0.24/0.45 semila2013987940me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell,type,
% 0.24/0.45 semila598060698te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 0.24/0.45 semila513601829_com_o: ( com > $o ) > ( com > $o ) > com > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.24/0.45 semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____n,type,
% 0.24/0.45 semila129691299tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_Eo,type,
% 0.24/0.45 semila854092349_inf_o: $o > $o > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Com__Opname_M_Eo_,type,
% 0.24/0.45 semila181081674me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell,type,
% 0.24/0.45 semila1853742644te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 0.24/0.45 semila1562558655_com_o: ( com > $o ) > ( com > $o ) > com > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.24/0.45 semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____n,type,
% 0.24/0.45 semila1122118281tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_Eo,type,
% 0.24/0.45 semila10642723_sup_o: $o > $o > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Map_Odom_000tc__Com__Ocom_000tc__Com__Ocom,type,
% 0.24/0.45 dom_com_com: ( com > option_com ) > com > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,type,
% 0.24/0.45 dom_pname_com: ( pname > option_com ) > pname > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.24/0.45 dom_pname_pname: ( pname > option_pname ) > pname > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otripl,type,
% 0.24/0.45 dom_pn1412407212_state: ( pname > option1624383643_state ) > pname > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Map_Odom_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_,type,
% 0.24/0.45 dom_Ho1805192458_pname: ( hoare_1708887482_state > option_pname ) > hoare_1708887482_state > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Map_Odom_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate__005,type,
% 0.24/0.45 dom_Ho1703271284_state: ( hoare_1708887482_state > option1624383643_state ) > hoare_1708887482_state > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Map_Orestrict__map_000tc__Com__Opname_000tc__Com__Ocom,type,
% 0.24/0.45 restri1382200118me_com: ( pname > option_com ) > ( pname > $o ) > pname > option_com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Natural_Oevalc,type,
% 0.24/0.45 evalc: com > state > state > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Option_Ois__none_000tc__Com__Ocom,type,
% 0.24/0.45 is_none_com: option_com > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Option_Ois__none_000tc__Com__Opname,type,
% 0.24/0.45 is_none_pname: option_pname > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Option_Ois__none_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com_,type,
% 0.24/0.45 is_non163157940_state: option1624383643_state > $o ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Option_Ooption_ONone_000tc__Com__Ocom,type,
% 0.24/0.45 none_com: option_com ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Option_Ooption_ONone_000tc__Com__Opname,type,
% 0.24/0.45 none_pname: option_pname ).
% 0.24/0.45
% 0.24/0.45 thf(sy_c_Option_Ooption_ONone_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__,type,
% 0.24/0.45 none_H1106584047_state: option1624383643_state ).
% 0.24/0.45
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% 0.24/0.46 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
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% 0.24/0.46 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Hoare____Mirabelle____nqh,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com_,type,
% 0.24/0.46 image_909543877tate_o: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__006,type,
% 0.24/0.46 image_2051418740_pname: ( ( hoare_1708887482_state > $o ) > pname ) > ( ( hoare_1708887482_state > $o ) > $o ) > pname > $o ).
% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__007,type,
% 0.24/0.46 image_27005066_state: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Com__Ocom_000tc__Com__Ocom,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Com__Ocom_000tc__Com__Opname,type,
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% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Com__Ocom_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otripl,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv,type,
% 0.24/0.46 image_425134806tate_o: ( pname > hoare_1708887482_state > $o ) > ( pname > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Ocom,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otri,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_008,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_010,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_011,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oinsert_000_Eo,type,
% 0.24/0.46 insert_o: $o > ( $o > $o ) > $o > $o ).
% 0.24/0.46
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Osta,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Othe__elem_000tc__Com__Ocom,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__O,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_Set_Ovimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otr,type,
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% 0.24/0.46 thf(sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_fequal_000tc__Com__Ocom,type,
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% 0.24/0.46
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_fequal_000tc__Com__Ostate,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.24/0.46 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.24/0.46
% 0.24/0.46 thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_c_member_000_Eo,type,
% 0.24/0.46 member_o: $o > ( $o > $o ) > $o ).
% 0.24/0.46
% 0.24/0.46 thf(sy_c_member_000tc__Com__Ocom,type,
% 0.24/0.46 member_com: com > ( com > $o ) > $o ).
% 0.24/0.46
% 0.24/0.46 thf(sy_c_member_000tc__Com__Opname,type,
% 0.24/0.46 member_pname: pname > ( pname > $o ) > $o ).
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% 0.24/0.46 thf(sy_c_member_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,
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% 0.24/0.46
% 0.24/0.46 thf(sy_v_Fa,type,
% 0.24/0.46 fa: hoare_1708887482_state > $o ).
% 0.24/0.46
% 0.24/0.46 thf(sy_v_pn,type,
% 0.24/0.46 pn: pname ).
% 0.24/0.46
% 0.24/0.46 thf(sy_v_y,type,
% 0.24/0.46 y: com ).
% 0.24/0.46
% 0.24/0.46 %----Relevant facts (1199)
% 0.24/0.46 thf(fact_0_empty,axiom,
% 0.24/0.46 ! [G_7: hoare_1708887482_state > $o] : ( hoare_90032982_state @ G_7 @ bot_bo19817387tate_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_1_asm,axiom,
% 0.24/0.46 ! [Ts_7: hoare_1708887482_state > $o,G_39: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ Ts_7 @ G_39 )
% 0.24/0.46 => ( hoare_90032982_state @ G_39 @ Ts_7 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_2_weaken,axiom,
% 0.24/0.46 ! [Ts_6: hoare_1708887482_state > $o,G_38: hoare_1708887482_state > $o,Ts_5: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( hoare_90032982_state @ G_38 @ Ts_5 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ Ts_6 @ Ts_5 )
% 0.24/0.46 => ( hoare_90032982_state @ G_38 @ Ts_6 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_3_thin,axiom,
% 0.24/0.46 ! [G_37: hoare_1708887482_state > $o,G_36: hoare_1708887482_state > $o,Ts_4: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( hoare_90032982_state @ G_36 @ Ts_4 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ G_36 @ G_37 )
% 0.24/0.46 => ( hoare_90032982_state @ G_37 @ Ts_4 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_4_cut,axiom,
% 0.24/0.46 ! [G_35: hoare_1708887482_state > $o,G_34: hoare_1708887482_state > $o,Ts_3: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( hoare_90032982_state @ G_34 @ Ts_3 )
% 0.24/0.46 => ( ( hoare_90032982_state @ G_35 @ G_34 )
% 0.24/0.46 => ( hoare_90032982_state @ G_35 @ Ts_3 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_5_hoare__derivs_Oinsert,axiom,
% 0.24/0.46 ! [Ts_2: hoare_1708887482_state > $o,G_33: hoare_1708887482_state > $o,T_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( hoare_90032982_state @ G_33 @ ( insert528405184_state @ T_3 @ bot_bo19817387tate_o ) )
% 0.24/0.46 => ( ( hoare_90032982_state @ G_33 @ Ts_2 )
% 0.24/0.46 => ( hoare_90032982_state @ G_33 @ ( insert528405184_state @ T_3 @ Ts_2 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_6_derivs__insertD,axiom,
% 0.24/0.46 ! [G_32: hoare_1708887482_state > $o,T_2: hoare_1708887482_state,Ts_1: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( hoare_90032982_state @ G_32 @ ( insert528405184_state @ T_2 @ Ts_1 ) )
% 0.24/0.46 => ( ( hoare_90032982_state @ G_32 @ ( insert528405184_state @ T_2 @ bot_bo19817387tate_o ) )
% 0.24/0.46 & ( hoare_90032982_state @ G_32 @ Ts_1 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_7_MGT__BodyN,axiom,
% 0.24/0.46 ! [Pn_1: pname,G_7: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( hoare_90032982_state @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ G_7 ) @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn_1 ) ) ) @ bot_bo19817387tate_o ) )
% 0.24/0.46 => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ bot_bo19817387tate_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_8_finite__Collect__subsets,axiom,
% 0.24/0.46 ! [A_274: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ A_274 )
% 0.24/0.46 => ( finite1066544169me_o_o
% 0.24/0.46 @ ( collect_pname_o_o
% 0.24/0.46 @ ^ [B_84: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_84 @ A_274 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_9_finite__Collect__subsets,axiom,
% 0.24/0.46 ! [A_274: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ A_274 )
% 0.24/0.46 => ( finite1019950101te_o_o
% 0.24/0.46 @ ( collec58007891te_o_o
% 0.24/0.46 @ ^ [B_84: ( hoare_1708887482_state > $o ) > $o] : ( ord_le1728773982te_o_o @ B_84 @ A_274 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_10_finite__Collect__subsets,axiom,
% 0.24/0.46 ! [A_274: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ A_274 )
% 0.24/0.46 => ( finite1329924456tate_o
% 0.24/0.46 @ ( collec219771562tate_o
% 0.24/0.46 @ ^ [B_84: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ B_84 @ A_274 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_11_finite__Collect__subsets,axiom,
% 0.24/0.46 ! [A_274: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ A_274 )
% 0.24/0.46 => ( finite297249702name_o
% 0.24/0.46 @ ( collect_pname_o
% 0.24/0.46 @ ^ [B_84: pname > $o] : ( ord_less_eq_pname_o @ B_84 @ A_274 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_12_finite__imageI,axiom,
% 0.24/0.46 ! [H_2: hoare_1708887482_state > pname > $o,F_88: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ F_88 )
% 0.24/0.46 => ( finite297249702name_o @ ( image_1552895654name_o @ H_2 @ F_88 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_13_finite__imageI,axiom,
% 0.24/0.46 ! [H_2: hoare_1708887482_state > hoare_1708887482_state > $o,F_88: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ F_88 )
% 0.24/0.46 => ( finite1329924456tate_o @ ( image_1551509096tate_o @ H_2 @ F_88 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_14_finite__imageI,axiom,
% 0.24/0.46 ! [H_2: pname > pname > $o,F_88: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ F_88 )
% 0.24/0.46 => ( finite297249702name_o @ ( image_pname_pname_o @ H_2 @ F_88 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_15_finite__imageI,axiom,
% 0.24/0.46 ! [H_2: pname > hoare_1708887482_state > $o,F_88: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ F_88 )
% 0.24/0.46 => ( finite1329924456tate_o @ ( image_425134806tate_o @ H_2 @ F_88 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_16_finite__imageI,axiom,
% 0.24/0.46 ! [H_2: ( pname > $o ) > hoare_1708887482_state,F_88: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ F_88 )
% 0.24/0.46 => ( finite1625599783_state @ ( image_1922967206_state @ H_2 @ F_88 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_17_finite__imageI,axiom,
% 0.24/0.46 ! [H_2: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,F_88: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ F_88 )
% 0.24/0.46 => ( finite1625599783_state @ ( image_27005066_state @ H_2 @ F_88 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_18_finite__imageI,axiom,
% 0.24/0.46 ! [H_2: ( pname > $o ) > pname,F_88: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ F_88 )
% 0.24/0.46 => ( finite_finite_pname @ ( image_pname_o_pname @ H_2 @ F_88 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_19_finite__imageI,axiom,
% 0.24/0.46 ! [H_2: ( hoare_1708887482_state > $o ) > pname,F_88: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ F_88 )
% 0.24/0.46 => ( finite_finite_pname @ ( image_2051418740_pname @ H_2 @ F_88 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_20_finite__imageI,axiom,
% 0.24/0.46 ! [H_2: pname > hoare_1708887482_state,F_88: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ F_88 )
% 0.24/0.46 => ( finite1625599783_state @ ( image_1116629049_state @ H_2 @ F_88 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_21_empty__subsetI,axiom,
% 0.24/0.46 ! [A_273: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_273 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_22_empty__subsetI,axiom,
% 0.24/0.46 ! [A_273: com > $o] : ( ord_less_eq_com_o @ bot_bot_com_o @ A_273 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_23_empty__subsetI,axiom,
% 0.24/0.46 ! [A_273: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ bot_bo19817387tate_o @ A_273 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_24_finite_OinsertI,axiom,
% 0.24/0.46 ! [A_272: com,A_271: com > $o] :
% 0.24/0.46 ( ( finite_finite_com @ A_271 )
% 0.24/0.46 => ( finite_finite_com @ ( insert_com @ A_272 @ A_271 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_25_finite_OinsertI,axiom,
% 0.24/0.46 ! [A_272: pname > $o,A_271: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ A_271 )
% 0.24/0.46 => ( finite297249702name_o @ ( insert_pname_o @ A_272 @ A_271 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_26_finite_OinsertI,axiom,
% 0.24/0.46 ! [A_272: hoare_1708887482_state > $o,A_271: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ A_271 )
% 0.24/0.46 => ( finite1329924456tate_o @ ( insert949073679tate_o @ A_272 @ A_271 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_27_finite_OinsertI,axiom,
% 0.24/0.46 ! [A_272: pname,A_271: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ A_271 )
% 0.24/0.46 => ( finite_finite_pname @ ( insert_pname @ A_272 @ A_271 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_28_finite_OinsertI,axiom,
% 0.24/0.46 ! [A_272: hoare_1708887482_state,A_271: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ A_271 )
% 0.24/0.46 => ( finite1625599783_state @ ( insert528405184_state @ A_272 @ A_271 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_29_finite_OemptyI,axiom,
% 0.24/0.46 finite297249702name_o @ bot_bot_pname_o_o ).
% 0.24/0.46
% 0.24/0.46 thf(fact_30_finite_OemptyI,axiom,
% 0.24/0.46 finite1329924456tate_o @ bot_bo1678742418te_o_o ).
% 0.24/0.46
% 0.24/0.46 thf(fact_31_finite_OemptyI,axiom,
% 0.24/0.46 finite_finite_com @ bot_bot_com_o ).
% 0.24/0.46
% 0.24/0.46 thf(fact_32_finite_OemptyI,axiom,
% 0.24/0.46 finite1625599783_state @ bot_bo19817387tate_o ).
% 0.24/0.46
% 0.24/0.46 thf(fact_33_finite_OemptyI,axiom,
% 0.24/0.46 finite_finite_pname @ bot_bot_pname_o ).
% 0.24/0.46
% 0.24/0.46 thf(fact_34_finite__Collect__conjI,axiom,
% 0.24/0.46 ! [Q_26: ( pname > $o ) > $o,P_45: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_45 ) )
% 0.24/0.46 | ( finite297249702name_o @ ( collect_pname_o @ Q_26 ) ) )
% 0.24/0.46 => ( finite297249702name_o
% 0.24/0.46 @ ( collect_pname_o
% 0.24/0.46 @ ^ [X_3: pname > $o] : ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_35_finite__Collect__conjI,axiom,
% 0.24/0.46 ! [Q_26: ( hoare_1708887482_state > $o ) > $o,P_45: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( ( finite1329924456tate_o @ ( collec219771562tate_o @ P_45 ) )
% 0.24/0.46 | ( finite1329924456tate_o @ ( collec219771562tate_o @ Q_26 ) ) )
% 0.24/0.46 => ( finite1329924456tate_o
% 0.24/0.46 @ ( collec219771562tate_o
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_36_finite__Collect__conjI,axiom,
% 0.24/0.46 ! [Q_26: hoare_1708887482_state > $o,P_45: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ( finite1625599783_state @ ( collec1568722789_state @ P_45 ) )
% 0.24/0.46 | ( finite1625599783_state @ ( collec1568722789_state @ Q_26 ) ) )
% 0.24/0.46 => ( finite1625599783_state
% 0.24/0.46 @ ( collec1568722789_state
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_37_finite__Collect__conjI,axiom,
% 0.24/0.46 ! [Q_26: pname > $o,P_45: pname > $o] :
% 0.24/0.46 ( ( ( finite_finite_pname @ ( collect_pname @ P_45 ) )
% 0.24/0.46 | ( finite_finite_pname @ ( collect_pname @ Q_26 ) ) )
% 0.24/0.46 => ( finite_finite_pname
% 0.24/0.46 @ ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_38_image__constant__conv,axiom,
% 0.24/0.46 ! [C_68: pname,A_270: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ( A_270 = bot_bo19817387tate_o )
% 0.24/0.46 => ( ( image_1509414295_pname
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : C_68
% 0.24/0.46 @ A_270 )
% 0.24/0.46 = bot_bot_pname_o ) )
% 0.24/0.46 & ( ( A_270 != bot_bo19817387tate_o )
% 0.24/0.46 => ( ( image_1509414295_pname
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : C_68
% 0.24/0.46 @ A_270 )
% 0.24/0.46 = ( insert_pname @ C_68 @ bot_bot_pname_o ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_39_image__constant__conv,axiom,
% 0.24/0.46 ! [C_68: com,A_270: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ( A_270 = bot_bo19817387tate_o )
% 0.24/0.46 => ( ( image_1604448413te_com
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : C_68
% 0.24/0.46 @ A_270 )
% 0.24/0.46 = bot_bot_com_o ) )
% 0.24/0.46 & ( ( A_270 != bot_bo19817387tate_o )
% 0.24/0.46 => ( ( image_1604448413te_com
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : C_68
% 0.24/0.46 @ A_270 )
% 0.24/0.46 = ( insert_com @ C_68 @ bot_bot_com_o ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_40_image__constant__conv,axiom,
% 0.24/0.46 ! [C_68: hoare_1708887482_state,A_270: com > $o] :
% 0.24/0.46 ( ( ( A_270 = bot_bot_com_o )
% 0.24/0.46 => ( ( image_934102463_state
% 0.24/0.46 @ ^ [X_3: com] : C_68
% 0.24/0.46 @ A_270 )
% 0.24/0.46 = bot_bo19817387tate_o ) )
% 0.24/0.46 & ( ( A_270 != bot_bot_com_o )
% 0.24/0.46 => ( ( image_934102463_state
% 0.24/0.46 @ ^ [X_3: com] : C_68
% 0.24/0.46 @ A_270 )
% 0.24/0.46 = ( insert528405184_state @ C_68 @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_41_image__constant__conv,axiom,
% 0.24/0.46 ! [C_68: hoare_1708887482_state,A_270: pname > $o] :
% 0.24/0.46 ( ( ( A_270 = bot_bot_pname_o )
% 0.24/0.46 => ( ( image_1116629049_state
% 0.24/0.46 @ ^ [X_3: pname] : C_68
% 0.24/0.46 @ A_270 )
% 0.24/0.46 = bot_bo19817387tate_o ) )
% 0.24/0.46 & ( ( A_270 != bot_bot_pname_o )
% 0.24/0.46 => ( ( image_1116629049_state
% 0.24/0.46 @ ^ [X_3: pname] : C_68
% 0.24/0.46 @ A_270 )
% 0.24/0.46 = ( insert528405184_state @ C_68 @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_42_image__constant,axiom,
% 0.24/0.46 ! [C_67: pname,X_119: hoare_1708887482_state,A_269: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ X_119 @ A_269 )
% 0.24/0.46 => ( ( image_1509414295_pname
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : C_67
% 0.24/0.46 @ A_269 )
% 0.24/0.46 = ( insert_pname @ C_67 @ bot_bot_pname_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_43_image__constant,axiom,
% 0.24/0.46 ! [C_67: com,X_119: hoare_1708887482_state,A_269: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ X_119 @ A_269 )
% 0.24/0.46 => ( ( image_1604448413te_com
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : C_67
% 0.24/0.46 @ A_269 )
% 0.24/0.46 = ( insert_com @ C_67 @ bot_bot_com_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_44_image__constant,axiom,
% 0.24/0.46 ! [C_67: pname,X_119: pname,A_269: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_119 @ A_269 )
% 0.24/0.46 => ( ( image_pname_pname
% 0.24/0.46 @ ^ [X_3: pname] : C_67
% 0.24/0.46 @ A_269 )
% 0.24/0.46 = ( insert_pname @ C_67 @ bot_bot_pname_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_45_image__constant,axiom,
% 0.24/0.46 ! [C_67: com,X_119: pname,A_269: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_119 @ A_269 )
% 0.24/0.46 => ( ( image_pname_com
% 0.24/0.46 @ ^ [X_3: pname] : C_67
% 0.24/0.46 @ A_269 )
% 0.24/0.46 = ( insert_com @ C_67 @ bot_bot_com_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_46_image__constant,axiom,
% 0.24/0.46 ! [C_67: hoare_1708887482_state,X_119: com,A_269: com > $o] :
% 0.24/0.46 ( ( member_com @ X_119 @ A_269 )
% 0.24/0.46 => ( ( image_934102463_state
% 0.24/0.46 @ ^ [X_3: com] : C_67
% 0.24/0.46 @ A_269 )
% 0.24/0.46 = ( insert528405184_state @ C_67 @ bot_bo19817387tate_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_47_image__constant,axiom,
% 0.24/0.46 ! [C_67: hoare_1708887482_state,X_119: pname,A_269: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_119 @ A_269 )
% 0.24/0.46 => ( ( image_1116629049_state
% 0.24/0.46 @ ^ [X_3: pname] : C_67
% 0.24/0.46 @ A_269 )
% 0.24/0.46 = ( insert528405184_state @ C_67 @ bot_bo19817387tate_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_48_insert__dom,axiom,
% 0.24/0.46 ! [F_87: com > option_com,X_118: com,Y_53: com] :
% 0.24/0.46 ( ( ( F_87 @ X_118 )
% 0.24/0.46 = ( some_com @ Y_53 ) )
% 0.24/0.46 => ( ( insert_com @ X_118 @ ( dom_com_com @ F_87 ) )
% 0.24/0.46 = ( dom_com_com @ F_87 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_49_insert__dom,axiom,
% 0.24/0.46 ! [F_87: hoare_1708887482_state > option_pname,X_118: hoare_1708887482_state,Y_53: pname] :
% 0.24/0.46 ( ( ( F_87 @ X_118 )
% 0.24/0.46 = ( some_pname @ Y_53 ) )
% 0.24/0.46 => ( ( insert528405184_state @ X_118 @ ( dom_Ho1805192458_pname @ F_87 ) )
% 0.24/0.46 = ( dom_Ho1805192458_pname @ F_87 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_50_insert__dom,axiom,
% 0.24/0.46 ! [F_87: hoare_1708887482_state > option1624383643_state,X_118: hoare_1708887482_state,Y_53: hoare_1708887482_state] :
% 0.24/0.46 ( ( ( F_87 @ X_118 )
% 0.24/0.46 = ( some_H1974565227_state @ Y_53 ) )
% 0.24/0.46 => ( ( insert528405184_state @ X_118 @ ( dom_Ho1703271284_state @ F_87 ) )
% 0.24/0.46 = ( dom_Ho1703271284_state @ F_87 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_51_insert__dom,axiom,
% 0.24/0.46 ! [F_87: pname > option_com,X_118: pname,Y_53: com] :
% 0.24/0.46 ( ( ( F_87 @ X_118 )
% 0.24/0.46 = ( some_com @ Y_53 ) )
% 0.24/0.46 => ( ( insert_pname @ X_118 @ ( dom_pname_com @ F_87 ) )
% 0.24/0.46 = ( dom_pname_com @ F_87 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_52_finite__surj,axiom,
% 0.24/0.46 ! [B_171: ( pname > $o ) > $o,F_86: hoare_1708887482_state > pname > $o,A_268: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ A_268 )
% 0.24/0.46 => ( ( ord_le1205211808me_o_o @ B_171 @ ( image_1552895654name_o @ F_86 @ A_268 ) )
% 0.24/0.46 => ( finite297249702name_o @ B_171 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_53_finite__surj,axiom,
% 0.24/0.46 ! [B_171: ( hoare_1708887482_state > $o ) > $o,F_86: hoare_1708887482_state > hoare_1708887482_state > $o,A_268: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ A_268 )
% 0.24/0.46 => ( ( ord_le1728773982te_o_o @ B_171 @ ( image_1551509096tate_o @ F_86 @ A_268 ) )
% 0.24/0.46 => ( finite1329924456tate_o @ B_171 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_54_finite__surj,axiom,
% 0.24/0.46 ! [B_171: pname > $o,F_86: hoare_1708887482_state > pname,A_268: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ A_268 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_171 @ ( image_1509414295_pname @ F_86 @ A_268 ) )
% 0.24/0.46 => ( finite_finite_pname @ B_171 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_55_finite__surj,axiom,
% 0.24/0.46 ! [B_171: ( pname > $o ) > $o,F_86: pname > pname > $o,A_268: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ A_268 )
% 0.24/0.46 => ( ( ord_le1205211808me_o_o @ B_171 @ ( image_pname_pname_o @ F_86 @ A_268 ) )
% 0.24/0.46 => ( finite297249702name_o @ B_171 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_56_finite__surj,axiom,
% 0.24/0.46 ! [B_171: ( hoare_1708887482_state > $o ) > $o,F_86: pname > hoare_1708887482_state > $o,A_268: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ A_268 )
% 0.24/0.46 => ( ( ord_le1728773982te_o_o @ B_171 @ ( image_425134806tate_o @ F_86 @ A_268 ) )
% 0.24/0.46 => ( finite1329924456tate_o @ B_171 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_57_finite__surj,axiom,
% 0.24/0.46 ! [B_171: pname > $o,F_86: pname > pname,A_268: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ A_268 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_171 @ ( image_pname_pname @ F_86 @ A_268 ) )
% 0.24/0.46 => ( finite_finite_pname @ B_171 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_58_finite__surj,axiom,
% 0.24/0.46 ! [B_171: hoare_1708887482_state > $o,F_86: ( pname > $o ) > hoare_1708887482_state,A_268: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ A_268 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ B_171 @ ( image_1922967206_state @ F_86 @ A_268 ) )
% 0.24/0.46 => ( finite1625599783_state @ B_171 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_59_finite__surj,axiom,
% 0.24/0.46 ! [B_171: hoare_1708887482_state > $o,F_86: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,A_268: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ A_268 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ B_171 @ ( image_27005066_state @ F_86 @ A_268 ) )
% 0.24/0.46 => ( finite1625599783_state @ B_171 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_60_finite__surj,axiom,
% 0.24/0.46 ! [B_171: pname > $o,F_86: ( pname > $o ) > pname,A_268: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ A_268 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_171 @ ( image_pname_o_pname @ F_86 @ A_268 ) )
% 0.24/0.46 => ( finite_finite_pname @ B_171 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_61_finite__surj,axiom,
% 0.24/0.46 ! [B_171: pname > $o,F_86: ( hoare_1708887482_state > $o ) > pname,A_268: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ A_268 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_171 @ ( image_2051418740_pname @ F_86 @ A_268 ) )
% 0.24/0.46 => ( finite_finite_pname @ B_171 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_62_finite__surj,axiom,
% 0.24/0.46 ! [B_171: hoare_1708887482_state > $o,F_86: pname > hoare_1708887482_state,A_268: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ A_268 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ B_171 @ ( image_1116629049_state @ F_86 @ A_268 ) )
% 0.24/0.46 => ( finite1625599783_state @ B_171 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_63_subset__singletonD,axiom,
% 0.24/0.46 ! [A_267: pname > $o,X_117: pname] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_267 @ ( insert_pname @ X_117 @ bot_bot_pname_o ) )
% 0.24/0.46 => ( ( A_267 = bot_bot_pname_o )
% 0.24/0.46 | ( A_267
% 0.24/0.46 = ( insert_pname @ X_117 @ bot_bot_pname_o ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_64_subset__singletonD,axiom,
% 0.24/0.46 ! [A_267: com > $o,X_117: com] :
% 0.24/0.46 ( ( ord_less_eq_com_o @ A_267 @ ( insert_com @ X_117 @ bot_bot_com_o ) )
% 0.24/0.46 => ( ( A_267 = bot_bot_com_o )
% 0.24/0.46 | ( A_267
% 0.24/0.46 = ( insert_com @ X_117 @ bot_bot_com_o ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_65_subset__singletonD,axiom,
% 0.24/0.46 ! [A_267: hoare_1708887482_state > $o,X_117: hoare_1708887482_state] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_267 @ ( insert528405184_state @ X_117 @ bot_bo19817387tate_o ) )
% 0.24/0.46 => ( ( A_267 = bot_bo19817387tate_o )
% 0.24/0.46 | ( A_267
% 0.24/0.46 = ( insert528405184_state @ X_117 @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_66_MGF,axiom,
% 0.24/0.46 ! [C_34: com] :
% 0.24/0.46 ( hoare_1160767572gleton
% 0.24/0.46 => ( wT_bodies
% 0.24/0.46 => ( ( wt @ C_34 )
% 0.24/0.46 => ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_67_emptyE,axiom,
% 0.24/0.46 ! [A_266: com] :
% 0.24/0.46 ~ ( member_com @ A_266 @ bot_bot_com_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_68_emptyE,axiom,
% 0.24/0.46 ! [A_266: hoare_1708887482_state] :
% 0.24/0.46 ~ ( member451959335_state @ A_266 @ bot_bo19817387tate_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_69_emptyE,axiom,
% 0.24/0.46 ! [A_266: pname] :
% 0.24/0.46 ~ ( member_pname @ A_266 @ bot_bot_pname_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_70_insertCI,axiom,
% 0.24/0.46 ! [B_170: com,A_265: com,B_169: com > $o] :
% 0.24/0.46 ( ( ~ ( member_com @ A_265 @ B_169 )
% 0.24/0.46 => ( A_265 = B_170 ) )
% 0.24/0.46 => ( member_com @ A_265 @ ( insert_com @ B_170 @ B_169 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_71_insertCI,axiom,
% 0.24/0.46 ! [B_170: pname,A_265: pname,B_169: pname > $o] :
% 0.24/0.46 ( ( ~ ( member_pname @ A_265 @ B_169 )
% 0.24/0.46 => ( A_265 = B_170 ) )
% 0.24/0.46 => ( member_pname @ A_265 @ ( insert_pname @ B_170 @ B_169 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_72_insertCI,axiom,
% 0.24/0.46 ! [B_170: hoare_1708887482_state,A_265: hoare_1708887482_state,B_169: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ~ ( member451959335_state @ A_265 @ B_169 )
% 0.24/0.46 => ( A_265 = B_170 ) )
% 0.24/0.46 => ( member451959335_state @ A_265 @ ( insert528405184_state @ B_170 @ B_169 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_73_insertE,axiom,
% 0.24/0.46 ! [A_264: com,B_168: com,A_263: com > $o] :
% 0.24/0.46 ( ( member_com @ A_264 @ ( insert_com @ B_168 @ A_263 ) )
% 0.24/0.46 => ( ( A_264 != B_168 )
% 0.24/0.46 => ( member_com @ A_264 @ A_263 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_74_insertE,axiom,
% 0.24/0.46 ! [A_264: pname,B_168: pname,A_263: pname > $o] :
% 0.24/0.46 ( ( member_pname @ A_264 @ ( insert_pname @ B_168 @ A_263 ) )
% 0.24/0.46 => ( ( A_264 != B_168 )
% 0.24/0.46 => ( member_pname @ A_264 @ A_263 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_75_insertE,axiom,
% 0.24/0.46 ! [A_264: hoare_1708887482_state,B_168: hoare_1708887482_state,A_263: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ A_264 @ ( insert528405184_state @ B_168 @ A_263 ) )
% 0.24/0.46 => ( ( A_264 != B_168 )
% 0.24/0.46 => ( member451959335_state @ A_264 @ A_263 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_76_equalityI,axiom,
% 0.24/0.46 ! [A_262: pname > $o,B_167: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_262 @ B_167 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_167 @ A_262 )
% 0.24/0.46 => ( A_262 = B_167 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_77_equalityI,axiom,
% 0.24/0.46 ! [A_262: hoare_1708887482_state > $o,B_167: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_262 @ B_167 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ B_167 @ A_262 )
% 0.24/0.46 => ( A_262 = B_167 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_78_subsetD,axiom,
% 0.24/0.46 ! [C_66: com,A_261: com > $o,B_166: com > $o] :
% 0.24/0.46 ( ( ord_less_eq_com_o @ A_261 @ B_166 )
% 0.24/0.46 => ( ( member_com @ C_66 @ A_261 )
% 0.24/0.46 => ( member_com @ C_66 @ B_166 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_79_subsetD,axiom,
% 0.24/0.46 ! [C_66: hoare_1708887482_state,A_261: hoare_1708887482_state > $o,B_166: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_261 @ B_166 )
% 0.24/0.46 => ( ( member451959335_state @ C_66 @ A_261 )
% 0.24/0.46 => ( member451959335_state @ C_66 @ B_166 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_80_subsetD,axiom,
% 0.24/0.46 ! [C_66: pname,A_261: pname > $o,B_166: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_261 @ B_166 )
% 0.24/0.46 => ( ( member_pname @ C_66 @ A_261 )
% 0.24/0.46 => ( member_pname @ C_66 @ B_166 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_81_image__eqI,axiom,
% 0.24/0.46 ! [A_260: hoare_1708887482_state > $o,B_165: com,F_85: hoare_1708887482_state > com,X_116: hoare_1708887482_state] :
% 0.24/0.46 ( ( B_165
% 0.24/0.46 = ( F_85 @ X_116 ) )
% 0.24/0.46 => ( ( member451959335_state @ X_116 @ A_260 )
% 0.24/0.46 => ( member_com @ B_165 @ ( image_1604448413te_com @ F_85 @ A_260 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_82_image__eqI,axiom,
% 0.24/0.46 ! [A_260: pname > $o,B_165: com,F_85: pname > com,X_116: pname] :
% 0.24/0.46 ( ( B_165
% 0.24/0.46 = ( F_85 @ X_116 ) )
% 0.24/0.46 => ( ( member_pname @ X_116 @ A_260 )
% 0.24/0.46 => ( member_com @ B_165 @ ( image_pname_com @ F_85 @ A_260 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_83_image__eqI,axiom,
% 0.24/0.46 ! [A_260: com > $o,B_165: hoare_1708887482_state,F_85: com > hoare_1708887482_state,X_116: com] :
% 0.24/0.46 ( ( B_165
% 0.24/0.46 = ( F_85 @ X_116 ) )
% 0.24/0.46 => ( ( member_com @ X_116 @ A_260 )
% 0.24/0.46 => ( member451959335_state @ B_165 @ ( image_934102463_state @ F_85 @ A_260 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_84_image__eqI,axiom,
% 0.24/0.46 ! [A_260: com > $o,B_165: pname,F_85: com > pname,X_116: com] :
% 0.24/0.46 ( ( B_165
% 0.24/0.46 = ( F_85 @ X_116 ) )
% 0.24/0.46 => ( ( member_com @ X_116 @ A_260 )
% 0.24/0.46 => ( member_pname @ B_165 @ ( image_com_pname @ F_85 @ A_260 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_85_image__eqI,axiom,
% 0.24/0.46 ! [A_260: pname > $o,B_165: hoare_1708887482_state,F_85: pname > hoare_1708887482_state,X_116: pname] :
% 0.24/0.46 ( ( B_165
% 0.24/0.46 = ( F_85 @ X_116 ) )
% 0.24/0.46 => ( ( member_pname @ X_116 @ A_260 )
% 0.24/0.46 => ( member451959335_state @ B_165 @ ( image_1116629049_state @ F_85 @ A_260 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_86_equals0D,axiom,
% 0.24/0.46 ! [A_259: com,A_258: com > $o] :
% 0.24/0.46 ( ( A_258 = bot_bot_com_o )
% 0.24/0.46 => ~ ( member_com @ A_259 @ A_258 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_87_equals0D,axiom,
% 0.24/0.46 ! [A_259: hoare_1708887482_state,A_258: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( A_258 = bot_bo19817387tate_o )
% 0.24/0.46 => ~ ( member451959335_state @ A_259 @ A_258 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_88_equals0D,axiom,
% 0.24/0.46 ! [A_259: pname,A_258: pname > $o] :
% 0.24/0.46 ( ( A_258 = bot_bot_pname_o )
% 0.24/0.46 => ~ ( member_pname @ A_259 @ A_258 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_89_Collect__empty__eq,axiom,
% 0.24/0.46 ! [P_44: pname > $o] :
% 0.24/0.46 ( ( ( collect_pname @ P_44 )
% 0.24/0.46 = bot_bot_pname_o )
% 0.24/0.46 <=> ! [X_3: pname] :
% 0.24/0.46 ~ ( P_44 @ X_3 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_90_Collect__empty__eq,axiom,
% 0.24/0.46 ! [P_44: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( ( collect_pname_o @ P_44 )
% 0.24/0.46 = bot_bot_pname_o_o )
% 0.24/0.46 <=> ! [X_3: pname > $o] :
% 0.24/0.46 ~ ( P_44 @ X_3 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_91_Collect__empty__eq,axiom,
% 0.24/0.46 ! [P_44: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( ( collec219771562tate_o @ P_44 )
% 0.24/0.46 = bot_bo1678742418te_o_o )
% 0.24/0.46 <=> ! [X_3: hoare_1708887482_state > $o] :
% 0.24/0.46 ~ ( P_44 @ X_3 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_92_Collect__empty__eq,axiom,
% 0.24/0.46 ! [P_44: com > $o] :
% 0.24/0.46 ( ( ( collect_com @ P_44 )
% 0.24/0.46 = bot_bot_com_o )
% 0.24/0.46 <=> ! [X_3: com] :
% 0.24/0.46 ~ ( P_44 @ X_3 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_93_Collect__empty__eq,axiom,
% 0.24/0.46 ! [P_44: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ( collec1568722789_state @ P_44 )
% 0.24/0.46 = bot_bo19817387tate_o )
% 0.24/0.46 <=> ! [X_3: hoare_1708887482_state] :
% 0.24/0.46 ~ ( P_44 @ X_3 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_94_empty__iff,axiom,
% 0.24/0.46 ! [C_65: com] :
% 0.24/0.46 ~ ( member_com @ C_65 @ bot_bot_com_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_95_empty__iff,axiom,
% 0.24/0.46 ! [C_65: hoare_1708887482_state] :
% 0.24/0.46 ~ ( member451959335_state @ C_65 @ bot_bo19817387tate_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_96_empty__iff,axiom,
% 0.24/0.46 ! [C_65: pname] :
% 0.24/0.46 ~ ( member_pname @ C_65 @ bot_bot_pname_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_97_empty__Collect__eq,axiom,
% 0.24/0.46 ! [P_43: pname > $o] :
% 0.24/0.46 ( ( bot_bot_pname_o
% 0.24/0.46 = ( collect_pname @ P_43 ) )
% 0.24/0.46 <=> ! [X_3: pname] :
% 0.24/0.46 ~ ( P_43 @ X_3 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_98_empty__Collect__eq,axiom,
% 0.24/0.46 ! [P_43: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( bot_bot_pname_o_o
% 0.24/0.46 = ( collect_pname_o @ P_43 ) )
% 0.24/0.46 <=> ! [X_3: pname > $o] :
% 0.24/0.46 ~ ( P_43 @ X_3 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_99_empty__Collect__eq,axiom,
% 0.24/0.46 ! [P_43: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( bot_bo1678742418te_o_o
% 0.24/0.46 = ( collec219771562tate_o @ P_43 ) )
% 0.24/0.46 <=> ! [X_3: hoare_1708887482_state > $o] :
% 0.24/0.46 ~ ( P_43 @ X_3 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_100_empty__Collect__eq,axiom,
% 0.24/0.46 ! [P_43: com > $o] :
% 0.24/0.46 ( ( bot_bot_com_o
% 0.24/0.46 = ( collect_com @ P_43 ) )
% 0.24/0.46 <=> ! [X_3: com] :
% 0.24/0.46 ~ ( P_43 @ X_3 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_101_empty__Collect__eq,axiom,
% 0.24/0.46 ! [P_43: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( bot_bo19817387tate_o
% 0.24/0.46 = ( collec1568722789_state @ P_43 ) )
% 0.24/0.46 <=> ! [X_3: hoare_1708887482_state] :
% 0.24/0.46 ~ ( P_43 @ X_3 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_102_ex__in__conv,axiom,
% 0.24/0.46 ! [A_257: com > $o] :
% 0.24/0.46 ( ? [X_3: com] : ( member_com @ X_3 @ A_257 )
% 0.24/0.46 <=> ( A_257 != bot_bot_com_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_103_ex__in__conv,axiom,
% 0.24/0.46 ! [A_257: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ? [X_3: hoare_1708887482_state] : ( member451959335_state @ X_3 @ A_257 )
% 0.24/0.46 <=> ( A_257 != bot_bo19817387tate_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_104_ex__in__conv,axiom,
% 0.24/0.46 ! [A_257: pname > $o] :
% 0.24/0.46 ( ? [X_3: pname] : ( member_pname @ X_3 @ A_257 )
% 0.24/0.46 <=> ( A_257 != bot_bot_pname_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_105_all__not__in__conv,axiom,
% 0.24/0.46 ! [A_256: com > $o] :
% 0.24/0.46 ( ! [X_3: com] :
% 0.24/0.46 ~ ( member_com @ X_3 @ A_256 )
% 0.24/0.46 <=> ( A_256 = bot_bot_com_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_106_all__not__in__conv,axiom,
% 0.24/0.46 ! [A_256: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ! [X_3: hoare_1708887482_state] :
% 0.24/0.46 ~ ( member451959335_state @ X_3 @ A_256 )
% 0.24/0.46 <=> ( A_256 = bot_bo19817387tate_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_107_all__not__in__conv,axiom,
% 0.24/0.46 ! [A_256: pname > $o] :
% 0.24/0.46 ( ! [X_3: pname] :
% 0.24/0.46 ~ ( member_pname @ X_3 @ A_256 )
% 0.24/0.46 <=> ( A_256 = bot_bot_pname_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_108_empty__def,axiom,
% 0.24/0.46 ( bot_bot_pname_o
% 0.24/0.46 = ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : $false ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_109_empty__def,axiom,
% 0.24/0.46 ( bot_bot_pname_o_o
% 0.24/0.46 = ( collect_pname_o
% 0.24/0.46 @ ^ [X_3: pname > $o] : $false ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_110_empty__def,axiom,
% 0.24/0.46 ( bot_bo1678742418te_o_o
% 0.24/0.46 = ( collec219771562tate_o
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state > $o] : $false ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_111_empty__def,axiom,
% 0.24/0.46 ( bot_bot_com_o
% 0.24/0.46 = ( collect_com
% 0.24/0.46 @ ^ [X_3: com] : $false ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_112_empty__def,axiom,
% 0.24/0.46 ( bot_bo19817387tate_o
% 0.24/0.46 = ( collec1568722789_state
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : $false ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_113_insert__absorb,axiom,
% 0.24/0.46 ! [A_255: com,A_254: com > $o] :
% 0.24/0.46 ( ( member_com @ A_255 @ A_254 )
% 0.24/0.46 => ( ( insert_com @ A_255 @ A_254 )
% 0.24/0.46 = A_254 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_114_insert__absorb,axiom,
% 0.24/0.46 ! [A_255: pname,A_254: pname > $o] :
% 0.24/0.46 ( ( member_pname @ A_255 @ A_254 )
% 0.24/0.46 => ( ( insert_pname @ A_255 @ A_254 )
% 0.24/0.46 = A_254 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_115_insert__absorb,axiom,
% 0.24/0.46 ! [A_255: hoare_1708887482_state,A_254: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ A_255 @ A_254 )
% 0.24/0.46 => ( ( insert528405184_state @ A_255 @ A_254 )
% 0.24/0.46 = A_254 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_116_insertI2,axiom,
% 0.24/0.46 ! [B_164: com,A_253: com,B_163: com > $o] :
% 0.24/0.46 ( ( member_com @ A_253 @ B_163 )
% 0.24/0.46 => ( member_com @ A_253 @ ( insert_com @ B_164 @ B_163 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_117_insertI2,axiom,
% 0.24/0.46 ! [B_164: pname,A_253: pname,B_163: pname > $o] :
% 0.24/0.46 ( ( member_pname @ A_253 @ B_163 )
% 0.24/0.46 => ( member_pname @ A_253 @ ( insert_pname @ B_164 @ B_163 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_118_insertI2,axiom,
% 0.24/0.46 ! [B_164: hoare_1708887482_state,A_253: hoare_1708887482_state,B_163: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ A_253 @ B_163 )
% 0.24/0.46 => ( member451959335_state @ A_253 @ ( insert528405184_state @ B_164 @ B_163 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_119_insert__ident,axiom,
% 0.24/0.46 ! [B_162: com > $o,X_115: com,A_252: com > $o] :
% 0.24/0.46 ( ~ ( member_com @ X_115 @ A_252 )
% 0.24/0.46 => ( ~ ( member_com @ X_115 @ B_162 )
% 0.24/0.46 => ( ( ( insert_com @ X_115 @ A_252 )
% 0.24/0.46 = ( insert_com @ X_115 @ B_162 ) )
% 0.24/0.46 <=> ( A_252 = B_162 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_120_insert__ident,axiom,
% 0.24/0.46 ! [B_162: pname > $o,X_115: pname,A_252: pname > $o] :
% 0.24/0.46 ( ~ ( member_pname @ X_115 @ A_252 )
% 0.24/0.46 => ( ~ ( member_pname @ X_115 @ B_162 )
% 0.24/0.46 => ( ( ( insert_pname @ X_115 @ A_252 )
% 0.24/0.46 = ( insert_pname @ X_115 @ B_162 ) )
% 0.24/0.46 <=> ( A_252 = B_162 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_121_insert__ident,axiom,
% 0.24/0.46 ! [B_162: hoare_1708887482_state > $o,X_115: hoare_1708887482_state,A_252: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ~ ( member451959335_state @ X_115 @ A_252 )
% 0.24/0.46 => ( ~ ( member451959335_state @ X_115 @ B_162 )
% 0.24/0.46 => ( ( ( insert528405184_state @ X_115 @ A_252 )
% 0.24/0.46 = ( insert528405184_state @ X_115 @ B_162 ) )
% 0.24/0.46 <=> ( A_252 = B_162 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_122_insert__code,axiom,
% 0.24/0.46 ! [Y_52: pname,A_251: pname > $o,X_114: pname] :
% 0.24/0.46 ( ( insert_pname @ Y_52 @ A_251 @ X_114 )
% 0.24/0.46 <=> ( ( Y_52 = X_114 )
% 0.24/0.46 | ( A_251 @ X_114 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_123_insert__code,axiom,
% 0.24/0.46 ! [Y_52: com,A_251: com > $o,X_114: com] :
% 0.24/0.46 ( ( insert_com @ Y_52 @ A_251 @ X_114 )
% 0.24/0.46 <=> ( ( Y_52 = X_114 )
% 0.24/0.46 | ( A_251 @ X_114 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_124_insert__code,axiom,
% 0.24/0.46 ! [Y_52: hoare_1708887482_state,A_251: hoare_1708887482_state > $o,X_114: hoare_1708887482_state] :
% 0.24/0.46 ( ( insert528405184_state @ Y_52 @ A_251 @ X_114 )
% 0.24/0.46 <=> ( ( Y_52 = X_114 )
% 0.24/0.46 | ( A_251 @ X_114 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_125_insert__iff,axiom,
% 0.24/0.46 ! [A_250: com,B_161: com,A_249: com > $o] :
% 0.24/0.46 ( ( member_com @ A_250 @ ( insert_com @ B_161 @ A_249 ) )
% 0.24/0.46 <=> ( ( A_250 = B_161 )
% 0.24/0.46 | ( member_com @ A_250 @ A_249 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_126_insert__iff,axiom,
% 0.24/0.46 ! [A_250: pname,B_161: pname,A_249: pname > $o] :
% 0.24/0.46 ( ( member_pname @ A_250 @ ( insert_pname @ B_161 @ A_249 ) )
% 0.24/0.46 <=> ( ( A_250 = B_161 )
% 0.24/0.46 | ( member_pname @ A_250 @ A_249 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_127_insert__iff,axiom,
% 0.24/0.46 ! [A_250: hoare_1708887482_state,B_161: hoare_1708887482_state,A_249: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ A_250 @ ( insert528405184_state @ B_161 @ A_249 ) )
% 0.24/0.46 <=> ( ( A_250 = B_161 )
% 0.24/0.46 | ( member451959335_state @ A_250 @ A_249 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_128_insert__commute,axiom,
% 0.24/0.46 ! [X_113: pname,Y_51: pname,A_248: pname > $o] :
% 0.24/0.46 ( ( insert_pname @ X_113 @ ( insert_pname @ Y_51 @ A_248 ) )
% 0.24/0.46 = ( insert_pname @ Y_51 @ ( insert_pname @ X_113 @ A_248 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_129_insert__commute,axiom,
% 0.24/0.46 ! [X_113: com,Y_51: com,A_248: com > $o] :
% 0.24/0.46 ( ( insert_com @ X_113 @ ( insert_com @ Y_51 @ A_248 ) )
% 0.24/0.46 = ( insert_com @ Y_51 @ ( insert_com @ X_113 @ A_248 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_130_insert__commute,axiom,
% 0.24/0.46 ! [X_113: hoare_1708887482_state,Y_51: hoare_1708887482_state,A_248: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( insert528405184_state @ X_113 @ ( insert528405184_state @ Y_51 @ A_248 ) )
% 0.24/0.46 = ( insert528405184_state @ Y_51 @ ( insert528405184_state @ X_113 @ A_248 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_131_insert__absorb2,axiom,
% 0.24/0.46 ! [X_112: pname,A_247: pname > $o] :
% 0.24/0.46 ( ( insert_pname @ X_112 @ ( insert_pname @ X_112 @ A_247 ) )
% 0.24/0.46 = ( insert_pname @ X_112 @ A_247 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_132_insert__absorb2,axiom,
% 0.24/0.46 ! [X_112: com,A_247: com > $o] :
% 0.24/0.46 ( ( insert_com @ X_112 @ ( insert_com @ X_112 @ A_247 ) )
% 0.24/0.46 = ( insert_com @ X_112 @ A_247 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_133_insert__absorb2,axiom,
% 0.24/0.46 ! [X_112: hoare_1708887482_state,A_247: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( insert528405184_state @ X_112 @ ( insert528405184_state @ X_112 @ A_247 ) )
% 0.24/0.46 = ( insert528405184_state @ X_112 @ A_247 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_134_insert__Collect,axiom,
% 0.24/0.46 ! [A_246: pname,P_42: pname > $o] :
% 0.24/0.46 ( ( insert_pname @ A_246 @ ( collect_pname @ P_42 ) )
% 0.24/0.46 = ( collect_pname
% 0.24/0.46 @ ^ [U_2: pname] : ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_135_insert__Collect,axiom,
% 0.24/0.46 ! [A_246: com,P_42: com > $o] :
% 0.24/0.46 ( ( insert_com @ A_246 @ ( collect_com @ P_42 ) )
% 0.24/0.46 = ( collect_com
% 0.24/0.46 @ ^ [U_2: com] : ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_136_insert__Collect,axiom,
% 0.24/0.46 ! [A_246: pname > $o,P_42: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( insert_pname_o @ A_246 @ ( collect_pname_o @ P_42 ) )
% 0.24/0.46 = ( collect_pname_o
% 0.24/0.46 @ ^ [U_2: pname > $o] : ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_137_insert__Collect,axiom,
% 0.24/0.46 ! [A_246: hoare_1708887482_state > $o,P_42: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( insert949073679tate_o @ A_246 @ ( collec219771562tate_o @ P_42 ) )
% 0.24/0.46 = ( collec219771562tate_o
% 0.24/0.46 @ ^ [U_2: hoare_1708887482_state > $o] : ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_138_insert__Collect,axiom,
% 0.24/0.46 ! [A_246: hoare_1708887482_state,P_42: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( insert528405184_state @ A_246 @ ( collec1568722789_state @ P_42 ) )
% 0.24/0.46 = ( collec1568722789_state
% 0.24/0.46 @ ^ [U_2: hoare_1708887482_state] : ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_139_insert__compr,axiom,
% 0.24/0.46 ! [A_245: com,B_160: com > $o] :
% 0.24/0.46 ( ( insert_com @ A_245 @ B_160 )
% 0.24/0.46 = ( collect_com
% 0.24/0.46 @ ^ [X_3: com] : ( (|) @ ( X_3 = A_245 ) @ ( member_com @ X_3 @ B_160 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_140_insert__compr,axiom,
% 0.24/0.46 ! [A_245: pname > $o,B_160: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( insert_pname_o @ A_245 @ B_160 )
% 0.24/0.46 = ( collect_pname_o
% 0.24/0.46 @ ^ [X_3: pname > $o] : ( (|) @ ( X_3 = A_245 ) @ ( member_pname_o @ X_3 @ B_160 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_141_insert__compr,axiom,
% 0.24/0.46 ! [A_245: hoare_1708887482_state > $o,B_160: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( insert949073679tate_o @ A_245 @ B_160 )
% 0.24/0.46 = ( collec219771562tate_o
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state > $o] : ( (|) @ ( X_3 = A_245 ) @ ( member814030440tate_o @ X_3 @ B_160 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_142_insert__compr,axiom,
% 0.24/0.46 ! [A_245: pname,B_160: pname > $o] :
% 0.24/0.46 ( ( insert_pname @ A_245 @ B_160 )
% 0.24/0.46 = ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : ( (|) @ ( X_3 = A_245 ) @ ( member_pname @ X_3 @ B_160 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_143_insert__compr,axiom,
% 0.24/0.46 ! [A_245: hoare_1708887482_state,B_160: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( insert528405184_state @ A_245 @ B_160 )
% 0.24/0.46 = ( collec1568722789_state
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : ( (|) @ ( X_3 = A_245 ) @ ( member451959335_state @ X_3 @ B_160 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_144_insertI1,axiom,
% 0.24/0.46 ! [A_244: com,B_159: com > $o] : ( member_com @ A_244 @ ( insert_com @ A_244 @ B_159 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_145_insertI1,axiom,
% 0.24/0.46 ! [A_244: pname,B_159: pname > $o] : ( member_pname @ A_244 @ ( insert_pname @ A_244 @ B_159 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_146_insertI1,axiom,
% 0.24/0.46 ! [A_244: hoare_1708887482_state,B_159: hoare_1708887482_state > $o] : ( member451959335_state @ A_244 @ ( insert528405184_state @ A_244 @ B_159 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_147_equalityE,axiom,
% 0.24/0.46 ! [A_243: pname > $o,B_158: pname > $o] :
% 0.24/0.46 ( ( A_243 = B_158 )
% 0.24/0.46 => ~ ( ( ord_less_eq_pname_o @ A_243 @ B_158 )
% 0.24/0.46 => ~ ( ord_less_eq_pname_o @ B_158 @ A_243 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_148_equalityE,axiom,
% 0.24/0.46 ! [A_243: hoare_1708887482_state > $o,B_158: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( A_243 = B_158 )
% 0.24/0.46 => ~ ( ( ord_le777019615tate_o @ A_243 @ B_158 )
% 0.24/0.46 => ~ ( ord_le777019615tate_o @ B_158 @ A_243 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_149_subset__trans,axiom,
% 0.24/0.46 ! [C_64: pname > $o,A_242: pname > $o,B_157: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_242 @ B_157 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_157 @ C_64 )
% 0.24/0.46 => ( ord_less_eq_pname_o @ A_242 @ C_64 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_150_subset__trans,axiom,
% 0.24/0.46 ! [C_64: hoare_1708887482_state > $o,A_242: hoare_1708887482_state > $o,B_157: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_242 @ B_157 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ B_157 @ C_64 )
% 0.24/0.46 => ( ord_le777019615tate_o @ A_242 @ C_64 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_151_set__mp,axiom,
% 0.24/0.46 ! [X_111: com,A_241: com > $o,B_156: com > $o] :
% 0.24/0.46 ( ( ord_less_eq_com_o @ A_241 @ B_156 )
% 0.24/0.46 => ( ( member_com @ X_111 @ A_241 )
% 0.24/0.46 => ( member_com @ X_111 @ B_156 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_152_set__mp,axiom,
% 0.24/0.46 ! [X_111: hoare_1708887482_state,A_241: hoare_1708887482_state > $o,B_156: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_241 @ B_156 )
% 0.24/0.46 => ( ( member451959335_state @ X_111 @ A_241 )
% 0.24/0.46 => ( member451959335_state @ X_111 @ B_156 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_153_set__mp,axiom,
% 0.24/0.46 ! [X_111: pname,A_241: pname > $o,B_156: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_241 @ B_156 )
% 0.24/0.46 => ( ( member_pname @ X_111 @ A_241 )
% 0.24/0.46 => ( member_pname @ X_111 @ B_156 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_154_set__rev__mp,axiom,
% 0.24/0.46 ! [B_155: com > $o,X_110: com,A_240: com > $o] :
% 0.24/0.46 ( ( member_com @ X_110 @ A_240 )
% 0.24/0.46 => ( ( ord_less_eq_com_o @ A_240 @ B_155 )
% 0.24/0.46 => ( member_com @ X_110 @ B_155 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_155_set__rev__mp,axiom,
% 0.24/0.46 ! [B_155: hoare_1708887482_state > $o,X_110: hoare_1708887482_state,A_240: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ X_110 @ A_240 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ A_240 @ B_155 )
% 0.24/0.46 => ( member451959335_state @ X_110 @ B_155 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_156_set__rev__mp,axiom,
% 0.24/0.46 ! [B_155: pname > $o,X_110: pname,A_240: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_110 @ A_240 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ A_240 @ B_155 )
% 0.24/0.46 => ( member_pname @ X_110 @ B_155 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_157_in__mono,axiom,
% 0.24/0.46 ! [X_109: com,A_239: com > $o,B_154: com > $o] :
% 0.24/0.46 ( ( ord_less_eq_com_o @ A_239 @ B_154 )
% 0.24/0.46 => ( ( member_com @ X_109 @ A_239 )
% 0.24/0.46 => ( member_com @ X_109 @ B_154 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_158_in__mono,axiom,
% 0.24/0.46 ! [X_109: hoare_1708887482_state,A_239: hoare_1708887482_state > $o,B_154: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_239 @ B_154 )
% 0.24/0.46 => ( ( member451959335_state @ X_109 @ A_239 )
% 0.24/0.46 => ( member451959335_state @ X_109 @ B_154 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_159_in__mono,axiom,
% 0.24/0.46 ! [X_109: pname,A_239: pname > $o,B_154: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_239 @ B_154 )
% 0.24/0.46 => ( ( member_pname @ X_109 @ A_239 )
% 0.24/0.46 => ( member_pname @ X_109 @ B_154 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_160_equalityD2,axiom,
% 0.24/0.46 ! [A_238: pname > $o,B_153: pname > $o] :
% 0.24/0.46 ( ( A_238 = B_153 )
% 0.24/0.46 => ( ord_less_eq_pname_o @ B_153 @ A_238 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_161_equalityD2,axiom,
% 0.24/0.46 ! [A_238: hoare_1708887482_state > $o,B_153: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( A_238 = B_153 )
% 0.24/0.46 => ( ord_le777019615tate_o @ B_153 @ A_238 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_162_equalityD1,axiom,
% 0.24/0.46 ! [A_237: pname > $o,B_152: pname > $o] :
% 0.24/0.46 ( ( A_237 = B_152 )
% 0.24/0.46 => ( ord_less_eq_pname_o @ A_237 @ B_152 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_163_equalityD1,axiom,
% 0.24/0.46 ! [A_237: hoare_1708887482_state > $o,B_152: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( A_237 = B_152 )
% 0.24/0.46 => ( ord_le777019615tate_o @ A_237 @ B_152 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_164_set__eq__subset,axiom,
% 0.24/0.46 ! [A_236: pname > $o,B_151: pname > $o] :
% 0.24/0.46 ( ( A_236 = B_151 )
% 0.24/0.46 <=> ( ( ord_less_eq_pname_o @ A_236 @ B_151 )
% 0.24/0.46 & ( ord_less_eq_pname_o @ B_151 @ A_236 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_165_set__eq__subset,axiom,
% 0.24/0.46 ! [A_236: hoare_1708887482_state > $o,B_151: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( A_236 = B_151 )
% 0.24/0.46 <=> ( ( ord_le777019615tate_o @ A_236 @ B_151 )
% 0.24/0.46 & ( ord_le777019615tate_o @ B_151 @ A_236 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_166_subset__refl,axiom,
% 0.24/0.46 ! [A_235: pname > $o] : ( ord_less_eq_pname_o @ A_235 @ A_235 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_167_subset__refl,axiom,
% 0.24/0.46 ! [A_235: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A_235 @ A_235 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_168_rev__image__eqI,axiom,
% 0.24/0.46 ! [B_150: com,F_84: hoare_1708887482_state > com,X_108: hoare_1708887482_state,A_234: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ X_108 @ A_234 )
% 0.24/0.46 => ( ( B_150
% 0.24/0.46 = ( F_84 @ X_108 ) )
% 0.24/0.46 => ( member_com @ B_150 @ ( image_1604448413te_com @ F_84 @ A_234 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_169_rev__image__eqI,axiom,
% 0.24/0.46 ! [B_150: com,F_84: pname > com,X_108: pname,A_234: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_108 @ A_234 )
% 0.24/0.46 => ( ( B_150
% 0.24/0.46 = ( F_84 @ X_108 ) )
% 0.24/0.46 => ( member_com @ B_150 @ ( image_pname_com @ F_84 @ A_234 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_170_rev__image__eqI,axiom,
% 0.24/0.46 ! [B_150: hoare_1708887482_state,F_84: com > hoare_1708887482_state,X_108: com,A_234: com > $o] :
% 0.24/0.46 ( ( member_com @ X_108 @ A_234 )
% 0.24/0.46 => ( ( B_150
% 0.24/0.46 = ( F_84 @ X_108 ) )
% 0.24/0.46 => ( member451959335_state @ B_150 @ ( image_934102463_state @ F_84 @ A_234 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_171_rev__image__eqI,axiom,
% 0.24/0.46 ! [B_150: pname,F_84: com > pname,X_108: com,A_234: com > $o] :
% 0.24/0.46 ( ( member_com @ X_108 @ A_234 )
% 0.24/0.46 => ( ( B_150
% 0.24/0.46 = ( F_84 @ X_108 ) )
% 0.24/0.46 => ( member_pname @ B_150 @ ( image_com_pname @ F_84 @ A_234 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_172_rev__image__eqI,axiom,
% 0.24/0.46 ! [B_150: hoare_1708887482_state,F_84: pname > hoare_1708887482_state,X_108: pname,A_234: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_108 @ A_234 )
% 0.24/0.46 => ( ( B_150
% 0.24/0.46 = ( F_84 @ X_108 ) )
% 0.24/0.46 => ( member451959335_state @ B_150 @ ( image_1116629049_state @ F_84 @ A_234 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_173_imageI,axiom,
% 0.24/0.46 ! [F_83: hoare_1708887482_state > com,X_107: hoare_1708887482_state,A_233: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ X_107 @ A_233 )
% 0.24/0.46 => ( member_com @ ( F_83 @ X_107 ) @ ( image_1604448413te_com @ F_83 @ A_233 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_174_imageI,axiom,
% 0.24/0.46 ! [F_83: pname > com,X_107: pname,A_233: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_107 @ A_233 )
% 0.24/0.46 => ( member_com @ ( F_83 @ X_107 ) @ ( image_pname_com @ F_83 @ A_233 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_175_imageI,axiom,
% 0.24/0.46 ! [F_83: com > hoare_1708887482_state,X_107: com,A_233: com > $o] :
% 0.24/0.46 ( ( member_com @ X_107 @ A_233 )
% 0.24/0.46 => ( member451959335_state @ ( F_83 @ X_107 ) @ ( image_934102463_state @ F_83 @ A_233 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_176_imageI,axiom,
% 0.24/0.46 ! [F_83: com > pname,X_107: com,A_233: com > $o] :
% 0.24/0.46 ( ( member_com @ X_107 @ A_233 )
% 0.24/0.46 => ( member_pname @ ( F_83 @ X_107 ) @ ( image_com_pname @ F_83 @ A_233 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_177_imageI,axiom,
% 0.24/0.46 ! [F_83: pname > hoare_1708887482_state,X_107: pname,A_233: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_107 @ A_233 )
% 0.24/0.46 => ( member451959335_state @ ( F_83 @ X_107 ) @ ( image_1116629049_state @ F_83 @ A_233 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_178_image__iff,axiom,
% 0.24/0.46 ! [Z_21: hoare_1708887482_state,F_82: pname > hoare_1708887482_state,A_232: pname > $o] :
% 0.24/0.46 ( ( member451959335_state @ Z_21 @ ( image_1116629049_state @ F_82 @ A_232 ) )
% 0.24/0.46 <=> ? [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ A_232 )
% 0.24/0.46 & ( Z_21
% 0.24/0.46 = ( F_82 @ X_3 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_179_finite__Collect__disjI,axiom,
% 0.24/0.46 ! [P_41: ( pname > $o ) > $o,Q_25: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o
% 0.24/0.46 @ ( collect_pname_o
% 0.24/0.46 @ ^ [X_3: pname > $o] : ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
% 0.24/0.46 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_41 ) )
% 0.24/0.46 & ( finite297249702name_o @ ( collect_pname_o @ Q_25 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_180_finite__Collect__disjI,axiom,
% 0.24/0.46 ! [P_41: ( hoare_1708887482_state > $o ) > $o,Q_25: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o
% 0.24/0.46 @ ( collec219771562tate_o
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state > $o] : ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
% 0.24/0.46 <=> ( ( finite1329924456tate_o @ ( collec219771562tate_o @ P_41 ) )
% 0.24/0.46 & ( finite1329924456tate_o @ ( collec219771562tate_o @ Q_25 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_181_finite__Collect__disjI,axiom,
% 0.24/0.46 ! [P_41: hoare_1708887482_state > $o,Q_25: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state
% 0.24/0.46 @ ( collec1568722789_state
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
% 0.24/0.46 <=> ( ( finite1625599783_state @ ( collec1568722789_state @ P_41 ) )
% 0.24/0.46 & ( finite1625599783_state @ ( collec1568722789_state @ Q_25 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_182_finite__Collect__disjI,axiom,
% 0.24/0.46 ! [P_41: pname > $o,Q_25: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname
% 0.24/0.46 @ ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
% 0.24/0.46 <=> ( ( finite_finite_pname @ ( collect_pname @ P_41 ) )
% 0.24/0.46 & ( finite_finite_pname @ ( collect_pname @ Q_25 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_183_insert__compr__raw,axiom,
% 0.24/0.46 ! [X_3: com,Xa: com > $o] :
% 0.24/0.46 ( ( insert_com @ X_3 @ Xa )
% 0.24/0.46 = ( collect_com
% 0.24/0.46 @ ^ [Y_4: com] : ( (|) @ ( Y_4 = X_3 ) @ ( member_com @ Y_4 @ Xa ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_184_insert__compr__raw,axiom,
% 0.24/0.46 ! [X_3: pname > $o,Xa: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( insert_pname_o @ X_3 @ Xa )
% 0.24/0.46 = ( collect_pname_o
% 0.24/0.46 @ ^ [Y_4: pname > $o] : ( (|) @ ( Y_4 = X_3 ) @ ( member_pname_o @ Y_4 @ Xa ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_185_insert__compr__raw,axiom,
% 0.24/0.46 ! [X_3: hoare_1708887482_state > $o,Xa: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( insert949073679tate_o @ X_3 @ Xa )
% 0.24/0.46 = ( collec219771562tate_o
% 0.24/0.46 @ ^ [Y_4: hoare_1708887482_state > $o] : ( (|) @ ( Y_4 = X_3 ) @ ( member814030440tate_o @ Y_4 @ Xa ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_186_insert__compr__raw,axiom,
% 0.24/0.46 ! [X_3: pname,Xa: pname > $o] :
% 0.24/0.46 ( ( insert_pname @ X_3 @ Xa )
% 0.24/0.46 = ( collect_pname
% 0.24/0.46 @ ^ [Y_4: pname] : ( (|) @ ( Y_4 = X_3 ) @ ( member_pname @ Y_4 @ Xa ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_187_insert__compr__raw,axiom,
% 0.24/0.46 ! [X_3: hoare_1708887482_state,Xa: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( insert528405184_state @ X_3 @ Xa )
% 0.24/0.46 = ( collec1568722789_state
% 0.24/0.46 @ ^ [Y_4: hoare_1708887482_state] : ( (|) @ ( Y_4 = X_3 ) @ ( member451959335_state @ Y_4 @ Xa ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_188_singleton__inject,axiom,
% 0.24/0.46 ! [A_231: pname,B_149: pname] :
% 0.24/0.46 ( ( ( insert_pname @ A_231 @ bot_bot_pname_o )
% 0.24/0.46 = ( insert_pname @ B_149 @ bot_bot_pname_o ) )
% 0.24/0.46 => ( A_231 = B_149 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_189_singleton__inject,axiom,
% 0.24/0.46 ! [A_231: com,B_149: com] :
% 0.24/0.46 ( ( ( insert_com @ A_231 @ bot_bot_com_o )
% 0.24/0.46 = ( insert_com @ B_149 @ bot_bot_com_o ) )
% 0.24/0.46 => ( A_231 = B_149 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_190_singleton__inject,axiom,
% 0.24/0.46 ! [A_231: hoare_1708887482_state,B_149: hoare_1708887482_state] :
% 0.24/0.46 ( ( ( insert528405184_state @ A_231 @ bot_bo19817387tate_o )
% 0.24/0.46 = ( insert528405184_state @ B_149 @ bot_bo19817387tate_o ) )
% 0.24/0.46 => ( A_231 = B_149 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_191_singletonE,axiom,
% 0.24/0.46 ! [B_148: com,A_230: com] :
% 0.24/0.46 ( ( member_com @ B_148 @ ( insert_com @ A_230 @ bot_bot_com_o ) )
% 0.24/0.46 => ( B_148 = A_230 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_192_singletonE,axiom,
% 0.24/0.46 ! [B_148: pname,A_230: pname] :
% 0.24/0.46 ( ( member_pname @ B_148 @ ( insert_pname @ A_230 @ bot_bot_pname_o ) )
% 0.24/0.46 => ( B_148 = A_230 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_193_singletonE,axiom,
% 0.24/0.46 ! [B_148: hoare_1708887482_state,A_230: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ B_148 @ ( insert528405184_state @ A_230 @ bot_bo19817387tate_o ) )
% 0.24/0.46 => ( B_148 = A_230 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_194_doubleton__eq__iff,axiom,
% 0.24/0.46 ! [A_229: pname,B_147: pname,C_63: pname,D_7: pname] :
% 0.24/0.46 ( ( ( insert_pname @ A_229 @ ( insert_pname @ B_147 @ bot_bot_pname_o ) )
% 0.24/0.46 = ( insert_pname @ C_63 @ ( insert_pname @ D_7 @ bot_bot_pname_o ) ) )
% 0.24/0.46 <=> ( ( ( A_229 = C_63 )
% 0.24/0.46 & ( B_147 = D_7 ) )
% 0.24/0.46 | ( ( A_229 = D_7 )
% 0.24/0.46 & ( B_147 = C_63 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_195_doubleton__eq__iff,axiom,
% 0.24/0.46 ! [A_229: com,B_147: com,C_63: com,D_7: com] :
% 0.24/0.46 ( ( ( insert_com @ A_229 @ ( insert_com @ B_147 @ bot_bot_com_o ) )
% 0.24/0.46 = ( insert_com @ C_63 @ ( insert_com @ D_7 @ bot_bot_com_o ) ) )
% 0.24/0.46 <=> ( ( ( A_229 = C_63 )
% 0.24/0.46 & ( B_147 = D_7 ) )
% 0.24/0.46 | ( ( A_229 = D_7 )
% 0.24/0.46 & ( B_147 = C_63 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_196_doubleton__eq__iff,axiom,
% 0.24/0.46 ! [A_229: hoare_1708887482_state,B_147: hoare_1708887482_state,C_63: hoare_1708887482_state,D_7: hoare_1708887482_state] :
% 0.24/0.46 ( ( ( insert528405184_state @ A_229 @ ( insert528405184_state @ B_147 @ bot_bo19817387tate_o ) )
% 0.24/0.46 = ( insert528405184_state @ C_63 @ ( insert528405184_state @ D_7 @ bot_bo19817387tate_o ) ) )
% 0.24/0.46 <=> ( ( ( A_229 = C_63 )
% 0.24/0.46 & ( B_147 = D_7 ) )
% 0.24/0.46 | ( ( A_229 = D_7 )
% 0.24/0.46 & ( B_147 = C_63 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_197_singleton__iff,axiom,
% 0.24/0.46 ! [B_146: com,A_228: com] :
% 0.24/0.46 ( ( member_com @ B_146 @ ( insert_com @ A_228 @ bot_bot_com_o ) )
% 0.24/0.46 <=> ( B_146 = A_228 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_198_singleton__iff,axiom,
% 0.24/0.46 ! [B_146: pname,A_228: pname] :
% 0.24/0.46 ( ( member_pname @ B_146 @ ( insert_pname @ A_228 @ bot_bot_pname_o ) )
% 0.24/0.46 <=> ( B_146 = A_228 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_199_singleton__iff,axiom,
% 0.24/0.46 ! [B_146: hoare_1708887482_state,A_228: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ B_146 @ ( insert528405184_state @ A_228 @ bot_bo19817387tate_o ) )
% 0.24/0.46 <=> ( B_146 = A_228 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_200_insert__not__empty,axiom,
% 0.24/0.46 ! [A_227: pname,A_226: pname > $o] :
% 0.24/0.46 ( ( insert_pname @ A_227 @ A_226 )
% 0.24/0.46 != bot_bot_pname_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_201_insert__not__empty,axiom,
% 0.24/0.46 ! [A_227: com,A_226: com > $o] :
% 0.24/0.46 ( ( insert_com @ A_227 @ A_226 )
% 0.24/0.46 != bot_bot_com_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_202_insert__not__empty,axiom,
% 0.24/0.46 ! [A_227: hoare_1708887482_state,A_226: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( insert528405184_state @ A_227 @ A_226 )
% 0.24/0.46 != bot_bo19817387tate_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_203_empty__not__insert,axiom,
% 0.24/0.46 ! [A_225: pname,A_224: pname > $o] :
% 0.24/0.46 ( bot_bot_pname_o
% 0.24/0.46 != ( insert_pname @ A_225 @ A_224 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_204_empty__not__insert,axiom,
% 0.24/0.46 ! [A_225: com,A_224: com > $o] :
% 0.24/0.46 ( bot_bot_com_o
% 0.24/0.46 != ( insert_com @ A_225 @ A_224 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_205_empty__not__insert,axiom,
% 0.24/0.46 ! [A_225: hoare_1708887482_state,A_224: hoare_1708887482_state > $o] :
% 0.24/0.46 ( bot_bo19817387tate_o
% 0.24/0.46 != ( insert528405184_state @ A_225 @ A_224 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_206_finite__insert,axiom,
% 0.24/0.46 ! [A_223: com,A_222: com > $o] :
% 0.24/0.46 ( ( finite_finite_com @ ( insert_com @ A_223 @ A_222 ) )
% 0.24/0.46 <=> ( finite_finite_com @ A_222 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_207_finite__insert,axiom,
% 0.24/0.46 ! [A_223: pname > $o,A_222: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ ( insert_pname_o @ A_223 @ A_222 ) )
% 0.24/0.46 <=> ( finite297249702name_o @ A_222 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_208_finite__insert,axiom,
% 0.24/0.46 ! [A_223: hoare_1708887482_state > $o,A_222: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ ( insert949073679tate_o @ A_223 @ A_222 ) )
% 0.24/0.46 <=> ( finite1329924456tate_o @ A_222 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_209_finite__insert,axiom,
% 0.24/0.46 ! [A_223: pname,A_222: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ ( insert_pname @ A_223 @ A_222 ) )
% 0.24/0.46 <=> ( finite_finite_pname @ A_222 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_210_finite__insert,axiom,
% 0.24/0.46 ! [A_223: hoare_1708887482_state,A_222: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ ( insert528405184_state @ A_223 @ A_222 ) )
% 0.24/0.46 <=> ( finite1625599783_state @ A_222 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_211_subset__empty,axiom,
% 0.24/0.46 ! [A_221: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_221 @ bot_bot_pname_o )
% 0.24/0.46 <=> ( A_221 = bot_bot_pname_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_212_subset__empty,axiom,
% 0.24/0.46 ! [A_221: com > $o] :
% 0.24/0.46 ( ( ord_less_eq_com_o @ A_221 @ bot_bot_com_o )
% 0.24/0.46 <=> ( A_221 = bot_bot_com_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_213_subset__empty,axiom,
% 0.24/0.46 ! [A_221: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_221 @ bot_bo19817387tate_o )
% 0.24/0.46 <=> ( A_221 = bot_bo19817387tate_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_214_image__is__empty,axiom,
% 0.24/0.46 ! [F_81: com > hoare_1708887482_state,A_220: com > $o] :
% 0.24/0.46 ( ( ( image_934102463_state @ F_81 @ A_220 )
% 0.24/0.46 = bot_bo19817387tate_o )
% 0.24/0.46 <=> ( A_220 = bot_bot_com_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_215_image__is__empty,axiom,
% 0.24/0.46 ! [F_81: hoare_1708887482_state > pname,A_220: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ( image_1509414295_pname @ F_81 @ A_220 )
% 0.24/0.46 = bot_bot_pname_o )
% 0.24/0.46 <=> ( A_220 = bot_bo19817387tate_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_216_image__is__empty,axiom,
% 0.24/0.46 ! [F_81: hoare_1708887482_state > com,A_220: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ( image_1604448413te_com @ F_81 @ A_220 )
% 0.24/0.46 = bot_bot_com_o )
% 0.24/0.46 <=> ( A_220 = bot_bo19817387tate_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_217_image__is__empty,axiom,
% 0.24/0.46 ! [F_81: pname > hoare_1708887482_state,A_220: pname > $o] :
% 0.24/0.46 ( ( ( image_1116629049_state @ F_81 @ A_220 )
% 0.24/0.46 = bot_bo19817387tate_o )
% 0.24/0.46 <=> ( A_220 = bot_bot_pname_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_218_image__empty,axiom,
% 0.24/0.46 ! [F_80: hoare_1708887482_state > pname] :
% 0.24/0.46 ( ( image_1509414295_pname @ F_80 @ bot_bo19817387tate_o )
% 0.24/0.46 = bot_bot_pname_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_219_image__empty,axiom,
% 0.24/0.46 ! [F_80: hoare_1708887482_state > com] :
% 0.24/0.46 ( ( image_1604448413te_com @ F_80 @ bot_bo19817387tate_o )
% 0.24/0.46 = bot_bot_com_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_220_image__empty,axiom,
% 0.24/0.46 ! [F_80: com > hoare_1708887482_state] :
% 0.24/0.46 ( ( image_934102463_state @ F_80 @ bot_bot_com_o )
% 0.24/0.46 = bot_bo19817387tate_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_221_image__empty,axiom,
% 0.24/0.46 ! [F_80: pname > hoare_1708887482_state] :
% 0.24/0.46 ( ( image_1116629049_state @ F_80 @ bot_bot_pname_o )
% 0.24/0.46 = bot_bo19817387tate_o ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_222_empty__is__image,axiom,
% 0.24/0.46 ! [F_79: com > hoare_1708887482_state,A_219: com > $o] :
% 0.24/0.46 ( ( bot_bo19817387tate_o
% 0.24/0.46 = ( image_934102463_state @ F_79 @ A_219 ) )
% 0.24/0.46 <=> ( A_219 = bot_bot_com_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_223_empty__is__image,axiom,
% 0.24/0.46 ! [F_79: hoare_1708887482_state > pname,A_219: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( bot_bot_pname_o
% 0.24/0.46 = ( image_1509414295_pname @ F_79 @ A_219 ) )
% 0.24/0.46 <=> ( A_219 = bot_bo19817387tate_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_224_empty__is__image,axiom,
% 0.24/0.46 ! [F_79: hoare_1708887482_state > com,A_219: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( bot_bot_com_o
% 0.24/0.46 = ( image_1604448413te_com @ F_79 @ A_219 ) )
% 0.24/0.46 <=> ( A_219 = bot_bo19817387tate_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_225_empty__is__image,axiom,
% 0.24/0.46 ! [F_79: pname > hoare_1708887482_state,A_219: pname > $o] :
% 0.24/0.46 ( ( bot_bo19817387tate_o
% 0.24/0.46 = ( image_1116629049_state @ F_79 @ A_219 ) )
% 0.24/0.46 <=> ( A_219 = bot_bot_pname_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_226_finite__subset,axiom,
% 0.24/0.46 ! [A_218: ( pname > $o ) > $o,B_145: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( ord_le1205211808me_o_o @ A_218 @ B_145 )
% 0.24/0.46 => ( ( finite297249702name_o @ B_145 )
% 0.24/0.46 => ( finite297249702name_o @ A_218 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_227_finite__subset,axiom,
% 0.24/0.46 ! [A_218: ( hoare_1708887482_state > $o ) > $o,B_145: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( ord_le1728773982te_o_o @ A_218 @ B_145 )
% 0.24/0.46 => ( ( finite1329924456tate_o @ B_145 )
% 0.24/0.46 => ( finite1329924456tate_o @ A_218 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_228_finite__subset,axiom,
% 0.24/0.46 ! [A_218: hoare_1708887482_state > $o,B_145: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_218 @ B_145 )
% 0.24/0.46 => ( ( finite1625599783_state @ B_145 )
% 0.24/0.46 => ( finite1625599783_state @ A_218 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_229_finite__subset,axiom,
% 0.24/0.46 ! [A_218: pname > $o,B_145: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_218 @ B_145 )
% 0.24/0.46 => ( ( finite_finite_pname @ B_145 )
% 0.24/0.46 => ( finite_finite_pname @ A_218 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_230_rev__finite__subset,axiom,
% 0.24/0.46 ! [A_217: ( pname > $o ) > $o,B_144: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ B_144 )
% 0.24/0.46 => ( ( ord_le1205211808me_o_o @ A_217 @ B_144 )
% 0.24/0.46 => ( finite297249702name_o @ A_217 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_231_rev__finite__subset,axiom,
% 0.24/0.46 ! [A_217: ( hoare_1708887482_state > $o ) > $o,B_144: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ B_144 )
% 0.24/0.46 => ( ( ord_le1728773982te_o_o @ A_217 @ B_144 )
% 0.24/0.46 => ( finite1329924456tate_o @ A_217 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_232_rev__finite__subset,axiom,
% 0.24/0.46 ! [A_217: hoare_1708887482_state > $o,B_144: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ B_144 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ A_217 @ B_144 )
% 0.24/0.46 => ( finite1625599783_state @ A_217 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_233_rev__finite__subset,axiom,
% 0.24/0.46 ! [A_217: pname > $o,B_144: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ B_144 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ A_217 @ B_144 )
% 0.24/0.46 => ( finite_finite_pname @ A_217 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_234_insert__mono,axiom,
% 0.24/0.46 ! [A_216: pname,C_62: pname > $o,D_6: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ C_62 @ D_6 )
% 0.24/0.46 => ( ord_less_eq_pname_o @ ( insert_pname @ A_216 @ C_62 ) @ ( insert_pname @ A_216 @ D_6 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_235_insert__mono,axiom,
% 0.24/0.46 ! [A_216: com,C_62: com > $o,D_6: com > $o] :
% 0.24/0.46 ( ( ord_less_eq_com_o @ C_62 @ D_6 )
% 0.24/0.46 => ( ord_less_eq_com_o @ ( insert_com @ A_216 @ C_62 ) @ ( insert_com @ A_216 @ D_6 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_236_insert__mono,axiom,
% 0.24/0.46 ! [A_216: hoare_1708887482_state,C_62: hoare_1708887482_state > $o,D_6: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ C_62 @ D_6 )
% 0.24/0.46 => ( ord_le777019615tate_o @ ( insert528405184_state @ A_216 @ C_62 ) @ ( insert528405184_state @ A_216 @ D_6 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_237_mem__def,axiom,
% 0.24/0.46 ! [X_106: com,A_215: com > $o] :
% 0.24/0.46 ( ( member_com @ X_106 @ A_215 )
% 0.24/0.46 <=> ( A_215 @ X_106 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_238_mem__def,axiom,
% 0.24/0.46 ! [X_106: hoare_1708887482_state,A_215: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ X_106 @ A_215 )
% 0.24/0.46 <=> ( A_215 @ X_106 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_239_mem__def,axiom,
% 0.24/0.46 ! [X_106: pname,A_215: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_106 @ A_215 )
% 0.24/0.46 <=> ( A_215 @ X_106 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_240_Collect__def,axiom,
% 0.24/0.46 ! [P_40: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( collec1568722789_state @ P_40 )
% 0.24/0.46 = P_40 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_241_Collect__def,axiom,
% 0.24/0.46 ! [P_40: pname > $o] :
% 0.24/0.46 ( ( collect_pname @ P_40 )
% 0.24/0.46 = P_40 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_242_Collect__def,axiom,
% 0.24/0.46 ! [P_40: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( collect_pname_o @ P_40 )
% 0.24/0.46 = P_40 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_243_Collect__def,axiom,
% 0.24/0.46 ! [P_40: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( collec219771562tate_o @ P_40 )
% 0.24/0.46 = P_40 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_244_subset__insertI2,axiom,
% 0.24/0.46 ! [B_143: pname,A_214: pname > $o,B_142: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_214 @ B_142 )
% 0.24/0.46 => ( ord_less_eq_pname_o @ A_214 @ ( insert_pname @ B_143 @ B_142 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_245_subset__insertI2,axiom,
% 0.24/0.46 ! [B_143: com,A_214: com > $o,B_142: com > $o] :
% 0.24/0.46 ( ( ord_less_eq_com_o @ A_214 @ B_142 )
% 0.24/0.46 => ( ord_less_eq_com_o @ A_214 @ ( insert_com @ B_143 @ B_142 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_246_subset__insertI2,axiom,
% 0.24/0.46 ! [B_143: hoare_1708887482_state,A_214: hoare_1708887482_state > $o,B_142: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_214 @ B_142 )
% 0.24/0.46 => ( ord_le777019615tate_o @ A_214 @ ( insert528405184_state @ B_143 @ B_142 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_247_subset__insert,axiom,
% 0.24/0.46 ! [B_141: com > $o,X_105: com,A_213: com > $o] :
% 0.24/0.46 ( ~ ( member_com @ X_105 @ A_213 )
% 0.24/0.46 => ( ( ord_less_eq_com_o @ A_213 @ ( insert_com @ X_105 @ B_141 ) )
% 0.24/0.46 <=> ( ord_less_eq_com_o @ A_213 @ B_141 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_248_subset__insert,axiom,
% 0.24/0.46 ! [B_141: pname > $o,X_105: pname,A_213: pname > $o] :
% 0.24/0.46 ( ~ ( member_pname @ X_105 @ A_213 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ A_213 @ ( insert_pname @ X_105 @ B_141 ) )
% 0.24/0.46 <=> ( ord_less_eq_pname_o @ A_213 @ B_141 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_249_subset__insert,axiom,
% 0.24/0.46 ! [B_141: hoare_1708887482_state > $o,X_105: hoare_1708887482_state,A_213: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ~ ( member451959335_state @ X_105 @ A_213 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ A_213 @ ( insert528405184_state @ X_105 @ B_141 ) )
% 0.24/0.46 <=> ( ord_le777019615tate_o @ A_213 @ B_141 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_250_insert__subset,axiom,
% 0.24/0.46 ! [X_104: com,A_212: com > $o,B_140: com > $o] :
% 0.24/0.46 ( ( ord_less_eq_com_o @ ( insert_com @ X_104 @ A_212 ) @ B_140 )
% 0.24/0.46 <=> ( ( member_com @ X_104 @ B_140 )
% 0.24/0.46 & ( ord_less_eq_com_o @ A_212 @ B_140 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_251_insert__subset,axiom,
% 0.24/0.46 ! [X_104: pname,A_212: pname > $o,B_140: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_104 @ A_212 ) @ B_140 )
% 0.24/0.46 <=> ( ( member_pname @ X_104 @ B_140 )
% 0.24/0.46 & ( ord_less_eq_pname_o @ A_212 @ B_140 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_252_insert__subset,axiom,
% 0.24/0.46 ! [X_104: hoare_1708887482_state,A_212: hoare_1708887482_state > $o,B_140: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ ( insert528405184_state @ X_104 @ A_212 ) @ B_140 )
% 0.24/0.46 <=> ( ( member451959335_state @ X_104 @ B_140 )
% 0.24/0.46 & ( ord_le777019615tate_o @ A_212 @ B_140 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_253_subset__insertI,axiom,
% 0.24/0.46 ! [B_139: pname > $o,A_211: pname] : ( ord_less_eq_pname_o @ B_139 @ ( insert_pname @ A_211 @ B_139 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_254_subset__insertI,axiom,
% 0.24/0.46 ! [B_139: com > $o,A_211: com] : ( ord_less_eq_com_o @ B_139 @ ( insert_com @ A_211 @ B_139 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_255_subset__insertI,axiom,
% 0.24/0.46 ! [B_139: hoare_1708887482_state > $o,A_211: hoare_1708887482_state] : ( ord_le777019615tate_o @ B_139 @ ( insert528405184_state @ A_211 @ B_139 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_256_insert__image,axiom,
% 0.24/0.46 ! [F_78: hoare_1708887482_state > pname,X_103: hoare_1708887482_state,A_210: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ X_103 @ A_210 )
% 0.24/0.46 => ( ( insert_pname @ ( F_78 @ X_103 ) @ ( image_1509414295_pname @ F_78 @ A_210 ) )
% 0.24/0.46 = ( image_1509414295_pname @ F_78 @ A_210 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_257_insert__image,axiom,
% 0.24/0.46 ! [F_78: hoare_1708887482_state > com,X_103: hoare_1708887482_state,A_210: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ X_103 @ A_210 )
% 0.24/0.46 => ( ( insert_com @ ( F_78 @ X_103 ) @ ( image_1604448413te_com @ F_78 @ A_210 ) )
% 0.24/0.46 = ( image_1604448413te_com @ F_78 @ A_210 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_258_insert__image,axiom,
% 0.24/0.46 ! [F_78: pname > pname,X_103: pname,A_210: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_103 @ A_210 )
% 0.24/0.46 => ( ( insert_pname @ ( F_78 @ X_103 ) @ ( image_pname_pname @ F_78 @ A_210 ) )
% 0.24/0.46 = ( image_pname_pname @ F_78 @ A_210 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_259_insert__image,axiom,
% 0.24/0.46 ! [F_78: pname > com,X_103: pname,A_210: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_103 @ A_210 )
% 0.24/0.46 => ( ( insert_com @ ( F_78 @ X_103 ) @ ( image_pname_com @ F_78 @ A_210 ) )
% 0.24/0.46 = ( image_pname_com @ F_78 @ A_210 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_260_insert__image,axiom,
% 0.24/0.46 ! [F_78: com > hoare_1708887482_state,X_103: com,A_210: com > $o] :
% 0.24/0.46 ( ( member_com @ X_103 @ A_210 )
% 0.24/0.46 => ( ( insert528405184_state @ ( F_78 @ X_103 ) @ ( image_934102463_state @ F_78 @ A_210 ) )
% 0.24/0.46 = ( image_934102463_state @ F_78 @ A_210 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_261_insert__image,axiom,
% 0.24/0.46 ! [F_78: pname > hoare_1708887482_state,X_103: pname,A_210: pname > $o] :
% 0.24/0.46 ( ( member_pname @ X_103 @ A_210 )
% 0.24/0.46 => ( ( insert528405184_state @ ( F_78 @ X_103 ) @ ( image_1116629049_state @ F_78 @ A_210 ) )
% 0.24/0.46 = ( image_1116629049_state @ F_78 @ A_210 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_262_image__insert,axiom,
% 0.24/0.46 ! [F_77: hoare_1708887482_state > pname,A_209: hoare_1708887482_state,B_138: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( image_1509414295_pname @ F_77 @ ( insert528405184_state @ A_209 @ B_138 ) )
% 0.24/0.46 = ( insert_pname @ ( F_77 @ A_209 ) @ ( image_1509414295_pname @ F_77 @ B_138 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_263_image__insert,axiom,
% 0.24/0.46 ! [F_77: hoare_1708887482_state > com,A_209: hoare_1708887482_state,B_138: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( image_1604448413te_com @ F_77 @ ( insert528405184_state @ A_209 @ B_138 ) )
% 0.24/0.46 = ( insert_com @ ( F_77 @ A_209 ) @ ( image_1604448413te_com @ F_77 @ B_138 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_264_image__insert,axiom,
% 0.24/0.46 ! [F_77: com > hoare_1708887482_state,A_209: com,B_138: com > $o] :
% 0.24/0.46 ( ( image_934102463_state @ F_77 @ ( insert_com @ A_209 @ B_138 ) )
% 0.24/0.46 = ( insert528405184_state @ ( F_77 @ A_209 ) @ ( image_934102463_state @ F_77 @ B_138 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_265_image__insert,axiom,
% 0.24/0.46 ! [F_77: pname > hoare_1708887482_state,A_209: pname,B_138: pname > $o] :
% 0.24/0.46 ( ( image_1116629049_state @ F_77 @ ( insert_pname @ A_209 @ B_138 ) )
% 0.24/0.46 = ( insert528405184_state @ ( F_77 @ A_209 ) @ ( image_1116629049_state @ F_77 @ B_138 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_266_image__mono,axiom,
% 0.24/0.46 ! [F_76: hoare_1708887482_state > pname,A_208: hoare_1708887482_state > $o,B_137: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_208 @ B_137 )
% 0.24/0.46 => ( ord_less_eq_pname_o @ ( image_1509414295_pname @ F_76 @ A_208 ) @ ( image_1509414295_pname @ F_76 @ B_137 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_267_image__mono,axiom,
% 0.24/0.46 ! [F_76: pname > hoare_1708887482_state,A_208: pname > $o,B_137: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_208 @ B_137 )
% 0.24/0.46 => ( ord_le777019615tate_o @ ( image_1116629049_state @ F_76 @ A_208 ) @ ( image_1116629049_state @ F_76 @ B_137 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_268_subset__image__iff,axiom,
% 0.24/0.46 ! [B_136: pname > $o,F_75: hoare_1708887482_state > pname,A_207: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ B_136 @ ( image_1509414295_pname @ F_75 @ A_207 ) )
% 0.24/0.46 <=> ? [AA: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ AA @ A_207 )
% 0.24/0.46 & ( B_136
% 0.24/0.46 = ( image_1509414295_pname @ F_75 @ AA ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_269_subset__image__iff,axiom,
% 0.24/0.46 ! [B_136: hoare_1708887482_state > $o,F_75: pname > hoare_1708887482_state,A_207: pname > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ B_136 @ ( image_1116629049_state @ F_75 @ A_207 ) )
% 0.24/0.46 <=> ? [AA: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ AA @ A_207 )
% 0.24/0.46 & ( B_136
% 0.24/0.46 = ( image_1116629049_state @ F_75 @ AA ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_270_domI,axiom,
% 0.24/0.46 ! [M_5: com > option_com,A_206: com,B_135: com] :
% 0.24/0.46 ( ( ( M_5 @ A_206 )
% 0.24/0.46 = ( some_com @ B_135 ) )
% 0.24/0.46 => ( member_com @ A_206 @ ( dom_com_com @ M_5 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_271_domI,axiom,
% 0.24/0.46 ! [M_5: hoare_1708887482_state > option_pname,A_206: hoare_1708887482_state,B_135: pname] :
% 0.24/0.46 ( ( ( M_5 @ A_206 )
% 0.24/0.46 = ( some_pname @ B_135 ) )
% 0.24/0.46 => ( member451959335_state @ A_206 @ ( dom_Ho1805192458_pname @ M_5 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_272_domI,axiom,
% 0.24/0.46 ! [M_5: hoare_1708887482_state > option1624383643_state,A_206: hoare_1708887482_state,B_135: hoare_1708887482_state] :
% 0.24/0.46 ( ( ( M_5 @ A_206 )
% 0.24/0.46 = ( some_H1974565227_state @ B_135 ) )
% 0.24/0.46 => ( member451959335_state @ A_206 @ ( dom_Ho1703271284_state @ M_5 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_273_domI,axiom,
% 0.24/0.46 ! [M_5: pname > option_pname,A_206: pname,B_135: pname] :
% 0.24/0.46 ( ( ( M_5 @ A_206 )
% 0.24/0.46 = ( some_pname @ B_135 ) )
% 0.24/0.46 => ( member_pname @ A_206 @ ( dom_pname_pname @ M_5 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_274_domI,axiom,
% 0.24/0.46 ! [M_5: pname > option1624383643_state,A_206: pname,B_135: hoare_1708887482_state] :
% 0.24/0.46 ( ( ( M_5 @ A_206 )
% 0.24/0.46 = ( some_H1974565227_state @ B_135 ) )
% 0.24/0.46 => ( member_pname @ A_206 @ ( dom_pn1412407212_state @ M_5 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_275_domI,axiom,
% 0.24/0.46 ! [M_5: pname > option_com,A_206: pname,B_135: com] :
% 0.24/0.46 ( ( ( M_5 @ A_206 )
% 0.24/0.46 = ( some_com @ B_135 ) )
% 0.24/0.46 => ( member_pname @ A_206 @ ( dom_pname_com @ M_5 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_276_Collect__conv__if,axiom,
% 0.24/0.46 ! [P_39: pname > $o,A_205: pname] :
% 0.24/0.46 ( ( ( P_39 @ A_205 )
% 0.24/0.46 => ( ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 0.24/0.46 = ( insert_pname @ A_205 @ bot_bot_pname_o ) ) )
% 0.24/0.46 & ( ~ ( P_39 @ A_205 )
% 0.24/0.46 => ( ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 0.24/0.46 = bot_bot_pname_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_277_Collect__conv__if,axiom,
% 0.24/0.46 ! [P_39: com > $o,A_205: com] :
% 0.24/0.46 ( ( ( P_39 @ A_205 )
% 0.24/0.46 => ( ( collect_com
% 0.24/0.46 @ ^ [X_3: com] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 0.24/0.46 = ( insert_com @ A_205 @ bot_bot_com_o ) ) )
% 0.24/0.46 & ( ~ ( P_39 @ A_205 )
% 0.24/0.46 => ( ( collect_com
% 0.24/0.46 @ ^ [X_3: com] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 0.24/0.46 = bot_bot_com_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_278_Collect__conv__if,axiom,
% 0.24/0.46 ! [P_39: ( pname > $o ) > $o,A_205: pname > $o] :
% 0.24/0.46 ( ( ( P_39 @ A_205 )
% 0.24/0.46 => ( ( collect_pname_o
% 0.24/0.46 @ ^ [X_3: pname > $o] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 0.24/0.46 = ( insert_pname_o @ A_205 @ bot_bot_pname_o_o ) ) )
% 0.24/0.46 & ( ~ ( P_39 @ A_205 )
% 0.24/0.46 => ( ( collect_pname_o
% 0.24/0.46 @ ^ [X_3: pname > $o] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 0.24/0.46 = bot_bot_pname_o_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_279_Collect__conv__if,axiom,
% 0.24/0.46 ! [P_39: ( hoare_1708887482_state > $o ) > $o,A_205: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ( P_39 @ A_205 )
% 0.24/0.46 => ( ( collec219771562tate_o
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 0.24/0.46 = ( insert949073679tate_o @ A_205 @ bot_bo1678742418te_o_o ) ) )
% 0.24/0.46 & ( ~ ( P_39 @ A_205 )
% 0.24/0.46 => ( ( collec219771562tate_o
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 0.24/0.46 = bot_bo1678742418te_o_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_280_Collect__conv__if,axiom,
% 0.24/0.46 ! [P_39: hoare_1708887482_state > $o,A_205: hoare_1708887482_state] :
% 0.24/0.46 ( ( ( P_39 @ A_205 )
% 0.24/0.46 => ( ( collec1568722789_state
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 0.24/0.46 = ( insert528405184_state @ A_205 @ bot_bo19817387tate_o ) ) )
% 0.24/0.46 & ( ~ ( P_39 @ A_205 )
% 0.24/0.46 => ( ( collec1568722789_state
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 0.24/0.46 = bot_bo19817387tate_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_281_Collect__conv__if2,axiom,
% 0.24/0.46 ! [P_38: pname > $o,A_204: pname] :
% 0.24/0.46 ( ( ( P_38 @ A_204 )
% 0.24/0.46 => ( ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 0.24/0.46 = ( insert_pname @ A_204 @ bot_bot_pname_o ) ) )
% 0.24/0.46 & ( ~ ( P_38 @ A_204 )
% 0.24/0.46 => ( ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 0.24/0.46 = bot_bot_pname_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_282_Collect__conv__if2,axiom,
% 0.24/0.46 ! [P_38: com > $o,A_204: com] :
% 0.24/0.46 ( ( ( P_38 @ A_204 )
% 0.24/0.46 => ( ( collect_com
% 0.24/0.46 @ ^ [X_3: com] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 0.24/0.46 = ( insert_com @ A_204 @ bot_bot_com_o ) ) )
% 0.24/0.46 & ( ~ ( P_38 @ A_204 )
% 0.24/0.46 => ( ( collect_com
% 0.24/0.46 @ ^ [X_3: com] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 0.24/0.46 = bot_bot_com_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_283_Collect__conv__if2,axiom,
% 0.24/0.46 ! [P_38: ( pname > $o ) > $o,A_204: pname > $o] :
% 0.24/0.46 ( ( ( P_38 @ A_204 )
% 0.24/0.46 => ( ( collect_pname_o
% 0.24/0.46 @ ^ [X_3: pname > $o] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 0.24/0.46 = ( insert_pname_o @ A_204 @ bot_bot_pname_o_o ) ) )
% 0.24/0.46 & ( ~ ( P_38 @ A_204 )
% 0.24/0.46 => ( ( collect_pname_o
% 0.24/0.46 @ ^ [X_3: pname > $o] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 0.24/0.46 = bot_bot_pname_o_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_284_Collect__conv__if2,axiom,
% 0.24/0.46 ! [P_38: ( hoare_1708887482_state > $o ) > $o,A_204: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ( P_38 @ A_204 )
% 0.24/0.46 => ( ( collec219771562tate_o
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 0.24/0.46 = ( insert949073679tate_o @ A_204 @ bot_bo1678742418te_o_o ) ) )
% 0.24/0.46 & ( ~ ( P_38 @ A_204 )
% 0.24/0.46 => ( ( collec219771562tate_o
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 0.24/0.46 = bot_bo1678742418te_o_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_285_Collect__conv__if2,axiom,
% 0.24/0.46 ! [P_38: hoare_1708887482_state > $o,A_204: hoare_1708887482_state] :
% 0.24/0.46 ( ( ( P_38 @ A_204 )
% 0.24/0.46 => ( ( collec1568722789_state
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 0.24/0.46 = ( insert528405184_state @ A_204 @ bot_bo19817387tate_o ) ) )
% 0.24/0.46 & ( ~ ( P_38 @ A_204 )
% 0.24/0.46 => ( ( collec1568722789_state
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 0.24/0.46 = bot_bo19817387tate_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_286_singleton__conv,axiom,
% 0.24/0.46 ! [A_203: pname] :
% 0.24/0.46 ( ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : ( X_3 = A_203 ) )
% 0.24/0.46 = ( insert_pname @ A_203 @ bot_bot_pname_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_287_singleton__conv,axiom,
% 0.24/0.46 ! [A_203: com] :
% 0.24/0.46 ( ( collect_com
% 0.24/0.46 @ ^ [X_3: com] : ( X_3 = A_203 ) )
% 0.24/0.46 = ( insert_com @ A_203 @ bot_bot_com_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_288_singleton__conv,axiom,
% 0.24/0.46 ! [A_203: pname > $o] :
% 0.24/0.46 ( ( collect_pname_o
% 0.24/0.46 @ ^ [X_3: pname > $o] : ( X_3 = A_203 ) )
% 0.24/0.46 = ( insert_pname_o @ A_203 @ bot_bot_pname_o_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_289_singleton__conv,axiom,
% 0.24/0.46 ! [A_203: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( collec219771562tate_o
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state > $o] : ( X_3 = A_203 ) )
% 0.24/0.46 = ( insert949073679tate_o @ A_203 @ bot_bo1678742418te_o_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_290_singleton__conv,axiom,
% 0.24/0.46 ! [A_203: hoare_1708887482_state] :
% 0.24/0.46 ( ( collec1568722789_state
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : ( X_3 = A_203 ) )
% 0.24/0.46 = ( insert528405184_state @ A_203 @ bot_bo19817387tate_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_291_singleton__conv2,axiom,
% 0.24/0.46 ! [A_202: pname] :
% 0.24/0.46 ( ( collect_pname @ ( fequal_pname @ A_202 ) )
% 0.24/0.46 = ( insert_pname @ A_202 @ bot_bot_pname_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_292_singleton__conv2,axiom,
% 0.24/0.46 ! [A_202: com] :
% 0.24/0.46 ( ( collect_com @ ( fequal_com @ A_202 ) )
% 0.24/0.46 = ( insert_com @ A_202 @ bot_bot_com_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_293_singleton__conv2,axiom,
% 0.24/0.46 ! [A_202: pname > $o] :
% 0.24/0.46 ( ( collect_pname_o @ ( fequal_pname_o @ A_202 ) )
% 0.24/0.46 = ( insert_pname_o @ A_202 @ bot_bot_pname_o_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_294_singleton__conv2,axiom,
% 0.24/0.46 ! [A_202: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( collec219771562tate_o @ ( fequal1436017556tate_o @ A_202 ) )
% 0.24/0.46 = ( insert949073679tate_o @ A_202 @ bot_bo1678742418te_o_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_295_singleton__conv2,axiom,
% 0.24/0.46 ! [A_202: hoare_1708887482_state] :
% 0.24/0.46 ( ( collec1568722789_state @ ( fequal224822779_state @ A_202 ) )
% 0.24/0.46 = ( insert528405184_state @ A_202 @ bot_bo19817387tate_o ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_296_MGF__lemma1,axiom,
% 0.24/0.46 ! [C_34: com,G_7: hoare_1708887482_state > $o] :
% 0.24/0.46 ( hoare_1160767572gleton
% 0.24/0.46 => ( ! [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ ( dom_pname_com @ body ) )
% 0.24/0.46 => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ X_3 ) ) @ bot_bo19817387tate_o ) ) )
% 0.24/0.46 => ( ( wt @ C_34 )
% 0.24/0.46 => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_297_WT__bodiesD,axiom,
% 0.24/0.46 ! [Pn_1: pname,B_82: com] :
% 0.24/0.46 ( wT_bodies
% 0.24/0.46 => ( ( ( body @ Pn_1 )
% 0.24/0.46 = ( some_com @ B_82 ) )
% 0.24/0.46 => ( wt @ B_82 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_298_imageE,axiom,
% 0.24/0.46 ! [B_134: hoare_1708887482_state,F_74: com > hoare_1708887482_state,A_201: com > $o] :
% 0.24/0.46 ( ( member451959335_state @ B_134 @ ( image_934102463_state @ F_74 @ A_201 ) )
% 0.24/0.46 => ~ ! [X_3: com] :
% 0.24/0.46 ( ( B_134
% 0.24/0.46 = ( F_74 @ X_3 ) )
% 0.24/0.46 => ~ ( member_com @ X_3 @ A_201 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_299_imageE,axiom,
% 0.24/0.46 ! [B_134: pname,F_74: com > pname,A_201: com > $o] :
% 0.24/0.46 ( ( member_pname @ B_134 @ ( image_com_pname @ F_74 @ A_201 ) )
% 0.24/0.46 => ~ ! [X_3: com] :
% 0.24/0.46 ( ( B_134
% 0.24/0.46 = ( F_74 @ X_3 ) )
% 0.24/0.46 => ~ ( member_com @ X_3 @ A_201 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_300_imageE,axiom,
% 0.24/0.46 ! [B_134: com,F_74: hoare_1708887482_state > com,A_201: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member_com @ B_134 @ ( image_1604448413te_com @ F_74 @ A_201 ) )
% 0.24/0.46 => ~ ! [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( B_134
% 0.24/0.46 = ( F_74 @ X_3 ) )
% 0.24/0.46 => ~ ( member451959335_state @ X_3 @ A_201 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_301_imageE,axiom,
% 0.24/0.46 ! [B_134: com,F_74: pname > com,A_201: pname > $o] :
% 0.24/0.46 ( ( member_com @ B_134 @ ( image_pname_com @ F_74 @ A_201 ) )
% 0.24/0.46 => ~ ! [X_3: pname] :
% 0.24/0.46 ( ( B_134
% 0.24/0.46 = ( F_74 @ X_3 ) )
% 0.24/0.46 => ~ ( member_pname @ X_3 @ A_201 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_302_imageE,axiom,
% 0.24/0.46 ! [B_134: hoare_1708887482_state,F_74: pname > hoare_1708887482_state,A_201: pname > $o] :
% 0.24/0.46 ( ( member451959335_state @ B_134 @ ( image_1116629049_state @ F_74 @ A_201 ) )
% 0.24/0.46 => ~ ! [X_3: pname] :
% 0.24/0.46 ( ( B_134
% 0.24/0.46 = ( F_74 @ X_3 ) )
% 0.24/0.46 => ~ ( member_pname @ X_3 @ A_201 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_303_finite__subset__induct,axiom,
% 0.24/0.46 ! [P_37: ( com > $o ) > $o,A_200: com > $o,F_73: com > $o] :
% 0.24/0.46 ( ( finite_finite_com @ F_73 )
% 0.24/0.46 => ( ( ord_less_eq_com_o @ F_73 @ A_200 )
% 0.24/0.46 => ( ( P_37 @ bot_bot_com_o )
% 0.24/0.46 => ( ! [A_6: com,F_53: com > $o] :
% 0.24/0.46 ( ( finite_finite_com @ F_53 )
% 0.24/0.46 => ( ( member_com @ A_6 @ A_200 )
% 0.24/0.46 => ( ~ ( member_com @ A_6 @ F_53 )
% 0.24/0.46 => ( ( P_37 @ F_53 )
% 0.24/0.46 => ( P_37 @ ( insert_com @ A_6 @ F_53 ) ) ) ) ) )
% 0.24/0.46 => ( P_37 @ F_73 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_304_finite__subset__induct,axiom,
% 0.24/0.46 ! [P_37: ( ( pname > $o ) > $o ) > $o,A_200: ( pname > $o ) > $o,F_73: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ F_73 )
% 0.24/0.46 => ( ( ord_le1205211808me_o_o @ F_73 @ A_200 )
% 0.24/0.46 => ( ( P_37 @ bot_bot_pname_o_o )
% 0.24/0.46 => ( ! [A_6: pname > $o,F_53: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ F_53 )
% 0.24/0.46 => ( ( member_pname_o @ A_6 @ A_200 )
% 0.24/0.46 => ( ~ ( member_pname_o @ A_6 @ F_53 )
% 0.24/0.46 => ( ( P_37 @ F_53 )
% 0.24/0.46 => ( P_37 @ ( insert_pname_o @ A_6 @ F_53 ) ) ) ) ) )
% 0.24/0.46 => ( P_37 @ F_73 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_305_finite__subset__induct,axiom,
% 0.24/0.46 ! [P_37: ( ( hoare_1708887482_state > $o ) > $o ) > $o,A_200: ( hoare_1708887482_state > $o ) > $o,F_73: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ F_73 )
% 0.24/0.46 => ( ( ord_le1728773982te_o_o @ F_73 @ A_200 )
% 0.24/0.46 => ( ( P_37 @ bot_bo1678742418te_o_o )
% 0.24/0.46 => ( ! [A_6: hoare_1708887482_state > $o,F_53: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ F_53 )
% 0.24/0.46 => ( ( member814030440tate_o @ A_6 @ A_200 )
% 0.24/0.46 => ( ~ ( member814030440tate_o @ A_6 @ F_53 )
% 0.24/0.46 => ( ( P_37 @ F_53 )
% 0.24/0.46 => ( P_37 @ ( insert949073679tate_o @ A_6 @ F_53 ) ) ) ) ) )
% 0.24/0.46 => ( P_37 @ F_73 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_306_finite__subset__induct,axiom,
% 0.24/0.46 ! [P_37: ( pname > $o ) > $o,A_200: pname > $o,F_73: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ F_73 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ F_73 @ A_200 )
% 0.24/0.46 => ( ( P_37 @ bot_bot_pname_o )
% 0.24/0.46 => ( ! [A_6: pname,F_53: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ F_53 )
% 0.24/0.46 => ( ( member_pname @ A_6 @ A_200 )
% 0.24/0.46 => ( ~ ( member_pname @ A_6 @ F_53 )
% 0.24/0.46 => ( ( P_37 @ F_53 )
% 0.24/0.46 => ( P_37 @ ( insert_pname @ A_6 @ F_53 ) ) ) ) ) )
% 0.24/0.46 => ( P_37 @ F_73 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_307_finite__subset__induct,axiom,
% 0.24/0.46 ! [P_37: ( hoare_1708887482_state > $o ) > $o,A_200: hoare_1708887482_state > $o,F_73: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ F_73 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ F_73 @ A_200 )
% 0.24/0.46 => ( ( P_37 @ bot_bo19817387tate_o )
% 0.24/0.46 => ( ! [A_6: hoare_1708887482_state,F_53: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ F_53 )
% 0.24/0.46 => ( ( member451959335_state @ A_6 @ A_200 )
% 0.24/0.46 => ( ~ ( member451959335_state @ A_6 @ F_53 )
% 0.24/0.46 => ( ( P_37 @ F_53 )
% 0.24/0.46 => ( P_37 @ ( insert528405184_state @ A_6 @ F_53 ) ) ) ) ) )
% 0.24/0.46 => ( P_37 @ F_73 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_308_WTs__elim__cases_I7_J,axiom,
% 0.24/0.46 ! [P: pname] :
% 0.24/0.46 ( ( wt @ ( body_1 @ P ) )
% 0.24/0.46 => ~ ! [Y_4: com] :
% 0.24/0.46 ( ( body @ P )
% 0.24/0.46 != ( some_com @ Y_4 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_309_subsetI,axiom,
% 0.24/0.46 ! [B_133: com > $o,A_199: com > $o] :
% 0.24/0.46 ( ! [X_3: com] :
% 0.24/0.46 ( ( member_com @ X_3 @ A_199 )
% 0.24/0.46 => ( member_com @ X_3 @ B_133 ) )
% 0.24/0.46 => ( ord_less_eq_com_o @ A_199 @ B_133 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_310_subsetI,axiom,
% 0.24/0.46 ! [B_133: hoare_1708887482_state > $o,A_199: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ! [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ A_199 )
% 0.24/0.46 => ( member451959335_state @ X_3 @ B_133 ) )
% 0.24/0.46 => ( ord_le777019615tate_o @ A_199 @ B_133 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_311_subsetI,axiom,
% 0.24/0.46 ! [B_133: pname > $o,A_199: pname > $o] :
% 0.24/0.46 ( ! [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ A_199 )
% 0.24/0.46 => ( member_pname @ X_3 @ B_133 ) )
% 0.24/0.46 => ( ord_less_eq_pname_o @ A_199 @ B_133 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_312_finite__subset__image,axiom,
% 0.24/0.46 ! [F_72: ( pname > $o ) > hoare_1708887482_state,A_198: ( pname > $o ) > $o,B_132: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ B_132 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ B_132 @ ( image_1922967206_state @ F_72 @ A_198 ) )
% 0.24/0.46 => ? [C_61: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( ord_le1205211808me_o_o @ C_61 @ A_198 )
% 0.24/0.46 & ( finite297249702name_o @ C_61 )
% 0.24/0.46 & ( B_132
% 0.24/0.46 = ( image_1922967206_state @ F_72 @ C_61 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_313_finite__subset__image,axiom,
% 0.24/0.46 ! [F_72: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,A_198: ( hoare_1708887482_state > $o ) > $o,B_132: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ B_132 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ B_132 @ ( image_27005066_state @ F_72 @ A_198 ) )
% 0.24/0.46 => ? [C_61: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( ord_le1728773982te_o_o @ C_61 @ A_198 )
% 0.24/0.46 & ( finite1329924456tate_o @ C_61 )
% 0.24/0.46 & ( B_132
% 0.24/0.46 = ( image_27005066_state @ F_72 @ C_61 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_314_finite__subset__image,axiom,
% 0.24/0.46 ! [F_72: ( pname > $o ) > pname,A_198: ( pname > $o ) > $o,B_132: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ B_132 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_132 @ ( image_pname_o_pname @ F_72 @ A_198 ) )
% 0.24/0.46 => ? [C_61: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( ord_le1205211808me_o_o @ C_61 @ A_198 )
% 0.24/0.46 & ( finite297249702name_o @ C_61 )
% 0.24/0.46 & ( B_132
% 0.24/0.46 = ( image_pname_o_pname @ F_72 @ C_61 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_315_finite__subset__image,axiom,
% 0.24/0.46 ! [F_72: ( hoare_1708887482_state > $o ) > pname,A_198: ( hoare_1708887482_state > $o ) > $o,B_132: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ B_132 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_132 @ ( image_2051418740_pname @ F_72 @ A_198 ) )
% 0.24/0.46 => ? [C_61: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( ord_le1728773982te_o_o @ C_61 @ A_198 )
% 0.24/0.46 & ( finite1329924456tate_o @ C_61 )
% 0.24/0.46 & ( B_132
% 0.24/0.46 = ( image_2051418740_pname @ F_72 @ C_61 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_316_finite__subset__image,axiom,
% 0.24/0.46 ! [F_72: hoare_1708887482_state > pname > $o,A_198: hoare_1708887482_state > $o,B_132: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ B_132 )
% 0.24/0.46 => ( ( ord_le1205211808me_o_o @ B_132 @ ( image_1552895654name_o @ F_72 @ A_198 ) )
% 0.24/0.46 => ? [C_61: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ C_61 @ A_198 )
% 0.24/0.46 & ( finite1625599783_state @ C_61 )
% 0.24/0.46 & ( B_132
% 0.24/0.46 = ( image_1552895654name_o @ F_72 @ C_61 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_317_finite__subset__image,axiom,
% 0.24/0.46 ! [F_72: hoare_1708887482_state > hoare_1708887482_state > $o,A_198: hoare_1708887482_state > $o,B_132: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ B_132 )
% 0.24/0.46 => ( ( ord_le1728773982te_o_o @ B_132 @ ( image_1551509096tate_o @ F_72 @ A_198 ) )
% 0.24/0.46 => ? [C_61: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ C_61 @ A_198 )
% 0.24/0.46 & ( finite1625599783_state @ C_61 )
% 0.24/0.46 & ( B_132
% 0.24/0.46 = ( image_1551509096tate_o @ F_72 @ C_61 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_318_finite__subset__image,axiom,
% 0.24/0.46 ! [F_72: hoare_1708887482_state > pname,A_198: hoare_1708887482_state > $o,B_132: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ B_132 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_132 @ ( image_1509414295_pname @ F_72 @ A_198 ) )
% 0.24/0.46 => ? [C_61: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ C_61 @ A_198 )
% 0.24/0.46 & ( finite1625599783_state @ C_61 )
% 0.24/0.46 & ( B_132
% 0.24/0.46 = ( image_1509414295_pname @ F_72 @ C_61 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_319_finite__subset__image,axiom,
% 0.24/0.46 ! [F_72: pname > pname > $o,A_198: pname > $o,B_132: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ B_132 )
% 0.24/0.46 => ( ( ord_le1205211808me_o_o @ B_132 @ ( image_pname_pname_o @ F_72 @ A_198 ) )
% 0.24/0.46 => ? [C_61: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
% 0.24/0.46 & ( finite_finite_pname @ C_61 )
% 0.24/0.46 & ( B_132
% 0.24/0.46 = ( image_pname_pname_o @ F_72 @ C_61 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_320_finite__subset__image,axiom,
% 0.24/0.46 ! [F_72: pname > hoare_1708887482_state > $o,A_198: pname > $o,B_132: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ B_132 )
% 0.24/0.46 => ( ( ord_le1728773982te_o_o @ B_132 @ ( image_425134806tate_o @ F_72 @ A_198 ) )
% 0.24/0.46 => ? [C_61: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
% 0.24/0.46 & ( finite_finite_pname @ C_61 )
% 0.24/0.46 & ( B_132
% 0.24/0.46 = ( image_425134806tate_o @ F_72 @ C_61 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_321_finite__subset__image,axiom,
% 0.24/0.46 ! [F_72: pname > pname,A_198: pname > $o,B_132: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ B_132 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_132 @ ( image_pname_pname @ F_72 @ A_198 ) )
% 0.24/0.46 => ? [C_61: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
% 0.24/0.46 & ( finite_finite_pname @ C_61 )
% 0.24/0.46 & ( B_132
% 0.24/0.46 = ( image_pname_pname @ F_72 @ C_61 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_322_finite__subset__image,axiom,
% 0.24/0.46 ! [F_72: pname > hoare_1708887482_state,A_198: pname > $o,B_132: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ B_132 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ B_132 @ ( image_1116629049_state @ F_72 @ A_198 ) )
% 0.24/0.46 => ? [C_61: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
% 0.24/0.46 & ( finite_finite_pname @ C_61 )
% 0.24/0.46 & ( B_132
% 0.24/0.46 = ( image_1116629049_state @ F_72 @ C_61 ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_323_finite__dom__body,axiom,
% 0.24/0.46 finite_finite_pname @ ( dom_pname_com @ body ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_324_finite__induct,axiom,
% 0.24/0.46 ! [P_36: ( com > $o ) > $o,F_71: com > $o] :
% 0.24/0.46 ( ( finite_finite_com @ F_71 )
% 0.24/0.46 => ( ( P_36 @ bot_bot_com_o )
% 0.24/0.46 => ( ! [X_3: com,F_53: com > $o] :
% 0.24/0.46 ( ( finite_finite_com @ F_53 )
% 0.24/0.46 => ( ~ ( member_com @ X_3 @ F_53 )
% 0.24/0.46 => ( ( P_36 @ F_53 )
% 0.24/0.46 => ( P_36 @ ( insert_com @ X_3 @ F_53 ) ) ) ) )
% 0.24/0.46 => ( P_36 @ F_71 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_325_finite__induct,axiom,
% 0.24/0.46 ! [P_36: ( ( pname > $o ) > $o ) > $o,F_71: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ F_71 )
% 0.24/0.46 => ( ( P_36 @ bot_bot_pname_o_o )
% 0.24/0.46 => ( ! [X_3: pname > $o,F_53: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ F_53 )
% 0.24/0.46 => ( ~ ( member_pname_o @ X_3 @ F_53 )
% 0.24/0.46 => ( ( P_36 @ F_53 )
% 0.24/0.46 => ( P_36 @ ( insert_pname_o @ X_3 @ F_53 ) ) ) ) )
% 0.24/0.46 => ( P_36 @ F_71 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_326_finite__induct,axiom,
% 0.24/0.46 ! [P_36: ( ( hoare_1708887482_state > $o ) > $o ) > $o,F_71: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ F_71 )
% 0.24/0.46 => ( ( P_36 @ bot_bo1678742418te_o_o )
% 0.24/0.46 => ( ! [X_3: hoare_1708887482_state > $o,F_53: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ F_53 )
% 0.24/0.46 => ( ~ ( member814030440tate_o @ X_3 @ F_53 )
% 0.24/0.46 => ( ( P_36 @ F_53 )
% 0.24/0.46 => ( P_36 @ ( insert949073679tate_o @ X_3 @ F_53 ) ) ) ) )
% 0.24/0.46 => ( P_36 @ F_71 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_327_finite__induct,axiom,
% 0.24/0.46 ! [P_36: ( pname > $o ) > $o,F_71: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ F_71 )
% 0.24/0.46 => ( ( P_36 @ bot_bot_pname_o )
% 0.24/0.46 => ( ! [X_3: pname,F_53: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ F_53 )
% 0.24/0.46 => ( ~ ( member_pname @ X_3 @ F_53 )
% 0.24/0.46 => ( ( P_36 @ F_53 )
% 0.24/0.46 => ( P_36 @ ( insert_pname @ X_3 @ F_53 ) ) ) ) )
% 0.24/0.46 => ( P_36 @ F_71 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_328_finite__induct,axiom,
% 0.24/0.46 ! [P_36: ( hoare_1708887482_state > $o ) > $o,F_71: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ F_71 )
% 0.24/0.46 => ( ( P_36 @ bot_bo19817387tate_o )
% 0.24/0.46 => ( ! [X_3: hoare_1708887482_state,F_53: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ F_53 )
% 0.24/0.46 => ( ~ ( member451959335_state @ X_3 @ F_53 )
% 0.24/0.46 => ( ( P_36 @ F_53 )
% 0.24/0.46 => ( P_36 @ ( insert528405184_state @ X_3 @ F_53 ) ) ) ) )
% 0.24/0.46 => ( P_36 @ F_71 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_329_finite_Osimps,axiom,
% 0.24/0.46 ! [A_197: com > $o] :
% 0.24/0.46 ( ( finite_finite_com @ A_197 )
% 0.24/0.46 <=> ( ( A_197 = bot_bot_com_o )
% 0.24/0.46 | ? [A_39: com > $o,A_6: com] :
% 0.24/0.46 ( ( A_197
% 0.24/0.46 = ( insert_com @ A_6 @ A_39 ) )
% 0.24/0.46 & ( finite_finite_com @ A_39 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_330_finite_Osimps,axiom,
% 0.24/0.46 ! [A_197: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ A_197 )
% 0.24/0.46 <=> ( ( A_197 = bot_bot_pname_o_o )
% 0.24/0.46 | ? [A_39: ( pname > $o ) > $o,A_6: pname > $o] :
% 0.24/0.46 ( ( A_197
% 0.24/0.46 = ( insert_pname_o @ A_6 @ A_39 ) )
% 0.24/0.46 & ( finite297249702name_o @ A_39 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_331_finite_Osimps,axiom,
% 0.24/0.46 ! [A_197: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ A_197 )
% 0.24/0.46 <=> ( ( A_197 = bot_bo1678742418te_o_o )
% 0.24/0.46 | ? [A_39: ( hoare_1708887482_state > $o ) > $o,A_6: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( A_197
% 0.24/0.46 = ( insert949073679tate_o @ A_6 @ A_39 ) )
% 0.24/0.46 & ( finite1329924456tate_o @ A_39 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_332_finite_Osimps,axiom,
% 0.24/0.46 ! [A_197: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ A_197 )
% 0.24/0.46 <=> ( ( A_197 = bot_bot_pname_o )
% 0.24/0.46 | ? [A_39: pname > $o,A_6: pname] :
% 0.24/0.46 ( ( A_197
% 0.24/0.46 = ( insert_pname @ A_6 @ A_39 ) )
% 0.24/0.46 & ( finite_finite_pname @ A_39 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_333_finite_Osimps,axiom,
% 0.24/0.46 ! [A_197: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ A_197 )
% 0.24/0.46 <=> ( ( A_197 = bot_bo19817387tate_o )
% 0.24/0.46 | ? [A_39: hoare_1708887482_state > $o,A_6: hoare_1708887482_state] :
% 0.24/0.46 ( ( A_197
% 0.24/0.46 = ( insert528405184_state @ A_6 @ A_39 ) )
% 0.24/0.46 & ( finite1625599783_state @ A_39 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_334_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: com > hoare_1708887482_state,A_196: com > $o] :
% 0.24/0.46 ( ~ ( finite_finite_com @ A_196 )
% 0.24/0.46 => ( ( finite1625599783_state @ ( image_934102463_state @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: com] :
% 0.24/0.46 ( ( member_com @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite_finite_com
% 0.24/0.46 @ ( collect_com
% 0.24/0.46 @ ^ [A_6: com] :
% 0.24/0.46 ( (&) @ ( member_com @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_335_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: hoare_1708887482_state > hoare_1708887482_state,A_196: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ~ ( finite1625599783_state @ A_196 )
% 0.24/0.46 => ( ( finite1625599783_state @ ( image_757158439_state @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite1625599783_state
% 0.24/0.46 @ ( collec1568722789_state
% 0.24/0.46 @ ^ [A_6: hoare_1708887482_state] :
% 0.24/0.46 ( (&) @ ( member451959335_state @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_336_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: ( pname > $o ) > hoare_1708887482_state,A_196: ( pname > $o ) > $o] :
% 0.24/0.46 ( ~ ( finite297249702name_o @ A_196 )
% 0.24/0.46 => ( ( finite1625599783_state @ ( image_1922967206_state @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: pname > $o] :
% 0.24/0.46 ( ( member_pname_o @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite297249702name_o
% 0.24/0.46 @ ( collect_pname_o
% 0.24/0.46 @ ^ [A_6: pname > $o] :
% 0.24/0.46 ( (&) @ ( member_pname_o @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_337_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,A_196: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ~ ( finite1329924456tate_o @ A_196 )
% 0.24/0.46 => ( ( finite1625599783_state @ ( image_27005066_state @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member814030440tate_o @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite1329924456tate_o
% 0.24/0.46 @ ( collec219771562tate_o
% 0.24/0.46 @ ^ [A_6: hoare_1708887482_state > $o] :
% 0.24/0.46 ( (&) @ ( member814030440tate_o @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_338_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: com > pname,A_196: com > $o] :
% 0.24/0.46 ( ~ ( finite_finite_com @ A_196 )
% 0.24/0.46 => ( ( finite_finite_pname @ ( image_com_pname @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: com] :
% 0.24/0.46 ( ( member_com @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite_finite_com
% 0.24/0.46 @ ( collect_com
% 0.24/0.46 @ ^ [A_6: com] :
% 0.24/0.46 ( (&) @ ( member_com @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_339_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: hoare_1708887482_state > pname,A_196: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ~ ( finite1625599783_state @ A_196 )
% 0.24/0.46 => ( ( finite_finite_pname @ ( image_1509414295_pname @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite1625599783_state
% 0.24/0.46 @ ( collec1568722789_state
% 0.24/0.46 @ ^ [A_6: hoare_1708887482_state] :
% 0.24/0.46 ( (&) @ ( member451959335_state @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_340_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: pname > pname,A_196: pname > $o] :
% 0.24/0.46 ( ~ ( finite_finite_pname @ A_196 )
% 0.24/0.46 => ( ( finite_finite_pname @ ( image_pname_pname @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite_finite_pname
% 0.24/0.46 @ ( collect_pname
% 0.24/0.46 @ ^ [A_6: pname] :
% 0.24/0.46 ( (&) @ ( member_pname @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_341_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: ( pname > $o ) > pname,A_196: ( pname > $o ) > $o] :
% 0.24/0.46 ( ~ ( finite297249702name_o @ A_196 )
% 0.24/0.46 => ( ( finite_finite_pname @ ( image_pname_o_pname @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: pname > $o] :
% 0.24/0.46 ( ( member_pname_o @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite297249702name_o
% 0.24/0.46 @ ( collect_pname_o
% 0.24/0.46 @ ^ [A_6: pname > $o] :
% 0.24/0.46 ( (&) @ ( member_pname_o @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_342_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: ( hoare_1708887482_state > $o ) > pname,A_196: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ~ ( finite1329924456tate_o @ A_196 )
% 0.24/0.46 => ( ( finite_finite_pname @ ( image_2051418740_pname @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member814030440tate_o @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite1329924456tate_o
% 0.24/0.46 @ ( collec219771562tate_o
% 0.24/0.46 @ ^ [A_6: hoare_1708887482_state > $o] :
% 0.24/0.46 ( (&) @ ( member814030440tate_o @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_343_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: hoare_1708887482_state > pname > $o,A_196: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ~ ( finite1625599783_state @ A_196 )
% 0.24/0.46 => ( ( finite297249702name_o @ ( image_1552895654name_o @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite1625599783_state
% 0.24/0.46 @ ( collec1568722789_state
% 0.24/0.46 @ ^ [A_6: hoare_1708887482_state] :
% 0.24/0.46 ( (&) @ ( member451959335_state @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_344_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: hoare_1708887482_state > hoare_1708887482_state > $o,A_196: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ~ ( finite1625599783_state @ A_196 )
% 0.24/0.46 => ( ( finite1329924456tate_o @ ( image_1551509096tate_o @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite1625599783_state
% 0.24/0.46 @ ( collec1568722789_state
% 0.24/0.46 @ ^ [A_6: hoare_1708887482_state] :
% 0.24/0.46 ( (&) @ ( member451959335_state @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_345_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: pname > pname > $o,A_196: pname > $o] :
% 0.24/0.46 ( ~ ( finite_finite_pname @ A_196 )
% 0.24/0.46 => ( ( finite297249702name_o @ ( image_pname_pname_o @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite_finite_pname
% 0.24/0.46 @ ( collect_pname
% 0.24/0.46 @ ^ [A_6: pname] :
% 0.24/0.46 ( (&) @ ( member_pname @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_346_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: pname > hoare_1708887482_state > $o,A_196: pname > $o] :
% 0.24/0.46 ( ~ ( finite_finite_pname @ A_196 )
% 0.24/0.46 => ( ( finite1329924456tate_o @ ( image_425134806tate_o @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite_finite_pname
% 0.24/0.46 @ ( collect_pname
% 0.24/0.46 @ ^ [A_6: pname] :
% 0.24/0.46 ( (&) @ ( member_pname @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_347_pigeonhole__infinite,axiom,
% 0.24/0.46 ! [F_70: pname > hoare_1708887482_state,A_196: pname > $o] :
% 0.24/0.46 ( ~ ( finite_finite_pname @ A_196 )
% 0.24/0.46 => ( ( finite1625599783_state @ ( image_1116629049_state @ F_70 @ A_196 ) )
% 0.24/0.46 => ? [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ A_196 )
% 0.24/0.46 & ~ ( finite_finite_pname
% 0.24/0.46 @ ( collect_pname
% 0.24/0.46 @ ^ [A_6: pname] :
% 0.24/0.46 ( (&) @ ( member_pname @ A_6 @ A_196 )
% 0.24/0.46 @ ( ( F_70 @ A_6 )
% 0.24/0.46 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_348_com_Osimps_I6_J,axiom,
% 0.24/0.46 ! [Pname_1: pname,Pname: pname] :
% 0.24/0.46 ( ( ( body_1 @ Pname_1 )
% 0.24/0.46 = ( body_1 @ Pname ) )
% 0.24/0.46 <=> ( Pname_1 = Pname ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_349_MGT__Body,axiom,
% 0.24/0.46 ! [G_7: hoare_1708887482_state > $o,Procs_3: pname > $o] :
% 0.24/0.46 ( ( hoare_90032982_state
% 0.24/0.46 @ ( semila1122118281tate_o @ G_7
% 0.24/0.46 @ ( image_1116629049_state
% 0.24/0.46 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.24/0.46 @ Procs_3 ) )
% 0.24/0.46 @ ( image_1116629049_state
% 0.24/0.46 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
% 0.24/0.46 @ Procs_3 ) )
% 0.24/0.46 => ( ( finite_finite_pname @ Procs_3 )
% 0.24/0.46 => ( hoare_90032982_state @ G_7
% 0.24/0.46 @ ( image_1116629049_state
% 0.24/0.46 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.24/0.46 @ Procs_3 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_350_domD,axiom,
% 0.24/0.46 ! [A_195: com,M_4: com > option_com] :
% 0.24/0.46 ( ( member_com @ A_195 @ ( dom_com_com @ M_4 ) )
% 0.24/0.46 => ? [B_131: com] :
% 0.24/0.46 ( ( M_4 @ A_195 )
% 0.24/0.46 = ( some_com @ B_131 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_351_domD,axiom,
% 0.24/0.46 ! [A_195: hoare_1708887482_state,M_4: hoare_1708887482_state > option_pname] :
% 0.24/0.46 ( ( member451959335_state @ A_195 @ ( dom_Ho1805192458_pname @ M_4 ) )
% 0.24/0.46 => ? [B_131: pname] :
% 0.24/0.46 ( ( M_4 @ A_195 )
% 0.24/0.46 = ( some_pname @ B_131 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_352_domD,axiom,
% 0.24/0.46 ! [A_195: hoare_1708887482_state,M_4: hoare_1708887482_state > option1624383643_state] :
% 0.24/0.46 ( ( member451959335_state @ A_195 @ ( dom_Ho1703271284_state @ M_4 ) )
% 0.24/0.46 => ? [B_131: hoare_1708887482_state] :
% 0.24/0.46 ( ( M_4 @ A_195 )
% 0.24/0.46 = ( some_H1974565227_state @ B_131 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_353_domD,axiom,
% 0.24/0.46 ! [A_195: pname,M_4: pname > option_pname] :
% 0.24/0.46 ( ( member_pname @ A_195 @ ( dom_pname_pname @ M_4 ) )
% 0.24/0.46 => ? [B_131: pname] :
% 0.24/0.46 ( ( M_4 @ A_195 )
% 0.24/0.46 = ( some_pname @ B_131 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_354_domD,axiom,
% 0.24/0.46 ! [A_195: pname,M_4: pname > option1624383643_state] :
% 0.24/0.46 ( ( member_pname @ A_195 @ ( dom_pn1412407212_state @ M_4 ) )
% 0.24/0.46 => ? [B_131: hoare_1708887482_state] :
% 0.24/0.46 ( ( M_4 @ A_195 )
% 0.24/0.46 = ( some_H1974565227_state @ B_131 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_355_domD,axiom,
% 0.24/0.46 ! [A_195: pname,M_4: pname > option_com] :
% 0.24/0.46 ( ( member_pname @ A_195 @ ( dom_pname_com @ M_4 ) )
% 0.24/0.46 => ? [B_131: com] :
% 0.24/0.46 ( ( M_4 @ A_195 )
% 0.24/0.46 = ( some_com @ B_131 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_356_the__elem__eq,axiom,
% 0.24/0.46 ! [X_102: pname] :
% 0.24/0.46 ( ( the_elem_pname @ ( insert_pname @ X_102 @ bot_bot_pname_o ) )
% 0.24/0.46 = X_102 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_357_the__elem__eq,axiom,
% 0.24/0.46 ! [X_102: com] :
% 0.24/0.46 ( ( the_elem_com @ ( insert_com @ X_102 @ bot_bot_com_o ) )
% 0.24/0.46 = X_102 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_358_the__elem__eq,axiom,
% 0.24/0.46 ! [X_102: hoare_1708887482_state] :
% 0.24/0.46 ( ( the_el864710747_state @ ( insert528405184_state @ X_102 @ bot_bo19817387tate_o ) )
% 0.24/0.46 = X_102 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_359_image__subsetI,axiom,
% 0.24/0.46 ! [F_69: hoare_1708887482_state > com,B_130: com > $o,A_194: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ! [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ A_194 )
% 0.24/0.46 => ( member_com @ ( F_69 @ X_3 ) @ B_130 ) )
% 0.24/0.46 => ( ord_less_eq_com_o @ ( image_1604448413te_com @ F_69 @ A_194 ) @ B_130 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_360_image__subsetI,axiom,
% 0.24/0.46 ! [F_69: hoare_1708887482_state > pname,B_130: pname > $o,A_194: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ! [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ A_194 )
% 0.24/0.46 => ( member_pname @ ( F_69 @ X_3 ) @ B_130 ) )
% 0.24/0.46 => ( ord_less_eq_pname_o @ ( image_1509414295_pname @ F_69 @ A_194 ) @ B_130 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_361_image__subsetI,axiom,
% 0.24/0.46 ! [F_69: pname > com,B_130: com > $o,A_194: pname > $o] :
% 0.24/0.46 ( ! [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ A_194 )
% 0.24/0.46 => ( member_com @ ( F_69 @ X_3 ) @ B_130 ) )
% 0.24/0.46 => ( ord_less_eq_com_o @ ( image_pname_com @ F_69 @ A_194 ) @ B_130 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_362_image__subsetI,axiom,
% 0.24/0.46 ! [F_69: pname > pname,B_130: pname > $o,A_194: pname > $o] :
% 0.24/0.46 ( ! [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ A_194 )
% 0.24/0.46 => ( member_pname @ ( F_69 @ X_3 ) @ B_130 ) )
% 0.24/0.46 => ( ord_less_eq_pname_o @ ( image_pname_pname @ F_69 @ A_194 ) @ B_130 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_363_image__subsetI,axiom,
% 0.24/0.46 ! [F_69: com > hoare_1708887482_state,B_130: hoare_1708887482_state > $o,A_194: com > $o] :
% 0.24/0.46 ( ! [X_3: com] :
% 0.24/0.46 ( ( member_com @ X_3 @ A_194 )
% 0.24/0.46 => ( member451959335_state @ ( F_69 @ X_3 ) @ B_130 ) )
% 0.24/0.46 => ( ord_le777019615tate_o @ ( image_934102463_state @ F_69 @ A_194 ) @ B_130 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_364_image__subsetI,axiom,
% 0.24/0.46 ! [F_69: com > pname,B_130: pname > $o,A_194: com > $o] :
% 0.24/0.46 ( ! [X_3: com] :
% 0.24/0.46 ( ( member_com @ X_3 @ A_194 )
% 0.24/0.46 => ( member_pname @ ( F_69 @ X_3 ) @ B_130 ) )
% 0.24/0.46 => ( ord_less_eq_pname_o @ ( image_com_pname @ F_69 @ A_194 ) @ B_130 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_365_image__subsetI,axiom,
% 0.24/0.46 ! [F_69: pname > hoare_1708887482_state,B_130: hoare_1708887482_state > $o,A_194: pname > $o] :
% 0.24/0.46 ( ! [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ A_194 )
% 0.24/0.46 => ( member451959335_state @ ( F_69 @ X_3 ) @ B_130 ) )
% 0.24/0.46 => ( ord_le777019615tate_o @ ( image_1116629049_state @ F_69 @ A_194 ) @ B_130 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_366_order__refl,axiom,
% 0.24/0.46 ! [X_101: pname > $o] : ( ord_less_eq_pname_o @ X_101 @ X_101 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_367_order__refl,axiom,
% 0.24/0.46 ! [X_101: $o] : ( ord_less_eq_o @ X_101 @ X_101 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_368_order__refl,axiom,
% 0.24/0.46 ! [X_101: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ X_101 @ X_101 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_369_nonempty__iff,axiom,
% 0.24/0.46 ! [A_193: com > $o] :
% 0.24/0.46 ( ( A_193 != bot_bot_com_o )
% 0.24/0.46 <=> ? [X_3: com,B_84: com > $o] :
% 0.24/0.46 ( ( A_193
% 0.24/0.46 = ( insert_com @ X_3 @ B_84 ) )
% 0.24/0.46 & ~ ( member_com @ X_3 @ B_84 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_370_nonempty__iff,axiom,
% 0.24/0.46 ! [A_193: pname > $o] :
% 0.24/0.46 ( ( A_193 != bot_bot_pname_o )
% 0.24/0.46 <=> ? [X_3: pname,B_84: pname > $o] :
% 0.24/0.46 ( ( A_193
% 0.24/0.46 = ( insert_pname @ X_3 @ B_84 ) )
% 0.24/0.46 & ~ ( member_pname @ X_3 @ B_84 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_371_nonempty__iff,axiom,
% 0.24/0.46 ! [A_193: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( A_193 != bot_bo19817387tate_o )
% 0.24/0.46 <=> ? [X_3: hoare_1708887482_state,B_84: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( A_193
% 0.24/0.46 = ( insert528405184_state @ X_3 @ B_84 ) )
% 0.24/0.46 & ~ ( member451959335_state @ X_3 @ B_84 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_372_the_Osimps,axiom,
% 0.24/0.46 ! [X_100: pname] :
% 0.24/0.46 ( ( the_pname_1 @ ( some_pname @ X_100 ) )
% 0.24/0.46 = X_100 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_373_the_Osimps,axiom,
% 0.24/0.46 ! [X_100: hoare_1708887482_state] :
% 0.24/0.46 ( ( the_Ho963921505_state @ ( some_H1974565227_state @ X_100 ) )
% 0.24/0.46 = X_100 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_374_the_Osimps,axiom,
% 0.24/0.46 ! [X_100: com] :
% 0.24/0.46 ( ( the_com @ ( some_com @ X_100 ) )
% 0.24/0.46 = X_100 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_375_weak__Body,axiom,
% 0.24/0.46 ! [G_31: hoare_1708887482_state > $o,P_35: state > state > $o,Pn_4: pname,Q_24: state > state > $o] :
% 0.24/0.46 ( ( hoare_90032982_state @ G_31 @ ( insert528405184_state @ ( hoare_858012674_state @ P_35 @ ( the_com @ ( body @ Pn_4 ) ) @ Q_24 ) @ bot_bo19817387tate_o ) )
% 0.24/0.46 => ( hoare_90032982_state @ G_31 @ ( insert528405184_state @ ( hoare_858012674_state @ P_35 @ ( body_1 @ Pn_4 ) @ Q_24 ) @ bot_bo19817387tate_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_376_BodyN,axiom,
% 0.24/0.46 ! [P_34: state > state > $o,Pn_3: pname,Q_23: state > state > $o,G_30: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( hoare_90032982_state @ ( insert528405184_state @ ( hoare_858012674_state @ P_34 @ ( body_1 @ Pn_3 ) @ Q_23 ) @ G_30 ) @ ( insert528405184_state @ ( hoare_858012674_state @ P_34 @ ( the_com @ ( body @ Pn_3 ) ) @ Q_23 ) @ bot_bo19817387tate_o ) )
% 0.24/0.46 => ( hoare_90032982_state @ G_30 @ ( insert528405184_state @ ( hoare_858012674_state @ P_34 @ ( body_1 @ Pn_3 ) @ Q_23 ) @ bot_bo19817387tate_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_377_state__not__singleton__def,axiom,
% 0.24/0.46 ( hoare_1160767572gleton
% 0.24/0.46 <=> ? [S_2: state,T_1: state] : ( S_2 != T_1 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_378_UnCI,axiom,
% 0.24/0.46 ! [A_192: com > $o,C_60: com,B_129: com > $o] :
% 0.24/0.46 ( ( ~ ( member_com @ C_60 @ B_129 )
% 0.24/0.46 => ( member_com @ C_60 @ A_192 ) )
% 0.24/0.46 => ( member_com @ C_60 @ ( semila1562558655_com_o @ A_192 @ B_129 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_379_UnCI,axiom,
% 0.24/0.46 ! [A_192: hoare_1708887482_state > $o,C_60: hoare_1708887482_state,B_129: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ~ ( member451959335_state @ C_60 @ B_129 )
% 0.24/0.46 => ( member451959335_state @ C_60 @ A_192 ) )
% 0.24/0.46 => ( member451959335_state @ C_60 @ ( semila1122118281tate_o @ A_192 @ B_129 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_380_UnCI,axiom,
% 0.24/0.46 ! [A_192: pname > $o,C_60: pname,B_129: pname > $o] :
% 0.24/0.46 ( ( ~ ( member_pname @ C_60 @ B_129 )
% 0.24/0.46 => ( member_pname @ C_60 @ A_192 ) )
% 0.24/0.46 => ( member_pname @ C_60 @ ( semila1780557381name_o @ A_192 @ B_129 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_381_UnE,axiom,
% 0.24/0.46 ! [C_59: com,A_191: com > $o,B_128: com > $o] :
% 0.24/0.46 ( ( member_com @ C_59 @ ( semila1562558655_com_o @ A_191 @ B_128 ) )
% 0.24/0.46 => ( ~ ( member_com @ C_59 @ A_191 )
% 0.24/0.46 => ( member_com @ C_59 @ B_128 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_382_UnE,axiom,
% 0.24/0.46 ! [C_59: hoare_1708887482_state,A_191: hoare_1708887482_state > $o,B_128: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ C_59 @ ( semila1122118281tate_o @ A_191 @ B_128 ) )
% 0.24/0.46 => ( ~ ( member451959335_state @ C_59 @ A_191 )
% 0.24/0.46 => ( member451959335_state @ C_59 @ B_128 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_383_UnE,axiom,
% 0.24/0.46 ! [C_59: pname,A_191: pname > $o,B_128: pname > $o] :
% 0.24/0.46 ( ( member_pname @ C_59 @ ( semila1780557381name_o @ A_191 @ B_128 ) )
% 0.24/0.46 => ( ~ ( member_pname @ C_59 @ A_191 )
% 0.24/0.46 => ( member_pname @ C_59 @ B_128 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_384_triple_Oinject,axiom,
% 0.24/0.46 ! [Fun1_2: state > state > $o,Com_4: com,Fun2_2: state > state > $o,Fun1_1: state > state > $o,Com_3: com,Fun2_1: state > state > $o] :
% 0.24/0.46 ( ( ( hoare_858012674_state @ Fun1_2 @ Com_4 @ Fun2_2 )
% 0.24/0.46 = ( hoare_858012674_state @ Fun1_1 @ Com_3 @ Fun2_1 ) )
% 0.24/0.46 <=> ( ( Fun1_2 = Fun1_1 )
% 0.24/0.46 & ( Com_4 = Com_3 )
% 0.24/0.46 & ( Fun2_2 = Fun2_1 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_385_UnI2,axiom,
% 0.24/0.46 ! [A_190: com > $o,C_58: com,B_127: com > $o] :
% 0.24/0.46 ( ( member_com @ C_58 @ B_127 )
% 0.24/0.46 => ( member_com @ C_58 @ ( semila1562558655_com_o @ A_190 @ B_127 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_386_UnI2,axiom,
% 0.24/0.46 ! [A_190: hoare_1708887482_state > $o,C_58: hoare_1708887482_state,B_127: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ C_58 @ B_127 )
% 0.24/0.46 => ( member451959335_state @ C_58 @ ( semila1122118281tate_o @ A_190 @ B_127 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_387_UnI2,axiom,
% 0.24/0.46 ! [A_190: pname > $o,C_58: pname,B_127: pname > $o] :
% 0.24/0.46 ( ( member_pname @ C_58 @ B_127 )
% 0.24/0.46 => ( member_pname @ C_58 @ ( semila1780557381name_o @ A_190 @ B_127 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_388_UnI1,axiom,
% 0.24/0.46 ! [B_126: com > $o,C_57: com,A_189: com > $o] :
% 0.24/0.46 ( ( member_com @ C_57 @ A_189 )
% 0.24/0.46 => ( member_com @ C_57 @ ( semila1562558655_com_o @ A_189 @ B_126 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_389_UnI1,axiom,
% 0.24/0.46 ! [B_126: hoare_1708887482_state > $o,C_57: hoare_1708887482_state,A_189: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ C_57 @ A_189 )
% 0.24/0.46 => ( member451959335_state @ C_57 @ ( semila1122118281tate_o @ A_189 @ B_126 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_390_UnI1,axiom,
% 0.24/0.46 ! [B_126: pname > $o,C_57: pname,A_189: pname > $o] :
% 0.24/0.46 ( ( member_pname @ C_57 @ A_189 )
% 0.24/0.46 => ( member_pname @ C_57 @ ( semila1780557381name_o @ A_189 @ B_126 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_391_ball__Un,axiom,
% 0.24/0.46 ! [P_33: pname > $o,A_188: pname > $o,B_125: pname > $o] :
% 0.24/0.46 ( ! [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ ( semila1780557381name_o @ A_188 @ B_125 ) )
% 0.24/0.46 => ( P_33 @ X_3 ) )
% 0.24/0.46 <=> ( ! [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ A_188 )
% 0.24/0.46 => ( P_33 @ X_3 ) )
% 0.24/0.46 & ! [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ B_125 )
% 0.24/0.46 => ( P_33 @ X_3 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_392_ball__Un,axiom,
% 0.24/0.46 ! [P_33: hoare_1708887482_state > $o,A_188: hoare_1708887482_state > $o,B_125: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ! [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ ( semila1122118281tate_o @ A_188 @ B_125 ) )
% 0.24/0.46 => ( P_33 @ X_3 ) )
% 0.24/0.46 <=> ( ! [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ A_188 )
% 0.24/0.46 => ( P_33 @ X_3 ) )
% 0.24/0.46 & ! [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ B_125 )
% 0.24/0.46 => ( P_33 @ X_3 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_393_bex__Un,axiom,
% 0.24/0.46 ! [P_32: pname > $o,A_187: pname > $o,B_124: pname > $o] :
% 0.24/0.46 ( ? [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ ( semila1780557381name_o @ A_187 @ B_124 ) )
% 0.24/0.46 & ( P_32 @ X_3 ) )
% 0.24/0.46 <=> ( ? [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ A_187 )
% 0.24/0.46 & ( P_32 @ X_3 ) )
% 0.24/0.46 | ? [X_3: pname] :
% 0.24/0.46 ( ( member_pname @ X_3 @ B_124 )
% 0.24/0.46 & ( P_32 @ X_3 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_394_bex__Un,axiom,
% 0.24/0.46 ! [P_32: hoare_1708887482_state > $o,A_187: hoare_1708887482_state > $o,B_124: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ? [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ ( semila1122118281tate_o @ A_187 @ B_124 ) )
% 0.24/0.46 & ( P_32 @ X_3 ) )
% 0.24/0.46 <=> ( ? [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ A_187 )
% 0.24/0.46 & ( P_32 @ X_3 ) )
% 0.24/0.46 | ? [X_3: hoare_1708887482_state] :
% 0.24/0.46 ( ( member451959335_state @ X_3 @ B_124 )
% 0.24/0.46 & ( P_32 @ X_3 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_395_Un__assoc,axiom,
% 0.24/0.46 ! [A_186: pname > $o,B_123: pname > $o,C_56: pname > $o] :
% 0.24/0.46 ( ( semila1780557381name_o @ ( semila1780557381name_o @ A_186 @ B_123 ) @ C_56 )
% 0.24/0.46 = ( semila1780557381name_o @ A_186 @ ( semila1780557381name_o @ B_123 @ C_56 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_396_Un__assoc,axiom,
% 0.24/0.46 ! [A_186: hoare_1708887482_state > $o,B_123: hoare_1708887482_state > $o,C_56: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A_186 @ B_123 ) @ C_56 )
% 0.24/0.46 = ( semila1122118281tate_o @ A_186 @ ( semila1122118281tate_o @ B_123 @ C_56 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_397_Un__iff,axiom,
% 0.24/0.46 ! [C_55: com,A_185: com > $o,B_122: com > $o] :
% 0.24/0.46 ( ( member_com @ C_55 @ ( semila1562558655_com_o @ A_185 @ B_122 ) )
% 0.24/0.46 <=> ( ( member_com @ C_55 @ A_185 )
% 0.24/0.46 | ( member_com @ C_55 @ B_122 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_398_Un__iff,axiom,
% 0.24/0.46 ! [C_55: hoare_1708887482_state,A_185: hoare_1708887482_state > $o,B_122: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( member451959335_state @ C_55 @ ( semila1122118281tate_o @ A_185 @ B_122 ) )
% 0.24/0.46 <=> ( ( member451959335_state @ C_55 @ A_185 )
% 0.24/0.46 | ( member451959335_state @ C_55 @ B_122 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_399_Un__iff,axiom,
% 0.24/0.46 ! [C_55: pname,A_185: pname > $o,B_122: pname > $o] :
% 0.24/0.46 ( ( member_pname @ C_55 @ ( semila1780557381name_o @ A_185 @ B_122 ) )
% 0.24/0.46 <=> ( ( member_pname @ C_55 @ A_185 )
% 0.24/0.46 | ( member_pname @ C_55 @ B_122 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_400_Un__left__commute,axiom,
% 0.24/0.46 ! [A_184: pname > $o,B_121: pname > $o,C_54: pname > $o] :
% 0.24/0.46 ( ( semila1780557381name_o @ A_184 @ ( semila1780557381name_o @ B_121 @ C_54 ) )
% 0.24/0.46 = ( semila1780557381name_o @ B_121 @ ( semila1780557381name_o @ A_184 @ C_54 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_401_Un__left__commute,axiom,
% 0.24/0.46 ! [A_184: hoare_1708887482_state > $o,B_121: hoare_1708887482_state > $o,C_54: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( semila1122118281tate_o @ A_184 @ ( semila1122118281tate_o @ B_121 @ C_54 ) )
% 0.24/0.46 = ( semila1122118281tate_o @ B_121 @ ( semila1122118281tate_o @ A_184 @ C_54 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_402_Un__left__absorb,axiom,
% 0.24/0.46 ! [A_183: pname > $o,B_120: pname > $o] :
% 0.24/0.46 ( ( semila1780557381name_o @ A_183 @ ( semila1780557381name_o @ A_183 @ B_120 ) )
% 0.24/0.46 = ( semila1780557381name_o @ A_183 @ B_120 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_403_Un__left__absorb,axiom,
% 0.24/0.46 ! [A_183: hoare_1708887482_state > $o,B_120: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( semila1122118281tate_o @ A_183 @ ( semila1122118281tate_o @ A_183 @ B_120 ) )
% 0.24/0.46 = ( semila1122118281tate_o @ A_183 @ B_120 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_404_Un__commute,axiom,
% 0.24/0.46 ! [A_182: pname > $o,B_119: pname > $o] :
% 0.24/0.46 ( ( semila1780557381name_o @ A_182 @ B_119 )
% 0.24/0.46 = ( semila1780557381name_o @ B_119 @ A_182 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_405_Un__commute,axiom,
% 0.24/0.46 ! [A_182: hoare_1708887482_state > $o,B_119: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( semila1122118281tate_o @ A_182 @ B_119 )
% 0.24/0.46 = ( semila1122118281tate_o @ B_119 @ A_182 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_406_Un__def,axiom,
% 0.24/0.46 ! [A_181: com > $o,B_118: com > $o] :
% 0.24/0.46 ( ( semila1562558655_com_o @ A_181 @ B_118 )
% 0.24/0.46 = ( collect_com
% 0.24/0.46 @ ^ [X_3: com] : ( (|) @ ( member_com @ X_3 @ A_181 ) @ ( member_com @ X_3 @ B_118 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_407_Un__def,axiom,
% 0.24/0.46 ! [A_181: ( pname > $o ) > $o,B_118: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( semila181081674me_o_o @ A_181 @ B_118 )
% 0.24/0.46 = ( collect_pname_o
% 0.24/0.46 @ ^ [X_3: pname > $o] : ( (|) @ ( member_pname_o @ X_3 @ A_181 ) @ ( member_pname_o @ X_3 @ B_118 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_408_Un__def,axiom,
% 0.24/0.46 ! [A_181: ( hoare_1708887482_state > $o ) > $o,B_118: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( semila1853742644te_o_o @ A_181 @ B_118 )
% 0.24/0.46 = ( collec219771562tate_o
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state > $o] : ( (|) @ ( member814030440tate_o @ X_3 @ A_181 ) @ ( member814030440tate_o @ X_3 @ B_118 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_409_Un__def,axiom,
% 0.24/0.46 ! [A_181: hoare_1708887482_state > $o,B_118: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( semila1122118281tate_o @ A_181 @ B_118 )
% 0.24/0.46 = ( collec1568722789_state
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : ( (|) @ ( member451959335_state @ X_3 @ A_181 ) @ ( member451959335_state @ X_3 @ B_118 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_410_Un__def,axiom,
% 0.24/0.46 ! [A_181: pname > $o,B_118: pname > $o] :
% 0.24/0.46 ( ( semila1780557381name_o @ A_181 @ B_118 )
% 0.24/0.46 = ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : ( (|) @ ( member_pname @ X_3 @ A_181 ) @ ( member_pname @ X_3 @ B_118 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_411_Un__absorb,axiom,
% 0.24/0.46 ! [A_180: pname > $o] :
% 0.24/0.46 ( ( semila1780557381name_o @ A_180 @ A_180 )
% 0.24/0.46 = A_180 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_412_Un__absorb,axiom,
% 0.24/0.46 ! [A_180: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( semila1122118281tate_o @ A_180 @ A_180 )
% 0.24/0.46 = A_180 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_413_Collect__disj__eq,axiom,
% 0.24/0.46 ! [P_31: pname > $o,Q_22: pname > $o] :
% 0.24/0.46 ( ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
% 0.24/0.46 = ( semila1780557381name_o @ ( collect_pname @ P_31 ) @ ( collect_pname @ Q_22 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_414_Collect__disj__eq,axiom,
% 0.24/0.46 ! [P_31: ( pname > $o ) > $o,Q_22: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( collect_pname_o
% 0.24/0.46 @ ^ [X_3: pname > $o] : ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
% 0.24/0.46 = ( semila181081674me_o_o @ ( collect_pname_o @ P_31 ) @ ( collect_pname_o @ Q_22 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_415_Collect__disj__eq,axiom,
% 0.24/0.46 ! [P_31: ( hoare_1708887482_state > $o ) > $o,Q_22: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( collec219771562tate_o
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state > $o] : ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
% 0.24/0.46 = ( semila1853742644te_o_o @ ( collec219771562tate_o @ P_31 ) @ ( collec219771562tate_o @ Q_22 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_416_Collect__disj__eq,axiom,
% 0.24/0.46 ! [P_31: hoare_1708887482_state > $o,Q_22: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( collec1568722789_state
% 0.24/0.46 @ ^ [X_3: hoare_1708887482_state] : ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
% 0.24/0.46 = ( semila1122118281tate_o @ ( collec1568722789_state @ P_31 ) @ ( collec1568722789_state @ Q_22 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_417_Un__empty,axiom,
% 0.24/0.46 ! [A_179: pname > $o,B_117: pname > $o] :
% 0.24/0.46 ( ( ( semila1780557381name_o @ A_179 @ B_117 )
% 0.24/0.46 = bot_bot_pname_o )
% 0.24/0.46 <=> ( ( A_179 = bot_bot_pname_o )
% 0.24/0.46 & ( B_117 = bot_bot_pname_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_418_Un__empty,axiom,
% 0.24/0.46 ! [A_179: com > $o,B_117: com > $o] :
% 0.24/0.46 ( ( ( semila1562558655_com_o @ A_179 @ B_117 )
% 0.24/0.46 = bot_bot_com_o )
% 0.24/0.46 <=> ( ( A_179 = bot_bot_com_o )
% 0.24/0.46 & ( B_117 = bot_bot_com_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_419_Un__empty,axiom,
% 0.24/0.46 ! [A_179: hoare_1708887482_state > $o,B_117: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ( semila1122118281tate_o @ A_179 @ B_117 )
% 0.24/0.46 = bot_bo19817387tate_o )
% 0.24/0.46 <=> ( ( A_179 = bot_bo19817387tate_o )
% 0.24/0.46 & ( B_117 = bot_bo19817387tate_o ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_420_Un__empty__right,axiom,
% 0.24/0.46 ! [A_178: pname > $o] :
% 0.24/0.46 ( ( semila1780557381name_o @ A_178 @ bot_bot_pname_o )
% 0.24/0.46 = A_178 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_421_Un__empty__right,axiom,
% 0.24/0.46 ! [A_178: com > $o] :
% 0.24/0.46 ( ( semila1562558655_com_o @ A_178 @ bot_bot_com_o )
% 0.24/0.46 = A_178 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_422_Un__empty__right,axiom,
% 0.24/0.46 ! [A_178: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( semila1122118281tate_o @ A_178 @ bot_bo19817387tate_o )
% 0.24/0.46 = A_178 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_423_Un__empty__left,axiom,
% 0.24/0.46 ! [B_116: pname > $o] :
% 0.24/0.46 ( ( semila1780557381name_o @ bot_bot_pname_o @ B_116 )
% 0.24/0.46 = B_116 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_424_Un__empty__left,axiom,
% 0.24/0.46 ! [B_116: com > $o] :
% 0.24/0.46 ( ( semila1562558655_com_o @ bot_bot_com_o @ B_116 )
% 0.24/0.46 = B_116 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_425_Un__empty__left,axiom,
% 0.24/0.46 ! [B_116: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( semila1122118281tate_o @ bot_bo19817387tate_o @ B_116 )
% 0.24/0.46 = B_116 ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_426_finite__UnI,axiom,
% 0.24/0.46 ! [G_29: ( pname > $o ) > $o,F_68: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ F_68 )
% 0.24/0.46 => ( ( finite297249702name_o @ G_29 )
% 0.24/0.46 => ( finite297249702name_o @ ( semila181081674me_o_o @ F_68 @ G_29 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_427_finite__UnI,axiom,
% 0.24/0.46 ! [G_29: ( hoare_1708887482_state > $o ) > $o,F_68: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ F_68 )
% 0.24/0.46 => ( ( finite1329924456tate_o @ G_29 )
% 0.24/0.46 => ( finite1329924456tate_o @ ( semila1853742644te_o_o @ F_68 @ G_29 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_428_finite__UnI,axiom,
% 0.24/0.46 ! [G_29: hoare_1708887482_state > $o,F_68: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ F_68 )
% 0.24/0.46 => ( ( finite1625599783_state @ G_29 )
% 0.24/0.46 => ( finite1625599783_state @ ( semila1122118281tate_o @ F_68 @ G_29 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_429_finite__UnI,axiom,
% 0.24/0.46 ! [G_29: pname > $o,F_68: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ F_68 )
% 0.24/0.46 => ( ( finite_finite_pname @ G_29 )
% 0.24/0.46 => ( finite_finite_pname @ ( semila1780557381name_o @ F_68 @ G_29 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_430_finite__Un,axiom,
% 0.24/0.46 ! [F_67: ( pname > $o ) > $o,G_28: ( pname > $o ) > $o] :
% 0.24/0.46 ( ( finite297249702name_o @ ( semila181081674me_o_o @ F_67 @ G_28 ) )
% 0.24/0.46 <=> ( ( finite297249702name_o @ F_67 )
% 0.24/0.46 & ( finite297249702name_o @ G_28 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_431_finite__Un,axiom,
% 0.24/0.46 ! [F_67: ( hoare_1708887482_state > $o ) > $o,G_28: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.46 ( ( finite1329924456tate_o @ ( semila1853742644te_o_o @ F_67 @ G_28 ) )
% 0.24/0.46 <=> ( ( finite1329924456tate_o @ F_67 )
% 0.24/0.46 & ( finite1329924456tate_o @ G_28 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_432_finite__Un,axiom,
% 0.24/0.46 ! [F_67: hoare_1708887482_state > $o,G_28: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( finite1625599783_state @ ( semila1122118281tate_o @ F_67 @ G_28 ) )
% 0.24/0.46 <=> ( ( finite1625599783_state @ F_67 )
% 0.24/0.46 & ( finite1625599783_state @ G_28 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_433_finite__Un,axiom,
% 0.24/0.46 ! [F_67: pname > $o,G_28: pname > $o] :
% 0.24/0.46 ( ( finite_finite_pname @ ( semila1780557381name_o @ F_67 @ G_28 ) )
% 0.24/0.46 <=> ( ( finite_finite_pname @ F_67 )
% 0.24/0.46 & ( finite_finite_pname @ G_28 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_434_Un__insert__left,axiom,
% 0.24/0.46 ! [A_177: pname,B_115: pname > $o,C_53: pname > $o] :
% 0.24/0.46 ( ( semila1780557381name_o @ ( insert_pname @ A_177 @ B_115 ) @ C_53 )
% 0.24/0.46 = ( insert_pname @ A_177 @ ( semila1780557381name_o @ B_115 @ C_53 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_435_Un__insert__left,axiom,
% 0.24/0.46 ! [A_177: com,B_115: com > $o,C_53: com > $o] :
% 0.24/0.46 ( ( semila1562558655_com_o @ ( insert_com @ A_177 @ B_115 ) @ C_53 )
% 0.24/0.46 = ( insert_com @ A_177 @ ( semila1562558655_com_o @ B_115 @ C_53 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_436_Un__insert__left,axiom,
% 0.24/0.46 ! [A_177: hoare_1708887482_state,B_115: hoare_1708887482_state > $o,C_53: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( semila1122118281tate_o @ ( insert528405184_state @ A_177 @ B_115 ) @ C_53 )
% 0.24/0.46 = ( insert528405184_state @ A_177 @ ( semila1122118281tate_o @ B_115 @ C_53 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_437_Un__insert__right,axiom,
% 0.24/0.46 ! [A_176: pname > $o,A_175: pname,B_114: pname > $o] :
% 0.24/0.46 ( ( semila1780557381name_o @ A_176 @ ( insert_pname @ A_175 @ B_114 ) )
% 0.24/0.46 = ( insert_pname @ A_175 @ ( semila1780557381name_o @ A_176 @ B_114 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_438_Un__insert__right,axiom,
% 0.24/0.46 ! [A_176: com > $o,A_175: com,B_114: com > $o] :
% 0.24/0.46 ( ( semila1562558655_com_o @ A_176 @ ( insert_com @ A_175 @ B_114 ) )
% 0.24/0.46 = ( insert_com @ A_175 @ ( semila1562558655_com_o @ A_176 @ B_114 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_439_Un__insert__right,axiom,
% 0.24/0.46 ! [A_176: hoare_1708887482_state > $o,A_175: hoare_1708887482_state,B_114: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( semila1122118281tate_o @ A_176 @ ( insert528405184_state @ A_175 @ B_114 ) )
% 0.24/0.46 = ( insert528405184_state @ A_175 @ ( semila1122118281tate_o @ A_176 @ B_114 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_440_Un__mono,axiom,
% 0.24/0.46 ! [B_113: pname > $o,D_5: pname > $o,A_174: pname > $o,C_52: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_174 @ C_52 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_113 @ D_5 )
% 0.24/0.46 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_174 @ B_113 ) @ ( semila1780557381name_o @ C_52 @ D_5 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_441_Un__mono,axiom,
% 0.24/0.46 ! [B_113: hoare_1708887482_state > $o,D_5: hoare_1708887482_state > $o,A_174: hoare_1708887482_state > $o,C_52: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_174 @ C_52 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ B_113 @ D_5 )
% 0.24/0.46 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_174 @ B_113 ) @ ( semila1122118281tate_o @ C_52 @ D_5 ) ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_442_Un__least,axiom,
% 0.24/0.46 ! [B_112: pname > $o,A_173: pname > $o,C_51: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_173 @ C_51 )
% 0.24/0.46 => ( ( ord_less_eq_pname_o @ B_112 @ C_51 )
% 0.24/0.46 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_173 @ B_112 ) @ C_51 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_443_Un__least,axiom,
% 0.24/0.46 ! [B_112: hoare_1708887482_state > $o,A_173: hoare_1708887482_state > $o,C_51: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_173 @ C_51 )
% 0.24/0.46 => ( ( ord_le777019615tate_o @ B_112 @ C_51 )
% 0.24/0.46 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_173 @ B_112 ) @ C_51 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_444_Un__absorb2,axiom,
% 0.24/0.46 ! [B_111: pname > $o,A_172: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ B_111 @ A_172 )
% 0.24/0.46 => ( ( semila1780557381name_o @ A_172 @ B_111 )
% 0.24/0.46 = A_172 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_445_Un__absorb2,axiom,
% 0.24/0.46 ! [B_111: hoare_1708887482_state > $o,A_172: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ B_111 @ A_172 )
% 0.24/0.46 => ( ( semila1122118281tate_o @ A_172 @ B_111 )
% 0.24/0.46 = A_172 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_446_Un__absorb1,axiom,
% 0.24/0.46 ! [A_171: pname > $o,B_110: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_171 @ B_110 )
% 0.24/0.46 => ( ( semila1780557381name_o @ A_171 @ B_110 )
% 0.24/0.46 = B_110 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_447_Un__absorb1,axiom,
% 0.24/0.46 ! [A_171: hoare_1708887482_state > $o,B_110: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_171 @ B_110 )
% 0.24/0.46 => ( ( semila1122118281tate_o @ A_171 @ B_110 )
% 0.24/0.46 = B_110 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_448_subset__Un__eq,axiom,
% 0.24/0.46 ! [A_170: pname > $o,B_109: pname > $o] :
% 0.24/0.46 ( ( ord_less_eq_pname_o @ A_170 @ B_109 )
% 0.24/0.46 <=> ( ( semila1780557381name_o @ A_170 @ B_109 )
% 0.24/0.46 = B_109 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_449_subset__Un__eq,axiom,
% 0.24/0.46 ! [A_170: hoare_1708887482_state > $o,B_109: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( ord_le777019615tate_o @ A_170 @ B_109 )
% 0.24/0.46 <=> ( ( semila1122118281tate_o @ A_170 @ B_109 )
% 0.24/0.46 = B_109 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_450_Un__upper2,axiom,
% 0.24/0.46 ! [B_108: pname > $o,A_169: pname > $o] : ( ord_less_eq_pname_o @ B_108 @ ( semila1780557381name_o @ A_169 @ B_108 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_451_Un__upper2,axiom,
% 0.24/0.46 ! [B_108: hoare_1708887482_state > $o,A_169: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ B_108 @ ( semila1122118281tate_o @ A_169 @ B_108 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_452_Un__upper1,axiom,
% 0.24/0.46 ! [A_168: pname > $o,B_107: pname > $o] : ( ord_less_eq_pname_o @ A_168 @ ( semila1780557381name_o @ A_168 @ B_107 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_453_Un__upper1,axiom,
% 0.24/0.46 ! [A_168: hoare_1708887482_state > $o,B_107: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A_168 @ ( semila1122118281tate_o @ A_168 @ B_107 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_454_image__Un,axiom,
% 0.24/0.46 ! [F_66: hoare_1708887482_state > pname,A_167: hoare_1708887482_state > $o,B_106: hoare_1708887482_state > $o] :
% 0.24/0.46 ( ( image_1509414295_pname @ F_66 @ ( semila1122118281tate_o @ A_167 @ B_106 ) )
% 0.24/0.46 = ( semila1780557381name_o @ ( image_1509414295_pname @ F_66 @ A_167 ) @ ( image_1509414295_pname @ F_66 @ B_106 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_455_image__Un,axiom,
% 0.24/0.46 ! [F_66: pname > hoare_1708887482_state,A_167: pname > $o,B_106: pname > $o] :
% 0.24/0.46 ( ( image_1116629049_state @ F_66 @ ( semila1780557381name_o @ A_167 @ B_106 ) )
% 0.24/0.46 = ( semila1122118281tate_o @ ( image_1116629049_state @ F_66 @ A_167 ) @ ( image_1116629049_state @ F_66 @ B_106 ) ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_456_insert__def,axiom,
% 0.24/0.46 ! [A_166: pname,B_105: pname > $o] :
% 0.24/0.46 ( ( insert_pname @ A_166 @ B_105 )
% 0.24/0.46 = ( semila1780557381name_o
% 0.24/0.46 @ ( collect_pname
% 0.24/0.46 @ ^ [X_3: pname] : ( X_3 = A_166 ) )
% 0.24/0.46 @ B_105 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_457_insert__def,axiom,
% 0.24/0.46 ! [A_166: com,B_105: com > $o] :
% 0.24/0.46 ( ( insert_com @ A_166 @ B_105 )
% 0.24/0.46 = ( semila1562558655_com_o
% 0.24/0.46 @ ( collect_com
% 0.24/0.46 @ ^ [X_3: com] : ( X_3 = A_166 ) )
% 0.24/0.46 @ B_105 ) ) ).
% 0.24/0.46
% 0.24/0.46 thf(fact_458_insert__def,axiom,
% 0.24/0.46 ! [A_166: pname > $o,B_105: ( pname > $o ) > $o] :
% 0.24/0.47 ( ( insert_pname_o @ A_166 @ B_105 )
% 0.24/0.47 = ( semila181081674me_o_o
% 0.24/0.47 @ ( collect_pname_o
% 0.24/0.47 @ ^ [X_3: pname > $o] : ( X_3 = A_166 ) )
% 0.24/0.47 @ B_105 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_459_insert__def,axiom,
% 0.24/0.47 ! [A_166: hoare_1708887482_state > $o,B_105: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.47 ( ( insert949073679tate_o @ A_166 @ B_105 )
% 0.24/0.47 = ( semila1853742644te_o_o
% 0.24/0.47 @ ( collec219771562tate_o
% 0.24/0.47 @ ^ [X_3: hoare_1708887482_state > $o] : ( X_3 = A_166 ) )
% 0.24/0.47 @ B_105 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_460_insert__def,axiom,
% 0.24/0.47 ! [A_166: hoare_1708887482_state,B_105: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( insert528405184_state @ A_166 @ B_105 )
% 0.24/0.47 = ( semila1122118281tate_o
% 0.24/0.47 @ ( collec1568722789_state
% 0.24/0.47 @ ^ [X_3: hoare_1708887482_state] : ( X_3 = A_166 ) )
% 0.24/0.47 @ B_105 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_461_insert__is__Un,axiom,
% 0.24/0.47 ! [A_165: pname,A_164: pname > $o] :
% 0.24/0.47 ( ( insert_pname @ A_165 @ A_164 )
% 0.24/0.47 = ( semila1780557381name_o @ ( insert_pname @ A_165 @ bot_bot_pname_o ) @ A_164 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_462_insert__is__Un,axiom,
% 0.24/0.47 ! [A_165: com,A_164: com > $o] :
% 0.24/0.47 ( ( insert_com @ A_165 @ A_164 )
% 0.24/0.47 = ( semila1562558655_com_o @ ( insert_com @ A_165 @ bot_bot_com_o ) @ A_164 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_463_insert__is__Un,axiom,
% 0.24/0.47 ! [A_165: hoare_1708887482_state,A_164: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( insert528405184_state @ A_165 @ A_164 )
% 0.24/0.47 = ( semila1122118281tate_o @ ( insert528405184_state @ A_165 @ bot_bo19817387tate_o ) @ A_164 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_464_hoare__derivs_OBody,axiom,
% 0.24/0.47 ! [G_27: hoare_1708887482_state > $o,P_30: pname > state > state > $o,Q_21: pname > state > state > $o,Procs_2: pname > $o] :
% 0.24/0.47 ( ( hoare_90032982_state
% 0.24/0.47 @ ( semila1122118281tate_o @ G_27
% 0.24/0.47 @ ( image_1116629049_state
% 0.24/0.47 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_30 @ P_27 ) @ ( body_1 @ P_27 ) @ ( Q_21 @ P_27 ) )
% 0.24/0.47 @ Procs_2 ) )
% 0.24/0.47 @ ( image_1116629049_state
% 0.24/0.47 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_30 @ P_27 ) @ ( the_com @ ( body @ P_27 ) ) @ ( Q_21 @ P_27 ) )
% 0.24/0.47 @ Procs_2 ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_27
% 0.24/0.47 @ ( image_1116629049_state
% 0.24/0.47 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_30 @ P_27 ) @ ( body_1 @ P_27 ) @ ( Q_21 @ P_27 ) )
% 0.24/0.47 @ Procs_2 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_465_xt1_I6_J,axiom,
% 0.24/0.47 ! [Z_20: pname > $o,Y_50: pname > $o,X_99: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ Y_50 @ X_99 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ Z_20 @ Y_50 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ Z_20 @ X_99 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_466_xt1_I6_J,axiom,
% 0.24/0.47 ! [Z_20: $o,Y_50: $o,X_99: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ Y_50 @ X_99 )
% 0.24/0.47 => ( ( ord_less_eq_o @ Z_20 @ Y_50 )
% 0.24/0.47 => ( ord_less_eq_o @ Z_20 @ X_99 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_467_xt1_I6_J,axiom,
% 0.24/0.47 ! [Z_20: hoare_1708887482_state > $o,Y_50: hoare_1708887482_state > $o,X_99: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ Y_50 @ X_99 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ Z_20 @ Y_50 )
% 0.24/0.47 => ( ord_le777019615tate_o @ Z_20 @ X_99 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_468_xt1_I5_J,axiom,
% 0.24/0.47 ! [Y_49: pname > $o,X_98: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ Y_49 @ X_98 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ X_98 @ Y_49 )
% 0.24/0.47 => ( X_98 = Y_49 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_469_xt1_I5_J,axiom,
% 0.24/0.47 ! [Y_49: $o,X_98: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ Y_49 @ X_98 )
% 0.24/0.47 => ( ( ord_less_eq_o @ X_98 @ Y_49 )
% 0.24/0.47 => ( X_98
% 0.24/0.47 <=> Y_49 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_470_xt1_I5_J,axiom,
% 0.24/0.47 ! [Y_49: hoare_1708887482_state > $o,X_98: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ Y_49 @ X_98 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ X_98 @ Y_49 )
% 0.24/0.47 => ( X_98 = Y_49 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_471_order__trans,axiom,
% 0.24/0.47 ! [Z_19: pname > $o,X_97: pname > $o,Y_48: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_97 @ Y_48 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ Y_48 @ Z_19 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ X_97 @ Z_19 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_472_order__trans,axiom,
% 0.24/0.47 ! [Z_19: $o,X_97: $o,Y_48: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_97 @ Y_48 )
% 0.24/0.47 => ( ( ord_less_eq_o @ Y_48 @ Z_19 )
% 0.24/0.47 => ( ord_less_eq_o @ X_97 @ Z_19 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_473_order__trans,axiom,
% 0.24/0.47 ! [Z_19: hoare_1708887482_state > $o,X_97: hoare_1708887482_state > $o,Y_48: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_97 @ Y_48 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ Y_48 @ Z_19 )
% 0.24/0.47 => ( ord_le777019615tate_o @ X_97 @ Z_19 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_474_order__antisym,axiom,
% 0.24/0.47 ! [X_96: pname > $o,Y_47: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_96 @ Y_47 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ Y_47 @ X_96 )
% 0.24/0.47 => ( X_96 = Y_47 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_475_order__antisym,axiom,
% 0.24/0.47 ! [X_96: $o,Y_47: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_96 @ Y_47 )
% 0.24/0.47 => ( ( ord_less_eq_o @ Y_47 @ X_96 )
% 0.24/0.47 => ( X_96
% 0.24/0.47 <=> Y_47 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_476_order__antisym,axiom,
% 0.24/0.47 ! [X_96: hoare_1708887482_state > $o,Y_47: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_96 @ Y_47 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ Y_47 @ X_96 )
% 0.24/0.47 => ( X_96 = Y_47 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_477_xt1_I4_J,axiom,
% 0.24/0.47 ! [C_50: pname > $o,B_104: pname > $o,A_163: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ B_104 @ A_163 )
% 0.24/0.47 => ( ( B_104 = C_50 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ C_50 @ A_163 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_478_xt1_I4_J,axiom,
% 0.24/0.47 ! [C_50: $o,B_104: $o,A_163: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ B_104 @ A_163 )
% 0.24/0.47 => ( ( B_104
% 0.24/0.47 <=> C_50 )
% 0.24/0.47 => ( ord_less_eq_o @ C_50 @ A_163 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_479_xt1_I4_J,axiom,
% 0.24/0.47 ! [C_50: hoare_1708887482_state > $o,B_104: hoare_1708887482_state > $o,A_163: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ B_104 @ A_163 )
% 0.24/0.47 => ( ( B_104 = C_50 )
% 0.24/0.47 => ( ord_le777019615tate_o @ C_50 @ A_163 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_480_ord__le__eq__trans,axiom,
% 0.24/0.47 ! [C_49: pname > $o,A_162: pname > $o,B_103: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ A_162 @ B_103 )
% 0.24/0.47 => ( ( B_103 = C_49 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ A_162 @ C_49 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_481_ord__le__eq__trans,axiom,
% 0.24/0.47 ! [C_49: $o,A_162: $o,B_103: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ A_162 @ B_103 )
% 0.24/0.47 => ( ( B_103
% 0.24/0.47 <=> C_49 )
% 0.24/0.47 => ( ord_less_eq_o @ A_162 @ C_49 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_482_ord__le__eq__trans,axiom,
% 0.24/0.47 ! [C_49: hoare_1708887482_state > $o,A_162: hoare_1708887482_state > $o,B_103: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ A_162 @ B_103 )
% 0.24/0.47 => ( ( B_103 = C_49 )
% 0.24/0.47 => ( ord_le777019615tate_o @ A_162 @ C_49 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_483_xt1_I3_J,axiom,
% 0.24/0.47 ! [C_48: pname > $o,A_161: pname > $o,B_102: pname > $o] :
% 0.24/0.47 ( ( A_161 = B_102 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ C_48 @ B_102 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ C_48 @ A_161 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_484_xt1_I3_J,axiom,
% 0.24/0.47 ! [C_48: $o,B_102: $o,A_161: $o] :
% 0.24/0.47 ( ( A_161
% 0.24/0.47 <=> B_102 )
% 0.24/0.47 => ( ( ord_less_eq_o @ C_48 @ B_102 )
% 0.24/0.47 => ( ord_less_eq_o @ C_48 @ A_161 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_485_xt1_I3_J,axiom,
% 0.24/0.47 ! [C_48: hoare_1708887482_state > $o,A_161: hoare_1708887482_state > $o,B_102: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( A_161 = B_102 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ C_48 @ B_102 )
% 0.24/0.47 => ( ord_le777019615tate_o @ C_48 @ A_161 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_486_ord__eq__le__trans,axiom,
% 0.24/0.47 ! [C_47: pname > $o,A_160: pname > $o,B_101: pname > $o] :
% 0.24/0.47 ( ( A_160 = B_101 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ B_101 @ C_47 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ A_160 @ C_47 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_487_ord__eq__le__trans,axiom,
% 0.24/0.47 ! [C_47: $o,B_101: $o,A_160: $o] :
% 0.24/0.47 ( ( A_160
% 0.24/0.47 <=> B_101 )
% 0.24/0.47 => ( ( ord_less_eq_o @ B_101 @ C_47 )
% 0.24/0.47 => ( ord_less_eq_o @ A_160 @ C_47 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_488_ord__eq__le__trans,axiom,
% 0.24/0.47 ! [C_47: hoare_1708887482_state > $o,A_160: hoare_1708887482_state > $o,B_101: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( A_160 = B_101 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ B_101 @ C_47 )
% 0.24/0.47 => ( ord_le777019615tate_o @ A_160 @ C_47 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_489_order__antisym__conv,axiom,
% 0.24/0.47 ! [Y_46: pname > $o,X_95: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ Y_46 @ X_95 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ X_95 @ Y_46 )
% 0.24/0.47 <=> ( X_95 = Y_46 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_490_order__antisym__conv,axiom,
% 0.24/0.47 ! [Y_46: $o,X_95: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ Y_46 @ X_95 )
% 0.24/0.47 => ( ( ord_less_eq_o @ X_95 @ Y_46 )
% 0.24/0.47 <=> ( X_95
% 0.24/0.47 <=> Y_46 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_491_order__antisym__conv,axiom,
% 0.24/0.47 ! [Y_46: hoare_1708887482_state > $o,X_95: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ Y_46 @ X_95 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ X_95 @ Y_46 )
% 0.24/0.47 <=> ( X_95 = Y_46 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_492_order__eq__refl,axiom,
% 0.24/0.47 ! [X_94: pname > $o,Y_45: pname > $o] :
% 0.24/0.47 ( ( X_94 = Y_45 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ X_94 @ Y_45 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_493_order__eq__refl,axiom,
% 0.24/0.47 ! [Y_45: $o,X_94: $o] :
% 0.24/0.47 ( ( X_94
% 0.24/0.47 <=> Y_45 )
% 0.24/0.47 => ( ord_less_eq_o @ X_94 @ Y_45 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_494_order__eq__refl,axiom,
% 0.24/0.47 ! [X_94: hoare_1708887482_state > $o,Y_45: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( X_94 = Y_45 )
% 0.24/0.47 => ( ord_le777019615tate_o @ X_94 @ Y_45 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_495_order__eq__iff,axiom,
% 0.24/0.47 ! [X_93: pname > $o,Y_44: pname > $o] :
% 0.24/0.47 ( ( X_93 = Y_44 )
% 0.24/0.47 <=> ( ( ord_less_eq_pname_o @ X_93 @ Y_44 )
% 0.24/0.47 & ( ord_less_eq_pname_o @ Y_44 @ X_93 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_496_order__eq__iff,axiom,
% 0.24/0.47 ! [Y_44: $o,X_93: $o] :
% 0.24/0.47 ( ( X_93
% 0.24/0.47 <=> Y_44 )
% 0.24/0.47 <=> ( ( ord_less_eq_o @ X_93 @ Y_44 )
% 0.24/0.47 & ( ord_less_eq_o @ Y_44 @ X_93 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_497_order__eq__iff,axiom,
% 0.24/0.47 ! [X_93: hoare_1708887482_state > $o,Y_44: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( X_93 = Y_44 )
% 0.24/0.47 <=> ( ( ord_le777019615tate_o @ X_93 @ Y_44 )
% 0.24/0.47 & ( ord_le777019615tate_o @ Y_44 @ X_93 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_498_option_Oinject,axiom,
% 0.24/0.47 ! [A_159: pname,A_158: pname] :
% 0.24/0.47 ( ( ( some_pname @ A_159 )
% 0.24/0.47 = ( some_pname @ A_158 ) )
% 0.24/0.47 <=> ( A_159 = A_158 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_499_option_Oinject,axiom,
% 0.24/0.47 ! [A_159: hoare_1708887482_state,A_158: hoare_1708887482_state] :
% 0.24/0.47 ( ( ( some_H1974565227_state @ A_159 )
% 0.24/0.47 = ( some_H1974565227_state @ A_158 ) )
% 0.24/0.47 <=> ( A_159 = A_158 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_500_option_Oinject,axiom,
% 0.24/0.47 ! [A_159: com,A_158: com] :
% 0.24/0.47 ( ( ( some_com @ A_159 )
% 0.24/0.47 = ( some_com @ A_158 ) )
% 0.24/0.47 <=> ( A_159 = A_158 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_501_constant,axiom,
% 0.24/0.47 ! [G_26: hoare_1708887482_state > $o,P_29: state > state > $o,C_46: com,Q_20: state > state > $o,C_45: $o] :
% 0.24/0.47 ( ( C_45
% 0.24/0.47 => ( hoare_90032982_state @ G_26 @ ( insert528405184_state @ ( hoare_858012674_state @ P_29 @ C_46 @ Q_20 ) @ bot_bo19817387tate_o ) ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_26
% 0.24/0.47 @ ( insert528405184_state
% 0.24/0.47 @ ( hoare_858012674_state
% 0.24/0.47 @ ^ [Z_11: state,S_2: state] : ( (&) @ ( P_29 @ Z_11 @ S_2 ) @ C_45 )
% 0.24/0.47 @ C_46
% 0.24/0.47 @ Q_20 )
% 0.24/0.47 @ bot_bo19817387tate_o ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_502_Body1,axiom,
% 0.24/0.47 ! [Pn_2: pname,G_25: hoare_1708887482_state > $o,P_28: pname > state > state > $o,Q_19: pname > state > state > $o,Procs_1: pname > $o] :
% 0.24/0.47 ( ( hoare_90032982_state
% 0.24/0.47 @ ( semila1122118281tate_o @ G_25
% 0.24/0.47 @ ( image_1116629049_state
% 0.24/0.47 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_28 @ P_27 ) @ ( body_1 @ P_27 ) @ ( Q_19 @ P_27 ) )
% 0.24/0.47 @ Procs_1 ) )
% 0.24/0.47 @ ( image_1116629049_state
% 0.24/0.47 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_28 @ P_27 ) @ ( the_com @ ( body @ P_27 ) ) @ ( Q_19 @ P_27 ) )
% 0.24/0.47 @ Procs_1 ) )
% 0.24/0.47 => ( ( member_pname @ Pn_2 @ Procs_1 )
% 0.24/0.47 => ( hoare_90032982_state @ G_25 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_28 @ Pn_2 ) @ ( body_1 @ Pn_2 ) @ ( Q_19 @ Pn_2 ) ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_503_le__bot,axiom,
% 0.24/0.47 ! [A_157: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ A_157 @ bot_bot_pname_o )
% 0.24/0.47 => ( A_157 = bot_bot_pname_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_504_le__bot,axiom,
% 0.24/0.47 ! [A_157: com > $o] :
% 0.24/0.47 ( ( ord_less_eq_com_o @ A_157 @ bot_bot_com_o )
% 0.24/0.47 => ( A_157 = bot_bot_com_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_505_le__bot,axiom,
% 0.24/0.47 ! [A_157: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ A_157 @ bot_bot_o )
% 0.24/0.47 => ( A_157
% 0.24/0.47 <=> bot_bot_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_506_le__bot,axiom,
% 0.24/0.47 ! [A_157: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ A_157 @ bot_bo19817387tate_o )
% 0.24/0.47 => ( A_157 = bot_bo19817387tate_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_507_bot__unique,axiom,
% 0.24/0.47 ! [A_156: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ A_156 @ bot_bot_pname_o )
% 0.24/0.47 <=> ( A_156 = bot_bot_pname_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_508_bot__unique,axiom,
% 0.24/0.47 ! [A_156: com > $o] :
% 0.24/0.47 ( ( ord_less_eq_com_o @ A_156 @ bot_bot_com_o )
% 0.24/0.47 <=> ( A_156 = bot_bot_com_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_509_bot__unique,axiom,
% 0.24/0.47 ! [A_156: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ A_156 @ bot_bot_o )
% 0.24/0.47 <=> ( A_156
% 0.24/0.47 <=> bot_bot_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_510_bot__unique,axiom,
% 0.24/0.47 ! [A_156: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ A_156 @ bot_bo19817387tate_o )
% 0.24/0.47 <=> ( A_156 = bot_bo19817387tate_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_511_bot__least,axiom,
% 0.24/0.47 ! [A_155: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_155 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_512_bot__least,axiom,
% 0.24/0.47 ! [A_155: com > $o] : ( ord_less_eq_com_o @ bot_bot_com_o @ A_155 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_513_bot__least,axiom,
% 0.24/0.47 ! [A_155: $o] : ( ord_less_eq_o @ bot_bot_o @ A_155 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_514_bot__least,axiom,
% 0.24/0.47 ! [A_155: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ bot_bo19817387tate_o @ A_155 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_515_le__funE,axiom,
% 0.24/0.47 ! [X_92: pname,F_65: pname > $o,G_24: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ F_65 @ G_24 )
% 0.24/0.47 => ( ord_less_eq_o @ ( F_65 @ X_92 ) @ ( G_24 @ X_92 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_516_le__funE,axiom,
% 0.24/0.47 ! [X_92: hoare_1708887482_state,F_65: hoare_1708887482_state > $o,G_24: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ F_65 @ G_24 )
% 0.24/0.47 => ( ord_less_eq_o @ ( F_65 @ X_92 ) @ ( G_24 @ X_92 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_517_le__funD,axiom,
% 0.24/0.47 ! [X_91: pname,F_64: pname > $o,G_23: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ F_64 @ G_23 )
% 0.24/0.47 => ( ord_less_eq_o @ ( F_64 @ X_91 ) @ ( G_23 @ X_91 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_518_le__funD,axiom,
% 0.24/0.47 ! [X_91: hoare_1708887482_state,F_64: hoare_1708887482_state > $o,G_23: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ F_64 @ G_23 )
% 0.24/0.47 => ( ord_less_eq_o @ ( F_64 @ X_91 ) @ ( G_23 @ X_91 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_519_le__fun__def,axiom,
% 0.24/0.47 ! [F_63: pname > $o,G_22: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ F_63 @ G_22 )
% 0.24/0.47 <=> ! [X_3: pname] : ( ord_less_eq_o @ ( F_63 @ X_3 ) @ ( G_22 @ X_3 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_520_le__fun__def,axiom,
% 0.24/0.47 ! [F_63: hoare_1708887482_state > $o,G_22: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ F_63 @ G_22 )
% 0.24/0.47 <=> ! [X_3: hoare_1708887482_state] : ( ord_less_eq_o @ ( F_63 @ X_3 ) @ ( G_22 @ X_3 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_521_bot__apply,axiom,
% 0.24/0.47 ! [X_90: pname] :
% 0.24/0.47 ( ( bot_bot_pname_o @ X_90 )
% 0.24/0.47 <=> bot_bot_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_522_bot__apply,axiom,
% 0.24/0.47 ! [X_90: com] :
% 0.24/0.47 ( ( bot_bot_com_o @ X_90 )
% 0.24/0.47 <=> bot_bot_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_523_bot__apply,axiom,
% 0.24/0.47 ! [X_90: hoare_1708887482_state] :
% 0.24/0.47 ( ( bot_bo19817387tate_o @ X_90 )
% 0.24/0.47 <=> bot_bot_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_524_bot__fun__def,axiom,
% 0.24/0.47 ! [X_3: pname] :
% 0.24/0.47 ( ( bot_bot_pname_o @ X_3 )
% 0.24/0.47 <=> bot_bot_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_525_bot__fun__def,axiom,
% 0.24/0.47 ! [X_3: com] :
% 0.24/0.47 ( ( bot_bot_com_o @ X_3 )
% 0.24/0.47 <=> bot_bot_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_526_bot__fun__def,axiom,
% 0.24/0.47 ! [X_3: hoare_1708887482_state] :
% 0.24/0.47 ( ( bot_bo19817387tate_o @ X_3 )
% 0.24/0.47 <=> bot_bot_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_527_finite__pointwise,axiom,
% 0.24/0.47 ! [P_26: ( pname > $o ) > state > state > $o,Q_18: ( pname > $o ) > state > state > $o,G_21: hoare_1708887482_state > $o,P_25: ( pname > $o ) > state > state > $o,C0_1: ( pname > $o ) > com,Q_17: ( pname > $o ) > state > state > $o,U_1: ( pname > $o ) > $o] :
% 0.24/0.47 ( ( finite297249702name_o @ U_1 )
% 0.24/0.47 => ( ! [P_27: pname > $o] :
% 0.24/0.47 ( ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) ) @ bot_bo19817387tate_o ) ) )
% 0.24/0.47 => ( ( hoare_90032982_state @ G_21
% 0.24/0.47 @ ( image_1922967206_state
% 0.24/0.47 @ ^ [P_27: pname > $o] : ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) )
% 0.24/0.47 @ U_1 ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_21
% 0.24/0.47 @ ( image_1922967206_state
% 0.24/0.47 @ ^ [P_27: pname > $o] : ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) )
% 0.24/0.47 @ U_1 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_528_finite__pointwise,axiom,
% 0.24/0.47 ! [P_26: ( hoare_1708887482_state > $o ) > state > state > $o,Q_18: ( hoare_1708887482_state > $o ) > state > state > $o,G_21: hoare_1708887482_state > $o,P_25: ( hoare_1708887482_state > $o ) > state > state > $o,C0_1: ( hoare_1708887482_state > $o ) > com,Q_17: ( hoare_1708887482_state > $o ) > state > state > $o,U_1: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.47 ( ( finite1329924456tate_o @ U_1 )
% 0.24/0.47 => ( ! [P_27: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) ) @ bot_bo19817387tate_o ) ) )
% 0.24/0.47 => ( ( hoare_90032982_state @ G_21
% 0.24/0.47 @ ( image_27005066_state
% 0.24/0.47 @ ^ [P_27: hoare_1708887482_state > $o] : ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) )
% 0.24/0.47 @ U_1 ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_21
% 0.24/0.47 @ ( image_27005066_state
% 0.24/0.47 @ ^ [P_27: hoare_1708887482_state > $o] : ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) )
% 0.24/0.47 @ U_1 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_529_finite__pointwise,axiom,
% 0.24/0.47 ! [P_26: pname > state > state > $o,Q_18: pname > state > state > $o,G_21: hoare_1708887482_state > $o,P_25: pname > state > state > $o,C0_1: pname > com,Q_17: pname > state > state > $o,U_1: pname > $o] :
% 0.24/0.47 ( ( finite_finite_pname @ U_1 )
% 0.24/0.47 => ( ! [P_27: pname] :
% 0.24/0.47 ( ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) ) @ bot_bo19817387tate_o ) ) )
% 0.24/0.47 => ( ( hoare_90032982_state @ G_21
% 0.24/0.47 @ ( image_1116629049_state
% 0.24/0.47 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) )
% 0.24/0.47 @ U_1 ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_21
% 0.24/0.47 @ ( image_1116629049_state
% 0.24/0.47 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) )
% 0.24/0.47 @ U_1 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_530_escape,axiom,
% 0.24/0.47 ! [G_20: hoare_1708887482_state > $o,C_44: com,Q_16: state > state > $o,P_24: state > state > $o] :
% 0.24/0.47 ( ! [Z_11: state,S_2: state] :
% 0.24/0.47 ( ( P_24 @ Z_11 @ S_2 )
% 0.24/0.47 => ( hoare_90032982_state @ G_20
% 0.24/0.47 @ ( insert528405184_state
% 0.24/0.47 @ ( hoare_858012674_state
% 0.24/0.47 @ ^ [Za: state,S_3: state] : ( S_3 = S_2 )
% 0.24/0.47 @ C_44
% 0.24/0.47 @ ^ [Z_12: state] : ( Q_16 @ Z_11 ) )
% 0.24/0.47 @ bot_bo19817387tate_o ) ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_20 @ ( insert528405184_state @ ( hoare_858012674_state @ P_24 @ C_44 @ Q_16 ) @ bot_bo19817387tate_o ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_531_Body__sound__lemma,axiom,
% 0.24/0.47 ! [G_19: hoare_1708887482_state > $o,P_23: pname > state > state > $o,Q_15: pname > state > state > $o,Procs: pname > $o] :
% 0.24/0.47 ( ( hoare_496444244_state
% 0.24/0.47 @ ( semila1122118281tate_o @ G_19
% 0.24/0.47 @ ( image_1116629049_state
% 0.24/0.47 @ ^ [Pn: pname] : ( hoare_858012674_state @ ( P_23 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_15 @ Pn ) )
% 0.24/0.47 @ Procs ) )
% 0.24/0.47 @ ( image_1116629049_state
% 0.24/0.47 @ ^ [Pn: pname] : ( hoare_858012674_state @ ( P_23 @ Pn ) @ ( the_com @ ( body @ Pn ) ) @ ( Q_15 @ Pn ) )
% 0.24/0.47 @ Procs ) )
% 0.24/0.47 => ( hoare_496444244_state @ G_19
% 0.24/0.47 @ ( image_1116629049_state
% 0.24/0.47 @ ^ [Pn: pname] : ( hoare_858012674_state @ ( P_23 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_15 @ Pn ) )
% 0.24/0.47 @ Procs ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_532_conseq1,axiom,
% 0.24/0.47 ! [P_22: state > state > $o,G_18: hoare_1708887482_state > $o,P_21: state > state > $o,C_43: com,Q_14: state > state > $o] :
% 0.24/0.47 ( ( hoare_90032982_state @ G_18 @ ( insert528405184_state @ ( hoare_858012674_state @ P_21 @ C_43 @ Q_14 ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( ! [Z_11: state,S_2: state] :
% 0.24/0.47 ( ( P_22 @ Z_11 @ S_2 )
% 0.24/0.47 => ( P_21 @ Z_11 @ S_2 ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_18 @ ( insert528405184_state @ ( hoare_858012674_state @ P_22 @ C_43 @ Q_14 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_533_conseq2,axiom,
% 0.24/0.47 ! [Q_13: state > state > $o,G_17: hoare_1708887482_state > $o,P_20: state > state > $o,C_42: com,Q_12: state > state > $o] :
% 0.24/0.47 ( ( hoare_90032982_state @ G_17 @ ( insert528405184_state @ ( hoare_858012674_state @ P_20 @ C_42 @ Q_12 ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( ! [Z_11: state,S_2: state] :
% 0.24/0.47 ( ( Q_12 @ Z_11 @ S_2 )
% 0.24/0.47 => ( Q_13 @ Z_11 @ S_2 ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_17 @ ( insert528405184_state @ ( hoare_858012674_state @ P_20 @ C_42 @ Q_13 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_534_MGF__complete,axiom,
% 0.24/0.47 ! [P: state > state > $o,Q_11: state > state > $o,C_34: com] :
% 0.24/0.47 ( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( ( hoare_496444244_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_858012674_state @ P @ C_34 @ Q_11 ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_858012674_state @ P @ C_34 @ Q_11 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_535_sup1E,axiom,
% 0.24/0.47 ! [A_154: pname > $o,B_100: pname > $o,X_89: pname] :
% 0.24/0.47 ( ( semila1780557381name_o @ A_154 @ B_100 @ X_89 )
% 0.24/0.47 => ( ~ ( A_154 @ X_89 )
% 0.24/0.47 => ( B_100 @ X_89 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_536_sup1E,axiom,
% 0.24/0.47 ! [A_154: hoare_1708887482_state > $o,B_100: hoare_1708887482_state > $o,X_89: hoare_1708887482_state] :
% 0.24/0.47 ( ( semila1122118281tate_o @ A_154 @ B_100 @ X_89 )
% 0.24/0.47 => ( ~ ( A_154 @ X_89 )
% 0.24/0.47 => ( B_100 @ X_89 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_537_sup1CI,axiom,
% 0.24/0.47 ! [A_153: pname > $o,B_99: pname > $o,X_88: pname] :
% 0.24/0.47 ( ( ~ ( B_99 @ X_88 )
% 0.24/0.47 => ( A_153 @ X_88 ) )
% 0.24/0.47 => ( semila1780557381name_o @ A_153 @ B_99 @ X_88 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_538_sup1CI,axiom,
% 0.24/0.47 ! [A_153: hoare_1708887482_state > $o,B_99: hoare_1708887482_state > $o,X_88: hoare_1708887482_state] :
% 0.24/0.47 ( ( ~ ( B_99 @ X_88 )
% 0.24/0.47 => ( A_153 @ X_88 ) )
% 0.24/0.47 => ( semila1122118281tate_o @ A_153 @ B_99 @ X_88 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_539_conseq12,axiom,
% 0.24/0.47 ! [Q_10: state > state > $o,P_19: state > state > $o,G_16: hoare_1708887482_state > $o,P_18: state > state > $o,C_41: com,Q_9: state > state > $o] :
% 0.24/0.47 ( ( hoare_90032982_state @ G_16 @ ( insert528405184_state @ ( hoare_858012674_state @ P_18 @ C_41 @ Q_9 ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( ! [Z_11: state,S_2: state] :
% 0.24/0.47 ( ( P_19 @ Z_11 @ S_2 )
% 0.24/0.47 => ! [S_3: state] :
% 0.24/0.47 ( ! [Z_12: state] :
% 0.24/0.47 ( ( P_18 @ Z_12 @ S_2 )
% 0.24/0.47 => ( Q_9 @ Z_12 @ S_3 ) )
% 0.24/0.47 => ( Q_10 @ Z_11 @ S_3 ) ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_16 @ ( insert528405184_state @ ( hoare_858012674_state @ P_19 @ C_41 @ Q_10 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_540_hoare__sound,axiom,
% 0.24/0.47 ! [G_15: hoare_1708887482_state > $o,Ts: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( hoare_90032982_state @ G_15 @ Ts )
% 0.24/0.47 => ( hoare_496444244_state @ G_15 @ Ts ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_541_bot__empty__eq,axiom,
% 0.24/0.47 ! [X_3: com] :
% 0.24/0.47 ( ( bot_bot_com_o @ X_3 )
% 0.24/0.47 <=> ( member_com @ X_3 @ bot_bot_com_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_542_bot__empty__eq,axiom,
% 0.24/0.47 ! [X_3: hoare_1708887482_state] :
% 0.24/0.47 ( ( bot_bo19817387tate_o @ X_3 )
% 0.24/0.47 <=> ( member451959335_state @ X_3 @ bot_bo19817387tate_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_543_bot__empty__eq,axiom,
% 0.24/0.47 ! [X_3: pname] :
% 0.24/0.47 ( ( bot_bot_pname_o @ X_3 )
% 0.24/0.47 <=> ( member_pname @ X_3 @ bot_bot_pname_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_544_rev__predicate1D,axiom,
% 0.24/0.47 ! [Q_8: pname > $o,P_17: pname > $o,X_87: pname] :
% 0.24/0.47 ( ( P_17 @ X_87 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ P_17 @ Q_8 )
% 0.24/0.47 => ( Q_8 @ X_87 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_545_rev__predicate1D,axiom,
% 0.24/0.47 ! [Q_8: hoare_1708887482_state > $o,P_17: hoare_1708887482_state > $o,X_87: hoare_1708887482_state] :
% 0.24/0.47 ( ( P_17 @ X_87 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ P_17 @ Q_8 )
% 0.24/0.47 => ( Q_8 @ X_87 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_546_predicate1D,axiom,
% 0.24/0.47 ! [X_86: pname,P_16: pname > $o,Q_7: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ P_16 @ Q_7 )
% 0.24/0.47 => ( ( P_16 @ X_86 )
% 0.24/0.47 => ( Q_7 @ X_86 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_547_predicate1D,axiom,
% 0.24/0.47 ! [X_86: hoare_1708887482_state,P_16: hoare_1708887482_state > $o,Q_7: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ P_16 @ Q_7 )
% 0.24/0.47 => ( ( P_16 @ X_86 )
% 0.24/0.47 => ( Q_7 @ X_86 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_548_sup1I2,axiom,
% 0.24/0.47 ! [A_152: pname > $o,B_98: pname > $o,X_85: pname] :
% 0.24/0.47 ( ( B_98 @ X_85 )
% 0.24/0.47 => ( semila1780557381name_o @ A_152 @ B_98 @ X_85 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_549_sup1I2,axiom,
% 0.24/0.47 ! [A_152: hoare_1708887482_state > $o,B_98: hoare_1708887482_state > $o,X_85: hoare_1708887482_state] :
% 0.24/0.47 ( ( B_98 @ X_85 )
% 0.24/0.47 => ( semila1122118281tate_o @ A_152 @ B_98 @ X_85 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_550_sup1I1,axiom,
% 0.24/0.47 ! [B_97: pname > $o,A_151: pname > $o,X_84: pname] :
% 0.24/0.47 ( ( A_151 @ X_84 )
% 0.24/0.47 => ( semila1780557381name_o @ A_151 @ B_97 @ X_84 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_551_sup1I1,axiom,
% 0.24/0.47 ! [B_97: hoare_1708887482_state > $o,A_151: hoare_1708887482_state > $o,X_84: hoare_1708887482_state] :
% 0.24/0.47 ( ( A_151 @ X_84 )
% 0.24/0.47 => ( semila1122118281tate_o @ A_151 @ B_97 @ X_84 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_552_pred__subset__eq,axiom,
% 0.24/0.47 ! [R_3: com > $o,S_6: com > $o] :
% 0.24/0.47 ( ( ord_less_eq_com_o
% 0.24/0.47 @ ^ [X_3: com] : ( member_com @ X_3 @ R_3 )
% 0.24/0.47 @ ^ [X_3: com] : ( member_com @ X_3 @ S_6 ) )
% 0.24/0.47 <=> ( ord_less_eq_com_o @ R_3 @ S_6 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_553_pred__subset__eq,axiom,
% 0.24/0.47 ! [R_3: hoare_1708887482_state > $o,S_6: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o
% 0.24/0.47 @ ^ [X_3: hoare_1708887482_state] : ( member451959335_state @ X_3 @ R_3 )
% 0.24/0.47 @ ^ [X_3: hoare_1708887482_state] : ( member451959335_state @ X_3 @ S_6 ) )
% 0.24/0.47 <=> ( ord_le777019615tate_o @ R_3 @ S_6 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_554_pred__subset__eq,axiom,
% 0.24/0.47 ! [R_3: pname > $o,S_6: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o
% 0.24/0.47 @ ^ [X_3: pname] : ( member_pname @ X_3 @ R_3 )
% 0.24/0.47 @ ^ [X_3: pname] : ( member_pname @ X_3 @ S_6 ) )
% 0.24/0.47 <=> ( ord_less_eq_pname_o @ R_3 @ S_6 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_555_sup__Un__eq,axiom,
% 0.24/0.47 ! [R_2: com > $o,S_5: com > $o,X_3: com] :
% 0.24/0.47 ( ( semila1562558655_com_o
% 0.24/0.47 @ ^ [Y_4: com] : ( member_com @ Y_4 @ R_2 )
% 0.24/0.47 @ ^ [Y_4: com] : ( member_com @ Y_4 @ S_5 )
% 0.24/0.47 @ X_3 )
% 0.24/0.47 <=> ( member_com @ X_3 @ ( semila1562558655_com_o @ R_2 @ S_5 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_556_sup__Un__eq,axiom,
% 0.24/0.47 ! [R_2: hoare_1708887482_state > $o,S_5: hoare_1708887482_state > $o,X_3: hoare_1708887482_state] :
% 0.24/0.47 ( ( semila1122118281tate_o
% 0.24/0.47 @ ^ [Y_4: hoare_1708887482_state] : ( member451959335_state @ Y_4 @ R_2 )
% 0.24/0.47 @ ^ [Y_4: hoare_1708887482_state] : ( member451959335_state @ Y_4 @ S_5 )
% 0.24/0.47 @ X_3 )
% 0.24/0.47 <=> ( member451959335_state @ X_3 @ ( semila1122118281tate_o @ R_2 @ S_5 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_557_sup__Un__eq,axiom,
% 0.24/0.47 ! [R_2: pname > $o,S_5: pname > $o,X_3: pname] :
% 0.24/0.47 ( ( semila1780557381name_o
% 0.24/0.47 @ ^ [Y_4: pname] : ( member_pname @ Y_4 @ R_2 )
% 0.24/0.47 @ ^ [Y_4: pname] : ( member_pname @ Y_4 @ S_5 )
% 0.24/0.47 @ X_3 )
% 0.24/0.47 <=> ( member_pname @ X_3 @ ( semila1780557381name_o @ R_2 @ S_5 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_558_le__funI,axiom,
% 0.24/0.47 ! [F_62: pname > $o,G_14: pname > $o] :
% 0.24/0.47 ( ! [X_3: pname] : ( ord_less_eq_o @ ( F_62 @ X_3 ) @ ( G_14 @ X_3 ) )
% 0.24/0.47 => ( ord_less_eq_pname_o @ F_62 @ G_14 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_559_le__funI,axiom,
% 0.24/0.47 ! [F_62: hoare_1708887482_state > $o,G_14: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ! [X_3: hoare_1708887482_state] : ( ord_less_eq_o @ ( F_62 @ X_3 ) @ ( G_14 @ X_3 ) )
% 0.24/0.47 => ( ord_le777019615tate_o @ F_62 @ G_14 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_560_Option_Oset_Osimps_I2_J,axiom,
% 0.24/0.47 ! [X_83: pname] :
% 0.24/0.47 ( ( set_pname @ ( some_pname @ X_83 ) )
% 0.24/0.47 = ( insert_pname @ X_83 @ bot_bot_pname_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_561_Option_Oset_Osimps_I2_J,axiom,
% 0.24/0.47 ! [X_83: com] :
% 0.24/0.47 ( ( set_com @ ( some_com @ X_83 ) )
% 0.24/0.47 = ( insert_com @ X_83 @ bot_bot_com_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_562_Option_Oset_Osimps_I2_J,axiom,
% 0.24/0.47 ! [X_83: hoare_1708887482_state] :
% 0.24/0.47 ( ( set_Ho525251890_state @ ( some_H1974565227_state @ X_83 ) )
% 0.24/0.47 = ( insert528405184_state @ X_83 @ bot_bo19817387tate_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_563_sup__apply,axiom,
% 0.24/0.47 ! [F_61: pname > $o,G_13: pname > $o,X_82: pname] :
% 0.24/0.47 ( ( semila1780557381name_o @ F_61 @ G_13 @ X_82 )
% 0.24/0.47 <=> ( semila10642723_sup_o @ ( F_61 @ X_82 ) @ ( G_13 @ X_82 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_564_sup__apply,axiom,
% 0.24/0.47 ! [F_61: hoare_1708887482_state > $o,G_13: hoare_1708887482_state > $o,X_82: hoare_1708887482_state] :
% 0.24/0.47 ( ( semila1122118281tate_o @ F_61 @ G_13 @ X_82 )
% 0.24/0.47 <=> ( semila10642723_sup_o @ ( F_61 @ X_82 ) @ ( G_13 @ X_82 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_565_sup__fun__def,axiom,
% 0.24/0.47 ! [F_60: pname > $o,G_12: pname > $o,X_3: pname] :
% 0.24/0.47 ( ( semila1780557381name_o @ F_60 @ G_12 @ X_3 )
% 0.24/0.47 <=> ( semila10642723_sup_o @ ( F_60 @ X_3 ) @ ( G_12 @ X_3 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_566_sup__fun__def,axiom,
% 0.24/0.47 ! [F_60: hoare_1708887482_state > $o,G_12: hoare_1708887482_state > $o,X_3: hoare_1708887482_state] :
% 0.24/0.47 ( ( semila1122118281tate_o @ F_60 @ G_12 @ X_3 )
% 0.24/0.47 <=> ( semila10642723_sup_o @ ( F_60 @ X_3 ) @ ( G_12 @ X_3 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_567_single__stateE,axiom,
% 0.24/0.47 ( hoare_1160767572gleton
% 0.24/0.47 => ! [T_1: state] :
% 0.24/0.47 ~ ! [S_2: state] : ( S_2 = T_1 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_568_sup__eq__bot__iff,axiom,
% 0.24/0.47 ! [X_81: pname > $o,Y_43: pname > $o] :
% 0.24/0.47 ( ( ( semila1780557381name_o @ X_81 @ Y_43 )
% 0.24/0.47 = bot_bot_pname_o )
% 0.24/0.47 <=> ( ( X_81 = bot_bot_pname_o )
% 0.24/0.47 & ( Y_43 = bot_bot_pname_o ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_569_sup__eq__bot__iff,axiom,
% 0.24/0.47 ! [X_81: com > $o,Y_43: com > $o] :
% 0.24/0.47 ( ( ( semila1562558655_com_o @ X_81 @ Y_43 )
% 0.24/0.47 = bot_bot_com_o )
% 0.24/0.47 <=> ( ( X_81 = bot_bot_com_o )
% 0.24/0.47 & ( Y_43 = bot_bot_com_o ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_570_sup__eq__bot__iff,axiom,
% 0.24/0.47 ! [X_81: $o,Y_43: $o] :
% 0.24/0.47 ( ( ( semila10642723_sup_o @ X_81 @ Y_43 )
% 0.24/0.47 <=> bot_bot_o )
% 0.24/0.47 <=> ( ( X_81
% 0.24/0.47 <=> bot_bot_o )
% 0.24/0.47 & ( Y_43
% 0.24/0.47 <=> bot_bot_o ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_571_sup__eq__bot__iff,axiom,
% 0.24/0.47 ! [X_81: hoare_1708887482_state > $o,Y_43: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ( semila1122118281tate_o @ X_81 @ Y_43 )
% 0.24/0.47 = bot_bo19817387tate_o )
% 0.24/0.47 <=> ( ( X_81 = bot_bo19817387tate_o )
% 0.24/0.47 & ( Y_43 = bot_bo19817387tate_o ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_572_elem__set,axiom,
% 0.24/0.47 ! [X_80: com,Xo_1: option_com] :
% 0.24/0.47 ( ( member_com @ X_80 @ ( set_com @ Xo_1 ) )
% 0.24/0.47 <=> ( Xo_1
% 0.24/0.47 = ( some_com @ X_80 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_573_elem__set,axiom,
% 0.24/0.47 ! [X_80: hoare_1708887482_state,Xo_1: option1624383643_state] :
% 0.24/0.47 ( ( member451959335_state @ X_80 @ ( set_Ho525251890_state @ Xo_1 ) )
% 0.24/0.47 <=> ( Xo_1
% 0.24/0.47 = ( some_H1974565227_state @ X_80 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_574_elem__set,axiom,
% 0.24/0.47 ! [X_80: pname,Xo_1: option_pname] :
% 0.24/0.47 ( ( member_pname @ X_80 @ ( set_pname @ Xo_1 ) )
% 0.24/0.47 <=> ( Xo_1
% 0.24/0.47 = ( some_pname @ X_80 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_575_sup_Oidem,axiom,
% 0.24/0.47 ! [A_150: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ A_150 @ A_150 )
% 0.24/0.47 = A_150 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_576_sup_Oidem,axiom,
% 0.24/0.47 ! [A_150: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ A_150 @ A_150 )
% 0.24/0.47 <=> A_150 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_577_sup_Oidem,axiom,
% 0.24/0.47 ! [A_150: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ A_150 @ A_150 )
% 0.24/0.47 = A_150 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_578_sup__idem,axiom,
% 0.24/0.47 ! [X_79: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ X_79 @ X_79 )
% 0.24/0.47 = X_79 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_579_sup__idem,axiom,
% 0.24/0.47 ! [X_79: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ X_79 @ X_79 )
% 0.24/0.47 <=> X_79 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_580_sup__idem,axiom,
% 0.24/0.47 ! [X_79: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ X_79 @ X_79 )
% 0.24/0.47 = X_79 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_581_sup_Ocommute,axiom,
% 0.24/0.47 ! [A_149: pname > $o,B_96: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ A_149 @ B_96 )
% 0.24/0.47 = ( semila1780557381name_o @ B_96 @ A_149 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_582_sup_Ocommute,axiom,
% 0.24/0.47 ! [A_149: $o,B_96: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ A_149 @ B_96 )
% 0.24/0.47 <=> ( semila10642723_sup_o @ B_96 @ A_149 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_583_sup_Ocommute,axiom,
% 0.24/0.47 ! [A_149: hoare_1708887482_state > $o,B_96: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ A_149 @ B_96 )
% 0.24/0.47 = ( semila1122118281tate_o @ B_96 @ A_149 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_584_inf__sup__aci_I5_J,axiom,
% 0.24/0.47 ! [X_78: pname > $o,Y_42: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ X_78 @ Y_42 )
% 0.24/0.47 = ( semila1780557381name_o @ Y_42 @ X_78 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_585_inf__sup__aci_I5_J,axiom,
% 0.24/0.47 ! [X_78: $o,Y_42: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ X_78 @ Y_42 )
% 0.24/0.47 <=> ( semila10642723_sup_o @ Y_42 @ X_78 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_586_inf__sup__aci_I5_J,axiom,
% 0.24/0.47 ! [X_78: hoare_1708887482_state > $o,Y_42: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ X_78 @ Y_42 )
% 0.24/0.47 = ( semila1122118281tate_o @ Y_42 @ X_78 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_587_sup__commute,axiom,
% 0.24/0.47 ! [X_77: pname > $o,Y_41: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ X_77 @ Y_41 )
% 0.24/0.47 = ( semila1780557381name_o @ Y_41 @ X_77 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_588_sup__commute,axiom,
% 0.24/0.47 ! [X_77: $o,Y_41: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ X_77 @ Y_41 )
% 0.24/0.47 <=> ( semila10642723_sup_o @ Y_41 @ X_77 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_589_sup__commute,axiom,
% 0.24/0.47 ! [X_77: hoare_1708887482_state > $o,Y_41: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ X_77 @ Y_41 )
% 0.24/0.47 = ( semila1122118281tate_o @ Y_41 @ X_77 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_590_sup_Oleft__idem,axiom,
% 0.24/0.47 ! [A_148: pname > $o,B_95: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ A_148 @ ( semila1780557381name_o @ A_148 @ B_95 ) )
% 0.24/0.47 = ( semila1780557381name_o @ A_148 @ B_95 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_591_sup_Oleft__idem,axiom,
% 0.24/0.47 ! [A_148: $o,B_95: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ A_148 @ ( semila10642723_sup_o @ A_148 @ B_95 ) )
% 0.24/0.47 <=> ( semila10642723_sup_o @ A_148 @ B_95 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_592_sup_Oleft__idem,axiom,
% 0.24/0.47 ! [A_148: hoare_1708887482_state > $o,B_95: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ A_148 @ ( semila1122118281tate_o @ A_148 @ B_95 ) )
% 0.24/0.47 = ( semila1122118281tate_o @ A_148 @ B_95 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_593_inf__sup__aci_I8_J,axiom,
% 0.24/0.47 ! [X_76: pname > $o,Y_40: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ X_76 @ ( semila1780557381name_o @ X_76 @ Y_40 ) )
% 0.24/0.47 = ( semila1780557381name_o @ X_76 @ Y_40 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_594_inf__sup__aci_I8_J,axiom,
% 0.24/0.47 ! [X_76: $o,Y_40: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ X_76 @ ( semila10642723_sup_o @ X_76 @ Y_40 ) )
% 0.24/0.47 <=> ( semila10642723_sup_o @ X_76 @ Y_40 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_595_inf__sup__aci_I8_J,axiom,
% 0.24/0.47 ! [X_76: hoare_1708887482_state > $o,Y_40: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ X_76 @ ( semila1122118281tate_o @ X_76 @ Y_40 ) )
% 0.24/0.47 = ( semila1122118281tate_o @ X_76 @ Y_40 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_596_sup__left__idem,axiom,
% 0.24/0.47 ! [X_75: pname > $o,Y_39: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ X_75 @ ( semila1780557381name_o @ X_75 @ Y_39 ) )
% 0.24/0.47 = ( semila1780557381name_o @ X_75 @ Y_39 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_597_sup__left__idem,axiom,
% 0.24/0.47 ! [X_75: $o,Y_39: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ X_75 @ ( semila10642723_sup_o @ X_75 @ Y_39 ) )
% 0.24/0.47 <=> ( semila10642723_sup_o @ X_75 @ Y_39 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_598_sup__left__idem,axiom,
% 0.24/0.47 ! [X_75: hoare_1708887482_state > $o,Y_39: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ X_75 @ ( semila1122118281tate_o @ X_75 @ Y_39 ) )
% 0.24/0.47 = ( semila1122118281tate_o @ X_75 @ Y_39 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_599_sup_Oleft__commute,axiom,
% 0.24/0.47 ! [B_94: pname > $o,A_147: pname > $o,C_40: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ B_94 @ ( semila1780557381name_o @ A_147 @ C_40 ) )
% 0.24/0.47 = ( semila1780557381name_o @ A_147 @ ( semila1780557381name_o @ B_94 @ C_40 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_600_sup_Oleft__commute,axiom,
% 0.24/0.47 ! [B_94: $o,A_147: $o,C_40: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ B_94 @ ( semila10642723_sup_o @ A_147 @ C_40 ) )
% 0.24/0.47 <=> ( semila10642723_sup_o @ A_147 @ ( semila10642723_sup_o @ B_94 @ C_40 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_601_sup_Oleft__commute,axiom,
% 0.24/0.47 ! [B_94: hoare_1708887482_state > $o,A_147: hoare_1708887482_state > $o,C_40: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ B_94 @ ( semila1122118281tate_o @ A_147 @ C_40 ) )
% 0.24/0.47 = ( semila1122118281tate_o @ A_147 @ ( semila1122118281tate_o @ B_94 @ C_40 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_602_inf__sup__aci_I7_J,axiom,
% 0.24/0.47 ! [X_74: pname > $o,Y_38: pname > $o,Z_18: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ X_74 @ ( semila1780557381name_o @ Y_38 @ Z_18 ) )
% 0.24/0.47 = ( semila1780557381name_o @ Y_38 @ ( semila1780557381name_o @ X_74 @ Z_18 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_603_inf__sup__aci_I7_J,axiom,
% 0.24/0.47 ! [X_74: $o,Y_38: $o,Z_18: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ X_74 @ ( semila10642723_sup_o @ Y_38 @ Z_18 ) )
% 0.24/0.47 <=> ( semila10642723_sup_o @ Y_38 @ ( semila10642723_sup_o @ X_74 @ Z_18 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_604_inf__sup__aci_I7_J,axiom,
% 0.24/0.47 ! [X_74: hoare_1708887482_state > $o,Y_38: hoare_1708887482_state > $o,Z_18: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ X_74 @ ( semila1122118281tate_o @ Y_38 @ Z_18 ) )
% 0.24/0.47 = ( semila1122118281tate_o @ Y_38 @ ( semila1122118281tate_o @ X_74 @ Z_18 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_605_sup__left__commute,axiom,
% 0.24/0.47 ! [X_73: pname > $o,Y_37: pname > $o,Z_17: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ X_73 @ ( semila1780557381name_o @ Y_37 @ Z_17 ) )
% 0.24/0.47 = ( semila1780557381name_o @ Y_37 @ ( semila1780557381name_o @ X_73 @ Z_17 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_606_sup__left__commute,axiom,
% 0.24/0.47 ! [X_73: $o,Y_37: $o,Z_17: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ X_73 @ ( semila10642723_sup_o @ Y_37 @ Z_17 ) )
% 0.24/0.47 <=> ( semila10642723_sup_o @ Y_37 @ ( semila10642723_sup_o @ X_73 @ Z_17 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_607_sup__left__commute,axiom,
% 0.24/0.47 ! [X_73: hoare_1708887482_state > $o,Y_37: hoare_1708887482_state > $o,Z_17: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ X_73 @ ( semila1122118281tate_o @ Y_37 @ Z_17 ) )
% 0.24/0.47 = ( semila1122118281tate_o @ Y_37 @ ( semila1122118281tate_o @ X_73 @ Z_17 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_608_sup_Oassoc,axiom,
% 0.24/0.47 ! [A_146: pname > $o,B_93: pname > $o,C_39: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ ( semila1780557381name_o @ A_146 @ B_93 ) @ C_39 )
% 0.24/0.47 = ( semila1780557381name_o @ A_146 @ ( semila1780557381name_o @ B_93 @ C_39 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_609_sup_Oassoc,axiom,
% 0.24/0.47 ! [A_146: $o,B_93: $o,C_39: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ A_146 @ B_93 ) @ C_39 )
% 0.24/0.47 <=> ( semila10642723_sup_o @ A_146 @ ( semila10642723_sup_o @ B_93 @ C_39 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_610_sup_Oassoc,axiom,
% 0.24/0.47 ! [A_146: hoare_1708887482_state > $o,B_93: hoare_1708887482_state > $o,C_39: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A_146 @ B_93 ) @ C_39 )
% 0.24/0.47 = ( semila1122118281tate_o @ A_146 @ ( semila1122118281tate_o @ B_93 @ C_39 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_611_inf__sup__aci_I6_J,axiom,
% 0.24/0.47 ! [X_72: pname > $o,Y_36: pname > $o,Z_16: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ ( semila1780557381name_o @ X_72 @ Y_36 ) @ Z_16 )
% 0.24/0.47 = ( semila1780557381name_o @ X_72 @ ( semila1780557381name_o @ Y_36 @ Z_16 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_612_inf__sup__aci_I6_J,axiom,
% 0.24/0.47 ! [X_72: $o,Y_36: $o,Z_16: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ X_72 @ Y_36 ) @ Z_16 )
% 0.24/0.47 <=> ( semila10642723_sup_o @ X_72 @ ( semila10642723_sup_o @ Y_36 @ Z_16 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_613_inf__sup__aci_I6_J,axiom,
% 0.24/0.47 ! [X_72: hoare_1708887482_state > $o,Y_36: hoare_1708887482_state > $o,Z_16: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ X_72 @ Y_36 ) @ Z_16 )
% 0.24/0.47 = ( semila1122118281tate_o @ X_72 @ ( semila1122118281tate_o @ Y_36 @ Z_16 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_614_sup__assoc,axiom,
% 0.24/0.47 ! [X_71: pname > $o,Y_35: pname > $o,Z_15: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ ( semila1780557381name_o @ X_71 @ Y_35 ) @ Z_15 )
% 0.24/0.47 = ( semila1780557381name_o @ X_71 @ ( semila1780557381name_o @ Y_35 @ Z_15 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_615_sup__assoc,axiom,
% 0.24/0.47 ! [X_71: $o,Y_35: $o,Z_15: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ X_71 @ Y_35 ) @ Z_15 )
% 0.24/0.47 <=> ( semila10642723_sup_o @ X_71 @ ( semila10642723_sup_o @ Y_35 @ Z_15 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_616_sup__assoc,axiom,
% 0.24/0.47 ! [X_71: hoare_1708887482_state > $o,Y_35: hoare_1708887482_state > $o,Z_15: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ X_71 @ Y_35 ) @ Z_15 )
% 0.24/0.47 = ( semila1122118281tate_o @ X_71 @ ( semila1122118281tate_o @ Y_35 @ Z_15 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_617_inf__sup__ord_I3_J,axiom,
% 0.24/0.47 ! [X_70: pname > $o,Y_34: pname > $o] : ( ord_less_eq_pname_o @ X_70 @ ( semila1780557381name_o @ X_70 @ Y_34 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_618_inf__sup__ord_I3_J,axiom,
% 0.24/0.47 ! [X_70: $o,Y_34: $o] : ( ord_less_eq_o @ X_70 @ ( semila10642723_sup_o @ X_70 @ Y_34 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_619_inf__sup__ord_I3_J,axiom,
% 0.24/0.47 ! [X_70: hoare_1708887482_state > $o,Y_34: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ X_70 @ ( semila1122118281tate_o @ X_70 @ Y_34 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_620_sup__ge1,axiom,
% 0.24/0.47 ! [X_69: pname > $o,Y_33: pname > $o] : ( ord_less_eq_pname_o @ X_69 @ ( semila1780557381name_o @ X_69 @ Y_33 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_621_sup__ge1,axiom,
% 0.24/0.47 ! [X_69: $o,Y_33: $o] : ( ord_less_eq_o @ X_69 @ ( semila10642723_sup_o @ X_69 @ Y_33 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_622_sup__ge1,axiom,
% 0.24/0.47 ! [X_69: hoare_1708887482_state > $o,Y_33: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ X_69 @ ( semila1122118281tate_o @ X_69 @ Y_33 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_623_inf__sup__ord_I4_J,axiom,
% 0.24/0.47 ! [Y_32: pname > $o,X_68: pname > $o] : ( ord_less_eq_pname_o @ Y_32 @ ( semila1780557381name_o @ X_68 @ Y_32 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_624_inf__sup__ord_I4_J,axiom,
% 0.24/0.47 ! [Y_32: $o,X_68: $o] : ( ord_less_eq_o @ Y_32 @ ( semila10642723_sup_o @ X_68 @ Y_32 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_625_inf__sup__ord_I4_J,axiom,
% 0.24/0.47 ! [Y_32: hoare_1708887482_state > $o,X_68: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ Y_32 @ ( semila1122118281tate_o @ X_68 @ Y_32 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_626_sup__ge2,axiom,
% 0.24/0.47 ! [Y_31: pname > $o,X_67: pname > $o] : ( ord_less_eq_pname_o @ Y_31 @ ( semila1780557381name_o @ X_67 @ Y_31 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_627_sup__ge2,axiom,
% 0.24/0.47 ! [Y_31: $o,X_67: $o] : ( ord_less_eq_o @ Y_31 @ ( semila10642723_sup_o @ X_67 @ Y_31 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_628_sup__ge2,axiom,
% 0.24/0.47 ! [Y_31: hoare_1708887482_state > $o,X_67: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ Y_31 @ ( semila1122118281tate_o @ X_67 @ Y_31 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_629_le__iff__sup,axiom,
% 0.24/0.47 ! [X_66: pname > $o,Y_30: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_66 @ Y_30 )
% 0.24/0.47 <=> ( ( semila1780557381name_o @ X_66 @ Y_30 )
% 0.24/0.47 = Y_30 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_630_le__iff__sup,axiom,
% 0.24/0.47 ! [X_66: $o,Y_30: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_66 @ Y_30 )
% 0.24/0.47 <=> ( ( semila10642723_sup_o @ X_66 @ Y_30 )
% 0.24/0.47 <=> Y_30 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_631_le__iff__sup,axiom,
% 0.24/0.47 ! [X_66: hoare_1708887482_state > $o,Y_30: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_66 @ Y_30 )
% 0.24/0.47 <=> ( ( semila1122118281tate_o @ X_66 @ Y_30 )
% 0.24/0.47 = Y_30 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_632_le__sup__iff,axiom,
% 0.24/0.47 ! [X_65: pname > $o,Y_29: pname > $o,Z_14: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_65 @ Y_29 ) @ Z_14 )
% 0.24/0.47 <=> ( ( ord_less_eq_pname_o @ X_65 @ Z_14 )
% 0.24/0.47 & ( ord_less_eq_pname_o @ Y_29 @ Z_14 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_633_le__sup__iff,axiom,
% 0.24/0.47 ! [X_65: $o,Y_29: $o,Z_14: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ ( semila10642723_sup_o @ X_65 @ Y_29 ) @ Z_14 )
% 0.24/0.47 <=> ( ( ord_less_eq_o @ X_65 @ Z_14 )
% 0.24/0.47 & ( ord_less_eq_o @ Y_29 @ Z_14 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_634_le__sup__iff,axiom,
% 0.24/0.47 ! [X_65: hoare_1708887482_state > $o,Y_29: hoare_1708887482_state > $o,Z_14: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ ( semila1122118281tate_o @ X_65 @ Y_29 ) @ Z_14 )
% 0.24/0.47 <=> ( ( ord_le777019615tate_o @ X_65 @ Z_14 )
% 0.24/0.47 & ( ord_le777019615tate_o @ Y_29 @ Z_14 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_635_le__supI1,axiom,
% 0.24/0.47 ! [B_92: pname > $o,X_64: pname > $o,A_145: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_64 @ A_145 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ X_64 @ ( semila1780557381name_o @ A_145 @ B_92 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_636_le__supI1,axiom,
% 0.24/0.47 ! [B_92: $o,X_64: $o,A_145: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_64 @ A_145 )
% 0.24/0.47 => ( ord_less_eq_o @ X_64 @ ( semila10642723_sup_o @ A_145 @ B_92 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_637_le__supI1,axiom,
% 0.24/0.47 ! [B_92: hoare_1708887482_state > $o,X_64: hoare_1708887482_state > $o,A_145: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_64 @ A_145 )
% 0.24/0.47 => ( ord_le777019615tate_o @ X_64 @ ( semila1122118281tate_o @ A_145 @ B_92 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_638_le__supI2,axiom,
% 0.24/0.47 ! [A_144: pname > $o,X_63: pname > $o,B_91: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_63 @ B_91 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ X_63 @ ( semila1780557381name_o @ A_144 @ B_91 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_639_le__supI2,axiom,
% 0.24/0.47 ! [A_144: $o,X_63: $o,B_91: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_63 @ B_91 )
% 0.24/0.47 => ( ord_less_eq_o @ X_63 @ ( semila10642723_sup_o @ A_144 @ B_91 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_640_le__supI2,axiom,
% 0.24/0.47 ! [A_144: hoare_1708887482_state > $o,X_63: hoare_1708887482_state > $o,B_91: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_63 @ B_91 )
% 0.24/0.47 => ( ord_le777019615tate_o @ X_63 @ ( semila1122118281tate_o @ A_144 @ B_91 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_641_sup__absorb2,axiom,
% 0.24/0.47 ! [X_62: pname > $o,Y_28: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_62 @ Y_28 )
% 0.24/0.47 => ( ( semila1780557381name_o @ X_62 @ Y_28 )
% 0.24/0.47 = Y_28 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_642_sup__absorb2,axiom,
% 0.24/0.47 ! [X_62: $o,Y_28: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_62 @ Y_28 )
% 0.24/0.47 => ( ( semila10642723_sup_o @ X_62 @ Y_28 )
% 0.24/0.47 <=> Y_28 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_643_sup__absorb2,axiom,
% 0.24/0.47 ! [X_62: hoare_1708887482_state > $o,Y_28: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_62 @ Y_28 )
% 0.24/0.47 => ( ( semila1122118281tate_o @ X_62 @ Y_28 )
% 0.24/0.47 = Y_28 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_644_sup__absorb1,axiom,
% 0.24/0.47 ! [Y_27: pname > $o,X_61: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ Y_27 @ X_61 )
% 0.24/0.47 => ( ( semila1780557381name_o @ X_61 @ Y_27 )
% 0.24/0.47 = X_61 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_645_sup__absorb1,axiom,
% 0.24/0.47 ! [Y_27: $o,X_61: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ Y_27 @ X_61 )
% 0.24/0.47 => ( ( semila10642723_sup_o @ X_61 @ Y_27 )
% 0.24/0.47 <=> X_61 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_646_sup__absorb1,axiom,
% 0.24/0.47 ! [Y_27: hoare_1708887482_state > $o,X_61: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ Y_27 @ X_61 )
% 0.24/0.47 => ( ( semila1122118281tate_o @ X_61 @ Y_27 )
% 0.24/0.47 = X_61 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_647_le__supI,axiom,
% 0.24/0.47 ! [B_90: pname > $o,A_143: pname > $o,X_60: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ A_143 @ X_60 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ B_90 @ X_60 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_143 @ B_90 ) @ X_60 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_648_le__supI,axiom,
% 0.24/0.47 ! [B_90: $o,A_143: $o,X_60: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ A_143 @ X_60 )
% 0.24/0.47 => ( ( ord_less_eq_o @ B_90 @ X_60 )
% 0.24/0.47 => ( ord_less_eq_o @ ( semila10642723_sup_o @ A_143 @ B_90 ) @ X_60 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_649_le__supI,axiom,
% 0.24/0.47 ! [B_90: hoare_1708887482_state > $o,A_143: hoare_1708887482_state > $o,X_60: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ A_143 @ X_60 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ B_90 @ X_60 )
% 0.24/0.47 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_143 @ B_90 ) @ X_60 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_650_sup__least,axiom,
% 0.24/0.47 ! [Z_13: pname > $o,Y_26: pname > $o,X_59: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ Y_26 @ X_59 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ Z_13 @ X_59 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ Y_26 @ Z_13 ) @ X_59 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_651_sup__least,axiom,
% 0.24/0.47 ! [Z_13: $o,Y_26: $o,X_59: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ Y_26 @ X_59 )
% 0.24/0.47 => ( ( ord_less_eq_o @ Z_13 @ X_59 )
% 0.24/0.47 => ( ord_less_eq_o @ ( semila10642723_sup_o @ Y_26 @ Z_13 ) @ X_59 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_652_sup__least,axiom,
% 0.24/0.47 ! [Z_13: hoare_1708887482_state > $o,Y_26: hoare_1708887482_state > $o,X_59: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ Y_26 @ X_59 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ Z_13 @ X_59 )
% 0.24/0.47 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ Y_26 @ Z_13 ) @ X_59 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_653_sup__mono,axiom,
% 0.24/0.47 ! [B_89: pname > $o,D_4: pname > $o,A_142: pname > $o,C_38: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ A_142 @ C_38 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ B_89 @ D_4 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_142 @ B_89 ) @ ( semila1780557381name_o @ C_38 @ D_4 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_654_sup__mono,axiom,
% 0.24/0.47 ! [B_89: $o,D_4: $o,A_142: $o,C_38: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ A_142 @ C_38 )
% 0.24/0.47 => ( ( ord_less_eq_o @ B_89 @ D_4 )
% 0.24/0.47 => ( ord_less_eq_o @ ( semila10642723_sup_o @ A_142 @ B_89 ) @ ( semila10642723_sup_o @ C_38 @ D_4 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_655_sup__mono,axiom,
% 0.24/0.47 ! [B_89: hoare_1708887482_state > $o,D_4: hoare_1708887482_state > $o,A_142: hoare_1708887482_state > $o,C_38: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ A_142 @ C_38 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ B_89 @ D_4 )
% 0.24/0.47 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_142 @ B_89 ) @ ( semila1122118281tate_o @ C_38 @ D_4 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_656_le__supE,axiom,
% 0.24/0.47 ! [A_141: pname > $o,B_88: pname > $o,X_58: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_141 @ B_88 ) @ X_58 )
% 0.24/0.47 => ~ ( ( ord_less_eq_pname_o @ A_141 @ X_58 )
% 0.24/0.47 => ~ ( ord_less_eq_pname_o @ B_88 @ X_58 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_657_le__supE,axiom,
% 0.24/0.47 ! [A_141: $o,B_88: $o,X_58: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ ( semila10642723_sup_o @ A_141 @ B_88 ) @ X_58 )
% 0.24/0.47 => ~ ( ( ord_less_eq_o @ A_141 @ X_58 )
% 0.24/0.47 => ~ ( ord_less_eq_o @ B_88 @ X_58 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_658_le__supE,axiom,
% 0.24/0.47 ! [A_141: hoare_1708887482_state > $o,B_88: hoare_1708887482_state > $o,X_58: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_141 @ B_88 ) @ X_58 )
% 0.24/0.47 => ~ ( ( ord_le777019615tate_o @ A_141 @ X_58 )
% 0.24/0.47 => ~ ( ord_le777019615tate_o @ B_88 @ X_58 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_659_sup__bot__left,axiom,
% 0.24/0.47 ! [X_57: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ bot_bot_pname_o @ X_57 )
% 0.24/0.47 = X_57 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_660_sup__bot__left,axiom,
% 0.24/0.47 ! [X_57: com > $o] :
% 0.24/0.47 ( ( semila1562558655_com_o @ bot_bot_com_o @ X_57 )
% 0.24/0.47 = X_57 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_661_sup__bot__left,axiom,
% 0.24/0.47 ! [X_57: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ bot_bot_o @ X_57 )
% 0.24/0.47 <=> X_57 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_662_sup__bot__left,axiom,
% 0.24/0.47 ! [X_57: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ bot_bo19817387tate_o @ X_57 )
% 0.24/0.47 = X_57 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_663_sup__bot__right,axiom,
% 0.24/0.47 ! [X_56: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ X_56 @ bot_bot_pname_o )
% 0.24/0.47 = X_56 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_664_sup__bot__right,axiom,
% 0.24/0.47 ! [X_56: com > $o] :
% 0.24/0.47 ( ( semila1562558655_com_o @ X_56 @ bot_bot_com_o )
% 0.24/0.47 = X_56 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_665_sup__bot__right,axiom,
% 0.24/0.47 ! [X_56: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ X_56 @ bot_bot_o )
% 0.24/0.47 <=> X_56 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_666_sup__bot__right,axiom,
% 0.24/0.47 ! [X_56: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ X_56 @ bot_bo19817387tate_o )
% 0.24/0.47 = X_56 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_667_ospec,axiom,
% 0.24/0.47 ! [X_55: pname,P_15: pname > $o,A_140: option_pname] :
% 0.24/0.47 ( ! [X_3: pname] :
% 0.24/0.47 ( ( member_pname @ X_3 @ ( set_pname @ A_140 ) )
% 0.24/0.47 => ( P_15 @ X_3 ) )
% 0.24/0.47 => ( ( A_140
% 0.24/0.47 = ( some_pname @ X_55 ) )
% 0.24/0.47 => ( P_15 @ X_55 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_668_ospec,axiom,
% 0.24/0.47 ! [X_55: hoare_1708887482_state,P_15: hoare_1708887482_state > $o,A_140: option1624383643_state] :
% 0.24/0.47 ( ! [X_3: hoare_1708887482_state] :
% 0.24/0.47 ( ( member451959335_state @ X_3 @ ( set_Ho525251890_state @ A_140 ) )
% 0.24/0.47 => ( P_15 @ X_3 ) )
% 0.24/0.47 => ( ( A_140
% 0.24/0.47 = ( some_H1974565227_state @ X_55 ) )
% 0.24/0.47 => ( P_15 @ X_55 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_669_ospec,axiom,
% 0.24/0.47 ! [X_55: com,P_15: com > $o,A_140: option_com] :
% 0.24/0.47 ( ! [X_3: com] :
% 0.24/0.47 ( ( member_com @ X_3 @ ( set_com @ A_140 ) )
% 0.24/0.47 => ( P_15 @ X_3 ) )
% 0.24/0.47 => ( ( A_140
% 0.24/0.47 = ( some_com @ X_55 ) )
% 0.24/0.47 => ( P_15 @ X_55 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_670_folding__one__idem_Ounion__idem,axiom,
% 0.24/0.47 ! [B_87: ( pname > $o ) > $o,A_139: ( pname > $o ) > $o,F_59: ( pname > $o ) > ( pname > $o ) > pname > $o,F_58: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.47 ( ( finite697516351name_o @ F_59 @ F_58 )
% 0.24/0.47 => ( ( finite297249702name_o @ A_139 )
% 0.24/0.47 => ( ( A_139 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ( finite297249702name_o @ B_87 )
% 0.24/0.47 => ( ( B_87 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ( F_58 @ ( semila181081674me_o_o @ A_139 @ B_87 ) )
% 0.24/0.47 = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_671_folding__one__idem_Ounion__idem,axiom,
% 0.24/0.47 ! [B_87: ( hoare_1708887482_state > $o ) > $o,A_139: ( hoare_1708887482_state > $o ) > $o,F_59: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_58: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite621643279tate_o @ F_59 @ F_58 )
% 0.24/0.47 => ( ( finite1329924456tate_o @ A_139 )
% 0.24/0.47 => ( ( A_139 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( finite1329924456tate_o @ B_87 )
% 0.24/0.47 => ( ( B_87 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( F_58 @ ( semila1853742644te_o_o @ A_139 @ B_87 ) )
% 0.24/0.47 = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_672_folding__one__idem_Ounion__idem,axiom,
% 0.24/0.47 ! [B_87: com > $o,A_139: com > $o,F_59: com > com > com,F_58: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite666746948em_com @ F_59 @ F_58 )
% 0.24/0.47 => ( ( finite_finite_com @ A_139 )
% 0.24/0.47 => ( ( A_139 != bot_bot_com_o )
% 0.24/0.47 => ( ( finite_finite_com @ B_87 )
% 0.24/0.47 => ( ( B_87 != bot_bot_com_o )
% 0.24/0.47 => ( ( F_58 @ ( semila1562558655_com_o @ A_139 @ B_87 ) )
% 0.24/0.47 = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_673_folding__one__idem_Ounion__idem,axiom,
% 0.24/0.47 ! [B_87: hoare_1708887482_state > $o,A_139: hoare_1708887482_state > $o,F_59: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_58: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1347568576_state @ F_59 @ F_58 )
% 0.24/0.47 => ( ( finite1625599783_state @ A_139 )
% 0.24/0.47 => ( ( A_139 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ( finite1625599783_state @ B_87 )
% 0.24/0.47 => ( ( B_87 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ( F_58 @ ( semila1122118281tate_o @ A_139 @ B_87 ) )
% 0.24/0.47 = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_674_folding__one__idem_Ounion__idem,axiom,
% 0.24/0.47 ! [B_87: pname > $o,A_139: pname > $o,F_59: pname > pname > pname,F_58: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite89670078_pname @ F_59 @ F_58 )
% 0.24/0.47 => ( ( finite_finite_pname @ A_139 )
% 0.24/0.47 => ( ( A_139 != bot_bot_pname_o )
% 0.24/0.47 => ( ( finite_finite_pname @ B_87 )
% 0.24/0.47 => ( ( B_87 != bot_bot_pname_o )
% 0.24/0.47 => ( ( F_58 @ ( semila1780557381name_o @ A_139 @ B_87 ) )
% 0.24/0.47 = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_675_folding__one__idem_Osubset__idem,axiom,
% 0.24/0.47 ! [B_86: ( pname > $o ) > $o,A_138: ( pname > $o ) > $o,F_57: ( pname > $o ) > ( pname > $o ) > pname > $o,F_56: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.47 ( ( finite697516351name_o @ F_57 @ F_56 )
% 0.24/0.47 => ( ( finite297249702name_o @ A_138 )
% 0.24/0.47 => ( ( B_86 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ( ord_le1205211808me_o_o @ B_86 @ A_138 )
% 0.24/0.47 => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
% 0.24/0.47 = ( F_56 @ A_138 ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_676_folding__one__idem_Osubset__idem,axiom,
% 0.24/0.47 ! [B_86: ( hoare_1708887482_state > $o ) > $o,A_138: ( hoare_1708887482_state > $o ) > $o,F_57: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_56: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite621643279tate_o @ F_57 @ F_56 )
% 0.24/0.47 => ( ( finite1329924456tate_o @ A_138 )
% 0.24/0.47 => ( ( B_86 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( ord_le1728773982te_o_o @ B_86 @ A_138 )
% 0.24/0.47 => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
% 0.24/0.47 = ( F_56 @ A_138 ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_677_folding__one__idem_Osubset__idem,axiom,
% 0.24/0.47 ! [B_86: com > $o,A_138: com > $o,F_57: com > com > com,F_56: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite666746948em_com @ F_57 @ F_56 )
% 0.24/0.47 => ( ( finite_finite_com @ A_138 )
% 0.24/0.47 => ( ( B_86 != bot_bot_com_o )
% 0.24/0.47 => ( ( ord_less_eq_com_o @ B_86 @ A_138 )
% 0.24/0.47 => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
% 0.24/0.47 = ( F_56 @ A_138 ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_678_folding__one__idem_Osubset__idem,axiom,
% 0.24/0.47 ! [B_86: hoare_1708887482_state > $o,A_138: hoare_1708887482_state > $o,F_57: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_56: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1347568576_state @ F_57 @ F_56 )
% 0.24/0.47 => ( ( finite1625599783_state @ A_138 )
% 0.24/0.47 => ( ( B_86 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ B_86 @ A_138 )
% 0.24/0.47 => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
% 0.24/0.47 = ( F_56 @ A_138 ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_679_folding__one__idem_Osubset__idem,axiom,
% 0.24/0.47 ! [B_86: pname > $o,A_138: pname > $o,F_57: pname > pname > pname,F_56: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite89670078_pname @ F_57 @ F_56 )
% 0.24/0.47 => ( ( finite_finite_pname @ A_138 )
% 0.24/0.47 => ( ( B_86 != bot_bot_pname_o )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ B_86 @ A_138 )
% 0.24/0.47 => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
% 0.24/0.47 = ( F_56 @ A_138 ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_680_hoare__derivs_OSkip,axiom,
% 0.24/0.47 ! [G_11: hoare_1708887482_state > $o,P_14: state > state > $o] : ( hoare_90032982_state @ G_11 @ ( insert528405184_state @ ( hoare_858012674_state @ P_14 @ skip @ P_14 ) @ bot_bo19817387tate_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_681_folding__one__idem_Oinsert__idem,axiom,
% 0.24/0.47 ! [X_54: com,A_137: com > $o,F_55: com > com > com,F_54: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite666746948em_com @ F_55 @ F_54 )
% 0.24/0.47 => ( ( finite_finite_com @ A_137 )
% 0.24/0.47 => ( ( A_137 != bot_bot_com_o )
% 0.24/0.47 => ( ( F_54 @ ( insert_com @ X_54 @ A_137 ) )
% 0.24/0.47 = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_682_folding__one__idem_Oinsert__idem,axiom,
% 0.24/0.47 ! [X_54: pname > $o,A_137: ( pname > $o ) > $o,F_55: ( pname > $o ) > ( pname > $o ) > pname > $o,F_54: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.47 ( ( finite697516351name_o @ F_55 @ F_54 )
% 0.24/0.47 => ( ( finite297249702name_o @ A_137 )
% 0.24/0.47 => ( ( A_137 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ( F_54 @ ( insert_pname_o @ X_54 @ A_137 ) )
% 0.24/0.47 = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_683_folding__one__idem_Oinsert__idem,axiom,
% 0.24/0.47 ! [X_54: hoare_1708887482_state > $o,A_137: ( hoare_1708887482_state > $o ) > $o,F_55: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_54: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite621643279tate_o @ F_55 @ F_54 )
% 0.24/0.47 => ( ( finite1329924456tate_o @ A_137 )
% 0.24/0.47 => ( ( A_137 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( F_54 @ ( insert949073679tate_o @ X_54 @ A_137 ) )
% 0.24/0.47 = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_684_folding__one__idem_Oinsert__idem,axiom,
% 0.24/0.47 ! [X_54: pname,A_137: pname > $o,F_55: pname > pname > pname,F_54: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite89670078_pname @ F_55 @ F_54 )
% 0.24/0.47 => ( ( finite_finite_pname @ A_137 )
% 0.24/0.47 => ( ( A_137 != bot_bot_pname_o )
% 0.24/0.47 => ( ( F_54 @ ( insert_pname @ X_54 @ A_137 ) )
% 0.24/0.47 = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_685_folding__one__idem_Oinsert__idem,axiom,
% 0.24/0.47 ! [X_54: hoare_1708887482_state,A_137: hoare_1708887482_state > $o,F_55: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_54: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1347568576_state @ F_55 @ F_54 )
% 0.24/0.47 => ( ( finite1625599783_state @ A_137 )
% 0.24/0.47 => ( ( A_137 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ( F_54 @ ( insert528405184_state @ X_54 @ A_137 ) )
% 0.24/0.47 = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_686_finite__ne__induct,axiom,
% 0.24/0.47 ! [P_13: ( com > $o ) > $o,F_52: com > $o] :
% 0.24/0.47 ( ( finite_finite_com @ F_52 )
% 0.24/0.47 => ( ( F_52 != bot_bot_com_o )
% 0.24/0.47 => ( ! [X_3: com] : ( P_13 @ ( insert_com @ X_3 @ bot_bot_com_o ) )
% 0.24/0.47 => ( ! [X_3: com,F_53: com > $o] :
% 0.24/0.47 ( ( finite_finite_com @ F_53 )
% 0.24/0.47 => ( ( F_53 != bot_bot_com_o )
% 0.24/0.47 => ( ~ ( member_com @ X_3 @ F_53 )
% 0.24/0.47 => ( ( P_13 @ F_53 )
% 0.24/0.47 => ( P_13 @ ( insert_com @ X_3 @ F_53 ) ) ) ) ) )
% 0.24/0.47 => ( P_13 @ F_52 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_687_finite__ne__induct,axiom,
% 0.24/0.47 ! [P_13: ( ( pname > $o ) > $o ) > $o,F_52: ( pname > $o ) > $o] :
% 0.24/0.47 ( ( finite297249702name_o @ F_52 )
% 0.24/0.47 => ( ( F_52 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ! [X_3: pname > $o] : ( P_13 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
% 0.24/0.47 => ( ! [X_3: pname > $o,F_53: ( pname > $o ) > $o] :
% 0.24/0.47 ( ( finite297249702name_o @ F_53 )
% 0.24/0.47 => ( ( F_53 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ~ ( member_pname_o @ X_3 @ F_53 )
% 0.24/0.47 => ( ( P_13 @ F_53 )
% 0.24/0.47 => ( P_13 @ ( insert_pname_o @ X_3 @ F_53 ) ) ) ) ) )
% 0.24/0.47 => ( P_13 @ F_52 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_688_finite__ne__induct,axiom,
% 0.24/0.47 ! [P_13: ( ( hoare_1708887482_state > $o ) > $o ) > $o,F_52: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.47 ( ( finite1329924456tate_o @ F_52 )
% 0.24/0.47 => ( ( F_52 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ! [X_3: hoare_1708887482_state > $o] : ( P_13 @ ( insert949073679tate_o @ X_3 @ bot_bo1678742418te_o_o ) )
% 0.24/0.47 => ( ! [X_3: hoare_1708887482_state > $o,F_53: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.47 ( ( finite1329924456tate_o @ F_53 )
% 0.24/0.47 => ( ( F_53 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ~ ( member814030440tate_o @ X_3 @ F_53 )
% 0.24/0.47 => ( ( P_13 @ F_53 )
% 0.24/0.47 => ( P_13 @ ( insert949073679tate_o @ X_3 @ F_53 ) ) ) ) ) )
% 0.24/0.47 => ( P_13 @ F_52 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_689_finite__ne__induct,axiom,
% 0.24/0.47 ! [P_13: ( pname > $o ) > $o,F_52: pname > $o] :
% 0.24/0.47 ( ( finite_finite_pname @ F_52 )
% 0.24/0.47 => ( ( F_52 != bot_bot_pname_o )
% 0.24/0.47 => ( ! [X_3: pname] : ( P_13 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
% 0.24/0.47 => ( ! [X_3: pname,F_53: pname > $o] :
% 0.24/0.47 ( ( finite_finite_pname @ F_53 )
% 0.24/0.47 => ( ( F_53 != bot_bot_pname_o )
% 0.24/0.47 => ( ~ ( member_pname @ X_3 @ F_53 )
% 0.24/0.47 => ( ( P_13 @ F_53 )
% 0.24/0.47 => ( P_13 @ ( insert_pname @ X_3 @ F_53 ) ) ) ) ) )
% 0.24/0.47 => ( P_13 @ F_52 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_690_finite__ne__induct,axiom,
% 0.24/0.47 ! [P_13: ( hoare_1708887482_state > $o ) > $o,F_52: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite1625599783_state @ F_52 )
% 0.24/0.47 => ( ( F_52 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ! [X_3: hoare_1708887482_state] : ( P_13 @ ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( ! [X_3: hoare_1708887482_state,F_53: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite1625599783_state @ F_53 )
% 0.24/0.47 => ( ( F_53 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ~ ( member451959335_state @ X_3 @ F_53 )
% 0.24/0.47 => ( ( P_13 @ F_53 )
% 0.24/0.47 => ( P_13 @ ( insert528405184_state @ X_3 @ F_53 ) ) ) ) ) )
% 0.24/0.47 => ( P_13 @ F_52 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_691_LoopF,axiom,
% 0.24/0.47 ! [G_10: hoare_1708887482_state > $o,P_12: state > state > $o,B_85: state > $o,C_37: com] :
% 0.24/0.47 ( hoare_90032982_state @ G_10
% 0.24/0.47 @ ( insert528405184_state
% 0.24/0.47 @ ( hoare_858012674_state
% 0.24/0.47 @ ^ [Z_11: state,S_2: state] : ( (&) @ ( P_12 @ Z_11 @ S_2 ) @ ( (~) @ ( B_85 @ S_2 ) ) )
% 0.24/0.47 @ ( while @ B_85 @ C_37 )
% 0.24/0.47 @ P_12 )
% 0.24/0.47 @ bot_bo19817387tate_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_692_Comp,axiom,
% 0.24/0.47 ! [D_3: com,R_1: state > state > $o,G_9: hoare_1708887482_state > $o,P_11: state > state > $o,C_36: com,Q_6: state > state > $o] :
% 0.24/0.47 ( ( hoare_90032982_state @ G_9 @ ( insert528405184_state @ ( hoare_858012674_state @ P_11 @ C_36 @ Q_6 ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( ( hoare_90032982_state @ G_9 @ ( insert528405184_state @ ( hoare_858012674_state @ Q_6 @ D_3 @ R_1 ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_9 @ ( insert528405184_state @ ( hoare_858012674_state @ P_11 @ ( semi @ C_36 @ D_3 ) @ R_1 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_693_WTs__elim__cases_I6_J,axiom,
% 0.24/0.47 ! [B_82: state > $o,C_34: com] :
% 0.24/0.47 ( ( wt @ ( while @ B_82 @ C_34 ) )
% 0.24/0.47 => ( wt @ C_34 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_694_WTs__elim__cases_I4_J,axiom,
% 0.24/0.47 ! [C1: com,C2: com] :
% 0.24/0.47 ( ( wt @ ( semi @ C1 @ C2 ) )
% 0.24/0.47 => ~ ( ( wt @ C1 )
% 0.24/0.47 => ~ ( wt @ C2 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_695_folding__one__idem_Oidem,axiom,
% 0.24/0.47 ! [X_53: hoare_1708887482_state,F_51: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_50: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1347568576_state @ F_51 @ F_50 )
% 0.24/0.47 => ( ( F_51 @ X_53 @ X_53 )
% 0.24/0.47 = X_53 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_696_folding__one__idem_Oidem,axiom,
% 0.24/0.47 ! [X_53: pname,F_51: pname > pname > pname,F_50: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite89670078_pname @ F_51 @ F_50 )
% 0.24/0.47 => ( ( F_51 @ X_53 @ X_53 )
% 0.24/0.47 = X_53 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_697_com_Osimps_I12_J,axiom,
% 0.24/0.47 ! [Com1_1: com,Com2_1: com] :
% 0.24/0.47 ( skip
% 0.24/0.47 != ( semi @ Com1_1 @ Com2_1 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_698_com_Osimps_I16_J,axiom,
% 0.24/0.47 ! [Fun_1: state > $o,Com_2: com] :
% 0.24/0.47 ( skip
% 0.24/0.47 != ( while @ Fun_1 @ Com_2 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_699_com_Osimps_I13_J,axiom,
% 0.24/0.47 ! [Com1_1: com,Com2_1: com] :
% 0.24/0.47 ( ( semi @ Com1_1 @ Com2_1 )
% 0.24/0.47 != skip ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_700_com_Osimps_I17_J,axiom,
% 0.24/0.47 ! [Fun_1: state > $o,Com_2: com] :
% 0.24/0.47 ( ( while @ Fun_1 @ Com_2 )
% 0.24/0.47 != skip ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_701_com_Osimps_I46_J,axiom,
% 0.24/0.47 ! [Com1: com,Com2: com,Fun_1: state > $o,Com_2: com] :
% 0.24/0.47 ( ( semi @ Com1 @ Com2 )
% 0.24/0.47 != ( while @ Fun_1 @ Com_2 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_702_com_Osimps_I47_J,axiom,
% 0.24/0.47 ! [Fun_1: state > $o,Com_2: com,Com1: com,Com2: com] :
% 0.24/0.47 ( ( while @ Fun_1 @ Com_2 )
% 0.24/0.47 != ( semi @ Com1 @ Com2 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_703_com_Osimps_I3_J,axiom,
% 0.24/0.47 ! [Com1: com,Com2: com,Com1_1: com,Com2_1: com] :
% 0.24/0.47 ( ( ( semi @ Com1 @ Com2 )
% 0.24/0.47 = ( semi @ Com1_1 @ Com2_1 ) )
% 0.24/0.47 <=> ( ( Com1 = Com1_1 )
% 0.24/0.47 & ( Com2 = Com2_1 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_704_com_Osimps_I5_J,axiom,
% 0.24/0.47 ! [Fun: state > $o,Com_1: com,Fun_1: state > $o,Com_2: com] :
% 0.24/0.47 ( ( ( while @ Fun @ Com_1 )
% 0.24/0.47 = ( while @ Fun_1 @ Com_2 ) )
% 0.24/0.47 <=> ( ( Fun = Fun_1 )
% 0.24/0.47 & ( Com_1 = Com_2 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_705_com_Osimps_I59_J,axiom,
% 0.24/0.47 ! [Pname: pname,Fun: state > $o,Com_1: com] :
% 0.24/0.47 ( ( body_1 @ Pname )
% 0.24/0.47 != ( while @ Fun @ Com_1 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_706_com_Osimps_I58_J,axiom,
% 0.24/0.47 ! [Fun: state > $o,Com_1: com,Pname: pname] :
% 0.24/0.47 ( ( while @ Fun @ Com_1 )
% 0.24/0.47 != ( body_1 @ Pname ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_707_While,axiom,
% 0.24/0.47 ! [B_82: state > $o,C_34: com] :
% 0.24/0.47 ( ( wt @ C_34 )
% 0.24/0.47 => ( wt @ ( while @ B_82 @ C_34 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_708_com_Osimps_I49_J,axiom,
% 0.24/0.47 ! [Pname: pname,Com1: com,Com2: com] :
% 0.24/0.47 ( ( body_1 @ Pname )
% 0.24/0.47 != ( semi @ Com1 @ Com2 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_709_com_Osimps_I48_J,axiom,
% 0.24/0.47 ! [Com1: com,Com2: com,Pname: pname] :
% 0.24/0.47 ( ( semi @ Com1 @ Com2 )
% 0.24/0.47 != ( body_1 @ Pname ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_710_WT_OSemi,axiom,
% 0.24/0.47 ! [C1: com,C0: com] :
% 0.24/0.47 ( ( wt @ C0 )
% 0.24/0.47 => ( ( wt @ C1 )
% 0.24/0.47 => ( wt @ ( semi @ C0 @ C1 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_711_com_Osimps_I18_J,axiom,
% 0.24/0.47 ! [Pname: pname] :
% 0.24/0.47 ( skip
% 0.24/0.47 != ( body_1 @ Pname ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_712_com_Osimps_I19_J,axiom,
% 0.24/0.47 ! [Pname: pname] :
% 0.24/0.47 ( ( body_1 @ Pname )
% 0.24/0.47 != skip ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_713_WT_OSkip,axiom,
% 0.24/0.47 wt @ skip ).
% 0.24/0.47
% 0.24/0.47 thf(fact_714_folding__one__idem_Oin__idem,axiom,
% 0.24/0.47 ! [X_52: com,A_136: com > $o,F_49: com > com > com,F_48: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite666746948em_com @ F_49 @ F_48 )
% 0.24/0.47 => ( ( finite_finite_com @ A_136 )
% 0.24/0.47 => ( ( member_com @ X_52 @ A_136 )
% 0.24/0.47 => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
% 0.24/0.47 = ( F_48 @ A_136 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_715_folding__one__idem_Oin__idem,axiom,
% 0.24/0.47 ! [X_52: pname,A_136: pname > $o,F_49: pname > pname > pname,F_48: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite89670078_pname @ F_49 @ F_48 )
% 0.24/0.47 => ( ( finite_finite_pname @ A_136 )
% 0.24/0.47 => ( ( member_pname @ X_52 @ A_136 )
% 0.24/0.47 => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
% 0.24/0.47 = ( F_48 @ A_136 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_716_folding__one__idem_Oin__idem,axiom,
% 0.24/0.47 ! [X_52: hoare_1708887482_state,A_136: hoare_1708887482_state > $o,F_49: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_48: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1347568576_state @ F_49 @ F_48 )
% 0.24/0.47 => ( ( finite1625599783_state @ A_136 )
% 0.24/0.47 => ( ( member451959335_state @ X_52 @ A_136 )
% 0.24/0.47 => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
% 0.24/0.47 = ( F_48 @ A_136 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_717_folding__one__idem_Oin__idem,axiom,
% 0.24/0.47 ! [X_52: pname > $o,A_136: ( pname > $o ) > $o,F_49: ( pname > $o ) > ( pname > $o ) > pname > $o,F_48: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.47 ( ( finite697516351name_o @ F_49 @ F_48 )
% 0.24/0.47 => ( ( finite297249702name_o @ A_136 )
% 0.24/0.47 => ( ( member_pname_o @ X_52 @ A_136 )
% 0.24/0.47 => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
% 0.24/0.47 = ( F_48 @ A_136 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_718_folding__one__idem_Oin__idem,axiom,
% 0.24/0.47 ! [X_52: hoare_1708887482_state > $o,A_136: ( hoare_1708887482_state > $o ) > $o,F_49: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_48: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite621643279tate_o @ F_49 @ F_48 )
% 0.24/0.47 => ( ( finite1329924456tate_o @ A_136 )
% 0.24/0.47 => ( ( member814030440tate_o @ X_52 @ A_136 )
% 0.24/0.47 => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
% 0.24/0.47 = ( F_48 @ A_136 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_719_folding__one__idem_Ohom__commute,axiom,
% 0.24/0.47 ! [N_1: ( pname > $o ) > $o,H_1: ( pname > $o ) > pname > $o,F_47: ( pname > $o ) > ( pname > $o ) > pname > $o,F_46: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.47 ( ( finite697516351name_o @ F_47 @ F_46 )
% 0.24/0.47 => ( ! [X_3: pname > $o,Y_4: pname > $o] :
% 0.24/0.47 ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
% 0.24/0.47 = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
% 0.24/0.47 => ( ( finite297249702name_o @ N_1 )
% 0.24/0.47 => ( ( N_1 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ( H_1 @ ( F_46 @ N_1 ) )
% 0.24/0.47 = ( F_46 @ ( image_1085733413name_o @ H_1 @ N_1 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_720_folding__one__idem_Ohom__commute,axiom,
% 0.24/0.47 ! [N_1: ( hoare_1708887482_state > $o ) > $o,H_1: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_47: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_46: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite621643279tate_o @ F_47 @ F_46 )
% 0.24/0.47 => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
% 0.24/0.47 = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
% 0.24/0.47 => ( ( finite1329924456tate_o @ N_1 )
% 0.24/0.47 => ( ( N_1 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( H_1 @ ( F_46 @ N_1 ) )
% 0.24/0.47 = ( F_46 @ ( image_909543877tate_o @ H_1 @ N_1 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_721_folding__one__idem_Ohom__commute,axiom,
% 0.24/0.47 ! [N_1: pname > $o,H_1: pname > pname,F_47: pname > pname > pname,F_46: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite89670078_pname @ F_47 @ F_46 )
% 0.24/0.47 => ( ! [X_3: pname,Y_4: pname] :
% 0.24/0.47 ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
% 0.24/0.47 = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
% 0.24/0.47 => ( ( finite_finite_pname @ N_1 )
% 0.24/0.47 => ( ( N_1 != bot_bot_pname_o )
% 0.24/0.47 => ( ( H_1 @ ( F_46 @ N_1 ) )
% 0.24/0.47 = ( F_46 @ ( image_pname_pname @ H_1 @ N_1 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_722_folding__one__idem_Ohom__commute,axiom,
% 0.24/0.47 ! [N_1: hoare_1708887482_state > $o,H_1: hoare_1708887482_state > hoare_1708887482_state,F_47: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_46: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1347568576_state @ F_47 @ F_46 )
% 0.24/0.47 => ( ! [X_3: hoare_1708887482_state,Y_4: hoare_1708887482_state] :
% 0.24/0.47 ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
% 0.24/0.47 = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
% 0.24/0.47 => ( ( finite1625599783_state @ N_1 )
% 0.24/0.47 => ( ( N_1 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ( H_1 @ ( F_46 @ N_1 ) )
% 0.24/0.47 = ( F_46 @ ( image_757158439_state @ H_1 @ N_1 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_723_folding__one__idem_Ohom__commute,axiom,
% 0.24/0.47 ! [N_1: com > $o,H_1: com > com,F_47: com > com > com,F_46: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite666746948em_com @ F_47 @ F_46 )
% 0.24/0.47 => ( ! [X_3: com,Y_4: com] :
% 0.24/0.47 ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
% 0.24/0.47 = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
% 0.24/0.47 => ( ( finite_finite_com @ N_1 )
% 0.24/0.47 => ( ( N_1 != bot_bot_com_o )
% 0.24/0.47 => ( ( H_1 @ ( F_46 @ N_1 ) )
% 0.24/0.47 = ( F_46 @ ( image_com_com @ H_1 @ N_1 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_724_the__elem__def,axiom,
% 0.24/0.47 ! [X_51: com > $o] :
% 0.24/0.47 ( ( the_elem_com @ X_51 )
% 0.24/0.47 = ( the_com_1
% 0.24/0.47 @ ^ [X_3: com] :
% 0.24/0.47 ( X_51
% 0.24/0.47 = ( insert_com @ X_3 @ bot_bot_com_o ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_725_the__elem__def,axiom,
% 0.24/0.47 ! [X_51: pname > $o] :
% 0.24/0.47 ( ( the_elem_pname @ X_51 )
% 0.24/0.47 = ( the_pname
% 0.24/0.47 @ ^ [X_3: pname] :
% 0.24/0.47 ( X_51
% 0.24/0.47 = ( insert_pname @ X_3 @ bot_bot_pname_o ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_726_the__elem__def,axiom,
% 0.24/0.47 ! [X_51: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( the_el864710747_state @ X_51 )
% 0.24/0.47 = ( the_Ho851197897_state
% 0.24/0.47 @ ^ [X_3: hoare_1708887482_state] :
% 0.24/0.47 ( X_51
% 0.24/0.47 = ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_727_folding__one_Oinsert,axiom,
% 0.24/0.47 ! [X_50: com,A_135: com > $o,F_45: com > com > com,F_44: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite860057415ne_com @ F_45 @ F_44 )
% 0.24/0.47 => ( ( finite_finite_com @ A_135 )
% 0.24/0.47 => ( ~ ( member_com @ X_50 @ A_135 )
% 0.24/0.47 => ( ( A_135 != bot_bot_com_o )
% 0.24/0.47 => ( ( F_44 @ ( insert_com @ X_50 @ A_135 ) )
% 0.24/0.47 = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_728_folding__one_Oinsert,axiom,
% 0.24/0.47 ! [X_50: pname,A_135: pname > $o,F_45: pname > pname > pname,F_44: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite1282449217_pname @ F_45 @ F_44 )
% 0.24/0.47 => ( ( finite_finite_pname @ A_135 )
% 0.24/0.47 => ( ~ ( member_pname @ X_50 @ A_135 )
% 0.24/0.47 => ( ( A_135 != bot_bot_pname_o )
% 0.24/0.47 => ( ( F_44 @ ( insert_pname @ X_50 @ A_135 ) )
% 0.24/0.47 = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_729_folding__one_Oinsert,axiom,
% 0.24/0.47 ! [X_50: hoare_1708887482_state,A_135: hoare_1708887482_state > $o,F_45: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_44: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1615457021_state @ F_45 @ F_44 )
% 0.24/0.47 => ( ( finite1625599783_state @ A_135 )
% 0.24/0.47 => ( ~ ( member451959335_state @ X_50 @ A_135 )
% 0.24/0.47 => ( ( A_135 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ( F_44 @ ( insert528405184_state @ X_50 @ A_135 ) )
% 0.24/0.47 = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_730_folding__one_Oinsert,axiom,
% 0.24/0.47 ! [X_50: pname > $o,A_135: ( pname > $o ) > $o,F_45: ( pname > $o ) > ( pname > $o ) > pname > $o,F_44: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.47 ( ( finite349908348name_o @ F_45 @ F_44 )
% 0.24/0.47 => ( ( finite297249702name_o @ A_135 )
% 0.24/0.47 => ( ~ ( member_pname_o @ X_50 @ A_135 )
% 0.24/0.47 => ( ( A_135 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ( F_44 @ ( insert_pname_o @ X_50 @ A_135 ) )
% 0.24/0.47 = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_731_folding__one_Oinsert,axiom,
% 0.24/0.47 ! [X_50: hoare_1708887482_state > $o,A_135: ( hoare_1708887482_state > $o ) > $o,F_45: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_44: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite928843026tate_o @ F_45 @ F_44 )
% 0.24/0.47 => ( ( finite1329924456tate_o @ A_135 )
% 0.24/0.47 => ( ~ ( member814030440tate_o @ X_50 @ A_135 )
% 0.24/0.47 => ( ( A_135 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( F_44 @ ( insert949073679tate_o @ X_50 @ A_135 ) )
% 0.24/0.47 = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_732_triple_Oexhaust,axiom,
% 0.24/0.47 ! [Y_25: hoare_1708887482_state] :
% 0.24/0.47 ~ ! [Fun1: state > state > $o,Com: com,Fun2: state > state > $o] :
% 0.24/0.47 ( Y_25
% 0.24/0.47 != ( hoare_858012674_state @ Fun1 @ Com @ Fun2 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_733_folding__one_Osingleton,axiom,
% 0.24/0.47 ! [X_49: com,F_43: com > com > com,F_42: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite860057415ne_com @ F_43 @ F_42 )
% 0.24/0.47 => ( ( F_42 @ ( insert_com @ X_49 @ bot_bot_com_o ) )
% 0.24/0.47 = X_49 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_734_folding__one_Osingleton,axiom,
% 0.24/0.47 ! [X_49: pname,F_43: pname > pname > pname,F_42: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite1282449217_pname @ F_43 @ F_42 )
% 0.24/0.47 => ( ( F_42 @ ( insert_pname @ X_49 @ bot_bot_pname_o ) )
% 0.24/0.47 = X_49 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_735_folding__one_Osingleton,axiom,
% 0.24/0.47 ! [X_49: hoare_1708887482_state,F_43: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_42: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1615457021_state @ F_43 @ F_42 )
% 0.24/0.47 => ( ( F_42 @ ( insert528405184_state @ X_49 @ bot_bo19817387tate_o ) )
% 0.24/0.47 = X_49 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_736_folding__one_Oclosed,axiom,
% 0.24/0.47 ! [A_134: com > $o,F_41: com > com > com,F_40: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite860057415ne_com @ F_41 @ F_40 )
% 0.24/0.47 => ( ( finite_finite_com @ A_134 )
% 0.24/0.47 => ( ( A_134 != bot_bot_com_o )
% 0.24/0.47 => ( ! [X_3: com,Y_4: com] : ( member_com @ ( F_41 @ X_3 @ Y_4 ) @ ( insert_com @ X_3 @ ( insert_com @ Y_4 @ bot_bot_com_o ) ) )
% 0.24/0.47 => ( member_com @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_737_folding__one_Oclosed,axiom,
% 0.24/0.47 ! [A_134: pname > $o,F_41: pname > pname > pname,F_40: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite1282449217_pname @ F_41 @ F_40 )
% 0.24/0.47 => ( ( finite_finite_pname @ A_134 )
% 0.24/0.47 => ( ( A_134 != bot_bot_pname_o )
% 0.24/0.47 => ( ! [X_3: pname,Y_4: pname] : ( member_pname @ ( F_41 @ X_3 @ Y_4 ) @ ( insert_pname @ X_3 @ ( insert_pname @ Y_4 @ bot_bot_pname_o ) ) )
% 0.24/0.47 => ( member_pname @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_738_folding__one_Oclosed,axiom,
% 0.24/0.47 ! [A_134: hoare_1708887482_state > $o,F_41: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_40: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1615457021_state @ F_41 @ F_40 )
% 0.24/0.47 => ( ( finite1625599783_state @ A_134 )
% 0.24/0.47 => ( ( A_134 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ! [X_3: hoare_1708887482_state,Y_4: hoare_1708887482_state] : ( member451959335_state @ ( F_41 @ X_3 @ Y_4 ) @ ( insert528405184_state @ X_3 @ ( insert528405184_state @ Y_4 @ bot_bo19817387tate_o ) ) )
% 0.24/0.47 => ( member451959335_state @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_739_folding__one_Oclosed,axiom,
% 0.24/0.47 ! [A_134: ( pname > $o ) > $o,F_41: ( pname > $o ) > ( pname > $o ) > pname > $o,F_40: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.47 ( ( finite349908348name_o @ F_41 @ F_40 )
% 0.24/0.47 => ( ( finite297249702name_o @ A_134 )
% 0.24/0.47 => ( ( A_134 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ! [X_3: pname > $o,Y_4: pname > $o] : ( member_pname_o @ ( F_41 @ X_3 @ Y_4 ) @ ( insert_pname_o @ X_3 @ ( insert_pname_o @ Y_4 @ bot_bot_pname_o_o ) ) )
% 0.24/0.47 => ( member_pname_o @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_740_folding__one_Oclosed,axiom,
% 0.24/0.47 ! [A_134: ( hoare_1708887482_state > $o ) > $o,F_41: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_40: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite928843026tate_o @ F_41 @ F_40 )
% 0.24/0.47 => ( ( finite1329924456tate_o @ A_134 )
% 0.24/0.47 => ( ( A_134 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] : ( member814030440tate_o @ ( F_41 @ X_3 @ Y_4 ) @ ( insert949073679tate_o @ X_3 @ ( insert949073679tate_o @ Y_4 @ bot_bo1678742418te_o_o ) ) )
% 0.24/0.47 => ( member814030440tate_o @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_741_image__cong,axiom,
% 0.24/0.47 ! [F_39: pname > hoare_1708887482_state,G_8: pname > hoare_1708887482_state,M_3: pname > $o,N: pname > $o] :
% 0.24/0.47 ( ( M_3 = N )
% 0.24/0.47 => ( ! [X_3: pname] :
% 0.24/0.47 ( ( member_pname @ X_3 @ N )
% 0.24/0.47 => ( ( F_39 @ X_3 )
% 0.24/0.47 = ( G_8 @ X_3 ) ) )
% 0.24/0.47 => ( ( image_1116629049_state @ F_39 @ M_3 )
% 0.24/0.47 = ( image_1116629049_state @ G_8 @ N ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_742_Collect__mono,axiom,
% 0.24/0.47 ! [Q_5: hoare_1708887482_state > $o,P_10: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ! [X_3: hoare_1708887482_state] :
% 0.24/0.47 ( ( P_10 @ X_3 )
% 0.24/0.47 => ( Q_5 @ X_3 ) )
% 0.24/0.47 => ( ord_le777019615tate_o @ ( collec1568722789_state @ P_10 ) @ ( collec1568722789_state @ Q_5 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_743_Collect__mono,axiom,
% 0.24/0.47 ! [Q_5: pname > $o,P_10: pname > $o] :
% 0.24/0.47 ( ! [X_3: pname] :
% 0.24/0.47 ( ( P_10 @ X_3 )
% 0.24/0.47 => ( Q_5 @ X_3 ) )
% 0.24/0.47 => ( ord_less_eq_pname_o @ ( collect_pname @ P_10 ) @ ( collect_pname @ Q_5 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_744_Collect__mono,axiom,
% 0.24/0.47 ! [Q_5: ( pname > $o ) > $o,P_10: ( pname > $o ) > $o] :
% 0.24/0.47 ( ! [X_3: pname > $o] :
% 0.24/0.47 ( ( P_10 @ X_3 )
% 0.24/0.47 => ( Q_5 @ X_3 ) )
% 0.24/0.47 => ( ord_le1205211808me_o_o @ ( collect_pname_o @ P_10 ) @ ( collect_pname_o @ Q_5 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_745_Collect__mono,axiom,
% 0.24/0.47 ! [Q_5: ( hoare_1708887482_state > $o ) > $o,P_10: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.47 ( ! [X_3: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( P_10 @ X_3 )
% 0.24/0.47 => ( Q_5 @ X_3 ) )
% 0.24/0.47 => ( ord_le1728773982te_o_o @ ( collec219771562tate_o @ P_10 ) @ ( collec219771562tate_o @ Q_5 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_746_predicate1I,axiom,
% 0.24/0.47 ! [Q_4: pname > $o,P_9: pname > $o] :
% 0.24/0.47 ( ! [X_3: pname] :
% 0.24/0.47 ( ( P_9 @ X_3 )
% 0.24/0.47 => ( Q_4 @ X_3 ) )
% 0.24/0.47 => ( ord_less_eq_pname_o @ P_9 @ Q_4 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_747_predicate1I,axiom,
% 0.24/0.47 ! [Q_4: hoare_1708887482_state > $o,P_9: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ! [X_3: hoare_1708887482_state] :
% 0.24/0.47 ( ( P_9 @ X_3 )
% 0.24/0.47 => ( Q_4 @ X_3 ) )
% 0.24/0.47 => ( ord_le777019615tate_o @ P_9 @ Q_4 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_748_mk__disjoint__insert,axiom,
% 0.24/0.47 ! [A_133: com,A_132: com > $o] :
% 0.24/0.47 ( ( member_com @ A_133 @ A_132 )
% 0.24/0.47 => ? [B_84: com > $o] :
% 0.24/0.47 ( ( A_132
% 0.24/0.47 = ( insert_com @ A_133 @ B_84 ) )
% 0.24/0.47 & ~ ( member_com @ A_133 @ B_84 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_749_mk__disjoint__insert,axiom,
% 0.24/0.47 ! [A_133: pname,A_132: pname > $o] :
% 0.24/0.47 ( ( member_pname @ A_133 @ A_132 )
% 0.24/0.47 => ? [B_84: pname > $o] :
% 0.24/0.47 ( ( A_132
% 0.24/0.47 = ( insert_pname @ A_133 @ B_84 ) )
% 0.24/0.47 & ~ ( member_pname @ A_133 @ B_84 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_750_mk__disjoint__insert,axiom,
% 0.24/0.47 ! [A_133: hoare_1708887482_state,A_132: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ A_133 @ A_132 )
% 0.24/0.47 => ? [B_84: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( A_132
% 0.24/0.47 = ( insert528405184_state @ A_133 @ B_84 ) )
% 0.24/0.47 & ~ ( member451959335_state @ A_133 @ B_84 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_751_Set_Oset__insert,axiom,
% 0.24/0.47 ! [X_48: com,A_131: com > $o] :
% 0.24/0.47 ( ( member_com @ X_48 @ A_131 )
% 0.24/0.47 => ~ ! [B_84: com > $o] :
% 0.24/0.47 ( ( A_131
% 0.24/0.47 = ( insert_com @ X_48 @ B_84 ) )
% 0.24/0.47 => ( member_com @ X_48 @ B_84 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_752_Set_Oset__insert,axiom,
% 0.24/0.47 ! [X_48: pname,A_131: pname > $o] :
% 0.24/0.47 ( ( member_pname @ X_48 @ A_131 )
% 0.24/0.47 => ~ ! [B_84: pname > $o] :
% 0.24/0.47 ( ( A_131
% 0.24/0.47 = ( insert_pname @ X_48 @ B_84 ) )
% 0.24/0.47 => ( member_pname @ X_48 @ B_84 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_753_Set_Oset__insert,axiom,
% 0.24/0.47 ! [X_48: hoare_1708887482_state,A_131: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ X_48 @ A_131 )
% 0.24/0.47 => ~ ! [B_84: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( A_131
% 0.24/0.47 = ( insert528405184_state @ X_48 @ B_84 ) )
% 0.24/0.47 => ( member451959335_state @ X_48 @ B_84 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_754_equals0I,axiom,
% 0.24/0.47 ! [A_130: com > $o] :
% 0.24/0.47 ( ! [Y_4: com] :
% 0.24/0.47 ~ ( member_com @ Y_4 @ A_130 )
% 0.24/0.47 => ( A_130 = bot_bot_com_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_755_equals0I,axiom,
% 0.24/0.47 ! [A_130: pname > $o] :
% 0.24/0.47 ( ! [Y_4: pname] :
% 0.24/0.47 ~ ( member_pname @ Y_4 @ A_130 )
% 0.24/0.47 => ( A_130 = bot_bot_pname_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_756_equals0I,axiom,
% 0.24/0.47 ! [A_130: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ! [Y_4: hoare_1708887482_state] :
% 0.24/0.47 ~ ( member451959335_state @ Y_4 @ A_130 )
% 0.24/0.47 => ( A_130 = bot_bo19817387tate_o ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_757_MGT__alternD,axiom,
% 0.24/0.47 ! [G_7: hoare_1708887482_state > $o,C_34: com] :
% 0.24/0.47 ( hoare_1160767572gleton
% 0.24/0.47 => ( ( hoare_90032982_state @ G_7
% 0.24/0.47 @ ( insert528405184_state
% 0.24/0.47 @ ( hoare_858012674_state
% 0.24/0.47 @ ^ [Z_11: state,S0_1: state] :
% 0.24/0.47 ! [S1: state] : ( (=>) @ ( evalc @ C_34 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
% 0.24/0.47 @ C_34
% 0.24/0.47 @ fequal_state )
% 0.24/0.47 @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_758_xt1_I15_J,axiom,
% 0.24/0.47 ! [C_35: $o,F_38: $o > $o,B_83: $o,A_129: $o] :
% 0.24/0.47 ( ( A_129
% 0.24/0.47 <=> ( F_38 @ B_83 ) )
% 0.24/0.47 => ( ( ord_less_eq_o @ C_35 @ B_83 )
% 0.24/0.47 => ( ! [X_3: $o,Y_4: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ Y_4 @ X_3 )
% 0.24/0.47 => ( ord_less_eq_o @ ( F_38 @ Y_4 ) @ ( F_38 @ X_3 ) ) )
% 0.24/0.47 => ( ord_less_eq_o @ ( F_38 @ C_35 ) @ A_129 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_759_xt1_I15_J,axiom,
% 0.24/0.47 ! [C_35: pname > $o,A_129: pname > $o,F_38: ( pname > $o ) > pname > $o,B_83: pname > $o] :
% 0.24/0.47 ( ( A_129
% 0.24/0.47 = ( F_38 @ B_83 ) )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ C_35 @ B_83 )
% 0.24/0.47 => ( ! [X_3: pname > $o,Y_4: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ Y_4 @ X_3 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ ( F_38 @ Y_4 ) @ ( F_38 @ X_3 ) ) )
% 0.24/0.47 => ( ord_less_eq_pname_o @ ( F_38 @ C_35 ) @ A_129 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_760_xt1_I15_J,axiom,
% 0.24/0.47 ! [C_35: hoare_1708887482_state > $o,A_129: hoare_1708887482_state > $o,F_38: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,B_83: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( A_129
% 0.24/0.47 = ( F_38 @ B_83 ) )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ C_35 @ B_83 )
% 0.24/0.47 => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ Y_4 @ X_3 )
% 0.24/0.47 => ( ord_le777019615tate_o @ ( F_38 @ Y_4 ) @ ( F_38 @ X_3 ) ) )
% 0.24/0.47 => ( ord_le777019615tate_o @ ( F_38 @ C_35 ) @ A_129 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_761_MGT__alternI,axiom,
% 0.24/0.47 ! [G_7: hoare_1708887482_state > $o,C_34: com] :
% 0.24/0.47 ( ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_7
% 0.24/0.47 @ ( insert528405184_state
% 0.24/0.47 @ ( hoare_858012674_state
% 0.24/0.47 @ ^ [Z_11: state,S0_1: state] :
% 0.24/0.47 ! [S1: state] : ( (=>) @ ( evalc @ C_34 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
% 0.24/0.47 @ C_34
% 0.24/0.47 @ fequal_state )
% 0.24/0.47 @ bot_bo19817387tate_o ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_762_MGT__def,axiom,
% 0.24/0.47 ! [C_34: com] :
% 0.24/0.47 ( ( hoare_Mirabelle_MGT @ C_34 )
% 0.24/0.47 = ( hoare_858012674_state @ fequal_state @ C_34 @ ( evalc @ C_34 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_763_evalc__elim__cases_I6_J,axiom,
% 0.24/0.47 ! [P: pname,S_4: state,S1_1: state] :
% 0.24/0.47 ( ( evalc @ ( body_1 @ P ) @ S_4 @ S1_1 )
% 0.24/0.47 => ( evalc @ ( the_com @ ( body @ P ) ) @ S_4 @ S1_1 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_764_evalc_OBody,axiom,
% 0.24/0.47 ! [Pn_1: pname,S0: state,S1_1: state] :
% 0.24/0.47 ( ( evalc @ ( the_com @ ( body @ Pn_1 ) ) @ S0 @ S1_1 )
% 0.24/0.47 => ( evalc @ ( body_1 @ Pn_1 ) @ S0 @ S1_1 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_765_evalc__elim__cases_I1_J,axiom,
% 0.24/0.47 ! [S_4: state,T: state] :
% 0.24/0.47 ( ( evalc @ skip @ S_4 @ T )
% 0.24/0.47 => ( T = S_4 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_766_evalc_OSkip,axiom,
% 0.24/0.47 ! [S_4: state] : ( evalc @ skip @ S_4 @ S_4 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_767_evalc_OSemi,axiom,
% 0.24/0.47 ! [C1: com,S2: state,C0: com,S0: state,S1_1: state] :
% 0.24/0.47 ( ( evalc @ C0 @ S0 @ S1_1 )
% 0.24/0.47 => ( ( evalc @ C1 @ S1_1 @ S2 )
% 0.24/0.47 => ( evalc @ ( semi @ C0 @ C1 ) @ S0 @ S2 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_768_evalc_OWhileTrue,axiom,
% 0.24/0.47 ! [S2: state,C_34: com,S1_1: state,B_82: state > $o,S0: state] :
% 0.24/0.47 ( ( B_82 @ S0 )
% 0.24/0.47 => ( ( evalc @ C_34 @ S0 @ S1_1 )
% 0.24/0.47 => ( ( evalc @ ( while @ B_82 @ C_34 ) @ S1_1 @ S2 )
% 0.24/0.47 => ( evalc @ ( while @ B_82 @ C_34 ) @ S0 @ S2 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_769_evalc_OWhileFalse,axiom,
% 0.24/0.47 ! [C_34: com,B_82: state > $o,S_4: state] :
% 0.24/0.47 ( ~ ( B_82 @ S_4 )
% 0.24/0.47 => ( evalc @ ( while @ B_82 @ C_34 ) @ S_4 @ S_4 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_770_com__det,axiom,
% 0.24/0.47 ! [U: state,C_34: com,S_4: state,T: state] :
% 0.24/0.47 ( ( evalc @ C_34 @ S_4 @ T )
% 0.24/0.47 => ( ( evalc @ C_34 @ S_4 @ U )
% 0.24/0.47 => ( U = T ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_771_evalc__elim__cases_I4_J,axiom,
% 0.24/0.47 ! [C1: com,C2: com,S_4: state,T: state] :
% 0.24/0.47 ( ( evalc @ ( semi @ C1 @ C2 ) @ S_4 @ T )
% 0.24/0.47 => ~ ! [S1: state] :
% 0.24/0.47 ( ( evalc @ C1 @ S_4 @ S1 )
% 0.24/0.47 => ~ ( evalc @ C2 @ S1 @ T ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_772_evalc__WHILE__case,axiom,
% 0.24/0.47 ! [B_82: state > $o,C_34: com,S_4: state,T: state] :
% 0.24/0.47 ( ( evalc @ ( while @ B_82 @ C_34 ) @ S_4 @ T )
% 0.24/0.47 => ( ( ( T = S_4 )
% 0.24/0.47 => ( B_82 @ S_4 ) )
% 0.24/0.47 => ~ ( ( B_82 @ S_4 )
% 0.24/0.47 => ! [S1: state] :
% 0.24/0.47 ( ( evalc @ C_34 @ S_4 @ S1 )
% 0.24/0.47 => ~ ( evalc @ ( while @ B_82 @ C_34 ) @ S1 @ T ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_773_xt1_I16_J,axiom,
% 0.24/0.47 ! [C_33: $o,F_37: $o > $o,B_81: $o,A_128: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ B_81 @ A_128 )
% 0.24/0.47 => ( ( ( F_37 @ B_81 )
% 0.24/0.47 <=> C_33 )
% 0.24/0.47 => ( ! [X_3: $o,Y_4: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ Y_4 @ X_3 )
% 0.24/0.47 => ( ord_less_eq_o @ ( F_37 @ Y_4 ) @ ( F_37 @ X_3 ) ) )
% 0.24/0.47 => ( ord_less_eq_o @ C_33 @ ( F_37 @ A_128 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_774_xt1_I16_J,axiom,
% 0.24/0.47 ! [F_37: ( pname > $o ) > pname > $o,C_33: pname > $o,B_81: pname > $o,A_128: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ B_81 @ A_128 )
% 0.24/0.47 => ( ( ( F_37 @ B_81 )
% 0.24/0.47 = C_33 )
% 0.24/0.47 => ( ! [X_3: pname > $o,Y_4: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ Y_4 @ X_3 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ ( F_37 @ Y_4 ) @ ( F_37 @ X_3 ) ) )
% 0.24/0.47 => ( ord_less_eq_pname_o @ C_33 @ ( F_37 @ A_128 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_775_xt1_I16_J,axiom,
% 0.24/0.47 ! [F_37: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,C_33: hoare_1708887482_state > $o,B_81: hoare_1708887482_state > $o,A_128: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ B_81 @ A_128 )
% 0.24/0.47 => ( ( ( F_37 @ B_81 )
% 0.24/0.47 = C_33 )
% 0.24/0.47 => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ Y_4 @ X_3 )
% 0.24/0.47 => ( ord_le777019615tate_o @ ( F_37 @ Y_4 ) @ ( F_37 @ X_3 ) ) )
% 0.24/0.47 => ( ord_le777019615tate_o @ C_33 @ ( F_37 @ A_128 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_776_folding__one_Ounion__inter,axiom,
% 0.24/0.47 ! [B_80: ( pname > $o ) > $o,A_127: ( pname > $o ) > $o,F_36: ( pname > $o ) > ( pname > $o ) > pname > $o,F_35: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.47 ( ( finite349908348name_o @ F_36 @ F_35 )
% 0.24/0.47 => ( ( finite297249702name_o @ A_127 )
% 0.24/0.47 => ( ( finite297249702name_o @ B_80 )
% 0.24/0.47 => ( ( ( semila2013987940me_o_o @ A_127 @ B_80 )
% 0.24/0.47 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ( F_36 @ ( F_35 @ ( semila181081674me_o_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila2013987940me_o_o @ A_127 @ B_80 ) ) )
% 0.24/0.47 = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_777_folding__one_Ounion__inter,axiom,
% 0.24/0.47 ! [B_80: ( hoare_1708887482_state > $o ) > $o,A_127: ( hoare_1708887482_state > $o ) > $o,F_36: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_35: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite928843026tate_o @ F_36 @ F_35 )
% 0.24/0.47 => ( ( finite1329924456tate_o @ A_127 )
% 0.24/0.47 => ( ( finite1329924456tate_o @ B_80 )
% 0.24/0.47 => ( ( ( semila598060698te_o_o @ A_127 @ B_80 )
% 0.24/0.47 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( F_36 @ ( F_35 @ ( semila1853742644te_o_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila598060698te_o_o @ A_127 @ B_80 ) ) )
% 0.24/0.47 = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_778_folding__one_Ounion__inter,axiom,
% 0.24/0.47 ! [B_80: pname > $o,A_127: pname > $o,F_36: pname > pname > pname,F_35: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite1282449217_pname @ F_36 @ F_35 )
% 0.24/0.47 => ( ( finite_finite_pname @ A_127 )
% 0.24/0.47 => ( ( finite_finite_pname @ B_80 )
% 0.24/0.47 => ( ( ( semila1673364395name_o @ A_127 @ B_80 )
% 0.24/0.47 != bot_bot_pname_o )
% 0.24/0.47 => ( ( F_36 @ ( F_35 @ ( semila1780557381name_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila1673364395name_o @ A_127 @ B_80 ) ) )
% 0.24/0.47 = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_779_folding__one_Ounion__inter,axiom,
% 0.24/0.47 ! [B_80: hoare_1708887482_state > $o,A_127: hoare_1708887482_state > $o,F_36: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_35: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1615457021_state @ F_36 @ F_35 )
% 0.24/0.47 => ( ( finite1625599783_state @ A_127 )
% 0.24/0.47 => ( ( finite1625599783_state @ B_80 )
% 0.24/0.47 => ( ( ( semila129691299tate_o @ A_127 @ B_80 )
% 0.24/0.47 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ( F_36 @ ( F_35 @ ( semila1122118281tate_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila129691299tate_o @ A_127 @ B_80 ) ) )
% 0.24/0.47 = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_780_folding__one_Ounion__inter,axiom,
% 0.24/0.47 ! [B_80: com > $o,A_127: com > $o,F_36: com > com > com,F_35: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite860057415ne_com @ F_36 @ F_35 )
% 0.24/0.47 => ( ( finite_finite_com @ A_127 )
% 0.24/0.47 => ( ( finite_finite_com @ B_80 )
% 0.24/0.47 => ( ( ( semila513601829_com_o @ A_127 @ B_80 )
% 0.24/0.47 != bot_bot_com_o )
% 0.24/0.47 => ( ( F_36 @ ( F_35 @ ( semila1562558655_com_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila513601829_com_o @ A_127 @ B_80 ) ) )
% 0.24/0.47 = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_781_folding__one_Ounion__disjoint,axiom,
% 0.24/0.47 ! [B_79: ( pname > $o ) > $o,A_126: ( pname > $o ) > $o,F_34: ( pname > $o ) > ( pname > $o ) > pname > $o,F_33: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.47 ( ( finite349908348name_o @ F_34 @ F_33 )
% 0.24/0.47 => ( ( finite297249702name_o @ A_126 )
% 0.24/0.47 => ( ( A_126 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ( finite297249702name_o @ B_79 )
% 0.24/0.47 => ( ( B_79 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ( ( semila2013987940me_o_o @ A_126 @ B_79 )
% 0.24/0.47 = bot_bot_pname_o_o )
% 0.24/0.47 => ( ( F_33 @ ( semila181081674me_o_o @ A_126 @ B_79 ) )
% 0.24/0.47 = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_782_folding__one_Ounion__disjoint,axiom,
% 0.24/0.47 ! [B_79: ( hoare_1708887482_state > $o ) > $o,A_126: ( hoare_1708887482_state > $o ) > $o,F_34: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_33: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite928843026tate_o @ F_34 @ F_33 )
% 0.24/0.47 => ( ( finite1329924456tate_o @ A_126 )
% 0.24/0.47 => ( ( A_126 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( finite1329924456tate_o @ B_79 )
% 0.24/0.47 => ( ( B_79 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( ( semila598060698te_o_o @ A_126 @ B_79 )
% 0.24/0.47 = bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( F_33 @ ( semila1853742644te_o_o @ A_126 @ B_79 ) )
% 0.24/0.47 = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_783_folding__one_Ounion__disjoint,axiom,
% 0.24/0.47 ! [B_79: pname > $o,A_126: pname > $o,F_34: pname > pname > pname,F_33: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite1282449217_pname @ F_34 @ F_33 )
% 0.24/0.47 => ( ( finite_finite_pname @ A_126 )
% 0.24/0.47 => ( ( A_126 != bot_bot_pname_o )
% 0.24/0.47 => ( ( finite_finite_pname @ B_79 )
% 0.24/0.47 => ( ( B_79 != bot_bot_pname_o )
% 0.24/0.47 => ( ( ( semila1673364395name_o @ A_126 @ B_79 )
% 0.24/0.47 = bot_bot_pname_o )
% 0.24/0.47 => ( ( F_33 @ ( semila1780557381name_o @ A_126 @ B_79 ) )
% 0.24/0.47 = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_784_folding__one_Ounion__disjoint,axiom,
% 0.24/0.47 ! [B_79: hoare_1708887482_state > $o,A_126: hoare_1708887482_state > $o,F_34: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_33: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1615457021_state @ F_34 @ F_33 )
% 0.24/0.47 => ( ( finite1625599783_state @ A_126 )
% 0.24/0.47 => ( ( A_126 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ( finite1625599783_state @ B_79 )
% 0.24/0.47 => ( ( B_79 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ( ( semila129691299tate_o @ A_126 @ B_79 )
% 0.24/0.47 = bot_bo19817387tate_o )
% 0.24/0.47 => ( ( F_33 @ ( semila1122118281tate_o @ A_126 @ B_79 ) )
% 0.24/0.47 = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_785_folding__one_Ounion__disjoint,axiom,
% 0.24/0.47 ! [B_79: com > $o,A_126: com > $o,F_34: com > com > com,F_33: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite860057415ne_com @ F_34 @ F_33 )
% 0.24/0.47 => ( ( finite_finite_com @ A_126 )
% 0.24/0.47 => ( ( A_126 != bot_bot_com_o )
% 0.24/0.47 => ( ( finite_finite_com @ B_79 )
% 0.24/0.47 => ( ( B_79 != bot_bot_com_o )
% 0.24/0.47 => ( ( ( semila513601829_com_o @ A_126 @ B_79 )
% 0.24/0.47 = bot_bot_com_o )
% 0.24/0.47 => ( ( F_33 @ ( semila1562558655_com_o @ A_126 @ B_79 ) )
% 0.24/0.47 = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_786_folding__one_Oinsert__remove,axiom,
% 0.24/0.47 ! [X_47: com,A_125: com > $o,F_32: com > com > com,F_31: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite860057415ne_com @ F_32 @ F_31 )
% 0.24/0.47 => ( ( finite_finite_com @ A_125 )
% 0.24/0.47 => ( ( ( ( minus_minus_com_o @ A_125 @ ( insert_com @ X_47 @ bot_bot_com_o ) )
% 0.24/0.47 = bot_bot_com_o )
% 0.24/0.47 => ( ( F_31 @ ( insert_com @ X_47 @ A_125 ) )
% 0.24/0.47 = X_47 ) )
% 0.24/0.47 & ( ( ( minus_minus_com_o @ A_125 @ ( insert_com @ X_47 @ bot_bot_com_o ) )
% 0.24/0.47 != bot_bot_com_o )
% 0.24/0.47 => ( ( F_31 @ ( insert_com @ X_47 @ A_125 ) )
% 0.24/0.47 = ( F_32 @ X_47 @ ( F_31 @ ( minus_minus_com_o @ A_125 @ ( insert_com @ X_47 @ bot_bot_com_o ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_787_folding__one_Oinsert__remove,axiom,
% 0.24/0.47 ! [X_47: pname,A_125: pname > $o,F_32: pname > pname > pname,F_31: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite1282449217_pname @ F_32 @ F_31 )
% 0.24/0.47 => ( ( finite_finite_pname @ A_125 )
% 0.24/0.47 => ( ( ( ( minus_minus_pname_o @ A_125 @ ( insert_pname @ X_47 @ bot_bot_pname_o ) )
% 0.24/0.47 = bot_bot_pname_o )
% 0.24/0.47 => ( ( F_31 @ ( insert_pname @ X_47 @ A_125 ) )
% 0.24/0.47 = X_47 ) )
% 0.24/0.47 & ( ( ( minus_minus_pname_o @ A_125 @ ( insert_pname @ X_47 @ bot_bot_pname_o ) )
% 0.24/0.47 != bot_bot_pname_o )
% 0.24/0.47 => ( ( F_31 @ ( insert_pname @ X_47 @ A_125 ) )
% 0.24/0.47 = ( F_32 @ X_47 @ ( F_31 @ ( minus_minus_pname_o @ A_125 @ ( insert_pname @ X_47 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_788_folding__one_Oinsert__remove,axiom,
% 0.24/0.47 ! [X_47: hoare_1708887482_state,A_125: hoare_1708887482_state > $o,F_32: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_31: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1615457021_state @ F_32 @ F_31 )
% 0.24/0.47 => ( ( finite1625599783_state @ A_125 )
% 0.24/0.47 => ( ( ( ( minus_2056855718tate_o @ A_125 @ ( insert528405184_state @ X_47 @ bot_bo19817387tate_o ) )
% 0.24/0.47 = bot_bo19817387tate_o )
% 0.24/0.47 => ( ( F_31 @ ( insert528405184_state @ X_47 @ A_125 ) )
% 0.24/0.47 = X_47 ) )
% 0.24/0.47 & ( ( ( minus_2056855718tate_o @ A_125 @ ( insert528405184_state @ X_47 @ bot_bo19817387tate_o ) )
% 0.24/0.47 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ( F_31 @ ( insert528405184_state @ X_47 @ A_125 ) )
% 0.24/0.47 = ( F_32 @ X_47 @ ( F_31 @ ( minus_2056855718tate_o @ A_125 @ ( insert528405184_state @ X_47 @ bot_bo19817387tate_o ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_789_folding__one_Oinsert__remove,axiom,
% 0.24/0.47 ! [X_47: pname > $o,A_125: ( pname > $o ) > $o,F_32: ( pname > $o ) > ( pname > $o ) > pname > $o,F_31: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.47 ( ( finite349908348name_o @ F_32 @ F_31 )
% 0.24/0.47 => ( ( finite297249702name_o @ A_125 )
% 0.24/0.47 => ( ( ( ( minus_1480864103me_o_o @ A_125 @ ( insert_pname_o @ X_47 @ bot_bot_pname_o_o ) )
% 0.24/0.47 = bot_bot_pname_o_o )
% 0.24/0.47 => ( ( F_31 @ ( insert_pname_o @ X_47 @ A_125 ) )
% 0.24/0.47 = X_47 ) )
% 0.24/0.47 & ( ( ( minus_1480864103me_o_o @ A_125 @ ( insert_pname_o @ X_47 @ bot_bot_pname_o_o ) )
% 0.24/0.47 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ( F_31 @ ( insert_pname_o @ X_47 @ A_125 ) )
% 0.24/0.47 = ( F_32 @ X_47 @ ( F_31 @ ( minus_1480864103me_o_o @ A_125 @ ( insert_pname_o @ X_47 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_790_folding__one_Oinsert__remove,axiom,
% 0.24/0.47 ! [X_47: hoare_1708887482_state > $o,A_125: ( hoare_1708887482_state > $o ) > $o,F_32: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_31: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite928843026tate_o @ F_32 @ F_31 )
% 0.24/0.47 => ( ( finite1329924456tate_o @ A_125 )
% 0.24/0.47 => ( ( ( ( minus_548038231te_o_o @ A_125 @ ( insert949073679tate_o @ X_47 @ bot_bo1678742418te_o_o ) )
% 0.24/0.47 = bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( F_31 @ ( insert949073679tate_o @ X_47 @ A_125 ) )
% 0.24/0.47 = X_47 ) )
% 0.24/0.47 & ( ( ( minus_548038231te_o_o @ A_125 @ ( insert949073679tate_o @ X_47 @ bot_bo1678742418te_o_o ) )
% 0.24/0.47 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( F_31 @ ( insert949073679tate_o @ X_47 @ A_125 ) )
% 0.24/0.47 = ( F_32 @ X_47 @ ( F_31 @ ( minus_548038231te_o_o @ A_125 @ ( insert949073679tate_o @ X_47 @ bot_bo1678742418te_o_o ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_791_folding__one_Oremove,axiom,
% 0.24/0.47 ! [X_46: com,A_124: com > $o,F_30: com > com > com,F_29: ( com > $o ) > com] :
% 0.24/0.47 ( ( finite860057415ne_com @ F_30 @ F_29 )
% 0.24/0.47 => ( ( finite_finite_com @ A_124 )
% 0.24/0.47 => ( ( member_com @ X_46 @ A_124 )
% 0.24/0.47 => ( ( ( ( minus_minus_com_o @ A_124 @ ( insert_com @ X_46 @ bot_bot_com_o ) )
% 0.24/0.47 = bot_bot_com_o )
% 0.24/0.47 => ( ( F_29 @ A_124 )
% 0.24/0.47 = X_46 ) )
% 0.24/0.47 & ( ( ( minus_minus_com_o @ A_124 @ ( insert_com @ X_46 @ bot_bot_com_o ) )
% 0.24/0.47 != bot_bot_com_o )
% 0.24/0.47 => ( ( F_29 @ A_124 )
% 0.24/0.47 = ( F_30 @ X_46 @ ( F_29 @ ( minus_minus_com_o @ A_124 @ ( insert_com @ X_46 @ bot_bot_com_o ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_792_folding__one_Oremove,axiom,
% 0.24/0.47 ! [X_46: pname,A_124: pname > $o,F_30: pname > pname > pname,F_29: ( pname > $o ) > pname] :
% 0.24/0.47 ( ( finite1282449217_pname @ F_30 @ F_29 )
% 0.24/0.47 => ( ( finite_finite_pname @ A_124 )
% 0.24/0.47 => ( ( member_pname @ X_46 @ A_124 )
% 0.24/0.47 => ( ( ( ( minus_minus_pname_o @ A_124 @ ( insert_pname @ X_46 @ bot_bot_pname_o ) )
% 0.24/0.47 = bot_bot_pname_o )
% 0.24/0.47 => ( ( F_29 @ A_124 )
% 0.24/0.47 = X_46 ) )
% 0.24/0.47 & ( ( ( minus_minus_pname_o @ A_124 @ ( insert_pname @ X_46 @ bot_bot_pname_o ) )
% 0.24/0.47 != bot_bot_pname_o )
% 0.24/0.47 => ( ( F_29 @ A_124 )
% 0.24/0.47 = ( F_30 @ X_46 @ ( F_29 @ ( minus_minus_pname_o @ A_124 @ ( insert_pname @ X_46 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_793_folding__one_Oremove,axiom,
% 0.24/0.47 ! [X_46: hoare_1708887482_state,A_124: hoare_1708887482_state > $o,F_30: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_29: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.47 ( ( finite1615457021_state @ F_30 @ F_29 )
% 0.24/0.47 => ( ( finite1625599783_state @ A_124 )
% 0.24/0.47 => ( ( member451959335_state @ X_46 @ A_124 )
% 0.24/0.47 => ( ( ( ( minus_2056855718tate_o @ A_124 @ ( insert528405184_state @ X_46 @ bot_bo19817387tate_o ) )
% 0.24/0.47 = bot_bo19817387tate_o )
% 0.24/0.47 => ( ( F_29 @ A_124 )
% 0.24/0.47 = X_46 ) )
% 0.24/0.47 & ( ( ( minus_2056855718tate_o @ A_124 @ ( insert528405184_state @ X_46 @ bot_bo19817387tate_o ) )
% 0.24/0.47 != bot_bo19817387tate_o )
% 0.24/0.47 => ( ( F_29 @ A_124 )
% 0.24/0.47 = ( F_30 @ X_46 @ ( F_29 @ ( minus_2056855718tate_o @ A_124 @ ( insert528405184_state @ X_46 @ bot_bo19817387tate_o ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_794_folding__one_Oremove,axiom,
% 0.24/0.47 ! [X_46: pname > $o,A_124: ( pname > $o ) > $o,F_30: ( pname > $o ) > ( pname > $o ) > pname > $o,F_29: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.47 ( ( finite349908348name_o @ F_30 @ F_29 )
% 0.24/0.47 => ( ( finite297249702name_o @ A_124 )
% 0.24/0.47 => ( ( member_pname_o @ X_46 @ A_124 )
% 0.24/0.47 => ( ( ( ( minus_1480864103me_o_o @ A_124 @ ( insert_pname_o @ X_46 @ bot_bot_pname_o_o ) )
% 0.24/0.47 = bot_bot_pname_o_o )
% 0.24/0.47 => ( ( F_29 @ A_124 )
% 0.24/0.47 = X_46 ) )
% 0.24/0.47 & ( ( ( minus_1480864103me_o_o @ A_124 @ ( insert_pname_o @ X_46 @ bot_bot_pname_o_o ) )
% 0.24/0.47 != bot_bot_pname_o_o )
% 0.24/0.47 => ( ( F_29 @ A_124 )
% 0.24/0.47 = ( F_30 @ X_46 @ ( F_29 @ ( minus_1480864103me_o_o @ A_124 @ ( insert_pname_o @ X_46 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_795_folding__one_Oremove,axiom,
% 0.24/0.47 ! [X_46: hoare_1708887482_state > $o,A_124: ( hoare_1708887482_state > $o ) > $o,F_30: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_29: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite928843026tate_o @ F_30 @ F_29 )
% 0.24/0.47 => ( ( finite1329924456tate_o @ A_124 )
% 0.24/0.47 => ( ( member814030440tate_o @ X_46 @ A_124 )
% 0.24/0.47 => ( ( ( ( minus_548038231te_o_o @ A_124 @ ( insert949073679tate_o @ X_46 @ bot_bo1678742418te_o_o ) )
% 0.24/0.47 = bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( F_29 @ A_124 )
% 0.24/0.47 = X_46 ) )
% 0.24/0.47 & ( ( ( minus_548038231te_o_o @ A_124 @ ( insert949073679tate_o @ X_46 @ bot_bo1678742418te_o_o ) )
% 0.24/0.47 != bot_bo1678742418te_o_o )
% 0.24/0.47 => ( ( F_29 @ A_124 )
% 0.24/0.47 = ( F_30 @ X_46 @ ( F_29 @ ( minus_548038231te_o_o @ A_124 @ ( insert949073679tate_o @ X_46 @ bot_bo1678742418te_o_o ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_796_is__none__code_I2_J,axiom,
% 0.24/0.47 ! [X_45: pname] :
% 0.24/0.47 ~ ( is_none_pname @ ( some_pname @ X_45 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_797_is__none__code_I2_J,axiom,
% 0.24/0.47 ! [X_45: hoare_1708887482_state] :
% 0.24/0.47 ~ ( is_non163157940_state @ ( some_H1974565227_state @ X_45 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_798_is__none__code_I2_J,axiom,
% 0.24/0.47 ! [X_45: com] :
% 0.24/0.47 ~ ( is_none_com @ ( some_com @ X_45 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_799_conseq,axiom,
% 0.24/0.47 ! [Q_2: state > state > $o,G_6: hoare_1708887482_state > $o,C_32: com,P_7: state > state > $o] :
% 0.24/0.47 ( ! [Z_11: state,S_2: state] :
% 0.24/0.47 ( ( P_7 @ Z_11 @ S_2 )
% 0.24/0.47 => ? [P_8: state > state > $o,Q_3: state > state > $o] :
% 0.24/0.47 ( ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ P_8 @ C_32 @ Q_3 ) @ bot_bo19817387tate_o ) )
% 0.24/0.47 & ! [S_3: state] :
% 0.24/0.47 ( ! [Z_12: state] :
% 0.24/0.47 ( ( P_8 @ Z_12 @ S_2 )
% 0.24/0.47 => ( Q_3 @ Z_12 @ S_3 ) )
% 0.24/0.47 => ( Q_2 @ Z_11 @ S_3 ) ) ) )
% 0.24/0.47 => ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ P_7 @ C_32 @ Q_2 ) @ bot_bo19817387tate_o ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_800_IntE,axiom,
% 0.24/0.47 ! [C_31: com,A_123: com > $o,B_78: com > $o] :
% 0.24/0.47 ( ( member_com @ C_31 @ ( semila513601829_com_o @ A_123 @ B_78 ) )
% 0.24/0.47 => ~ ( ( member_com @ C_31 @ A_123 )
% 0.24/0.47 => ~ ( member_com @ C_31 @ B_78 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_801_IntE,axiom,
% 0.24/0.47 ! [C_31: pname,A_123: pname > $o,B_78: pname > $o] :
% 0.24/0.47 ( ( member_pname @ C_31 @ ( semila1673364395name_o @ A_123 @ B_78 ) )
% 0.24/0.47 => ~ ( ( member_pname @ C_31 @ A_123 )
% 0.24/0.47 => ~ ( member_pname @ C_31 @ B_78 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_802_IntE,axiom,
% 0.24/0.47 ! [C_31: hoare_1708887482_state,A_123: hoare_1708887482_state > $o,B_78: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ C_31 @ ( semila129691299tate_o @ A_123 @ B_78 ) )
% 0.24/0.47 => ~ ( ( member451959335_state @ C_31 @ A_123 )
% 0.24/0.47 => ~ ( member451959335_state @ C_31 @ B_78 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_803_IntI,axiom,
% 0.24/0.47 ! [B_77: com > $o,C_30: com,A_122: com > $o] :
% 0.24/0.47 ( ( member_com @ C_30 @ A_122 )
% 0.24/0.47 => ( ( member_com @ C_30 @ B_77 )
% 0.24/0.47 => ( member_com @ C_30 @ ( semila513601829_com_o @ A_122 @ B_77 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_804_IntI,axiom,
% 0.24/0.47 ! [B_77: pname > $o,C_30: pname,A_122: pname > $o] :
% 0.24/0.47 ( ( member_pname @ C_30 @ A_122 )
% 0.24/0.47 => ( ( member_pname @ C_30 @ B_77 )
% 0.24/0.47 => ( member_pname @ C_30 @ ( semila1673364395name_o @ A_122 @ B_77 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_805_IntI,axiom,
% 0.24/0.47 ! [B_77: hoare_1708887482_state > $o,C_30: hoare_1708887482_state,A_122: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ C_30 @ A_122 )
% 0.24/0.47 => ( ( member451959335_state @ C_30 @ B_77 )
% 0.24/0.47 => ( member451959335_state @ C_30 @ ( semila129691299tate_o @ A_122 @ B_77 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_806_DiffE,axiom,
% 0.24/0.47 ! [C_29: com,A_121: com > $o,B_76: com > $o] :
% 0.24/0.47 ( ( member_com @ C_29 @ ( minus_minus_com_o @ A_121 @ B_76 ) )
% 0.24/0.47 => ~ ( ( member_com @ C_29 @ A_121 )
% 0.24/0.47 => ( member_com @ C_29 @ B_76 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_807_DiffE,axiom,
% 0.24/0.47 ! [C_29: pname,A_121: pname > $o,B_76: pname > $o] :
% 0.24/0.47 ( ( member_pname @ C_29 @ ( minus_minus_pname_o @ A_121 @ B_76 ) )
% 0.24/0.47 => ~ ( ( member_pname @ C_29 @ A_121 )
% 0.24/0.47 => ( member_pname @ C_29 @ B_76 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_808_DiffE,axiom,
% 0.24/0.47 ! [C_29: hoare_1708887482_state,A_121: hoare_1708887482_state > $o,B_76: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ C_29 @ ( minus_2056855718tate_o @ A_121 @ B_76 ) )
% 0.24/0.47 => ~ ( ( member451959335_state @ C_29 @ A_121 )
% 0.24/0.47 => ( member451959335_state @ C_29 @ B_76 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_809_DiffI,axiom,
% 0.24/0.47 ! [B_75: com > $o,C_28: com,A_120: com > $o] :
% 0.24/0.47 ( ( member_com @ C_28 @ A_120 )
% 0.24/0.47 => ( ~ ( member_com @ C_28 @ B_75 )
% 0.24/0.47 => ( member_com @ C_28 @ ( minus_minus_com_o @ A_120 @ B_75 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_810_DiffI,axiom,
% 0.24/0.47 ! [B_75: pname > $o,C_28: pname,A_120: pname > $o] :
% 0.24/0.47 ( ( member_pname @ C_28 @ A_120 )
% 0.24/0.47 => ( ~ ( member_pname @ C_28 @ B_75 )
% 0.24/0.47 => ( member_pname @ C_28 @ ( minus_minus_pname_o @ A_120 @ B_75 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_811_DiffI,axiom,
% 0.24/0.47 ! [B_75: hoare_1708887482_state > $o,C_28: hoare_1708887482_state,A_120: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ C_28 @ A_120 )
% 0.24/0.47 => ( ~ ( member451959335_state @ C_28 @ B_75 )
% 0.24/0.47 => ( member451959335_state @ C_28 @ ( minus_2056855718tate_o @ A_120 @ B_75 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_812_finite__Int,axiom,
% 0.24/0.47 ! [G_5: ( pname > $o ) > $o,F_28: ( pname > $o ) > $o] :
% 0.24/0.47 ( ( ( finite297249702name_o @ F_28 )
% 0.24/0.47 | ( finite297249702name_o @ G_5 ) )
% 0.24/0.47 => ( finite297249702name_o @ ( semila2013987940me_o_o @ F_28 @ G_5 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_813_finite__Int,axiom,
% 0.24/0.47 ! [G_5: ( hoare_1708887482_state > $o ) > $o,F_28: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.47 ( ( ( finite1329924456tate_o @ F_28 )
% 0.24/0.47 | ( finite1329924456tate_o @ G_5 ) )
% 0.24/0.47 => ( finite1329924456tate_o @ ( semila598060698te_o_o @ F_28 @ G_5 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_814_finite__Int,axiom,
% 0.24/0.47 ! [G_5: pname > $o,F_28: pname > $o] :
% 0.24/0.47 ( ( ( finite_finite_pname @ F_28 )
% 0.24/0.47 | ( finite_finite_pname @ G_5 ) )
% 0.24/0.47 => ( finite_finite_pname @ ( semila1673364395name_o @ F_28 @ G_5 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_815_finite__Int,axiom,
% 0.24/0.47 ! [G_5: hoare_1708887482_state > $o,F_28: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ( finite1625599783_state @ F_28 )
% 0.24/0.47 | ( finite1625599783_state @ G_5 ) )
% 0.24/0.47 => ( finite1625599783_state @ ( semila129691299tate_o @ F_28 @ G_5 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_816_finite__Diff,axiom,
% 0.24/0.47 ! [B_74: ( pname > $o ) > $o,A_119: ( pname > $o ) > $o] :
% 0.24/0.47 ( ( finite297249702name_o @ A_119 )
% 0.24/0.47 => ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_119 @ B_74 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_817_finite__Diff,axiom,
% 0.24/0.47 ! [B_74: ( hoare_1708887482_state > $o ) > $o,A_119: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.47 ( ( finite1329924456tate_o @ A_119 )
% 0.24/0.47 => ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_119 @ B_74 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_818_finite__Diff,axiom,
% 0.24/0.47 ! [B_74: pname > $o,A_119: pname > $o] :
% 0.24/0.47 ( ( finite_finite_pname @ A_119 )
% 0.24/0.47 => ( finite_finite_pname @ ( minus_minus_pname_o @ A_119 @ B_74 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_819_finite__Diff,axiom,
% 0.24/0.47 ! [B_74: hoare_1708887482_state > $o,A_119: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( finite1625599783_state @ A_119 )
% 0.24/0.47 => ( finite1625599783_state @ ( minus_2056855718tate_o @ A_119 @ B_74 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_820_inf__Int__eq,axiom,
% 0.24/0.47 ! [R: com > $o,S_1: com > $o,X_3: com] :
% 0.24/0.47 ( ( semila513601829_com_o
% 0.24/0.47 @ ^ [Y_4: com] : ( member_com @ Y_4 @ R )
% 0.24/0.47 @ ^ [Y_4: com] : ( member_com @ Y_4 @ S_1 )
% 0.24/0.47 @ X_3 )
% 0.24/0.47 <=> ( member_com @ X_3 @ ( semila513601829_com_o @ R @ S_1 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_821_inf__Int__eq,axiom,
% 0.24/0.47 ! [R: pname > $o,S_1: pname > $o,X_3: pname] :
% 0.24/0.47 ( ( semila1673364395name_o
% 0.24/0.47 @ ^ [Y_4: pname] : ( member_pname @ Y_4 @ R )
% 0.24/0.47 @ ^ [Y_4: pname] : ( member_pname @ Y_4 @ S_1 )
% 0.24/0.47 @ X_3 )
% 0.24/0.47 <=> ( member_pname @ X_3 @ ( semila1673364395name_o @ R @ S_1 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_822_inf__Int__eq,axiom,
% 0.24/0.47 ! [R: hoare_1708887482_state > $o,S_1: hoare_1708887482_state > $o,X_3: hoare_1708887482_state] :
% 0.24/0.47 ( ( semila129691299tate_o
% 0.24/0.47 @ ^ [Y_4: hoare_1708887482_state] : ( member451959335_state @ Y_4 @ R )
% 0.24/0.47 @ ^ [Y_4: hoare_1708887482_state] : ( member451959335_state @ Y_4 @ S_1 )
% 0.24/0.47 @ X_3 )
% 0.24/0.47 <=> ( member451959335_state @ X_3 @ ( semila129691299tate_o @ R @ S_1 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_823_Diff__disjoint,axiom,
% 0.24/0.47 ! [A_118: com > $o,B_73: com > $o] :
% 0.24/0.47 ( ( semila513601829_com_o @ A_118 @ ( minus_minus_com_o @ B_73 @ A_118 ) )
% 0.24/0.47 = bot_bot_com_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_824_Diff__disjoint,axiom,
% 0.24/0.47 ! [A_118: pname > $o,B_73: pname > $o] :
% 0.24/0.47 ( ( semila1673364395name_o @ A_118 @ ( minus_minus_pname_o @ B_73 @ A_118 ) )
% 0.24/0.47 = bot_bot_pname_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_825_Diff__disjoint,axiom,
% 0.24/0.47 ! [A_118: hoare_1708887482_state > $o,B_73: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila129691299tate_o @ A_118 @ ( minus_2056855718tate_o @ B_73 @ A_118 ) )
% 0.24/0.47 = bot_bo19817387tate_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_826_Diff__triv,axiom,
% 0.24/0.47 ! [A_117: com > $o,B_72: com > $o] :
% 0.24/0.47 ( ( ( semila513601829_com_o @ A_117 @ B_72 )
% 0.24/0.47 = bot_bot_com_o )
% 0.24/0.47 => ( ( minus_minus_com_o @ A_117 @ B_72 )
% 0.24/0.47 = A_117 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_827_Diff__triv,axiom,
% 0.24/0.47 ! [A_117: pname > $o,B_72: pname > $o] :
% 0.24/0.47 ( ( ( semila1673364395name_o @ A_117 @ B_72 )
% 0.24/0.47 = bot_bot_pname_o )
% 0.24/0.47 => ( ( minus_minus_pname_o @ A_117 @ B_72 )
% 0.24/0.47 = A_117 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_828_Diff__triv,axiom,
% 0.24/0.47 ! [A_117: hoare_1708887482_state > $o,B_72: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ( semila129691299tate_o @ A_117 @ B_72 )
% 0.24/0.47 = bot_bo19817387tate_o )
% 0.24/0.47 => ( ( minus_2056855718tate_o @ A_117 @ B_72 )
% 0.24/0.47 = A_117 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_829_DiffD2,axiom,
% 0.24/0.47 ! [C_27: com,A_116: com > $o,B_71: com > $o] :
% 0.24/0.47 ( ( member_com @ C_27 @ ( minus_minus_com_o @ A_116 @ B_71 ) )
% 0.24/0.47 => ~ ( member_com @ C_27 @ B_71 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_830_DiffD2,axiom,
% 0.24/0.47 ! [C_27: pname,A_116: pname > $o,B_71: pname > $o] :
% 0.24/0.47 ( ( member_pname @ C_27 @ ( minus_minus_pname_o @ A_116 @ B_71 ) )
% 0.24/0.47 => ~ ( member_pname @ C_27 @ B_71 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_831_DiffD2,axiom,
% 0.24/0.47 ! [C_27: hoare_1708887482_state,A_116: hoare_1708887482_state > $o,B_71: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ C_27 @ ( minus_2056855718tate_o @ A_116 @ B_71 ) )
% 0.24/0.47 => ~ ( member451959335_state @ C_27 @ B_71 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_832_IntD2,axiom,
% 0.24/0.47 ! [C_26: com,A_115: com > $o,B_70: com > $o] :
% 0.24/0.47 ( ( member_com @ C_26 @ ( semila513601829_com_o @ A_115 @ B_70 ) )
% 0.24/0.47 => ( member_com @ C_26 @ B_70 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_833_IntD2,axiom,
% 0.24/0.47 ! [C_26: pname,A_115: pname > $o,B_70: pname > $o] :
% 0.24/0.47 ( ( member_pname @ C_26 @ ( semila1673364395name_o @ A_115 @ B_70 ) )
% 0.24/0.47 => ( member_pname @ C_26 @ B_70 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_834_IntD2,axiom,
% 0.24/0.47 ! [C_26: hoare_1708887482_state,A_115: hoare_1708887482_state > $o,B_70: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ C_26 @ ( semila129691299tate_o @ A_115 @ B_70 ) )
% 0.24/0.47 => ( member451959335_state @ C_26 @ B_70 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_835_IntD1,axiom,
% 0.24/0.47 ! [C_25: com,A_114: com > $o,B_69: com > $o] :
% 0.24/0.47 ( ( member_com @ C_25 @ ( semila513601829_com_o @ A_114 @ B_69 ) )
% 0.24/0.47 => ( member_com @ C_25 @ A_114 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_836_IntD1,axiom,
% 0.24/0.47 ! [C_25: pname,A_114: pname > $o,B_69: pname > $o] :
% 0.24/0.47 ( ( member_pname @ C_25 @ ( semila1673364395name_o @ A_114 @ B_69 ) )
% 0.24/0.47 => ( member_pname @ C_25 @ A_114 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_837_IntD1,axiom,
% 0.24/0.47 ! [C_25: hoare_1708887482_state,A_114: hoare_1708887482_state > $o,B_69: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ C_25 @ ( semila129691299tate_o @ A_114 @ B_69 ) )
% 0.24/0.47 => ( member451959335_state @ C_25 @ A_114 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_838_DiffD1,axiom,
% 0.24/0.47 ! [C_24: com,A_113: com > $o,B_68: com > $o] :
% 0.24/0.47 ( ( member_com @ C_24 @ ( minus_minus_com_o @ A_113 @ B_68 ) )
% 0.24/0.47 => ( member_com @ C_24 @ A_113 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_839_DiffD1,axiom,
% 0.24/0.47 ! [C_24: pname,A_113: pname > $o,B_68: pname > $o] :
% 0.24/0.47 ( ( member_pname @ C_24 @ ( minus_minus_pname_o @ A_113 @ B_68 ) )
% 0.24/0.47 => ( member_pname @ C_24 @ A_113 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_840_DiffD1,axiom,
% 0.24/0.47 ! [C_24: hoare_1708887482_state,A_113: hoare_1708887482_state > $o,B_68: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ C_24 @ ( minus_2056855718tate_o @ A_113 @ B_68 ) )
% 0.24/0.47 => ( member451959335_state @ C_24 @ A_113 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_841_Int__iff,axiom,
% 0.24/0.47 ! [C_23: com,A_112: com > $o,B_67: com > $o] :
% 0.24/0.47 ( ( member_com @ C_23 @ ( semila513601829_com_o @ A_112 @ B_67 ) )
% 0.24/0.47 <=> ( ( member_com @ C_23 @ A_112 )
% 0.24/0.47 & ( member_com @ C_23 @ B_67 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_842_Int__iff,axiom,
% 0.24/0.47 ! [C_23: pname,A_112: pname > $o,B_67: pname > $o] :
% 0.24/0.47 ( ( member_pname @ C_23 @ ( semila1673364395name_o @ A_112 @ B_67 ) )
% 0.24/0.47 <=> ( ( member_pname @ C_23 @ A_112 )
% 0.24/0.47 & ( member_pname @ C_23 @ B_67 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_843_Int__iff,axiom,
% 0.24/0.47 ! [C_23: hoare_1708887482_state,A_112: hoare_1708887482_state > $o,B_67: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ C_23 @ ( semila129691299tate_o @ A_112 @ B_67 ) )
% 0.24/0.47 <=> ( ( member451959335_state @ C_23 @ A_112 )
% 0.24/0.47 & ( member451959335_state @ C_23 @ B_67 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_844_Diff__iff,axiom,
% 0.24/0.47 ! [C_22: com,A_111: com > $o,B_66: com > $o] :
% 0.24/0.47 ( ( member_com @ C_22 @ ( minus_minus_com_o @ A_111 @ B_66 ) )
% 0.24/0.47 <=> ( ( member_com @ C_22 @ A_111 )
% 0.24/0.47 & ~ ( member_com @ C_22 @ B_66 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_845_Diff__iff,axiom,
% 0.24/0.47 ! [C_22: pname,A_111: pname > $o,B_66: pname > $o] :
% 0.24/0.47 ( ( member_pname @ C_22 @ ( minus_minus_pname_o @ A_111 @ B_66 ) )
% 0.24/0.47 <=> ( ( member_pname @ C_22 @ A_111 )
% 0.24/0.47 & ~ ( member_pname @ C_22 @ B_66 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_846_Diff__iff,axiom,
% 0.24/0.47 ! [C_22: hoare_1708887482_state,A_111: hoare_1708887482_state > $o,B_66: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ C_22 @ ( minus_2056855718tate_o @ A_111 @ B_66 ) )
% 0.24/0.47 <=> ( ( member451959335_state @ C_22 @ A_111 )
% 0.24/0.47 & ~ ( member451959335_state @ C_22 @ B_66 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_847_Int__def,axiom,
% 0.24/0.47 ! [A_110: com > $o,B_65: com > $o] :
% 0.24/0.47 ( ( semila513601829_com_o @ A_110 @ B_65 )
% 0.24/0.47 = ( collect_com
% 0.24/0.47 @ ^ [X_3: com] : ( (&) @ ( member_com @ X_3 @ A_110 ) @ ( member_com @ X_3 @ B_65 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_848_Int__def,axiom,
% 0.24/0.47 ! [A_110: pname > $o,B_65: pname > $o] :
% 0.24/0.47 ( ( semila1673364395name_o @ A_110 @ B_65 )
% 0.24/0.47 = ( collect_pname
% 0.24/0.47 @ ^ [X_3: pname] : ( (&) @ ( member_pname @ X_3 @ A_110 ) @ ( member_pname @ X_3 @ B_65 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_849_Int__def,axiom,
% 0.24/0.47 ! [A_110: hoare_1708887482_state > $o,B_65: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila129691299tate_o @ A_110 @ B_65 )
% 0.24/0.47 = ( collec1568722789_state
% 0.24/0.47 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( member451959335_state @ X_3 @ A_110 ) @ ( member451959335_state @ X_3 @ B_65 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_850_Int__def,axiom,
% 0.24/0.47 ! [A_110: ( pname > $o ) > $o,B_65: ( pname > $o ) > $o] :
% 0.24/0.47 ( ( semila2013987940me_o_o @ A_110 @ B_65 )
% 0.24/0.47 = ( collect_pname_o
% 0.24/0.47 @ ^ [X_3: pname > $o] : ( (&) @ ( member_pname_o @ X_3 @ A_110 ) @ ( member_pname_o @ X_3 @ B_65 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_851_Int__def,axiom,
% 0.24/0.47 ! [A_110: ( hoare_1708887482_state > $o ) > $o,B_65: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.47 ( ( semila598060698te_o_o @ A_110 @ B_65 )
% 0.24/0.47 = ( collec219771562tate_o
% 0.24/0.47 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( member814030440tate_o @ X_3 @ A_110 ) @ ( member814030440tate_o @ X_3 @ B_65 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_852_set__diff__eq,axiom,
% 0.24/0.47 ! [A_109: com > $o,B_64: com > $o] :
% 0.24/0.47 ( ( minus_minus_com_o @ A_109 @ B_64 )
% 0.24/0.47 = ( collect_com
% 0.24/0.47 @ ^ [X_3: com] : ( (&) @ ( member_com @ X_3 @ A_109 ) @ ( (~) @ ( member_com @ X_3 @ B_64 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_853_set__diff__eq,axiom,
% 0.24/0.47 ! [A_109: pname > $o,B_64: pname > $o] :
% 0.24/0.47 ( ( minus_minus_pname_o @ A_109 @ B_64 )
% 0.24/0.47 = ( collect_pname
% 0.24/0.47 @ ^ [X_3: pname] : ( (&) @ ( member_pname @ X_3 @ A_109 ) @ ( (~) @ ( member_pname @ X_3 @ B_64 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_854_set__diff__eq,axiom,
% 0.24/0.47 ! [A_109: hoare_1708887482_state > $o,B_64: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( minus_2056855718tate_o @ A_109 @ B_64 )
% 0.24/0.47 = ( collec1568722789_state
% 0.24/0.47 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( member451959335_state @ X_3 @ A_109 ) @ ( (~) @ ( member451959335_state @ X_3 @ B_64 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_855_set__diff__eq,axiom,
% 0.24/0.47 ! [A_109: ( pname > $o ) > $o,B_64: ( pname > $o ) > $o] :
% 0.24/0.47 ( ( minus_1480864103me_o_o @ A_109 @ B_64 )
% 0.24/0.47 = ( collect_pname_o
% 0.24/0.47 @ ^ [X_3: pname > $o] : ( (&) @ ( member_pname_o @ X_3 @ A_109 ) @ ( (~) @ ( member_pname_o @ X_3 @ B_64 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_856_set__diff__eq,axiom,
% 0.24/0.47 ! [A_109: ( hoare_1708887482_state > $o ) > $o,B_64: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.47 ( ( minus_548038231te_o_o @ A_109 @ B_64 )
% 0.24/0.47 = ( collec219771562tate_o
% 0.24/0.47 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( member814030440tate_o @ X_3 @ A_109 ) @ ( (~) @ ( member814030440tate_o @ X_3 @ B_64 ) ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_857_Int__Collect,axiom,
% 0.24/0.47 ! [X_44: com,A_108: com > $o,P_6: com > $o] :
% 0.24/0.47 ( ( member_com @ X_44 @ ( semila513601829_com_o @ A_108 @ ( collect_com @ P_6 ) ) )
% 0.24/0.47 <=> ( ( member_com @ X_44 @ A_108 )
% 0.24/0.47 & ( P_6 @ X_44 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_858_Int__Collect,axiom,
% 0.24/0.47 ! [X_44: pname,A_108: pname > $o,P_6: pname > $o] :
% 0.24/0.47 ( ( member_pname @ X_44 @ ( semila1673364395name_o @ A_108 @ ( collect_pname @ P_6 ) ) )
% 0.24/0.47 <=> ( ( member_pname @ X_44 @ A_108 )
% 0.24/0.47 & ( P_6 @ X_44 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_859_Int__Collect,axiom,
% 0.24/0.47 ! [X_44: hoare_1708887482_state,A_108: hoare_1708887482_state > $o,P_6: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( member451959335_state @ X_44 @ ( semila129691299tate_o @ A_108 @ ( collec1568722789_state @ P_6 ) ) )
% 0.24/0.47 <=> ( ( member451959335_state @ X_44 @ A_108 )
% 0.24/0.47 & ( P_6 @ X_44 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_860_Int__Collect,axiom,
% 0.24/0.47 ! [X_44: pname > $o,A_108: ( pname > $o ) > $o,P_6: ( pname > $o ) > $o] :
% 0.24/0.47 ( ( member_pname_o @ X_44 @ ( semila2013987940me_o_o @ A_108 @ ( collect_pname_o @ P_6 ) ) )
% 0.24/0.47 <=> ( ( member_pname_o @ X_44 @ A_108 )
% 0.24/0.47 & ( P_6 @ X_44 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_861_Int__Collect,axiom,
% 0.24/0.47 ! [X_44: hoare_1708887482_state > $o,A_108: ( hoare_1708887482_state > $o ) > $o,P_6: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.47 ( ( member814030440tate_o @ X_44 @ ( semila598060698te_o_o @ A_108 @ ( collec219771562tate_o @ P_6 ) ) )
% 0.24/0.47 <=> ( ( member814030440tate_o @ X_44 @ A_108 )
% 0.24/0.47 & ( P_6 @ X_44 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_862_Collect__conj__eq,axiom,
% 0.24/0.47 ! [P_5: hoare_1708887482_state > $o,Q_1: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( collec1568722789_state
% 0.24/0.47 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
% 0.24/0.47 = ( semila129691299tate_o @ ( collec1568722789_state @ P_5 ) @ ( collec1568722789_state @ Q_1 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_863_Collect__conj__eq,axiom,
% 0.24/0.47 ! [P_5: pname > $o,Q_1: pname > $o] :
% 0.24/0.47 ( ( collect_pname
% 0.24/0.47 @ ^ [X_3: pname] : ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
% 0.24/0.47 = ( semila1673364395name_o @ ( collect_pname @ P_5 ) @ ( collect_pname @ Q_1 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_864_Collect__conj__eq,axiom,
% 0.24/0.47 ! [P_5: ( pname > $o ) > $o,Q_1: ( pname > $o ) > $o] :
% 0.24/0.47 ( ( collect_pname_o
% 0.24/0.47 @ ^ [X_3: pname > $o] : ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
% 0.24/0.47 = ( semila2013987940me_o_o @ ( collect_pname_o @ P_5 ) @ ( collect_pname_o @ Q_1 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_865_Collect__conj__eq,axiom,
% 0.24/0.47 ! [P_5: ( hoare_1708887482_state > $o ) > $o,Q_1: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.47 ( ( collec219771562tate_o
% 0.24/0.47 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
% 0.24/0.47 = ( semila598060698te_o_o @ ( collec219771562tate_o @ P_5 ) @ ( collec219771562tate_o @ Q_1 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_866_Diff__Int,axiom,
% 0.24/0.47 ! [A_107: pname > $o,B_63: pname > $o,C_21: pname > $o] :
% 0.24/0.47 ( ( minus_minus_pname_o @ A_107 @ ( semila1673364395name_o @ B_63 @ C_21 ) )
% 0.24/0.47 = ( semila1780557381name_o @ ( minus_minus_pname_o @ A_107 @ B_63 ) @ ( minus_minus_pname_o @ A_107 @ C_21 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_867_Diff__Int,axiom,
% 0.24/0.47 ! [A_107: hoare_1708887482_state > $o,B_63: hoare_1708887482_state > $o,C_21: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( minus_2056855718tate_o @ A_107 @ ( semila129691299tate_o @ B_63 @ C_21 ) )
% 0.24/0.47 = ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A_107 @ B_63 ) @ ( minus_2056855718tate_o @ A_107 @ C_21 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_868_Diff__Un,axiom,
% 0.24/0.47 ! [A_106: pname > $o,B_62: pname > $o,C_20: pname > $o] :
% 0.24/0.47 ( ( minus_minus_pname_o @ A_106 @ ( semila1780557381name_o @ B_62 @ C_20 ) )
% 0.24/0.47 = ( semila1673364395name_o @ ( minus_minus_pname_o @ A_106 @ B_62 ) @ ( minus_minus_pname_o @ A_106 @ C_20 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_869_Diff__Un,axiom,
% 0.24/0.47 ! [A_106: hoare_1708887482_state > $o,B_62: hoare_1708887482_state > $o,C_20: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( minus_2056855718tate_o @ A_106 @ ( semila1122118281tate_o @ B_62 @ C_20 ) )
% 0.24/0.47 = ( semila129691299tate_o @ ( minus_2056855718tate_o @ A_106 @ B_62 ) @ ( minus_2056855718tate_o @ A_106 @ C_20 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_870_Un__Diff__Int,axiom,
% 0.24/0.47 ! [A_105: pname > $o,B_61: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ ( minus_minus_pname_o @ A_105 @ B_61 ) @ ( semila1673364395name_o @ A_105 @ B_61 ) )
% 0.24/0.47 = A_105 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_871_Un__Diff__Int,axiom,
% 0.24/0.47 ! [A_105: hoare_1708887482_state > $o,B_61: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A_105 @ B_61 ) @ ( semila129691299tate_o @ A_105 @ B_61 ) )
% 0.24/0.47 = A_105 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_872_inf__sup__ord_I1_J,axiom,
% 0.24/0.47 ! [X_43: $o,Y_24: $o] : ( ord_less_eq_o @ ( semila854092349_inf_o @ X_43 @ Y_24 ) @ X_43 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_873_inf__sup__ord_I1_J,axiom,
% 0.24/0.47 ! [X_43: pname > $o,Y_24: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_43 @ Y_24 ) @ X_43 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_874_inf__sup__ord_I1_J,axiom,
% 0.24/0.47 ! [X_43: hoare_1708887482_state > $o,Y_24: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_43 @ Y_24 ) @ X_43 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_875_inf__le1,axiom,
% 0.24/0.47 ! [X_42: $o,Y_23: $o] : ( ord_less_eq_o @ ( semila854092349_inf_o @ X_42 @ Y_23 ) @ X_42 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_876_inf__le1,axiom,
% 0.24/0.47 ! [X_42: pname > $o,Y_23: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_42 @ Y_23 ) @ X_42 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_877_inf__le1,axiom,
% 0.24/0.47 ! [X_42: hoare_1708887482_state > $o,Y_23: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_42 @ Y_23 ) @ X_42 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_878_inf__sup__ord_I2_J,axiom,
% 0.24/0.47 ! [X_41: $o,Y_22: $o] : ( ord_less_eq_o @ ( semila854092349_inf_o @ X_41 @ Y_22 ) @ Y_22 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_879_inf__sup__ord_I2_J,axiom,
% 0.24/0.47 ! [X_41: pname > $o,Y_22: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_41 @ Y_22 ) @ Y_22 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_880_inf__sup__ord_I2_J,axiom,
% 0.24/0.47 ! [X_41: hoare_1708887482_state > $o,Y_22: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_41 @ Y_22 ) @ Y_22 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_881_inf__le2,axiom,
% 0.24/0.47 ! [X_40: $o,Y_21: $o] : ( ord_less_eq_o @ ( semila854092349_inf_o @ X_40 @ Y_21 ) @ Y_21 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_882_inf__le2,axiom,
% 0.24/0.47 ! [X_40: pname > $o,Y_21: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_40 @ Y_21 ) @ Y_21 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_883_inf__le2,axiom,
% 0.24/0.47 ! [X_40: hoare_1708887482_state > $o,Y_21: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_40 @ Y_21 ) @ Y_21 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_884_le__iff__inf,axiom,
% 0.24/0.47 ! [X_39: $o,Y_20: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_39 @ Y_20 )
% 0.24/0.47 <=> ( ( semila854092349_inf_o @ X_39 @ Y_20 )
% 0.24/0.47 <=> X_39 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_885_le__iff__inf,axiom,
% 0.24/0.47 ! [X_39: pname > $o,Y_20: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_39 @ Y_20 )
% 0.24/0.47 <=> ( ( semila1673364395name_o @ X_39 @ Y_20 )
% 0.24/0.47 = X_39 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_886_le__iff__inf,axiom,
% 0.24/0.47 ! [X_39: hoare_1708887482_state > $o,Y_20: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_39 @ Y_20 )
% 0.24/0.47 <=> ( ( semila129691299tate_o @ X_39 @ Y_20 )
% 0.24/0.47 = X_39 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_887_le__inf__iff,axiom,
% 0.24/0.47 ! [X_38: $o,Y_19: $o,Z_10: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_38 @ ( semila854092349_inf_o @ Y_19 @ Z_10 ) )
% 0.24/0.47 <=> ( ( ord_less_eq_o @ X_38 @ Y_19 )
% 0.24/0.47 & ( ord_less_eq_o @ X_38 @ Z_10 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_888_le__inf__iff,axiom,
% 0.24/0.47 ! [X_38: pname > $o,Y_19: pname > $o,Z_10: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_38 @ ( semila1673364395name_o @ Y_19 @ Z_10 ) )
% 0.24/0.47 <=> ( ( ord_less_eq_pname_o @ X_38 @ Y_19 )
% 0.24/0.47 & ( ord_less_eq_pname_o @ X_38 @ Z_10 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_889_le__inf__iff,axiom,
% 0.24/0.47 ! [X_38: hoare_1708887482_state > $o,Y_19: hoare_1708887482_state > $o,Z_10: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_38 @ ( semila129691299tate_o @ Y_19 @ Z_10 ) )
% 0.24/0.47 <=> ( ( ord_le777019615tate_o @ X_38 @ Y_19 )
% 0.24/0.47 & ( ord_le777019615tate_o @ X_38 @ Z_10 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_890_le__infI1,axiom,
% 0.24/0.47 ! [B_60: $o,A_104: $o,X_37: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ A_104 @ X_37 )
% 0.24/0.47 => ( ord_less_eq_o @ ( semila854092349_inf_o @ A_104 @ B_60 ) @ X_37 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_891_le__infI1,axiom,
% 0.24/0.47 ! [B_60: pname > $o,A_104: pname > $o,X_37: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ A_104 @ X_37 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_104 @ B_60 ) @ X_37 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_892_le__infI1,axiom,
% 0.24/0.47 ! [B_60: hoare_1708887482_state > $o,A_104: hoare_1708887482_state > $o,X_37: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ A_104 @ X_37 )
% 0.24/0.47 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_104 @ B_60 ) @ X_37 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_893_le__infI2,axiom,
% 0.24/0.47 ! [A_103: $o,B_59: $o,X_36: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ B_59 @ X_36 )
% 0.24/0.47 => ( ord_less_eq_o @ ( semila854092349_inf_o @ A_103 @ B_59 ) @ X_36 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_894_le__infI2,axiom,
% 0.24/0.47 ! [A_103: pname > $o,B_59: pname > $o,X_36: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ B_59 @ X_36 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_103 @ B_59 ) @ X_36 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_895_le__infI2,axiom,
% 0.24/0.47 ! [A_103: hoare_1708887482_state > $o,B_59: hoare_1708887482_state > $o,X_36: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ B_59 @ X_36 )
% 0.24/0.47 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_103 @ B_59 ) @ X_36 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_896_inf__absorb1,axiom,
% 0.24/0.47 ! [X_35: $o,Y_18: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_35 @ Y_18 )
% 0.24/0.47 => ( ( semila854092349_inf_o @ X_35 @ Y_18 )
% 0.24/0.47 <=> X_35 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_897_inf__absorb1,axiom,
% 0.24/0.47 ! [X_35: pname > $o,Y_18: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_35 @ Y_18 )
% 0.24/0.47 => ( ( semila1673364395name_o @ X_35 @ Y_18 )
% 0.24/0.47 = X_35 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_898_inf__absorb1,axiom,
% 0.24/0.47 ! [X_35: hoare_1708887482_state > $o,Y_18: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_35 @ Y_18 )
% 0.24/0.47 => ( ( semila129691299tate_o @ X_35 @ Y_18 )
% 0.24/0.47 = X_35 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_899_inf__absorb2,axiom,
% 0.24/0.47 ! [Y_17: $o,X_34: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ Y_17 @ X_34 )
% 0.24/0.47 => ( ( semila854092349_inf_o @ X_34 @ Y_17 )
% 0.24/0.47 <=> Y_17 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_900_inf__absorb2,axiom,
% 0.24/0.47 ! [Y_17: pname > $o,X_34: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ Y_17 @ X_34 )
% 0.24/0.47 => ( ( semila1673364395name_o @ X_34 @ Y_17 )
% 0.24/0.47 = Y_17 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_901_inf__absorb2,axiom,
% 0.24/0.47 ! [Y_17: hoare_1708887482_state > $o,X_34: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ Y_17 @ X_34 )
% 0.24/0.47 => ( ( semila129691299tate_o @ X_34 @ Y_17 )
% 0.24/0.47 = Y_17 ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_902_le__infI,axiom,
% 0.24/0.47 ! [B_58: $o,X_33: $o,A_102: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_33 @ A_102 )
% 0.24/0.47 => ( ( ord_less_eq_o @ X_33 @ B_58 )
% 0.24/0.47 => ( ord_less_eq_o @ X_33 @ ( semila854092349_inf_o @ A_102 @ B_58 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_903_le__infI,axiom,
% 0.24/0.47 ! [B_58: pname > $o,X_33: pname > $o,A_102: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_33 @ A_102 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ X_33 @ B_58 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ X_33 @ ( semila1673364395name_o @ A_102 @ B_58 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_904_le__infI,axiom,
% 0.24/0.47 ! [B_58: hoare_1708887482_state > $o,X_33: hoare_1708887482_state > $o,A_102: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_33 @ A_102 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ X_33 @ B_58 )
% 0.24/0.47 => ( ord_le777019615tate_o @ X_33 @ ( semila129691299tate_o @ A_102 @ B_58 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_905_inf__greatest,axiom,
% 0.24/0.47 ! [Z_9: $o,X_32: $o,Y_16: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_32 @ Y_16 )
% 0.24/0.47 => ( ( ord_less_eq_o @ X_32 @ Z_9 )
% 0.24/0.47 => ( ord_less_eq_o @ X_32 @ ( semila854092349_inf_o @ Y_16 @ Z_9 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_906_inf__greatest,axiom,
% 0.24/0.47 ! [Z_9: pname > $o,X_32: pname > $o,Y_16: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_32 @ Y_16 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ X_32 @ Z_9 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ X_32 @ ( semila1673364395name_o @ Y_16 @ Z_9 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_907_inf__greatest,axiom,
% 0.24/0.47 ! [Z_9: hoare_1708887482_state > $o,X_32: hoare_1708887482_state > $o,Y_16: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_32 @ Y_16 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ X_32 @ Z_9 )
% 0.24/0.47 => ( ord_le777019615tate_o @ X_32 @ ( semila129691299tate_o @ Y_16 @ Z_9 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_908_inf__mono,axiom,
% 0.24/0.47 ! [B_57: $o,D_2: $o,A_101: $o,C_19: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ A_101 @ C_19 )
% 0.24/0.47 => ( ( ord_less_eq_o @ B_57 @ D_2 )
% 0.24/0.47 => ( ord_less_eq_o @ ( semila854092349_inf_o @ A_101 @ B_57 ) @ ( semila854092349_inf_o @ C_19 @ D_2 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_909_inf__mono,axiom,
% 0.24/0.47 ! [B_57: pname > $o,D_2: pname > $o,A_101: pname > $o,C_19: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ A_101 @ C_19 )
% 0.24/0.47 => ( ( ord_less_eq_pname_o @ B_57 @ D_2 )
% 0.24/0.47 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_101 @ B_57 ) @ ( semila1673364395name_o @ C_19 @ D_2 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_910_inf__mono,axiom,
% 0.24/0.47 ! [B_57: hoare_1708887482_state > $o,D_2: hoare_1708887482_state > $o,A_101: hoare_1708887482_state > $o,C_19: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ A_101 @ C_19 )
% 0.24/0.47 => ( ( ord_le777019615tate_o @ B_57 @ D_2 )
% 0.24/0.47 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_101 @ B_57 ) @ ( semila129691299tate_o @ C_19 @ D_2 ) ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_911_le__infE,axiom,
% 0.24/0.47 ! [X_31: $o,A_100: $o,B_56: $o] :
% 0.24/0.47 ( ( ord_less_eq_o @ X_31 @ ( semila854092349_inf_o @ A_100 @ B_56 ) )
% 0.24/0.47 => ~ ( ( ord_less_eq_o @ X_31 @ A_100 )
% 0.24/0.47 => ~ ( ord_less_eq_o @ X_31 @ B_56 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_912_le__infE,axiom,
% 0.24/0.47 ! [X_31: pname > $o,A_100: pname > $o,B_56: pname > $o] :
% 0.24/0.47 ( ( ord_less_eq_pname_o @ X_31 @ ( semila1673364395name_o @ A_100 @ B_56 ) )
% 0.24/0.47 => ~ ( ( ord_less_eq_pname_o @ X_31 @ A_100 )
% 0.24/0.47 => ~ ( ord_less_eq_pname_o @ X_31 @ B_56 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_913_le__infE,axiom,
% 0.24/0.47 ! [X_31: hoare_1708887482_state > $o,A_100: hoare_1708887482_state > $o,B_56: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( ord_le777019615tate_o @ X_31 @ ( semila129691299tate_o @ A_100 @ B_56 ) )
% 0.24/0.47 => ~ ( ( ord_le777019615tate_o @ X_31 @ A_100 )
% 0.24/0.47 => ~ ( ord_le777019615tate_o @ X_31 @ B_56 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_914_inf__bot__right,axiom,
% 0.24/0.47 ! [X_30: com > $o] :
% 0.24/0.47 ( ( semila513601829_com_o @ X_30 @ bot_bot_com_o )
% 0.24/0.47 = bot_bot_com_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_915_inf__bot__right,axiom,
% 0.24/0.47 ! [X_30: $o] :
% 0.24/0.47 ( ( semila854092349_inf_o @ X_30 @ bot_bot_o )
% 0.24/0.47 <=> bot_bot_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_916_inf__bot__right,axiom,
% 0.24/0.47 ! [X_30: pname > $o] :
% 0.24/0.47 ( ( semila1673364395name_o @ X_30 @ bot_bot_pname_o )
% 0.24/0.47 = bot_bot_pname_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_917_inf__bot__right,axiom,
% 0.24/0.47 ! [X_30: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila129691299tate_o @ X_30 @ bot_bo19817387tate_o )
% 0.24/0.47 = bot_bo19817387tate_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_918_inf__bot__left,axiom,
% 0.24/0.47 ! [X_29: com > $o] :
% 0.24/0.47 ( ( semila513601829_com_o @ bot_bot_com_o @ X_29 )
% 0.24/0.47 = bot_bot_com_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_919_inf__bot__left,axiom,
% 0.24/0.47 ! [X_29: $o] :
% 0.24/0.47 ( ( semila854092349_inf_o @ bot_bot_o @ X_29 )
% 0.24/0.47 <=> bot_bot_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_920_inf__bot__left,axiom,
% 0.24/0.47 ! [X_29: pname > $o] :
% 0.24/0.47 ( ( semila1673364395name_o @ bot_bot_pname_o @ X_29 )
% 0.24/0.47 = bot_bot_pname_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_921_inf__bot__left,axiom,
% 0.24/0.47 ! [X_29: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila129691299tate_o @ bot_bo19817387tate_o @ X_29 )
% 0.24/0.47 = bot_bo19817387tate_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_922_inf__sup__absorb,axiom,
% 0.24/0.47 ! [X_28: $o,Y_15: $o] :
% 0.24/0.47 ( ( semila854092349_inf_o @ X_28 @ ( semila10642723_sup_o @ X_28 @ Y_15 ) )
% 0.24/0.47 <=> X_28 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_923_inf__sup__absorb,axiom,
% 0.24/0.47 ! [X_28: pname > $o,Y_15: pname > $o] :
% 0.24/0.47 ( ( semila1673364395name_o @ X_28 @ ( semila1780557381name_o @ X_28 @ Y_15 ) )
% 0.24/0.47 = X_28 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_924_inf__sup__absorb,axiom,
% 0.24/0.47 ! [X_28: hoare_1708887482_state > $o,Y_15: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila129691299tate_o @ X_28 @ ( semila1122118281tate_o @ X_28 @ Y_15 ) )
% 0.24/0.47 = X_28 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_925_sup__inf__absorb,axiom,
% 0.24/0.47 ! [X_27: $o,Y_14: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ X_27 @ ( semila854092349_inf_o @ X_27 @ Y_14 ) )
% 0.24/0.47 <=> X_27 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_926_sup__inf__absorb,axiom,
% 0.24/0.47 ! [X_27: pname > $o,Y_14: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ X_27 @ ( semila1673364395name_o @ X_27 @ Y_14 ) )
% 0.24/0.47 = X_27 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_927_sup__inf__absorb,axiom,
% 0.24/0.47 ! [X_27: hoare_1708887482_state > $o,Y_14: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ X_27 @ ( semila129691299tate_o @ X_27 @ Y_14 ) )
% 0.24/0.47 = X_27 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_928_inf__sup__distrib1,axiom,
% 0.24/0.47 ! [X_26: $o,Y_13: $o,Z_8: $o] :
% 0.24/0.47 ( ( semila854092349_inf_o @ X_26 @ ( semila10642723_sup_o @ Y_13 @ Z_8 ) )
% 0.24/0.47 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_26 @ Y_13 ) @ ( semila854092349_inf_o @ X_26 @ Z_8 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_929_inf__sup__distrib1,axiom,
% 0.24/0.47 ! [X_26: pname > $o,Y_13: pname > $o,Z_8: pname > $o] :
% 0.24/0.47 ( ( semila1673364395name_o @ X_26 @ ( semila1780557381name_o @ Y_13 @ Z_8 ) )
% 0.24/0.47 = ( semila1780557381name_o @ ( semila1673364395name_o @ X_26 @ Y_13 ) @ ( semila1673364395name_o @ X_26 @ Z_8 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_930_inf__sup__distrib1,axiom,
% 0.24/0.47 ! [X_26: hoare_1708887482_state > $o,Y_13: hoare_1708887482_state > $o,Z_8: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila129691299tate_o @ X_26 @ ( semila1122118281tate_o @ Y_13 @ Z_8 ) )
% 0.24/0.47 = ( semila1122118281tate_o @ ( semila129691299tate_o @ X_26 @ Y_13 ) @ ( semila129691299tate_o @ X_26 @ Z_8 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_931_sup__inf__distrib1,axiom,
% 0.24/0.47 ! [X_25: $o,Y_12: $o,Z_7: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ X_25 @ ( semila854092349_inf_o @ Y_12 @ Z_7 ) )
% 0.24/0.47 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_25 @ Y_12 ) @ ( semila10642723_sup_o @ X_25 @ Z_7 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_932_sup__inf__distrib1,axiom,
% 0.24/0.47 ! [X_25: pname > $o,Y_12: pname > $o,Z_7: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ X_25 @ ( semila1673364395name_o @ Y_12 @ Z_7 ) )
% 0.24/0.47 = ( semila1673364395name_o @ ( semila1780557381name_o @ X_25 @ Y_12 ) @ ( semila1780557381name_o @ X_25 @ Z_7 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_933_sup__inf__distrib1,axiom,
% 0.24/0.47 ! [X_25: hoare_1708887482_state > $o,Y_12: hoare_1708887482_state > $o,Z_7: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ X_25 @ ( semila129691299tate_o @ Y_12 @ Z_7 ) )
% 0.24/0.47 = ( semila129691299tate_o @ ( semila1122118281tate_o @ X_25 @ Y_12 ) @ ( semila1122118281tate_o @ X_25 @ Z_7 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_934_inf__sup__distrib2,axiom,
% 0.24/0.47 ! [Y_11: $o,Z_6: $o,X_24: $o] :
% 0.24/0.47 ( ( semila854092349_inf_o @ ( semila10642723_sup_o @ Y_11 @ Z_6 ) @ X_24 )
% 0.24/0.47 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ Y_11 @ X_24 ) @ ( semila854092349_inf_o @ Z_6 @ X_24 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_935_inf__sup__distrib2,axiom,
% 0.24/0.47 ! [Y_11: pname > $o,Z_6: pname > $o,X_24: pname > $o] :
% 0.24/0.47 ( ( semila1673364395name_o @ ( semila1780557381name_o @ Y_11 @ Z_6 ) @ X_24 )
% 0.24/0.47 = ( semila1780557381name_o @ ( semila1673364395name_o @ Y_11 @ X_24 ) @ ( semila1673364395name_o @ Z_6 @ X_24 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_936_inf__sup__distrib2,axiom,
% 0.24/0.47 ! [Y_11: hoare_1708887482_state > $o,Z_6: hoare_1708887482_state > $o,X_24: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila129691299tate_o @ ( semila1122118281tate_o @ Y_11 @ Z_6 ) @ X_24 )
% 0.24/0.47 = ( semila1122118281tate_o @ ( semila129691299tate_o @ Y_11 @ X_24 ) @ ( semila129691299tate_o @ Z_6 @ X_24 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_937_sup__inf__distrib2,axiom,
% 0.24/0.47 ! [Y_10: $o,Z_5: $o,X_23: $o] :
% 0.24/0.47 ( ( semila10642723_sup_o @ ( semila854092349_inf_o @ Y_10 @ Z_5 ) @ X_23 )
% 0.24/0.47 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ Y_10 @ X_23 ) @ ( semila10642723_sup_o @ Z_5 @ X_23 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_938_sup__inf__distrib2,axiom,
% 0.24/0.47 ! [Y_10: pname > $o,Z_5: pname > $o,X_23: pname > $o] :
% 0.24/0.47 ( ( semila1780557381name_o @ ( semila1673364395name_o @ Y_10 @ Z_5 ) @ X_23 )
% 0.24/0.47 = ( semila1673364395name_o @ ( semila1780557381name_o @ Y_10 @ X_23 ) @ ( semila1780557381name_o @ Z_5 @ X_23 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_939_sup__inf__distrib2,axiom,
% 0.24/0.47 ! [Y_10: hoare_1708887482_state > $o,Z_5: hoare_1708887482_state > $o,X_23: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( semila1122118281tate_o @ ( semila129691299tate_o @ Y_10 @ Z_5 ) @ X_23 )
% 0.24/0.47 = ( semila129691299tate_o @ ( semila1122118281tate_o @ Y_10 @ X_23 ) @ ( semila1122118281tate_o @ Z_5 @ X_23 ) ) ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_940_Diff__cancel,axiom,
% 0.24/0.47 ! [A_99: com > $o] :
% 0.24/0.47 ( ( minus_minus_com_o @ A_99 @ A_99 )
% 0.24/0.47 = bot_bot_com_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_941_Diff__cancel,axiom,
% 0.24/0.47 ! [A_99: pname > $o] :
% 0.24/0.47 ( ( minus_minus_pname_o @ A_99 @ A_99 )
% 0.24/0.47 = bot_bot_pname_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_942_Diff__cancel,axiom,
% 0.24/0.47 ! [A_99: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( minus_2056855718tate_o @ A_99 @ A_99 )
% 0.24/0.47 = bot_bo19817387tate_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_943_Diff__empty,axiom,
% 0.24/0.47 ! [A_98: com > $o] :
% 0.24/0.47 ( ( minus_minus_com_o @ A_98 @ bot_bot_com_o )
% 0.24/0.47 = A_98 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_944_Diff__empty,axiom,
% 0.24/0.47 ! [A_98: pname > $o] :
% 0.24/0.47 ( ( minus_minus_pname_o @ A_98 @ bot_bot_pname_o )
% 0.24/0.47 = A_98 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_945_Diff__empty,axiom,
% 0.24/0.47 ! [A_98: hoare_1708887482_state > $o] :
% 0.24/0.47 ( ( minus_2056855718tate_o @ A_98 @ bot_bo19817387tate_o )
% 0.24/0.47 = A_98 ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_946_empty__Diff,axiom,
% 0.24/0.47 ! [A_97: com > $o] :
% 0.24/0.47 ( ( minus_minus_com_o @ bot_bot_com_o @ A_97 )
% 0.24/0.47 = bot_bot_com_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_947_empty__Diff,axiom,
% 0.24/0.47 ! [A_97: pname > $o] :
% 0.24/0.47 ( ( minus_minus_pname_o @ bot_bot_pname_o @ A_97 )
% 0.24/0.47 = bot_bot_pname_o ) ).
% 0.24/0.47
% 0.24/0.47 thf(fact_948_empty__Diff,axiom,
% 0.24/0.47 ! [A_97: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( minus_2056855718tate_o @ bot_bo19817387tate_o @ A_97 )
% 0.24/0.48 = bot_bo19817387tate_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_949_finite__Diff2,axiom,
% 0.24/0.48 ! [A_96: ( pname > $o ) > $o,B_55: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ B_55 )
% 0.24/0.48 => ( ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_96 @ B_55 ) )
% 0.24/0.48 <=> ( finite297249702name_o @ A_96 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_950_finite__Diff2,axiom,
% 0.24/0.48 ! [A_96: ( hoare_1708887482_state > $o ) > $o,B_55: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ B_55 )
% 0.24/0.48 => ( ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_96 @ B_55 ) )
% 0.24/0.48 <=> ( finite1329924456tate_o @ A_96 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_951_finite__Diff2,axiom,
% 0.24/0.48 ! [A_96: pname > $o,B_55: pname > $o] :
% 0.24/0.48 ( ( finite_finite_pname @ B_55 )
% 0.24/0.48 => ( ( finite_finite_pname @ ( minus_minus_pname_o @ A_96 @ B_55 ) )
% 0.24/0.48 <=> ( finite_finite_pname @ A_96 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_952_finite__Diff2,axiom,
% 0.24/0.48 ! [A_96: hoare_1708887482_state > $o,B_55: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( finite1625599783_state @ B_55 )
% 0.24/0.48 => ( ( finite1625599783_state @ ( minus_2056855718tate_o @ A_96 @ B_55 ) )
% 0.24/0.48 <=> ( finite1625599783_state @ A_96 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_953_insert__Diff1,axiom,
% 0.24/0.48 ! [A_95: com > $o,X_22: com,B_54: com > $o] :
% 0.24/0.48 ( ( member_com @ X_22 @ B_54 )
% 0.24/0.48 => ( ( minus_minus_com_o @ ( insert_com @ X_22 @ A_95 ) @ B_54 )
% 0.24/0.48 = ( minus_minus_com_o @ A_95 @ B_54 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_954_insert__Diff1,axiom,
% 0.24/0.48 ! [A_95: pname > $o,X_22: pname,B_54: pname > $o] :
% 0.24/0.48 ( ( member_pname @ X_22 @ B_54 )
% 0.24/0.48 => ( ( minus_minus_pname_o @ ( insert_pname @ X_22 @ A_95 ) @ B_54 )
% 0.24/0.48 = ( minus_minus_pname_o @ A_95 @ B_54 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_955_insert__Diff1,axiom,
% 0.24/0.48 ! [A_95: hoare_1708887482_state > $o,X_22: hoare_1708887482_state,B_54: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( member451959335_state @ X_22 @ B_54 )
% 0.24/0.48 => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_22 @ A_95 ) @ B_54 )
% 0.24/0.48 = ( minus_2056855718tate_o @ A_95 @ B_54 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_956_insert__Diff__if,axiom,
% 0.24/0.48 ! [A_94: com > $o,X_21: com,B_53: com > $o] :
% 0.24/0.48 ( ( ( member_com @ X_21 @ B_53 )
% 0.24/0.48 => ( ( minus_minus_com_o @ ( insert_com @ X_21 @ A_94 ) @ B_53 )
% 0.24/0.48 = ( minus_minus_com_o @ A_94 @ B_53 ) ) )
% 0.24/0.48 & ( ~ ( member_com @ X_21 @ B_53 )
% 0.24/0.48 => ( ( minus_minus_com_o @ ( insert_com @ X_21 @ A_94 ) @ B_53 )
% 0.24/0.48 = ( insert_com @ X_21 @ ( minus_minus_com_o @ A_94 @ B_53 ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_957_insert__Diff__if,axiom,
% 0.24/0.48 ! [A_94: pname > $o,X_21: pname,B_53: pname > $o] :
% 0.24/0.48 ( ( ( member_pname @ X_21 @ B_53 )
% 0.24/0.48 => ( ( minus_minus_pname_o @ ( insert_pname @ X_21 @ A_94 ) @ B_53 )
% 0.24/0.48 = ( minus_minus_pname_o @ A_94 @ B_53 ) ) )
% 0.24/0.48 & ( ~ ( member_pname @ X_21 @ B_53 )
% 0.24/0.48 => ( ( minus_minus_pname_o @ ( insert_pname @ X_21 @ A_94 ) @ B_53 )
% 0.24/0.48 = ( insert_pname @ X_21 @ ( minus_minus_pname_o @ A_94 @ B_53 ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_958_insert__Diff__if,axiom,
% 0.24/0.48 ! [A_94: hoare_1708887482_state > $o,X_21: hoare_1708887482_state,B_53: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ( member451959335_state @ X_21 @ B_53 )
% 0.24/0.48 => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_21 @ A_94 ) @ B_53 )
% 0.24/0.48 = ( minus_2056855718tate_o @ A_94 @ B_53 ) ) )
% 0.24/0.48 & ( ~ ( member451959335_state @ X_21 @ B_53 )
% 0.24/0.48 => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_21 @ A_94 ) @ B_53 )
% 0.24/0.48 = ( insert528405184_state @ X_21 @ ( minus_2056855718tate_o @ A_94 @ B_53 ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_959_disjoint__iff__not__equal,axiom,
% 0.24/0.48 ! [A_93: com > $o,B_52: com > $o] :
% 0.24/0.48 ( ( ( semila513601829_com_o @ A_93 @ B_52 )
% 0.24/0.48 = bot_bot_com_o )
% 0.24/0.48 <=> ! [X_3: com] :
% 0.24/0.48 ( ( member_com @ X_3 @ A_93 )
% 0.24/0.48 => ! [Xa: com] :
% 0.24/0.48 ( ( member_com @ Xa @ B_52 )
% 0.24/0.48 => ( X_3 != Xa ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_960_disjoint__iff__not__equal,axiom,
% 0.24/0.48 ! [A_93: pname > $o,B_52: pname > $o] :
% 0.24/0.48 ( ( ( semila1673364395name_o @ A_93 @ B_52 )
% 0.24/0.48 = bot_bot_pname_o )
% 0.24/0.48 <=> ! [X_3: pname] :
% 0.24/0.48 ( ( member_pname @ X_3 @ A_93 )
% 0.24/0.48 => ! [Xa: pname] :
% 0.24/0.48 ( ( member_pname @ Xa @ B_52 )
% 0.24/0.48 => ( X_3 != Xa ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_961_disjoint__iff__not__equal,axiom,
% 0.24/0.48 ! [A_93: hoare_1708887482_state > $o,B_52: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ( semila129691299tate_o @ A_93 @ B_52 )
% 0.24/0.48 = bot_bo19817387tate_o )
% 0.24/0.48 <=> ! [X_3: hoare_1708887482_state] :
% 0.24/0.48 ( ( member451959335_state @ X_3 @ A_93 )
% 0.24/0.48 => ! [Xa: hoare_1708887482_state] :
% 0.24/0.48 ( ( member451959335_state @ Xa @ B_52 )
% 0.24/0.48 => ( X_3 != Xa ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_962_Int__empty__right,axiom,
% 0.24/0.48 ! [A_92: com > $o] :
% 0.24/0.48 ( ( semila513601829_com_o @ A_92 @ bot_bot_com_o )
% 0.24/0.48 = bot_bot_com_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_963_Int__empty__right,axiom,
% 0.24/0.48 ! [A_92: pname > $o] :
% 0.24/0.48 ( ( semila1673364395name_o @ A_92 @ bot_bot_pname_o )
% 0.24/0.48 = bot_bot_pname_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_964_Int__empty__right,axiom,
% 0.24/0.48 ! [A_92: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila129691299tate_o @ A_92 @ bot_bo19817387tate_o )
% 0.24/0.48 = bot_bo19817387tate_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_965_Int__empty__left,axiom,
% 0.24/0.48 ! [B_51: com > $o] :
% 0.24/0.48 ( ( semila513601829_com_o @ bot_bot_com_o @ B_51 )
% 0.24/0.48 = bot_bot_com_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_966_Int__empty__left,axiom,
% 0.24/0.48 ! [B_51: pname > $o] :
% 0.24/0.48 ( ( semila1673364395name_o @ bot_bot_pname_o @ B_51 )
% 0.24/0.48 = bot_bot_pname_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_967_Int__empty__left,axiom,
% 0.24/0.48 ! [B_51: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila129691299tate_o @ bot_bo19817387tate_o @ B_51 )
% 0.24/0.48 = bot_bo19817387tate_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_968_double__diff,axiom,
% 0.24/0.48 ! [C_18: pname > $o,A_91: pname > $o,B_50: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ A_91 @ B_50 )
% 0.24/0.48 => ( ( ord_less_eq_pname_o @ B_50 @ C_18 )
% 0.24/0.48 => ( ( minus_minus_pname_o @ B_50 @ ( minus_minus_pname_o @ C_18 @ A_91 ) )
% 0.24/0.48 = A_91 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_969_double__diff,axiom,
% 0.24/0.48 ! [C_18: hoare_1708887482_state > $o,A_91: hoare_1708887482_state > $o,B_50: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ A_91 @ B_50 )
% 0.24/0.48 => ( ( ord_le777019615tate_o @ B_50 @ C_18 )
% 0.24/0.48 => ( ( minus_2056855718tate_o @ B_50 @ ( minus_2056855718tate_o @ C_18 @ A_91 ) )
% 0.24/0.48 = A_91 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_970_Diff__mono,axiom,
% 0.24/0.48 ! [D_1: pname > $o,B_49: pname > $o,A_90: pname > $o,C_17: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ A_90 @ C_17 )
% 0.24/0.48 => ( ( ord_less_eq_pname_o @ D_1 @ B_49 )
% 0.24/0.48 => ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_90 @ B_49 ) @ ( minus_minus_pname_o @ C_17 @ D_1 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_971_Diff__mono,axiom,
% 0.24/0.48 ! [D_1: hoare_1708887482_state > $o,B_49: hoare_1708887482_state > $o,A_90: hoare_1708887482_state > $o,C_17: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ A_90 @ C_17 )
% 0.24/0.48 => ( ( ord_le777019615tate_o @ D_1 @ B_49 )
% 0.24/0.48 => ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_90 @ B_49 ) @ ( minus_2056855718tate_o @ C_17 @ D_1 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_972_Diff__subset,axiom,
% 0.24/0.48 ! [A_89: pname > $o,B_48: pname > $o] : ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_89 @ B_48 ) @ A_89 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_973_Diff__subset,axiom,
% 0.24/0.48 ! [A_89: hoare_1708887482_state > $o,B_48: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_89 @ B_48 ) @ A_89 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_974_Un__Diff,axiom,
% 0.24/0.48 ! [A_88: pname > $o,B_47: pname > $o,C_16: pname > $o] :
% 0.24/0.48 ( ( minus_minus_pname_o @ ( semila1780557381name_o @ A_88 @ B_47 ) @ C_16 )
% 0.24/0.48 = ( semila1780557381name_o @ ( minus_minus_pname_o @ A_88 @ C_16 ) @ ( minus_minus_pname_o @ B_47 @ C_16 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_975_Un__Diff,axiom,
% 0.24/0.48 ! [A_88: hoare_1708887482_state > $o,B_47: hoare_1708887482_state > $o,C_16: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( minus_2056855718tate_o @ ( semila1122118281tate_o @ A_88 @ B_47 ) @ C_16 )
% 0.24/0.48 = ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A_88 @ C_16 ) @ ( minus_2056855718tate_o @ B_47 @ C_16 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_976_Un__Diff__cancel2,axiom,
% 0.24/0.48 ! [B_46: pname > $o,A_87: pname > $o] :
% 0.24/0.48 ( ( semila1780557381name_o @ ( minus_minus_pname_o @ B_46 @ A_87 ) @ A_87 )
% 0.24/0.48 = ( semila1780557381name_o @ B_46 @ A_87 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_977_Un__Diff__cancel2,axiom,
% 0.24/0.48 ! [B_46: hoare_1708887482_state > $o,A_87: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila1122118281tate_o @ ( minus_2056855718tate_o @ B_46 @ A_87 ) @ A_87 )
% 0.24/0.48 = ( semila1122118281tate_o @ B_46 @ A_87 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_978_Un__Diff__cancel,axiom,
% 0.24/0.48 ! [A_86: pname > $o,B_45: pname > $o] :
% 0.24/0.48 ( ( semila1780557381name_o @ A_86 @ ( minus_minus_pname_o @ B_45 @ A_86 ) )
% 0.24/0.48 = ( semila1780557381name_o @ A_86 @ B_45 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_979_Un__Diff__cancel,axiom,
% 0.24/0.48 ! [A_86: hoare_1708887482_state > $o,B_45: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila1122118281tate_o @ A_86 @ ( minus_2056855718tate_o @ B_45 @ A_86 ) )
% 0.24/0.48 = ( semila1122118281tate_o @ A_86 @ B_45 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_980_Int__insert__left__if1,axiom,
% 0.24/0.48 ! [B_44: com > $o,A_85: com,C_15: com > $o] :
% 0.24/0.48 ( ( member_com @ A_85 @ C_15 )
% 0.24/0.48 => ( ( semila513601829_com_o @ ( insert_com @ A_85 @ B_44 ) @ C_15 )
% 0.24/0.48 = ( insert_com @ A_85 @ ( semila513601829_com_o @ B_44 @ C_15 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_981_Int__insert__left__if1,axiom,
% 0.24/0.48 ! [B_44: pname > $o,A_85: pname,C_15: pname > $o] :
% 0.24/0.48 ( ( member_pname @ A_85 @ C_15 )
% 0.24/0.48 => ( ( semila1673364395name_o @ ( insert_pname @ A_85 @ B_44 ) @ C_15 )
% 0.24/0.48 = ( insert_pname @ A_85 @ ( semila1673364395name_o @ B_44 @ C_15 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_982_Int__insert__left__if1,axiom,
% 0.24/0.48 ! [B_44: hoare_1708887482_state > $o,A_85: hoare_1708887482_state,C_15: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( member451959335_state @ A_85 @ C_15 )
% 0.24/0.48 => ( ( semila129691299tate_o @ ( insert528405184_state @ A_85 @ B_44 ) @ C_15 )
% 0.24/0.48 = ( insert528405184_state @ A_85 @ ( semila129691299tate_o @ B_44 @ C_15 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_983_Int__insert__right__if1,axiom,
% 0.24/0.48 ! [B_43: com > $o,A_84: com,A_83: com > $o] :
% 0.24/0.48 ( ( member_com @ A_84 @ A_83 )
% 0.24/0.48 => ( ( semila513601829_com_o @ A_83 @ ( insert_com @ A_84 @ B_43 ) )
% 0.24/0.48 = ( insert_com @ A_84 @ ( semila513601829_com_o @ A_83 @ B_43 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_984_Int__insert__right__if1,axiom,
% 0.24/0.48 ! [B_43: pname > $o,A_84: pname,A_83: pname > $o] :
% 0.24/0.48 ( ( member_pname @ A_84 @ A_83 )
% 0.24/0.48 => ( ( semila1673364395name_o @ A_83 @ ( insert_pname @ A_84 @ B_43 ) )
% 0.24/0.48 = ( insert_pname @ A_84 @ ( semila1673364395name_o @ A_83 @ B_43 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_985_Int__insert__right__if1,axiom,
% 0.24/0.48 ! [B_43: hoare_1708887482_state > $o,A_84: hoare_1708887482_state,A_83: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( member451959335_state @ A_84 @ A_83 )
% 0.24/0.48 => ( ( semila129691299tate_o @ A_83 @ ( insert528405184_state @ A_84 @ B_43 ) )
% 0.24/0.48 = ( insert528405184_state @ A_84 @ ( semila129691299tate_o @ A_83 @ B_43 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_986_Int__insert__left__if0,axiom,
% 0.24/0.48 ! [B_42: com > $o,A_82: com,C_14: com > $o] :
% 0.24/0.48 ( ~ ( member_com @ A_82 @ C_14 )
% 0.24/0.48 => ( ( semila513601829_com_o @ ( insert_com @ A_82 @ B_42 ) @ C_14 )
% 0.24/0.48 = ( semila513601829_com_o @ B_42 @ C_14 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_987_Int__insert__left__if0,axiom,
% 0.24/0.48 ! [B_42: pname > $o,A_82: pname,C_14: pname > $o] :
% 0.24/0.48 ( ~ ( member_pname @ A_82 @ C_14 )
% 0.24/0.48 => ( ( semila1673364395name_o @ ( insert_pname @ A_82 @ B_42 ) @ C_14 )
% 0.24/0.48 = ( semila1673364395name_o @ B_42 @ C_14 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_988_Int__insert__left__if0,axiom,
% 0.24/0.48 ! [B_42: hoare_1708887482_state > $o,A_82: hoare_1708887482_state,C_14: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ~ ( member451959335_state @ A_82 @ C_14 )
% 0.24/0.48 => ( ( semila129691299tate_o @ ( insert528405184_state @ A_82 @ B_42 ) @ C_14 )
% 0.24/0.48 = ( semila129691299tate_o @ B_42 @ C_14 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_989_Int__insert__right__if0,axiom,
% 0.24/0.48 ! [B_41: com > $o,A_81: com,A_80: com > $o] :
% 0.24/0.48 ( ~ ( member_com @ A_81 @ A_80 )
% 0.24/0.48 => ( ( semila513601829_com_o @ A_80 @ ( insert_com @ A_81 @ B_41 ) )
% 0.24/0.48 = ( semila513601829_com_o @ A_80 @ B_41 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_990_Int__insert__right__if0,axiom,
% 0.24/0.48 ! [B_41: pname > $o,A_81: pname,A_80: pname > $o] :
% 0.24/0.48 ( ~ ( member_pname @ A_81 @ A_80 )
% 0.24/0.48 => ( ( semila1673364395name_o @ A_80 @ ( insert_pname @ A_81 @ B_41 ) )
% 0.24/0.48 = ( semila1673364395name_o @ A_80 @ B_41 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_991_Int__insert__right__if0,axiom,
% 0.24/0.48 ! [B_41: hoare_1708887482_state > $o,A_81: hoare_1708887482_state,A_80: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ~ ( member451959335_state @ A_81 @ A_80 )
% 0.24/0.48 => ( ( semila129691299tate_o @ A_80 @ ( insert528405184_state @ A_81 @ B_41 ) )
% 0.24/0.48 = ( semila129691299tate_o @ A_80 @ B_41 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_992_insert__inter__insert,axiom,
% 0.24/0.48 ! [A_79: com,A_78: com > $o,B_40: com > $o] :
% 0.24/0.48 ( ( semila513601829_com_o @ ( insert_com @ A_79 @ A_78 ) @ ( insert_com @ A_79 @ B_40 ) )
% 0.24/0.48 = ( insert_com @ A_79 @ ( semila513601829_com_o @ A_78 @ B_40 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_993_insert__inter__insert,axiom,
% 0.24/0.48 ! [A_79: pname,A_78: pname > $o,B_40: pname > $o] :
% 0.24/0.48 ( ( semila1673364395name_o @ ( insert_pname @ A_79 @ A_78 ) @ ( insert_pname @ A_79 @ B_40 ) )
% 0.24/0.48 = ( insert_pname @ A_79 @ ( semila1673364395name_o @ A_78 @ B_40 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_994_insert__inter__insert,axiom,
% 0.24/0.48 ! [A_79: hoare_1708887482_state,A_78: hoare_1708887482_state > $o,B_40: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila129691299tate_o @ ( insert528405184_state @ A_79 @ A_78 ) @ ( insert528405184_state @ A_79 @ B_40 ) )
% 0.24/0.48 = ( insert528405184_state @ A_79 @ ( semila129691299tate_o @ A_78 @ B_40 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_995_Int__insert__left,axiom,
% 0.24/0.48 ! [B_39: com > $o,A_77: com,C_13: com > $o] :
% 0.24/0.48 ( ( ( member_com @ A_77 @ C_13 )
% 0.24/0.48 => ( ( semila513601829_com_o @ ( insert_com @ A_77 @ B_39 ) @ C_13 )
% 0.24/0.48 = ( insert_com @ A_77 @ ( semila513601829_com_o @ B_39 @ C_13 ) ) ) )
% 0.24/0.48 & ( ~ ( member_com @ A_77 @ C_13 )
% 0.24/0.48 => ( ( semila513601829_com_o @ ( insert_com @ A_77 @ B_39 ) @ C_13 )
% 0.24/0.48 = ( semila513601829_com_o @ B_39 @ C_13 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_996_Int__insert__left,axiom,
% 0.24/0.48 ! [B_39: pname > $o,A_77: pname,C_13: pname > $o] :
% 0.24/0.48 ( ( ( member_pname @ A_77 @ C_13 )
% 0.24/0.48 => ( ( semila1673364395name_o @ ( insert_pname @ A_77 @ B_39 ) @ C_13 )
% 0.24/0.48 = ( insert_pname @ A_77 @ ( semila1673364395name_o @ B_39 @ C_13 ) ) ) )
% 0.24/0.48 & ( ~ ( member_pname @ A_77 @ C_13 )
% 0.24/0.48 => ( ( semila1673364395name_o @ ( insert_pname @ A_77 @ B_39 ) @ C_13 )
% 0.24/0.48 = ( semila1673364395name_o @ B_39 @ C_13 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_997_Int__insert__left,axiom,
% 0.24/0.48 ! [B_39: hoare_1708887482_state > $o,A_77: hoare_1708887482_state,C_13: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ( member451959335_state @ A_77 @ C_13 )
% 0.24/0.48 => ( ( semila129691299tate_o @ ( insert528405184_state @ A_77 @ B_39 ) @ C_13 )
% 0.24/0.48 = ( insert528405184_state @ A_77 @ ( semila129691299tate_o @ B_39 @ C_13 ) ) ) )
% 0.24/0.48 & ( ~ ( member451959335_state @ A_77 @ C_13 )
% 0.24/0.48 => ( ( semila129691299tate_o @ ( insert528405184_state @ A_77 @ B_39 ) @ C_13 )
% 0.24/0.48 = ( semila129691299tate_o @ B_39 @ C_13 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_998_Int__insert__right,axiom,
% 0.24/0.48 ! [B_38: com > $o,A_76: com,A_75: com > $o] :
% 0.24/0.48 ( ( ( member_com @ A_76 @ A_75 )
% 0.24/0.48 => ( ( semila513601829_com_o @ A_75 @ ( insert_com @ A_76 @ B_38 ) )
% 0.24/0.48 = ( insert_com @ A_76 @ ( semila513601829_com_o @ A_75 @ B_38 ) ) ) )
% 0.24/0.48 & ( ~ ( member_com @ A_76 @ A_75 )
% 0.24/0.48 => ( ( semila513601829_com_o @ A_75 @ ( insert_com @ A_76 @ B_38 ) )
% 0.24/0.48 = ( semila513601829_com_o @ A_75 @ B_38 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_999_Int__insert__right,axiom,
% 0.24/0.48 ! [B_38: pname > $o,A_76: pname,A_75: pname > $o] :
% 0.24/0.48 ( ( ( member_pname @ A_76 @ A_75 )
% 0.24/0.48 => ( ( semila1673364395name_o @ A_75 @ ( insert_pname @ A_76 @ B_38 ) )
% 0.24/0.48 = ( insert_pname @ A_76 @ ( semila1673364395name_o @ A_75 @ B_38 ) ) ) )
% 0.24/0.48 & ( ~ ( member_pname @ A_76 @ A_75 )
% 0.24/0.48 => ( ( semila1673364395name_o @ A_75 @ ( insert_pname @ A_76 @ B_38 ) )
% 0.24/0.48 = ( semila1673364395name_o @ A_75 @ B_38 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1000_Int__insert__right,axiom,
% 0.24/0.48 ! [B_38: hoare_1708887482_state > $o,A_76: hoare_1708887482_state,A_75: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ( member451959335_state @ A_76 @ A_75 )
% 0.24/0.48 => ( ( semila129691299tate_o @ A_75 @ ( insert528405184_state @ A_76 @ B_38 ) )
% 0.24/0.48 = ( insert528405184_state @ A_76 @ ( semila129691299tate_o @ A_75 @ B_38 ) ) ) )
% 0.24/0.48 & ( ~ ( member451959335_state @ A_76 @ A_75 )
% 0.24/0.48 => ( ( semila129691299tate_o @ A_75 @ ( insert528405184_state @ A_76 @ B_38 ) )
% 0.24/0.48 = ( semila129691299tate_o @ A_75 @ B_38 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1001_Int__mono,axiom,
% 0.24/0.48 ! [B_37: pname > $o,D: pname > $o,A_74: pname > $o,C_12: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ A_74 @ C_12 )
% 0.24/0.48 => ( ( ord_less_eq_pname_o @ B_37 @ D )
% 0.24/0.48 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_74 @ B_37 ) @ ( semila1673364395name_o @ C_12 @ D ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1002_Int__mono,axiom,
% 0.24/0.48 ! [B_37: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o,A_74: hoare_1708887482_state > $o,C_12: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ A_74 @ C_12 )
% 0.24/0.48 => ( ( ord_le777019615tate_o @ B_37 @ D )
% 0.24/0.48 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_74 @ B_37 ) @ ( semila129691299tate_o @ C_12 @ D ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1003_Int__greatest,axiom,
% 0.24/0.48 ! [B_36: pname > $o,C_11: pname > $o,A_73: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ C_11 @ A_73 )
% 0.24/0.48 => ( ( ord_less_eq_pname_o @ C_11 @ B_36 )
% 0.24/0.48 => ( ord_less_eq_pname_o @ C_11 @ ( semila1673364395name_o @ A_73 @ B_36 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1004_Int__greatest,axiom,
% 0.24/0.48 ! [B_36: hoare_1708887482_state > $o,C_11: hoare_1708887482_state > $o,A_73: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ C_11 @ A_73 )
% 0.24/0.48 => ( ( ord_le777019615tate_o @ C_11 @ B_36 )
% 0.24/0.48 => ( ord_le777019615tate_o @ C_11 @ ( semila129691299tate_o @ A_73 @ B_36 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1005_Int__absorb1,axiom,
% 0.24/0.48 ! [B_35: pname > $o,A_72: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ B_35 @ A_72 )
% 0.24/0.48 => ( ( semila1673364395name_o @ A_72 @ B_35 )
% 0.24/0.48 = B_35 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1006_Int__absorb1,axiom,
% 0.24/0.48 ! [B_35: hoare_1708887482_state > $o,A_72: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ B_35 @ A_72 )
% 0.24/0.48 => ( ( semila129691299tate_o @ A_72 @ B_35 )
% 0.24/0.48 = B_35 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1007_Int__absorb2,axiom,
% 0.24/0.48 ! [A_71: pname > $o,B_34: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ A_71 @ B_34 )
% 0.24/0.48 => ( ( semila1673364395name_o @ A_71 @ B_34 )
% 0.24/0.48 = A_71 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1008_Int__absorb2,axiom,
% 0.24/0.48 ! [A_71: hoare_1708887482_state > $o,B_34: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ A_71 @ B_34 )
% 0.24/0.48 => ( ( semila129691299tate_o @ A_71 @ B_34 )
% 0.24/0.48 = A_71 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1009_Int__lower2,axiom,
% 0.24/0.48 ! [A_70: pname > $o,B_33: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_70 @ B_33 ) @ B_33 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1010_Int__lower2,axiom,
% 0.24/0.48 ! [A_70: hoare_1708887482_state > $o,B_33: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_70 @ B_33 ) @ B_33 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1011_Int__lower1,axiom,
% 0.24/0.48 ! [A_69: pname > $o,B_32: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_69 @ B_32 ) @ A_69 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1012_Int__lower1,axiom,
% 0.24/0.48 ! [A_69: hoare_1708887482_state > $o,B_32: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_69 @ B_32 ) @ A_69 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1013_Un__Int__crazy,axiom,
% 0.24/0.48 ! [A_68: pname > $o,B_31: pname > $o,C_10: pname > $o] :
% 0.24/0.48 ( ( semila1780557381name_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ A_68 @ B_31 ) @ ( semila1673364395name_o @ B_31 @ C_10 ) ) @ ( semila1673364395name_o @ C_10 @ A_68 ) )
% 0.24/0.48 = ( semila1673364395name_o @ ( semila1673364395name_o @ ( semila1780557381name_o @ A_68 @ B_31 ) @ ( semila1780557381name_o @ B_31 @ C_10 ) ) @ ( semila1780557381name_o @ C_10 @ A_68 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1014_Un__Int__crazy,axiom,
% 0.24/0.48 ! [A_68: hoare_1708887482_state > $o,B_31: hoare_1708887482_state > $o,C_10: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ ( semila129691299tate_o @ A_68 @ B_31 ) @ ( semila129691299tate_o @ B_31 @ C_10 ) ) @ ( semila129691299tate_o @ C_10 @ A_68 ) )
% 0.24/0.48 = ( semila129691299tate_o @ ( semila129691299tate_o @ ( semila1122118281tate_o @ A_68 @ B_31 ) @ ( semila1122118281tate_o @ B_31 @ C_10 ) ) @ ( semila1122118281tate_o @ C_10 @ A_68 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1015_Un__Int__distrib2,axiom,
% 0.24/0.48 ! [B_30: pname > $o,C_9: pname > $o,A_67: pname > $o] :
% 0.24/0.48 ( ( semila1780557381name_o @ ( semila1673364395name_o @ B_30 @ C_9 ) @ A_67 )
% 0.24/0.48 = ( semila1673364395name_o @ ( semila1780557381name_o @ B_30 @ A_67 ) @ ( semila1780557381name_o @ C_9 @ A_67 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1016_Un__Int__distrib2,axiom,
% 0.24/0.48 ! [B_30: hoare_1708887482_state > $o,C_9: hoare_1708887482_state > $o,A_67: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila1122118281tate_o @ ( semila129691299tate_o @ B_30 @ C_9 ) @ A_67 )
% 0.24/0.48 = ( semila129691299tate_o @ ( semila1122118281tate_o @ B_30 @ A_67 ) @ ( semila1122118281tate_o @ C_9 @ A_67 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1017_Int__Un__distrib2,axiom,
% 0.24/0.48 ! [B_29: pname > $o,C_8: pname > $o,A_66: pname > $o] :
% 0.24/0.48 ( ( semila1673364395name_o @ ( semila1780557381name_o @ B_29 @ C_8 ) @ A_66 )
% 0.24/0.48 = ( semila1780557381name_o @ ( semila1673364395name_o @ B_29 @ A_66 ) @ ( semila1673364395name_o @ C_8 @ A_66 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1018_Int__Un__distrib2,axiom,
% 0.24/0.48 ! [B_29: hoare_1708887482_state > $o,C_8: hoare_1708887482_state > $o,A_66: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila129691299tate_o @ ( semila1122118281tate_o @ B_29 @ C_8 ) @ A_66 )
% 0.24/0.48 = ( semila1122118281tate_o @ ( semila129691299tate_o @ B_29 @ A_66 ) @ ( semila129691299tate_o @ C_8 @ A_66 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1019_Un__Int__distrib,axiom,
% 0.24/0.48 ! [A_65: pname > $o,B_28: pname > $o,C_7: pname > $o] :
% 0.24/0.48 ( ( semila1780557381name_o @ A_65 @ ( semila1673364395name_o @ B_28 @ C_7 ) )
% 0.24/0.48 = ( semila1673364395name_o @ ( semila1780557381name_o @ A_65 @ B_28 ) @ ( semila1780557381name_o @ A_65 @ C_7 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1020_Un__Int__distrib,axiom,
% 0.24/0.48 ! [A_65: hoare_1708887482_state > $o,B_28: hoare_1708887482_state > $o,C_7: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila1122118281tate_o @ A_65 @ ( semila129691299tate_o @ B_28 @ C_7 ) )
% 0.24/0.48 = ( semila129691299tate_o @ ( semila1122118281tate_o @ A_65 @ B_28 ) @ ( semila1122118281tate_o @ A_65 @ C_7 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1021_Int__Un__distrib,axiom,
% 0.24/0.48 ! [A_64: pname > $o,B_27: pname > $o,C_6: pname > $o] :
% 0.24/0.48 ( ( semila1673364395name_o @ A_64 @ ( semila1780557381name_o @ B_27 @ C_6 ) )
% 0.24/0.48 = ( semila1780557381name_o @ ( semila1673364395name_o @ A_64 @ B_27 ) @ ( semila1673364395name_o @ A_64 @ C_6 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1022_Int__Un__distrib,axiom,
% 0.24/0.48 ! [A_64: hoare_1708887482_state > $o,B_27: hoare_1708887482_state > $o,C_6: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila129691299tate_o @ A_64 @ ( semila1122118281tate_o @ B_27 @ C_6 ) )
% 0.24/0.48 = ( semila1122118281tate_o @ ( semila129691299tate_o @ A_64 @ B_27 ) @ ( semila129691299tate_o @ A_64 @ C_6 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1023_distrib__inf__le,axiom,
% 0.24/0.48 ! [X_20: $o,Y_9: $o,Z_4: $o] : ( ord_less_eq_o @ ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_20 @ Y_9 ) @ ( semila854092349_inf_o @ X_20 @ Z_4 ) ) @ ( semila854092349_inf_o @ X_20 @ ( semila10642723_sup_o @ Y_9 @ Z_4 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1024_distrib__inf__le,axiom,
% 0.24/0.48 ! [X_20: pname > $o,Y_9: pname > $o,Z_4: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ X_20 @ Y_9 ) @ ( semila1673364395name_o @ X_20 @ Z_4 ) ) @ ( semila1673364395name_o @ X_20 @ ( semila1780557381name_o @ Y_9 @ Z_4 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1025_distrib__inf__le,axiom,
% 0.24/0.48 ! [X_20: hoare_1708887482_state > $o,Y_9: hoare_1708887482_state > $o,Z_4: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila1122118281tate_o @ ( semila129691299tate_o @ X_20 @ Y_9 ) @ ( semila129691299tate_o @ X_20 @ Z_4 ) ) @ ( semila129691299tate_o @ X_20 @ ( semila1122118281tate_o @ Y_9 @ Z_4 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1026_distrib__sup__le,axiom,
% 0.24/0.48 ! [X_19: $o,Y_8: $o,Z_3: $o] : ( ord_less_eq_o @ ( semila10642723_sup_o @ X_19 @ ( semila854092349_inf_o @ Y_8 @ Z_3 ) ) @ ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_19 @ Y_8 ) @ ( semila10642723_sup_o @ X_19 @ Z_3 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1027_distrib__sup__le,axiom,
% 0.24/0.48 ! [X_19: pname > $o,Y_8: pname > $o,Z_3: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_19 @ ( semila1673364395name_o @ Y_8 @ Z_3 ) ) @ ( semila1673364395name_o @ ( semila1780557381name_o @ X_19 @ Y_8 ) @ ( semila1780557381name_o @ X_19 @ Z_3 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1028_distrib__sup__le,axiom,
% 0.24/0.48 ! [X_19: hoare_1708887482_state > $o,Y_8: hoare_1708887482_state > $o,Z_3: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila1122118281tate_o @ X_19 @ ( semila129691299tate_o @ Y_8 @ Z_3 ) ) @ ( semila129691299tate_o @ ( semila1122118281tate_o @ X_19 @ Y_8 ) @ ( semila1122118281tate_o @ X_19 @ Z_3 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1029_insert__Diff,axiom,
% 0.24/0.48 ! [A_63: com,A_62: com > $o] :
% 0.24/0.48 ( ( member_com @ A_63 @ A_62 )
% 0.24/0.48 => ( ( insert_com @ A_63 @ ( minus_minus_com_o @ A_62 @ ( insert_com @ A_63 @ bot_bot_com_o ) ) )
% 0.24/0.48 = A_62 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1030_insert__Diff,axiom,
% 0.24/0.48 ! [A_63: pname,A_62: pname > $o] :
% 0.24/0.48 ( ( member_pname @ A_63 @ A_62 )
% 0.24/0.48 => ( ( insert_pname @ A_63 @ ( minus_minus_pname_o @ A_62 @ ( insert_pname @ A_63 @ bot_bot_pname_o ) ) )
% 0.24/0.48 = A_62 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1031_insert__Diff,axiom,
% 0.24/0.48 ! [A_63: hoare_1708887482_state,A_62: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( member451959335_state @ A_63 @ A_62 )
% 0.24/0.48 => ( ( insert528405184_state @ A_63 @ ( minus_2056855718tate_o @ A_62 @ ( insert528405184_state @ A_63 @ bot_bo19817387tate_o ) ) )
% 0.24/0.48 = A_62 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1032_Diff__insert__absorb,axiom,
% 0.24/0.48 ! [X_18: com,A_61: com > $o] :
% 0.24/0.48 ( ~ ( member_com @ X_18 @ A_61 )
% 0.24/0.48 => ( ( minus_minus_com_o @ ( insert_com @ X_18 @ A_61 ) @ ( insert_com @ X_18 @ bot_bot_com_o ) )
% 0.24/0.48 = A_61 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1033_Diff__insert__absorb,axiom,
% 0.24/0.48 ! [X_18: pname,A_61: pname > $o] :
% 0.24/0.48 ( ~ ( member_pname @ X_18 @ A_61 )
% 0.24/0.48 => ( ( minus_minus_pname_o @ ( insert_pname @ X_18 @ A_61 ) @ ( insert_pname @ X_18 @ bot_bot_pname_o ) )
% 0.24/0.48 = A_61 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1034_Diff__insert__absorb,axiom,
% 0.24/0.48 ! [X_18: hoare_1708887482_state,A_61: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ~ ( member451959335_state @ X_18 @ A_61 )
% 0.24/0.48 => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_18 @ A_61 ) @ ( insert528405184_state @ X_18 @ bot_bo19817387tate_o ) )
% 0.24/0.48 = A_61 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1035_insert__Diff__single,axiom,
% 0.24/0.48 ! [A_60: com,A_59: com > $o] :
% 0.24/0.48 ( ( insert_com @ A_60 @ ( minus_minus_com_o @ A_59 @ ( insert_com @ A_60 @ bot_bot_com_o ) ) )
% 0.24/0.48 = ( insert_com @ A_60 @ A_59 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1036_insert__Diff__single,axiom,
% 0.24/0.48 ! [A_60: pname,A_59: pname > $o] :
% 0.24/0.48 ( ( insert_pname @ A_60 @ ( minus_minus_pname_o @ A_59 @ ( insert_pname @ A_60 @ bot_bot_pname_o ) ) )
% 0.24/0.48 = ( insert_pname @ A_60 @ A_59 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1037_insert__Diff__single,axiom,
% 0.24/0.48 ! [A_60: hoare_1708887482_state,A_59: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( insert528405184_state @ A_60 @ ( minus_2056855718tate_o @ A_59 @ ( insert528405184_state @ A_60 @ bot_bo19817387tate_o ) ) )
% 0.24/0.48 = ( insert528405184_state @ A_60 @ A_59 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1038_Diff__insert2,axiom,
% 0.24/0.48 ! [A_58: com > $o,A_57: com,B_26: com > $o] :
% 0.24/0.48 ( ( minus_minus_com_o @ A_58 @ ( insert_com @ A_57 @ B_26 ) )
% 0.24/0.48 = ( minus_minus_com_o @ ( minus_minus_com_o @ A_58 @ ( insert_com @ A_57 @ bot_bot_com_o ) ) @ B_26 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1039_Diff__insert2,axiom,
% 0.24/0.48 ! [A_58: pname > $o,A_57: pname,B_26: pname > $o] :
% 0.24/0.48 ( ( minus_minus_pname_o @ A_58 @ ( insert_pname @ A_57 @ B_26 ) )
% 0.24/0.48 = ( minus_minus_pname_o @ ( minus_minus_pname_o @ A_58 @ ( insert_pname @ A_57 @ bot_bot_pname_o ) ) @ B_26 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1040_Diff__insert2,axiom,
% 0.24/0.48 ! [A_58: hoare_1708887482_state > $o,A_57: hoare_1708887482_state,B_26: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( minus_2056855718tate_o @ A_58 @ ( insert528405184_state @ A_57 @ B_26 ) )
% 0.24/0.48 = ( minus_2056855718tate_o @ ( minus_2056855718tate_o @ A_58 @ ( insert528405184_state @ A_57 @ bot_bo19817387tate_o ) ) @ B_26 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1041_Diff__insert,axiom,
% 0.24/0.48 ! [A_56: com > $o,A_55: com,B_25: com > $o] :
% 0.24/0.48 ( ( minus_minus_com_o @ A_56 @ ( insert_com @ A_55 @ B_25 ) )
% 0.24/0.48 = ( minus_minus_com_o @ ( minus_minus_com_o @ A_56 @ B_25 ) @ ( insert_com @ A_55 @ bot_bot_com_o ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1042_Diff__insert,axiom,
% 0.24/0.48 ! [A_56: pname > $o,A_55: pname,B_25: pname > $o] :
% 0.24/0.48 ( ( minus_minus_pname_o @ A_56 @ ( insert_pname @ A_55 @ B_25 ) )
% 0.24/0.48 = ( minus_minus_pname_o @ ( minus_minus_pname_o @ A_56 @ B_25 ) @ ( insert_pname @ A_55 @ bot_bot_pname_o ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1043_Diff__insert,axiom,
% 0.24/0.48 ! [A_56: hoare_1708887482_state > $o,A_55: hoare_1708887482_state,B_25: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( minus_2056855718tate_o @ A_56 @ ( insert528405184_state @ A_55 @ B_25 ) )
% 0.24/0.48 = ( minus_2056855718tate_o @ ( minus_2056855718tate_o @ A_56 @ B_25 ) @ ( insert528405184_state @ A_55 @ bot_bo19817387tate_o ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1044_finite__Diff__insert,axiom,
% 0.24/0.48 ! [A_54: com > $o,A_53: com,B_24: com > $o] :
% 0.24/0.48 ( ( finite_finite_com @ ( minus_minus_com_o @ A_54 @ ( insert_com @ A_53 @ B_24 ) ) )
% 0.24/0.48 <=> ( finite_finite_com @ ( minus_minus_com_o @ A_54 @ B_24 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1045_finite__Diff__insert,axiom,
% 0.24/0.48 ! [A_54: pname > $o,A_53: pname,B_24: pname > $o] :
% 0.24/0.48 ( ( finite_finite_pname @ ( minus_minus_pname_o @ A_54 @ ( insert_pname @ A_53 @ B_24 ) ) )
% 0.24/0.48 <=> ( finite_finite_pname @ ( minus_minus_pname_o @ A_54 @ B_24 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1046_finite__Diff__insert,axiom,
% 0.24/0.48 ! [A_54: hoare_1708887482_state > $o,A_53: hoare_1708887482_state,B_24: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( finite1625599783_state @ ( minus_2056855718tate_o @ A_54 @ ( insert528405184_state @ A_53 @ B_24 ) ) )
% 0.24/0.48 <=> ( finite1625599783_state @ ( minus_2056855718tate_o @ A_54 @ B_24 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1047_finite__Diff__insert,axiom,
% 0.24/0.48 ! [A_54: ( pname > $o ) > $o,A_53: pname > $o,B_24: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_54 @ ( insert_pname_o @ A_53 @ B_24 ) ) )
% 0.24/0.48 <=> ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_54 @ B_24 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1048_finite__Diff__insert,axiom,
% 0.24/0.48 ! [A_54: ( hoare_1708887482_state > $o ) > $o,A_53: hoare_1708887482_state > $o,B_24: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_54 @ ( insert949073679tate_o @ A_53 @ B_24 ) ) )
% 0.24/0.48 <=> ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_54 @ B_24 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1049_image__diff__subset,axiom,
% 0.24/0.48 ! [F_27: pname > hoare_1708887482_state,A_52: pname > $o,B_23: pname > $o] : ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ ( image_1116629049_state @ F_27 @ A_52 ) @ ( image_1116629049_state @ F_27 @ B_23 ) ) @ ( image_1116629049_state @ F_27 @ ( minus_minus_pname_o @ A_52 @ B_23 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1050_Diff__partition,axiom,
% 0.24/0.48 ! [A_51: pname > $o,B_22: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ A_51 @ B_22 )
% 0.24/0.48 => ( ( semila1780557381name_o @ A_51 @ ( minus_minus_pname_o @ B_22 @ A_51 ) )
% 0.24/0.48 = B_22 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1051_Diff__partition,axiom,
% 0.24/0.48 ! [A_51: hoare_1708887482_state > $o,B_22: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ A_51 @ B_22 )
% 0.24/0.48 => ( ( semila1122118281tate_o @ A_51 @ ( minus_2056855718tate_o @ B_22 @ A_51 ) )
% 0.24/0.48 = B_22 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1052_Diff__subset__conv,axiom,
% 0.24/0.48 ! [A_50: pname > $o,B_21: pname > $o,C_5: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_50 @ B_21 ) @ C_5 )
% 0.24/0.48 <=> ( ord_less_eq_pname_o @ A_50 @ ( semila1780557381name_o @ B_21 @ C_5 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1053_Diff__subset__conv,axiom,
% 0.24/0.48 ! [A_50: hoare_1708887482_state > $o,B_21: hoare_1708887482_state > $o,C_5: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_50 @ B_21 ) @ C_5 )
% 0.24/0.48 <=> ( ord_le777019615tate_o @ A_50 @ ( semila1122118281tate_o @ B_21 @ C_5 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1054_image__Int__subset,axiom,
% 0.24/0.48 ! [F_26: pname > hoare_1708887482_state,A_49: pname > $o,B_20: pname > $o] : ( ord_le777019615tate_o @ ( image_1116629049_state @ F_26 @ ( semila1673364395name_o @ A_49 @ B_20 ) ) @ ( semila129691299tate_o @ ( image_1116629049_state @ F_26 @ A_49 ) @ ( image_1116629049_state @ F_26 @ B_20 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1055_Un__Int__assoc__eq,axiom,
% 0.24/0.48 ! [A_48: pname > $o,B_19: pname > $o,C_4: pname > $o] :
% 0.24/0.48 ( ( ( semila1780557381name_o @ ( semila1673364395name_o @ A_48 @ B_19 ) @ C_4 )
% 0.24/0.48 = ( semila1673364395name_o @ A_48 @ ( semila1780557381name_o @ B_19 @ C_4 ) ) )
% 0.24/0.48 <=> ( ord_less_eq_pname_o @ C_4 @ A_48 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1056_Un__Int__assoc__eq,axiom,
% 0.24/0.48 ! [A_48: hoare_1708887482_state > $o,B_19: hoare_1708887482_state > $o,C_4: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ( semila1122118281tate_o @ ( semila129691299tate_o @ A_48 @ B_19 ) @ C_4 )
% 0.24/0.48 = ( semila129691299tate_o @ A_48 @ ( semila1122118281tate_o @ B_19 @ C_4 ) ) )
% 0.24/0.48 <=> ( ord_le777019615tate_o @ C_4 @ A_48 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1057_if__image__distrib,axiom,
% 0.24/0.48 ! [P_4: pname > $o,F_25: pname > hoare_1708887482_state,G_4: pname > hoare_1708887482_state,S: pname > $o] :
% 0.24/0.48 ( ( image_1116629049_state
% 0.24/0.48 @ ^ [X_3: pname] : ( if_Hoa1374726218_state @ ( P_4 @ X_3 ) @ ( F_25 @ X_3 ) @ ( G_4 @ X_3 ) )
% 0.24/0.48 @ S )
% 0.24/0.48 = ( semila1122118281tate_o @ ( image_1116629049_state @ F_25 @ ( semila1673364395name_o @ S @ ( collect_pname @ P_4 ) ) )
% 0.24/0.48 @ ( image_1116629049_state @ G_4
% 0.24/0.48 @ ( semila1673364395name_o @ S
% 0.24/0.48 @ ( collect_pname
% 0.24/0.48 @ ^ [X_3: pname] : ( (~) @ ( P_4 @ X_3 ) ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1058_dom__if,axiom,
% 0.24/0.48 ! [P_3: pname > $o,F_24: pname > option_com,G_3: pname > option_com] :
% 0.24/0.48 ( ( dom_pname_com
% 0.24/0.48 @ ^ [X_3: pname] : ( if_option_com @ ( P_3 @ X_3 ) @ ( F_24 @ X_3 ) @ ( G_3 @ X_3 ) ) )
% 0.24/0.48 = ( semila1780557381name_o @ ( semila1673364395name_o @ ( dom_pname_com @ F_24 ) @ ( collect_pname @ P_3 ) )
% 0.24/0.48 @ ( semila1673364395name_o @ ( dom_pname_com @ G_3 )
% 0.24/0.48 @ ( collect_pname
% 0.24/0.48 @ ^ [X_3: pname] : ( (~) @ ( P_3 @ X_3 ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1059_diff__single__insert,axiom,
% 0.24/0.48 ! [A_47: com > $o,X_17: com,B_18: com > $o] :
% 0.24/0.48 ( ( ord_less_eq_com_o @ ( minus_minus_com_o @ A_47 @ ( insert_com @ X_17 @ bot_bot_com_o ) ) @ B_18 )
% 0.24/0.48 => ( ( member_com @ X_17 @ A_47 )
% 0.24/0.48 => ( ord_less_eq_com_o @ A_47 @ ( insert_com @ X_17 @ B_18 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1060_diff__single__insert,axiom,
% 0.24/0.48 ! [A_47: pname > $o,X_17: pname,B_18: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_47 @ ( insert_pname @ X_17 @ bot_bot_pname_o ) ) @ B_18 )
% 0.24/0.48 => ( ( member_pname @ X_17 @ A_47 )
% 0.24/0.48 => ( ord_less_eq_pname_o @ A_47 @ ( insert_pname @ X_17 @ B_18 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1061_diff__single__insert,axiom,
% 0.24/0.48 ! [A_47: hoare_1708887482_state > $o,X_17: hoare_1708887482_state,B_18: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_47 @ ( insert528405184_state @ X_17 @ bot_bo19817387tate_o ) ) @ B_18 )
% 0.24/0.48 => ( ( member451959335_state @ X_17 @ A_47 )
% 0.24/0.48 => ( ord_le777019615tate_o @ A_47 @ ( insert528405184_state @ X_17 @ B_18 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1062_subset__insert__iff,axiom,
% 0.24/0.48 ! [A_46: com > $o,X_16: com,B_17: com > $o] :
% 0.24/0.48 ( ( ord_less_eq_com_o @ A_46 @ ( insert_com @ X_16 @ B_17 ) )
% 0.24/0.48 <=> ( ( ( member_com @ X_16 @ A_46 )
% 0.24/0.48 => ( ord_less_eq_com_o @ ( minus_minus_com_o @ A_46 @ ( insert_com @ X_16 @ bot_bot_com_o ) ) @ B_17 ) )
% 0.24/0.48 & ( ~ ( member_com @ X_16 @ A_46 )
% 0.24/0.48 => ( ord_less_eq_com_o @ A_46 @ B_17 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1063_subset__insert__iff,axiom,
% 0.24/0.48 ! [A_46: pname > $o,X_16: pname,B_17: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ A_46 @ ( insert_pname @ X_16 @ B_17 ) )
% 0.24/0.48 <=> ( ( ( member_pname @ X_16 @ A_46 )
% 0.24/0.48 => ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_46 @ ( insert_pname @ X_16 @ bot_bot_pname_o ) ) @ B_17 ) )
% 0.24/0.48 & ( ~ ( member_pname @ X_16 @ A_46 )
% 0.24/0.48 => ( ord_less_eq_pname_o @ A_46 @ B_17 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1064_subset__insert__iff,axiom,
% 0.24/0.48 ! [A_46: hoare_1708887482_state > $o,X_16: hoare_1708887482_state,B_17: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ A_46 @ ( insert528405184_state @ X_16 @ B_17 ) )
% 0.24/0.48 <=> ( ( ( member451959335_state @ X_16 @ A_46 )
% 0.24/0.48 => ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_46 @ ( insert528405184_state @ X_16 @ bot_bo19817387tate_o ) ) @ B_17 ) )
% 0.24/0.48 & ( ~ ( member451959335_state @ X_16 @ A_46 )
% 0.24/0.48 => ( ord_le777019615tate_o @ A_46 @ B_17 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1065_finite__empty__induct,axiom,
% 0.24/0.48 ! [P_2: ( com > $o ) > $o,A_45: com > $o] :
% 0.24/0.48 ( ( finite_finite_com @ A_45 )
% 0.24/0.48 => ( ( P_2 @ A_45 )
% 0.24/0.48 => ( ! [A_6: com,A_39: com > $o] :
% 0.24/0.48 ( ( finite_finite_com @ A_39 )
% 0.24/0.48 => ( ( member_com @ A_6 @ A_39 )
% 0.24/0.48 => ( ( P_2 @ A_39 )
% 0.24/0.48 => ( P_2 @ ( minus_minus_com_o @ A_39 @ ( insert_com @ A_6 @ bot_bot_com_o ) ) ) ) ) )
% 0.24/0.48 => ( P_2 @ bot_bot_com_o ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1066_finite__empty__induct,axiom,
% 0.24/0.48 ! [P_2: ( pname > $o ) > $o,A_45: pname > $o] :
% 0.24/0.48 ( ( finite_finite_pname @ A_45 )
% 0.24/0.48 => ( ( P_2 @ A_45 )
% 0.24/0.48 => ( ! [A_6: pname,A_39: pname > $o] :
% 0.24/0.48 ( ( finite_finite_pname @ A_39 )
% 0.24/0.48 => ( ( member_pname @ A_6 @ A_39 )
% 0.24/0.48 => ( ( P_2 @ A_39 )
% 0.24/0.48 => ( P_2 @ ( minus_minus_pname_o @ A_39 @ ( insert_pname @ A_6 @ bot_bot_pname_o ) ) ) ) ) )
% 0.24/0.48 => ( P_2 @ bot_bot_pname_o ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1067_finite__empty__induct,axiom,
% 0.24/0.48 ! [P_2: ( hoare_1708887482_state > $o ) > $o,A_45: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( finite1625599783_state @ A_45 )
% 0.24/0.48 => ( ( P_2 @ A_45 )
% 0.24/0.48 => ( ! [A_6: hoare_1708887482_state,A_39: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( finite1625599783_state @ A_39 )
% 0.24/0.48 => ( ( member451959335_state @ A_6 @ A_39 )
% 0.24/0.48 => ( ( P_2 @ A_39 )
% 0.24/0.48 => ( P_2 @ ( minus_2056855718tate_o @ A_39 @ ( insert528405184_state @ A_6 @ bot_bo19817387tate_o ) ) ) ) ) )
% 0.24/0.48 => ( P_2 @ bot_bo19817387tate_o ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1068_finite__empty__induct,axiom,
% 0.24/0.48 ! [P_2: ( ( pname > $o ) > $o ) > $o,A_45: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_45 )
% 0.24/0.48 => ( ( P_2 @ A_45 )
% 0.24/0.48 => ( ! [A_6: pname > $o,A_39: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_39 )
% 0.24/0.48 => ( ( member_pname_o @ A_6 @ A_39 )
% 0.24/0.48 => ( ( P_2 @ A_39 )
% 0.24/0.48 => ( P_2 @ ( minus_1480864103me_o_o @ A_39 @ ( insert_pname_o @ A_6 @ bot_bot_pname_o_o ) ) ) ) ) )
% 0.24/0.48 => ( P_2 @ bot_bot_pname_o_o ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1069_finite__empty__induct,axiom,
% 0.24/0.48 ! [P_2: ( ( hoare_1708887482_state > $o ) > $o ) > $o,A_45: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_45 )
% 0.24/0.48 => ( ( P_2 @ A_45 )
% 0.24/0.48 => ( ! [A_6: hoare_1708887482_state > $o,A_39: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_39 )
% 0.24/0.48 => ( ( member814030440tate_o @ A_6 @ A_39 )
% 0.24/0.48 => ( ( P_2 @ A_39 )
% 0.24/0.48 => ( P_2 @ ( minus_548038231te_o_o @ A_39 @ ( insert949073679tate_o @ A_6 @ bot_bo1678742418te_o_o ) ) ) ) ) )
% 0.24/0.48 => ( P_2 @ bot_bo1678742418te_o_o ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1070_dom__override__on,axiom,
% 0.24/0.48 ! [F_23: pname > option_com,G_2: pname > option_com,A_44: pname > $o] :
% 0.24/0.48 ( ( dom_pname_com @ ( overri1496249029on_com @ F_23 @ G_2 @ A_44 ) )
% 0.24/0.48 = ( semila1780557381name_o
% 0.24/0.48 @ ( minus_minus_pname_o @ ( dom_pname_com @ F_23 )
% 0.24/0.48 @ ( collect_pname
% 0.24/0.48 @ ^ [A_6: pname] : ( member_pname @ A_6 @ ( minus_minus_pname_o @ A_44 @ ( dom_pname_com @ G_2 ) ) ) ) )
% 0.24/0.48 @ ( collect_pname
% 0.24/0.48 @ ^ [A_6: pname] : ( member_pname @ A_6 @ ( semila1673364395name_o @ A_44 @ ( dom_pname_com @ G_2 ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1071_Int__Collect__mono,axiom,
% 0.24/0.48 ! [Q: com > $o,P_1: com > $o,A_43: com > $o,B_16: com > $o] :
% 0.24/0.48 ( ( ord_less_eq_com_o @ A_43 @ B_16 )
% 0.24/0.48 => ( ! [X_3: com] :
% 0.24/0.48 ( ( member_com @ X_3 @ A_43 )
% 0.24/0.48 => ( ( P_1 @ X_3 )
% 0.24/0.48 => ( Q @ X_3 ) ) )
% 0.24/0.48 => ( ord_less_eq_com_o @ ( semila513601829_com_o @ A_43 @ ( collect_com @ P_1 ) ) @ ( semila513601829_com_o @ B_16 @ ( collect_com @ Q ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1072_Int__Collect__mono,axiom,
% 0.24/0.48 ! [Q: pname > $o,P_1: pname > $o,A_43: pname > $o,B_16: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ A_43 @ B_16 )
% 0.24/0.48 => ( ! [X_3: pname] :
% 0.24/0.48 ( ( member_pname @ X_3 @ A_43 )
% 0.24/0.48 => ( ( P_1 @ X_3 )
% 0.24/0.48 => ( Q @ X_3 ) ) )
% 0.24/0.48 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_43 @ ( collect_pname @ P_1 ) ) @ ( semila1673364395name_o @ B_16 @ ( collect_pname @ Q ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1073_Int__Collect__mono,axiom,
% 0.24/0.48 ! [Q: hoare_1708887482_state > $o,P_1: hoare_1708887482_state > $o,A_43: hoare_1708887482_state > $o,B_16: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ A_43 @ B_16 )
% 0.24/0.48 => ( ! [X_3: hoare_1708887482_state] :
% 0.24/0.48 ( ( member451959335_state @ X_3 @ A_43 )
% 0.24/0.48 => ( ( P_1 @ X_3 )
% 0.24/0.48 => ( Q @ X_3 ) ) )
% 0.24/0.48 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_43 @ ( collec1568722789_state @ P_1 ) ) @ ( semila129691299tate_o @ B_16 @ ( collec1568722789_state @ Q ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1074_Int__Collect__mono,axiom,
% 0.24/0.48 ! [Q: ( pname > $o ) > $o,P_1: ( pname > $o ) > $o,A_43: ( pname > $o ) > $o,B_16: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( ord_le1205211808me_o_o @ A_43 @ B_16 )
% 0.24/0.48 => ( ! [X_3: pname > $o] :
% 0.24/0.48 ( ( member_pname_o @ X_3 @ A_43 )
% 0.24/0.48 => ( ( P_1 @ X_3 )
% 0.24/0.48 => ( Q @ X_3 ) ) )
% 0.24/0.48 => ( ord_le1205211808me_o_o @ ( semila2013987940me_o_o @ A_43 @ ( collect_pname_o @ P_1 ) ) @ ( semila2013987940me_o_o @ B_16 @ ( collect_pname_o @ Q ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1075_Int__Collect__mono,axiom,
% 0.24/0.48 ! [Q: ( hoare_1708887482_state > $o ) > $o,P_1: ( hoare_1708887482_state > $o ) > $o,A_43: ( hoare_1708887482_state > $o ) > $o,B_16: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( ord_le1728773982te_o_o @ A_43 @ B_16 )
% 0.24/0.48 => ( ! [X_3: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( member814030440tate_o @ X_3 @ A_43 )
% 0.24/0.48 => ( ( P_1 @ X_3 )
% 0.24/0.48 => ( Q @ X_3 ) ) )
% 0.24/0.48 => ( ord_le1728773982te_o_o @ ( semila598060698te_o_o @ A_43 @ ( collec219771562tate_o @ P_1 ) ) @ ( semila598060698te_o_o @ B_16 @ ( collec219771562tate_o @ Q ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1076_distrib__imp2,axiom,
% 0.24/0.48 ! [X_15: $o,Y_7: $o,Z_2: $o] :
% 0.24/0.48 ( ! [X_3: $o,Y_4: $o,Z_1: $o] :
% 0.24/0.48 ( ( semila10642723_sup_o @ X_3 @ ( semila854092349_inf_o @ Y_4 @ Z_1 ) )
% 0.24/0.48 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_3 @ Y_4 ) @ ( semila10642723_sup_o @ X_3 @ Z_1 ) ) )
% 0.24/0.48 => ( ( semila854092349_inf_o @ X_15 @ ( semila10642723_sup_o @ Y_7 @ Z_2 ) )
% 0.24/0.48 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_15 @ Y_7 ) @ ( semila854092349_inf_o @ X_15 @ Z_2 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1077_distrib__imp2,axiom,
% 0.24/0.48 ! [X_15: pname > $o,Y_7: pname > $o,Z_2: pname > $o] :
% 0.24/0.48 ( ! [X_3: pname > $o,Y_4: pname > $o,Z_1: pname > $o] :
% 0.24/0.48 ( ( semila1780557381name_o @ X_3 @ ( semila1673364395name_o @ Y_4 @ Z_1 ) )
% 0.24/0.48 = ( semila1673364395name_o @ ( semila1780557381name_o @ X_3 @ Y_4 ) @ ( semila1780557381name_o @ X_3 @ Z_1 ) ) )
% 0.24/0.48 => ( ( semila1673364395name_o @ X_15 @ ( semila1780557381name_o @ Y_7 @ Z_2 ) )
% 0.24/0.48 = ( semila1780557381name_o @ ( semila1673364395name_o @ X_15 @ Y_7 ) @ ( semila1673364395name_o @ X_15 @ Z_2 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1078_distrib__imp2,axiom,
% 0.24/0.48 ! [X_15: hoare_1708887482_state > $o,Y_7: hoare_1708887482_state > $o,Z_2: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o,Z_1: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila1122118281tate_o @ X_3 @ ( semila129691299tate_o @ Y_4 @ Z_1 ) )
% 0.24/0.48 = ( semila129691299tate_o @ ( semila1122118281tate_o @ X_3 @ Y_4 ) @ ( semila1122118281tate_o @ X_3 @ Z_1 ) ) )
% 0.24/0.48 => ( ( semila129691299tate_o @ X_15 @ ( semila1122118281tate_o @ Y_7 @ Z_2 ) )
% 0.24/0.48 = ( semila1122118281tate_o @ ( semila129691299tate_o @ X_15 @ Y_7 ) @ ( semila129691299tate_o @ X_15 @ Z_2 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1079_distrib__imp1,axiom,
% 0.24/0.48 ! [X_14: $o,Y_6: $o,Z: $o] :
% 0.24/0.48 ( ! [X_3: $o,Y_4: $o,Z_1: $o] :
% 0.24/0.48 ( ( semila854092349_inf_o @ X_3 @ ( semila10642723_sup_o @ Y_4 @ Z_1 ) )
% 0.24/0.48 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_3 @ Y_4 ) @ ( semila854092349_inf_o @ X_3 @ Z_1 ) ) )
% 0.24/0.48 => ( ( semila10642723_sup_o @ X_14 @ ( semila854092349_inf_o @ Y_6 @ Z ) )
% 0.24/0.48 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_14 @ Y_6 ) @ ( semila10642723_sup_o @ X_14 @ Z ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1080_distrib__imp1,axiom,
% 0.24/0.48 ! [X_14: pname > $o,Y_6: pname > $o,Z: pname > $o] :
% 0.24/0.48 ( ! [X_3: pname > $o,Y_4: pname > $o,Z_1: pname > $o] :
% 0.24/0.48 ( ( semila1673364395name_o @ X_3 @ ( semila1780557381name_o @ Y_4 @ Z_1 ) )
% 0.24/0.48 = ( semila1780557381name_o @ ( semila1673364395name_o @ X_3 @ Y_4 ) @ ( semila1673364395name_o @ X_3 @ Z_1 ) ) )
% 0.24/0.48 => ( ( semila1780557381name_o @ X_14 @ ( semila1673364395name_o @ Y_6 @ Z ) )
% 0.24/0.48 = ( semila1673364395name_o @ ( semila1780557381name_o @ X_14 @ Y_6 ) @ ( semila1780557381name_o @ X_14 @ Z ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1081_distrib__imp1,axiom,
% 0.24/0.48 ! [X_14: hoare_1708887482_state > $o,Y_6: hoare_1708887482_state > $o,Z: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o,Z_1: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila129691299tate_o @ X_3 @ ( semila1122118281tate_o @ Y_4 @ Z_1 ) )
% 0.24/0.48 = ( semila1122118281tate_o @ ( semila129691299tate_o @ X_3 @ Y_4 ) @ ( semila129691299tate_o @ X_3 @ Z_1 ) ) )
% 0.24/0.48 => ( ( semila1122118281tate_o @ X_14 @ ( semila129691299tate_o @ Y_6 @ Z ) )
% 0.24/0.48 = ( semila129691299tate_o @ ( semila1122118281tate_o @ X_14 @ Y_6 ) @ ( semila1122118281tate_o @ X_14 @ Z ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1082_flat__lub__def,axiom,
% 0.24/0.48 ! [A_42: com > $o,B_15: com] :
% 0.24/0.48 ( ( ( ord_less_eq_com_o @ A_42 @ ( insert_com @ B_15 @ bot_bot_com_o ) )
% 0.24/0.48 => ( ( partial_flat_lub_com @ B_15 @ A_42 )
% 0.24/0.48 = B_15 ) )
% 0.24/0.48 & ( ~ ( ord_less_eq_com_o @ A_42 @ ( insert_com @ B_15 @ bot_bot_com_o ) )
% 0.24/0.48 => ( ( partial_flat_lub_com @ B_15 @ A_42 )
% 0.24/0.48 = ( the_com_1
% 0.24/0.48 @ ^ [X_3: com] : ( member_com @ X_3 @ ( minus_minus_com_o @ A_42 @ ( insert_com @ B_15 @ bot_bot_com_o ) ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1083_flat__lub__def,axiom,
% 0.24/0.48 ! [A_42: pname > $o,B_15: pname] :
% 0.24/0.48 ( ( ( ord_less_eq_pname_o @ A_42 @ ( insert_pname @ B_15 @ bot_bot_pname_o ) )
% 0.24/0.48 => ( ( partia752020666_pname @ B_15 @ A_42 )
% 0.24/0.48 = B_15 ) )
% 0.24/0.48 & ( ~ ( ord_less_eq_pname_o @ A_42 @ ( insert_pname @ B_15 @ bot_bot_pname_o ) )
% 0.24/0.48 => ( ( partia752020666_pname @ B_15 @ A_42 )
% 0.24/0.48 = ( the_pname
% 0.24/0.48 @ ^ [X_3: pname] : ( member_pname @ X_3 @ ( minus_minus_pname_o @ A_42 @ ( insert_pname @ B_15 @ bot_bot_pname_o ) ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1084_flat__lub__def,axiom,
% 0.24/0.48 ! [A_42: hoare_1708887482_state > $o,B_15: hoare_1708887482_state] :
% 0.24/0.48 ( ( ( ord_le777019615tate_o @ A_42 @ ( insert528405184_state @ B_15 @ bot_bo19817387tate_o ) )
% 0.24/0.48 => ( ( partia1256728516_state @ B_15 @ A_42 )
% 0.24/0.48 = B_15 ) )
% 0.24/0.48 & ( ~ ( ord_le777019615tate_o @ A_42 @ ( insert528405184_state @ B_15 @ bot_bo19817387tate_o ) )
% 0.24/0.48 => ( ( partia1256728516_state @ B_15 @ A_42 )
% 0.24/0.48 = ( the_Ho851197897_state
% 0.24/0.48 @ ^ [X_3: hoare_1708887482_state] : ( member451959335_state @ X_3 @ ( minus_2056855718tate_o @ A_42 @ ( insert528405184_state @ B_15 @ bot_bo19817387tate_o ) ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1085_comp__fun__idem__remove,axiom,
% 0.24/0.48 ( finite567462577_com_o
% 0.24/0.48 @ ^ [X_3: com,A_39: com > $o] : ( minus_minus_com_o @ A_39 @ ( insert_com @ X_3 @ bot_bot_com_o ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1086_comp__fun__idem__remove,axiom,
% 0.24/0.48 ( finite1123817265name_o
% 0.24/0.48 @ ^ [X_3: pname,A_39: pname > $o] : ( minus_minus_pname_o @ A_39 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1087_comp__fun__idem__remove,axiom,
% 0.24/0.48 ( finite662762081tate_o
% 0.24/0.48 @ ^ [X_3: hoare_1708887482_state,A_39: hoare_1708887482_state > $o] : ( minus_2056855718tate_o @ A_39 @ ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1088_fun__upd__image,axiom,
% 0.24/0.48 ! [F_22: pname > hoare_1708887482_state,Y_5: hoare_1708887482_state,X_13: pname,A_41: pname > $o] :
% 0.24/0.48 ( ( ( member_pname @ X_13 @ A_41 )
% 0.24/0.48 => ( ( image_1116629049_state @ ( fun_up1986763201_state @ F_22 @ X_13 @ Y_5 ) @ A_41 )
% 0.24/0.48 = ( insert528405184_state @ Y_5 @ ( image_1116629049_state @ F_22 @ ( minus_minus_pname_o @ A_41 @ ( insert_pname @ X_13 @ bot_bot_pname_o ) ) ) ) ) )
% 0.24/0.48 & ( ~ ( member_pname @ X_13 @ A_41 )
% 0.24/0.48 => ( ( image_1116629049_state @ ( fun_up1986763201_state @ F_22 @ X_13 @ Y_5 ) @ A_41 )
% 0.24/0.48 = ( image_1116629049_state @ F_22 @ A_41 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1089_comp__fun__idem__insert,axiom,
% 0.24/0.48 finite567462577_com_o @ insert_com ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1090_comp__fun__idem__insert,axiom,
% 0.24/0.48 finite1123817265name_o @ insert_pname ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1091_comp__fun__idem__insert,axiom,
% 0.24/0.48 finite662762081tate_o @ insert528405184_state ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1092_comp__fun__idem__sup,axiom,
% 0.24/0.48 finite2048025996em_o_o @ semila10642723_sup_o ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1093_comp__fun__idem__sup,axiom,
% 0.24/0.48 finite138924780name_o @ semila1780557381name_o ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1094_comp__fun__idem__sup,axiom,
% 0.24/0.48 finite2034616076tate_o @ semila1122118281tate_o ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1095_inj__on__Un,axiom,
% 0.24/0.48 ! [F_21: pname > hoare_1708887482_state,A_40: pname > $o,B_14: pname > $o] :
% 0.24/0.48 ( ( inj_on1553129421_state @ F_21 @ ( semila1780557381name_o @ A_40 @ B_14 ) )
% 0.24/0.48 <=> ( ( inj_on1553129421_state @ F_21 @ A_40 )
% 0.24/0.48 & ( inj_on1553129421_state @ F_21 @ B_14 )
% 0.24/0.48 & ( ( semila129691299tate_o @ ( image_1116629049_state @ F_21 @ ( minus_minus_pname_o @ A_40 @ B_14 ) ) @ ( image_1116629049_state @ F_21 @ ( minus_minus_pname_o @ B_14 @ A_40 ) ) )
% 0.24/0.48 = bot_bo19817387tate_o ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1096_dom__eq__singleton__conv,axiom,
% 0.24/0.48 ! [F_20: pname > option_com,X_12: pname] :
% 0.24/0.48 ( ( ( dom_pname_com @ F_20 )
% 0.24/0.48 = ( insert_pname @ X_12 @ bot_bot_pname_o ) )
% 0.24/0.48 <=> ? [V: com] :
% 0.24/0.48 ( F_20
% 0.24/0.48 = ( fun_up879233478on_com
% 0.24/0.48 @ ^ [X_3: pname] : none_com
% 0.24/0.48 @ X_12
% 0.24/0.48 @ ( some_com @ V ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1097_minus__fold__remove,axiom,
% 0.24/0.48 ! [B_13: com > $o,A_38: com > $o] :
% 0.24/0.48 ( ( finite_finite_com @ A_38 )
% 0.24/0.48 => ( ( minus_minus_com_o @ B_13 @ A_38 )
% 0.24/0.48 = ( finite504235573_com_o
% 0.24/0.48 @ ^ [X_3: com,A_39: com > $o] : ( minus_minus_com_o @ A_39 @ ( insert_com @ X_3 @ bot_bot_com_o ) )
% 0.24/0.48 @ B_13
% 0.24/0.48 @ A_38 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1098_minus__fold__remove,axiom,
% 0.24/0.48 ! [B_13: pname > $o,A_38: pname > $o] :
% 0.24/0.48 ( ( finite_finite_pname @ A_38 )
% 0.24/0.48 => ( ( minus_minus_pname_o @ B_13 @ A_38 )
% 0.24/0.48 = ( finite603803317name_o
% 0.24/0.48 @ ^ [X_3: pname,A_39: pname > $o] : ( minus_minus_pname_o @ A_39 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
% 0.24/0.48 @ B_13
% 0.24/0.48 @ A_38 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1099_minus__fold__remove,axiom,
% 0.24/0.48 ! [B_13: hoare_1708887482_state > $o,A_38: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( finite1625599783_state @ A_38 )
% 0.24/0.48 => ( ( minus_2056855718tate_o @ B_13 @ A_38 )
% 0.24/0.48 = ( finite96880613tate_o
% 0.24/0.48 @ ^ [X_3: hoare_1708887482_state,A_39: hoare_1708887482_state > $o] : ( minus_2056855718tate_o @ A_39 @ ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) )
% 0.24/0.48 @ B_13
% 0.24/0.48 @ A_38 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1100_minus__fold__remove,axiom,
% 0.24/0.48 ! [B_13: ( pname > $o ) > $o,A_38: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_38 )
% 0.24/0.48 => ( ( minus_1480864103me_o_o @ B_13 @ A_38 )
% 0.24/0.48 = ( finite1849951719me_o_o
% 0.24/0.48 @ ^ [X_3: pname > $o,A_39: ( pname > $o ) > $o] : ( minus_1480864103me_o_o @ A_39 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
% 0.24/0.48 @ B_13
% 0.24/0.48 @ A_38 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1101_minus__fold__remove,axiom,
% 0.24/0.48 ! [B_13: ( hoare_1708887482_state > $o ) > $o,A_38: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_38 )
% 0.24/0.48 => ( ( minus_548038231te_o_o @ B_13 @ A_38 )
% 0.24/0.48 = ( finite463603445te_o_o
% 0.24/0.48 @ ^ [X_3: hoare_1708887482_state > $o,A_39: ( hoare_1708887482_state > $o ) > $o] : ( minus_548038231te_o_o @ A_39 @ ( insert949073679tate_o @ X_3 @ bot_bo1678742418te_o_o ) )
% 0.24/0.48 @ B_13
% 0.24/0.48 @ A_38 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1102_image__eq__fold__image,axiom,
% 0.24/0.48 ! [F_19: pname > hoare_1708887482_state,A_37: pname > $o] :
% 0.24/0.48 ( ( finite_finite_pname @ A_37 )
% 0.24/0.48 => ( ( image_1116629049_state @ F_19 @ A_37 )
% 0.24/0.48 = ( finite2139561282_pname @ semila1122118281tate_o
% 0.24/0.48 @ ^ [X_3: pname] : ( insert528405184_state @ ( F_19 @ X_3 ) @ bot_bo19817387tate_o )
% 0.24/0.48 @ bot_bo19817387tate_o
% 0.24/0.48 @ A_37 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1103_inj__Some,axiom,
% 0.24/0.48 ! [A_36: pname > $o] : ( inj_on737724108_pname @ some_pname @ A_36 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1104_inj__Some,axiom,
% 0.24/0.48 ! [A_36: hoare_1708887482_state > $o] : ( inj_on945311362_state @ some_H1974565227_state @ A_36 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1105_inj__Some,axiom,
% 0.24/0.48 ! [A_36: com > $o] : ( inj_on11367768on_com @ some_com @ A_36 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1106_option_Osimps_I2_J,axiom,
% 0.24/0.48 ! [A_35: com] :
% 0.24/0.48 ( none_com
% 0.24/0.48 != ( some_com @ A_35 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1107_option_Osimps_I2_J,axiom,
% 0.24/0.48 ! [A_35: pname] :
% 0.24/0.48 ( none_pname
% 0.24/0.48 != ( some_pname @ A_35 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1108_option_Osimps_I2_J,axiom,
% 0.24/0.48 ! [A_35: hoare_1708887482_state] :
% 0.24/0.48 ( none_H1106584047_state
% 0.24/0.48 != ( some_H1974565227_state @ A_35 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1109_option_Osimps_I3_J,axiom,
% 0.24/0.48 ! [A_34: com] :
% 0.24/0.48 ( ( some_com @ A_34 )
% 0.24/0.48 != none_com ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1110_option_Osimps_I3_J,axiom,
% 0.24/0.48 ! [A_34: pname] :
% 0.24/0.48 ( ( some_pname @ A_34 )
% 0.24/0.48 != none_pname ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1111_option_Osimps_I3_J,axiom,
% 0.24/0.48 ! [A_34: hoare_1708887482_state] :
% 0.24/0.48 ( ( some_H1974565227_state @ A_34 )
% 0.24/0.48 != none_H1106584047_state ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1112_not__Some__eq,axiom,
% 0.24/0.48 ! [X_11: option_com] :
% 0.24/0.48 ( ! [Y_4: com] :
% 0.24/0.48 ( X_11
% 0.24/0.48 != ( some_com @ Y_4 ) )
% 0.24/0.48 <=> ( X_11 = none_com ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1113_not__Some__eq,axiom,
% 0.24/0.48 ! [X_11: option_pname] :
% 0.24/0.48 ( ! [Y_4: pname] :
% 0.24/0.48 ( X_11
% 0.24/0.48 != ( some_pname @ Y_4 ) )
% 0.24/0.48 <=> ( X_11 = none_pname ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1114_not__Some__eq,axiom,
% 0.24/0.48 ! [X_11: option1624383643_state] :
% 0.24/0.48 ( ! [Y_4: hoare_1708887482_state] :
% 0.24/0.48 ( X_11
% 0.24/0.48 != ( some_H1974565227_state @ Y_4 ) )
% 0.24/0.48 <=> ( X_11 = none_H1106584047_state ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1115_not__None__eq,axiom,
% 0.24/0.48 ! [X_10: option_com] :
% 0.24/0.48 ( ( X_10 != none_com )
% 0.24/0.48 <=> ? [Y_4: com] :
% 0.24/0.48 ( X_10
% 0.24/0.48 = ( some_com @ Y_4 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1116_not__None__eq,axiom,
% 0.24/0.48 ! [X_10: option_pname] :
% 0.24/0.48 ( ( X_10 != none_pname )
% 0.24/0.48 <=> ? [Y_4: pname] :
% 0.24/0.48 ( X_10
% 0.24/0.48 = ( some_pname @ Y_4 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1117_not__None__eq,axiom,
% 0.24/0.48 ! [X_10: option1624383643_state] :
% 0.24/0.48 ( ( X_10 != none_H1106584047_state )
% 0.24/0.48 <=> ? [Y_4: hoare_1708887482_state] :
% 0.24/0.48 ( X_10
% 0.24/0.48 = ( some_H1974565227_state @ Y_4 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1118_dom__def,axiom,
% 0.24/0.48 ! [M_2: pname > option_com] :
% 0.24/0.48 ( ( dom_pname_com @ M_2 )
% 0.24/0.48 = ( collect_pname
% 0.24/0.48 @ ^ [A_6: pname] :
% 0.24/0.48 ( (~)
% 0.24/0.48 @ ( ( M_2 @ A_6 )
% 0.24/0.48 = none_com ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1119_domIff,axiom,
% 0.24/0.48 ! [A_33: pname,M_1: pname > option_com] :
% 0.24/0.48 ( ( member_pname @ A_33 @ ( dom_pname_com @ M_1 ) )
% 0.24/0.48 <=> ( ( M_1 @ A_33 )
% 0.24/0.48 != none_com ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1120_finite__imageD,axiom,
% 0.24/0.48 ! [F_18: pname > hoare_1708887482_state,A_32: pname > $o] :
% 0.24/0.48 ( ( finite1625599783_state @ ( image_1116629049_state @ F_18 @ A_32 ) )
% 0.24/0.48 => ( ( inj_on1553129421_state @ F_18 @ A_32 )
% 0.24/0.48 => ( finite_finite_pname @ A_32 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1121_inj__on__Un__image__eq__iff,axiom,
% 0.24/0.48 ! [F_17: pname > hoare_1708887482_state,A_31: pname > $o,B_12: pname > $o] :
% 0.24/0.48 ( ( inj_on1553129421_state @ F_17 @ ( semila1780557381name_o @ A_31 @ B_12 ) )
% 0.24/0.48 => ( ( ( image_1116629049_state @ F_17 @ A_31 )
% 0.24/0.48 = ( image_1116629049_state @ F_17 @ B_12 ) )
% 0.24/0.48 <=> ( A_31 = B_12 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1122_is__none__def,axiom,
% 0.24/0.48 ! [X_9: option_com] :
% 0.24/0.48 ( ( is_none_com @ X_9 )
% 0.24/0.48 <=> ( X_9 = none_com ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1123_is__none__code_I1_J,axiom,
% 0.24/0.48 is_none_com @ none_com ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1124_inj__on__fun__updI,axiom,
% 0.24/0.48 ! [X_8: pname,Y_3: hoare_1708887482_state,F_16: pname > hoare_1708887482_state,A_30: pname > $o] :
% 0.24/0.48 ( ( inj_on1553129421_state @ F_16 @ A_30 )
% 0.24/0.48 => ( ~ ( member451959335_state @ Y_3 @ ( image_1116629049_state @ F_16 @ A_30 ) )
% 0.24/0.48 => ( inj_on1553129421_state @ ( fun_up1986763201_state @ F_16 @ X_8 @ Y_3 ) @ A_30 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1125_sup__le__fold__sup,axiom,
% 0.24/0.48 ! [B_11: pname > $o,A_29: pname > $o,A_28: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_28 )
% 0.24/0.48 => ( ( member_pname_o @ A_29 @ A_28 )
% 0.24/0.48 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_29 @ B_11 ) @ ( finite472615016name_o @ semila1780557381name_o @ B_11 @ A_28 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1126_sup__le__fold__sup,axiom,
% 0.24/0.48 ! [B_11: hoare_1708887482_state > $o,A_29: hoare_1708887482_state > $o,A_28: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_28 )
% 0.24/0.48 => ( ( member814030440tate_o @ A_29 @ A_28 )
% 0.24/0.48 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_29 @ B_11 ) @ ( finite822533768tate_o @ semila1122118281tate_o @ B_11 @ A_28 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1127_sup__le__fold__sup,axiom,
% 0.24/0.48 ! [B_11: $o,A_29: $o,A_28: $o > $o] :
% 0.24/0.48 ( ( finite_finite_o @ A_28 )
% 0.24/0.48 => ( ( member_o @ A_29 @ A_28 )
% 0.24/0.48 => ( ord_less_eq_o @ ( semila10642723_sup_o @ A_29 @ B_11 ) @ ( finite_fold_o_o @ semila10642723_sup_o @ B_11 @ A_28 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1128_fold__inf__le__inf,axiom,
% 0.24/0.48 ! [B_10: pname > $o,A_27: pname > $o,A_26: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_26 )
% 0.24/0.48 => ( ( member_pname_o @ A_27 @ A_26 )
% 0.24/0.48 => ( ord_less_eq_pname_o @ ( finite472615016name_o @ semila1673364395name_o @ B_10 @ A_26 ) @ ( semila1673364395name_o @ A_27 @ B_10 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1129_fold__inf__le__inf,axiom,
% 0.24/0.48 ! [B_10: hoare_1708887482_state > $o,A_27: hoare_1708887482_state > $o,A_26: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_26 )
% 0.24/0.48 => ( ( member814030440tate_o @ A_27 @ A_26 )
% 0.24/0.48 => ( ord_le777019615tate_o @ ( finite822533768tate_o @ semila129691299tate_o @ B_10 @ A_26 ) @ ( semila129691299tate_o @ A_27 @ B_10 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1130_fold__inf__le__inf,axiom,
% 0.24/0.48 ! [B_10: $o,A_27: $o,A_26: $o > $o] :
% 0.24/0.48 ( ( finite_finite_o @ A_26 )
% 0.24/0.48 => ( ( member_o @ A_27 @ A_26 )
% 0.24/0.48 => ( ord_less_eq_o @ ( finite_fold_o_o @ semila854092349_inf_o @ B_10 @ A_26 ) @ ( semila854092349_inf_o @ A_27 @ B_10 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1131_fold__sup__insert,axiom,
% 0.24/0.48 ! [B_9: pname > $o,A_25: pname > $o,A_24: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_24 )
% 0.24/0.48 => ( ( finite472615016name_o @ semila1780557381name_o @ B_9 @ ( insert_pname_o @ A_25 @ A_24 ) )
% 0.24/0.48 = ( semila1780557381name_o @ A_25 @ ( finite472615016name_o @ semila1780557381name_o @ B_9 @ A_24 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1132_fold__sup__insert,axiom,
% 0.24/0.48 ! [B_9: hoare_1708887482_state > $o,A_25: hoare_1708887482_state > $o,A_24: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_24 )
% 0.24/0.48 => ( ( finite822533768tate_o @ semila1122118281tate_o @ B_9 @ ( insert949073679tate_o @ A_25 @ A_24 ) )
% 0.24/0.48 = ( semila1122118281tate_o @ A_25 @ ( finite822533768tate_o @ semila1122118281tate_o @ B_9 @ A_24 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1133_fold__sup__insert,axiom,
% 0.24/0.48 ! [B_9: $o,A_25: $o,A_24: $o > $o] :
% 0.24/0.48 ( ( finite_finite_o @ A_24 )
% 0.24/0.48 => ( ( finite_fold_o_o @ semila10642723_sup_o @ B_9 @ ( insert_o @ A_25 @ A_24 ) )
% 0.24/0.48 <=> ( semila10642723_sup_o @ A_25 @ ( finite_fold_o_o @ semila10642723_sup_o @ B_9 @ A_24 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1134_fold__inf__insert,axiom,
% 0.24/0.48 ! [B_8: pname > $o,A_23: pname > $o,A_22: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_22 )
% 0.24/0.48 => ( ( finite472615016name_o @ semila1673364395name_o @ B_8 @ ( insert_pname_o @ A_23 @ A_22 ) )
% 0.24/0.48 = ( semila1673364395name_o @ A_23 @ ( finite472615016name_o @ semila1673364395name_o @ B_8 @ A_22 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1135_fold__inf__insert,axiom,
% 0.24/0.48 ! [B_8: hoare_1708887482_state > $o,A_23: hoare_1708887482_state > $o,A_22: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_22 )
% 0.24/0.48 => ( ( finite822533768tate_o @ semila129691299tate_o @ B_8 @ ( insert949073679tate_o @ A_23 @ A_22 ) )
% 0.24/0.48 = ( semila129691299tate_o @ A_23 @ ( finite822533768tate_o @ semila129691299tate_o @ B_8 @ A_22 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1136_dom__eq__empty__conv,axiom,
% 0.24/0.48 ! [F_15: pname > option_com] :
% 0.24/0.48 ( ( ( dom_pname_com @ F_15 )
% 0.24/0.48 = bot_bot_pname_o )
% 0.24/0.48 <=> ! [X_3: pname] :
% 0.24/0.48 ( ( F_15 @ X_3 )
% 0.24/0.48 = none_com ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1137_dom__empty,axiom,
% 0.24/0.48 ( ( dom_pname_com
% 0.24/0.48 @ ^ [X_3: pname] : none_com )
% 0.24/0.48 = bot_bot_pname_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1138_Option_Oset_Osimps_I1_J,axiom,
% 0.24/0.48 ( ( set_com @ none_com )
% 0.24/0.48 = bot_bot_com_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1139_Option_Oset_Osimps_I1_J,axiom,
% 0.24/0.48 ( ( set_pname @ none_pname )
% 0.24/0.48 = bot_bot_pname_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1140_Option_Oset_Osimps_I1_J,axiom,
% 0.24/0.48 ( ( set_Ho525251890_state @ none_H1106584047_state )
% 0.24/0.48 = bot_bo19817387tate_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1141_set__empty__eq,axiom,
% 0.24/0.48 ! [Xo: option_com] :
% 0.24/0.48 ( ( ( set_com @ Xo )
% 0.24/0.48 = bot_bot_com_o )
% 0.24/0.48 <=> ( Xo = none_com ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1142_set__empty__eq,axiom,
% 0.24/0.48 ! [Xo: option_pname] :
% 0.24/0.48 ( ( ( set_pname @ Xo )
% 0.24/0.48 = bot_bot_pname_o )
% 0.24/0.48 <=> ( Xo = none_pname ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1143_set__empty__eq,axiom,
% 0.24/0.48 ! [Xo: option1624383643_state] :
% 0.24/0.48 ( ( ( set_Ho525251890_state @ Xo )
% 0.24/0.48 = bot_bo19817387tate_o )
% 0.24/0.48 <=> ( Xo = none_H1106584047_state ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1144_endo__inj__surj,axiom,
% 0.24/0.48 ! [F_14: ( pname > $o ) > pname > $o,A_21: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_21 )
% 0.24/0.48 => ( ( ord_le1205211808me_o_o @ ( image_1085733413name_o @ F_14 @ A_21 ) @ A_21 )
% 0.24/0.48 => ( ( inj_on691924881name_o @ F_14 @ A_21 )
% 0.24/0.48 => ( ( image_1085733413name_o @ F_14 @ A_21 )
% 0.24/0.48 = A_21 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1145_endo__inj__surj,axiom,
% 0.24/0.48 ! [F_14: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,A_21: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_21 )
% 0.24/0.48 => ( ( ord_le1728773982te_o_o @ ( image_909543877tate_o @ F_14 @ A_21 ) @ A_21 )
% 0.24/0.48 => ( ( inj_on176908593tate_o @ F_14 @ A_21 )
% 0.24/0.48 => ( ( image_909543877tate_o @ F_14 @ A_21 )
% 0.24/0.48 = A_21 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1146_endo__inj__surj,axiom,
% 0.24/0.48 ! [F_14: pname > pname,A_21: pname > $o] :
% 0.24/0.48 ( ( finite_finite_pname @ A_21 )
% 0.24/0.48 => ( ( ord_less_eq_pname_o @ ( image_pname_pname @ F_14 @ A_21 ) @ A_21 )
% 0.24/0.48 => ( ( inj_on_pname_pname @ F_14 @ A_21 )
% 0.24/0.48 => ( ( image_pname_pname @ F_14 @ A_21 )
% 0.24/0.48 = A_21 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1147_endo__inj__surj,axiom,
% 0.24/0.48 ! [F_14: hoare_1708887482_state > hoare_1708887482_state,A_21: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( finite1625599783_state @ A_21 )
% 0.24/0.48 => ( ( ord_le777019615tate_o @ ( image_757158439_state @ F_14 @ A_21 ) @ A_21 )
% 0.24/0.48 => ( ( inj_on632008595_state @ F_14 @ A_21 )
% 0.24/0.48 => ( ( image_757158439_state @ F_14 @ A_21 )
% 0.24/0.48 = A_21 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1148_finite__surj__inj,axiom,
% 0.24/0.48 ! [F_13: ( pname > $o ) > pname > $o,A_20: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_20 )
% 0.24/0.48 => ( ( ord_le1205211808me_o_o @ A_20 @ ( image_1085733413name_o @ F_13 @ A_20 ) )
% 0.24/0.48 => ( inj_on691924881name_o @ F_13 @ A_20 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1149_finite__surj__inj,axiom,
% 0.24/0.48 ! [F_13: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,A_20: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_20 )
% 0.24/0.48 => ( ( ord_le1728773982te_o_o @ A_20 @ ( image_909543877tate_o @ F_13 @ A_20 ) )
% 0.24/0.48 => ( inj_on176908593tate_o @ F_13 @ A_20 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1150_finite__surj__inj,axiom,
% 0.24/0.48 ! [F_13: pname > pname,A_20: pname > $o] :
% 0.24/0.48 ( ( finite_finite_pname @ A_20 )
% 0.24/0.48 => ( ( ord_less_eq_pname_o @ A_20 @ ( image_pname_pname @ F_13 @ A_20 ) )
% 0.24/0.48 => ( inj_on_pname_pname @ F_13 @ A_20 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1151_finite__surj__inj,axiom,
% 0.24/0.48 ! [F_13: hoare_1708887482_state > hoare_1708887482_state,A_20: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( finite1625599783_state @ A_20 )
% 0.24/0.48 => ( ( ord_le777019615tate_o @ A_20 @ ( image_757158439_state @ F_13 @ A_20 ) )
% 0.24/0.48 => ( inj_on632008595_state @ F_13 @ A_20 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1152_inj__on__image__Int,axiom,
% 0.24/0.48 ! [B_7: pname > $o,A_19: pname > $o,F_12: pname > hoare_1708887482_state,C_3: pname > $o] :
% 0.24/0.48 ( ( inj_on1553129421_state @ F_12 @ C_3 )
% 0.24/0.48 => ( ( ord_less_eq_pname_o @ A_19 @ C_3 )
% 0.24/0.48 => ( ( ord_less_eq_pname_o @ B_7 @ C_3 )
% 0.24/0.48 => ( ( image_1116629049_state @ F_12 @ ( semila1673364395name_o @ A_19 @ B_7 ) )
% 0.24/0.48 = ( semila129691299tate_o @ ( image_1116629049_state @ F_12 @ A_19 ) @ ( image_1116629049_state @ F_12 @ B_7 ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1153_inj__on__image__set__diff,axiom,
% 0.24/0.48 ! [B_6: pname > $o,A_18: pname > $o,F_11: pname > hoare_1708887482_state,C_2: pname > $o] :
% 0.24/0.48 ( ( inj_on1553129421_state @ F_11 @ C_2 )
% 0.24/0.48 => ( ( ord_less_eq_pname_o @ A_18 @ C_2 )
% 0.24/0.48 => ( ( ord_less_eq_pname_o @ B_6 @ C_2 )
% 0.24/0.48 => ( ( image_1116629049_state @ F_11 @ ( minus_minus_pname_o @ A_18 @ B_6 ) )
% 0.24/0.48 = ( minus_2056855718tate_o @ ( image_1116629049_state @ F_11 @ A_18 ) @ ( image_1116629049_state @ F_11 @ B_6 ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1154_union__fold__insert,axiom,
% 0.24/0.48 ! [B_5: com > $o,A_17: com > $o] :
% 0.24/0.48 ( ( finite_finite_com @ A_17 )
% 0.24/0.48 => ( ( semila1562558655_com_o @ A_17 @ B_5 )
% 0.24/0.48 = ( finite504235573_com_o @ insert_com @ B_5 @ A_17 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1155_union__fold__insert,axiom,
% 0.24/0.48 ! [B_5: pname > $o,A_17: pname > $o] :
% 0.24/0.48 ( ( finite_finite_pname @ A_17 )
% 0.24/0.48 => ( ( semila1780557381name_o @ A_17 @ B_5 )
% 0.24/0.48 = ( finite603803317name_o @ insert_pname @ B_5 @ A_17 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1156_union__fold__insert,axiom,
% 0.24/0.48 ! [B_5: hoare_1708887482_state > $o,A_17: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( finite1625599783_state @ A_17 )
% 0.24/0.48 => ( ( semila1122118281tate_o @ A_17 @ B_5 )
% 0.24/0.48 = ( finite96880613tate_o @ insert528405184_state @ B_5 @ A_17 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1157_union__fold__insert,axiom,
% 0.24/0.48 ! [B_5: ( pname > $o ) > $o,A_17: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_17 )
% 0.24/0.48 => ( ( semila181081674me_o_o @ A_17 @ B_5 )
% 0.24/0.48 = ( finite1849951719me_o_o @ insert_pname_o @ B_5 @ A_17 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1158_union__fold__insert,axiom,
% 0.24/0.48 ! [B_5: ( hoare_1708887482_state > $o ) > $o,A_17: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_17 )
% 0.24/0.48 => ( ( semila1853742644te_o_o @ A_17 @ B_5 )
% 0.24/0.48 = ( finite463603445te_o_o @ insert949073679tate_o @ B_5 @ A_17 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1159_dom__minus,axiom,
% 0.24/0.48 ! [A_16: pname > $o,F_10: pname > option_com,X_7: pname] :
% 0.24/0.48 ( ( ( F_10 @ X_7 )
% 0.24/0.48 = none_com )
% 0.24/0.48 => ( ( minus_minus_pname_o @ ( dom_pname_com @ F_10 ) @ ( insert_pname @ X_7 @ A_16 ) )
% 0.24/0.48 = ( minus_minus_pname_o @ ( dom_pname_com @ F_10 ) @ A_16 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1160_Sup__fin_Oidem,axiom,
% 0.24/0.48 ! [X_6: $o] :
% 0.24/0.48 ( ( semila10642723_sup_o @ X_6 @ X_6 )
% 0.24/0.48 <=> X_6 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1161_Sup__fin_Oidem,axiom,
% 0.24/0.48 ! [X_6: pname > $o] :
% 0.24/0.48 ( ( semila1780557381name_o @ X_6 @ X_6 )
% 0.24/0.48 = X_6 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1162_Sup__fin_Oidem,axiom,
% 0.24/0.48 ! [X_6: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( semila1122118281tate_o @ X_6 @ X_6 )
% 0.24/0.48 = X_6 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1163_folding__one_Oeq__fold_H,axiom,
% 0.24/0.48 ! [X_5: com,A_15: com > $o,F_9: com > com > com,F_8: ( com > $o ) > com] :
% 0.24/0.48 ( ( finite860057415ne_com @ F_9 @ F_8 )
% 0.24/0.48 => ( ( finite_finite_com @ A_15 )
% 0.24/0.48 => ( ~ ( member_com @ X_5 @ A_15 )
% 0.24/0.48 => ( ( F_8 @ ( insert_com @ X_5 @ A_15 ) )
% 0.24/0.48 = ( finite_fold_com_com @ F_9 @ X_5 @ A_15 ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1164_folding__one_Oeq__fold_H,axiom,
% 0.24/0.48 ! [X_5: pname,A_15: pname > $o,F_9: pname > pname > pname,F_8: ( pname > $o ) > pname] :
% 0.24/0.48 ( ( finite1282449217_pname @ F_9 @ F_8 )
% 0.24/0.48 => ( ( finite_finite_pname @ A_15 )
% 0.24/0.48 => ( ~ ( member_pname @ X_5 @ A_15 )
% 0.24/0.48 => ( ( F_8 @ ( insert_pname @ X_5 @ A_15 ) )
% 0.24/0.48 = ( finite1657623752_pname @ F_9 @ X_5 @ A_15 ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1165_folding__one_Oeq__fold_H,axiom,
% 0.24/0.48 ! [X_5: hoare_1708887482_state,A_15: hoare_1708887482_state > $o,F_9: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_8: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.48 ( ( finite1615457021_state @ F_9 @ F_8 )
% 0.24/0.48 => ( ( finite1625599783_state @ A_15 )
% 0.24/0.48 => ( ~ ( member451959335_state @ X_5 @ A_15 )
% 0.24/0.48 => ( ( F_8 @ ( insert528405184_state @ X_5 @ A_15 ) )
% 0.24/0.48 = ( finite309095018_state @ F_9 @ X_5 @ A_15 ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1166_folding__one_Oeq__fold_H,axiom,
% 0.24/0.48 ! [X_5: pname > $o,A_15: ( pname > $o ) > $o,F_9: ( pname > $o ) > ( pname > $o ) > pname > $o,F_8: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.48 ( ( finite349908348name_o @ F_9 @ F_8 )
% 0.24/0.48 => ( ( finite297249702name_o @ A_15 )
% 0.24/0.48 => ( ~ ( member_pname_o @ X_5 @ A_15 )
% 0.24/0.48 => ( ( F_8 @ ( insert_pname_o @ X_5 @ A_15 ) )
% 0.24/0.48 = ( finite472615016name_o @ F_9 @ X_5 @ A_15 ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1167_folding__one_Oeq__fold_H,axiom,
% 0.24/0.48 ! [X_5: hoare_1708887482_state > $o,A_15: ( hoare_1708887482_state > $o ) > $o,F_9: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_8: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( finite928843026tate_o @ F_9 @ F_8 )
% 0.24/0.48 => ( ( finite1329924456tate_o @ A_15 )
% 0.24/0.48 => ( ~ ( member814030440tate_o @ X_5 @ A_15 )
% 0.24/0.48 => ( ( F_8 @ ( insert949073679tate_o @ X_5 @ A_15 ) )
% 0.24/0.48 = ( finite822533768tate_o @ F_9 @ X_5 @ A_15 ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1168_folding__one__idem_Oeq__fold__idem_H,axiom,
% 0.24/0.48 ! [A_14: com,A_13: com > $o,F_7: com > com > com,F_6: ( com > $o ) > com] :
% 0.24/0.48 ( ( finite666746948em_com @ F_7 @ F_6 )
% 0.24/0.48 => ( ( finite_finite_com @ A_13 )
% 0.24/0.48 => ( ( F_6 @ ( insert_com @ A_14 @ A_13 ) )
% 0.24/0.48 = ( finite_fold_com_com @ F_7 @ A_14 @ A_13 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1169_folding__one__idem_Oeq__fold__idem_H,axiom,
% 0.24/0.48 ! [A_14: pname,A_13: pname > $o,F_7: pname > pname > pname,F_6: ( pname > $o ) > pname] :
% 0.24/0.48 ( ( finite89670078_pname @ F_7 @ F_6 )
% 0.24/0.48 => ( ( finite_finite_pname @ A_13 )
% 0.24/0.48 => ( ( F_6 @ ( insert_pname @ A_14 @ A_13 ) )
% 0.24/0.48 = ( finite1657623752_pname @ F_7 @ A_14 @ A_13 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1170_folding__one__idem_Oeq__fold__idem_H,axiom,
% 0.24/0.48 ! [A_14: hoare_1708887482_state,A_13: hoare_1708887482_state > $o,F_7: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_6: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 0.24/0.48 ( ( finite1347568576_state @ F_7 @ F_6 )
% 0.24/0.48 => ( ( finite1625599783_state @ A_13 )
% 0.24/0.48 => ( ( F_6 @ ( insert528405184_state @ A_14 @ A_13 ) )
% 0.24/0.48 = ( finite309095018_state @ F_7 @ A_14 @ A_13 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1171_folding__one__idem_Oeq__fold__idem_H,axiom,
% 0.24/0.48 ! [A_14: pname > $o,A_13: ( pname > $o ) > $o,F_7: ( pname > $o ) > ( pname > $o ) > pname > $o,F_6: ( ( pname > $o ) > $o ) > pname > $o] :
% 0.24/0.48 ( ( finite697516351name_o @ F_7 @ F_6 )
% 0.24/0.48 => ( ( finite297249702name_o @ A_13 )
% 0.24/0.48 => ( ( F_6 @ ( insert_pname_o @ A_14 @ A_13 ) )
% 0.24/0.48 = ( finite472615016name_o @ F_7 @ A_14 @ A_13 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1172_folding__one__idem_Oeq__fold__idem_H,axiom,
% 0.24/0.48 ! [A_14: hoare_1708887482_state > $o,A_13: ( hoare_1708887482_state > $o ) > $o,F_7: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_6: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( finite621643279tate_o @ F_7 @ F_6 )
% 0.24/0.48 => ( ( finite1329924456tate_o @ A_13 )
% 0.24/0.48 => ( ( F_6 @ ( insert949073679tate_o @ A_14 @ A_13 ) )
% 0.24/0.48 = ( finite822533768tate_o @ F_7 @ A_14 @ A_13 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1173_WT_OBody,axiom,
% 0.24/0.48 ! [Pn_1: pname] :
% 0.24/0.48 ( ( ( body @ Pn_1 )
% 0.24/0.48 != none_com )
% 0.24/0.48 => ( wt @ ( body_1 @ Pn_1 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1174_inj__on__insert,axiom,
% 0.24/0.48 ! [F_5: pname > hoare_1708887482_state,A_12: pname,A_11: pname > $o] :
% 0.24/0.48 ( ( inj_on1553129421_state @ F_5 @ ( insert_pname @ A_12 @ A_11 ) )
% 0.24/0.48 <=> ( ( inj_on1553129421_state @ F_5 @ A_11 )
% 0.24/0.48 & ~ ( member451959335_state @ ( F_5 @ A_12 ) @ ( image_1116629049_state @ F_5 @ ( minus_minus_pname_o @ A_11 @ ( insert_pname @ A_12 @ bot_bot_pname_o ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1175_dom__fun__upd,axiom,
% 0.24/0.48 ! [F_4: pname > option_com,X_4: pname,Y_2: option_com] :
% 0.24/0.48 ( ( ( Y_2 = none_com )
% 0.24/0.48 => ( ( dom_pname_com @ ( fun_up879233478on_com @ F_4 @ X_4 @ Y_2 ) )
% 0.24/0.48 = ( minus_minus_pname_o @ ( dom_pname_com @ F_4 ) @ ( insert_pname @ X_4 @ bot_bot_pname_o ) ) ) )
% 0.24/0.48 & ( ( Y_2 != none_com )
% 0.24/0.48 => ( ( dom_pname_com @ ( fun_up879233478on_com @ F_4 @ X_4 @ Y_2 ) )
% 0.24/0.48 = ( insert_pname @ X_4 @ ( dom_pname_com @ F_4 ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1176_inf__le__fold__inf,axiom,
% 0.24/0.48 ! [C_1: pname > $o,B_4: pname > $o,A_10: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_10 )
% 0.24/0.48 => ( ! [X_3: pname > $o] :
% 0.24/0.48 ( ( member_pname_o @ X_3 @ A_10 )
% 0.24/0.48 => ( ord_less_eq_pname_o @ B_4 @ X_3 ) )
% 0.24/0.48 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ B_4 @ C_1 ) @ ( finite472615016name_o @ semila1673364395name_o @ C_1 @ A_10 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1177_inf__le__fold__inf,axiom,
% 0.24/0.48 ! [C_1: hoare_1708887482_state > $o,B_4: hoare_1708887482_state > $o,A_10: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_10 )
% 0.24/0.48 => ( ! [X_3: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( member814030440tate_o @ X_3 @ A_10 )
% 0.24/0.48 => ( ord_le777019615tate_o @ B_4 @ X_3 ) )
% 0.24/0.48 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ B_4 @ C_1 ) @ ( finite822533768tate_o @ semila129691299tate_o @ C_1 @ A_10 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1178_inf__le__fold__inf,axiom,
% 0.24/0.48 ! [C_1: $o,B_4: $o,A_10: $o > $o] :
% 0.24/0.48 ( ( finite_finite_o @ A_10 )
% 0.24/0.48 => ( ! [X_3: $o] :
% 0.24/0.48 ( ( member_o @ X_3 @ A_10 )
% 0.24/0.48 => ( ord_less_eq_o @ B_4 @ X_3 ) )
% 0.24/0.48 => ( ord_less_eq_o @ ( semila854092349_inf_o @ B_4 @ C_1 ) @ ( finite_fold_o_o @ semila854092349_inf_o @ C_1 @ A_10 ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1179_fold__sup__le__sup,axiom,
% 0.24/0.48 ! [C: pname > $o,B_3: pname > $o,A_9: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_9 )
% 0.24/0.48 => ( ! [X_3: pname > $o] :
% 0.24/0.48 ( ( member_pname_o @ X_3 @ A_9 )
% 0.24/0.48 => ( ord_less_eq_pname_o @ X_3 @ B_3 ) )
% 0.24/0.48 => ( ord_less_eq_pname_o @ ( finite472615016name_o @ semila1780557381name_o @ C @ A_9 ) @ ( semila1780557381name_o @ B_3 @ C ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1180_fold__sup__le__sup,axiom,
% 0.24/0.48 ! [C: hoare_1708887482_state > $o,B_3: hoare_1708887482_state > $o,A_9: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_9 )
% 0.24/0.48 => ( ! [X_3: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( member814030440tate_o @ X_3 @ A_9 )
% 0.24/0.48 => ( ord_le777019615tate_o @ X_3 @ B_3 ) )
% 0.24/0.48 => ( ord_le777019615tate_o @ ( finite822533768tate_o @ semila1122118281tate_o @ C @ A_9 ) @ ( semila1122118281tate_o @ B_3 @ C ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1181_fold__sup__le__sup,axiom,
% 0.24/0.48 ! [C: $o,B_3: $o,A_9: $o > $o] :
% 0.24/0.48 ( ( finite_finite_o @ A_9 )
% 0.24/0.48 => ( ! [X_3: $o] :
% 0.24/0.48 ( ( member_o @ X_3 @ A_9 )
% 0.24/0.48 => ( ord_less_eq_o @ X_3 @ B_3 ) )
% 0.24/0.48 => ( ord_less_eq_o @ ( finite_fold_o_o @ semila10642723_sup_o @ C @ A_9 ) @ ( semila10642723_sup_o @ B_3 @ C ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1182_inj__on__iff__surj,axiom,
% 0.24/0.48 ! [A_8: pname > $o,A_7: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( A_7 != bot_bo19817387tate_o )
% 0.24/0.48 => ( ? [F_3: hoare_1708887482_state > pname] :
% 0.24/0.48 ( ( inj_on1945914667_pname @ F_3 @ A_7 )
% 0.24/0.48 & ( ord_less_eq_pname_o @ ( image_1509414295_pname @ F_3 @ A_7 ) @ A_8 ) )
% 0.24/0.48 <=> ? [G_1: pname > hoare_1708887482_state] :
% 0.24/0.48 ( ( image_1116629049_state @ G_1 @ A_8 )
% 0.24/0.48 = A_7 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1183_inj__on__iff__surj,axiom,
% 0.24/0.48 ! [A_8: hoare_1708887482_state > $o,A_7: pname > $o] :
% 0.24/0.48 ( ( A_7 != bot_bot_pname_o )
% 0.24/0.48 => ( ? [F_3: pname > hoare_1708887482_state] :
% 0.24/0.48 ( ( inj_on1553129421_state @ F_3 @ A_7 )
% 0.24/0.48 & ( ord_le777019615tate_o @ ( image_1116629049_state @ F_3 @ A_7 ) @ A_8 ) )
% 0.24/0.48 <=> ? [G_1: hoare_1708887482_state > pname] :
% 0.24/0.48 ( ( image_1509414295_pname @ G_1 @ A_8 )
% 0.24/0.48 = A_7 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1184_option_Oexhaust,axiom,
% 0.24/0.48 ! [Y_1: option_com] :
% 0.24/0.48 ( ( Y_1 != none_com )
% 0.24/0.48 => ~ ! [A_6: com] :
% 0.24/0.48 ( Y_1
% 0.24/0.48 != ( some_com @ A_6 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1185_option_Oexhaust,axiom,
% 0.24/0.48 ! [Y_1: option_pname] :
% 0.24/0.48 ( ( Y_1 != none_pname )
% 0.24/0.48 => ~ ! [A_6: pname] :
% 0.24/0.48 ( Y_1
% 0.24/0.48 != ( some_pname @ A_6 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1186_option_Oexhaust,axiom,
% 0.24/0.48 ! [Y_1: option1624383643_state] :
% 0.24/0.48 ( ( Y_1 != none_H1106584047_state )
% 0.24/0.48 => ~ ! [A_6: hoare_1708887482_state] :
% 0.24/0.48 ( Y_1
% 0.24/0.48 != ( some_H1974565227_state @ A_6 ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1187_Cantor__Bernstein__aux,axiom,
% 0.24/0.48 ! [G: hoare_1708887482_state > pname,B_2: hoare_1708887482_state > $o,F_2: pname > hoare_1708887482_state,A_4: pname > $o] :
% 0.24/0.48 ? [A_5: pname > $o] :
% 0.24/0.48 ( ( ord_less_eq_pname_o @ A_5 @ A_4 )
% 0.24/0.48 & ! [X_3: pname] :
% 0.24/0.48 ( ( member_pname @ X_3 @ A_5 )
% 0.24/0.48 => ~ ( member_pname @ X_3 @ ( image_1509414295_pname @ G @ ( minus_2056855718tate_o @ B_2 @ ( image_1116629049_state @ F_2 @ A_5 ) ) ) ) )
% 0.24/0.48 & ? [H: pname > hoare_1708887482_state] :
% 0.24/0.48 ( ! [X_3: pname] :
% 0.24/0.48 ( ( member_pname @ X_3 @ A_5 )
% 0.24/0.48 => ( ( H @ X_3 )
% 0.24/0.48 = ( F_2 @ X_3 ) ) )
% 0.24/0.48 & ! [X_3: pname] :
% 0.24/0.48 ( ( member_pname @ X_3 @ ( minus_minus_pname_o @ A_4 @ A_5 ) )
% 0.24/0.48 => ( ( member451959335_state @ ( H @ X_3 ) @ ( minus_2056855718tate_o @ B_2 @ ( image_1116629049_state @ F_2 @ A_5 ) ) )
% 0.24/0.48 & ( X_3
% 0.24/0.48 = ( G @ ( H @ X_3 ) ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1188_Cantor__Bernstein__aux,axiom,
% 0.24/0.48 ! [G: pname > hoare_1708887482_state,B_2: pname > $o,F_2: hoare_1708887482_state > pname,A_4: hoare_1708887482_state > $o] :
% 0.24/0.48 ? [A_5: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( ord_le777019615tate_o @ A_5 @ A_4 )
% 0.24/0.48 & ! [X_3: hoare_1708887482_state] :
% 0.24/0.48 ( ( member451959335_state @ X_3 @ A_5 )
% 0.24/0.48 => ~ ( member451959335_state @ X_3 @ ( image_1116629049_state @ G @ ( minus_minus_pname_o @ B_2 @ ( image_1509414295_pname @ F_2 @ A_5 ) ) ) ) )
% 0.24/0.48 & ? [H: hoare_1708887482_state > pname] :
% 0.24/0.48 ( ! [X_3: hoare_1708887482_state] :
% 0.24/0.48 ( ( member451959335_state @ X_3 @ A_5 )
% 0.24/0.48 => ( ( H @ X_3 )
% 0.24/0.48 = ( F_2 @ X_3 ) ) )
% 0.24/0.48 & ! [X_3: hoare_1708887482_state] :
% 0.24/0.48 ( ( member451959335_state @ X_3 @ ( minus_2056855718tate_o @ A_4 @ A_5 ) )
% 0.24/0.48 => ( ( member_pname @ ( H @ X_3 ) @ ( minus_minus_pname_o @ B_2 @ ( image_1509414295_pname @ F_2 @ A_5 ) ) )
% 0.24/0.48 & ( X_3
% 0.24/0.48 = ( G @ ( H @ X_3 ) ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1189_image__vimage__subset,axiom,
% 0.24/0.48 ! [F_1: pname > hoare_1708887482_state,A_3: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( image_1116629049_state @ F_1 @ ( vimage1943311875_state @ F_1 @ A_3 ) ) @ A_3 ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1190_dom__restrict,axiom,
% 0.24/0.48 ! [M: pname > option_com,A_2: pname > $o] :
% 0.24/0.48 ( ( dom_pname_com @ ( restri1382200118me_com @ M @ A_2 ) )
% 0.24/0.48 = ( semila1673364395name_o @ ( dom_pname_com @ M ) @ A_2 ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1191_Inf__fin_Ounion__disjoint,axiom,
% 0.24/0.48 ! [B_1: ( pname > $o ) > $o,A_1: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A_1 )
% 0.24/0.48 => ( ( A_1 != bot_bot_pname_o_o )
% 0.24/0.48 => ( ( finite297249702name_o @ B_1 )
% 0.24/0.48 => ( ( B_1 != bot_bot_pname_o_o )
% 0.24/0.48 => ( ( ( semila2013987940me_o_o @ A_1 @ B_1 )
% 0.24/0.48 = bot_bot_pname_o_o )
% 0.24/0.48 => ( ( big_la1126801287name_o @ ( semila181081674me_o_o @ A_1 @ B_1 ) )
% 0.24/0.48 = ( semila1673364395name_o @ ( big_la1126801287name_o @ A_1 ) @ ( big_la1126801287name_o @ B_1 ) ) ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1192_Inf__fin_Ounion__disjoint,axiom,
% 0.24/0.48 ! [B_1: ( hoare_1708887482_state > $o ) > $o,A_1: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A_1 )
% 0.24/0.48 => ( ( A_1 != bot_bo1678742418te_o_o )
% 0.24/0.48 => ( ( finite1329924456tate_o @ B_1 )
% 0.24/0.48 => ( ( B_1 != bot_bo1678742418te_o_o )
% 0.24/0.48 => ( ( ( semila598060698te_o_o @ A_1 @ B_1 )
% 0.24/0.48 = bot_bo1678742418te_o_o )
% 0.24/0.48 => ( ( big_la781588935tate_o @ ( semila1853742644te_o_o @ A_1 @ B_1 ) )
% 0.24/0.48 = ( semila129691299tate_o @ ( big_la781588935tate_o @ A_1 ) @ ( big_la781588935tate_o @ B_1 ) ) ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1193_Inf__fin_Ounion__inter,axiom,
% 0.24/0.48 ! [B: ( pname > $o ) > $o,A: ( pname > $o ) > $o] :
% 0.24/0.48 ( ( finite297249702name_o @ A )
% 0.24/0.48 => ( ( finite297249702name_o @ B )
% 0.24/0.48 => ( ( ( semila2013987940me_o_o @ A @ B )
% 0.24/0.48 != bot_bot_pname_o_o )
% 0.24/0.48 => ( ( semila1673364395name_o @ ( big_la1126801287name_o @ ( semila181081674me_o_o @ A @ B ) ) @ ( big_la1126801287name_o @ ( semila2013987940me_o_o @ A @ B ) ) )
% 0.24/0.48 = ( semila1673364395name_o @ ( big_la1126801287name_o @ A ) @ ( big_la1126801287name_o @ B ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1194_Inf__fin_Ounion__inter,axiom,
% 0.24/0.48 ! [B: ( hoare_1708887482_state > $o ) > $o,A: ( hoare_1708887482_state > $o ) > $o] :
% 0.24/0.48 ( ( finite1329924456tate_o @ A )
% 0.24/0.48 => ( ( finite1329924456tate_o @ B )
% 0.24/0.48 => ( ( ( semila598060698te_o_o @ A @ B )
% 0.24/0.48 != bot_bo1678742418te_o_o )
% 0.24/0.48 => ( ( semila129691299tate_o @ ( big_la781588935tate_o @ ( semila1853742644te_o_o @ A @ B ) ) @ ( big_la781588935tate_o @ ( semila598060698te_o_o @ A @ B ) ) )
% 0.24/0.48 = ( semila129691299tate_o @ ( big_la781588935tate_o @ A ) @ ( big_la781588935tate_o @ B ) ) ) ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1195_UNIV__I,axiom,
% 0.24/0.48 ! [X_2: com] : ( member_com @ X_2 @ top_top_com_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1196_UNIV__I,axiom,
% 0.24/0.48 ! [X_2: pname] : ( member_pname @ X_2 @ top_top_pname_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1197_UNIV__I,axiom,
% 0.24/0.48 ! [X_2: hoare_1708887482_state] : ( member451959335_state @ X_2 @ top_to832624271tate_o ) ).
% 0.24/0.48
% 0.24/0.48 thf(fact_1198_rangeI,axiom,
% 0.24/0.48 ! [F: pname > hoare_1708887482_state,X_1: pname] : ( member451959335_state @ ( F @ X_1 ) @ ( image_1116629049_state @ F @ top_top_pname_o ) ) ).
% 0.24/0.48
% 0.24/0.48 %----Helper facts (18)
% 0.24/0.48 thf(help_fequal_1_1_fequal_000tc__Com__Ocom_T,axiom,
% 0.24/0.48 ! [X: com,Y: com] :
% 0.24/0.48 ( ~ ( fequal_com @ X @ Y )
% 0.24/0.48 | ( X = Y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_fequal_2_1_fequal_000tc__Com__Ocom_T,axiom,
% 0.24/0.48 ! [X: com,Y: com] :
% 0.24/0.48 ( ( X != Y )
% 0.24/0.48 | ( fequal_com @ X @ Y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 0.24/0.48 ! [X: pname,Y: pname] :
% 0.24/0.48 ( ~ ( fequal_pname @ X @ Y )
% 0.24/0.48 | ( X = Y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 0.24/0.48 ! [X: pname,Y: pname] :
% 0.24/0.48 ( ( X != Y )
% 0.24/0.48 | ( fequal_pname @ X @ Y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_fequal_1_1_fequal_000tc__Com__Ostate_T,axiom,
% 0.24/0.48 ! [X: state,Y: state] :
% 0.24/0.48 ( ~ ( fequal_state @ X @ Y )
% 0.24/0.48 | ( X = Y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,
% 0.24/0.48 ! [X: state,Y: state] :
% 0.24/0.48 ( ( X != Y )
% 0.24/0.48 | ( fequal_state @ X @ Y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.24/0.48 ! [X: pname > $o,Y: pname > $o] :
% 0.24/0.48 ( ~ ( fequal_pname_o @ X @ Y )
% 0.24/0.48 | ( X = Y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.24/0.48 ! [X: pname > $o,Y: pname > $o] :
% 0.24/0.48 ( ( X != Y )
% 0.24/0.48 | ( fequal_pname_o @ X @ Y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 0.24/0.48 ! [X: option_com,Y: option_com] :
% 0.24/0.48 ( ( if_option_com @ $true @ X @ Y )
% 0.24/0.48 = X ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 0.24/0.48 ! [X: option_com,Y: option_com] :
% 0.24/0.48 ( ( if_option_com @ $false @ X @ Y )
% 0.24/0.48 = Y ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 0.24/0.48 ! [P: $o] :
% 0.24/0.48 ( ( P = $true )
% 0.24/0.48 | ( P = $false ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_If_1_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate,axiom,
% 0.24/0.48 ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
% 0.24/0.48 ( ( if_Hoa1374726218_state @ $true @ X @ Y )
% 0.24/0.48 = X ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_If_2_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate,axiom,
% 0.24/0.48 ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
% 0.24/0.48 ( ( if_Hoa1374726218_state @ $false @ X @ Y )
% 0.24/0.48 = Y ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_If_3_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate,axiom,
% 0.24/0.48 ! [P: $o] :
% 0.24/0.48 ( ( P = $true )
% 0.24/0.48 | ( P = $false ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,axiom,
% 0.24/0.48 ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
% 0.24/0.48 ( ~ ( fequal224822779_state @ X @ Y )
% 0.24/0.48 | ( X = Y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,axiom,
% 0.24/0.48 ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
% 0.24/0.48 ( ( X != Y )
% 0.24/0.48 | ( fequal224822779_state @ X @ Y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,axiom,
% 0.24/0.48 ! [X: hoare_1708887482_state > $o,Y: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ~ ( fequal1436017556tate_o @ X @ Y )
% 0.24/0.48 | ( X = Y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,axiom,
% 0.24/0.48 ! [X: hoare_1708887482_state > $o,Y: hoare_1708887482_state > $o] :
% 0.24/0.48 ( ( X != Y )
% 0.24/0.48 | ( fequal1436017556tate_o @ X @ Y ) ) ).
% 0.24/0.48
% 0.24/0.48 %----Conjectures (8)
% 0.24/0.48 thf(conj_0,hypothesis,
% 0.24/0.48 hoare_1160767572gleton ).
% 0.24/0.48
% 0.24/0.48 thf(conj_1,hypothesis,
% 0.24/0.48 wT_bodies ).
% 0.24/0.48
% 0.24/0.48 thf(conj_2,hypothesis,
% 0.24/0.48 finite1625599783_state @ fa ).
% 0.24/0.48
% 0.24/0.48 thf(conj_3,hypothesis,
% 0.24/0.48 ~ ( member451959335_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ) ).
% 0.24/0.48
% 0.24/0.48 thf(conj_4,hypothesis,
% 0.24/0.48 ( ord_le777019615tate_o @ fa
% 0.24/0.48 @ ( image_1116629049_state
% 0.24/0.48 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
% 0.24/0.48 @ ( dom_pname_com @ body ) ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(conj_5,hypothesis,
% 0.24/0.48 ( ( body @ pn )
% 0.24/0.48 = ( some_com @ y ) ) ).
% 0.24/0.48
% 0.24/0.48 thf(conj_6,hypothesis,
% 0.24/0.48 ( hoare_90032982_state
% 0.24/0.48 @ ( image_1116629049_state
% 0.24/0.48 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.24/0.48 @ ( dom_pname_com @ body ) )
% 0.24/0.48 @ fa ) ).
% 0.24/0.48
% 0.24/0.48 thf(conj_7,conjecture,
% 0.24/0.48 ( hoare_90032982_state
% 0.24/0.48 @ ( image_1116629049_state
% 0.24/0.48 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 0.24/0.48 @ ( dom_pname_com @ body ) )
% 0.24/0.48 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) ) ).
% 0.24/0.48
% 0.24/0.48 %------------------------------------------------------------------------------
% 0.24/0.48 ------------------------
% 3.30/1.65 ---- Embedded in THF ---
% 3.30/1.65 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.30/1.65 %%% Generated on Tue Feb 24 13:41:14 EST 2026
% 3.30/1.65 %%% using '$$dhol' embedding, version 1.3.0.
% 3.30/1.65 %%% Logic specification used:
% 3.30/1.65 %%% thf(spec, logic, $$dhol).
% 3.30/1.65
% 3.30/1.65 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2DTF15503.p
% See solution above
% 3.30/1.65 ------------------------
% 3.42/1.77 ---- Cleaned THF ---
% 3.42/1.78 thf(ty_ty_tc__Com__Ocom,type,
% 3.42/1.78 com: $tType ).
% 3.42/1.78
% 3.42/1.78 thf(ty_ty_tc__Com__Opname,type,
% 3.42/1.78 pname: $tType ).
% 3.42/1.78
% 3.42/1.78 thf(ty_ty_tc__Com__Ostate,type,
% 3.42/1.78 state: $tType ).
% 3.42/1.78
% 3.42/1.78 thf(ty_ty_tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,
% 3.42/1.78 hoare_1708887482_state: $tType ).
% 3.42/1.78
% 3.42/1.78 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 3.42/1.78 option_com: $tType ).
% 3.42/1.78
% 3.42/1.78 thf(ty_ty_tc__Option__Ooption_Itc__Com__Opname_J,type,
% 3.42/1.78 option_pname: $tType ).
% 3.42/1.78
% 3.42/1.78 thf(ty_ty_tc__Option__Ooption_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Co,type,
% 3.42/1.78 option1624383643_state: $tType ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.42/1.78 big_la1126801287name_o: ( ( pname > $o ) > $o ) > pname > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Hoare____Mirabelle___,type,
% 3.42/1.78 big_la781588935tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Com_OWT,type,
% 3.42/1.78 wt: com > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Com_OWT__bodies,type,
% 3.42/1.78 wT_bodies: $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Com_Obody,type,
% 3.42/1.78 body: pname > option_com ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Com_Ocom_OBODY,type,
% 3.42/1.78 body_1: pname > com ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Com_Ocom_OSKIP,type,
% 3.42/1.78 skip: com ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Com_Ocom_OSemi,type,
% 3.42/1.78 semi: com > com > com ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Com_Ocom_OWhile,type,
% 3.42/1.78 while: ( state > $o ) > com > com ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ocomp__fun__idem_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__C,type,
% 3.42/1.78 finite138924780name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ocomp__fun__idem_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv_,type,
% 3.42/1.78 finite2034616076tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ocomp__fun__idem_000_Eo_000_Eo,type,
% 3.42/1.78 finite2048025996em_o_o: ( $o > $o > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Ocom_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 3.42/1.78 finite567462577_com_o: ( com > ( com > $o ) > com > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Opname_000_062_Itc__Com__Opname_M_,type,
% 3.42/1.78 finite1123817265name_o: ( pname > ( pname > $o ) > pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otrip,type,
% 3.42/1.78 finite662762081tate_o: ( hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 3.42/1.78 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,
% 3.42/1.78 finite1019950101te_o_o: ( ( ( hoare_1708887482_state > $o ) > $o ) > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.42/1.78 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_,type,
% 3.42/1.78 finite1329924456tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofinite_000_Eo,type,
% 3.42/1.78 finite_finite_o: ( $o > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Ocom,type,
% 3.42/1.78 finite_finite_com: ( com > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 3.42/1.78 finite_finite_pname: ( pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__C,type,
% 3.42/1.78 finite1625599783_state: ( hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold_000_062_Itc__Com__Opname_M_Eo_J_000_062_I_062_Itc__Com__O,type,
% 3.42/1.78 finite1849951719me_o_o: ( ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_,type,
% 3.42/1.78 finite472615016name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,type,
% 3.42/1.78 finite463603445te_o_o: ( ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It_001,type,
% 3.42/1.78 finite822533768tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold_000_Eo_000_Eo,type,
% 3.42/1.78 finite_fold_o_o: ( $o > $o > $o ) > $o > ( $o > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold_000tc__Com__Ocom_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 3.42/1.78 finite504235573_com_o: ( com > ( com > $o ) > com > $o ) > ( com > $o ) > ( com > $o ) > com > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold_000tc__Com__Ocom_000tc__Com__Ocom,type,
% 3.42/1.78 finite_fold_com_com: ( com > com > com ) > com > ( com > $o ) > com ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.42/1.78 finite603803317name_o: ( pname > ( pname > $o ) > pname > $o ) > ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold_000tc__Com__Opname_000tc__Com__Opname,type,
% 3.42/1.78 finite1657623752_pname: ( pname > pname > pname ) > pname > ( pname > $o ) > pname ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,type,
% 3.42/1.78 finite96880613tate_o: ( hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com_002,type,
% 3.42/1.78 finite309095018_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr,type,
% 3.42/1.78 finite2139561282_pname: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( pname > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( pname > $o ) > hoare_1708887482_state > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.42/1.78 finite349908348name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,
% 3.42/1.78 finite928843026tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Ocom,type,
% 3.42/1.78 finite860057415ne_com: ( com > com > com ) > ( ( com > $o ) > com ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,type,
% 3.42/1.78 finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_,type,
% 3.42/1.78 finite1615457021_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.42/1.78 finite697516351name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Hoare____Mirabelle____nqhfsdfv,type,
% 3.42/1.78 finite621643279tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Ocom,type,
% 3.42/1.78 finite666746948em_com: ( com > com > com ) > ( ( com > $o ) > com ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,type,
% 3.42/1.78 finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,
% 3.42/1.78 finite1347568576_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Ofun__upd_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__O,type,
% 3.42/1.78 fun_up1986763201_state: ( pname > hoare_1708887482_state ) > pname > hoare_1708887482_state > pname > hoare_1708887482_state ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Ofun__upd_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 3.42/1.78 fun_up879233478on_com: ( pname > option_com ) > pname > option_com > pname > option_com ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Oinj__on_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_M_Eo_,type,
% 3.42/1.78 inj_on691924881name_o: ( ( pname > $o ) > pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Oinj__on_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Co,type,
% 3.42/1.78 inj_on176908593tate_o: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Oinj__on_000tc__Com__Ocom_000tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 3.42/1.78 inj_on11367768on_com: ( com > option_com ) > ( com > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Com__Opname,type,
% 3.42/1.78 inj_on_pname_pname: ( pname > pname ) > ( pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,
% 3.42/1.78 inj_on1553129421_state: ( pname > hoare_1708887482_state ) > ( pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Opname_J,type,
% 3.42/1.78 inj_on737724108_pname: ( pname > option_pname ) > ( pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost,type,
% 3.42/1.78 inj_on1945914667_pname: ( hoare_1708887482_state > pname ) > ( hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost_003,type,
% 3.42/1.78 inj_on632008595_state: ( hoare_1708887482_state > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost_004,type,
% 3.42/1.78 inj_on945311362_state: ( hoare_1708887482_state > option1624383643_state ) > ( hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Fun_Ooverride__on_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_,type,
% 3.42/1.78 overri1496249029on_com: ( pname > option_com ) > ( pname > option_com ) > ( pname > $o ) > pname > option_com ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 3.42/1.78 minus_1480864103me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsd,type,
% 3.42/1.78 minus_548038231te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 3.42/1.78 minus_minus_com_o: ( com > $o ) > ( com > $o ) > com > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.42/1.78 minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__,type,
% 3.42/1.78 minus_2056855718tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_HOL_OThe_000tc__Com__Ocom,type,
% 3.42/1.78 the_com_1: ( com > $o ) > com ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_HOL_OThe_000tc__Com__Opname,type,
% 3.42/1.78 the_pname: ( pname > $o ) > pname ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_,type,
% 3.42/1.78 the_Ho851197897_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_OMGT,type,
% 3.42/1.78 hoare_Mirabelle_MGT: com > hoare_1708887482_state ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__derivs_000tc__Com__Ostate,type,
% 3.42/1.78 hoare_90032982_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__valids_000tc__Com__Ostate,type,
% 3.42/1.78 hoare_496444244_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ostate__not__singleton,type,
% 3.42/1.78 hoare_1160767572gleton: $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple_000tc__Com__Ostate,type,
% 3.42/1.78 hoare_858012674_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1708887482_state ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,
% 3.42/1.78 if_Hoa1374726218_state: $o > hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_If_000tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 3.42/1.78 if_option_com: $o > option_com > option_com > option_com ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Com__Opname_M_Eo_,type,
% 3.42/1.78 semila2013987940me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell,type,
% 3.42/1.78 semila598060698te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 3.42/1.78 semila513601829_com_o: ( com > $o ) > ( com > $o ) > com > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.42/1.78 semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____n,type,
% 3.42/1.78 semila129691299tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_Eo,type,
% 3.42/1.78 semila854092349_inf_o: $o > $o > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Com__Opname_M_Eo_,type,
% 3.42/1.78 semila181081674me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell,type,
% 3.42/1.78 semila1853742644te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Ocom_M_Eo_J,type,
% 3.42/1.78 semila1562558655_com_o: ( com > $o ) > ( com > $o ) > com > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.42/1.78 semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____n,type,
% 3.42/1.78 semila1122118281tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_Eo,type,
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% 3.42/1.78 thf(sy_c_Map_Odom_000tc__Com__Ocom_000tc__Com__Ocom,type,
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% 3.42/1.78 thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,type,
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% 3.42/1.78 thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otripl,type,
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% 3.42/1.78 thf(sy_c_Map_Odom_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_,type,
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% 3.42/1.78 thf(sy_c_Map_Odom_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate__005,type,
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% 3.42/1.78 thf(sy_c_Map_Orestrict__map_000tc__Com__Opname_000tc__Com__Ocom,type,
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% 3.42/1.78 thf(sy_c_Natural_Oevalc,type,
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% 3.42/1.78 thf(sy_c_Option_Ooption_OSome_000tc__Com__Opname,type,
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% 3.42/1.78 thf(sy_c_Option_Ooption_OSome_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__,type,
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% 3.42/1.78 thf(sy_c_Option_Oset_000tc__Com__Ocom,type,
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% 3.42/1.78 thf(sy_c_Option_Oset_000tc__Com__Opname,type,
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% 3.42/1.78 thf(sy_c_Option_Oset_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Osta,type,
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% 3.42/1.78 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
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% 3.42/1.78 thf(sy_c_Option_Othe_000tc__Com__Opname,type,
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% 3.42/1.78 thf(sy_c_Option_Othe_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Osta,type,
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% 3.42/1.78
% 3.42/1.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
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% 3.42/1.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdf,type,
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% 3.42/1.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Ocom_M_Eo_J,type,
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% 3.42/1.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__O,type,
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% 3.42/1.78 thf(sy_c_Partial__Function_Oflat__lub_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otrip,type,
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% 3.42/1.78
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% 3.42/1.78
% 3.42/1.78 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 3.42/1.78 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost,type,
% 3.42/1.78 member814030440tate_o: ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_member_000_Eo,type,
% 3.42/1.78 member_o: $o > ( $o > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_member_000tc__Com__Ocom,type,
% 3.42/1.78 member_com: com > ( com > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_member_000tc__Com__Opname,type,
% 3.42/1.78 member_pname: pname > ( pname > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_c_member_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,
% 3.42/1.78 member451959335_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_v_Fa,type,
% 3.42/1.78 fa: hoare_1708887482_state > $o ).
% 3.42/1.78
% 3.42/1.78 thf(sy_v_pn,type,
% 3.42/1.78 pn: pname ).
% 3.42/1.78
% 3.42/1.78 thf(sy_v_y,type,
% 3.42/1.78 y: com ).
% 3.42/1.78
% 3.42/1.78 thf(fact_0_empty,axiom,
% 3.42/1.78 ! [G_7: hoare_1708887482_state > $o] : ( hoare_90032982_state @ G_7 @ bot_bo19817387tate_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_1_asm,axiom,
% 3.42/1.78 ! [Ts_7: hoare_1708887482_state > $o,G_39: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ Ts_7 @ G_39 )
% 3.42/1.78 => ( hoare_90032982_state @ G_39 @ Ts_7 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_2_weaken,axiom,
% 3.42/1.78 ! [Ts_6: hoare_1708887482_state > $o,G_38: hoare_1708887482_state > $o,Ts_5: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( hoare_90032982_state @ G_38 @ Ts_5 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ Ts_6 @ Ts_5 )
% 3.42/1.78 => ( hoare_90032982_state @ G_38 @ Ts_6 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_3_thin,axiom,
% 3.42/1.78 ! [G_37: hoare_1708887482_state > $o,G_36: hoare_1708887482_state > $o,Ts_4: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( hoare_90032982_state @ G_36 @ Ts_4 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ G_36 @ G_37 )
% 3.42/1.78 => ( hoare_90032982_state @ G_37 @ Ts_4 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_4_cut,axiom,
% 3.42/1.78 ! [G_35: hoare_1708887482_state > $o,G_34: hoare_1708887482_state > $o,Ts_3: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( hoare_90032982_state @ G_34 @ Ts_3 )
% 3.42/1.78 => ( ( hoare_90032982_state @ G_35 @ G_34 )
% 3.42/1.78 => ( hoare_90032982_state @ G_35 @ Ts_3 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_5_hoare__derivs_Oinsert,axiom,
% 3.42/1.78 ! [Ts_2: hoare_1708887482_state > $o,G_33: hoare_1708887482_state > $o,T_3: hoare_1708887482_state] :
% 3.42/1.78 ( ( hoare_90032982_state @ G_33 @ ( insert528405184_state @ T_3 @ bot_bo19817387tate_o ) )
% 3.42/1.78 => ( ( hoare_90032982_state @ G_33 @ Ts_2 )
% 3.42/1.78 => ( hoare_90032982_state @ G_33 @ ( insert528405184_state @ T_3 @ Ts_2 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_6_derivs__insertD,axiom,
% 3.42/1.78 ! [G_32: hoare_1708887482_state > $o,T_2: hoare_1708887482_state,Ts_1: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( hoare_90032982_state @ G_32 @ ( insert528405184_state @ T_2 @ Ts_1 ) )
% 3.42/1.78 => ( ( hoare_90032982_state @ G_32 @ ( insert528405184_state @ T_2 @ bot_bo19817387tate_o ) )
% 3.42/1.78 & ( hoare_90032982_state @ G_32 @ Ts_1 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_7_MGT__BodyN,axiom,
% 3.42/1.78 ! [Pn_1: pname,G_7: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( hoare_90032982_state @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ G_7 ) @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn_1 ) ) ) @ bot_bo19817387tate_o ) )
% 3.42/1.78 => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ bot_bo19817387tate_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_8_finite__Collect__subsets,axiom,
% 3.42/1.78 ! [A_274: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ A_274 )
% 3.42/1.78 => ( finite1066544169me_o_o
% 3.42/1.78 @ ( collect_pname_o_o
% 3.42/1.78 @ ^ [B_84: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_84 @ A_274 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_9_finite__Collect__subsets,axiom,
% 3.42/1.78 ! [A_274: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ A_274 )
% 3.42/1.78 => ( finite1019950101te_o_o
% 3.42/1.78 @ ( collec58007891te_o_o
% 3.42/1.78 @ ^ [B_84: ( hoare_1708887482_state > $o ) > $o] : ( ord_le1728773982te_o_o @ B_84 @ A_274 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_10_finite__Collect__subsets,axiom,
% 3.42/1.78 ! [A_274: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ A_274 )
% 3.42/1.78 => ( finite1329924456tate_o
% 3.42/1.78 @ ( collec219771562tate_o
% 3.42/1.78 @ ^ [B_84: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ B_84 @ A_274 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_11_finite__Collect__subsets,axiom,
% 3.42/1.78 ! [A_274: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ A_274 )
% 3.42/1.78 => ( finite297249702name_o
% 3.42/1.78 @ ( collect_pname_o
% 3.42/1.78 @ ^ [B_84: pname > $o] : ( ord_less_eq_pname_o @ B_84 @ A_274 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_12_finite__imageI,axiom,
% 3.42/1.78 ! [H_2: hoare_1708887482_state > pname > $o,F_88: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ F_88 )
% 3.42/1.78 => ( finite297249702name_o @ ( image_1552895654name_o @ H_2 @ F_88 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_13_finite__imageI,axiom,
% 3.42/1.78 ! [H_2: hoare_1708887482_state > hoare_1708887482_state > $o,F_88: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ F_88 )
% 3.42/1.78 => ( finite1329924456tate_o @ ( image_1551509096tate_o @ H_2 @ F_88 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_14_finite__imageI,axiom,
% 3.42/1.78 ! [H_2: pname > pname > $o,F_88: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ F_88 )
% 3.42/1.78 => ( finite297249702name_o @ ( image_pname_pname_o @ H_2 @ F_88 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_15_finite__imageI,axiom,
% 3.42/1.78 ! [H_2: pname > hoare_1708887482_state > $o,F_88: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ F_88 )
% 3.42/1.78 => ( finite1329924456tate_o @ ( image_425134806tate_o @ H_2 @ F_88 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_16_finite__imageI,axiom,
% 3.42/1.78 ! [H_2: ( pname > $o ) > hoare_1708887482_state,F_88: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ F_88 )
% 3.42/1.78 => ( finite1625599783_state @ ( image_1922967206_state @ H_2 @ F_88 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_17_finite__imageI,axiom,
% 3.42/1.78 ! [H_2: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,F_88: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ F_88 )
% 3.42/1.78 => ( finite1625599783_state @ ( image_27005066_state @ H_2 @ F_88 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_18_finite__imageI,axiom,
% 3.42/1.78 ! [H_2: ( pname > $o ) > pname,F_88: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ F_88 )
% 3.42/1.78 => ( finite_finite_pname @ ( image_pname_o_pname @ H_2 @ F_88 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_19_finite__imageI,axiom,
% 3.42/1.78 ! [H_2: ( hoare_1708887482_state > $o ) > pname,F_88: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ F_88 )
% 3.42/1.78 => ( finite_finite_pname @ ( image_2051418740_pname @ H_2 @ F_88 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_20_finite__imageI,axiom,
% 3.42/1.78 ! [H_2: pname > hoare_1708887482_state,F_88: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ F_88 )
% 3.42/1.78 => ( finite1625599783_state @ ( image_1116629049_state @ H_2 @ F_88 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_21_empty__subsetI,axiom,
% 3.42/1.78 ! [A_273: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_273 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_22_empty__subsetI,axiom,
% 3.42/1.78 ! [A_273: com > $o] : ( ord_less_eq_com_o @ bot_bot_com_o @ A_273 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_23_empty__subsetI,axiom,
% 3.42/1.78 ! [A_273: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ bot_bo19817387tate_o @ A_273 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_24_finite_OinsertI,axiom,
% 3.42/1.78 ! [A_272: com,A_271: com > $o] :
% 3.42/1.78 ( ( finite_finite_com @ A_271 )
% 3.42/1.78 => ( finite_finite_com @ ( insert_com @ A_272 @ A_271 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_25_finite_OinsertI,axiom,
% 3.42/1.78 ! [A_272: pname > $o,A_271: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ A_271 )
% 3.42/1.78 => ( finite297249702name_o @ ( insert_pname_o @ A_272 @ A_271 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_26_finite_OinsertI,axiom,
% 3.42/1.78 ! [A_272: hoare_1708887482_state > $o,A_271: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ A_271 )
% 3.42/1.78 => ( finite1329924456tate_o @ ( insert949073679tate_o @ A_272 @ A_271 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_27_finite_OinsertI,axiom,
% 3.42/1.78 ! [A_272: pname,A_271: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ A_271 )
% 3.42/1.78 => ( finite_finite_pname @ ( insert_pname @ A_272 @ A_271 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_28_finite_OinsertI,axiom,
% 3.42/1.78 ! [A_272: hoare_1708887482_state,A_271: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ A_271 )
% 3.42/1.78 => ( finite1625599783_state @ ( insert528405184_state @ A_272 @ A_271 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_29_finite_OemptyI,axiom,
% 3.42/1.78 finite297249702name_o @ bot_bot_pname_o_o ).
% 3.42/1.78
% 3.42/1.78 thf(fact_30_finite_OemptyI,axiom,
% 3.42/1.78 finite1329924456tate_o @ bot_bo1678742418te_o_o ).
% 3.42/1.78
% 3.42/1.78 thf(fact_31_finite_OemptyI,axiom,
% 3.42/1.78 finite_finite_com @ bot_bot_com_o ).
% 3.42/1.78
% 3.42/1.78 thf(fact_32_finite_OemptyI,axiom,
% 3.42/1.78 finite1625599783_state @ bot_bo19817387tate_o ).
% 3.42/1.78
% 3.42/1.78 thf(fact_33_finite_OemptyI,axiom,
% 3.42/1.78 finite_finite_pname @ bot_bot_pname_o ).
% 3.42/1.78
% 3.42/1.78 thf(fact_34_finite__Collect__conjI,axiom,
% 3.42/1.78 ! [Q_26: ( pname > $o ) > $o,P_45: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_45 ) )
% 3.42/1.78 | ( finite297249702name_o @ ( collect_pname_o @ Q_26 ) ) )
% 3.42/1.78 => ( finite297249702name_o
% 3.42/1.78 @ ( collect_pname_o
% 3.42/1.78 @ ^ [X_3: pname > $o] : ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_35_finite__Collect__conjI,axiom,
% 3.42/1.78 ! [Q_26: ( hoare_1708887482_state > $o ) > $o,P_45: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( ( finite1329924456tate_o @ ( collec219771562tate_o @ P_45 ) )
% 3.42/1.78 | ( finite1329924456tate_o @ ( collec219771562tate_o @ Q_26 ) ) )
% 3.42/1.78 => ( finite1329924456tate_o
% 3.42/1.78 @ ( collec219771562tate_o
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_36_finite__Collect__conjI,axiom,
% 3.42/1.78 ! [Q_26: hoare_1708887482_state > $o,P_45: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ( finite1625599783_state @ ( collec1568722789_state @ P_45 ) )
% 3.42/1.78 | ( finite1625599783_state @ ( collec1568722789_state @ Q_26 ) ) )
% 3.42/1.78 => ( finite1625599783_state
% 3.42/1.78 @ ( collec1568722789_state
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_37_finite__Collect__conjI,axiom,
% 3.42/1.78 ! [Q_26: pname > $o,P_45: pname > $o] :
% 3.42/1.78 ( ( ( finite_finite_pname @ ( collect_pname @ P_45 ) )
% 3.42/1.78 | ( finite_finite_pname @ ( collect_pname @ Q_26 ) ) )
% 3.42/1.78 => ( finite_finite_pname
% 3.42/1.78 @ ( collect_pname
% 3.42/1.78 @ ^ [X_3: pname] : ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_38_image__constant__conv,axiom,
% 3.42/1.78 ! [C_68: pname,A_270: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ( A_270 = bot_bo19817387tate_o )
% 3.42/1.78 => ( ( image_1509414295_pname
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : C_68
% 3.42/1.78 @ A_270 )
% 3.42/1.78 = bot_bot_pname_o ) )
% 3.42/1.78 & ( ( A_270 != bot_bo19817387tate_o )
% 3.42/1.78 => ( ( image_1509414295_pname
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : C_68
% 3.42/1.78 @ A_270 )
% 3.42/1.78 = ( insert_pname @ C_68 @ bot_bot_pname_o ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_39_image__constant__conv,axiom,
% 3.42/1.78 ! [C_68: com,A_270: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ( A_270 = bot_bo19817387tate_o )
% 3.42/1.78 => ( ( image_1604448413te_com
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : C_68
% 3.42/1.78 @ A_270 )
% 3.42/1.78 = bot_bot_com_o ) )
% 3.42/1.78 & ( ( A_270 != bot_bo19817387tate_o )
% 3.42/1.78 => ( ( image_1604448413te_com
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : C_68
% 3.42/1.78 @ A_270 )
% 3.42/1.78 = ( insert_com @ C_68 @ bot_bot_com_o ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_40_image__constant__conv,axiom,
% 3.42/1.78 ! [C_68: hoare_1708887482_state,A_270: com > $o] :
% 3.42/1.78 ( ( ( A_270 = bot_bot_com_o )
% 3.42/1.78 => ( ( image_934102463_state
% 3.42/1.78 @ ^ [X_3: com] : C_68
% 3.42/1.78 @ A_270 )
% 3.42/1.78 = bot_bo19817387tate_o ) )
% 3.42/1.78 & ( ( A_270 != bot_bot_com_o )
% 3.42/1.78 => ( ( image_934102463_state
% 3.42/1.78 @ ^ [X_3: com] : C_68
% 3.42/1.78 @ A_270 )
% 3.42/1.78 = ( insert528405184_state @ C_68 @ bot_bo19817387tate_o ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_41_image__constant__conv,axiom,
% 3.42/1.78 ! [C_68: hoare_1708887482_state,A_270: pname > $o] :
% 3.42/1.78 ( ( ( A_270 = bot_bot_pname_o )
% 3.42/1.78 => ( ( image_1116629049_state
% 3.42/1.78 @ ^ [X_3: pname] : C_68
% 3.42/1.78 @ A_270 )
% 3.42/1.78 = bot_bo19817387tate_o ) )
% 3.42/1.78 & ( ( A_270 != bot_bot_pname_o )
% 3.42/1.78 => ( ( image_1116629049_state
% 3.42/1.78 @ ^ [X_3: pname] : C_68
% 3.42/1.78 @ A_270 )
% 3.42/1.78 = ( insert528405184_state @ C_68 @ bot_bo19817387tate_o ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_42_image__constant,axiom,
% 3.42/1.78 ! [C_67: pname,X_119: hoare_1708887482_state,A_269: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ X_119 @ A_269 )
% 3.42/1.78 => ( ( image_1509414295_pname
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : C_67
% 3.42/1.78 @ A_269 )
% 3.42/1.78 = ( insert_pname @ C_67 @ bot_bot_pname_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_43_image__constant,axiom,
% 3.42/1.78 ! [C_67: com,X_119: hoare_1708887482_state,A_269: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ X_119 @ A_269 )
% 3.42/1.78 => ( ( image_1604448413te_com
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : C_67
% 3.42/1.78 @ A_269 )
% 3.42/1.78 = ( insert_com @ C_67 @ bot_bot_com_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_44_image__constant,axiom,
% 3.42/1.78 ! [C_67: pname,X_119: pname,A_269: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_119 @ A_269 )
% 3.42/1.78 => ( ( image_pname_pname
% 3.42/1.78 @ ^ [X_3: pname] : C_67
% 3.42/1.78 @ A_269 )
% 3.42/1.78 = ( insert_pname @ C_67 @ bot_bot_pname_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_45_image__constant,axiom,
% 3.42/1.78 ! [C_67: com,X_119: pname,A_269: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_119 @ A_269 )
% 3.42/1.78 => ( ( image_pname_com
% 3.42/1.78 @ ^ [X_3: pname] : C_67
% 3.42/1.78 @ A_269 )
% 3.42/1.78 = ( insert_com @ C_67 @ bot_bot_com_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_46_image__constant,axiom,
% 3.42/1.78 ! [C_67: hoare_1708887482_state,X_119: com,A_269: com > $o] :
% 3.42/1.78 ( ( member_com @ X_119 @ A_269 )
% 3.42/1.78 => ( ( image_934102463_state
% 3.42/1.78 @ ^ [X_3: com] : C_67
% 3.42/1.78 @ A_269 )
% 3.42/1.78 = ( insert528405184_state @ C_67 @ bot_bo19817387tate_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_47_image__constant,axiom,
% 3.42/1.78 ! [C_67: hoare_1708887482_state,X_119: pname,A_269: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_119 @ A_269 )
% 3.42/1.78 => ( ( image_1116629049_state
% 3.42/1.78 @ ^ [X_3: pname] : C_67
% 3.42/1.78 @ A_269 )
% 3.42/1.78 = ( insert528405184_state @ C_67 @ bot_bo19817387tate_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_48_insert__dom,axiom,
% 3.42/1.78 ! [F_87: com > option_com,X_118: com,Y_53: com] :
% 3.42/1.78 ( ( ( F_87 @ X_118 )
% 3.42/1.78 = ( some_com @ Y_53 ) )
% 3.42/1.78 => ( ( insert_com @ X_118 @ ( dom_com_com @ F_87 ) )
% 3.42/1.78 = ( dom_com_com @ F_87 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_49_insert__dom,axiom,
% 3.42/1.78 ! [F_87: hoare_1708887482_state > option_pname,X_118: hoare_1708887482_state,Y_53: pname] :
% 3.42/1.78 ( ( ( F_87 @ X_118 )
% 3.42/1.78 = ( some_pname @ Y_53 ) )
% 3.42/1.78 => ( ( insert528405184_state @ X_118 @ ( dom_Ho1805192458_pname @ F_87 ) )
% 3.42/1.78 = ( dom_Ho1805192458_pname @ F_87 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_50_insert__dom,axiom,
% 3.42/1.78 ! [F_87: hoare_1708887482_state > option1624383643_state,X_118: hoare_1708887482_state,Y_53: hoare_1708887482_state] :
% 3.42/1.78 ( ( ( F_87 @ X_118 )
% 3.42/1.78 = ( some_H1974565227_state @ Y_53 ) )
% 3.42/1.78 => ( ( insert528405184_state @ X_118 @ ( dom_Ho1703271284_state @ F_87 ) )
% 3.42/1.78 = ( dom_Ho1703271284_state @ F_87 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_51_insert__dom,axiom,
% 3.42/1.78 ! [F_87: pname > option_com,X_118: pname,Y_53: com] :
% 3.42/1.78 ( ( ( F_87 @ X_118 )
% 3.42/1.78 = ( some_com @ Y_53 ) )
% 3.42/1.78 => ( ( insert_pname @ X_118 @ ( dom_pname_com @ F_87 ) )
% 3.42/1.78 = ( dom_pname_com @ F_87 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_52_finite__surj,axiom,
% 3.42/1.78 ! [B_171: ( pname > $o ) > $o,F_86: hoare_1708887482_state > pname > $o,A_268: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ A_268 )
% 3.42/1.78 => ( ( ord_le1205211808me_o_o @ B_171 @ ( image_1552895654name_o @ F_86 @ A_268 ) )
% 3.42/1.78 => ( finite297249702name_o @ B_171 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_53_finite__surj,axiom,
% 3.42/1.78 ! [B_171: ( hoare_1708887482_state > $o ) > $o,F_86: hoare_1708887482_state > hoare_1708887482_state > $o,A_268: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ A_268 )
% 3.42/1.78 => ( ( ord_le1728773982te_o_o @ B_171 @ ( image_1551509096tate_o @ F_86 @ A_268 ) )
% 3.42/1.78 => ( finite1329924456tate_o @ B_171 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_54_finite__surj,axiom,
% 3.42/1.78 ! [B_171: pname > $o,F_86: hoare_1708887482_state > pname,A_268: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ A_268 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ B_171 @ ( image_1509414295_pname @ F_86 @ A_268 ) )
% 3.42/1.78 => ( finite_finite_pname @ B_171 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_55_finite__surj,axiom,
% 3.42/1.78 ! [B_171: ( pname > $o ) > $o,F_86: pname > pname > $o,A_268: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ A_268 )
% 3.42/1.78 => ( ( ord_le1205211808me_o_o @ B_171 @ ( image_pname_pname_o @ F_86 @ A_268 ) )
% 3.42/1.78 => ( finite297249702name_o @ B_171 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_56_finite__surj,axiom,
% 3.42/1.78 ! [B_171: ( hoare_1708887482_state > $o ) > $o,F_86: pname > hoare_1708887482_state > $o,A_268: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ A_268 )
% 3.42/1.78 => ( ( ord_le1728773982te_o_o @ B_171 @ ( image_425134806tate_o @ F_86 @ A_268 ) )
% 3.42/1.78 => ( finite1329924456tate_o @ B_171 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_57_finite__surj,axiom,
% 3.42/1.78 ! [B_171: pname > $o,F_86: pname > pname,A_268: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ A_268 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ B_171 @ ( image_pname_pname @ F_86 @ A_268 ) )
% 3.42/1.78 => ( finite_finite_pname @ B_171 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_58_finite__surj,axiom,
% 3.42/1.78 ! [B_171: hoare_1708887482_state > $o,F_86: ( pname > $o ) > hoare_1708887482_state,A_268: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ A_268 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ B_171 @ ( image_1922967206_state @ F_86 @ A_268 ) )
% 3.42/1.78 => ( finite1625599783_state @ B_171 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_59_finite__surj,axiom,
% 3.42/1.78 ! [B_171: hoare_1708887482_state > $o,F_86: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,A_268: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ A_268 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ B_171 @ ( image_27005066_state @ F_86 @ A_268 ) )
% 3.42/1.78 => ( finite1625599783_state @ B_171 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_60_finite__surj,axiom,
% 3.42/1.78 ! [B_171: pname > $o,F_86: ( pname > $o ) > pname,A_268: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ A_268 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ B_171 @ ( image_pname_o_pname @ F_86 @ A_268 ) )
% 3.42/1.78 => ( finite_finite_pname @ B_171 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_61_finite__surj,axiom,
% 3.42/1.78 ! [B_171: pname > $o,F_86: ( hoare_1708887482_state > $o ) > pname,A_268: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ A_268 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ B_171 @ ( image_2051418740_pname @ F_86 @ A_268 ) )
% 3.42/1.78 => ( finite_finite_pname @ B_171 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_62_finite__surj,axiom,
% 3.42/1.78 ! [B_171: hoare_1708887482_state > $o,F_86: pname > hoare_1708887482_state,A_268: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ A_268 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ B_171 @ ( image_1116629049_state @ F_86 @ A_268 ) )
% 3.42/1.78 => ( finite1625599783_state @ B_171 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_63_subset__singletonD,axiom,
% 3.42/1.78 ! [A_267: pname > $o,X_117: pname] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ A_267 @ ( insert_pname @ X_117 @ bot_bot_pname_o ) )
% 3.42/1.78 => ( ( A_267 = bot_bot_pname_o )
% 3.42/1.78 | ( A_267
% 3.42/1.78 = ( insert_pname @ X_117 @ bot_bot_pname_o ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_64_subset__singletonD,axiom,
% 3.42/1.78 ! [A_267: com > $o,X_117: com] :
% 3.42/1.78 ( ( ord_less_eq_com_o @ A_267 @ ( insert_com @ X_117 @ bot_bot_com_o ) )
% 3.42/1.78 => ( ( A_267 = bot_bot_com_o )
% 3.42/1.78 | ( A_267
% 3.42/1.78 = ( insert_com @ X_117 @ bot_bot_com_o ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_65_subset__singletonD,axiom,
% 3.42/1.78 ! [A_267: hoare_1708887482_state > $o,X_117: hoare_1708887482_state] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ A_267 @ ( insert528405184_state @ X_117 @ bot_bo19817387tate_o ) )
% 3.42/1.78 => ( ( A_267 = bot_bo19817387tate_o )
% 3.42/1.78 | ( A_267
% 3.42/1.78 = ( insert528405184_state @ X_117 @ bot_bo19817387tate_o ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_66_MGF,axiom,
% 3.42/1.78 ! [C_34: com] :
% 3.42/1.78 ( hoare_1160767572gleton
% 3.42/1.78 => ( wT_bodies
% 3.42/1.78 => ( ( wt @ C_34 )
% 3.42/1.78 => ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_67_emptyE,axiom,
% 3.42/1.78 ! [A_266: com] :
% 3.42/1.78 ~ ( member_com @ A_266 @ bot_bot_com_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_68_emptyE,axiom,
% 3.42/1.78 ! [A_266: hoare_1708887482_state] :
% 3.42/1.78 ~ ( member451959335_state @ A_266 @ bot_bo19817387tate_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_69_emptyE,axiom,
% 3.42/1.78 ! [A_266: pname] :
% 3.42/1.78 ~ ( member_pname @ A_266 @ bot_bot_pname_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_70_insertCI,axiom,
% 3.42/1.78 ! [B_170: com,A_265: com,B_169: com > $o] :
% 3.42/1.78 ( ( ~ ( member_com @ A_265 @ B_169 )
% 3.42/1.78 => ( A_265 = B_170 ) )
% 3.42/1.78 => ( member_com @ A_265 @ ( insert_com @ B_170 @ B_169 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_71_insertCI,axiom,
% 3.42/1.78 ! [B_170: pname,A_265: pname,B_169: pname > $o] :
% 3.42/1.78 ( ( ~ ( member_pname @ A_265 @ B_169 )
% 3.42/1.78 => ( A_265 = B_170 ) )
% 3.42/1.78 => ( member_pname @ A_265 @ ( insert_pname @ B_170 @ B_169 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_72_insertCI,axiom,
% 3.42/1.78 ! [B_170: hoare_1708887482_state,A_265: hoare_1708887482_state,B_169: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ~ ( member451959335_state @ A_265 @ B_169 )
% 3.42/1.78 => ( A_265 = B_170 ) )
% 3.42/1.78 => ( member451959335_state @ A_265 @ ( insert528405184_state @ B_170 @ B_169 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_73_insertE,axiom,
% 3.42/1.78 ! [A_264: com,B_168: com,A_263: com > $o] :
% 3.42/1.78 ( ( member_com @ A_264 @ ( insert_com @ B_168 @ A_263 ) )
% 3.42/1.78 => ( ( A_264 != B_168 )
% 3.42/1.78 => ( member_com @ A_264 @ A_263 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_74_insertE,axiom,
% 3.42/1.78 ! [A_264: pname,B_168: pname,A_263: pname > $o] :
% 3.42/1.78 ( ( member_pname @ A_264 @ ( insert_pname @ B_168 @ A_263 ) )
% 3.42/1.78 => ( ( A_264 != B_168 )
% 3.42/1.78 => ( member_pname @ A_264 @ A_263 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_75_insertE,axiom,
% 3.42/1.78 ! [A_264: hoare_1708887482_state,B_168: hoare_1708887482_state,A_263: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ A_264 @ ( insert528405184_state @ B_168 @ A_263 ) )
% 3.42/1.78 => ( ( A_264 != B_168 )
% 3.42/1.78 => ( member451959335_state @ A_264 @ A_263 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_76_equalityI,axiom,
% 3.42/1.78 ! [A_262: pname > $o,B_167: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ A_262 @ B_167 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ B_167 @ A_262 )
% 3.42/1.78 => ( A_262 = B_167 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_77_equalityI,axiom,
% 3.42/1.78 ! [A_262: hoare_1708887482_state > $o,B_167: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ A_262 @ B_167 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ B_167 @ A_262 )
% 3.42/1.78 => ( A_262 = B_167 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_78_subsetD,axiom,
% 3.42/1.78 ! [C_66: com,A_261: com > $o,B_166: com > $o] :
% 3.42/1.78 ( ( ord_less_eq_com_o @ A_261 @ B_166 )
% 3.42/1.78 => ( ( member_com @ C_66 @ A_261 )
% 3.42/1.78 => ( member_com @ C_66 @ B_166 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_79_subsetD,axiom,
% 3.42/1.78 ! [C_66: hoare_1708887482_state,A_261: hoare_1708887482_state > $o,B_166: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ A_261 @ B_166 )
% 3.42/1.78 => ( ( member451959335_state @ C_66 @ A_261 )
% 3.42/1.78 => ( member451959335_state @ C_66 @ B_166 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_80_subsetD,axiom,
% 3.42/1.78 ! [C_66: pname,A_261: pname > $o,B_166: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ A_261 @ B_166 )
% 3.42/1.78 => ( ( member_pname @ C_66 @ A_261 )
% 3.42/1.78 => ( member_pname @ C_66 @ B_166 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_81_image__eqI,axiom,
% 3.42/1.78 ! [A_260: hoare_1708887482_state > $o,B_165: com,F_85: hoare_1708887482_state > com,X_116: hoare_1708887482_state] :
% 3.42/1.78 ( ( B_165
% 3.42/1.78 = ( F_85 @ X_116 ) )
% 3.42/1.78 => ( ( member451959335_state @ X_116 @ A_260 )
% 3.42/1.78 => ( member_com @ B_165 @ ( image_1604448413te_com @ F_85 @ A_260 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_82_image__eqI,axiom,
% 3.42/1.78 ! [A_260: pname > $o,B_165: com,F_85: pname > com,X_116: pname] :
% 3.42/1.78 ( ( B_165
% 3.42/1.78 = ( F_85 @ X_116 ) )
% 3.42/1.78 => ( ( member_pname @ X_116 @ A_260 )
% 3.42/1.78 => ( member_com @ B_165 @ ( image_pname_com @ F_85 @ A_260 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_83_image__eqI,axiom,
% 3.42/1.78 ! [A_260: com > $o,B_165: hoare_1708887482_state,F_85: com > hoare_1708887482_state,X_116: com] :
% 3.42/1.78 ( ( B_165
% 3.42/1.78 = ( F_85 @ X_116 ) )
% 3.42/1.78 => ( ( member_com @ X_116 @ A_260 )
% 3.42/1.78 => ( member451959335_state @ B_165 @ ( image_934102463_state @ F_85 @ A_260 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_84_image__eqI,axiom,
% 3.42/1.78 ! [A_260: com > $o,B_165: pname,F_85: com > pname,X_116: com] :
% 3.42/1.78 ( ( B_165
% 3.42/1.78 = ( F_85 @ X_116 ) )
% 3.42/1.78 => ( ( member_com @ X_116 @ A_260 )
% 3.42/1.78 => ( member_pname @ B_165 @ ( image_com_pname @ F_85 @ A_260 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_85_image__eqI,axiom,
% 3.42/1.78 ! [A_260: pname > $o,B_165: hoare_1708887482_state,F_85: pname > hoare_1708887482_state,X_116: pname] :
% 3.42/1.78 ( ( B_165
% 3.42/1.78 = ( F_85 @ X_116 ) )
% 3.42/1.78 => ( ( member_pname @ X_116 @ A_260 )
% 3.42/1.78 => ( member451959335_state @ B_165 @ ( image_1116629049_state @ F_85 @ A_260 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_86_equals0D,axiom,
% 3.42/1.78 ! [A_259: com,A_258: com > $o] :
% 3.42/1.78 ( ( A_258 = bot_bot_com_o )
% 3.42/1.78 => ~ ( member_com @ A_259 @ A_258 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_87_equals0D,axiom,
% 3.42/1.78 ! [A_259: hoare_1708887482_state,A_258: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( A_258 = bot_bo19817387tate_o )
% 3.42/1.78 => ~ ( member451959335_state @ A_259 @ A_258 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_88_equals0D,axiom,
% 3.42/1.78 ! [A_259: pname,A_258: pname > $o] :
% 3.42/1.78 ( ( A_258 = bot_bot_pname_o )
% 3.42/1.78 => ~ ( member_pname @ A_259 @ A_258 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_89_Collect__empty__eq,axiom,
% 3.42/1.78 ! [P_44: pname > $o] :
% 3.42/1.78 ( ( ( collect_pname @ P_44 )
% 3.42/1.78 = bot_bot_pname_o )
% 3.42/1.78 <=> ! [X_3: pname] :
% 3.42/1.78 ~ ( P_44 @ X_3 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_90_Collect__empty__eq,axiom,
% 3.42/1.78 ! [P_44: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( ( collect_pname_o @ P_44 )
% 3.42/1.78 = bot_bot_pname_o_o )
% 3.42/1.78 <=> ! [X_3: pname > $o] :
% 3.42/1.78 ~ ( P_44 @ X_3 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_91_Collect__empty__eq,axiom,
% 3.42/1.78 ! [P_44: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( ( collec219771562tate_o @ P_44 )
% 3.42/1.78 = bot_bo1678742418te_o_o )
% 3.42/1.78 <=> ! [X_3: hoare_1708887482_state > $o] :
% 3.42/1.78 ~ ( P_44 @ X_3 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_92_Collect__empty__eq,axiom,
% 3.42/1.78 ! [P_44: com > $o] :
% 3.42/1.78 ( ( ( collect_com @ P_44 )
% 3.42/1.78 = bot_bot_com_o )
% 3.42/1.78 <=> ! [X_3: com] :
% 3.42/1.78 ~ ( P_44 @ X_3 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_93_Collect__empty__eq,axiom,
% 3.42/1.78 ! [P_44: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ( collec1568722789_state @ P_44 )
% 3.42/1.78 = bot_bo19817387tate_o )
% 3.42/1.78 <=> ! [X_3: hoare_1708887482_state] :
% 3.42/1.78 ~ ( P_44 @ X_3 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_94_empty__iff,axiom,
% 3.42/1.78 ! [C_65: com] :
% 3.42/1.78 ~ ( member_com @ C_65 @ bot_bot_com_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_95_empty__iff,axiom,
% 3.42/1.78 ! [C_65: hoare_1708887482_state] :
% 3.42/1.78 ~ ( member451959335_state @ C_65 @ bot_bo19817387tate_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_96_empty__iff,axiom,
% 3.42/1.78 ! [C_65: pname] :
% 3.42/1.78 ~ ( member_pname @ C_65 @ bot_bot_pname_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_97_empty__Collect__eq,axiom,
% 3.42/1.78 ! [P_43: pname > $o] :
% 3.42/1.78 ( ( bot_bot_pname_o
% 3.42/1.78 = ( collect_pname @ P_43 ) )
% 3.42/1.78 <=> ! [X_3: pname] :
% 3.42/1.78 ~ ( P_43 @ X_3 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_98_empty__Collect__eq,axiom,
% 3.42/1.78 ! [P_43: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( bot_bot_pname_o_o
% 3.42/1.78 = ( collect_pname_o @ P_43 ) )
% 3.42/1.78 <=> ! [X_3: pname > $o] :
% 3.42/1.78 ~ ( P_43 @ X_3 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_99_empty__Collect__eq,axiom,
% 3.42/1.78 ! [P_43: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( bot_bo1678742418te_o_o
% 3.42/1.78 = ( collec219771562tate_o @ P_43 ) )
% 3.42/1.78 <=> ! [X_3: hoare_1708887482_state > $o] :
% 3.42/1.78 ~ ( P_43 @ X_3 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_100_empty__Collect__eq,axiom,
% 3.42/1.78 ! [P_43: com > $o] :
% 3.42/1.78 ( ( bot_bot_com_o
% 3.42/1.78 = ( collect_com @ P_43 ) )
% 3.42/1.78 <=> ! [X_3: com] :
% 3.42/1.78 ~ ( P_43 @ X_3 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_101_empty__Collect__eq,axiom,
% 3.42/1.78 ! [P_43: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( bot_bo19817387tate_o
% 3.42/1.78 = ( collec1568722789_state @ P_43 ) )
% 3.42/1.78 <=> ! [X_3: hoare_1708887482_state] :
% 3.42/1.78 ~ ( P_43 @ X_3 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_102_ex__in__conv,axiom,
% 3.42/1.78 ! [A_257: com > $o] :
% 3.42/1.78 ( ? [X_3: com] : ( member_com @ X_3 @ A_257 )
% 3.42/1.78 <=> ( A_257 != bot_bot_com_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_103_ex__in__conv,axiom,
% 3.42/1.78 ! [A_257: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ? [X_3: hoare_1708887482_state] : ( member451959335_state @ X_3 @ A_257 )
% 3.42/1.78 <=> ( A_257 != bot_bo19817387tate_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_104_ex__in__conv,axiom,
% 3.42/1.78 ! [A_257: pname > $o] :
% 3.42/1.78 ( ? [X_3: pname] : ( member_pname @ X_3 @ A_257 )
% 3.42/1.78 <=> ( A_257 != bot_bot_pname_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_105_all__not__in__conv,axiom,
% 3.42/1.78 ! [A_256: com > $o] :
% 3.42/1.78 ( ! [X_3: com] :
% 3.42/1.78 ~ ( member_com @ X_3 @ A_256 )
% 3.42/1.78 <=> ( A_256 = bot_bot_com_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_106_all__not__in__conv,axiom,
% 3.42/1.78 ! [A_256: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ! [X_3: hoare_1708887482_state] :
% 3.42/1.78 ~ ( member451959335_state @ X_3 @ A_256 )
% 3.42/1.78 <=> ( A_256 = bot_bo19817387tate_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_107_all__not__in__conv,axiom,
% 3.42/1.78 ! [A_256: pname > $o] :
% 3.42/1.78 ( ! [X_3: pname] :
% 3.42/1.78 ~ ( member_pname @ X_3 @ A_256 )
% 3.42/1.78 <=> ( A_256 = bot_bot_pname_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_108_empty__def,axiom,
% 3.42/1.78 ( bot_bot_pname_o
% 3.42/1.78 = ( collect_pname
% 3.42/1.78 @ ^ [X_3: pname] : $false ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_109_empty__def,axiom,
% 3.42/1.78 ( bot_bot_pname_o_o
% 3.42/1.78 = ( collect_pname_o
% 3.42/1.78 @ ^ [X_3: pname > $o] : $false ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_110_empty__def,axiom,
% 3.42/1.78 ( bot_bo1678742418te_o_o
% 3.42/1.78 = ( collec219771562tate_o
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state > $o] : $false ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_111_empty__def,axiom,
% 3.42/1.78 ( bot_bot_com_o
% 3.42/1.78 = ( collect_com
% 3.42/1.78 @ ^ [X_3: com] : $false ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_112_empty__def,axiom,
% 3.42/1.78 ( bot_bo19817387tate_o
% 3.42/1.78 = ( collec1568722789_state
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : $false ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_113_insert__absorb,axiom,
% 3.42/1.78 ! [A_255: com,A_254: com > $o] :
% 3.42/1.78 ( ( member_com @ A_255 @ A_254 )
% 3.42/1.78 => ( ( insert_com @ A_255 @ A_254 )
% 3.42/1.78 = A_254 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_114_insert__absorb,axiom,
% 3.42/1.78 ! [A_255: pname,A_254: pname > $o] :
% 3.42/1.78 ( ( member_pname @ A_255 @ A_254 )
% 3.42/1.78 => ( ( insert_pname @ A_255 @ A_254 )
% 3.42/1.78 = A_254 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_115_insert__absorb,axiom,
% 3.42/1.78 ! [A_255: hoare_1708887482_state,A_254: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ A_255 @ A_254 )
% 3.42/1.78 => ( ( insert528405184_state @ A_255 @ A_254 )
% 3.42/1.78 = A_254 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_116_insertI2,axiom,
% 3.42/1.78 ! [B_164: com,A_253: com,B_163: com > $o] :
% 3.42/1.78 ( ( member_com @ A_253 @ B_163 )
% 3.42/1.78 => ( member_com @ A_253 @ ( insert_com @ B_164 @ B_163 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_117_insertI2,axiom,
% 3.42/1.78 ! [B_164: pname,A_253: pname,B_163: pname > $o] :
% 3.42/1.78 ( ( member_pname @ A_253 @ B_163 )
% 3.42/1.78 => ( member_pname @ A_253 @ ( insert_pname @ B_164 @ B_163 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_118_insertI2,axiom,
% 3.42/1.78 ! [B_164: hoare_1708887482_state,A_253: hoare_1708887482_state,B_163: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ A_253 @ B_163 )
% 3.42/1.78 => ( member451959335_state @ A_253 @ ( insert528405184_state @ B_164 @ B_163 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_119_insert__ident,axiom,
% 3.42/1.78 ! [B_162: com > $o,X_115: com,A_252: com > $o] :
% 3.42/1.78 ( ~ ( member_com @ X_115 @ A_252 )
% 3.42/1.78 => ( ~ ( member_com @ X_115 @ B_162 )
% 3.42/1.78 => ( ( ( insert_com @ X_115 @ A_252 )
% 3.42/1.78 = ( insert_com @ X_115 @ B_162 ) )
% 3.42/1.78 <=> ( A_252 = B_162 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_120_insert__ident,axiom,
% 3.42/1.78 ! [B_162: pname > $o,X_115: pname,A_252: pname > $o] :
% 3.42/1.78 ( ~ ( member_pname @ X_115 @ A_252 )
% 3.42/1.78 => ( ~ ( member_pname @ X_115 @ B_162 )
% 3.42/1.78 => ( ( ( insert_pname @ X_115 @ A_252 )
% 3.42/1.78 = ( insert_pname @ X_115 @ B_162 ) )
% 3.42/1.78 <=> ( A_252 = B_162 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_121_insert__ident,axiom,
% 3.42/1.78 ! [B_162: hoare_1708887482_state > $o,X_115: hoare_1708887482_state,A_252: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ~ ( member451959335_state @ X_115 @ A_252 )
% 3.42/1.78 => ( ~ ( member451959335_state @ X_115 @ B_162 )
% 3.42/1.78 => ( ( ( insert528405184_state @ X_115 @ A_252 )
% 3.42/1.78 = ( insert528405184_state @ X_115 @ B_162 ) )
% 3.42/1.78 <=> ( A_252 = B_162 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_122_insert__code,axiom,
% 3.42/1.78 ! [Y_52: pname,A_251: pname > $o,X_114: pname] :
% 3.42/1.78 ( ( insert_pname @ Y_52 @ A_251 @ X_114 )
% 3.42/1.78 <=> ( ( Y_52 = X_114 )
% 3.42/1.78 | ( A_251 @ X_114 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_123_insert__code,axiom,
% 3.42/1.78 ! [Y_52: com,A_251: com > $o,X_114: com] :
% 3.42/1.78 ( ( insert_com @ Y_52 @ A_251 @ X_114 )
% 3.42/1.78 <=> ( ( Y_52 = X_114 )
% 3.42/1.78 | ( A_251 @ X_114 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_124_insert__code,axiom,
% 3.42/1.78 ! [Y_52: hoare_1708887482_state,A_251: hoare_1708887482_state > $o,X_114: hoare_1708887482_state] :
% 3.42/1.78 ( ( insert528405184_state @ Y_52 @ A_251 @ X_114 )
% 3.42/1.78 <=> ( ( Y_52 = X_114 )
% 3.42/1.78 | ( A_251 @ X_114 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_125_insert__iff,axiom,
% 3.42/1.78 ! [A_250: com,B_161: com,A_249: com > $o] :
% 3.42/1.78 ( ( member_com @ A_250 @ ( insert_com @ B_161 @ A_249 ) )
% 3.42/1.78 <=> ( ( A_250 = B_161 )
% 3.42/1.78 | ( member_com @ A_250 @ A_249 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_126_insert__iff,axiom,
% 3.42/1.78 ! [A_250: pname,B_161: pname,A_249: pname > $o] :
% 3.42/1.78 ( ( member_pname @ A_250 @ ( insert_pname @ B_161 @ A_249 ) )
% 3.42/1.78 <=> ( ( A_250 = B_161 )
% 3.42/1.78 | ( member_pname @ A_250 @ A_249 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_127_insert__iff,axiom,
% 3.42/1.78 ! [A_250: hoare_1708887482_state,B_161: hoare_1708887482_state,A_249: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ A_250 @ ( insert528405184_state @ B_161 @ A_249 ) )
% 3.42/1.78 <=> ( ( A_250 = B_161 )
% 3.42/1.78 | ( member451959335_state @ A_250 @ A_249 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_128_insert__commute,axiom,
% 3.42/1.78 ! [X_113: pname,Y_51: pname,A_248: pname > $o] :
% 3.42/1.78 ( ( insert_pname @ X_113 @ ( insert_pname @ Y_51 @ A_248 ) )
% 3.42/1.78 = ( insert_pname @ Y_51 @ ( insert_pname @ X_113 @ A_248 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_129_insert__commute,axiom,
% 3.42/1.78 ! [X_113: com,Y_51: com,A_248: com > $o] :
% 3.42/1.78 ( ( insert_com @ X_113 @ ( insert_com @ Y_51 @ A_248 ) )
% 3.42/1.78 = ( insert_com @ Y_51 @ ( insert_com @ X_113 @ A_248 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_130_insert__commute,axiom,
% 3.42/1.78 ! [X_113: hoare_1708887482_state,Y_51: hoare_1708887482_state,A_248: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( insert528405184_state @ X_113 @ ( insert528405184_state @ Y_51 @ A_248 ) )
% 3.42/1.78 = ( insert528405184_state @ Y_51 @ ( insert528405184_state @ X_113 @ A_248 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_131_insert__absorb2,axiom,
% 3.42/1.78 ! [X_112: pname,A_247: pname > $o] :
% 3.42/1.78 ( ( insert_pname @ X_112 @ ( insert_pname @ X_112 @ A_247 ) )
% 3.42/1.78 = ( insert_pname @ X_112 @ A_247 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_132_insert__absorb2,axiom,
% 3.42/1.78 ! [X_112: com,A_247: com > $o] :
% 3.42/1.78 ( ( insert_com @ X_112 @ ( insert_com @ X_112 @ A_247 ) )
% 3.42/1.78 = ( insert_com @ X_112 @ A_247 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_133_insert__absorb2,axiom,
% 3.42/1.78 ! [X_112: hoare_1708887482_state,A_247: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( insert528405184_state @ X_112 @ ( insert528405184_state @ X_112 @ A_247 ) )
% 3.42/1.78 = ( insert528405184_state @ X_112 @ A_247 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_134_insert__Collect,axiom,
% 3.42/1.78 ! [A_246: pname,P_42: pname > $o] :
% 3.42/1.78 ( ( insert_pname @ A_246 @ ( collect_pname @ P_42 ) )
% 3.42/1.78 = ( collect_pname
% 3.42/1.78 @ ^ [U_2: pname] : ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_135_insert__Collect,axiom,
% 3.42/1.78 ! [A_246: com,P_42: com > $o] :
% 3.42/1.78 ( ( insert_com @ A_246 @ ( collect_com @ P_42 ) )
% 3.42/1.78 = ( collect_com
% 3.42/1.78 @ ^ [U_2: com] : ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_136_insert__Collect,axiom,
% 3.42/1.78 ! [A_246: pname > $o,P_42: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( insert_pname_o @ A_246 @ ( collect_pname_o @ P_42 ) )
% 3.42/1.78 = ( collect_pname_o
% 3.42/1.78 @ ^ [U_2: pname > $o] : ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_137_insert__Collect,axiom,
% 3.42/1.78 ! [A_246: hoare_1708887482_state > $o,P_42: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( insert949073679tate_o @ A_246 @ ( collec219771562tate_o @ P_42 ) )
% 3.42/1.78 = ( collec219771562tate_o
% 3.42/1.78 @ ^ [U_2: hoare_1708887482_state > $o] : ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_138_insert__Collect,axiom,
% 3.42/1.78 ! [A_246: hoare_1708887482_state,P_42: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( insert528405184_state @ A_246 @ ( collec1568722789_state @ P_42 ) )
% 3.42/1.78 = ( collec1568722789_state
% 3.42/1.78 @ ^ [U_2: hoare_1708887482_state] : ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_139_insert__compr,axiom,
% 3.42/1.78 ! [A_245: com,B_160: com > $o] :
% 3.42/1.78 ( ( insert_com @ A_245 @ B_160 )
% 3.42/1.78 = ( collect_com
% 3.42/1.78 @ ^ [X_3: com] : ( (|) @ ( X_3 = A_245 ) @ ( member_com @ X_3 @ B_160 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_140_insert__compr,axiom,
% 3.42/1.78 ! [A_245: pname > $o,B_160: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( insert_pname_o @ A_245 @ B_160 )
% 3.42/1.78 = ( collect_pname_o
% 3.42/1.78 @ ^ [X_3: pname > $o] : ( (|) @ ( X_3 = A_245 ) @ ( member_pname_o @ X_3 @ B_160 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_141_insert__compr,axiom,
% 3.42/1.78 ! [A_245: hoare_1708887482_state > $o,B_160: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( insert949073679tate_o @ A_245 @ B_160 )
% 3.42/1.78 = ( collec219771562tate_o
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state > $o] : ( (|) @ ( X_3 = A_245 ) @ ( member814030440tate_o @ X_3 @ B_160 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_142_insert__compr,axiom,
% 3.42/1.78 ! [A_245: pname,B_160: pname > $o] :
% 3.42/1.78 ( ( insert_pname @ A_245 @ B_160 )
% 3.42/1.78 = ( collect_pname
% 3.42/1.78 @ ^ [X_3: pname] : ( (|) @ ( X_3 = A_245 ) @ ( member_pname @ X_3 @ B_160 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_143_insert__compr,axiom,
% 3.42/1.78 ! [A_245: hoare_1708887482_state,B_160: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( insert528405184_state @ A_245 @ B_160 )
% 3.42/1.78 = ( collec1568722789_state
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : ( (|) @ ( X_3 = A_245 ) @ ( member451959335_state @ X_3 @ B_160 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_144_insertI1,axiom,
% 3.42/1.78 ! [A_244: com,B_159: com > $o] : ( member_com @ A_244 @ ( insert_com @ A_244 @ B_159 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_145_insertI1,axiom,
% 3.42/1.78 ! [A_244: pname,B_159: pname > $o] : ( member_pname @ A_244 @ ( insert_pname @ A_244 @ B_159 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_146_insertI1,axiom,
% 3.42/1.78 ! [A_244: hoare_1708887482_state,B_159: hoare_1708887482_state > $o] : ( member451959335_state @ A_244 @ ( insert528405184_state @ A_244 @ B_159 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_147_equalityE,axiom,
% 3.42/1.78 ! [A_243: pname > $o,B_158: pname > $o] :
% 3.42/1.78 ( ( A_243 = B_158 )
% 3.42/1.78 => ~ ( ( ord_less_eq_pname_o @ A_243 @ B_158 )
% 3.42/1.78 => ~ ( ord_less_eq_pname_o @ B_158 @ A_243 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_148_equalityE,axiom,
% 3.42/1.78 ! [A_243: hoare_1708887482_state > $o,B_158: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( A_243 = B_158 )
% 3.42/1.78 => ~ ( ( ord_le777019615tate_o @ A_243 @ B_158 )
% 3.42/1.78 => ~ ( ord_le777019615tate_o @ B_158 @ A_243 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_149_subset__trans,axiom,
% 3.42/1.78 ! [C_64: pname > $o,A_242: pname > $o,B_157: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ A_242 @ B_157 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ B_157 @ C_64 )
% 3.42/1.78 => ( ord_less_eq_pname_o @ A_242 @ C_64 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_150_subset__trans,axiom,
% 3.42/1.78 ! [C_64: hoare_1708887482_state > $o,A_242: hoare_1708887482_state > $o,B_157: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ A_242 @ B_157 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ B_157 @ C_64 )
% 3.42/1.78 => ( ord_le777019615tate_o @ A_242 @ C_64 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_151_set__mp,axiom,
% 3.42/1.78 ! [X_111: com,A_241: com > $o,B_156: com > $o] :
% 3.42/1.78 ( ( ord_less_eq_com_o @ A_241 @ B_156 )
% 3.42/1.78 => ( ( member_com @ X_111 @ A_241 )
% 3.42/1.78 => ( member_com @ X_111 @ B_156 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_152_set__mp,axiom,
% 3.42/1.78 ! [X_111: hoare_1708887482_state,A_241: hoare_1708887482_state > $o,B_156: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ A_241 @ B_156 )
% 3.42/1.78 => ( ( member451959335_state @ X_111 @ A_241 )
% 3.42/1.78 => ( member451959335_state @ X_111 @ B_156 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_153_set__mp,axiom,
% 3.42/1.78 ! [X_111: pname,A_241: pname > $o,B_156: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ A_241 @ B_156 )
% 3.42/1.78 => ( ( member_pname @ X_111 @ A_241 )
% 3.42/1.78 => ( member_pname @ X_111 @ B_156 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_154_set__rev__mp,axiom,
% 3.42/1.78 ! [B_155: com > $o,X_110: com,A_240: com > $o] :
% 3.42/1.78 ( ( member_com @ X_110 @ A_240 )
% 3.42/1.78 => ( ( ord_less_eq_com_o @ A_240 @ B_155 )
% 3.42/1.78 => ( member_com @ X_110 @ B_155 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_155_set__rev__mp,axiom,
% 3.42/1.78 ! [B_155: hoare_1708887482_state > $o,X_110: hoare_1708887482_state,A_240: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ X_110 @ A_240 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ A_240 @ B_155 )
% 3.42/1.78 => ( member451959335_state @ X_110 @ B_155 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_156_set__rev__mp,axiom,
% 3.42/1.78 ! [B_155: pname > $o,X_110: pname,A_240: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_110 @ A_240 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ A_240 @ B_155 )
% 3.42/1.78 => ( member_pname @ X_110 @ B_155 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_157_in__mono,axiom,
% 3.42/1.78 ! [X_109: com,A_239: com > $o,B_154: com > $o] :
% 3.42/1.78 ( ( ord_less_eq_com_o @ A_239 @ B_154 )
% 3.42/1.78 => ( ( member_com @ X_109 @ A_239 )
% 3.42/1.78 => ( member_com @ X_109 @ B_154 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_158_in__mono,axiom,
% 3.42/1.78 ! [X_109: hoare_1708887482_state,A_239: hoare_1708887482_state > $o,B_154: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ A_239 @ B_154 )
% 3.42/1.78 => ( ( member451959335_state @ X_109 @ A_239 )
% 3.42/1.78 => ( member451959335_state @ X_109 @ B_154 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_159_in__mono,axiom,
% 3.42/1.78 ! [X_109: pname,A_239: pname > $o,B_154: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ A_239 @ B_154 )
% 3.42/1.78 => ( ( member_pname @ X_109 @ A_239 )
% 3.42/1.78 => ( member_pname @ X_109 @ B_154 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_160_equalityD2,axiom,
% 3.42/1.78 ! [A_238: pname > $o,B_153: pname > $o] :
% 3.42/1.78 ( ( A_238 = B_153 )
% 3.42/1.78 => ( ord_less_eq_pname_o @ B_153 @ A_238 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_161_equalityD2,axiom,
% 3.42/1.78 ! [A_238: hoare_1708887482_state > $o,B_153: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( A_238 = B_153 )
% 3.42/1.78 => ( ord_le777019615tate_o @ B_153 @ A_238 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_162_equalityD1,axiom,
% 3.42/1.78 ! [A_237: pname > $o,B_152: pname > $o] :
% 3.42/1.78 ( ( A_237 = B_152 )
% 3.42/1.78 => ( ord_less_eq_pname_o @ A_237 @ B_152 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_163_equalityD1,axiom,
% 3.42/1.78 ! [A_237: hoare_1708887482_state > $o,B_152: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( A_237 = B_152 )
% 3.42/1.78 => ( ord_le777019615tate_o @ A_237 @ B_152 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_164_set__eq__subset,axiom,
% 3.42/1.78 ! [A_236: pname > $o,B_151: pname > $o] :
% 3.42/1.78 ( ( A_236 = B_151 )
% 3.42/1.78 <=> ( ( ord_less_eq_pname_o @ A_236 @ B_151 )
% 3.42/1.78 & ( ord_less_eq_pname_o @ B_151 @ A_236 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_165_set__eq__subset,axiom,
% 3.42/1.78 ! [A_236: hoare_1708887482_state > $o,B_151: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( A_236 = B_151 )
% 3.42/1.78 <=> ( ( ord_le777019615tate_o @ A_236 @ B_151 )
% 3.42/1.78 & ( ord_le777019615tate_o @ B_151 @ A_236 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_166_subset__refl,axiom,
% 3.42/1.78 ! [A_235: pname > $o] : ( ord_less_eq_pname_o @ A_235 @ A_235 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_167_subset__refl,axiom,
% 3.42/1.78 ! [A_235: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A_235 @ A_235 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_168_rev__image__eqI,axiom,
% 3.42/1.78 ! [B_150: com,F_84: hoare_1708887482_state > com,X_108: hoare_1708887482_state,A_234: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ X_108 @ A_234 )
% 3.42/1.78 => ( ( B_150
% 3.42/1.78 = ( F_84 @ X_108 ) )
% 3.42/1.78 => ( member_com @ B_150 @ ( image_1604448413te_com @ F_84 @ A_234 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_169_rev__image__eqI,axiom,
% 3.42/1.78 ! [B_150: com,F_84: pname > com,X_108: pname,A_234: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_108 @ A_234 )
% 3.42/1.78 => ( ( B_150
% 3.42/1.78 = ( F_84 @ X_108 ) )
% 3.42/1.78 => ( member_com @ B_150 @ ( image_pname_com @ F_84 @ A_234 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_170_rev__image__eqI,axiom,
% 3.42/1.78 ! [B_150: hoare_1708887482_state,F_84: com > hoare_1708887482_state,X_108: com,A_234: com > $o] :
% 3.42/1.78 ( ( member_com @ X_108 @ A_234 )
% 3.42/1.78 => ( ( B_150
% 3.42/1.78 = ( F_84 @ X_108 ) )
% 3.42/1.78 => ( member451959335_state @ B_150 @ ( image_934102463_state @ F_84 @ A_234 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_171_rev__image__eqI,axiom,
% 3.42/1.78 ! [B_150: pname,F_84: com > pname,X_108: com,A_234: com > $o] :
% 3.42/1.78 ( ( member_com @ X_108 @ A_234 )
% 3.42/1.78 => ( ( B_150
% 3.42/1.78 = ( F_84 @ X_108 ) )
% 3.42/1.78 => ( member_pname @ B_150 @ ( image_com_pname @ F_84 @ A_234 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_172_rev__image__eqI,axiom,
% 3.42/1.78 ! [B_150: hoare_1708887482_state,F_84: pname > hoare_1708887482_state,X_108: pname,A_234: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_108 @ A_234 )
% 3.42/1.78 => ( ( B_150
% 3.42/1.78 = ( F_84 @ X_108 ) )
% 3.42/1.78 => ( member451959335_state @ B_150 @ ( image_1116629049_state @ F_84 @ A_234 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_173_imageI,axiom,
% 3.42/1.78 ! [F_83: hoare_1708887482_state > com,X_107: hoare_1708887482_state,A_233: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ X_107 @ A_233 )
% 3.42/1.78 => ( member_com @ ( F_83 @ X_107 ) @ ( image_1604448413te_com @ F_83 @ A_233 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_174_imageI,axiom,
% 3.42/1.78 ! [F_83: pname > com,X_107: pname,A_233: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_107 @ A_233 )
% 3.42/1.78 => ( member_com @ ( F_83 @ X_107 ) @ ( image_pname_com @ F_83 @ A_233 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_175_imageI,axiom,
% 3.42/1.78 ! [F_83: com > hoare_1708887482_state,X_107: com,A_233: com > $o] :
% 3.42/1.78 ( ( member_com @ X_107 @ A_233 )
% 3.42/1.78 => ( member451959335_state @ ( F_83 @ X_107 ) @ ( image_934102463_state @ F_83 @ A_233 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_176_imageI,axiom,
% 3.42/1.78 ! [F_83: com > pname,X_107: com,A_233: com > $o] :
% 3.42/1.78 ( ( member_com @ X_107 @ A_233 )
% 3.42/1.78 => ( member_pname @ ( F_83 @ X_107 ) @ ( image_com_pname @ F_83 @ A_233 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_177_imageI,axiom,
% 3.42/1.78 ! [F_83: pname > hoare_1708887482_state,X_107: pname,A_233: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_107 @ A_233 )
% 3.42/1.78 => ( member451959335_state @ ( F_83 @ X_107 ) @ ( image_1116629049_state @ F_83 @ A_233 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_178_image__iff,axiom,
% 3.42/1.78 ! [Z_21: hoare_1708887482_state,F_82: pname > hoare_1708887482_state,A_232: pname > $o] :
% 3.42/1.78 ( ( member451959335_state @ Z_21 @ ( image_1116629049_state @ F_82 @ A_232 ) )
% 3.42/1.78 <=> ? [X_3: pname] :
% 3.42/1.78 ( ( member_pname @ X_3 @ A_232 )
% 3.42/1.78 & ( Z_21
% 3.42/1.78 = ( F_82 @ X_3 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_179_finite__Collect__disjI,axiom,
% 3.42/1.78 ! [P_41: ( pname > $o ) > $o,Q_25: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o
% 3.42/1.78 @ ( collect_pname_o
% 3.42/1.78 @ ^ [X_3: pname > $o] : ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
% 3.42/1.78 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_41 ) )
% 3.42/1.78 & ( finite297249702name_o @ ( collect_pname_o @ Q_25 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_180_finite__Collect__disjI,axiom,
% 3.42/1.78 ! [P_41: ( hoare_1708887482_state > $o ) > $o,Q_25: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o
% 3.42/1.78 @ ( collec219771562tate_o
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state > $o] : ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
% 3.42/1.78 <=> ( ( finite1329924456tate_o @ ( collec219771562tate_o @ P_41 ) )
% 3.42/1.78 & ( finite1329924456tate_o @ ( collec219771562tate_o @ Q_25 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_181_finite__Collect__disjI,axiom,
% 3.42/1.78 ! [P_41: hoare_1708887482_state > $o,Q_25: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state
% 3.42/1.78 @ ( collec1568722789_state
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
% 3.42/1.78 <=> ( ( finite1625599783_state @ ( collec1568722789_state @ P_41 ) )
% 3.42/1.78 & ( finite1625599783_state @ ( collec1568722789_state @ Q_25 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_182_finite__Collect__disjI,axiom,
% 3.42/1.78 ! [P_41: pname > $o,Q_25: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname
% 3.42/1.78 @ ( collect_pname
% 3.42/1.78 @ ^ [X_3: pname] : ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
% 3.42/1.78 <=> ( ( finite_finite_pname @ ( collect_pname @ P_41 ) )
% 3.42/1.78 & ( finite_finite_pname @ ( collect_pname @ Q_25 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_183_insert__compr__raw,axiom,
% 3.42/1.78 ! [X_3: com,Xa: com > $o] :
% 3.42/1.78 ( ( insert_com @ X_3 @ Xa )
% 3.42/1.78 = ( collect_com
% 3.42/1.78 @ ^ [Y_4: com] : ( (|) @ ( Y_4 = X_3 ) @ ( member_com @ Y_4 @ Xa ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_184_insert__compr__raw,axiom,
% 3.42/1.78 ! [X_3: pname > $o,Xa: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( insert_pname_o @ X_3 @ Xa )
% 3.42/1.78 = ( collect_pname_o
% 3.42/1.78 @ ^ [Y_4: pname > $o] : ( (|) @ ( Y_4 = X_3 ) @ ( member_pname_o @ Y_4 @ Xa ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_185_insert__compr__raw,axiom,
% 3.42/1.78 ! [X_3: hoare_1708887482_state > $o,Xa: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( insert949073679tate_o @ X_3 @ Xa )
% 3.42/1.78 = ( collec219771562tate_o
% 3.42/1.78 @ ^ [Y_4: hoare_1708887482_state > $o] : ( (|) @ ( Y_4 = X_3 ) @ ( member814030440tate_o @ Y_4 @ Xa ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_186_insert__compr__raw,axiom,
% 3.42/1.78 ! [X_3: pname,Xa: pname > $o] :
% 3.42/1.78 ( ( insert_pname @ X_3 @ Xa )
% 3.42/1.78 = ( collect_pname
% 3.42/1.78 @ ^ [Y_4: pname] : ( (|) @ ( Y_4 = X_3 ) @ ( member_pname @ Y_4 @ Xa ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_187_insert__compr__raw,axiom,
% 3.42/1.78 ! [X_3: hoare_1708887482_state,Xa: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( insert528405184_state @ X_3 @ Xa )
% 3.42/1.78 = ( collec1568722789_state
% 3.42/1.78 @ ^ [Y_4: hoare_1708887482_state] : ( (|) @ ( Y_4 = X_3 ) @ ( member451959335_state @ Y_4 @ Xa ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_188_singleton__inject,axiom,
% 3.42/1.78 ! [A_231: pname,B_149: pname] :
% 3.42/1.78 ( ( ( insert_pname @ A_231 @ bot_bot_pname_o )
% 3.42/1.78 = ( insert_pname @ B_149 @ bot_bot_pname_o ) )
% 3.42/1.78 => ( A_231 = B_149 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_189_singleton__inject,axiom,
% 3.42/1.78 ! [A_231: com,B_149: com] :
% 3.42/1.78 ( ( ( insert_com @ A_231 @ bot_bot_com_o )
% 3.42/1.78 = ( insert_com @ B_149 @ bot_bot_com_o ) )
% 3.42/1.78 => ( A_231 = B_149 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_190_singleton__inject,axiom,
% 3.42/1.78 ! [A_231: hoare_1708887482_state,B_149: hoare_1708887482_state] :
% 3.42/1.78 ( ( ( insert528405184_state @ A_231 @ bot_bo19817387tate_o )
% 3.42/1.78 = ( insert528405184_state @ B_149 @ bot_bo19817387tate_o ) )
% 3.42/1.78 => ( A_231 = B_149 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_191_singletonE,axiom,
% 3.42/1.78 ! [B_148: com,A_230: com] :
% 3.42/1.78 ( ( member_com @ B_148 @ ( insert_com @ A_230 @ bot_bot_com_o ) )
% 3.42/1.78 => ( B_148 = A_230 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_192_singletonE,axiom,
% 3.42/1.78 ! [B_148: pname,A_230: pname] :
% 3.42/1.78 ( ( member_pname @ B_148 @ ( insert_pname @ A_230 @ bot_bot_pname_o ) )
% 3.42/1.78 => ( B_148 = A_230 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_193_singletonE,axiom,
% 3.42/1.78 ! [B_148: hoare_1708887482_state,A_230: hoare_1708887482_state] :
% 3.42/1.78 ( ( member451959335_state @ B_148 @ ( insert528405184_state @ A_230 @ bot_bo19817387tate_o ) )
% 3.42/1.78 => ( B_148 = A_230 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_194_doubleton__eq__iff,axiom,
% 3.42/1.78 ! [A_229: pname,B_147: pname,C_63: pname,D_7: pname] :
% 3.42/1.78 ( ( ( insert_pname @ A_229 @ ( insert_pname @ B_147 @ bot_bot_pname_o ) )
% 3.42/1.78 = ( insert_pname @ C_63 @ ( insert_pname @ D_7 @ bot_bot_pname_o ) ) )
% 3.42/1.78 <=> ( ( ( A_229 = C_63 )
% 3.42/1.78 & ( B_147 = D_7 ) )
% 3.42/1.78 | ( ( A_229 = D_7 )
% 3.42/1.78 & ( B_147 = C_63 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_195_doubleton__eq__iff,axiom,
% 3.42/1.78 ! [A_229: com,B_147: com,C_63: com,D_7: com] :
% 3.42/1.78 ( ( ( insert_com @ A_229 @ ( insert_com @ B_147 @ bot_bot_com_o ) )
% 3.42/1.78 = ( insert_com @ C_63 @ ( insert_com @ D_7 @ bot_bot_com_o ) ) )
% 3.42/1.78 <=> ( ( ( A_229 = C_63 )
% 3.42/1.78 & ( B_147 = D_7 ) )
% 3.42/1.78 | ( ( A_229 = D_7 )
% 3.42/1.78 & ( B_147 = C_63 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_196_doubleton__eq__iff,axiom,
% 3.42/1.78 ! [A_229: hoare_1708887482_state,B_147: hoare_1708887482_state,C_63: hoare_1708887482_state,D_7: hoare_1708887482_state] :
% 3.42/1.78 ( ( ( insert528405184_state @ A_229 @ ( insert528405184_state @ B_147 @ bot_bo19817387tate_o ) )
% 3.42/1.78 = ( insert528405184_state @ C_63 @ ( insert528405184_state @ D_7 @ bot_bo19817387tate_o ) ) )
% 3.42/1.78 <=> ( ( ( A_229 = C_63 )
% 3.42/1.78 & ( B_147 = D_7 ) )
% 3.42/1.78 | ( ( A_229 = D_7 )
% 3.42/1.78 & ( B_147 = C_63 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_197_singleton__iff,axiom,
% 3.42/1.78 ! [B_146: com,A_228: com] :
% 3.42/1.78 ( ( member_com @ B_146 @ ( insert_com @ A_228 @ bot_bot_com_o ) )
% 3.42/1.78 <=> ( B_146 = A_228 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_198_singleton__iff,axiom,
% 3.42/1.78 ! [B_146: pname,A_228: pname] :
% 3.42/1.78 ( ( member_pname @ B_146 @ ( insert_pname @ A_228 @ bot_bot_pname_o ) )
% 3.42/1.78 <=> ( B_146 = A_228 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_199_singleton__iff,axiom,
% 3.42/1.78 ! [B_146: hoare_1708887482_state,A_228: hoare_1708887482_state] :
% 3.42/1.78 ( ( member451959335_state @ B_146 @ ( insert528405184_state @ A_228 @ bot_bo19817387tate_o ) )
% 3.42/1.78 <=> ( B_146 = A_228 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_200_insert__not__empty,axiom,
% 3.42/1.78 ! [A_227: pname,A_226: pname > $o] :
% 3.42/1.78 ( ( insert_pname @ A_227 @ A_226 )
% 3.42/1.78 != bot_bot_pname_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_201_insert__not__empty,axiom,
% 3.42/1.78 ! [A_227: com,A_226: com > $o] :
% 3.42/1.78 ( ( insert_com @ A_227 @ A_226 )
% 3.42/1.78 != bot_bot_com_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_202_insert__not__empty,axiom,
% 3.42/1.78 ! [A_227: hoare_1708887482_state,A_226: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( insert528405184_state @ A_227 @ A_226 )
% 3.42/1.78 != bot_bo19817387tate_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_203_empty__not__insert,axiom,
% 3.42/1.78 ! [A_225: pname,A_224: pname > $o] :
% 3.42/1.78 ( bot_bot_pname_o
% 3.42/1.78 != ( insert_pname @ A_225 @ A_224 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_204_empty__not__insert,axiom,
% 3.42/1.78 ! [A_225: com,A_224: com > $o] :
% 3.42/1.78 ( bot_bot_com_o
% 3.42/1.78 != ( insert_com @ A_225 @ A_224 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_205_empty__not__insert,axiom,
% 3.42/1.78 ! [A_225: hoare_1708887482_state,A_224: hoare_1708887482_state > $o] :
% 3.42/1.78 ( bot_bo19817387tate_o
% 3.42/1.78 != ( insert528405184_state @ A_225 @ A_224 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_206_finite__insert,axiom,
% 3.42/1.78 ! [A_223: com,A_222: com > $o] :
% 3.42/1.78 ( ( finite_finite_com @ ( insert_com @ A_223 @ A_222 ) )
% 3.42/1.78 <=> ( finite_finite_com @ A_222 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_207_finite__insert,axiom,
% 3.42/1.78 ! [A_223: pname > $o,A_222: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ ( insert_pname_o @ A_223 @ A_222 ) )
% 3.42/1.78 <=> ( finite297249702name_o @ A_222 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_208_finite__insert,axiom,
% 3.42/1.78 ! [A_223: hoare_1708887482_state > $o,A_222: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ ( insert949073679tate_o @ A_223 @ A_222 ) )
% 3.42/1.78 <=> ( finite1329924456tate_o @ A_222 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_209_finite__insert,axiom,
% 3.42/1.78 ! [A_223: pname,A_222: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ ( insert_pname @ A_223 @ A_222 ) )
% 3.42/1.78 <=> ( finite_finite_pname @ A_222 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_210_finite__insert,axiom,
% 3.42/1.78 ! [A_223: hoare_1708887482_state,A_222: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ ( insert528405184_state @ A_223 @ A_222 ) )
% 3.42/1.78 <=> ( finite1625599783_state @ A_222 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_211_subset__empty,axiom,
% 3.42/1.78 ! [A_221: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ A_221 @ bot_bot_pname_o )
% 3.42/1.78 <=> ( A_221 = bot_bot_pname_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_212_subset__empty,axiom,
% 3.42/1.78 ! [A_221: com > $o] :
% 3.42/1.78 ( ( ord_less_eq_com_o @ A_221 @ bot_bot_com_o )
% 3.42/1.78 <=> ( A_221 = bot_bot_com_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_213_subset__empty,axiom,
% 3.42/1.78 ! [A_221: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ A_221 @ bot_bo19817387tate_o )
% 3.42/1.78 <=> ( A_221 = bot_bo19817387tate_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_214_image__is__empty,axiom,
% 3.42/1.78 ! [F_81: com > hoare_1708887482_state,A_220: com > $o] :
% 3.42/1.78 ( ( ( image_934102463_state @ F_81 @ A_220 )
% 3.42/1.78 = bot_bo19817387tate_o )
% 3.42/1.78 <=> ( A_220 = bot_bot_com_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_215_image__is__empty,axiom,
% 3.42/1.78 ! [F_81: hoare_1708887482_state > pname,A_220: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ( image_1509414295_pname @ F_81 @ A_220 )
% 3.42/1.78 = bot_bot_pname_o )
% 3.42/1.78 <=> ( A_220 = bot_bo19817387tate_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_216_image__is__empty,axiom,
% 3.42/1.78 ! [F_81: hoare_1708887482_state > com,A_220: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ( image_1604448413te_com @ F_81 @ A_220 )
% 3.42/1.78 = bot_bot_com_o )
% 3.42/1.78 <=> ( A_220 = bot_bo19817387tate_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_217_image__is__empty,axiom,
% 3.42/1.78 ! [F_81: pname > hoare_1708887482_state,A_220: pname > $o] :
% 3.42/1.78 ( ( ( image_1116629049_state @ F_81 @ A_220 )
% 3.42/1.78 = bot_bo19817387tate_o )
% 3.42/1.78 <=> ( A_220 = bot_bot_pname_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_218_image__empty,axiom,
% 3.42/1.78 ! [F_80: hoare_1708887482_state > pname] :
% 3.42/1.78 ( ( image_1509414295_pname @ F_80 @ bot_bo19817387tate_o )
% 3.42/1.78 = bot_bot_pname_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_219_image__empty,axiom,
% 3.42/1.78 ! [F_80: hoare_1708887482_state > com] :
% 3.42/1.78 ( ( image_1604448413te_com @ F_80 @ bot_bo19817387tate_o )
% 3.42/1.78 = bot_bot_com_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_220_image__empty,axiom,
% 3.42/1.78 ! [F_80: com > hoare_1708887482_state] :
% 3.42/1.78 ( ( image_934102463_state @ F_80 @ bot_bot_com_o )
% 3.42/1.78 = bot_bo19817387tate_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_221_image__empty,axiom,
% 3.42/1.78 ! [F_80: pname > hoare_1708887482_state] :
% 3.42/1.78 ( ( image_1116629049_state @ F_80 @ bot_bot_pname_o )
% 3.42/1.78 = bot_bo19817387tate_o ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_222_empty__is__image,axiom,
% 3.42/1.78 ! [F_79: com > hoare_1708887482_state,A_219: com > $o] :
% 3.42/1.78 ( ( bot_bo19817387tate_o
% 3.42/1.78 = ( image_934102463_state @ F_79 @ A_219 ) )
% 3.42/1.78 <=> ( A_219 = bot_bot_com_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_223_empty__is__image,axiom,
% 3.42/1.78 ! [F_79: hoare_1708887482_state > pname,A_219: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( bot_bot_pname_o
% 3.42/1.78 = ( image_1509414295_pname @ F_79 @ A_219 ) )
% 3.42/1.78 <=> ( A_219 = bot_bo19817387tate_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_224_empty__is__image,axiom,
% 3.42/1.78 ! [F_79: hoare_1708887482_state > com,A_219: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( bot_bot_com_o
% 3.42/1.78 = ( image_1604448413te_com @ F_79 @ A_219 ) )
% 3.42/1.78 <=> ( A_219 = bot_bo19817387tate_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_225_empty__is__image,axiom,
% 3.42/1.78 ! [F_79: pname > hoare_1708887482_state,A_219: pname > $o] :
% 3.42/1.78 ( ( bot_bo19817387tate_o
% 3.42/1.78 = ( image_1116629049_state @ F_79 @ A_219 ) )
% 3.42/1.78 <=> ( A_219 = bot_bot_pname_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_226_finite__subset,axiom,
% 3.42/1.78 ! [A_218: ( pname > $o ) > $o,B_145: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( ord_le1205211808me_o_o @ A_218 @ B_145 )
% 3.42/1.78 => ( ( finite297249702name_o @ B_145 )
% 3.42/1.78 => ( finite297249702name_o @ A_218 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_227_finite__subset,axiom,
% 3.42/1.78 ! [A_218: ( hoare_1708887482_state > $o ) > $o,B_145: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( ord_le1728773982te_o_o @ A_218 @ B_145 )
% 3.42/1.78 => ( ( finite1329924456tate_o @ B_145 )
% 3.42/1.78 => ( finite1329924456tate_o @ A_218 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_228_finite__subset,axiom,
% 3.42/1.78 ! [A_218: hoare_1708887482_state > $o,B_145: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ A_218 @ B_145 )
% 3.42/1.78 => ( ( finite1625599783_state @ B_145 )
% 3.42/1.78 => ( finite1625599783_state @ A_218 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_229_finite__subset,axiom,
% 3.42/1.78 ! [A_218: pname > $o,B_145: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ A_218 @ B_145 )
% 3.42/1.78 => ( ( finite_finite_pname @ B_145 )
% 3.42/1.78 => ( finite_finite_pname @ A_218 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_230_rev__finite__subset,axiom,
% 3.42/1.78 ! [A_217: ( pname > $o ) > $o,B_144: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ B_144 )
% 3.42/1.78 => ( ( ord_le1205211808me_o_o @ A_217 @ B_144 )
% 3.42/1.78 => ( finite297249702name_o @ A_217 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_231_rev__finite__subset,axiom,
% 3.42/1.78 ! [A_217: ( hoare_1708887482_state > $o ) > $o,B_144: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ B_144 )
% 3.42/1.78 => ( ( ord_le1728773982te_o_o @ A_217 @ B_144 )
% 3.42/1.78 => ( finite1329924456tate_o @ A_217 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_232_rev__finite__subset,axiom,
% 3.42/1.78 ! [A_217: hoare_1708887482_state > $o,B_144: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ B_144 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ A_217 @ B_144 )
% 3.42/1.78 => ( finite1625599783_state @ A_217 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_233_rev__finite__subset,axiom,
% 3.42/1.78 ! [A_217: pname > $o,B_144: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ B_144 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ A_217 @ B_144 )
% 3.42/1.78 => ( finite_finite_pname @ A_217 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_234_insert__mono,axiom,
% 3.42/1.78 ! [A_216: pname,C_62: pname > $o,D_6: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ C_62 @ D_6 )
% 3.42/1.78 => ( ord_less_eq_pname_o @ ( insert_pname @ A_216 @ C_62 ) @ ( insert_pname @ A_216 @ D_6 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_235_insert__mono,axiom,
% 3.42/1.78 ! [A_216: com,C_62: com > $o,D_6: com > $o] :
% 3.42/1.78 ( ( ord_less_eq_com_o @ C_62 @ D_6 )
% 3.42/1.78 => ( ord_less_eq_com_o @ ( insert_com @ A_216 @ C_62 ) @ ( insert_com @ A_216 @ D_6 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_236_insert__mono,axiom,
% 3.42/1.78 ! [A_216: hoare_1708887482_state,C_62: hoare_1708887482_state > $o,D_6: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ C_62 @ D_6 )
% 3.42/1.78 => ( ord_le777019615tate_o @ ( insert528405184_state @ A_216 @ C_62 ) @ ( insert528405184_state @ A_216 @ D_6 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_237_mem__def,axiom,
% 3.42/1.78 ! [X_106: com,A_215: com > $o] :
% 3.42/1.78 ( ( member_com @ X_106 @ A_215 )
% 3.42/1.78 <=> ( A_215 @ X_106 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_238_mem__def,axiom,
% 3.42/1.78 ! [X_106: hoare_1708887482_state,A_215: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ X_106 @ A_215 )
% 3.42/1.78 <=> ( A_215 @ X_106 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_239_mem__def,axiom,
% 3.42/1.78 ! [X_106: pname,A_215: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_106 @ A_215 )
% 3.42/1.78 <=> ( A_215 @ X_106 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_240_Collect__def,axiom,
% 3.42/1.78 ! [P_40: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( collec1568722789_state @ P_40 )
% 3.42/1.78 = P_40 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_241_Collect__def,axiom,
% 3.42/1.78 ! [P_40: pname > $o] :
% 3.42/1.78 ( ( collect_pname @ P_40 )
% 3.42/1.78 = P_40 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_242_Collect__def,axiom,
% 3.42/1.78 ! [P_40: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( collect_pname_o @ P_40 )
% 3.42/1.78 = P_40 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_243_Collect__def,axiom,
% 3.42/1.78 ! [P_40: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( collec219771562tate_o @ P_40 )
% 3.42/1.78 = P_40 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_244_subset__insertI2,axiom,
% 3.42/1.78 ! [B_143: pname,A_214: pname > $o,B_142: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ A_214 @ B_142 )
% 3.42/1.78 => ( ord_less_eq_pname_o @ A_214 @ ( insert_pname @ B_143 @ B_142 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_245_subset__insertI2,axiom,
% 3.42/1.78 ! [B_143: com,A_214: com > $o,B_142: com > $o] :
% 3.42/1.78 ( ( ord_less_eq_com_o @ A_214 @ B_142 )
% 3.42/1.78 => ( ord_less_eq_com_o @ A_214 @ ( insert_com @ B_143 @ B_142 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_246_subset__insertI2,axiom,
% 3.42/1.78 ! [B_143: hoare_1708887482_state,A_214: hoare_1708887482_state > $o,B_142: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ A_214 @ B_142 )
% 3.42/1.78 => ( ord_le777019615tate_o @ A_214 @ ( insert528405184_state @ B_143 @ B_142 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_247_subset__insert,axiom,
% 3.42/1.78 ! [B_141: com > $o,X_105: com,A_213: com > $o] :
% 3.42/1.78 ( ~ ( member_com @ X_105 @ A_213 )
% 3.42/1.78 => ( ( ord_less_eq_com_o @ A_213 @ ( insert_com @ X_105 @ B_141 ) )
% 3.42/1.78 <=> ( ord_less_eq_com_o @ A_213 @ B_141 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_248_subset__insert,axiom,
% 3.42/1.78 ! [B_141: pname > $o,X_105: pname,A_213: pname > $o] :
% 3.42/1.78 ( ~ ( member_pname @ X_105 @ A_213 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ A_213 @ ( insert_pname @ X_105 @ B_141 ) )
% 3.42/1.78 <=> ( ord_less_eq_pname_o @ A_213 @ B_141 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_249_subset__insert,axiom,
% 3.42/1.78 ! [B_141: hoare_1708887482_state > $o,X_105: hoare_1708887482_state,A_213: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ~ ( member451959335_state @ X_105 @ A_213 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ A_213 @ ( insert528405184_state @ X_105 @ B_141 ) )
% 3.42/1.78 <=> ( ord_le777019615tate_o @ A_213 @ B_141 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_250_insert__subset,axiom,
% 3.42/1.78 ! [X_104: com,A_212: com > $o,B_140: com > $o] :
% 3.42/1.78 ( ( ord_less_eq_com_o @ ( insert_com @ X_104 @ A_212 ) @ B_140 )
% 3.42/1.78 <=> ( ( member_com @ X_104 @ B_140 )
% 3.42/1.78 & ( ord_less_eq_com_o @ A_212 @ B_140 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_251_insert__subset,axiom,
% 3.42/1.78 ! [X_104: pname,A_212: pname > $o,B_140: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_104 @ A_212 ) @ B_140 )
% 3.42/1.78 <=> ( ( member_pname @ X_104 @ B_140 )
% 3.42/1.78 & ( ord_less_eq_pname_o @ A_212 @ B_140 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_252_insert__subset,axiom,
% 3.42/1.78 ! [X_104: hoare_1708887482_state,A_212: hoare_1708887482_state > $o,B_140: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ ( insert528405184_state @ X_104 @ A_212 ) @ B_140 )
% 3.42/1.78 <=> ( ( member451959335_state @ X_104 @ B_140 )
% 3.42/1.78 & ( ord_le777019615tate_o @ A_212 @ B_140 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_253_subset__insertI,axiom,
% 3.42/1.78 ! [B_139: pname > $o,A_211: pname] : ( ord_less_eq_pname_o @ B_139 @ ( insert_pname @ A_211 @ B_139 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_254_subset__insertI,axiom,
% 3.42/1.78 ! [B_139: com > $o,A_211: com] : ( ord_less_eq_com_o @ B_139 @ ( insert_com @ A_211 @ B_139 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_255_subset__insertI,axiom,
% 3.42/1.78 ! [B_139: hoare_1708887482_state > $o,A_211: hoare_1708887482_state] : ( ord_le777019615tate_o @ B_139 @ ( insert528405184_state @ A_211 @ B_139 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_256_insert__image,axiom,
% 3.42/1.78 ! [F_78: hoare_1708887482_state > pname,X_103: hoare_1708887482_state,A_210: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ X_103 @ A_210 )
% 3.42/1.78 => ( ( insert_pname @ ( F_78 @ X_103 ) @ ( image_1509414295_pname @ F_78 @ A_210 ) )
% 3.42/1.78 = ( image_1509414295_pname @ F_78 @ A_210 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_257_insert__image,axiom,
% 3.42/1.78 ! [F_78: hoare_1708887482_state > com,X_103: hoare_1708887482_state,A_210: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ X_103 @ A_210 )
% 3.42/1.78 => ( ( insert_com @ ( F_78 @ X_103 ) @ ( image_1604448413te_com @ F_78 @ A_210 ) )
% 3.42/1.78 = ( image_1604448413te_com @ F_78 @ A_210 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_258_insert__image,axiom,
% 3.42/1.78 ! [F_78: pname > pname,X_103: pname,A_210: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_103 @ A_210 )
% 3.42/1.78 => ( ( insert_pname @ ( F_78 @ X_103 ) @ ( image_pname_pname @ F_78 @ A_210 ) )
% 3.42/1.78 = ( image_pname_pname @ F_78 @ A_210 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_259_insert__image,axiom,
% 3.42/1.78 ! [F_78: pname > com,X_103: pname,A_210: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_103 @ A_210 )
% 3.42/1.78 => ( ( insert_com @ ( F_78 @ X_103 ) @ ( image_pname_com @ F_78 @ A_210 ) )
% 3.42/1.78 = ( image_pname_com @ F_78 @ A_210 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_260_insert__image,axiom,
% 3.42/1.78 ! [F_78: com > hoare_1708887482_state,X_103: com,A_210: com > $o] :
% 3.42/1.78 ( ( member_com @ X_103 @ A_210 )
% 3.42/1.78 => ( ( insert528405184_state @ ( F_78 @ X_103 ) @ ( image_934102463_state @ F_78 @ A_210 ) )
% 3.42/1.78 = ( image_934102463_state @ F_78 @ A_210 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_261_insert__image,axiom,
% 3.42/1.78 ! [F_78: pname > hoare_1708887482_state,X_103: pname,A_210: pname > $o] :
% 3.42/1.78 ( ( member_pname @ X_103 @ A_210 )
% 3.42/1.78 => ( ( insert528405184_state @ ( F_78 @ X_103 ) @ ( image_1116629049_state @ F_78 @ A_210 ) )
% 3.42/1.78 = ( image_1116629049_state @ F_78 @ A_210 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_262_image__insert,axiom,
% 3.42/1.78 ! [F_77: hoare_1708887482_state > pname,A_209: hoare_1708887482_state,B_138: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( image_1509414295_pname @ F_77 @ ( insert528405184_state @ A_209 @ B_138 ) )
% 3.42/1.78 = ( insert_pname @ ( F_77 @ A_209 ) @ ( image_1509414295_pname @ F_77 @ B_138 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_263_image__insert,axiom,
% 3.42/1.78 ! [F_77: hoare_1708887482_state > com,A_209: hoare_1708887482_state,B_138: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( image_1604448413te_com @ F_77 @ ( insert528405184_state @ A_209 @ B_138 ) )
% 3.42/1.78 = ( insert_com @ ( F_77 @ A_209 ) @ ( image_1604448413te_com @ F_77 @ B_138 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_264_image__insert,axiom,
% 3.42/1.78 ! [F_77: com > hoare_1708887482_state,A_209: com,B_138: com > $o] :
% 3.42/1.78 ( ( image_934102463_state @ F_77 @ ( insert_com @ A_209 @ B_138 ) )
% 3.42/1.78 = ( insert528405184_state @ ( F_77 @ A_209 ) @ ( image_934102463_state @ F_77 @ B_138 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_265_image__insert,axiom,
% 3.42/1.78 ! [F_77: pname > hoare_1708887482_state,A_209: pname,B_138: pname > $o] :
% 3.42/1.78 ( ( image_1116629049_state @ F_77 @ ( insert_pname @ A_209 @ B_138 ) )
% 3.42/1.78 = ( insert528405184_state @ ( F_77 @ A_209 ) @ ( image_1116629049_state @ F_77 @ B_138 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_266_image__mono,axiom,
% 3.42/1.78 ! [F_76: hoare_1708887482_state > pname,A_208: hoare_1708887482_state > $o,B_137: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ A_208 @ B_137 )
% 3.42/1.78 => ( ord_less_eq_pname_o @ ( image_1509414295_pname @ F_76 @ A_208 ) @ ( image_1509414295_pname @ F_76 @ B_137 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_267_image__mono,axiom,
% 3.42/1.78 ! [F_76: pname > hoare_1708887482_state,A_208: pname > $o,B_137: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ A_208 @ B_137 )
% 3.42/1.78 => ( ord_le777019615tate_o @ ( image_1116629049_state @ F_76 @ A_208 ) @ ( image_1116629049_state @ F_76 @ B_137 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_268_subset__image__iff,axiom,
% 3.42/1.78 ! [B_136: pname > $o,F_75: hoare_1708887482_state > pname,A_207: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ B_136 @ ( image_1509414295_pname @ F_75 @ A_207 ) )
% 3.42/1.78 <=> ? [AA: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ AA @ A_207 )
% 3.42/1.78 & ( B_136
% 3.42/1.78 = ( image_1509414295_pname @ F_75 @ AA ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_269_subset__image__iff,axiom,
% 3.42/1.78 ! [B_136: hoare_1708887482_state > $o,F_75: pname > hoare_1708887482_state,A_207: pname > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ B_136 @ ( image_1116629049_state @ F_75 @ A_207 ) )
% 3.42/1.78 <=> ? [AA: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ AA @ A_207 )
% 3.42/1.78 & ( B_136
% 3.42/1.78 = ( image_1116629049_state @ F_75 @ AA ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_270_domI,axiom,
% 3.42/1.78 ! [M_5: com > option_com,A_206: com,B_135: com] :
% 3.42/1.78 ( ( ( M_5 @ A_206 )
% 3.42/1.78 = ( some_com @ B_135 ) )
% 3.42/1.78 => ( member_com @ A_206 @ ( dom_com_com @ M_5 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_271_domI,axiom,
% 3.42/1.78 ! [M_5: hoare_1708887482_state > option_pname,A_206: hoare_1708887482_state,B_135: pname] :
% 3.42/1.78 ( ( ( M_5 @ A_206 )
% 3.42/1.78 = ( some_pname @ B_135 ) )
% 3.42/1.78 => ( member451959335_state @ A_206 @ ( dom_Ho1805192458_pname @ M_5 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_272_domI,axiom,
% 3.42/1.78 ! [M_5: hoare_1708887482_state > option1624383643_state,A_206: hoare_1708887482_state,B_135: hoare_1708887482_state] :
% 3.42/1.78 ( ( ( M_5 @ A_206 )
% 3.42/1.78 = ( some_H1974565227_state @ B_135 ) )
% 3.42/1.78 => ( member451959335_state @ A_206 @ ( dom_Ho1703271284_state @ M_5 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_273_domI,axiom,
% 3.42/1.78 ! [M_5: pname > option_pname,A_206: pname,B_135: pname] :
% 3.42/1.78 ( ( ( M_5 @ A_206 )
% 3.42/1.78 = ( some_pname @ B_135 ) )
% 3.42/1.78 => ( member_pname @ A_206 @ ( dom_pname_pname @ M_5 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_274_domI,axiom,
% 3.42/1.78 ! [M_5: pname > option1624383643_state,A_206: pname,B_135: hoare_1708887482_state] :
% 3.42/1.78 ( ( ( M_5 @ A_206 )
% 3.42/1.78 = ( some_H1974565227_state @ B_135 ) )
% 3.42/1.78 => ( member_pname @ A_206 @ ( dom_pn1412407212_state @ M_5 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_275_domI,axiom,
% 3.42/1.78 ! [M_5: pname > option_com,A_206: pname,B_135: com] :
% 3.42/1.78 ( ( ( M_5 @ A_206 )
% 3.42/1.78 = ( some_com @ B_135 ) )
% 3.42/1.78 => ( member_pname @ A_206 @ ( dom_pname_com @ M_5 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_276_Collect__conv__if,axiom,
% 3.42/1.78 ! [P_39: pname > $o,A_205: pname] :
% 3.42/1.78 ( ( ( P_39 @ A_205 )
% 3.42/1.78 => ( ( collect_pname
% 3.42/1.78 @ ^ [X_3: pname] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 3.42/1.78 = ( insert_pname @ A_205 @ bot_bot_pname_o ) ) )
% 3.42/1.78 & ( ~ ( P_39 @ A_205 )
% 3.42/1.78 => ( ( collect_pname
% 3.42/1.78 @ ^ [X_3: pname] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 3.42/1.78 = bot_bot_pname_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_277_Collect__conv__if,axiom,
% 3.42/1.78 ! [P_39: com > $o,A_205: com] :
% 3.42/1.78 ( ( ( P_39 @ A_205 )
% 3.42/1.78 => ( ( collect_com
% 3.42/1.78 @ ^ [X_3: com] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 3.42/1.78 = ( insert_com @ A_205 @ bot_bot_com_o ) ) )
% 3.42/1.78 & ( ~ ( P_39 @ A_205 )
% 3.42/1.78 => ( ( collect_com
% 3.42/1.78 @ ^ [X_3: com] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 3.42/1.78 = bot_bot_com_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_278_Collect__conv__if,axiom,
% 3.42/1.78 ! [P_39: ( pname > $o ) > $o,A_205: pname > $o] :
% 3.42/1.78 ( ( ( P_39 @ A_205 )
% 3.42/1.78 => ( ( collect_pname_o
% 3.42/1.78 @ ^ [X_3: pname > $o] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 3.42/1.78 = ( insert_pname_o @ A_205 @ bot_bot_pname_o_o ) ) )
% 3.42/1.78 & ( ~ ( P_39 @ A_205 )
% 3.42/1.78 => ( ( collect_pname_o
% 3.42/1.78 @ ^ [X_3: pname > $o] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 3.42/1.78 = bot_bot_pname_o_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_279_Collect__conv__if,axiom,
% 3.42/1.78 ! [P_39: ( hoare_1708887482_state > $o ) > $o,A_205: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ( P_39 @ A_205 )
% 3.42/1.78 => ( ( collec219771562tate_o
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 3.42/1.78 = ( insert949073679tate_o @ A_205 @ bot_bo1678742418te_o_o ) ) )
% 3.42/1.78 & ( ~ ( P_39 @ A_205 )
% 3.42/1.78 => ( ( collec219771562tate_o
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 3.42/1.78 = bot_bo1678742418te_o_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_280_Collect__conv__if,axiom,
% 3.42/1.78 ! [P_39: hoare_1708887482_state > $o,A_205: hoare_1708887482_state] :
% 3.42/1.78 ( ( ( P_39 @ A_205 )
% 3.42/1.78 => ( ( collec1568722789_state
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 3.42/1.78 = ( insert528405184_state @ A_205 @ bot_bo19817387tate_o ) ) )
% 3.42/1.78 & ( ~ ( P_39 @ A_205 )
% 3.42/1.78 => ( ( collec1568722789_state
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
% 3.42/1.78 = bot_bo19817387tate_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_281_Collect__conv__if2,axiom,
% 3.42/1.78 ! [P_38: pname > $o,A_204: pname] :
% 3.42/1.78 ( ( ( P_38 @ A_204 )
% 3.42/1.78 => ( ( collect_pname
% 3.42/1.78 @ ^ [X_3: pname] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 3.42/1.78 = ( insert_pname @ A_204 @ bot_bot_pname_o ) ) )
% 3.42/1.78 & ( ~ ( P_38 @ A_204 )
% 3.42/1.78 => ( ( collect_pname
% 3.42/1.78 @ ^ [X_3: pname] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 3.42/1.78 = bot_bot_pname_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_282_Collect__conv__if2,axiom,
% 3.42/1.78 ! [P_38: com > $o,A_204: com] :
% 3.42/1.78 ( ( ( P_38 @ A_204 )
% 3.42/1.78 => ( ( collect_com
% 3.42/1.78 @ ^ [X_3: com] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 3.42/1.78 = ( insert_com @ A_204 @ bot_bot_com_o ) ) )
% 3.42/1.78 & ( ~ ( P_38 @ A_204 )
% 3.42/1.78 => ( ( collect_com
% 3.42/1.78 @ ^ [X_3: com] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 3.42/1.78 = bot_bot_com_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_283_Collect__conv__if2,axiom,
% 3.42/1.78 ! [P_38: ( pname > $o ) > $o,A_204: pname > $o] :
% 3.42/1.78 ( ( ( P_38 @ A_204 )
% 3.42/1.78 => ( ( collect_pname_o
% 3.42/1.78 @ ^ [X_3: pname > $o] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 3.42/1.78 = ( insert_pname_o @ A_204 @ bot_bot_pname_o_o ) ) )
% 3.42/1.78 & ( ~ ( P_38 @ A_204 )
% 3.42/1.78 => ( ( collect_pname_o
% 3.42/1.78 @ ^ [X_3: pname > $o] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 3.42/1.78 = bot_bot_pname_o_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_284_Collect__conv__if2,axiom,
% 3.42/1.78 ! [P_38: ( hoare_1708887482_state > $o ) > $o,A_204: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ( P_38 @ A_204 )
% 3.42/1.78 => ( ( collec219771562tate_o
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 3.42/1.78 = ( insert949073679tate_o @ A_204 @ bot_bo1678742418te_o_o ) ) )
% 3.42/1.78 & ( ~ ( P_38 @ A_204 )
% 3.42/1.78 => ( ( collec219771562tate_o
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 3.42/1.78 = bot_bo1678742418te_o_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_285_Collect__conv__if2,axiom,
% 3.42/1.78 ! [P_38: hoare_1708887482_state > $o,A_204: hoare_1708887482_state] :
% 3.42/1.78 ( ( ( P_38 @ A_204 )
% 3.42/1.78 => ( ( collec1568722789_state
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 3.42/1.78 = ( insert528405184_state @ A_204 @ bot_bo19817387tate_o ) ) )
% 3.42/1.78 & ( ~ ( P_38 @ A_204 )
% 3.42/1.78 => ( ( collec1568722789_state
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
% 3.42/1.78 = bot_bo19817387tate_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_286_singleton__conv,axiom,
% 3.42/1.78 ! [A_203: pname] :
% 3.42/1.78 ( ( collect_pname
% 3.42/1.78 @ ^ [X_3: pname] : ( X_3 = A_203 ) )
% 3.42/1.78 = ( insert_pname @ A_203 @ bot_bot_pname_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_287_singleton__conv,axiom,
% 3.42/1.78 ! [A_203: com] :
% 3.42/1.78 ( ( collect_com
% 3.42/1.78 @ ^ [X_3: com] : ( X_3 = A_203 ) )
% 3.42/1.78 = ( insert_com @ A_203 @ bot_bot_com_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_288_singleton__conv,axiom,
% 3.42/1.78 ! [A_203: pname > $o] :
% 3.42/1.78 ( ( collect_pname_o
% 3.42/1.78 @ ^ [X_3: pname > $o] : ( X_3 = A_203 ) )
% 3.42/1.78 = ( insert_pname_o @ A_203 @ bot_bot_pname_o_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_289_singleton__conv,axiom,
% 3.42/1.78 ! [A_203: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( collec219771562tate_o
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state > $o] : ( X_3 = A_203 ) )
% 3.42/1.78 = ( insert949073679tate_o @ A_203 @ bot_bo1678742418te_o_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_290_singleton__conv,axiom,
% 3.42/1.78 ! [A_203: hoare_1708887482_state] :
% 3.42/1.78 ( ( collec1568722789_state
% 3.42/1.78 @ ^ [X_3: hoare_1708887482_state] : ( X_3 = A_203 ) )
% 3.42/1.78 = ( insert528405184_state @ A_203 @ bot_bo19817387tate_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_291_singleton__conv2,axiom,
% 3.42/1.78 ! [A_202: pname] :
% 3.42/1.78 ( ( collect_pname @ ( fequal_pname @ A_202 ) )
% 3.42/1.78 = ( insert_pname @ A_202 @ bot_bot_pname_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_292_singleton__conv2,axiom,
% 3.42/1.78 ! [A_202: com] :
% 3.42/1.78 ( ( collect_com @ ( fequal_com @ A_202 ) )
% 3.42/1.78 = ( insert_com @ A_202 @ bot_bot_com_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_293_singleton__conv2,axiom,
% 3.42/1.78 ! [A_202: pname > $o] :
% 3.42/1.78 ( ( collect_pname_o @ ( fequal_pname_o @ A_202 ) )
% 3.42/1.78 = ( insert_pname_o @ A_202 @ bot_bot_pname_o_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_294_singleton__conv2,axiom,
% 3.42/1.78 ! [A_202: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( collec219771562tate_o @ ( fequal1436017556tate_o @ A_202 ) )
% 3.42/1.78 = ( insert949073679tate_o @ A_202 @ bot_bo1678742418te_o_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_295_singleton__conv2,axiom,
% 3.42/1.78 ! [A_202: hoare_1708887482_state] :
% 3.42/1.78 ( ( collec1568722789_state @ ( fequal224822779_state @ A_202 ) )
% 3.42/1.78 = ( insert528405184_state @ A_202 @ bot_bo19817387tate_o ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_296_MGF__lemma1,axiom,
% 3.42/1.78 ! [C_34: com,G_7: hoare_1708887482_state > $o] :
% 3.42/1.78 ( hoare_1160767572gleton
% 3.42/1.78 => ( ! [X_3: pname] :
% 3.42/1.78 ( ( member_pname @ X_3 @ ( dom_pname_com @ body ) )
% 3.42/1.78 => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ X_3 ) ) @ bot_bo19817387tate_o ) ) )
% 3.42/1.78 => ( ( wt @ C_34 )
% 3.42/1.78 => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_297_WT__bodiesD,axiom,
% 3.42/1.78 ! [Pn_1: pname,B_82: com] :
% 3.42/1.78 ( wT_bodies
% 3.42/1.78 => ( ( ( body @ Pn_1 )
% 3.42/1.78 = ( some_com @ B_82 ) )
% 3.42/1.78 => ( wt @ B_82 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_298_imageE,axiom,
% 3.42/1.78 ! [B_134: hoare_1708887482_state,F_74: com > hoare_1708887482_state,A_201: com > $o] :
% 3.42/1.78 ( ( member451959335_state @ B_134 @ ( image_934102463_state @ F_74 @ A_201 ) )
% 3.42/1.78 => ~ ! [X_3: com] :
% 3.42/1.78 ( ( B_134
% 3.42/1.78 = ( F_74 @ X_3 ) )
% 3.42/1.78 => ~ ( member_com @ X_3 @ A_201 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_299_imageE,axiom,
% 3.42/1.78 ! [B_134: pname,F_74: com > pname,A_201: com > $o] :
% 3.42/1.78 ( ( member_pname @ B_134 @ ( image_com_pname @ F_74 @ A_201 ) )
% 3.42/1.78 => ~ ! [X_3: com] :
% 3.42/1.78 ( ( B_134
% 3.42/1.78 = ( F_74 @ X_3 ) )
% 3.42/1.78 => ~ ( member_com @ X_3 @ A_201 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_300_imageE,axiom,
% 3.42/1.78 ! [B_134: com,F_74: hoare_1708887482_state > com,A_201: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member_com @ B_134 @ ( image_1604448413te_com @ F_74 @ A_201 ) )
% 3.42/1.78 => ~ ! [X_3: hoare_1708887482_state] :
% 3.42/1.78 ( ( B_134
% 3.42/1.78 = ( F_74 @ X_3 ) )
% 3.42/1.78 => ~ ( member451959335_state @ X_3 @ A_201 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_301_imageE,axiom,
% 3.42/1.78 ! [B_134: com,F_74: pname > com,A_201: pname > $o] :
% 3.42/1.78 ( ( member_com @ B_134 @ ( image_pname_com @ F_74 @ A_201 ) )
% 3.42/1.78 => ~ ! [X_3: pname] :
% 3.42/1.78 ( ( B_134
% 3.42/1.78 = ( F_74 @ X_3 ) )
% 3.42/1.78 => ~ ( member_pname @ X_3 @ A_201 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_302_imageE,axiom,
% 3.42/1.78 ! [B_134: hoare_1708887482_state,F_74: pname > hoare_1708887482_state,A_201: pname > $o] :
% 3.42/1.78 ( ( member451959335_state @ B_134 @ ( image_1116629049_state @ F_74 @ A_201 ) )
% 3.42/1.78 => ~ ! [X_3: pname] :
% 3.42/1.78 ( ( B_134
% 3.42/1.78 = ( F_74 @ X_3 ) )
% 3.42/1.78 => ~ ( member_pname @ X_3 @ A_201 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_303_finite__subset__induct,axiom,
% 3.42/1.78 ! [P_37: ( com > $o ) > $o,A_200: com > $o,F_73: com > $o] :
% 3.42/1.78 ( ( finite_finite_com @ F_73 )
% 3.42/1.78 => ( ( ord_less_eq_com_o @ F_73 @ A_200 )
% 3.42/1.78 => ( ( P_37 @ bot_bot_com_o )
% 3.42/1.78 => ( ! [A_6: com,F_53: com > $o] :
% 3.42/1.78 ( ( finite_finite_com @ F_53 )
% 3.42/1.78 => ( ( member_com @ A_6 @ A_200 )
% 3.42/1.78 => ( ~ ( member_com @ A_6 @ F_53 )
% 3.42/1.78 => ( ( P_37 @ F_53 )
% 3.42/1.78 => ( P_37 @ ( insert_com @ A_6 @ F_53 ) ) ) ) ) )
% 3.42/1.78 => ( P_37 @ F_73 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_304_finite__subset__induct,axiom,
% 3.42/1.78 ! [P_37: ( ( pname > $o ) > $o ) > $o,A_200: ( pname > $o ) > $o,F_73: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ F_73 )
% 3.42/1.78 => ( ( ord_le1205211808me_o_o @ F_73 @ A_200 )
% 3.42/1.78 => ( ( P_37 @ bot_bot_pname_o_o )
% 3.42/1.78 => ( ! [A_6: pname > $o,F_53: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ F_53 )
% 3.42/1.78 => ( ( member_pname_o @ A_6 @ A_200 )
% 3.42/1.78 => ( ~ ( member_pname_o @ A_6 @ F_53 )
% 3.42/1.78 => ( ( P_37 @ F_53 )
% 3.42/1.78 => ( P_37 @ ( insert_pname_o @ A_6 @ F_53 ) ) ) ) ) )
% 3.42/1.78 => ( P_37 @ F_73 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_305_finite__subset__induct,axiom,
% 3.42/1.78 ! [P_37: ( ( hoare_1708887482_state > $o ) > $o ) > $o,A_200: ( hoare_1708887482_state > $o ) > $o,F_73: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ F_73 )
% 3.42/1.78 => ( ( ord_le1728773982te_o_o @ F_73 @ A_200 )
% 3.42/1.78 => ( ( P_37 @ bot_bo1678742418te_o_o )
% 3.42/1.78 => ( ! [A_6: hoare_1708887482_state > $o,F_53: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ F_53 )
% 3.42/1.78 => ( ( member814030440tate_o @ A_6 @ A_200 )
% 3.42/1.78 => ( ~ ( member814030440tate_o @ A_6 @ F_53 )
% 3.42/1.78 => ( ( P_37 @ F_53 )
% 3.42/1.78 => ( P_37 @ ( insert949073679tate_o @ A_6 @ F_53 ) ) ) ) ) )
% 3.42/1.78 => ( P_37 @ F_73 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_306_finite__subset__induct,axiom,
% 3.42/1.78 ! [P_37: ( pname > $o ) > $o,A_200: pname > $o,F_73: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ F_73 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ F_73 @ A_200 )
% 3.42/1.78 => ( ( P_37 @ bot_bot_pname_o )
% 3.42/1.78 => ( ! [A_6: pname,F_53: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ F_53 )
% 3.42/1.78 => ( ( member_pname @ A_6 @ A_200 )
% 3.42/1.78 => ( ~ ( member_pname @ A_6 @ F_53 )
% 3.42/1.78 => ( ( P_37 @ F_53 )
% 3.42/1.78 => ( P_37 @ ( insert_pname @ A_6 @ F_53 ) ) ) ) ) )
% 3.42/1.78 => ( P_37 @ F_73 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_307_finite__subset__induct,axiom,
% 3.42/1.78 ! [P_37: ( hoare_1708887482_state > $o ) > $o,A_200: hoare_1708887482_state > $o,F_73: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ F_73 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ F_73 @ A_200 )
% 3.42/1.78 => ( ( P_37 @ bot_bo19817387tate_o )
% 3.42/1.78 => ( ! [A_6: hoare_1708887482_state,F_53: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ F_53 )
% 3.42/1.78 => ( ( member451959335_state @ A_6 @ A_200 )
% 3.42/1.78 => ( ~ ( member451959335_state @ A_6 @ F_53 )
% 3.42/1.78 => ( ( P_37 @ F_53 )
% 3.42/1.78 => ( P_37 @ ( insert528405184_state @ A_6 @ F_53 ) ) ) ) ) )
% 3.42/1.78 => ( P_37 @ F_73 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_308_WTs__elim__cases_I7_J,axiom,
% 3.42/1.78 ! [P: pname] :
% 3.42/1.78 ( ( wt @ ( body_1 @ P ) )
% 3.42/1.78 => ~ ! [Y_4: com] :
% 3.42/1.78 ( ( body @ P )
% 3.42/1.78 != ( some_com @ Y_4 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_309_subsetI,axiom,
% 3.42/1.78 ! [B_133: com > $o,A_199: com > $o] :
% 3.42/1.78 ( ! [X_3: com] :
% 3.42/1.78 ( ( member_com @ X_3 @ A_199 )
% 3.42/1.78 => ( member_com @ X_3 @ B_133 ) )
% 3.42/1.78 => ( ord_less_eq_com_o @ A_199 @ B_133 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_310_subsetI,axiom,
% 3.42/1.78 ! [B_133: hoare_1708887482_state > $o,A_199: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ! [X_3: hoare_1708887482_state] :
% 3.42/1.78 ( ( member451959335_state @ X_3 @ A_199 )
% 3.42/1.78 => ( member451959335_state @ X_3 @ B_133 ) )
% 3.42/1.78 => ( ord_le777019615tate_o @ A_199 @ B_133 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_311_subsetI,axiom,
% 3.42/1.78 ! [B_133: pname > $o,A_199: pname > $o] :
% 3.42/1.78 ( ! [X_3: pname] :
% 3.42/1.78 ( ( member_pname @ X_3 @ A_199 )
% 3.42/1.78 => ( member_pname @ X_3 @ B_133 ) )
% 3.42/1.78 => ( ord_less_eq_pname_o @ A_199 @ B_133 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_312_finite__subset__image,axiom,
% 3.42/1.78 ! [F_72: ( pname > $o ) > hoare_1708887482_state,A_198: ( pname > $o ) > $o,B_132: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ B_132 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ B_132 @ ( image_1922967206_state @ F_72 @ A_198 ) )
% 3.42/1.78 => ? [C_61: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( ord_le1205211808me_o_o @ C_61 @ A_198 )
% 3.42/1.78 & ( finite297249702name_o @ C_61 )
% 3.42/1.78 & ( B_132
% 3.42/1.78 = ( image_1922967206_state @ F_72 @ C_61 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_313_finite__subset__image,axiom,
% 3.42/1.78 ! [F_72: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,A_198: ( hoare_1708887482_state > $o ) > $o,B_132: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ B_132 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ B_132 @ ( image_27005066_state @ F_72 @ A_198 ) )
% 3.42/1.78 => ? [C_61: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( ord_le1728773982te_o_o @ C_61 @ A_198 )
% 3.42/1.78 & ( finite1329924456tate_o @ C_61 )
% 3.42/1.78 & ( B_132
% 3.42/1.78 = ( image_27005066_state @ F_72 @ C_61 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_314_finite__subset__image,axiom,
% 3.42/1.78 ! [F_72: ( pname > $o ) > pname,A_198: ( pname > $o ) > $o,B_132: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ B_132 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ B_132 @ ( image_pname_o_pname @ F_72 @ A_198 ) )
% 3.42/1.78 => ? [C_61: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( ord_le1205211808me_o_o @ C_61 @ A_198 )
% 3.42/1.78 & ( finite297249702name_o @ C_61 )
% 3.42/1.78 & ( B_132
% 3.42/1.78 = ( image_pname_o_pname @ F_72 @ C_61 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_315_finite__subset__image,axiom,
% 3.42/1.78 ! [F_72: ( hoare_1708887482_state > $o ) > pname,A_198: ( hoare_1708887482_state > $o ) > $o,B_132: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ B_132 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ B_132 @ ( image_2051418740_pname @ F_72 @ A_198 ) )
% 3.42/1.78 => ? [C_61: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( ord_le1728773982te_o_o @ C_61 @ A_198 )
% 3.42/1.78 & ( finite1329924456tate_o @ C_61 )
% 3.42/1.78 & ( B_132
% 3.42/1.78 = ( image_2051418740_pname @ F_72 @ C_61 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_316_finite__subset__image,axiom,
% 3.42/1.78 ! [F_72: hoare_1708887482_state > pname > $o,A_198: hoare_1708887482_state > $o,B_132: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ B_132 )
% 3.42/1.78 => ( ( ord_le1205211808me_o_o @ B_132 @ ( image_1552895654name_o @ F_72 @ A_198 ) )
% 3.42/1.78 => ? [C_61: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ C_61 @ A_198 )
% 3.42/1.78 & ( finite1625599783_state @ C_61 )
% 3.42/1.78 & ( B_132
% 3.42/1.78 = ( image_1552895654name_o @ F_72 @ C_61 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_317_finite__subset__image,axiom,
% 3.42/1.78 ! [F_72: hoare_1708887482_state > hoare_1708887482_state > $o,A_198: hoare_1708887482_state > $o,B_132: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ B_132 )
% 3.42/1.78 => ( ( ord_le1728773982te_o_o @ B_132 @ ( image_1551509096tate_o @ F_72 @ A_198 ) )
% 3.42/1.78 => ? [C_61: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ C_61 @ A_198 )
% 3.42/1.78 & ( finite1625599783_state @ C_61 )
% 3.42/1.78 & ( B_132
% 3.42/1.78 = ( image_1551509096tate_o @ F_72 @ C_61 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_318_finite__subset__image,axiom,
% 3.42/1.78 ! [F_72: hoare_1708887482_state > pname,A_198: hoare_1708887482_state > $o,B_132: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ B_132 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ B_132 @ ( image_1509414295_pname @ F_72 @ A_198 ) )
% 3.42/1.78 => ? [C_61: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ord_le777019615tate_o @ C_61 @ A_198 )
% 3.42/1.78 & ( finite1625599783_state @ C_61 )
% 3.42/1.78 & ( B_132
% 3.42/1.78 = ( image_1509414295_pname @ F_72 @ C_61 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_319_finite__subset__image,axiom,
% 3.42/1.78 ! [F_72: pname > pname > $o,A_198: pname > $o,B_132: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ B_132 )
% 3.42/1.78 => ( ( ord_le1205211808me_o_o @ B_132 @ ( image_pname_pname_o @ F_72 @ A_198 ) )
% 3.42/1.78 => ? [C_61: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
% 3.42/1.78 & ( finite_finite_pname @ C_61 )
% 3.42/1.78 & ( B_132
% 3.42/1.78 = ( image_pname_pname_o @ F_72 @ C_61 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_320_finite__subset__image,axiom,
% 3.42/1.78 ! [F_72: pname > hoare_1708887482_state > $o,A_198: pname > $o,B_132: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ B_132 )
% 3.42/1.78 => ( ( ord_le1728773982te_o_o @ B_132 @ ( image_425134806tate_o @ F_72 @ A_198 ) )
% 3.42/1.78 => ? [C_61: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
% 3.42/1.78 & ( finite_finite_pname @ C_61 )
% 3.42/1.78 & ( B_132
% 3.42/1.78 = ( image_425134806tate_o @ F_72 @ C_61 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_321_finite__subset__image,axiom,
% 3.42/1.78 ! [F_72: pname > pname,A_198: pname > $o,B_132: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ B_132 )
% 3.42/1.78 => ( ( ord_less_eq_pname_o @ B_132 @ ( image_pname_pname @ F_72 @ A_198 ) )
% 3.42/1.78 => ? [C_61: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
% 3.42/1.78 & ( finite_finite_pname @ C_61 )
% 3.42/1.78 & ( B_132
% 3.42/1.78 = ( image_pname_pname @ F_72 @ C_61 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_322_finite__subset__image,axiom,
% 3.42/1.78 ! [F_72: pname > hoare_1708887482_state,A_198: pname > $o,B_132: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ B_132 )
% 3.42/1.78 => ( ( ord_le777019615tate_o @ B_132 @ ( image_1116629049_state @ F_72 @ A_198 ) )
% 3.42/1.78 => ? [C_61: pname > $o] :
% 3.42/1.78 ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
% 3.42/1.78 & ( finite_finite_pname @ C_61 )
% 3.42/1.78 & ( B_132
% 3.42/1.78 = ( image_1116629049_state @ F_72 @ C_61 ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_323_finite__dom__body,axiom,
% 3.42/1.78 finite_finite_pname @ ( dom_pname_com @ body ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_324_finite__induct,axiom,
% 3.42/1.78 ! [P_36: ( com > $o ) > $o,F_71: com > $o] :
% 3.42/1.78 ( ( finite_finite_com @ F_71 )
% 3.42/1.78 => ( ( P_36 @ bot_bot_com_o )
% 3.42/1.78 => ( ! [X_3: com,F_53: com > $o] :
% 3.42/1.78 ( ( finite_finite_com @ F_53 )
% 3.42/1.78 => ( ~ ( member_com @ X_3 @ F_53 )
% 3.42/1.78 => ( ( P_36 @ F_53 )
% 3.42/1.78 => ( P_36 @ ( insert_com @ X_3 @ F_53 ) ) ) ) )
% 3.42/1.78 => ( P_36 @ F_71 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_325_finite__induct,axiom,
% 3.42/1.78 ! [P_36: ( ( pname > $o ) > $o ) > $o,F_71: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ F_71 )
% 3.42/1.78 => ( ( P_36 @ bot_bot_pname_o_o )
% 3.42/1.78 => ( ! [X_3: pname > $o,F_53: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ F_53 )
% 3.42/1.78 => ( ~ ( member_pname_o @ X_3 @ F_53 )
% 3.42/1.78 => ( ( P_36 @ F_53 )
% 3.42/1.78 => ( P_36 @ ( insert_pname_o @ X_3 @ F_53 ) ) ) ) )
% 3.42/1.78 => ( P_36 @ F_71 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_326_finite__induct,axiom,
% 3.42/1.78 ! [P_36: ( ( hoare_1708887482_state > $o ) > $o ) > $o,F_71: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ F_71 )
% 3.42/1.78 => ( ( P_36 @ bot_bo1678742418te_o_o )
% 3.42/1.78 => ( ! [X_3: hoare_1708887482_state > $o,F_53: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ F_53 )
% 3.42/1.78 => ( ~ ( member814030440tate_o @ X_3 @ F_53 )
% 3.42/1.78 => ( ( P_36 @ F_53 )
% 3.42/1.78 => ( P_36 @ ( insert949073679tate_o @ X_3 @ F_53 ) ) ) ) )
% 3.42/1.78 => ( P_36 @ F_71 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_327_finite__induct,axiom,
% 3.42/1.78 ! [P_36: ( pname > $o ) > $o,F_71: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ F_71 )
% 3.42/1.78 => ( ( P_36 @ bot_bot_pname_o )
% 3.42/1.78 => ( ! [X_3: pname,F_53: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ F_53 )
% 3.42/1.78 => ( ~ ( member_pname @ X_3 @ F_53 )
% 3.42/1.78 => ( ( P_36 @ F_53 )
% 3.42/1.78 => ( P_36 @ ( insert_pname @ X_3 @ F_53 ) ) ) ) )
% 3.42/1.78 => ( P_36 @ F_71 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_328_finite__induct,axiom,
% 3.42/1.78 ! [P_36: ( hoare_1708887482_state > $o ) > $o,F_71: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ F_71 )
% 3.42/1.78 => ( ( P_36 @ bot_bo19817387tate_o )
% 3.42/1.78 => ( ! [X_3: hoare_1708887482_state,F_53: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ F_53 )
% 3.42/1.78 => ( ~ ( member451959335_state @ X_3 @ F_53 )
% 3.42/1.78 => ( ( P_36 @ F_53 )
% 3.42/1.78 => ( P_36 @ ( insert528405184_state @ X_3 @ F_53 ) ) ) ) )
% 3.42/1.78 => ( P_36 @ F_71 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_329_finite_Osimps,axiom,
% 3.42/1.78 ! [A_197: com > $o] :
% 3.42/1.78 ( ( finite_finite_com @ A_197 )
% 3.42/1.78 <=> ( ( A_197 = bot_bot_com_o )
% 3.42/1.78 | ? [A_39: com > $o,A_6: com] :
% 3.42/1.78 ( ( A_197
% 3.42/1.78 = ( insert_com @ A_6 @ A_39 ) )
% 3.42/1.78 & ( finite_finite_com @ A_39 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_330_finite_Osimps,axiom,
% 3.42/1.78 ! [A_197: ( pname > $o ) > $o] :
% 3.42/1.78 ( ( finite297249702name_o @ A_197 )
% 3.42/1.78 <=> ( ( A_197 = bot_bot_pname_o_o )
% 3.42/1.78 | ? [A_39: ( pname > $o ) > $o,A_6: pname > $o] :
% 3.42/1.78 ( ( A_197
% 3.42/1.78 = ( insert_pname_o @ A_6 @ A_39 ) )
% 3.42/1.78 & ( finite297249702name_o @ A_39 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_331_finite_Osimps,axiom,
% 3.42/1.78 ! [A_197: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ( finite1329924456tate_o @ A_197 )
% 3.42/1.78 <=> ( ( A_197 = bot_bo1678742418te_o_o )
% 3.42/1.78 | ? [A_39: ( hoare_1708887482_state > $o ) > $o,A_6: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( A_197
% 3.42/1.78 = ( insert949073679tate_o @ A_6 @ A_39 ) )
% 3.42/1.78 & ( finite1329924456tate_o @ A_39 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_332_finite_Osimps,axiom,
% 3.42/1.78 ! [A_197: pname > $o] :
% 3.42/1.78 ( ( finite_finite_pname @ A_197 )
% 3.42/1.78 <=> ( ( A_197 = bot_bot_pname_o )
% 3.42/1.78 | ? [A_39: pname > $o,A_6: pname] :
% 3.42/1.78 ( ( A_197
% 3.42/1.78 = ( insert_pname @ A_6 @ A_39 ) )
% 3.42/1.78 & ( finite_finite_pname @ A_39 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_333_finite_Osimps,axiom,
% 3.42/1.78 ! [A_197: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( finite1625599783_state @ A_197 )
% 3.42/1.78 <=> ( ( A_197 = bot_bo19817387tate_o )
% 3.42/1.78 | ? [A_39: hoare_1708887482_state > $o,A_6: hoare_1708887482_state] :
% 3.42/1.78 ( ( A_197
% 3.42/1.78 = ( insert528405184_state @ A_6 @ A_39 ) )
% 3.42/1.78 & ( finite1625599783_state @ A_39 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_334_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: com > hoare_1708887482_state,A_196: com > $o] :
% 3.42/1.78 ( ~ ( finite_finite_com @ A_196 )
% 3.42/1.78 => ( ( finite1625599783_state @ ( image_934102463_state @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: com] :
% 3.42/1.78 ( ( member_com @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite_finite_com
% 3.42/1.78 @ ( collect_com
% 3.42/1.78 @ ^ [A_6: com] :
% 3.42/1.78 ( (&) @ ( member_com @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_335_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: hoare_1708887482_state > hoare_1708887482_state,A_196: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ~ ( finite1625599783_state @ A_196 )
% 3.42/1.78 => ( ( finite1625599783_state @ ( image_757158439_state @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: hoare_1708887482_state] :
% 3.42/1.78 ( ( member451959335_state @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite1625599783_state
% 3.42/1.78 @ ( collec1568722789_state
% 3.42/1.78 @ ^ [A_6: hoare_1708887482_state] :
% 3.42/1.78 ( (&) @ ( member451959335_state @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_336_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: ( pname > $o ) > hoare_1708887482_state,A_196: ( pname > $o ) > $o] :
% 3.42/1.78 ( ~ ( finite297249702name_o @ A_196 )
% 3.42/1.78 => ( ( finite1625599783_state @ ( image_1922967206_state @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: pname > $o] :
% 3.42/1.78 ( ( member_pname_o @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite297249702name_o
% 3.42/1.78 @ ( collect_pname_o
% 3.42/1.78 @ ^ [A_6: pname > $o] :
% 3.42/1.78 ( (&) @ ( member_pname_o @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_337_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,A_196: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ~ ( finite1329924456tate_o @ A_196 )
% 3.42/1.78 => ( ( finite1625599783_state @ ( image_27005066_state @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member814030440tate_o @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite1329924456tate_o
% 3.42/1.78 @ ( collec219771562tate_o
% 3.42/1.78 @ ^ [A_6: hoare_1708887482_state > $o] :
% 3.42/1.78 ( (&) @ ( member814030440tate_o @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_338_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: com > pname,A_196: com > $o] :
% 3.42/1.78 ( ~ ( finite_finite_com @ A_196 )
% 3.42/1.78 => ( ( finite_finite_pname @ ( image_com_pname @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: com] :
% 3.42/1.78 ( ( member_com @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite_finite_com
% 3.42/1.78 @ ( collect_com
% 3.42/1.78 @ ^ [A_6: com] :
% 3.42/1.78 ( (&) @ ( member_com @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_339_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: hoare_1708887482_state > pname,A_196: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ~ ( finite1625599783_state @ A_196 )
% 3.42/1.78 => ( ( finite_finite_pname @ ( image_1509414295_pname @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: hoare_1708887482_state] :
% 3.42/1.78 ( ( member451959335_state @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite1625599783_state
% 3.42/1.78 @ ( collec1568722789_state
% 3.42/1.78 @ ^ [A_6: hoare_1708887482_state] :
% 3.42/1.78 ( (&) @ ( member451959335_state @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_340_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: pname > pname,A_196: pname > $o] :
% 3.42/1.78 ( ~ ( finite_finite_pname @ A_196 )
% 3.42/1.78 => ( ( finite_finite_pname @ ( image_pname_pname @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: pname] :
% 3.42/1.78 ( ( member_pname @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite_finite_pname
% 3.42/1.78 @ ( collect_pname
% 3.42/1.78 @ ^ [A_6: pname] :
% 3.42/1.78 ( (&) @ ( member_pname @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_341_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: ( pname > $o ) > pname,A_196: ( pname > $o ) > $o] :
% 3.42/1.78 ( ~ ( finite297249702name_o @ A_196 )
% 3.42/1.78 => ( ( finite_finite_pname @ ( image_pname_o_pname @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: pname > $o] :
% 3.42/1.78 ( ( member_pname_o @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite297249702name_o
% 3.42/1.78 @ ( collect_pname_o
% 3.42/1.78 @ ^ [A_6: pname > $o] :
% 3.42/1.78 ( (&) @ ( member_pname_o @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_342_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: ( hoare_1708887482_state > $o ) > pname,A_196: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.78 ( ~ ( finite1329924456tate_o @ A_196 )
% 3.42/1.78 => ( ( finite_finite_pname @ ( image_2051418740_pname @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member814030440tate_o @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite1329924456tate_o
% 3.42/1.78 @ ( collec219771562tate_o
% 3.42/1.78 @ ^ [A_6: hoare_1708887482_state > $o] :
% 3.42/1.78 ( (&) @ ( member814030440tate_o @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_343_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: hoare_1708887482_state > pname > $o,A_196: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ~ ( finite1625599783_state @ A_196 )
% 3.42/1.78 => ( ( finite297249702name_o @ ( image_1552895654name_o @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: hoare_1708887482_state] :
% 3.42/1.78 ( ( member451959335_state @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite1625599783_state
% 3.42/1.78 @ ( collec1568722789_state
% 3.42/1.78 @ ^ [A_6: hoare_1708887482_state] :
% 3.42/1.78 ( (&) @ ( member451959335_state @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_344_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: hoare_1708887482_state > hoare_1708887482_state > $o,A_196: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ~ ( finite1625599783_state @ A_196 )
% 3.42/1.78 => ( ( finite1329924456tate_o @ ( image_1551509096tate_o @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: hoare_1708887482_state] :
% 3.42/1.78 ( ( member451959335_state @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite1625599783_state
% 3.42/1.78 @ ( collec1568722789_state
% 3.42/1.78 @ ^ [A_6: hoare_1708887482_state] :
% 3.42/1.78 ( (&) @ ( member451959335_state @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_345_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: pname > pname > $o,A_196: pname > $o] :
% 3.42/1.78 ( ~ ( finite_finite_pname @ A_196 )
% 3.42/1.78 => ( ( finite297249702name_o @ ( image_pname_pname_o @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: pname] :
% 3.42/1.78 ( ( member_pname @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite_finite_pname
% 3.42/1.78 @ ( collect_pname
% 3.42/1.78 @ ^ [A_6: pname] :
% 3.42/1.78 ( (&) @ ( member_pname @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_346_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: pname > hoare_1708887482_state > $o,A_196: pname > $o] :
% 3.42/1.78 ( ~ ( finite_finite_pname @ A_196 )
% 3.42/1.78 => ( ( finite1329924456tate_o @ ( image_425134806tate_o @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: pname] :
% 3.42/1.78 ( ( member_pname @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite_finite_pname
% 3.42/1.78 @ ( collect_pname
% 3.42/1.78 @ ^ [A_6: pname] :
% 3.42/1.78 ( (&) @ ( member_pname @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_347_pigeonhole__infinite,axiom,
% 3.42/1.78 ! [F_70: pname > hoare_1708887482_state,A_196: pname > $o] :
% 3.42/1.78 ( ~ ( finite_finite_pname @ A_196 )
% 3.42/1.78 => ( ( finite1625599783_state @ ( image_1116629049_state @ F_70 @ A_196 ) )
% 3.42/1.78 => ? [X_3: pname] :
% 3.42/1.78 ( ( member_pname @ X_3 @ A_196 )
% 3.42/1.78 & ~ ( finite_finite_pname
% 3.42/1.78 @ ( collect_pname
% 3.42/1.78 @ ^ [A_6: pname] :
% 3.42/1.78 ( (&) @ ( member_pname @ A_6 @ A_196 )
% 3.42/1.78 @ ( ( F_70 @ A_6 )
% 3.42/1.78 = ( F_70 @ X_3 ) ) ) ) ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_348_com_Osimps_I6_J,axiom,
% 3.42/1.78 ! [Pname_1: pname,Pname: pname] :
% 3.42/1.78 ( ( ( body_1 @ Pname_1 )
% 3.42/1.78 = ( body_1 @ Pname ) )
% 3.42/1.78 <=> ( Pname_1 = Pname ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_349_MGT__Body,axiom,
% 3.42/1.78 ! [G_7: hoare_1708887482_state > $o,Procs_3: pname > $o] :
% 3.42/1.78 ( ( hoare_90032982_state
% 3.42/1.78 @ ( semila1122118281tate_o @ G_7
% 3.42/1.78 @ ( image_1116629049_state
% 3.42/1.78 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 3.42/1.78 @ Procs_3 ) )
% 3.42/1.78 @ ( image_1116629049_state
% 3.42/1.78 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
% 3.42/1.78 @ Procs_3 ) )
% 3.42/1.78 => ( ( finite_finite_pname @ Procs_3 )
% 3.42/1.78 => ( hoare_90032982_state @ G_7
% 3.42/1.78 @ ( image_1116629049_state
% 3.42/1.78 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 3.42/1.78 @ Procs_3 ) ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_350_domD,axiom,
% 3.42/1.78 ! [A_195: com,M_4: com > option_com] :
% 3.42/1.78 ( ( member_com @ A_195 @ ( dom_com_com @ M_4 ) )
% 3.42/1.78 => ? [B_131: com] :
% 3.42/1.78 ( ( M_4 @ A_195 )
% 3.42/1.78 = ( some_com @ B_131 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_351_domD,axiom,
% 3.42/1.78 ! [A_195: hoare_1708887482_state,M_4: hoare_1708887482_state > option_pname] :
% 3.42/1.78 ( ( member451959335_state @ A_195 @ ( dom_Ho1805192458_pname @ M_4 ) )
% 3.42/1.78 => ? [B_131: pname] :
% 3.42/1.78 ( ( M_4 @ A_195 )
% 3.42/1.78 = ( some_pname @ B_131 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_352_domD,axiom,
% 3.42/1.78 ! [A_195: hoare_1708887482_state,M_4: hoare_1708887482_state > option1624383643_state] :
% 3.42/1.78 ( ( member451959335_state @ A_195 @ ( dom_Ho1703271284_state @ M_4 ) )
% 3.42/1.78 => ? [B_131: hoare_1708887482_state] :
% 3.42/1.78 ( ( M_4 @ A_195 )
% 3.42/1.78 = ( some_H1974565227_state @ B_131 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_353_domD,axiom,
% 3.42/1.78 ! [A_195: pname,M_4: pname > option_pname] :
% 3.42/1.78 ( ( member_pname @ A_195 @ ( dom_pname_pname @ M_4 ) )
% 3.42/1.78 => ? [B_131: pname] :
% 3.42/1.78 ( ( M_4 @ A_195 )
% 3.42/1.78 = ( some_pname @ B_131 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_354_domD,axiom,
% 3.42/1.78 ! [A_195: pname,M_4: pname > option1624383643_state] :
% 3.42/1.78 ( ( member_pname @ A_195 @ ( dom_pn1412407212_state @ M_4 ) )
% 3.42/1.78 => ? [B_131: hoare_1708887482_state] :
% 3.42/1.78 ( ( M_4 @ A_195 )
% 3.42/1.78 = ( some_H1974565227_state @ B_131 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_355_domD,axiom,
% 3.42/1.78 ! [A_195: pname,M_4: pname > option_com] :
% 3.42/1.78 ( ( member_pname @ A_195 @ ( dom_pname_com @ M_4 ) )
% 3.42/1.78 => ? [B_131: com] :
% 3.42/1.78 ( ( M_4 @ A_195 )
% 3.42/1.78 = ( some_com @ B_131 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_356_the__elem__eq,axiom,
% 3.42/1.78 ! [X_102: pname] :
% 3.42/1.78 ( ( the_elem_pname @ ( insert_pname @ X_102 @ bot_bot_pname_o ) )
% 3.42/1.78 = X_102 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_357_the__elem__eq,axiom,
% 3.42/1.78 ! [X_102: com] :
% 3.42/1.78 ( ( the_elem_com @ ( insert_com @ X_102 @ bot_bot_com_o ) )
% 3.42/1.78 = X_102 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_358_the__elem__eq,axiom,
% 3.42/1.78 ! [X_102: hoare_1708887482_state] :
% 3.42/1.78 ( ( the_el864710747_state @ ( insert528405184_state @ X_102 @ bot_bo19817387tate_o ) )
% 3.42/1.78 = X_102 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_359_image__subsetI,axiom,
% 3.42/1.78 ! [F_69: hoare_1708887482_state > com,B_130: com > $o,A_194: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ! [X_3: hoare_1708887482_state] :
% 3.42/1.78 ( ( member451959335_state @ X_3 @ A_194 )
% 3.42/1.78 => ( member_com @ ( F_69 @ X_3 ) @ B_130 ) )
% 3.42/1.78 => ( ord_less_eq_com_o @ ( image_1604448413te_com @ F_69 @ A_194 ) @ B_130 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_360_image__subsetI,axiom,
% 3.42/1.78 ! [F_69: hoare_1708887482_state > pname,B_130: pname > $o,A_194: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ! [X_3: hoare_1708887482_state] :
% 3.42/1.78 ( ( member451959335_state @ X_3 @ A_194 )
% 3.42/1.78 => ( member_pname @ ( F_69 @ X_3 ) @ B_130 ) )
% 3.42/1.78 => ( ord_less_eq_pname_o @ ( image_1509414295_pname @ F_69 @ A_194 ) @ B_130 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_361_image__subsetI,axiom,
% 3.42/1.78 ! [F_69: pname > com,B_130: com > $o,A_194: pname > $o] :
% 3.42/1.78 ( ! [X_3: pname] :
% 3.42/1.78 ( ( member_pname @ X_3 @ A_194 )
% 3.42/1.78 => ( member_com @ ( F_69 @ X_3 ) @ B_130 ) )
% 3.42/1.78 => ( ord_less_eq_com_o @ ( image_pname_com @ F_69 @ A_194 ) @ B_130 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_362_image__subsetI,axiom,
% 3.42/1.78 ! [F_69: pname > pname,B_130: pname > $o,A_194: pname > $o] :
% 3.42/1.78 ( ! [X_3: pname] :
% 3.42/1.78 ( ( member_pname @ X_3 @ A_194 )
% 3.42/1.78 => ( member_pname @ ( F_69 @ X_3 ) @ B_130 ) )
% 3.42/1.78 => ( ord_less_eq_pname_o @ ( image_pname_pname @ F_69 @ A_194 ) @ B_130 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_363_image__subsetI,axiom,
% 3.42/1.78 ! [F_69: com > hoare_1708887482_state,B_130: hoare_1708887482_state > $o,A_194: com > $o] :
% 3.42/1.78 ( ! [X_3: com] :
% 3.42/1.78 ( ( member_com @ X_3 @ A_194 )
% 3.42/1.78 => ( member451959335_state @ ( F_69 @ X_3 ) @ B_130 ) )
% 3.42/1.78 => ( ord_le777019615tate_o @ ( image_934102463_state @ F_69 @ A_194 ) @ B_130 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_364_image__subsetI,axiom,
% 3.42/1.78 ! [F_69: com > pname,B_130: pname > $o,A_194: com > $o] :
% 3.42/1.78 ( ! [X_3: com] :
% 3.42/1.78 ( ( member_com @ X_3 @ A_194 )
% 3.42/1.78 => ( member_pname @ ( F_69 @ X_3 ) @ B_130 ) )
% 3.42/1.78 => ( ord_less_eq_pname_o @ ( image_com_pname @ F_69 @ A_194 ) @ B_130 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_365_image__subsetI,axiom,
% 3.42/1.78 ! [F_69: pname > hoare_1708887482_state,B_130: hoare_1708887482_state > $o,A_194: pname > $o] :
% 3.42/1.78 ( ! [X_3: pname] :
% 3.42/1.78 ( ( member_pname @ X_3 @ A_194 )
% 3.42/1.78 => ( member451959335_state @ ( F_69 @ X_3 ) @ B_130 ) )
% 3.42/1.78 => ( ord_le777019615tate_o @ ( image_1116629049_state @ F_69 @ A_194 ) @ B_130 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_366_order__refl,axiom,
% 3.42/1.78 ! [X_101: pname > $o] : ( ord_less_eq_pname_o @ X_101 @ X_101 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_367_order__refl,axiom,
% 3.42/1.78 ! [X_101: $o] : ( ord_less_eq_o @ X_101 @ X_101 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_368_order__refl,axiom,
% 3.42/1.78 ! [X_101: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ X_101 @ X_101 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_369_nonempty__iff,axiom,
% 3.42/1.78 ! [A_193: com > $o] :
% 3.42/1.78 ( ( A_193 != bot_bot_com_o )
% 3.42/1.78 <=> ? [X_3: com,B_84: com > $o] :
% 3.42/1.78 ( ( A_193
% 3.42/1.78 = ( insert_com @ X_3 @ B_84 ) )
% 3.42/1.78 & ~ ( member_com @ X_3 @ B_84 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_370_nonempty__iff,axiom,
% 3.42/1.78 ! [A_193: pname > $o] :
% 3.42/1.78 ( ( A_193 != bot_bot_pname_o )
% 3.42/1.78 <=> ? [X_3: pname,B_84: pname > $o] :
% 3.42/1.78 ( ( A_193
% 3.42/1.78 = ( insert_pname @ X_3 @ B_84 ) )
% 3.42/1.78 & ~ ( member_pname @ X_3 @ B_84 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_371_nonempty__iff,axiom,
% 3.42/1.78 ! [A_193: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( A_193 != bot_bo19817387tate_o )
% 3.42/1.78 <=> ? [X_3: hoare_1708887482_state,B_84: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( A_193
% 3.42/1.78 = ( insert528405184_state @ X_3 @ B_84 ) )
% 3.42/1.78 & ~ ( member451959335_state @ X_3 @ B_84 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_372_the_Osimps,axiom,
% 3.42/1.78 ! [X_100: pname] :
% 3.42/1.78 ( ( the_pname_1 @ ( some_pname @ X_100 ) )
% 3.42/1.78 = X_100 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_373_the_Osimps,axiom,
% 3.42/1.78 ! [X_100: hoare_1708887482_state] :
% 3.42/1.78 ( ( the_Ho963921505_state @ ( some_H1974565227_state @ X_100 ) )
% 3.42/1.78 = X_100 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_374_the_Osimps,axiom,
% 3.42/1.78 ! [X_100: com] :
% 3.42/1.78 ( ( the_com @ ( some_com @ X_100 ) )
% 3.42/1.78 = X_100 ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_375_weak__Body,axiom,
% 3.42/1.78 ! [G_31: hoare_1708887482_state > $o,P_35: state > state > $o,Pn_4: pname,Q_24: state > state > $o] :
% 3.42/1.78 ( ( hoare_90032982_state @ G_31 @ ( insert528405184_state @ ( hoare_858012674_state @ P_35 @ ( the_com @ ( body @ Pn_4 ) ) @ Q_24 ) @ bot_bo19817387tate_o ) )
% 3.42/1.78 => ( hoare_90032982_state @ G_31 @ ( insert528405184_state @ ( hoare_858012674_state @ P_35 @ ( body_1 @ Pn_4 ) @ Q_24 ) @ bot_bo19817387tate_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_376_BodyN,axiom,
% 3.42/1.78 ! [P_34: state > state > $o,Pn_3: pname,Q_23: state > state > $o,G_30: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( hoare_90032982_state @ ( insert528405184_state @ ( hoare_858012674_state @ P_34 @ ( body_1 @ Pn_3 ) @ Q_23 ) @ G_30 ) @ ( insert528405184_state @ ( hoare_858012674_state @ P_34 @ ( the_com @ ( body @ Pn_3 ) ) @ Q_23 ) @ bot_bo19817387tate_o ) )
% 3.42/1.78 => ( hoare_90032982_state @ G_30 @ ( insert528405184_state @ ( hoare_858012674_state @ P_34 @ ( body_1 @ Pn_3 ) @ Q_23 ) @ bot_bo19817387tate_o ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_377_state__not__singleton__def,axiom,
% 3.42/1.78 ( hoare_1160767572gleton
% 3.42/1.78 <=> ? [S_2: state,T_1: state] : ( S_2 != T_1 ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_378_UnCI,axiom,
% 3.42/1.78 ! [A_192: com > $o,C_60: com,B_129: com > $o] :
% 3.42/1.78 ( ( ~ ( member_com @ C_60 @ B_129 )
% 3.42/1.78 => ( member_com @ C_60 @ A_192 ) )
% 3.42/1.78 => ( member_com @ C_60 @ ( semila1562558655_com_o @ A_192 @ B_129 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_379_UnCI,axiom,
% 3.42/1.78 ! [A_192: hoare_1708887482_state > $o,C_60: hoare_1708887482_state,B_129: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( ~ ( member451959335_state @ C_60 @ B_129 )
% 3.42/1.78 => ( member451959335_state @ C_60 @ A_192 ) )
% 3.42/1.78 => ( member451959335_state @ C_60 @ ( semila1122118281tate_o @ A_192 @ B_129 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_380_UnCI,axiom,
% 3.42/1.78 ! [A_192: pname > $o,C_60: pname,B_129: pname > $o] :
% 3.42/1.78 ( ( ~ ( member_pname @ C_60 @ B_129 )
% 3.42/1.78 => ( member_pname @ C_60 @ A_192 ) )
% 3.42/1.78 => ( member_pname @ C_60 @ ( semila1780557381name_o @ A_192 @ B_129 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_381_UnE,axiom,
% 3.42/1.78 ! [C_59: com,A_191: com > $o,B_128: com > $o] :
% 3.42/1.78 ( ( member_com @ C_59 @ ( semila1562558655_com_o @ A_191 @ B_128 ) )
% 3.42/1.78 => ( ~ ( member_com @ C_59 @ A_191 )
% 3.42/1.78 => ( member_com @ C_59 @ B_128 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_382_UnE,axiom,
% 3.42/1.78 ! [C_59: hoare_1708887482_state,A_191: hoare_1708887482_state > $o,B_128: hoare_1708887482_state > $o] :
% 3.42/1.78 ( ( member451959335_state @ C_59 @ ( semila1122118281tate_o @ A_191 @ B_128 ) )
% 3.42/1.78 => ( ~ ( member451959335_state @ C_59 @ A_191 )
% 3.42/1.78 => ( member451959335_state @ C_59 @ B_128 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_383_UnE,axiom,
% 3.42/1.78 ! [C_59: pname,A_191: pname > $o,B_128: pname > $o] :
% 3.42/1.78 ( ( member_pname @ C_59 @ ( semila1780557381name_o @ A_191 @ B_128 ) )
% 3.42/1.78 => ( ~ ( member_pname @ C_59 @ A_191 )
% 3.42/1.78 => ( member_pname @ C_59 @ B_128 ) ) ) ).
% 3.42/1.78
% 3.42/1.78 thf(fact_384_triple_Oinject,axiom,
% 3.42/1.78 ! [Fun1_2: state > state > $o,Com_4: com,Fun2_2: state > state > $o,Fun1_1: state > state > $o,Com_3: com,Fun2_1: state > state > $o] :
% 3.42/1.79 ( ( ( hoare_858012674_state @ Fun1_2 @ Com_4 @ Fun2_2 )
% 3.42/1.79 = ( hoare_858012674_state @ Fun1_1 @ Com_3 @ Fun2_1 ) )
% 3.42/1.79 <=> ( ( Fun1_2 = Fun1_1 )
% 3.42/1.79 & ( Com_4 = Com_3 )
% 3.42/1.79 & ( Fun2_2 = Fun2_1 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_385_UnI2,axiom,
% 3.42/1.79 ! [A_190: com > $o,C_58: com,B_127: com > $o] :
% 3.42/1.79 ( ( member_com @ C_58 @ B_127 )
% 3.42/1.79 => ( member_com @ C_58 @ ( semila1562558655_com_o @ A_190 @ B_127 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_386_UnI2,axiom,
% 3.42/1.79 ! [A_190: hoare_1708887482_state > $o,C_58: hoare_1708887482_state,B_127: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_58 @ B_127 )
% 3.42/1.79 => ( member451959335_state @ C_58 @ ( semila1122118281tate_o @ A_190 @ B_127 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_387_UnI2,axiom,
% 3.42/1.79 ! [A_190: pname > $o,C_58: pname,B_127: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_58 @ B_127 )
% 3.42/1.79 => ( member_pname @ C_58 @ ( semila1780557381name_o @ A_190 @ B_127 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_388_UnI1,axiom,
% 3.42/1.79 ! [B_126: com > $o,C_57: com,A_189: com > $o] :
% 3.42/1.79 ( ( member_com @ C_57 @ A_189 )
% 3.42/1.79 => ( member_com @ C_57 @ ( semila1562558655_com_o @ A_189 @ B_126 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_389_UnI1,axiom,
% 3.42/1.79 ! [B_126: hoare_1708887482_state > $o,C_57: hoare_1708887482_state,A_189: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_57 @ A_189 )
% 3.42/1.79 => ( member451959335_state @ C_57 @ ( semila1122118281tate_o @ A_189 @ B_126 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_390_UnI1,axiom,
% 3.42/1.79 ! [B_126: pname > $o,C_57: pname,A_189: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_57 @ A_189 )
% 3.42/1.79 => ( member_pname @ C_57 @ ( semila1780557381name_o @ A_189 @ B_126 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_391_ball__Un,axiom,
% 3.42/1.79 ! [P_33: pname > $o,A_188: pname > $o,B_125: pname > $o] :
% 3.42/1.79 ( ! [X_3: pname] :
% 3.42/1.79 ( ( member_pname @ X_3 @ ( semila1780557381name_o @ A_188 @ B_125 ) )
% 3.42/1.79 => ( P_33 @ X_3 ) )
% 3.42/1.79 <=> ( ! [X_3: pname] :
% 3.42/1.79 ( ( member_pname @ X_3 @ A_188 )
% 3.42/1.79 => ( P_33 @ X_3 ) )
% 3.42/1.79 & ! [X_3: pname] :
% 3.42/1.79 ( ( member_pname @ X_3 @ B_125 )
% 3.42/1.79 => ( P_33 @ X_3 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_392_ball__Un,axiom,
% 3.42/1.79 ! [P_33: hoare_1708887482_state > $o,A_188: hoare_1708887482_state > $o,B_125: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ! [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( member451959335_state @ X_3 @ ( semila1122118281tate_o @ A_188 @ B_125 ) )
% 3.42/1.79 => ( P_33 @ X_3 ) )
% 3.42/1.79 <=> ( ! [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( member451959335_state @ X_3 @ A_188 )
% 3.42/1.79 => ( P_33 @ X_3 ) )
% 3.42/1.79 & ! [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( member451959335_state @ X_3 @ B_125 )
% 3.42/1.79 => ( P_33 @ X_3 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_393_bex__Un,axiom,
% 3.42/1.79 ! [P_32: pname > $o,A_187: pname > $o,B_124: pname > $o] :
% 3.42/1.79 ( ? [X_3: pname] :
% 3.42/1.79 ( ( member_pname @ X_3 @ ( semila1780557381name_o @ A_187 @ B_124 ) )
% 3.42/1.79 & ( P_32 @ X_3 ) )
% 3.42/1.79 <=> ( ? [X_3: pname] :
% 3.42/1.79 ( ( member_pname @ X_3 @ A_187 )
% 3.42/1.79 & ( P_32 @ X_3 ) )
% 3.42/1.79 | ? [X_3: pname] :
% 3.42/1.79 ( ( member_pname @ X_3 @ B_124 )
% 3.42/1.79 & ( P_32 @ X_3 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_394_bex__Un,axiom,
% 3.42/1.79 ! [P_32: hoare_1708887482_state > $o,A_187: hoare_1708887482_state > $o,B_124: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ? [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( member451959335_state @ X_3 @ ( semila1122118281tate_o @ A_187 @ B_124 ) )
% 3.42/1.79 & ( P_32 @ X_3 ) )
% 3.42/1.79 <=> ( ? [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( member451959335_state @ X_3 @ A_187 )
% 3.42/1.79 & ( P_32 @ X_3 ) )
% 3.42/1.79 | ? [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( member451959335_state @ X_3 @ B_124 )
% 3.42/1.79 & ( P_32 @ X_3 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_395_Un__assoc,axiom,
% 3.42/1.79 ! [A_186: pname > $o,B_123: pname > $o,C_56: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ ( semila1780557381name_o @ A_186 @ B_123 ) @ C_56 )
% 3.42/1.79 = ( semila1780557381name_o @ A_186 @ ( semila1780557381name_o @ B_123 @ C_56 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_396_Un__assoc,axiom,
% 3.42/1.79 ! [A_186: hoare_1708887482_state > $o,B_123: hoare_1708887482_state > $o,C_56: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A_186 @ B_123 ) @ C_56 )
% 3.42/1.79 = ( semila1122118281tate_o @ A_186 @ ( semila1122118281tate_o @ B_123 @ C_56 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_397_Un__iff,axiom,
% 3.42/1.79 ! [C_55: com,A_185: com > $o,B_122: com > $o] :
% 3.42/1.79 ( ( member_com @ C_55 @ ( semila1562558655_com_o @ A_185 @ B_122 ) )
% 3.42/1.79 <=> ( ( member_com @ C_55 @ A_185 )
% 3.42/1.79 | ( member_com @ C_55 @ B_122 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_398_Un__iff,axiom,
% 3.42/1.79 ! [C_55: hoare_1708887482_state,A_185: hoare_1708887482_state > $o,B_122: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_55 @ ( semila1122118281tate_o @ A_185 @ B_122 ) )
% 3.42/1.79 <=> ( ( member451959335_state @ C_55 @ A_185 )
% 3.42/1.79 | ( member451959335_state @ C_55 @ B_122 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_399_Un__iff,axiom,
% 3.42/1.79 ! [C_55: pname,A_185: pname > $o,B_122: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_55 @ ( semila1780557381name_o @ A_185 @ B_122 ) )
% 3.42/1.79 <=> ( ( member_pname @ C_55 @ A_185 )
% 3.42/1.79 | ( member_pname @ C_55 @ B_122 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_400_Un__left__commute,axiom,
% 3.42/1.79 ! [A_184: pname > $o,B_121: pname > $o,C_54: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ A_184 @ ( semila1780557381name_o @ B_121 @ C_54 ) )
% 3.42/1.79 = ( semila1780557381name_o @ B_121 @ ( semila1780557381name_o @ A_184 @ C_54 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_401_Un__left__commute,axiom,
% 3.42/1.79 ! [A_184: hoare_1708887482_state > $o,B_121: hoare_1708887482_state > $o,C_54: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ A_184 @ ( semila1122118281tate_o @ B_121 @ C_54 ) )
% 3.42/1.79 = ( semila1122118281tate_o @ B_121 @ ( semila1122118281tate_o @ A_184 @ C_54 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_402_Un__left__absorb,axiom,
% 3.42/1.79 ! [A_183: pname > $o,B_120: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ A_183 @ ( semila1780557381name_o @ A_183 @ B_120 ) )
% 3.42/1.79 = ( semila1780557381name_o @ A_183 @ B_120 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_403_Un__left__absorb,axiom,
% 3.42/1.79 ! [A_183: hoare_1708887482_state > $o,B_120: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ A_183 @ ( semila1122118281tate_o @ A_183 @ B_120 ) )
% 3.42/1.79 = ( semila1122118281tate_o @ A_183 @ B_120 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_404_Un__commute,axiom,
% 3.42/1.79 ! [A_182: pname > $o,B_119: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ A_182 @ B_119 )
% 3.42/1.79 = ( semila1780557381name_o @ B_119 @ A_182 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_405_Un__commute,axiom,
% 3.42/1.79 ! [A_182: hoare_1708887482_state > $o,B_119: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ A_182 @ B_119 )
% 3.42/1.79 = ( semila1122118281tate_o @ B_119 @ A_182 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_406_Un__def,axiom,
% 3.42/1.79 ! [A_181: com > $o,B_118: com > $o] :
% 3.42/1.79 ( ( semila1562558655_com_o @ A_181 @ B_118 )
% 3.42/1.79 = ( collect_com
% 3.42/1.79 @ ^ [X_3: com] : ( (|) @ ( member_com @ X_3 @ A_181 ) @ ( member_com @ X_3 @ B_118 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_407_Un__def,axiom,
% 3.42/1.79 ! [A_181: ( pname > $o ) > $o,B_118: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( semila181081674me_o_o @ A_181 @ B_118 )
% 3.42/1.79 = ( collect_pname_o
% 3.42/1.79 @ ^ [X_3: pname > $o] : ( (|) @ ( member_pname_o @ X_3 @ A_181 ) @ ( member_pname_o @ X_3 @ B_118 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_408_Un__def,axiom,
% 3.42/1.79 ! [A_181: ( hoare_1708887482_state > $o ) > $o,B_118: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( semila1853742644te_o_o @ A_181 @ B_118 )
% 3.42/1.79 = ( collec219771562tate_o
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state > $o] : ( (|) @ ( member814030440tate_o @ X_3 @ A_181 ) @ ( member814030440tate_o @ X_3 @ B_118 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_409_Un__def,axiom,
% 3.42/1.79 ! [A_181: hoare_1708887482_state > $o,B_118: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ A_181 @ B_118 )
% 3.42/1.79 = ( collec1568722789_state
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state] : ( (|) @ ( member451959335_state @ X_3 @ A_181 ) @ ( member451959335_state @ X_3 @ B_118 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_410_Un__def,axiom,
% 3.42/1.79 ! [A_181: pname > $o,B_118: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ A_181 @ B_118 )
% 3.42/1.79 = ( collect_pname
% 3.42/1.79 @ ^ [X_3: pname] : ( (|) @ ( member_pname @ X_3 @ A_181 ) @ ( member_pname @ X_3 @ B_118 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_411_Un__absorb,axiom,
% 3.42/1.79 ! [A_180: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ A_180 @ A_180 )
% 3.42/1.79 = A_180 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_412_Un__absorb,axiom,
% 3.42/1.79 ! [A_180: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ A_180 @ A_180 )
% 3.42/1.79 = A_180 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_413_Collect__disj__eq,axiom,
% 3.42/1.79 ! [P_31: pname > $o,Q_22: pname > $o] :
% 3.42/1.79 ( ( collect_pname
% 3.42/1.79 @ ^ [X_3: pname] : ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
% 3.42/1.79 = ( semila1780557381name_o @ ( collect_pname @ P_31 ) @ ( collect_pname @ Q_22 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_414_Collect__disj__eq,axiom,
% 3.42/1.79 ! [P_31: ( pname > $o ) > $o,Q_22: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( collect_pname_o
% 3.42/1.79 @ ^ [X_3: pname > $o] : ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
% 3.42/1.79 = ( semila181081674me_o_o @ ( collect_pname_o @ P_31 ) @ ( collect_pname_o @ Q_22 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_415_Collect__disj__eq,axiom,
% 3.42/1.79 ! [P_31: ( hoare_1708887482_state > $o ) > $o,Q_22: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( collec219771562tate_o
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state > $o] : ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
% 3.42/1.79 = ( semila1853742644te_o_o @ ( collec219771562tate_o @ P_31 ) @ ( collec219771562tate_o @ Q_22 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_416_Collect__disj__eq,axiom,
% 3.42/1.79 ! [P_31: hoare_1708887482_state > $o,Q_22: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( collec1568722789_state
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state] : ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
% 3.42/1.79 = ( semila1122118281tate_o @ ( collec1568722789_state @ P_31 ) @ ( collec1568722789_state @ Q_22 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_417_Un__empty,axiom,
% 3.42/1.79 ! [A_179: pname > $o,B_117: pname > $o] :
% 3.42/1.79 ( ( ( semila1780557381name_o @ A_179 @ B_117 )
% 3.42/1.79 = bot_bot_pname_o )
% 3.42/1.79 <=> ( ( A_179 = bot_bot_pname_o )
% 3.42/1.79 & ( B_117 = bot_bot_pname_o ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_418_Un__empty,axiom,
% 3.42/1.79 ! [A_179: com > $o,B_117: com > $o] :
% 3.42/1.79 ( ( ( semila1562558655_com_o @ A_179 @ B_117 )
% 3.42/1.79 = bot_bot_com_o )
% 3.42/1.79 <=> ( ( A_179 = bot_bot_com_o )
% 3.42/1.79 & ( B_117 = bot_bot_com_o ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_419_Un__empty,axiom,
% 3.42/1.79 ! [A_179: hoare_1708887482_state > $o,B_117: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ( semila1122118281tate_o @ A_179 @ B_117 )
% 3.42/1.79 = bot_bo19817387tate_o )
% 3.42/1.79 <=> ( ( A_179 = bot_bo19817387tate_o )
% 3.42/1.79 & ( B_117 = bot_bo19817387tate_o ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_420_Un__empty__right,axiom,
% 3.42/1.79 ! [A_178: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ A_178 @ bot_bot_pname_o )
% 3.42/1.79 = A_178 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_421_Un__empty__right,axiom,
% 3.42/1.79 ! [A_178: com > $o] :
% 3.42/1.79 ( ( semila1562558655_com_o @ A_178 @ bot_bot_com_o )
% 3.42/1.79 = A_178 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_422_Un__empty__right,axiom,
% 3.42/1.79 ! [A_178: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ A_178 @ bot_bo19817387tate_o )
% 3.42/1.79 = A_178 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_423_Un__empty__left,axiom,
% 3.42/1.79 ! [B_116: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ bot_bot_pname_o @ B_116 )
% 3.42/1.79 = B_116 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_424_Un__empty__left,axiom,
% 3.42/1.79 ! [B_116: com > $o] :
% 3.42/1.79 ( ( semila1562558655_com_o @ bot_bot_com_o @ B_116 )
% 3.42/1.79 = B_116 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_425_Un__empty__left,axiom,
% 3.42/1.79 ! [B_116: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ bot_bo19817387tate_o @ B_116 )
% 3.42/1.79 = B_116 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_426_finite__UnI,axiom,
% 3.42/1.79 ! [G_29: ( pname > $o ) > $o,F_68: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( finite297249702name_o @ F_68 )
% 3.42/1.79 => ( ( finite297249702name_o @ G_29 )
% 3.42/1.79 => ( finite297249702name_o @ ( semila181081674me_o_o @ F_68 @ G_29 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_427_finite__UnI,axiom,
% 3.42/1.79 ! [G_29: ( hoare_1708887482_state > $o ) > $o,F_68: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( finite1329924456tate_o @ F_68 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ G_29 )
% 3.42/1.79 => ( finite1329924456tate_o @ ( semila1853742644te_o_o @ F_68 @ G_29 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_428_finite__UnI,axiom,
% 3.42/1.79 ! [G_29: hoare_1708887482_state > $o,F_68: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite1625599783_state @ F_68 )
% 3.42/1.79 => ( ( finite1625599783_state @ G_29 )
% 3.42/1.79 => ( finite1625599783_state @ ( semila1122118281tate_o @ F_68 @ G_29 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_429_finite__UnI,axiom,
% 3.42/1.79 ! [G_29: pname > $o,F_68: pname > $o] :
% 3.42/1.79 ( ( finite_finite_pname @ F_68 )
% 3.42/1.79 => ( ( finite_finite_pname @ G_29 )
% 3.42/1.79 => ( finite_finite_pname @ ( semila1780557381name_o @ F_68 @ G_29 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_430_finite__Un,axiom,
% 3.42/1.79 ! [F_67: ( pname > $o ) > $o,G_28: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( finite297249702name_o @ ( semila181081674me_o_o @ F_67 @ G_28 ) )
% 3.42/1.79 <=> ( ( finite297249702name_o @ F_67 )
% 3.42/1.79 & ( finite297249702name_o @ G_28 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_431_finite__Un,axiom,
% 3.42/1.79 ! [F_67: ( hoare_1708887482_state > $o ) > $o,G_28: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( finite1329924456tate_o @ ( semila1853742644te_o_o @ F_67 @ G_28 ) )
% 3.42/1.79 <=> ( ( finite1329924456tate_o @ F_67 )
% 3.42/1.79 & ( finite1329924456tate_o @ G_28 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_432_finite__Un,axiom,
% 3.42/1.79 ! [F_67: hoare_1708887482_state > $o,G_28: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite1625599783_state @ ( semila1122118281tate_o @ F_67 @ G_28 ) )
% 3.42/1.79 <=> ( ( finite1625599783_state @ F_67 )
% 3.42/1.79 & ( finite1625599783_state @ G_28 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_433_finite__Un,axiom,
% 3.42/1.79 ! [F_67: pname > $o,G_28: pname > $o] :
% 3.42/1.79 ( ( finite_finite_pname @ ( semila1780557381name_o @ F_67 @ G_28 ) )
% 3.42/1.79 <=> ( ( finite_finite_pname @ F_67 )
% 3.42/1.79 & ( finite_finite_pname @ G_28 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_434_Un__insert__left,axiom,
% 3.42/1.79 ! [A_177: pname,B_115: pname > $o,C_53: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ ( insert_pname @ A_177 @ B_115 ) @ C_53 )
% 3.42/1.79 = ( insert_pname @ A_177 @ ( semila1780557381name_o @ B_115 @ C_53 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_435_Un__insert__left,axiom,
% 3.42/1.79 ! [A_177: com,B_115: com > $o,C_53: com > $o] :
% 3.42/1.79 ( ( semila1562558655_com_o @ ( insert_com @ A_177 @ B_115 ) @ C_53 )
% 3.42/1.79 = ( insert_com @ A_177 @ ( semila1562558655_com_o @ B_115 @ C_53 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_436_Un__insert__left,axiom,
% 3.42/1.79 ! [A_177: hoare_1708887482_state,B_115: hoare_1708887482_state > $o,C_53: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ ( insert528405184_state @ A_177 @ B_115 ) @ C_53 )
% 3.42/1.79 = ( insert528405184_state @ A_177 @ ( semila1122118281tate_o @ B_115 @ C_53 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_437_Un__insert__right,axiom,
% 3.42/1.79 ! [A_176: pname > $o,A_175: pname,B_114: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ A_176 @ ( insert_pname @ A_175 @ B_114 ) )
% 3.42/1.79 = ( insert_pname @ A_175 @ ( semila1780557381name_o @ A_176 @ B_114 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_438_Un__insert__right,axiom,
% 3.42/1.79 ! [A_176: com > $o,A_175: com,B_114: com > $o] :
% 3.42/1.79 ( ( semila1562558655_com_o @ A_176 @ ( insert_com @ A_175 @ B_114 ) )
% 3.42/1.79 = ( insert_com @ A_175 @ ( semila1562558655_com_o @ A_176 @ B_114 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_439_Un__insert__right,axiom,
% 3.42/1.79 ! [A_176: hoare_1708887482_state > $o,A_175: hoare_1708887482_state,B_114: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ A_176 @ ( insert528405184_state @ A_175 @ B_114 ) )
% 3.42/1.79 = ( insert528405184_state @ A_175 @ ( semila1122118281tate_o @ A_176 @ B_114 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_440_Un__mono,axiom,
% 3.42/1.79 ! [B_113: pname > $o,D_5: pname > $o,A_174: pname > $o,C_52: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ A_174 @ C_52 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ B_113 @ D_5 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_174 @ B_113 ) @ ( semila1780557381name_o @ C_52 @ D_5 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_441_Un__mono,axiom,
% 3.42/1.79 ! [B_113: hoare_1708887482_state > $o,D_5: hoare_1708887482_state > $o,A_174: hoare_1708887482_state > $o,C_52: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ A_174 @ C_52 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ B_113 @ D_5 )
% 3.42/1.79 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_174 @ B_113 ) @ ( semila1122118281tate_o @ C_52 @ D_5 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_442_Un__least,axiom,
% 3.42/1.79 ! [B_112: pname > $o,A_173: pname > $o,C_51: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ A_173 @ C_51 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ B_112 @ C_51 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_173 @ B_112 ) @ C_51 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_443_Un__least,axiom,
% 3.42/1.79 ! [B_112: hoare_1708887482_state > $o,A_173: hoare_1708887482_state > $o,C_51: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ A_173 @ C_51 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ B_112 @ C_51 )
% 3.42/1.79 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_173 @ B_112 ) @ C_51 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_444_Un__absorb2,axiom,
% 3.42/1.79 ! [B_111: pname > $o,A_172: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ B_111 @ A_172 )
% 3.42/1.79 => ( ( semila1780557381name_o @ A_172 @ B_111 )
% 3.42/1.79 = A_172 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_445_Un__absorb2,axiom,
% 3.42/1.79 ! [B_111: hoare_1708887482_state > $o,A_172: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ B_111 @ A_172 )
% 3.42/1.79 => ( ( semila1122118281tate_o @ A_172 @ B_111 )
% 3.42/1.79 = A_172 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_446_Un__absorb1,axiom,
% 3.42/1.79 ! [A_171: pname > $o,B_110: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ A_171 @ B_110 )
% 3.42/1.79 => ( ( semila1780557381name_o @ A_171 @ B_110 )
% 3.42/1.79 = B_110 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_447_Un__absorb1,axiom,
% 3.42/1.79 ! [A_171: hoare_1708887482_state > $o,B_110: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ A_171 @ B_110 )
% 3.42/1.79 => ( ( semila1122118281tate_o @ A_171 @ B_110 )
% 3.42/1.79 = B_110 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_448_subset__Un__eq,axiom,
% 3.42/1.79 ! [A_170: pname > $o,B_109: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ A_170 @ B_109 )
% 3.42/1.79 <=> ( ( semila1780557381name_o @ A_170 @ B_109 )
% 3.42/1.79 = B_109 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_449_subset__Un__eq,axiom,
% 3.42/1.79 ! [A_170: hoare_1708887482_state > $o,B_109: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ A_170 @ B_109 )
% 3.42/1.79 <=> ( ( semila1122118281tate_o @ A_170 @ B_109 )
% 3.42/1.79 = B_109 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_450_Un__upper2,axiom,
% 3.42/1.79 ! [B_108: pname > $o,A_169: pname > $o] : ( ord_less_eq_pname_o @ B_108 @ ( semila1780557381name_o @ A_169 @ B_108 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_451_Un__upper2,axiom,
% 3.42/1.79 ! [B_108: hoare_1708887482_state > $o,A_169: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ B_108 @ ( semila1122118281tate_o @ A_169 @ B_108 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_452_Un__upper1,axiom,
% 3.42/1.79 ! [A_168: pname > $o,B_107: pname > $o] : ( ord_less_eq_pname_o @ A_168 @ ( semila1780557381name_o @ A_168 @ B_107 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_453_Un__upper1,axiom,
% 3.42/1.79 ! [A_168: hoare_1708887482_state > $o,B_107: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A_168 @ ( semila1122118281tate_o @ A_168 @ B_107 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_454_image__Un,axiom,
% 3.42/1.79 ! [F_66: hoare_1708887482_state > pname,A_167: hoare_1708887482_state > $o,B_106: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( image_1509414295_pname @ F_66 @ ( semila1122118281tate_o @ A_167 @ B_106 ) )
% 3.42/1.79 = ( semila1780557381name_o @ ( image_1509414295_pname @ F_66 @ A_167 ) @ ( image_1509414295_pname @ F_66 @ B_106 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_455_image__Un,axiom,
% 3.42/1.79 ! [F_66: pname > hoare_1708887482_state,A_167: pname > $o,B_106: pname > $o] :
% 3.42/1.79 ( ( image_1116629049_state @ F_66 @ ( semila1780557381name_o @ A_167 @ B_106 ) )
% 3.42/1.79 = ( semila1122118281tate_o @ ( image_1116629049_state @ F_66 @ A_167 ) @ ( image_1116629049_state @ F_66 @ B_106 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_456_insert__def,axiom,
% 3.42/1.79 ! [A_166: pname,B_105: pname > $o] :
% 3.42/1.79 ( ( insert_pname @ A_166 @ B_105 )
% 3.42/1.79 = ( semila1780557381name_o
% 3.42/1.79 @ ( collect_pname
% 3.42/1.79 @ ^ [X_3: pname] : ( X_3 = A_166 ) )
% 3.42/1.79 @ B_105 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_457_insert__def,axiom,
% 3.42/1.79 ! [A_166: com,B_105: com > $o] :
% 3.42/1.79 ( ( insert_com @ A_166 @ B_105 )
% 3.42/1.79 = ( semila1562558655_com_o
% 3.42/1.79 @ ( collect_com
% 3.42/1.79 @ ^ [X_3: com] : ( X_3 = A_166 ) )
% 3.42/1.79 @ B_105 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_458_insert__def,axiom,
% 3.42/1.79 ! [A_166: pname > $o,B_105: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( insert_pname_o @ A_166 @ B_105 )
% 3.42/1.79 = ( semila181081674me_o_o
% 3.42/1.79 @ ( collect_pname_o
% 3.42/1.79 @ ^ [X_3: pname > $o] : ( X_3 = A_166 ) )
% 3.42/1.79 @ B_105 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_459_insert__def,axiom,
% 3.42/1.79 ! [A_166: hoare_1708887482_state > $o,B_105: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( insert949073679tate_o @ A_166 @ B_105 )
% 3.42/1.79 = ( semila1853742644te_o_o
% 3.42/1.79 @ ( collec219771562tate_o
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state > $o] : ( X_3 = A_166 ) )
% 3.42/1.79 @ B_105 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_460_insert__def,axiom,
% 3.42/1.79 ! [A_166: hoare_1708887482_state,B_105: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( insert528405184_state @ A_166 @ B_105 )
% 3.42/1.79 = ( semila1122118281tate_o
% 3.42/1.79 @ ( collec1568722789_state
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state] : ( X_3 = A_166 ) )
% 3.42/1.79 @ B_105 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_461_insert__is__Un,axiom,
% 3.42/1.79 ! [A_165: pname,A_164: pname > $o] :
% 3.42/1.79 ( ( insert_pname @ A_165 @ A_164 )
% 3.42/1.79 = ( semila1780557381name_o @ ( insert_pname @ A_165 @ bot_bot_pname_o ) @ A_164 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_462_insert__is__Un,axiom,
% 3.42/1.79 ! [A_165: com,A_164: com > $o] :
% 3.42/1.79 ( ( insert_com @ A_165 @ A_164 )
% 3.42/1.79 = ( semila1562558655_com_o @ ( insert_com @ A_165 @ bot_bot_com_o ) @ A_164 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_463_insert__is__Un,axiom,
% 3.42/1.79 ! [A_165: hoare_1708887482_state,A_164: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( insert528405184_state @ A_165 @ A_164 )
% 3.42/1.79 = ( semila1122118281tate_o @ ( insert528405184_state @ A_165 @ bot_bo19817387tate_o ) @ A_164 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_464_hoare__derivs_OBody,axiom,
% 3.42/1.79 ! [G_27: hoare_1708887482_state > $o,P_30: pname > state > state > $o,Q_21: pname > state > state > $o,Procs_2: pname > $o] :
% 3.42/1.79 ( ( hoare_90032982_state
% 3.42/1.79 @ ( semila1122118281tate_o @ G_27
% 3.42/1.79 @ ( image_1116629049_state
% 3.42/1.79 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_30 @ P_27 ) @ ( body_1 @ P_27 ) @ ( Q_21 @ P_27 ) )
% 3.42/1.79 @ Procs_2 ) )
% 3.42/1.79 @ ( image_1116629049_state
% 3.42/1.79 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_30 @ P_27 ) @ ( the_com @ ( body @ P_27 ) ) @ ( Q_21 @ P_27 ) )
% 3.42/1.79 @ Procs_2 ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_27
% 3.42/1.79 @ ( image_1116629049_state
% 3.42/1.79 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_30 @ P_27 ) @ ( body_1 @ P_27 ) @ ( Q_21 @ P_27 ) )
% 3.42/1.79 @ Procs_2 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_465_xt1_I6_J,axiom,
% 3.42/1.79 ! [Z_20: pname > $o,Y_50: pname > $o,X_99: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ Y_50 @ X_99 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ Z_20 @ Y_50 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ Z_20 @ X_99 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_466_xt1_I6_J,axiom,
% 3.42/1.79 ! [Z_20: $o,Y_50: $o,X_99: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ Y_50 @ X_99 )
% 3.42/1.79 => ( ( ord_less_eq_o @ Z_20 @ Y_50 )
% 3.42/1.79 => ( ord_less_eq_o @ Z_20 @ X_99 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_467_xt1_I6_J,axiom,
% 3.42/1.79 ! [Z_20: hoare_1708887482_state > $o,Y_50: hoare_1708887482_state > $o,X_99: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ Y_50 @ X_99 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ Z_20 @ Y_50 )
% 3.42/1.79 => ( ord_le777019615tate_o @ Z_20 @ X_99 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_468_xt1_I5_J,axiom,
% 3.42/1.79 ! [Y_49: pname > $o,X_98: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ Y_49 @ X_98 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ X_98 @ Y_49 )
% 3.42/1.79 => ( X_98 = Y_49 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_469_xt1_I5_J,axiom,
% 3.42/1.79 ! [Y_49: $o,X_98: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ Y_49 @ X_98 )
% 3.42/1.79 => ( ( ord_less_eq_o @ X_98 @ Y_49 )
% 3.42/1.79 => ( X_98
% 3.42/1.79 <=> Y_49 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_470_xt1_I5_J,axiom,
% 3.42/1.79 ! [Y_49: hoare_1708887482_state > $o,X_98: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ Y_49 @ X_98 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ X_98 @ Y_49 )
% 3.42/1.79 => ( X_98 = Y_49 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_471_order__trans,axiom,
% 3.42/1.79 ! [Z_19: pname > $o,X_97: pname > $o,Y_48: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ X_97 @ Y_48 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ Y_48 @ Z_19 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ X_97 @ Z_19 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_472_order__trans,axiom,
% 3.42/1.79 ! [Z_19: $o,X_97: $o,Y_48: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ X_97 @ Y_48 )
% 3.42/1.79 => ( ( ord_less_eq_o @ Y_48 @ Z_19 )
% 3.42/1.79 => ( ord_less_eq_o @ X_97 @ Z_19 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_473_order__trans,axiom,
% 3.42/1.79 ! [Z_19: hoare_1708887482_state > $o,X_97: hoare_1708887482_state > $o,Y_48: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ X_97 @ Y_48 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ Y_48 @ Z_19 )
% 3.42/1.79 => ( ord_le777019615tate_o @ X_97 @ Z_19 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_474_order__antisym,axiom,
% 3.42/1.79 ! [X_96: pname > $o,Y_47: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ X_96 @ Y_47 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ Y_47 @ X_96 )
% 3.42/1.79 => ( X_96 = Y_47 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_475_order__antisym,axiom,
% 3.42/1.79 ! [X_96: $o,Y_47: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ X_96 @ Y_47 )
% 3.42/1.79 => ( ( ord_less_eq_o @ Y_47 @ X_96 )
% 3.42/1.79 => ( X_96
% 3.42/1.79 <=> Y_47 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_476_order__antisym,axiom,
% 3.42/1.79 ! [X_96: hoare_1708887482_state > $o,Y_47: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ X_96 @ Y_47 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ Y_47 @ X_96 )
% 3.42/1.79 => ( X_96 = Y_47 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_477_xt1_I4_J,axiom,
% 3.42/1.79 ! [C_50: pname > $o,B_104: pname > $o,A_163: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ B_104 @ A_163 )
% 3.42/1.79 => ( ( B_104 = C_50 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ C_50 @ A_163 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_478_xt1_I4_J,axiom,
% 3.42/1.79 ! [C_50: $o,B_104: $o,A_163: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ B_104 @ A_163 )
% 3.42/1.79 => ( ( B_104
% 3.42/1.79 <=> C_50 )
% 3.42/1.79 => ( ord_less_eq_o @ C_50 @ A_163 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_479_xt1_I4_J,axiom,
% 3.42/1.79 ! [C_50: hoare_1708887482_state > $o,B_104: hoare_1708887482_state > $o,A_163: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ B_104 @ A_163 )
% 3.42/1.79 => ( ( B_104 = C_50 )
% 3.42/1.79 => ( ord_le777019615tate_o @ C_50 @ A_163 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_480_ord__le__eq__trans,axiom,
% 3.42/1.79 ! [C_49: pname > $o,A_162: pname > $o,B_103: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ A_162 @ B_103 )
% 3.42/1.79 => ( ( B_103 = C_49 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ A_162 @ C_49 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_481_ord__le__eq__trans,axiom,
% 3.42/1.79 ! [C_49: $o,A_162: $o,B_103: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ A_162 @ B_103 )
% 3.42/1.79 => ( ( B_103
% 3.42/1.79 <=> C_49 )
% 3.42/1.79 => ( ord_less_eq_o @ A_162 @ C_49 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_482_ord__le__eq__trans,axiom,
% 3.42/1.79 ! [C_49: hoare_1708887482_state > $o,A_162: hoare_1708887482_state > $o,B_103: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ A_162 @ B_103 )
% 3.42/1.79 => ( ( B_103 = C_49 )
% 3.42/1.79 => ( ord_le777019615tate_o @ A_162 @ C_49 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_483_xt1_I3_J,axiom,
% 3.42/1.79 ! [C_48: pname > $o,A_161: pname > $o,B_102: pname > $o] :
% 3.42/1.79 ( ( A_161 = B_102 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ C_48 @ B_102 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ C_48 @ A_161 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_484_xt1_I3_J,axiom,
% 3.42/1.79 ! [C_48: $o,B_102: $o,A_161: $o] :
% 3.42/1.79 ( ( A_161
% 3.42/1.79 <=> B_102 )
% 3.42/1.79 => ( ( ord_less_eq_o @ C_48 @ B_102 )
% 3.42/1.79 => ( ord_less_eq_o @ C_48 @ A_161 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_485_xt1_I3_J,axiom,
% 3.42/1.79 ! [C_48: hoare_1708887482_state > $o,A_161: hoare_1708887482_state > $o,B_102: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( A_161 = B_102 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ C_48 @ B_102 )
% 3.42/1.79 => ( ord_le777019615tate_o @ C_48 @ A_161 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_486_ord__eq__le__trans,axiom,
% 3.42/1.79 ! [C_47: pname > $o,A_160: pname > $o,B_101: pname > $o] :
% 3.42/1.79 ( ( A_160 = B_101 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ B_101 @ C_47 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ A_160 @ C_47 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_487_ord__eq__le__trans,axiom,
% 3.42/1.79 ! [C_47: $o,B_101: $o,A_160: $o] :
% 3.42/1.79 ( ( A_160
% 3.42/1.79 <=> B_101 )
% 3.42/1.79 => ( ( ord_less_eq_o @ B_101 @ C_47 )
% 3.42/1.79 => ( ord_less_eq_o @ A_160 @ C_47 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_488_ord__eq__le__trans,axiom,
% 3.42/1.79 ! [C_47: hoare_1708887482_state > $o,A_160: hoare_1708887482_state > $o,B_101: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( A_160 = B_101 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ B_101 @ C_47 )
% 3.42/1.79 => ( ord_le777019615tate_o @ A_160 @ C_47 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_489_order__antisym__conv,axiom,
% 3.42/1.79 ! [Y_46: pname > $o,X_95: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ Y_46 @ X_95 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ X_95 @ Y_46 )
% 3.42/1.79 <=> ( X_95 = Y_46 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_490_order__antisym__conv,axiom,
% 3.42/1.79 ! [Y_46: $o,X_95: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ Y_46 @ X_95 )
% 3.42/1.79 => ( ( ord_less_eq_o @ X_95 @ Y_46 )
% 3.42/1.79 <=> ( X_95
% 3.42/1.79 <=> Y_46 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_491_order__antisym__conv,axiom,
% 3.42/1.79 ! [Y_46: hoare_1708887482_state > $o,X_95: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ Y_46 @ X_95 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ X_95 @ Y_46 )
% 3.42/1.79 <=> ( X_95 = Y_46 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_492_order__eq__refl,axiom,
% 3.42/1.79 ! [X_94: pname > $o,Y_45: pname > $o] :
% 3.42/1.79 ( ( X_94 = Y_45 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ X_94 @ Y_45 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_493_order__eq__refl,axiom,
% 3.42/1.79 ! [Y_45: $o,X_94: $o] :
% 3.42/1.79 ( ( X_94
% 3.42/1.79 <=> Y_45 )
% 3.42/1.79 => ( ord_less_eq_o @ X_94 @ Y_45 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_494_order__eq__refl,axiom,
% 3.42/1.79 ! [X_94: hoare_1708887482_state > $o,Y_45: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( X_94 = Y_45 )
% 3.42/1.79 => ( ord_le777019615tate_o @ X_94 @ Y_45 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_495_order__eq__iff,axiom,
% 3.42/1.79 ! [X_93: pname > $o,Y_44: pname > $o] :
% 3.42/1.79 ( ( X_93 = Y_44 )
% 3.42/1.79 <=> ( ( ord_less_eq_pname_o @ X_93 @ Y_44 )
% 3.42/1.79 & ( ord_less_eq_pname_o @ Y_44 @ X_93 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_496_order__eq__iff,axiom,
% 3.42/1.79 ! [Y_44: $o,X_93: $o] :
% 3.42/1.79 ( ( X_93
% 3.42/1.79 <=> Y_44 )
% 3.42/1.79 <=> ( ( ord_less_eq_o @ X_93 @ Y_44 )
% 3.42/1.79 & ( ord_less_eq_o @ Y_44 @ X_93 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_497_order__eq__iff,axiom,
% 3.42/1.79 ! [X_93: hoare_1708887482_state > $o,Y_44: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( X_93 = Y_44 )
% 3.42/1.79 <=> ( ( ord_le777019615tate_o @ X_93 @ Y_44 )
% 3.42/1.79 & ( ord_le777019615tate_o @ Y_44 @ X_93 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_498_option_Oinject,axiom,
% 3.42/1.79 ! [A_159: pname,A_158: pname] :
% 3.42/1.79 ( ( ( some_pname @ A_159 )
% 3.42/1.79 = ( some_pname @ A_158 ) )
% 3.42/1.79 <=> ( A_159 = A_158 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_499_option_Oinject,axiom,
% 3.42/1.79 ! [A_159: hoare_1708887482_state,A_158: hoare_1708887482_state] :
% 3.42/1.79 ( ( ( some_H1974565227_state @ A_159 )
% 3.42/1.79 = ( some_H1974565227_state @ A_158 ) )
% 3.42/1.79 <=> ( A_159 = A_158 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_500_option_Oinject,axiom,
% 3.42/1.79 ! [A_159: com,A_158: com] :
% 3.42/1.79 ( ( ( some_com @ A_159 )
% 3.42/1.79 = ( some_com @ A_158 ) )
% 3.42/1.79 <=> ( A_159 = A_158 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_501_constant,axiom,
% 3.42/1.79 ! [G_26: hoare_1708887482_state > $o,P_29: state > state > $o,C_46: com,Q_20: state > state > $o,C_45: $o] :
% 3.42/1.79 ( ( C_45
% 3.42/1.79 => ( hoare_90032982_state @ G_26 @ ( insert528405184_state @ ( hoare_858012674_state @ P_29 @ C_46 @ Q_20 ) @ bot_bo19817387tate_o ) ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_26
% 3.42/1.79 @ ( insert528405184_state
% 3.42/1.79 @ ( hoare_858012674_state
% 3.42/1.79 @ ^ [Z_11: state,S_2: state] : ( (&) @ ( P_29 @ Z_11 @ S_2 ) @ C_45 )
% 3.42/1.79 @ C_46
% 3.42/1.79 @ Q_20 )
% 3.42/1.79 @ bot_bo19817387tate_o ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_502_Body1,axiom,
% 3.42/1.79 ! [Pn_2: pname,G_25: hoare_1708887482_state > $o,P_28: pname > state > state > $o,Q_19: pname > state > state > $o,Procs_1: pname > $o] :
% 3.42/1.79 ( ( hoare_90032982_state
% 3.42/1.79 @ ( semila1122118281tate_o @ G_25
% 3.42/1.79 @ ( image_1116629049_state
% 3.42/1.79 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_28 @ P_27 ) @ ( body_1 @ P_27 ) @ ( Q_19 @ P_27 ) )
% 3.42/1.79 @ Procs_1 ) )
% 3.42/1.79 @ ( image_1116629049_state
% 3.42/1.79 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_28 @ P_27 ) @ ( the_com @ ( body @ P_27 ) ) @ ( Q_19 @ P_27 ) )
% 3.42/1.79 @ Procs_1 ) )
% 3.42/1.79 => ( ( member_pname @ Pn_2 @ Procs_1 )
% 3.42/1.79 => ( hoare_90032982_state @ G_25 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_28 @ Pn_2 ) @ ( body_1 @ Pn_2 ) @ ( Q_19 @ Pn_2 ) ) @ bot_bo19817387tate_o ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_503_le__bot,axiom,
% 3.42/1.79 ! [A_157: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ A_157 @ bot_bot_pname_o )
% 3.42/1.79 => ( A_157 = bot_bot_pname_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_504_le__bot,axiom,
% 3.42/1.79 ! [A_157: com > $o] :
% 3.42/1.79 ( ( ord_less_eq_com_o @ A_157 @ bot_bot_com_o )
% 3.42/1.79 => ( A_157 = bot_bot_com_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_505_le__bot,axiom,
% 3.42/1.79 ! [A_157: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ A_157 @ bot_bot_o )
% 3.42/1.79 => ( A_157
% 3.42/1.79 <=> bot_bot_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_506_le__bot,axiom,
% 3.42/1.79 ! [A_157: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ A_157 @ bot_bo19817387tate_o )
% 3.42/1.79 => ( A_157 = bot_bo19817387tate_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_507_bot__unique,axiom,
% 3.42/1.79 ! [A_156: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ A_156 @ bot_bot_pname_o )
% 3.42/1.79 <=> ( A_156 = bot_bot_pname_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_508_bot__unique,axiom,
% 3.42/1.79 ! [A_156: com > $o] :
% 3.42/1.79 ( ( ord_less_eq_com_o @ A_156 @ bot_bot_com_o )
% 3.42/1.79 <=> ( A_156 = bot_bot_com_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_509_bot__unique,axiom,
% 3.42/1.79 ! [A_156: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ A_156 @ bot_bot_o )
% 3.42/1.79 <=> ( A_156
% 3.42/1.79 <=> bot_bot_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_510_bot__unique,axiom,
% 3.42/1.79 ! [A_156: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ A_156 @ bot_bo19817387tate_o )
% 3.42/1.79 <=> ( A_156 = bot_bo19817387tate_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_511_bot__least,axiom,
% 3.42/1.79 ! [A_155: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_155 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_512_bot__least,axiom,
% 3.42/1.79 ! [A_155: com > $o] : ( ord_less_eq_com_o @ bot_bot_com_o @ A_155 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_513_bot__least,axiom,
% 3.42/1.79 ! [A_155: $o] : ( ord_less_eq_o @ bot_bot_o @ A_155 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_514_bot__least,axiom,
% 3.42/1.79 ! [A_155: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ bot_bo19817387tate_o @ A_155 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_515_le__funE,axiom,
% 3.42/1.79 ! [X_92: pname,F_65: pname > $o,G_24: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ F_65 @ G_24 )
% 3.42/1.79 => ( ord_less_eq_o @ ( F_65 @ X_92 ) @ ( G_24 @ X_92 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_516_le__funE,axiom,
% 3.42/1.79 ! [X_92: hoare_1708887482_state,F_65: hoare_1708887482_state > $o,G_24: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ F_65 @ G_24 )
% 3.42/1.79 => ( ord_less_eq_o @ ( F_65 @ X_92 ) @ ( G_24 @ X_92 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_517_le__funD,axiom,
% 3.42/1.79 ! [X_91: pname,F_64: pname > $o,G_23: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ F_64 @ G_23 )
% 3.42/1.79 => ( ord_less_eq_o @ ( F_64 @ X_91 ) @ ( G_23 @ X_91 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_518_le__funD,axiom,
% 3.42/1.79 ! [X_91: hoare_1708887482_state,F_64: hoare_1708887482_state > $o,G_23: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ F_64 @ G_23 )
% 3.42/1.79 => ( ord_less_eq_o @ ( F_64 @ X_91 ) @ ( G_23 @ X_91 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_519_le__fun__def,axiom,
% 3.42/1.79 ! [F_63: pname > $o,G_22: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ F_63 @ G_22 )
% 3.42/1.79 <=> ! [X_3: pname] : ( ord_less_eq_o @ ( F_63 @ X_3 ) @ ( G_22 @ X_3 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_520_le__fun__def,axiom,
% 3.42/1.79 ! [F_63: hoare_1708887482_state > $o,G_22: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ F_63 @ G_22 )
% 3.42/1.79 <=> ! [X_3: hoare_1708887482_state] : ( ord_less_eq_o @ ( F_63 @ X_3 ) @ ( G_22 @ X_3 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_521_bot__apply,axiom,
% 3.42/1.79 ! [X_90: pname] :
% 3.42/1.79 ( ( bot_bot_pname_o @ X_90 )
% 3.42/1.79 <=> bot_bot_o ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_522_bot__apply,axiom,
% 3.42/1.79 ! [X_90: com] :
% 3.42/1.79 ( ( bot_bot_com_o @ X_90 )
% 3.42/1.79 <=> bot_bot_o ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_523_bot__apply,axiom,
% 3.42/1.79 ! [X_90: hoare_1708887482_state] :
% 3.42/1.79 ( ( bot_bo19817387tate_o @ X_90 )
% 3.42/1.79 <=> bot_bot_o ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_524_bot__fun__def,axiom,
% 3.42/1.79 ! [X_3: pname] :
% 3.42/1.79 ( ( bot_bot_pname_o @ X_3 )
% 3.42/1.79 <=> bot_bot_o ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_525_bot__fun__def,axiom,
% 3.42/1.79 ! [X_3: com] :
% 3.42/1.79 ( ( bot_bot_com_o @ X_3 )
% 3.42/1.79 <=> bot_bot_o ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_526_bot__fun__def,axiom,
% 3.42/1.79 ! [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( bot_bo19817387tate_o @ X_3 )
% 3.42/1.79 <=> bot_bot_o ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_527_finite__pointwise,axiom,
% 3.42/1.79 ! [P_26: ( pname > $o ) > state > state > $o,Q_18: ( pname > $o ) > state > state > $o,G_21: hoare_1708887482_state > $o,P_25: ( pname > $o ) > state > state > $o,C0_1: ( pname > $o ) > com,Q_17: ( pname > $o ) > state > state > $o,U_1: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( finite297249702name_o @ U_1 )
% 3.42/1.79 => ( ! [P_27: pname > $o] :
% 3.42/1.79 ( ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) ) @ bot_bo19817387tate_o ) ) )
% 3.42/1.79 => ( ( hoare_90032982_state @ G_21
% 3.42/1.79 @ ( image_1922967206_state
% 3.42/1.79 @ ^ [P_27: pname > $o] : ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) )
% 3.42/1.79 @ U_1 ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_21
% 3.42/1.79 @ ( image_1922967206_state
% 3.42/1.79 @ ^ [P_27: pname > $o] : ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) )
% 3.42/1.79 @ U_1 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_528_finite__pointwise,axiom,
% 3.42/1.79 ! [P_26: ( hoare_1708887482_state > $o ) > state > state > $o,Q_18: ( hoare_1708887482_state > $o ) > state > state > $o,G_21: hoare_1708887482_state > $o,P_25: ( hoare_1708887482_state > $o ) > state > state > $o,C0_1: ( hoare_1708887482_state > $o ) > com,Q_17: ( hoare_1708887482_state > $o ) > state > state > $o,U_1: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( finite1329924456tate_o @ U_1 )
% 3.42/1.79 => ( ! [P_27: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) ) @ bot_bo19817387tate_o ) ) )
% 3.42/1.79 => ( ( hoare_90032982_state @ G_21
% 3.42/1.79 @ ( image_27005066_state
% 3.42/1.79 @ ^ [P_27: hoare_1708887482_state > $o] : ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) )
% 3.42/1.79 @ U_1 ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_21
% 3.42/1.79 @ ( image_27005066_state
% 3.42/1.79 @ ^ [P_27: hoare_1708887482_state > $o] : ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) )
% 3.42/1.79 @ U_1 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_529_finite__pointwise,axiom,
% 3.42/1.79 ! [P_26: pname > state > state > $o,Q_18: pname > state > state > $o,G_21: hoare_1708887482_state > $o,P_25: pname > state > state > $o,C0_1: pname > com,Q_17: pname > state > state > $o,U_1: pname > $o] :
% 3.42/1.79 ( ( finite_finite_pname @ U_1 )
% 3.42/1.79 => ( ! [P_27: pname] :
% 3.42/1.79 ( ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) ) @ bot_bo19817387tate_o ) ) )
% 3.42/1.79 => ( ( hoare_90032982_state @ G_21
% 3.42/1.79 @ ( image_1116629049_state
% 3.42/1.79 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) )
% 3.42/1.79 @ U_1 ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_21
% 3.42/1.79 @ ( image_1116629049_state
% 3.42/1.79 @ ^ [P_27: pname] : ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) )
% 3.42/1.79 @ U_1 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_530_escape,axiom,
% 3.42/1.79 ! [G_20: hoare_1708887482_state > $o,C_44: com,Q_16: state > state > $o,P_24: state > state > $o] :
% 3.42/1.79 ( ! [Z_11: state,S_2: state] :
% 3.42/1.79 ( ( P_24 @ Z_11 @ S_2 )
% 3.42/1.79 => ( hoare_90032982_state @ G_20
% 3.42/1.79 @ ( insert528405184_state
% 3.42/1.79 @ ( hoare_858012674_state
% 3.42/1.79 @ ^ [Za: state,S_3: state] : ( S_3 = S_2 )
% 3.42/1.79 @ C_44
% 3.42/1.79 @ ^ [Z_12: state] : ( Q_16 @ Z_11 ) )
% 3.42/1.79 @ bot_bo19817387tate_o ) ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_20 @ ( insert528405184_state @ ( hoare_858012674_state @ P_24 @ C_44 @ Q_16 ) @ bot_bo19817387tate_o ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_531_Body__sound__lemma,axiom,
% 3.42/1.79 ! [G_19: hoare_1708887482_state > $o,P_23: pname > state > state > $o,Q_15: pname > state > state > $o,Procs: pname > $o] :
% 3.42/1.79 ( ( hoare_496444244_state
% 3.42/1.79 @ ( semila1122118281tate_o @ G_19
% 3.42/1.79 @ ( image_1116629049_state
% 3.42/1.79 @ ^ [Pn: pname] : ( hoare_858012674_state @ ( P_23 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_15 @ Pn ) )
% 3.42/1.79 @ Procs ) )
% 3.42/1.79 @ ( image_1116629049_state
% 3.42/1.79 @ ^ [Pn: pname] : ( hoare_858012674_state @ ( P_23 @ Pn ) @ ( the_com @ ( body @ Pn ) ) @ ( Q_15 @ Pn ) )
% 3.42/1.79 @ Procs ) )
% 3.42/1.79 => ( hoare_496444244_state @ G_19
% 3.42/1.79 @ ( image_1116629049_state
% 3.42/1.79 @ ^ [Pn: pname] : ( hoare_858012674_state @ ( P_23 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_15 @ Pn ) )
% 3.42/1.79 @ Procs ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_532_conseq1,axiom,
% 3.42/1.79 ! [P_22: state > state > $o,G_18: hoare_1708887482_state > $o,P_21: state > state > $o,C_43: com,Q_14: state > state > $o] :
% 3.42/1.79 ( ( hoare_90032982_state @ G_18 @ ( insert528405184_state @ ( hoare_858012674_state @ P_21 @ C_43 @ Q_14 ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( ! [Z_11: state,S_2: state] :
% 3.42/1.79 ( ( P_22 @ Z_11 @ S_2 )
% 3.42/1.79 => ( P_21 @ Z_11 @ S_2 ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_18 @ ( insert528405184_state @ ( hoare_858012674_state @ P_22 @ C_43 @ Q_14 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_533_conseq2,axiom,
% 3.42/1.79 ! [Q_13: state > state > $o,G_17: hoare_1708887482_state > $o,P_20: state > state > $o,C_42: com,Q_12: state > state > $o] :
% 3.42/1.79 ( ( hoare_90032982_state @ G_17 @ ( insert528405184_state @ ( hoare_858012674_state @ P_20 @ C_42 @ Q_12 ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( ! [Z_11: state,S_2: state] :
% 3.42/1.79 ( ( Q_12 @ Z_11 @ S_2 )
% 3.42/1.79 => ( Q_13 @ Z_11 @ S_2 ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_17 @ ( insert528405184_state @ ( hoare_858012674_state @ P_20 @ C_42 @ Q_13 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_534_MGF__complete,axiom,
% 3.42/1.79 ! [P: state > state > $o,Q_11: state > state > $o,C_34: com] :
% 3.42/1.79 ( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( ( hoare_496444244_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_858012674_state @ P @ C_34 @ Q_11 ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_858012674_state @ P @ C_34 @ Q_11 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_535_sup1E,axiom,
% 3.42/1.79 ! [A_154: pname > $o,B_100: pname > $o,X_89: pname] :
% 3.42/1.79 ( ( semila1780557381name_o @ A_154 @ B_100 @ X_89 )
% 3.42/1.79 => ( ~ ( A_154 @ X_89 )
% 3.42/1.79 => ( B_100 @ X_89 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_536_sup1E,axiom,
% 3.42/1.79 ! [A_154: hoare_1708887482_state > $o,B_100: hoare_1708887482_state > $o,X_89: hoare_1708887482_state] :
% 3.42/1.79 ( ( semila1122118281tate_o @ A_154 @ B_100 @ X_89 )
% 3.42/1.79 => ( ~ ( A_154 @ X_89 )
% 3.42/1.79 => ( B_100 @ X_89 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_537_sup1CI,axiom,
% 3.42/1.79 ! [A_153: pname > $o,B_99: pname > $o,X_88: pname] :
% 3.42/1.79 ( ( ~ ( B_99 @ X_88 )
% 3.42/1.79 => ( A_153 @ X_88 ) )
% 3.42/1.79 => ( semila1780557381name_o @ A_153 @ B_99 @ X_88 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_538_sup1CI,axiom,
% 3.42/1.79 ! [A_153: hoare_1708887482_state > $o,B_99: hoare_1708887482_state > $o,X_88: hoare_1708887482_state] :
% 3.42/1.79 ( ( ~ ( B_99 @ X_88 )
% 3.42/1.79 => ( A_153 @ X_88 ) )
% 3.42/1.79 => ( semila1122118281tate_o @ A_153 @ B_99 @ X_88 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_539_conseq12,axiom,
% 3.42/1.79 ! [Q_10: state > state > $o,P_19: state > state > $o,G_16: hoare_1708887482_state > $o,P_18: state > state > $o,C_41: com,Q_9: state > state > $o] :
% 3.42/1.79 ( ( hoare_90032982_state @ G_16 @ ( insert528405184_state @ ( hoare_858012674_state @ P_18 @ C_41 @ Q_9 ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( ! [Z_11: state,S_2: state] :
% 3.42/1.79 ( ( P_19 @ Z_11 @ S_2 )
% 3.42/1.79 => ! [S_3: state] :
% 3.42/1.79 ( ! [Z_12: state] :
% 3.42/1.79 ( ( P_18 @ Z_12 @ S_2 )
% 3.42/1.79 => ( Q_9 @ Z_12 @ S_3 ) )
% 3.42/1.79 => ( Q_10 @ Z_11 @ S_3 ) ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_16 @ ( insert528405184_state @ ( hoare_858012674_state @ P_19 @ C_41 @ Q_10 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_540_hoare__sound,axiom,
% 3.42/1.79 ! [G_15: hoare_1708887482_state > $o,Ts: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( hoare_90032982_state @ G_15 @ Ts )
% 3.42/1.79 => ( hoare_496444244_state @ G_15 @ Ts ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_541_bot__empty__eq,axiom,
% 3.42/1.79 ! [X_3: com] :
% 3.42/1.79 ( ( bot_bot_com_o @ X_3 )
% 3.42/1.79 <=> ( member_com @ X_3 @ bot_bot_com_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_542_bot__empty__eq,axiom,
% 3.42/1.79 ! [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( bot_bo19817387tate_o @ X_3 )
% 3.42/1.79 <=> ( member451959335_state @ X_3 @ bot_bo19817387tate_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_543_bot__empty__eq,axiom,
% 3.42/1.79 ! [X_3: pname] :
% 3.42/1.79 ( ( bot_bot_pname_o @ X_3 )
% 3.42/1.79 <=> ( member_pname @ X_3 @ bot_bot_pname_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_544_rev__predicate1D,axiom,
% 3.42/1.79 ! [Q_8: pname > $o,P_17: pname > $o,X_87: pname] :
% 3.42/1.79 ( ( P_17 @ X_87 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ P_17 @ Q_8 )
% 3.42/1.79 => ( Q_8 @ X_87 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_545_rev__predicate1D,axiom,
% 3.42/1.79 ! [Q_8: hoare_1708887482_state > $o,P_17: hoare_1708887482_state > $o,X_87: hoare_1708887482_state] :
% 3.42/1.79 ( ( P_17 @ X_87 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ P_17 @ Q_8 )
% 3.42/1.79 => ( Q_8 @ X_87 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_546_predicate1D,axiom,
% 3.42/1.79 ! [X_86: pname,P_16: pname > $o,Q_7: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ P_16 @ Q_7 )
% 3.42/1.79 => ( ( P_16 @ X_86 )
% 3.42/1.79 => ( Q_7 @ X_86 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_547_predicate1D,axiom,
% 3.42/1.79 ! [X_86: hoare_1708887482_state,P_16: hoare_1708887482_state > $o,Q_7: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ P_16 @ Q_7 )
% 3.42/1.79 => ( ( P_16 @ X_86 )
% 3.42/1.79 => ( Q_7 @ X_86 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_548_sup1I2,axiom,
% 3.42/1.79 ! [A_152: pname > $o,B_98: pname > $o,X_85: pname] :
% 3.42/1.79 ( ( B_98 @ X_85 )
% 3.42/1.79 => ( semila1780557381name_o @ A_152 @ B_98 @ X_85 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_549_sup1I2,axiom,
% 3.42/1.79 ! [A_152: hoare_1708887482_state > $o,B_98: hoare_1708887482_state > $o,X_85: hoare_1708887482_state] :
% 3.42/1.79 ( ( B_98 @ X_85 )
% 3.42/1.79 => ( semila1122118281tate_o @ A_152 @ B_98 @ X_85 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_550_sup1I1,axiom,
% 3.42/1.79 ! [B_97: pname > $o,A_151: pname > $o,X_84: pname] :
% 3.42/1.79 ( ( A_151 @ X_84 )
% 3.42/1.79 => ( semila1780557381name_o @ A_151 @ B_97 @ X_84 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_551_sup1I1,axiom,
% 3.42/1.79 ! [B_97: hoare_1708887482_state > $o,A_151: hoare_1708887482_state > $o,X_84: hoare_1708887482_state] :
% 3.42/1.79 ( ( A_151 @ X_84 )
% 3.42/1.79 => ( semila1122118281tate_o @ A_151 @ B_97 @ X_84 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_552_pred__subset__eq,axiom,
% 3.42/1.79 ! [R_3: com > $o,S_6: com > $o] :
% 3.42/1.79 ( ( ord_less_eq_com_o
% 3.42/1.79 @ ^ [X_3: com] : ( member_com @ X_3 @ R_3 )
% 3.42/1.79 @ ^ [X_3: com] : ( member_com @ X_3 @ S_6 ) )
% 3.42/1.79 <=> ( ord_less_eq_com_o @ R_3 @ S_6 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_553_pred__subset__eq,axiom,
% 3.42/1.79 ! [R_3: hoare_1708887482_state > $o,S_6: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state] : ( member451959335_state @ X_3 @ R_3 )
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state] : ( member451959335_state @ X_3 @ S_6 ) )
% 3.42/1.79 <=> ( ord_le777019615tate_o @ R_3 @ S_6 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_554_pred__subset__eq,axiom,
% 3.42/1.79 ! [R_3: pname > $o,S_6: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o
% 3.42/1.79 @ ^ [X_3: pname] : ( member_pname @ X_3 @ R_3 )
% 3.42/1.79 @ ^ [X_3: pname] : ( member_pname @ X_3 @ S_6 ) )
% 3.42/1.79 <=> ( ord_less_eq_pname_o @ R_3 @ S_6 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_555_sup__Un__eq,axiom,
% 3.42/1.79 ! [R_2: com > $o,S_5: com > $o,X_3: com] :
% 3.42/1.79 ( ( semila1562558655_com_o
% 3.42/1.79 @ ^ [Y_4: com] : ( member_com @ Y_4 @ R_2 )
% 3.42/1.79 @ ^ [Y_4: com] : ( member_com @ Y_4 @ S_5 )
% 3.42/1.79 @ X_3 )
% 3.42/1.79 <=> ( member_com @ X_3 @ ( semila1562558655_com_o @ R_2 @ S_5 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_556_sup__Un__eq,axiom,
% 3.42/1.79 ! [R_2: hoare_1708887482_state > $o,S_5: hoare_1708887482_state > $o,X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( semila1122118281tate_o
% 3.42/1.79 @ ^ [Y_4: hoare_1708887482_state] : ( member451959335_state @ Y_4 @ R_2 )
% 3.42/1.79 @ ^ [Y_4: hoare_1708887482_state] : ( member451959335_state @ Y_4 @ S_5 )
% 3.42/1.79 @ X_3 )
% 3.42/1.79 <=> ( member451959335_state @ X_3 @ ( semila1122118281tate_o @ R_2 @ S_5 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_557_sup__Un__eq,axiom,
% 3.42/1.79 ! [R_2: pname > $o,S_5: pname > $o,X_3: pname] :
% 3.42/1.79 ( ( semila1780557381name_o
% 3.42/1.79 @ ^ [Y_4: pname] : ( member_pname @ Y_4 @ R_2 )
% 3.42/1.79 @ ^ [Y_4: pname] : ( member_pname @ Y_4 @ S_5 )
% 3.42/1.79 @ X_3 )
% 3.42/1.79 <=> ( member_pname @ X_3 @ ( semila1780557381name_o @ R_2 @ S_5 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_558_le__funI,axiom,
% 3.42/1.79 ! [F_62: pname > $o,G_14: pname > $o] :
% 3.42/1.79 ( ! [X_3: pname] : ( ord_less_eq_o @ ( F_62 @ X_3 ) @ ( G_14 @ X_3 ) )
% 3.42/1.79 => ( ord_less_eq_pname_o @ F_62 @ G_14 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_559_le__funI,axiom,
% 3.42/1.79 ! [F_62: hoare_1708887482_state > $o,G_14: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ! [X_3: hoare_1708887482_state] : ( ord_less_eq_o @ ( F_62 @ X_3 ) @ ( G_14 @ X_3 ) )
% 3.42/1.79 => ( ord_le777019615tate_o @ F_62 @ G_14 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_560_Option_Oset_Osimps_I2_J,axiom,
% 3.42/1.79 ! [X_83: pname] :
% 3.42/1.79 ( ( set_pname @ ( some_pname @ X_83 ) )
% 3.42/1.79 = ( insert_pname @ X_83 @ bot_bot_pname_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_561_Option_Oset_Osimps_I2_J,axiom,
% 3.42/1.79 ! [X_83: com] :
% 3.42/1.79 ( ( set_com @ ( some_com @ X_83 ) )
% 3.42/1.79 = ( insert_com @ X_83 @ bot_bot_com_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_562_Option_Oset_Osimps_I2_J,axiom,
% 3.42/1.79 ! [X_83: hoare_1708887482_state] :
% 3.42/1.79 ( ( set_Ho525251890_state @ ( some_H1974565227_state @ X_83 ) )
% 3.42/1.79 = ( insert528405184_state @ X_83 @ bot_bo19817387tate_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_563_sup__apply,axiom,
% 3.42/1.79 ! [F_61: pname > $o,G_13: pname > $o,X_82: pname] :
% 3.42/1.79 ( ( semila1780557381name_o @ F_61 @ G_13 @ X_82 )
% 3.42/1.79 <=> ( semila10642723_sup_o @ ( F_61 @ X_82 ) @ ( G_13 @ X_82 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_564_sup__apply,axiom,
% 3.42/1.79 ! [F_61: hoare_1708887482_state > $o,G_13: hoare_1708887482_state > $o,X_82: hoare_1708887482_state] :
% 3.42/1.79 ( ( semila1122118281tate_o @ F_61 @ G_13 @ X_82 )
% 3.42/1.79 <=> ( semila10642723_sup_o @ ( F_61 @ X_82 ) @ ( G_13 @ X_82 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_565_sup__fun__def,axiom,
% 3.42/1.79 ! [F_60: pname > $o,G_12: pname > $o,X_3: pname] :
% 3.42/1.79 ( ( semila1780557381name_o @ F_60 @ G_12 @ X_3 )
% 3.42/1.79 <=> ( semila10642723_sup_o @ ( F_60 @ X_3 ) @ ( G_12 @ X_3 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_566_sup__fun__def,axiom,
% 3.42/1.79 ! [F_60: hoare_1708887482_state > $o,G_12: hoare_1708887482_state > $o,X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( semila1122118281tate_o @ F_60 @ G_12 @ X_3 )
% 3.42/1.79 <=> ( semila10642723_sup_o @ ( F_60 @ X_3 ) @ ( G_12 @ X_3 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_567_single__stateE,axiom,
% 3.42/1.79 ( hoare_1160767572gleton
% 3.42/1.79 => ! [T_1: state] :
% 3.42/1.79 ~ ! [S_2: state] : ( S_2 = T_1 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_568_sup__eq__bot__iff,axiom,
% 3.42/1.79 ! [X_81: pname > $o,Y_43: pname > $o] :
% 3.42/1.79 ( ( ( semila1780557381name_o @ X_81 @ Y_43 )
% 3.42/1.79 = bot_bot_pname_o )
% 3.42/1.79 <=> ( ( X_81 = bot_bot_pname_o )
% 3.42/1.79 & ( Y_43 = bot_bot_pname_o ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_569_sup__eq__bot__iff,axiom,
% 3.42/1.79 ! [X_81: com > $o,Y_43: com > $o] :
% 3.42/1.79 ( ( ( semila1562558655_com_o @ X_81 @ Y_43 )
% 3.42/1.79 = bot_bot_com_o )
% 3.42/1.79 <=> ( ( X_81 = bot_bot_com_o )
% 3.42/1.79 & ( Y_43 = bot_bot_com_o ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_570_sup__eq__bot__iff,axiom,
% 3.42/1.79 ! [X_81: $o,Y_43: $o] :
% 3.42/1.79 ( ( ( semila10642723_sup_o @ X_81 @ Y_43 )
% 3.42/1.79 <=> bot_bot_o )
% 3.42/1.79 <=> ( ( X_81
% 3.42/1.79 <=> bot_bot_o )
% 3.42/1.79 & ( Y_43
% 3.42/1.79 <=> bot_bot_o ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_571_sup__eq__bot__iff,axiom,
% 3.42/1.79 ! [X_81: hoare_1708887482_state > $o,Y_43: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ( semila1122118281tate_o @ X_81 @ Y_43 )
% 3.42/1.79 = bot_bo19817387tate_o )
% 3.42/1.79 <=> ( ( X_81 = bot_bo19817387tate_o )
% 3.42/1.79 & ( Y_43 = bot_bo19817387tate_o ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_572_elem__set,axiom,
% 3.42/1.79 ! [X_80: com,Xo_1: option_com] :
% 3.42/1.79 ( ( member_com @ X_80 @ ( set_com @ Xo_1 ) )
% 3.42/1.79 <=> ( Xo_1
% 3.42/1.79 = ( some_com @ X_80 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_573_elem__set,axiom,
% 3.42/1.79 ! [X_80: hoare_1708887482_state,Xo_1: option1624383643_state] :
% 3.42/1.79 ( ( member451959335_state @ X_80 @ ( set_Ho525251890_state @ Xo_1 ) )
% 3.42/1.79 <=> ( Xo_1
% 3.42/1.79 = ( some_H1974565227_state @ X_80 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_574_elem__set,axiom,
% 3.42/1.79 ! [X_80: pname,Xo_1: option_pname] :
% 3.42/1.79 ( ( member_pname @ X_80 @ ( set_pname @ Xo_1 ) )
% 3.42/1.79 <=> ( Xo_1
% 3.42/1.79 = ( some_pname @ X_80 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_575_sup_Oidem,axiom,
% 3.42/1.79 ! [A_150: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ A_150 @ A_150 )
% 3.42/1.79 = A_150 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_576_sup_Oidem,axiom,
% 3.42/1.79 ! [A_150: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ A_150 @ A_150 )
% 3.42/1.79 <=> A_150 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_577_sup_Oidem,axiom,
% 3.42/1.79 ! [A_150: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ A_150 @ A_150 )
% 3.42/1.79 = A_150 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_578_sup__idem,axiom,
% 3.42/1.79 ! [X_79: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ X_79 @ X_79 )
% 3.42/1.79 = X_79 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_579_sup__idem,axiom,
% 3.42/1.79 ! [X_79: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ X_79 @ X_79 )
% 3.42/1.79 <=> X_79 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_580_sup__idem,axiom,
% 3.42/1.79 ! [X_79: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ X_79 @ X_79 )
% 3.42/1.79 = X_79 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_581_sup_Ocommute,axiom,
% 3.42/1.79 ! [A_149: pname > $o,B_96: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ A_149 @ B_96 )
% 3.42/1.79 = ( semila1780557381name_o @ B_96 @ A_149 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_582_sup_Ocommute,axiom,
% 3.42/1.79 ! [A_149: $o,B_96: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ A_149 @ B_96 )
% 3.42/1.79 <=> ( semila10642723_sup_o @ B_96 @ A_149 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_583_sup_Ocommute,axiom,
% 3.42/1.79 ! [A_149: hoare_1708887482_state > $o,B_96: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ A_149 @ B_96 )
% 3.42/1.79 = ( semila1122118281tate_o @ B_96 @ A_149 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_584_inf__sup__aci_I5_J,axiom,
% 3.42/1.79 ! [X_78: pname > $o,Y_42: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ X_78 @ Y_42 )
% 3.42/1.79 = ( semila1780557381name_o @ Y_42 @ X_78 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_585_inf__sup__aci_I5_J,axiom,
% 3.42/1.79 ! [X_78: $o,Y_42: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ X_78 @ Y_42 )
% 3.42/1.79 <=> ( semila10642723_sup_o @ Y_42 @ X_78 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_586_inf__sup__aci_I5_J,axiom,
% 3.42/1.79 ! [X_78: hoare_1708887482_state > $o,Y_42: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ X_78 @ Y_42 )
% 3.42/1.79 = ( semila1122118281tate_o @ Y_42 @ X_78 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_587_sup__commute,axiom,
% 3.42/1.79 ! [X_77: pname > $o,Y_41: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ X_77 @ Y_41 )
% 3.42/1.79 = ( semila1780557381name_o @ Y_41 @ X_77 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_588_sup__commute,axiom,
% 3.42/1.79 ! [X_77: $o,Y_41: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ X_77 @ Y_41 )
% 3.42/1.79 <=> ( semila10642723_sup_o @ Y_41 @ X_77 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_589_sup__commute,axiom,
% 3.42/1.79 ! [X_77: hoare_1708887482_state > $o,Y_41: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ X_77 @ Y_41 )
% 3.42/1.79 = ( semila1122118281tate_o @ Y_41 @ X_77 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_590_sup_Oleft__idem,axiom,
% 3.42/1.79 ! [A_148: pname > $o,B_95: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ A_148 @ ( semila1780557381name_o @ A_148 @ B_95 ) )
% 3.42/1.79 = ( semila1780557381name_o @ A_148 @ B_95 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_591_sup_Oleft__idem,axiom,
% 3.42/1.79 ! [A_148: $o,B_95: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ A_148 @ ( semila10642723_sup_o @ A_148 @ B_95 ) )
% 3.42/1.79 <=> ( semila10642723_sup_o @ A_148 @ B_95 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_592_sup_Oleft__idem,axiom,
% 3.42/1.79 ! [A_148: hoare_1708887482_state > $o,B_95: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ A_148 @ ( semila1122118281tate_o @ A_148 @ B_95 ) )
% 3.42/1.79 = ( semila1122118281tate_o @ A_148 @ B_95 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_593_inf__sup__aci_I8_J,axiom,
% 3.42/1.79 ! [X_76: pname > $o,Y_40: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ X_76 @ ( semila1780557381name_o @ X_76 @ Y_40 ) )
% 3.42/1.79 = ( semila1780557381name_o @ X_76 @ Y_40 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_594_inf__sup__aci_I8_J,axiom,
% 3.42/1.79 ! [X_76: $o,Y_40: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ X_76 @ ( semila10642723_sup_o @ X_76 @ Y_40 ) )
% 3.42/1.79 <=> ( semila10642723_sup_o @ X_76 @ Y_40 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_595_inf__sup__aci_I8_J,axiom,
% 3.42/1.79 ! [X_76: hoare_1708887482_state > $o,Y_40: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ X_76 @ ( semila1122118281tate_o @ X_76 @ Y_40 ) )
% 3.42/1.79 = ( semila1122118281tate_o @ X_76 @ Y_40 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_596_sup__left__idem,axiom,
% 3.42/1.79 ! [X_75: pname > $o,Y_39: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ X_75 @ ( semila1780557381name_o @ X_75 @ Y_39 ) )
% 3.42/1.79 = ( semila1780557381name_o @ X_75 @ Y_39 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_597_sup__left__idem,axiom,
% 3.42/1.79 ! [X_75: $o,Y_39: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ X_75 @ ( semila10642723_sup_o @ X_75 @ Y_39 ) )
% 3.42/1.79 <=> ( semila10642723_sup_o @ X_75 @ Y_39 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_598_sup__left__idem,axiom,
% 3.42/1.79 ! [X_75: hoare_1708887482_state > $o,Y_39: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ X_75 @ ( semila1122118281tate_o @ X_75 @ Y_39 ) )
% 3.42/1.79 = ( semila1122118281tate_o @ X_75 @ Y_39 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_599_sup_Oleft__commute,axiom,
% 3.42/1.79 ! [B_94: pname > $o,A_147: pname > $o,C_40: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ B_94 @ ( semila1780557381name_o @ A_147 @ C_40 ) )
% 3.42/1.79 = ( semila1780557381name_o @ A_147 @ ( semila1780557381name_o @ B_94 @ C_40 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_600_sup_Oleft__commute,axiom,
% 3.42/1.79 ! [B_94: $o,A_147: $o,C_40: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ B_94 @ ( semila10642723_sup_o @ A_147 @ C_40 ) )
% 3.42/1.79 <=> ( semila10642723_sup_o @ A_147 @ ( semila10642723_sup_o @ B_94 @ C_40 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_601_sup_Oleft__commute,axiom,
% 3.42/1.79 ! [B_94: hoare_1708887482_state > $o,A_147: hoare_1708887482_state > $o,C_40: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ B_94 @ ( semila1122118281tate_o @ A_147 @ C_40 ) )
% 3.42/1.79 = ( semila1122118281tate_o @ A_147 @ ( semila1122118281tate_o @ B_94 @ C_40 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_602_inf__sup__aci_I7_J,axiom,
% 3.42/1.79 ! [X_74: pname > $o,Y_38: pname > $o,Z_18: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ X_74 @ ( semila1780557381name_o @ Y_38 @ Z_18 ) )
% 3.42/1.79 = ( semila1780557381name_o @ Y_38 @ ( semila1780557381name_o @ X_74 @ Z_18 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_603_inf__sup__aci_I7_J,axiom,
% 3.42/1.79 ! [X_74: $o,Y_38: $o,Z_18: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ X_74 @ ( semila10642723_sup_o @ Y_38 @ Z_18 ) )
% 3.42/1.79 <=> ( semila10642723_sup_o @ Y_38 @ ( semila10642723_sup_o @ X_74 @ Z_18 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_604_inf__sup__aci_I7_J,axiom,
% 3.42/1.79 ! [X_74: hoare_1708887482_state > $o,Y_38: hoare_1708887482_state > $o,Z_18: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ X_74 @ ( semila1122118281tate_o @ Y_38 @ Z_18 ) )
% 3.42/1.79 = ( semila1122118281tate_o @ Y_38 @ ( semila1122118281tate_o @ X_74 @ Z_18 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_605_sup__left__commute,axiom,
% 3.42/1.79 ! [X_73: pname > $o,Y_37: pname > $o,Z_17: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ X_73 @ ( semila1780557381name_o @ Y_37 @ Z_17 ) )
% 3.42/1.79 = ( semila1780557381name_o @ Y_37 @ ( semila1780557381name_o @ X_73 @ Z_17 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_606_sup__left__commute,axiom,
% 3.42/1.79 ! [X_73: $o,Y_37: $o,Z_17: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ X_73 @ ( semila10642723_sup_o @ Y_37 @ Z_17 ) )
% 3.42/1.79 <=> ( semila10642723_sup_o @ Y_37 @ ( semila10642723_sup_o @ X_73 @ Z_17 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_607_sup__left__commute,axiom,
% 3.42/1.79 ! [X_73: hoare_1708887482_state > $o,Y_37: hoare_1708887482_state > $o,Z_17: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ X_73 @ ( semila1122118281tate_o @ Y_37 @ Z_17 ) )
% 3.42/1.79 = ( semila1122118281tate_o @ Y_37 @ ( semila1122118281tate_o @ X_73 @ Z_17 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_608_sup_Oassoc,axiom,
% 3.42/1.79 ! [A_146: pname > $o,B_93: pname > $o,C_39: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ ( semila1780557381name_o @ A_146 @ B_93 ) @ C_39 )
% 3.42/1.79 = ( semila1780557381name_o @ A_146 @ ( semila1780557381name_o @ B_93 @ C_39 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_609_sup_Oassoc,axiom,
% 3.42/1.79 ! [A_146: $o,B_93: $o,C_39: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ A_146 @ B_93 ) @ C_39 )
% 3.42/1.79 <=> ( semila10642723_sup_o @ A_146 @ ( semila10642723_sup_o @ B_93 @ C_39 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_610_sup_Oassoc,axiom,
% 3.42/1.79 ! [A_146: hoare_1708887482_state > $o,B_93: hoare_1708887482_state > $o,C_39: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A_146 @ B_93 ) @ C_39 )
% 3.42/1.79 = ( semila1122118281tate_o @ A_146 @ ( semila1122118281tate_o @ B_93 @ C_39 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_611_inf__sup__aci_I6_J,axiom,
% 3.42/1.79 ! [X_72: pname > $o,Y_36: pname > $o,Z_16: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ ( semila1780557381name_o @ X_72 @ Y_36 ) @ Z_16 )
% 3.42/1.79 = ( semila1780557381name_o @ X_72 @ ( semila1780557381name_o @ Y_36 @ Z_16 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_612_inf__sup__aci_I6_J,axiom,
% 3.42/1.79 ! [X_72: $o,Y_36: $o,Z_16: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ X_72 @ Y_36 ) @ Z_16 )
% 3.42/1.79 <=> ( semila10642723_sup_o @ X_72 @ ( semila10642723_sup_o @ Y_36 @ Z_16 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_613_inf__sup__aci_I6_J,axiom,
% 3.42/1.79 ! [X_72: hoare_1708887482_state > $o,Y_36: hoare_1708887482_state > $o,Z_16: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ X_72 @ Y_36 ) @ Z_16 )
% 3.42/1.79 = ( semila1122118281tate_o @ X_72 @ ( semila1122118281tate_o @ Y_36 @ Z_16 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_614_sup__assoc,axiom,
% 3.42/1.79 ! [X_71: pname > $o,Y_35: pname > $o,Z_15: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ ( semila1780557381name_o @ X_71 @ Y_35 ) @ Z_15 )
% 3.42/1.79 = ( semila1780557381name_o @ X_71 @ ( semila1780557381name_o @ Y_35 @ Z_15 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_615_sup__assoc,axiom,
% 3.42/1.79 ! [X_71: $o,Y_35: $o,Z_15: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ X_71 @ Y_35 ) @ Z_15 )
% 3.42/1.79 <=> ( semila10642723_sup_o @ X_71 @ ( semila10642723_sup_o @ Y_35 @ Z_15 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_616_sup__assoc,axiom,
% 3.42/1.79 ! [X_71: hoare_1708887482_state > $o,Y_35: hoare_1708887482_state > $o,Z_15: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ X_71 @ Y_35 ) @ Z_15 )
% 3.42/1.79 = ( semila1122118281tate_o @ X_71 @ ( semila1122118281tate_o @ Y_35 @ Z_15 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_617_inf__sup__ord_I3_J,axiom,
% 3.42/1.79 ! [X_70: pname > $o,Y_34: pname > $o] : ( ord_less_eq_pname_o @ X_70 @ ( semila1780557381name_o @ X_70 @ Y_34 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_618_inf__sup__ord_I3_J,axiom,
% 3.42/1.79 ! [X_70: $o,Y_34: $o] : ( ord_less_eq_o @ X_70 @ ( semila10642723_sup_o @ X_70 @ Y_34 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_619_inf__sup__ord_I3_J,axiom,
% 3.42/1.79 ! [X_70: hoare_1708887482_state > $o,Y_34: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ X_70 @ ( semila1122118281tate_o @ X_70 @ Y_34 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_620_sup__ge1,axiom,
% 3.42/1.79 ! [X_69: pname > $o,Y_33: pname > $o] : ( ord_less_eq_pname_o @ X_69 @ ( semila1780557381name_o @ X_69 @ Y_33 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_621_sup__ge1,axiom,
% 3.42/1.79 ! [X_69: $o,Y_33: $o] : ( ord_less_eq_o @ X_69 @ ( semila10642723_sup_o @ X_69 @ Y_33 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_622_sup__ge1,axiom,
% 3.42/1.79 ! [X_69: hoare_1708887482_state > $o,Y_33: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ X_69 @ ( semila1122118281tate_o @ X_69 @ Y_33 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_623_inf__sup__ord_I4_J,axiom,
% 3.42/1.79 ! [Y_32: pname > $o,X_68: pname > $o] : ( ord_less_eq_pname_o @ Y_32 @ ( semila1780557381name_o @ X_68 @ Y_32 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_624_inf__sup__ord_I4_J,axiom,
% 3.42/1.79 ! [Y_32: $o,X_68: $o] : ( ord_less_eq_o @ Y_32 @ ( semila10642723_sup_o @ X_68 @ Y_32 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_625_inf__sup__ord_I4_J,axiom,
% 3.42/1.79 ! [Y_32: hoare_1708887482_state > $o,X_68: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ Y_32 @ ( semila1122118281tate_o @ X_68 @ Y_32 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_626_sup__ge2,axiom,
% 3.42/1.79 ! [Y_31: pname > $o,X_67: pname > $o] : ( ord_less_eq_pname_o @ Y_31 @ ( semila1780557381name_o @ X_67 @ Y_31 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_627_sup__ge2,axiom,
% 3.42/1.79 ! [Y_31: $o,X_67: $o] : ( ord_less_eq_o @ Y_31 @ ( semila10642723_sup_o @ X_67 @ Y_31 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_628_sup__ge2,axiom,
% 3.42/1.79 ! [Y_31: hoare_1708887482_state > $o,X_67: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ Y_31 @ ( semila1122118281tate_o @ X_67 @ Y_31 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_629_le__iff__sup,axiom,
% 3.42/1.79 ! [X_66: pname > $o,Y_30: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ X_66 @ Y_30 )
% 3.42/1.79 <=> ( ( semila1780557381name_o @ X_66 @ Y_30 )
% 3.42/1.79 = Y_30 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_630_le__iff__sup,axiom,
% 3.42/1.79 ! [X_66: $o,Y_30: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ X_66 @ Y_30 )
% 3.42/1.79 <=> ( ( semila10642723_sup_o @ X_66 @ Y_30 )
% 3.42/1.79 <=> Y_30 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_631_le__iff__sup,axiom,
% 3.42/1.79 ! [X_66: hoare_1708887482_state > $o,Y_30: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ X_66 @ Y_30 )
% 3.42/1.79 <=> ( ( semila1122118281tate_o @ X_66 @ Y_30 )
% 3.42/1.79 = Y_30 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_632_le__sup__iff,axiom,
% 3.42/1.79 ! [X_65: pname > $o,Y_29: pname > $o,Z_14: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_65 @ Y_29 ) @ Z_14 )
% 3.42/1.79 <=> ( ( ord_less_eq_pname_o @ X_65 @ Z_14 )
% 3.42/1.79 & ( ord_less_eq_pname_o @ Y_29 @ Z_14 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_633_le__sup__iff,axiom,
% 3.42/1.79 ! [X_65: $o,Y_29: $o,Z_14: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ ( semila10642723_sup_o @ X_65 @ Y_29 ) @ Z_14 )
% 3.42/1.79 <=> ( ( ord_less_eq_o @ X_65 @ Z_14 )
% 3.42/1.79 & ( ord_less_eq_o @ Y_29 @ Z_14 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_634_le__sup__iff,axiom,
% 3.42/1.79 ! [X_65: hoare_1708887482_state > $o,Y_29: hoare_1708887482_state > $o,Z_14: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ ( semila1122118281tate_o @ X_65 @ Y_29 ) @ Z_14 )
% 3.42/1.79 <=> ( ( ord_le777019615tate_o @ X_65 @ Z_14 )
% 3.42/1.79 & ( ord_le777019615tate_o @ Y_29 @ Z_14 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_635_le__supI1,axiom,
% 3.42/1.79 ! [B_92: pname > $o,X_64: pname > $o,A_145: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ X_64 @ A_145 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ X_64 @ ( semila1780557381name_o @ A_145 @ B_92 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_636_le__supI1,axiom,
% 3.42/1.79 ! [B_92: $o,X_64: $o,A_145: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ X_64 @ A_145 )
% 3.42/1.79 => ( ord_less_eq_o @ X_64 @ ( semila10642723_sup_o @ A_145 @ B_92 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_637_le__supI1,axiom,
% 3.42/1.79 ! [B_92: hoare_1708887482_state > $o,X_64: hoare_1708887482_state > $o,A_145: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ X_64 @ A_145 )
% 3.42/1.79 => ( ord_le777019615tate_o @ X_64 @ ( semila1122118281tate_o @ A_145 @ B_92 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_638_le__supI2,axiom,
% 3.42/1.79 ! [A_144: pname > $o,X_63: pname > $o,B_91: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ X_63 @ B_91 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ X_63 @ ( semila1780557381name_o @ A_144 @ B_91 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_639_le__supI2,axiom,
% 3.42/1.79 ! [A_144: $o,X_63: $o,B_91: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ X_63 @ B_91 )
% 3.42/1.79 => ( ord_less_eq_o @ X_63 @ ( semila10642723_sup_o @ A_144 @ B_91 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_640_le__supI2,axiom,
% 3.42/1.79 ! [A_144: hoare_1708887482_state > $o,X_63: hoare_1708887482_state > $o,B_91: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ X_63 @ B_91 )
% 3.42/1.79 => ( ord_le777019615tate_o @ X_63 @ ( semila1122118281tate_o @ A_144 @ B_91 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_641_sup__absorb2,axiom,
% 3.42/1.79 ! [X_62: pname > $o,Y_28: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ X_62 @ Y_28 )
% 3.42/1.79 => ( ( semila1780557381name_o @ X_62 @ Y_28 )
% 3.42/1.79 = Y_28 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_642_sup__absorb2,axiom,
% 3.42/1.79 ! [X_62: $o,Y_28: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ X_62 @ Y_28 )
% 3.42/1.79 => ( ( semila10642723_sup_o @ X_62 @ Y_28 )
% 3.42/1.79 <=> Y_28 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_643_sup__absorb2,axiom,
% 3.42/1.79 ! [X_62: hoare_1708887482_state > $o,Y_28: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ X_62 @ Y_28 )
% 3.42/1.79 => ( ( semila1122118281tate_o @ X_62 @ Y_28 )
% 3.42/1.79 = Y_28 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_644_sup__absorb1,axiom,
% 3.42/1.79 ! [Y_27: pname > $o,X_61: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ Y_27 @ X_61 )
% 3.42/1.79 => ( ( semila1780557381name_o @ X_61 @ Y_27 )
% 3.42/1.79 = X_61 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_645_sup__absorb1,axiom,
% 3.42/1.79 ! [Y_27: $o,X_61: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ Y_27 @ X_61 )
% 3.42/1.79 => ( ( semila10642723_sup_o @ X_61 @ Y_27 )
% 3.42/1.79 <=> X_61 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_646_sup__absorb1,axiom,
% 3.42/1.79 ! [Y_27: hoare_1708887482_state > $o,X_61: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ Y_27 @ X_61 )
% 3.42/1.79 => ( ( semila1122118281tate_o @ X_61 @ Y_27 )
% 3.42/1.79 = X_61 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_647_le__supI,axiom,
% 3.42/1.79 ! [B_90: pname > $o,A_143: pname > $o,X_60: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ A_143 @ X_60 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ B_90 @ X_60 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_143 @ B_90 ) @ X_60 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_648_le__supI,axiom,
% 3.42/1.79 ! [B_90: $o,A_143: $o,X_60: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ A_143 @ X_60 )
% 3.42/1.79 => ( ( ord_less_eq_o @ B_90 @ X_60 )
% 3.42/1.79 => ( ord_less_eq_o @ ( semila10642723_sup_o @ A_143 @ B_90 ) @ X_60 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_649_le__supI,axiom,
% 3.42/1.79 ! [B_90: hoare_1708887482_state > $o,A_143: hoare_1708887482_state > $o,X_60: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ A_143 @ X_60 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ B_90 @ X_60 )
% 3.42/1.79 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_143 @ B_90 ) @ X_60 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_650_sup__least,axiom,
% 3.42/1.79 ! [Z_13: pname > $o,Y_26: pname > $o,X_59: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ Y_26 @ X_59 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ Z_13 @ X_59 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ Y_26 @ Z_13 ) @ X_59 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_651_sup__least,axiom,
% 3.42/1.79 ! [Z_13: $o,Y_26: $o,X_59: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ Y_26 @ X_59 )
% 3.42/1.79 => ( ( ord_less_eq_o @ Z_13 @ X_59 )
% 3.42/1.79 => ( ord_less_eq_o @ ( semila10642723_sup_o @ Y_26 @ Z_13 ) @ X_59 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_652_sup__least,axiom,
% 3.42/1.79 ! [Z_13: hoare_1708887482_state > $o,Y_26: hoare_1708887482_state > $o,X_59: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ Y_26 @ X_59 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ Z_13 @ X_59 )
% 3.42/1.79 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ Y_26 @ Z_13 ) @ X_59 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_653_sup__mono,axiom,
% 3.42/1.79 ! [B_89: pname > $o,D_4: pname > $o,A_142: pname > $o,C_38: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ A_142 @ C_38 )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ B_89 @ D_4 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_142 @ B_89 ) @ ( semila1780557381name_o @ C_38 @ D_4 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_654_sup__mono,axiom,
% 3.42/1.79 ! [B_89: $o,D_4: $o,A_142: $o,C_38: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ A_142 @ C_38 )
% 3.42/1.79 => ( ( ord_less_eq_o @ B_89 @ D_4 )
% 3.42/1.79 => ( ord_less_eq_o @ ( semila10642723_sup_o @ A_142 @ B_89 ) @ ( semila10642723_sup_o @ C_38 @ D_4 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_655_sup__mono,axiom,
% 3.42/1.79 ! [B_89: hoare_1708887482_state > $o,D_4: hoare_1708887482_state > $o,A_142: hoare_1708887482_state > $o,C_38: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ A_142 @ C_38 )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ B_89 @ D_4 )
% 3.42/1.79 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_142 @ B_89 ) @ ( semila1122118281tate_o @ C_38 @ D_4 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_656_le__supE,axiom,
% 3.42/1.79 ! [A_141: pname > $o,B_88: pname > $o,X_58: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_141 @ B_88 ) @ X_58 )
% 3.42/1.79 => ~ ( ( ord_less_eq_pname_o @ A_141 @ X_58 )
% 3.42/1.79 => ~ ( ord_less_eq_pname_o @ B_88 @ X_58 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_657_le__supE,axiom,
% 3.42/1.79 ! [A_141: $o,B_88: $o,X_58: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ ( semila10642723_sup_o @ A_141 @ B_88 ) @ X_58 )
% 3.42/1.79 => ~ ( ( ord_less_eq_o @ A_141 @ X_58 )
% 3.42/1.79 => ~ ( ord_less_eq_o @ B_88 @ X_58 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_658_le__supE,axiom,
% 3.42/1.79 ! [A_141: hoare_1708887482_state > $o,B_88: hoare_1708887482_state > $o,X_58: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_141 @ B_88 ) @ X_58 )
% 3.42/1.79 => ~ ( ( ord_le777019615tate_o @ A_141 @ X_58 )
% 3.42/1.79 => ~ ( ord_le777019615tate_o @ B_88 @ X_58 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_659_sup__bot__left,axiom,
% 3.42/1.79 ! [X_57: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ bot_bot_pname_o @ X_57 )
% 3.42/1.79 = X_57 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_660_sup__bot__left,axiom,
% 3.42/1.79 ! [X_57: com > $o] :
% 3.42/1.79 ( ( semila1562558655_com_o @ bot_bot_com_o @ X_57 )
% 3.42/1.79 = X_57 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_661_sup__bot__left,axiom,
% 3.42/1.79 ! [X_57: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ bot_bot_o @ X_57 )
% 3.42/1.79 <=> X_57 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_662_sup__bot__left,axiom,
% 3.42/1.79 ! [X_57: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ bot_bo19817387tate_o @ X_57 )
% 3.42/1.79 = X_57 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_663_sup__bot__right,axiom,
% 3.42/1.79 ! [X_56: pname > $o] :
% 3.42/1.79 ( ( semila1780557381name_o @ X_56 @ bot_bot_pname_o )
% 3.42/1.79 = X_56 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_664_sup__bot__right,axiom,
% 3.42/1.79 ! [X_56: com > $o] :
% 3.42/1.79 ( ( semila1562558655_com_o @ X_56 @ bot_bot_com_o )
% 3.42/1.79 = X_56 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_665_sup__bot__right,axiom,
% 3.42/1.79 ! [X_56: $o] :
% 3.42/1.79 ( ( semila10642723_sup_o @ X_56 @ bot_bot_o )
% 3.42/1.79 <=> X_56 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_666_sup__bot__right,axiom,
% 3.42/1.79 ! [X_56: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila1122118281tate_o @ X_56 @ bot_bo19817387tate_o )
% 3.42/1.79 = X_56 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_667_ospec,axiom,
% 3.42/1.79 ! [X_55: pname,P_15: pname > $o,A_140: option_pname] :
% 3.42/1.79 ( ! [X_3: pname] :
% 3.42/1.79 ( ( member_pname @ X_3 @ ( set_pname @ A_140 ) )
% 3.42/1.79 => ( P_15 @ X_3 ) )
% 3.42/1.79 => ( ( A_140
% 3.42/1.79 = ( some_pname @ X_55 ) )
% 3.42/1.79 => ( P_15 @ X_55 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_668_ospec,axiom,
% 3.42/1.79 ! [X_55: hoare_1708887482_state,P_15: hoare_1708887482_state > $o,A_140: option1624383643_state] :
% 3.42/1.79 ( ! [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( member451959335_state @ X_3 @ ( set_Ho525251890_state @ A_140 ) )
% 3.42/1.79 => ( P_15 @ X_3 ) )
% 3.42/1.79 => ( ( A_140
% 3.42/1.79 = ( some_H1974565227_state @ X_55 ) )
% 3.42/1.79 => ( P_15 @ X_55 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_669_ospec,axiom,
% 3.42/1.79 ! [X_55: com,P_15: com > $o,A_140: option_com] :
% 3.42/1.79 ( ! [X_3: com] :
% 3.42/1.79 ( ( member_com @ X_3 @ ( set_com @ A_140 ) )
% 3.42/1.79 => ( P_15 @ X_3 ) )
% 3.42/1.79 => ( ( A_140
% 3.42/1.79 = ( some_com @ X_55 ) )
% 3.42/1.79 => ( P_15 @ X_55 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_670_folding__one__idem_Ounion__idem,axiom,
% 3.42/1.79 ! [B_87: ( pname > $o ) > $o,A_139: ( pname > $o ) > $o,F_59: ( pname > $o ) > ( pname > $o ) > pname > $o,F_58: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.42/1.79 ( ( finite697516351name_o @ F_59 @ F_58 )
% 3.42/1.79 => ( ( finite297249702name_o @ A_139 )
% 3.42/1.79 => ( ( A_139 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ( finite297249702name_o @ B_87 )
% 3.42/1.79 => ( ( B_87 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ( F_58 @ ( semila181081674me_o_o @ A_139 @ B_87 ) )
% 3.42/1.79 = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_671_folding__one__idem_Ounion__idem,axiom,
% 3.42/1.79 ! [B_87: ( hoare_1708887482_state > $o ) > $o,A_139: ( hoare_1708887482_state > $o ) > $o,F_59: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_58: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite621643279tate_o @ F_59 @ F_58 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ A_139 )
% 3.42/1.79 => ( ( A_139 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( finite1329924456tate_o @ B_87 )
% 3.42/1.79 => ( ( B_87 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( F_58 @ ( semila1853742644te_o_o @ A_139 @ B_87 ) )
% 3.42/1.79 = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_672_folding__one__idem_Ounion__idem,axiom,
% 3.42/1.79 ! [B_87: com > $o,A_139: com > $o,F_59: com > com > com,F_58: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite666746948em_com @ F_59 @ F_58 )
% 3.42/1.79 => ( ( finite_finite_com @ A_139 )
% 3.42/1.79 => ( ( A_139 != bot_bot_com_o )
% 3.42/1.79 => ( ( finite_finite_com @ B_87 )
% 3.42/1.79 => ( ( B_87 != bot_bot_com_o )
% 3.42/1.79 => ( ( F_58 @ ( semila1562558655_com_o @ A_139 @ B_87 ) )
% 3.42/1.79 = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_673_folding__one__idem_Ounion__idem,axiom,
% 3.42/1.79 ! [B_87: hoare_1708887482_state > $o,A_139: hoare_1708887482_state > $o,F_59: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_58: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1347568576_state @ F_59 @ F_58 )
% 3.42/1.79 => ( ( finite1625599783_state @ A_139 )
% 3.42/1.79 => ( ( A_139 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ( finite1625599783_state @ B_87 )
% 3.42/1.79 => ( ( B_87 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ( F_58 @ ( semila1122118281tate_o @ A_139 @ B_87 ) )
% 3.42/1.79 = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_674_folding__one__idem_Ounion__idem,axiom,
% 3.42/1.79 ! [B_87: pname > $o,A_139: pname > $o,F_59: pname > pname > pname,F_58: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite89670078_pname @ F_59 @ F_58 )
% 3.42/1.79 => ( ( finite_finite_pname @ A_139 )
% 3.42/1.79 => ( ( A_139 != bot_bot_pname_o )
% 3.42/1.79 => ( ( finite_finite_pname @ B_87 )
% 3.42/1.79 => ( ( B_87 != bot_bot_pname_o )
% 3.42/1.79 => ( ( F_58 @ ( semila1780557381name_o @ A_139 @ B_87 ) )
% 3.42/1.79 = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_675_folding__one__idem_Osubset__idem,axiom,
% 3.42/1.79 ! [B_86: ( pname > $o ) > $o,A_138: ( pname > $o ) > $o,F_57: ( pname > $o ) > ( pname > $o ) > pname > $o,F_56: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.42/1.79 ( ( finite697516351name_o @ F_57 @ F_56 )
% 3.42/1.79 => ( ( finite297249702name_o @ A_138 )
% 3.42/1.79 => ( ( B_86 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ( ord_le1205211808me_o_o @ B_86 @ A_138 )
% 3.42/1.79 => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
% 3.42/1.79 = ( F_56 @ A_138 ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_676_folding__one__idem_Osubset__idem,axiom,
% 3.42/1.79 ! [B_86: ( hoare_1708887482_state > $o ) > $o,A_138: ( hoare_1708887482_state > $o ) > $o,F_57: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_56: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite621643279tate_o @ F_57 @ F_56 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ A_138 )
% 3.42/1.79 => ( ( B_86 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( ord_le1728773982te_o_o @ B_86 @ A_138 )
% 3.42/1.79 => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
% 3.42/1.79 = ( F_56 @ A_138 ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_677_folding__one__idem_Osubset__idem,axiom,
% 3.42/1.79 ! [B_86: com > $o,A_138: com > $o,F_57: com > com > com,F_56: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite666746948em_com @ F_57 @ F_56 )
% 3.42/1.79 => ( ( finite_finite_com @ A_138 )
% 3.42/1.79 => ( ( B_86 != bot_bot_com_o )
% 3.42/1.79 => ( ( ord_less_eq_com_o @ B_86 @ A_138 )
% 3.42/1.79 => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
% 3.42/1.79 = ( F_56 @ A_138 ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_678_folding__one__idem_Osubset__idem,axiom,
% 3.42/1.79 ! [B_86: hoare_1708887482_state > $o,A_138: hoare_1708887482_state > $o,F_57: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_56: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1347568576_state @ F_57 @ F_56 )
% 3.42/1.79 => ( ( finite1625599783_state @ A_138 )
% 3.42/1.79 => ( ( B_86 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ B_86 @ A_138 )
% 3.42/1.79 => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
% 3.42/1.79 = ( F_56 @ A_138 ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_679_folding__one__idem_Osubset__idem,axiom,
% 3.42/1.79 ! [B_86: pname > $o,A_138: pname > $o,F_57: pname > pname > pname,F_56: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite89670078_pname @ F_57 @ F_56 )
% 3.42/1.79 => ( ( finite_finite_pname @ A_138 )
% 3.42/1.79 => ( ( B_86 != bot_bot_pname_o )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ B_86 @ A_138 )
% 3.42/1.79 => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
% 3.42/1.79 = ( F_56 @ A_138 ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_680_hoare__derivs_OSkip,axiom,
% 3.42/1.79 ! [G_11: hoare_1708887482_state > $o,P_14: state > state > $o] : ( hoare_90032982_state @ G_11 @ ( insert528405184_state @ ( hoare_858012674_state @ P_14 @ skip @ P_14 ) @ bot_bo19817387tate_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_681_folding__one__idem_Oinsert__idem,axiom,
% 3.42/1.79 ! [X_54: com,A_137: com > $o,F_55: com > com > com,F_54: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite666746948em_com @ F_55 @ F_54 )
% 3.42/1.79 => ( ( finite_finite_com @ A_137 )
% 3.42/1.79 => ( ( A_137 != bot_bot_com_o )
% 3.42/1.79 => ( ( F_54 @ ( insert_com @ X_54 @ A_137 ) )
% 3.42/1.79 = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_682_folding__one__idem_Oinsert__idem,axiom,
% 3.42/1.79 ! [X_54: pname > $o,A_137: ( pname > $o ) > $o,F_55: ( pname > $o ) > ( pname > $o ) > pname > $o,F_54: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.42/1.79 ( ( finite697516351name_o @ F_55 @ F_54 )
% 3.42/1.79 => ( ( finite297249702name_o @ A_137 )
% 3.42/1.79 => ( ( A_137 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ( F_54 @ ( insert_pname_o @ X_54 @ A_137 ) )
% 3.42/1.79 = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_683_folding__one__idem_Oinsert__idem,axiom,
% 3.42/1.79 ! [X_54: hoare_1708887482_state > $o,A_137: ( hoare_1708887482_state > $o ) > $o,F_55: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_54: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite621643279tate_o @ F_55 @ F_54 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ A_137 )
% 3.42/1.79 => ( ( A_137 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( F_54 @ ( insert949073679tate_o @ X_54 @ A_137 ) )
% 3.42/1.79 = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_684_folding__one__idem_Oinsert__idem,axiom,
% 3.42/1.79 ! [X_54: pname,A_137: pname > $o,F_55: pname > pname > pname,F_54: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite89670078_pname @ F_55 @ F_54 )
% 3.42/1.79 => ( ( finite_finite_pname @ A_137 )
% 3.42/1.79 => ( ( A_137 != bot_bot_pname_o )
% 3.42/1.79 => ( ( F_54 @ ( insert_pname @ X_54 @ A_137 ) )
% 3.42/1.79 = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_685_folding__one__idem_Oinsert__idem,axiom,
% 3.42/1.79 ! [X_54: hoare_1708887482_state,A_137: hoare_1708887482_state > $o,F_55: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_54: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1347568576_state @ F_55 @ F_54 )
% 3.42/1.79 => ( ( finite1625599783_state @ A_137 )
% 3.42/1.79 => ( ( A_137 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ( F_54 @ ( insert528405184_state @ X_54 @ A_137 ) )
% 3.42/1.79 = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_686_finite__ne__induct,axiom,
% 3.42/1.79 ! [P_13: ( com > $o ) > $o,F_52: com > $o] :
% 3.42/1.79 ( ( finite_finite_com @ F_52 )
% 3.42/1.79 => ( ( F_52 != bot_bot_com_o )
% 3.42/1.79 => ( ! [X_3: com] : ( P_13 @ ( insert_com @ X_3 @ bot_bot_com_o ) )
% 3.42/1.79 => ( ! [X_3: com,F_53: com > $o] :
% 3.42/1.79 ( ( finite_finite_com @ F_53 )
% 3.42/1.79 => ( ( F_53 != bot_bot_com_o )
% 3.42/1.79 => ( ~ ( member_com @ X_3 @ F_53 )
% 3.42/1.79 => ( ( P_13 @ F_53 )
% 3.42/1.79 => ( P_13 @ ( insert_com @ X_3 @ F_53 ) ) ) ) ) )
% 3.42/1.79 => ( P_13 @ F_52 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_687_finite__ne__induct,axiom,
% 3.42/1.79 ! [P_13: ( ( pname > $o ) > $o ) > $o,F_52: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( finite297249702name_o @ F_52 )
% 3.42/1.79 => ( ( F_52 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ! [X_3: pname > $o] : ( P_13 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
% 3.42/1.79 => ( ! [X_3: pname > $o,F_53: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( finite297249702name_o @ F_53 )
% 3.42/1.79 => ( ( F_53 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ~ ( member_pname_o @ X_3 @ F_53 )
% 3.42/1.79 => ( ( P_13 @ F_53 )
% 3.42/1.79 => ( P_13 @ ( insert_pname_o @ X_3 @ F_53 ) ) ) ) ) )
% 3.42/1.79 => ( P_13 @ F_52 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_688_finite__ne__induct,axiom,
% 3.42/1.79 ! [P_13: ( ( hoare_1708887482_state > $o ) > $o ) > $o,F_52: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( finite1329924456tate_o @ F_52 )
% 3.42/1.79 => ( ( F_52 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ! [X_3: hoare_1708887482_state > $o] : ( P_13 @ ( insert949073679tate_o @ X_3 @ bot_bo1678742418te_o_o ) )
% 3.42/1.79 => ( ! [X_3: hoare_1708887482_state > $o,F_53: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( finite1329924456tate_o @ F_53 )
% 3.42/1.79 => ( ( F_53 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ~ ( member814030440tate_o @ X_3 @ F_53 )
% 3.42/1.79 => ( ( P_13 @ F_53 )
% 3.42/1.79 => ( P_13 @ ( insert949073679tate_o @ X_3 @ F_53 ) ) ) ) ) )
% 3.42/1.79 => ( P_13 @ F_52 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_689_finite__ne__induct,axiom,
% 3.42/1.79 ! [P_13: ( pname > $o ) > $o,F_52: pname > $o] :
% 3.42/1.79 ( ( finite_finite_pname @ F_52 )
% 3.42/1.79 => ( ( F_52 != bot_bot_pname_o )
% 3.42/1.79 => ( ! [X_3: pname] : ( P_13 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
% 3.42/1.79 => ( ! [X_3: pname,F_53: pname > $o] :
% 3.42/1.79 ( ( finite_finite_pname @ F_53 )
% 3.42/1.79 => ( ( F_53 != bot_bot_pname_o )
% 3.42/1.79 => ( ~ ( member_pname @ X_3 @ F_53 )
% 3.42/1.79 => ( ( P_13 @ F_53 )
% 3.42/1.79 => ( P_13 @ ( insert_pname @ X_3 @ F_53 ) ) ) ) ) )
% 3.42/1.79 => ( P_13 @ F_52 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_690_finite__ne__induct,axiom,
% 3.42/1.79 ! [P_13: ( hoare_1708887482_state > $o ) > $o,F_52: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite1625599783_state @ F_52 )
% 3.42/1.79 => ( ( F_52 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ! [X_3: hoare_1708887482_state] : ( P_13 @ ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( ! [X_3: hoare_1708887482_state,F_53: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite1625599783_state @ F_53 )
% 3.42/1.79 => ( ( F_53 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ~ ( member451959335_state @ X_3 @ F_53 )
% 3.42/1.79 => ( ( P_13 @ F_53 )
% 3.42/1.79 => ( P_13 @ ( insert528405184_state @ X_3 @ F_53 ) ) ) ) ) )
% 3.42/1.79 => ( P_13 @ F_52 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_691_LoopF,axiom,
% 3.42/1.79 ! [G_10: hoare_1708887482_state > $o,P_12: state > state > $o,B_85: state > $o,C_37: com] :
% 3.42/1.79 ( hoare_90032982_state @ G_10
% 3.42/1.79 @ ( insert528405184_state
% 3.42/1.79 @ ( hoare_858012674_state
% 3.42/1.79 @ ^ [Z_11: state,S_2: state] : ( (&) @ ( P_12 @ Z_11 @ S_2 ) @ ( (~) @ ( B_85 @ S_2 ) ) )
% 3.42/1.79 @ ( while @ B_85 @ C_37 )
% 3.42/1.79 @ P_12 )
% 3.42/1.79 @ bot_bo19817387tate_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_692_Comp,axiom,
% 3.42/1.79 ! [D_3: com,R_1: state > state > $o,G_9: hoare_1708887482_state > $o,P_11: state > state > $o,C_36: com,Q_6: state > state > $o] :
% 3.42/1.79 ( ( hoare_90032982_state @ G_9 @ ( insert528405184_state @ ( hoare_858012674_state @ P_11 @ C_36 @ Q_6 ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( ( hoare_90032982_state @ G_9 @ ( insert528405184_state @ ( hoare_858012674_state @ Q_6 @ D_3 @ R_1 ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_9 @ ( insert528405184_state @ ( hoare_858012674_state @ P_11 @ ( semi @ C_36 @ D_3 ) @ R_1 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_693_WTs__elim__cases_I6_J,axiom,
% 3.42/1.79 ! [B_82: state > $o,C_34: com] :
% 3.42/1.79 ( ( wt @ ( while @ B_82 @ C_34 ) )
% 3.42/1.79 => ( wt @ C_34 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_694_WTs__elim__cases_I4_J,axiom,
% 3.42/1.79 ! [C1: com,C2: com] :
% 3.42/1.79 ( ( wt @ ( semi @ C1 @ C2 ) )
% 3.42/1.79 => ~ ( ( wt @ C1 )
% 3.42/1.79 => ~ ( wt @ C2 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_695_folding__one__idem_Oidem,axiom,
% 3.42/1.79 ! [X_53: hoare_1708887482_state,F_51: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_50: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1347568576_state @ F_51 @ F_50 )
% 3.42/1.79 => ( ( F_51 @ X_53 @ X_53 )
% 3.42/1.79 = X_53 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_696_folding__one__idem_Oidem,axiom,
% 3.42/1.79 ! [X_53: pname,F_51: pname > pname > pname,F_50: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite89670078_pname @ F_51 @ F_50 )
% 3.42/1.79 => ( ( F_51 @ X_53 @ X_53 )
% 3.42/1.79 = X_53 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_697_com_Osimps_I12_J,axiom,
% 3.42/1.79 ! [Com1_1: com,Com2_1: com] :
% 3.42/1.79 ( skip
% 3.42/1.79 != ( semi @ Com1_1 @ Com2_1 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_698_com_Osimps_I16_J,axiom,
% 3.42/1.79 ! [Fun_1: state > $o,Com_2: com] :
% 3.42/1.79 ( skip
% 3.42/1.79 != ( while @ Fun_1 @ Com_2 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_699_com_Osimps_I13_J,axiom,
% 3.42/1.79 ! [Com1_1: com,Com2_1: com] :
% 3.42/1.79 ( ( semi @ Com1_1 @ Com2_1 )
% 3.42/1.79 != skip ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_700_com_Osimps_I17_J,axiom,
% 3.42/1.79 ! [Fun_1: state > $o,Com_2: com] :
% 3.42/1.79 ( ( while @ Fun_1 @ Com_2 )
% 3.42/1.79 != skip ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_701_com_Osimps_I46_J,axiom,
% 3.42/1.79 ! [Com1: com,Com2: com,Fun_1: state > $o,Com_2: com] :
% 3.42/1.79 ( ( semi @ Com1 @ Com2 )
% 3.42/1.79 != ( while @ Fun_1 @ Com_2 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_702_com_Osimps_I47_J,axiom,
% 3.42/1.79 ! [Fun_1: state > $o,Com_2: com,Com1: com,Com2: com] :
% 3.42/1.79 ( ( while @ Fun_1 @ Com_2 )
% 3.42/1.79 != ( semi @ Com1 @ Com2 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_703_com_Osimps_I3_J,axiom,
% 3.42/1.79 ! [Com1: com,Com2: com,Com1_1: com,Com2_1: com] :
% 3.42/1.79 ( ( ( semi @ Com1 @ Com2 )
% 3.42/1.79 = ( semi @ Com1_1 @ Com2_1 ) )
% 3.42/1.79 <=> ( ( Com1 = Com1_1 )
% 3.42/1.79 & ( Com2 = Com2_1 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_704_com_Osimps_I5_J,axiom,
% 3.42/1.79 ! [Fun: state > $o,Com_1: com,Fun_1: state > $o,Com_2: com] :
% 3.42/1.79 ( ( ( while @ Fun @ Com_1 )
% 3.42/1.79 = ( while @ Fun_1 @ Com_2 ) )
% 3.42/1.79 <=> ( ( Fun = Fun_1 )
% 3.42/1.79 & ( Com_1 = Com_2 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_705_com_Osimps_I59_J,axiom,
% 3.42/1.79 ! [Pname: pname,Fun: state > $o,Com_1: com] :
% 3.42/1.79 ( ( body_1 @ Pname )
% 3.42/1.79 != ( while @ Fun @ Com_1 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_706_com_Osimps_I58_J,axiom,
% 3.42/1.79 ! [Fun: state > $o,Com_1: com,Pname: pname] :
% 3.42/1.79 ( ( while @ Fun @ Com_1 )
% 3.42/1.79 != ( body_1 @ Pname ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_707_While,axiom,
% 3.42/1.79 ! [B_82: state > $o,C_34: com] :
% 3.42/1.79 ( ( wt @ C_34 )
% 3.42/1.79 => ( wt @ ( while @ B_82 @ C_34 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_708_com_Osimps_I49_J,axiom,
% 3.42/1.79 ! [Pname: pname,Com1: com,Com2: com] :
% 3.42/1.79 ( ( body_1 @ Pname )
% 3.42/1.79 != ( semi @ Com1 @ Com2 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_709_com_Osimps_I48_J,axiom,
% 3.42/1.79 ! [Com1: com,Com2: com,Pname: pname] :
% 3.42/1.79 ( ( semi @ Com1 @ Com2 )
% 3.42/1.79 != ( body_1 @ Pname ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_710_WT_OSemi,axiom,
% 3.42/1.79 ! [C1: com,C0: com] :
% 3.42/1.79 ( ( wt @ C0 )
% 3.42/1.79 => ( ( wt @ C1 )
% 3.42/1.79 => ( wt @ ( semi @ C0 @ C1 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_711_com_Osimps_I18_J,axiom,
% 3.42/1.79 ! [Pname: pname] :
% 3.42/1.79 ( skip
% 3.42/1.79 != ( body_1 @ Pname ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_712_com_Osimps_I19_J,axiom,
% 3.42/1.79 ! [Pname: pname] :
% 3.42/1.79 ( ( body_1 @ Pname )
% 3.42/1.79 != skip ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_713_WT_OSkip,axiom,
% 3.42/1.79 wt @ skip ).
% 3.42/1.79
% 3.42/1.79 thf(fact_714_folding__one__idem_Oin__idem,axiom,
% 3.42/1.79 ! [X_52: com,A_136: com > $o,F_49: com > com > com,F_48: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite666746948em_com @ F_49 @ F_48 )
% 3.42/1.79 => ( ( finite_finite_com @ A_136 )
% 3.42/1.79 => ( ( member_com @ X_52 @ A_136 )
% 3.42/1.79 => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
% 3.42/1.79 = ( F_48 @ A_136 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_715_folding__one__idem_Oin__idem,axiom,
% 3.42/1.79 ! [X_52: pname,A_136: pname > $o,F_49: pname > pname > pname,F_48: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite89670078_pname @ F_49 @ F_48 )
% 3.42/1.79 => ( ( finite_finite_pname @ A_136 )
% 3.42/1.79 => ( ( member_pname @ X_52 @ A_136 )
% 3.42/1.79 => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
% 3.42/1.79 = ( F_48 @ A_136 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_716_folding__one__idem_Oin__idem,axiom,
% 3.42/1.79 ! [X_52: hoare_1708887482_state,A_136: hoare_1708887482_state > $o,F_49: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_48: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1347568576_state @ F_49 @ F_48 )
% 3.42/1.79 => ( ( finite1625599783_state @ A_136 )
% 3.42/1.79 => ( ( member451959335_state @ X_52 @ A_136 )
% 3.42/1.79 => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
% 3.42/1.79 = ( F_48 @ A_136 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_717_folding__one__idem_Oin__idem,axiom,
% 3.42/1.79 ! [X_52: pname > $o,A_136: ( pname > $o ) > $o,F_49: ( pname > $o ) > ( pname > $o ) > pname > $o,F_48: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.42/1.79 ( ( finite697516351name_o @ F_49 @ F_48 )
% 3.42/1.79 => ( ( finite297249702name_o @ A_136 )
% 3.42/1.79 => ( ( member_pname_o @ X_52 @ A_136 )
% 3.42/1.79 => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
% 3.42/1.79 = ( F_48 @ A_136 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_718_folding__one__idem_Oin__idem,axiom,
% 3.42/1.79 ! [X_52: hoare_1708887482_state > $o,A_136: ( hoare_1708887482_state > $o ) > $o,F_49: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_48: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite621643279tate_o @ F_49 @ F_48 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ A_136 )
% 3.42/1.79 => ( ( member814030440tate_o @ X_52 @ A_136 )
% 3.42/1.79 => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
% 3.42/1.79 = ( F_48 @ A_136 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_719_folding__one__idem_Ohom__commute,axiom,
% 3.42/1.79 ! [N_1: ( pname > $o ) > $o,H_1: ( pname > $o ) > pname > $o,F_47: ( pname > $o ) > ( pname > $o ) > pname > $o,F_46: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.42/1.79 ( ( finite697516351name_o @ F_47 @ F_46 )
% 3.42/1.79 => ( ! [X_3: pname > $o,Y_4: pname > $o] :
% 3.42/1.79 ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
% 3.42/1.79 = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
% 3.42/1.79 => ( ( finite297249702name_o @ N_1 )
% 3.42/1.79 => ( ( N_1 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ( H_1 @ ( F_46 @ N_1 ) )
% 3.42/1.79 = ( F_46 @ ( image_1085733413name_o @ H_1 @ N_1 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_720_folding__one__idem_Ohom__commute,axiom,
% 3.42/1.79 ! [N_1: ( hoare_1708887482_state > $o ) > $o,H_1: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_47: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_46: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite621643279tate_o @ F_47 @ F_46 )
% 3.42/1.79 => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
% 3.42/1.79 = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
% 3.42/1.79 => ( ( finite1329924456tate_o @ N_1 )
% 3.42/1.79 => ( ( N_1 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( H_1 @ ( F_46 @ N_1 ) )
% 3.42/1.79 = ( F_46 @ ( image_909543877tate_o @ H_1 @ N_1 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_721_folding__one__idem_Ohom__commute,axiom,
% 3.42/1.79 ! [N_1: pname > $o,H_1: pname > pname,F_47: pname > pname > pname,F_46: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite89670078_pname @ F_47 @ F_46 )
% 3.42/1.79 => ( ! [X_3: pname,Y_4: pname] :
% 3.42/1.79 ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
% 3.42/1.79 = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
% 3.42/1.79 => ( ( finite_finite_pname @ N_1 )
% 3.42/1.79 => ( ( N_1 != bot_bot_pname_o )
% 3.42/1.79 => ( ( H_1 @ ( F_46 @ N_1 ) )
% 3.42/1.79 = ( F_46 @ ( image_pname_pname @ H_1 @ N_1 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_722_folding__one__idem_Ohom__commute,axiom,
% 3.42/1.79 ! [N_1: hoare_1708887482_state > $o,H_1: hoare_1708887482_state > hoare_1708887482_state,F_47: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_46: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1347568576_state @ F_47 @ F_46 )
% 3.42/1.79 => ( ! [X_3: hoare_1708887482_state,Y_4: hoare_1708887482_state] :
% 3.42/1.79 ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
% 3.42/1.79 = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
% 3.42/1.79 => ( ( finite1625599783_state @ N_1 )
% 3.42/1.79 => ( ( N_1 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ( H_1 @ ( F_46 @ N_1 ) )
% 3.42/1.79 = ( F_46 @ ( image_757158439_state @ H_1 @ N_1 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_723_folding__one__idem_Ohom__commute,axiom,
% 3.42/1.79 ! [N_1: com > $o,H_1: com > com,F_47: com > com > com,F_46: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite666746948em_com @ F_47 @ F_46 )
% 3.42/1.79 => ( ! [X_3: com,Y_4: com] :
% 3.42/1.79 ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
% 3.42/1.79 = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
% 3.42/1.79 => ( ( finite_finite_com @ N_1 )
% 3.42/1.79 => ( ( N_1 != bot_bot_com_o )
% 3.42/1.79 => ( ( H_1 @ ( F_46 @ N_1 ) )
% 3.42/1.79 = ( F_46 @ ( image_com_com @ H_1 @ N_1 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_724_the__elem__def,axiom,
% 3.42/1.79 ! [X_51: com > $o] :
% 3.42/1.79 ( ( the_elem_com @ X_51 )
% 3.42/1.79 = ( the_com_1
% 3.42/1.79 @ ^ [X_3: com] :
% 3.42/1.79 ( X_51
% 3.42/1.79 = ( insert_com @ X_3 @ bot_bot_com_o ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_725_the__elem__def,axiom,
% 3.42/1.79 ! [X_51: pname > $o] :
% 3.42/1.79 ( ( the_elem_pname @ X_51 )
% 3.42/1.79 = ( the_pname
% 3.42/1.79 @ ^ [X_3: pname] :
% 3.42/1.79 ( X_51
% 3.42/1.79 = ( insert_pname @ X_3 @ bot_bot_pname_o ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_726_the__elem__def,axiom,
% 3.42/1.79 ! [X_51: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( the_el864710747_state @ X_51 )
% 3.42/1.79 = ( the_Ho851197897_state
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( X_51
% 3.42/1.79 = ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_727_folding__one_Oinsert,axiom,
% 3.42/1.79 ! [X_50: com,A_135: com > $o,F_45: com > com > com,F_44: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite860057415ne_com @ F_45 @ F_44 )
% 3.42/1.79 => ( ( finite_finite_com @ A_135 )
% 3.42/1.79 => ( ~ ( member_com @ X_50 @ A_135 )
% 3.42/1.79 => ( ( A_135 != bot_bot_com_o )
% 3.42/1.79 => ( ( F_44 @ ( insert_com @ X_50 @ A_135 ) )
% 3.42/1.79 = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_728_folding__one_Oinsert,axiom,
% 3.42/1.79 ! [X_50: pname,A_135: pname > $o,F_45: pname > pname > pname,F_44: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite1282449217_pname @ F_45 @ F_44 )
% 3.42/1.79 => ( ( finite_finite_pname @ A_135 )
% 3.42/1.79 => ( ~ ( member_pname @ X_50 @ A_135 )
% 3.42/1.79 => ( ( A_135 != bot_bot_pname_o )
% 3.42/1.79 => ( ( F_44 @ ( insert_pname @ X_50 @ A_135 ) )
% 3.42/1.79 = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_729_folding__one_Oinsert,axiom,
% 3.42/1.79 ! [X_50: hoare_1708887482_state,A_135: hoare_1708887482_state > $o,F_45: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_44: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1615457021_state @ F_45 @ F_44 )
% 3.42/1.79 => ( ( finite1625599783_state @ A_135 )
% 3.42/1.79 => ( ~ ( member451959335_state @ X_50 @ A_135 )
% 3.42/1.79 => ( ( A_135 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ( F_44 @ ( insert528405184_state @ X_50 @ A_135 ) )
% 3.42/1.79 = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_730_folding__one_Oinsert,axiom,
% 3.42/1.79 ! [X_50: pname > $o,A_135: ( pname > $o ) > $o,F_45: ( pname > $o ) > ( pname > $o ) > pname > $o,F_44: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.42/1.79 ( ( finite349908348name_o @ F_45 @ F_44 )
% 3.42/1.79 => ( ( finite297249702name_o @ A_135 )
% 3.42/1.79 => ( ~ ( member_pname_o @ X_50 @ A_135 )
% 3.42/1.79 => ( ( A_135 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ( F_44 @ ( insert_pname_o @ X_50 @ A_135 ) )
% 3.42/1.79 = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_731_folding__one_Oinsert,axiom,
% 3.42/1.79 ! [X_50: hoare_1708887482_state > $o,A_135: ( hoare_1708887482_state > $o ) > $o,F_45: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_44: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite928843026tate_o @ F_45 @ F_44 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ A_135 )
% 3.42/1.79 => ( ~ ( member814030440tate_o @ X_50 @ A_135 )
% 3.42/1.79 => ( ( A_135 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( F_44 @ ( insert949073679tate_o @ X_50 @ A_135 ) )
% 3.42/1.79 = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_732_triple_Oexhaust,axiom,
% 3.42/1.79 ! [Y_25: hoare_1708887482_state] :
% 3.42/1.79 ~ ! [Fun1: state > state > $o,Com: com,Fun2: state > state > $o] :
% 3.42/1.79 ( Y_25
% 3.42/1.79 != ( hoare_858012674_state @ Fun1 @ Com @ Fun2 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_733_folding__one_Osingleton,axiom,
% 3.42/1.79 ! [X_49: com,F_43: com > com > com,F_42: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite860057415ne_com @ F_43 @ F_42 )
% 3.42/1.79 => ( ( F_42 @ ( insert_com @ X_49 @ bot_bot_com_o ) )
% 3.42/1.79 = X_49 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_734_folding__one_Osingleton,axiom,
% 3.42/1.79 ! [X_49: pname,F_43: pname > pname > pname,F_42: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite1282449217_pname @ F_43 @ F_42 )
% 3.42/1.79 => ( ( F_42 @ ( insert_pname @ X_49 @ bot_bot_pname_o ) )
% 3.42/1.79 = X_49 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_735_folding__one_Osingleton,axiom,
% 3.42/1.79 ! [X_49: hoare_1708887482_state,F_43: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_42: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1615457021_state @ F_43 @ F_42 )
% 3.42/1.79 => ( ( F_42 @ ( insert528405184_state @ X_49 @ bot_bo19817387tate_o ) )
% 3.42/1.79 = X_49 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_736_folding__one_Oclosed,axiom,
% 3.42/1.79 ! [A_134: com > $o,F_41: com > com > com,F_40: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite860057415ne_com @ F_41 @ F_40 )
% 3.42/1.79 => ( ( finite_finite_com @ A_134 )
% 3.42/1.79 => ( ( A_134 != bot_bot_com_o )
% 3.42/1.79 => ( ! [X_3: com,Y_4: com] : ( member_com @ ( F_41 @ X_3 @ Y_4 ) @ ( insert_com @ X_3 @ ( insert_com @ Y_4 @ bot_bot_com_o ) ) )
% 3.42/1.79 => ( member_com @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_737_folding__one_Oclosed,axiom,
% 3.42/1.79 ! [A_134: pname > $o,F_41: pname > pname > pname,F_40: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite1282449217_pname @ F_41 @ F_40 )
% 3.42/1.79 => ( ( finite_finite_pname @ A_134 )
% 3.42/1.79 => ( ( A_134 != bot_bot_pname_o )
% 3.42/1.79 => ( ! [X_3: pname,Y_4: pname] : ( member_pname @ ( F_41 @ X_3 @ Y_4 ) @ ( insert_pname @ X_3 @ ( insert_pname @ Y_4 @ bot_bot_pname_o ) ) )
% 3.42/1.79 => ( member_pname @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_738_folding__one_Oclosed,axiom,
% 3.42/1.79 ! [A_134: hoare_1708887482_state > $o,F_41: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_40: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1615457021_state @ F_41 @ F_40 )
% 3.42/1.79 => ( ( finite1625599783_state @ A_134 )
% 3.42/1.79 => ( ( A_134 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ! [X_3: hoare_1708887482_state,Y_4: hoare_1708887482_state] : ( member451959335_state @ ( F_41 @ X_3 @ Y_4 ) @ ( insert528405184_state @ X_3 @ ( insert528405184_state @ Y_4 @ bot_bo19817387tate_o ) ) )
% 3.42/1.79 => ( member451959335_state @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_739_folding__one_Oclosed,axiom,
% 3.42/1.79 ! [A_134: ( pname > $o ) > $o,F_41: ( pname > $o ) > ( pname > $o ) > pname > $o,F_40: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.42/1.79 ( ( finite349908348name_o @ F_41 @ F_40 )
% 3.42/1.79 => ( ( finite297249702name_o @ A_134 )
% 3.42/1.79 => ( ( A_134 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ! [X_3: pname > $o,Y_4: pname > $o] : ( member_pname_o @ ( F_41 @ X_3 @ Y_4 ) @ ( insert_pname_o @ X_3 @ ( insert_pname_o @ Y_4 @ bot_bot_pname_o_o ) ) )
% 3.42/1.79 => ( member_pname_o @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_740_folding__one_Oclosed,axiom,
% 3.42/1.79 ! [A_134: ( hoare_1708887482_state > $o ) > $o,F_41: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_40: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite928843026tate_o @ F_41 @ F_40 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ A_134 )
% 3.42/1.79 => ( ( A_134 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] : ( member814030440tate_o @ ( F_41 @ X_3 @ Y_4 ) @ ( insert949073679tate_o @ X_3 @ ( insert949073679tate_o @ Y_4 @ bot_bo1678742418te_o_o ) ) )
% 3.42/1.79 => ( member814030440tate_o @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_741_image__cong,axiom,
% 3.42/1.79 ! [F_39: pname > hoare_1708887482_state,G_8: pname > hoare_1708887482_state,M_3: pname > $o,N: pname > $o] :
% 3.42/1.79 ( ( M_3 = N )
% 3.42/1.79 => ( ! [X_3: pname] :
% 3.42/1.79 ( ( member_pname @ X_3 @ N )
% 3.42/1.79 => ( ( F_39 @ X_3 )
% 3.42/1.79 = ( G_8 @ X_3 ) ) )
% 3.42/1.79 => ( ( image_1116629049_state @ F_39 @ M_3 )
% 3.42/1.79 = ( image_1116629049_state @ G_8 @ N ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_742_Collect__mono,axiom,
% 3.42/1.79 ! [Q_5: hoare_1708887482_state > $o,P_10: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ! [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( P_10 @ X_3 )
% 3.42/1.79 => ( Q_5 @ X_3 ) )
% 3.42/1.79 => ( ord_le777019615tate_o @ ( collec1568722789_state @ P_10 ) @ ( collec1568722789_state @ Q_5 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_743_Collect__mono,axiom,
% 3.42/1.79 ! [Q_5: pname > $o,P_10: pname > $o] :
% 3.42/1.79 ( ! [X_3: pname] :
% 3.42/1.79 ( ( P_10 @ X_3 )
% 3.42/1.79 => ( Q_5 @ X_3 ) )
% 3.42/1.79 => ( ord_less_eq_pname_o @ ( collect_pname @ P_10 ) @ ( collect_pname @ Q_5 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_744_Collect__mono,axiom,
% 3.42/1.79 ! [Q_5: ( pname > $o ) > $o,P_10: ( pname > $o ) > $o] :
% 3.42/1.79 ( ! [X_3: pname > $o] :
% 3.42/1.79 ( ( P_10 @ X_3 )
% 3.42/1.79 => ( Q_5 @ X_3 ) )
% 3.42/1.79 => ( ord_le1205211808me_o_o @ ( collect_pname_o @ P_10 ) @ ( collect_pname_o @ Q_5 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_745_Collect__mono,axiom,
% 3.42/1.79 ! [Q_5: ( hoare_1708887482_state > $o ) > $o,P_10: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ! [X_3: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( P_10 @ X_3 )
% 3.42/1.79 => ( Q_5 @ X_3 ) )
% 3.42/1.79 => ( ord_le1728773982te_o_o @ ( collec219771562tate_o @ P_10 ) @ ( collec219771562tate_o @ Q_5 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_746_predicate1I,axiom,
% 3.42/1.79 ! [Q_4: pname > $o,P_9: pname > $o] :
% 3.42/1.79 ( ! [X_3: pname] :
% 3.42/1.79 ( ( P_9 @ X_3 )
% 3.42/1.79 => ( Q_4 @ X_3 ) )
% 3.42/1.79 => ( ord_less_eq_pname_o @ P_9 @ Q_4 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_747_predicate1I,axiom,
% 3.42/1.79 ! [Q_4: hoare_1708887482_state > $o,P_9: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ! [X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( P_9 @ X_3 )
% 3.42/1.79 => ( Q_4 @ X_3 ) )
% 3.42/1.79 => ( ord_le777019615tate_o @ P_9 @ Q_4 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_748_mk__disjoint__insert,axiom,
% 3.42/1.79 ! [A_133: com,A_132: com > $o] :
% 3.42/1.79 ( ( member_com @ A_133 @ A_132 )
% 3.42/1.79 => ? [B_84: com > $o] :
% 3.42/1.79 ( ( A_132
% 3.42/1.79 = ( insert_com @ A_133 @ B_84 ) )
% 3.42/1.79 & ~ ( member_com @ A_133 @ B_84 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_749_mk__disjoint__insert,axiom,
% 3.42/1.79 ! [A_133: pname,A_132: pname > $o] :
% 3.42/1.79 ( ( member_pname @ A_133 @ A_132 )
% 3.42/1.79 => ? [B_84: pname > $o] :
% 3.42/1.79 ( ( A_132
% 3.42/1.79 = ( insert_pname @ A_133 @ B_84 ) )
% 3.42/1.79 & ~ ( member_pname @ A_133 @ B_84 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_750_mk__disjoint__insert,axiom,
% 3.42/1.79 ! [A_133: hoare_1708887482_state,A_132: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ A_133 @ A_132 )
% 3.42/1.79 => ? [B_84: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( A_132
% 3.42/1.79 = ( insert528405184_state @ A_133 @ B_84 ) )
% 3.42/1.79 & ~ ( member451959335_state @ A_133 @ B_84 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_751_Set_Oset__insert,axiom,
% 3.42/1.79 ! [X_48: com,A_131: com > $o] :
% 3.42/1.79 ( ( member_com @ X_48 @ A_131 )
% 3.42/1.79 => ~ ! [B_84: com > $o] :
% 3.42/1.79 ( ( A_131
% 3.42/1.79 = ( insert_com @ X_48 @ B_84 ) )
% 3.42/1.79 => ( member_com @ X_48 @ B_84 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_752_Set_Oset__insert,axiom,
% 3.42/1.79 ! [X_48: pname,A_131: pname > $o] :
% 3.42/1.79 ( ( member_pname @ X_48 @ A_131 )
% 3.42/1.79 => ~ ! [B_84: pname > $o] :
% 3.42/1.79 ( ( A_131
% 3.42/1.79 = ( insert_pname @ X_48 @ B_84 ) )
% 3.42/1.79 => ( member_pname @ X_48 @ B_84 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_753_Set_Oset__insert,axiom,
% 3.42/1.79 ! [X_48: hoare_1708887482_state,A_131: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ X_48 @ A_131 )
% 3.42/1.79 => ~ ! [B_84: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( A_131
% 3.42/1.79 = ( insert528405184_state @ X_48 @ B_84 ) )
% 3.42/1.79 => ( member451959335_state @ X_48 @ B_84 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_754_equals0I,axiom,
% 3.42/1.79 ! [A_130: com > $o] :
% 3.42/1.79 ( ! [Y_4: com] :
% 3.42/1.79 ~ ( member_com @ Y_4 @ A_130 )
% 3.42/1.79 => ( A_130 = bot_bot_com_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_755_equals0I,axiom,
% 3.42/1.79 ! [A_130: pname > $o] :
% 3.42/1.79 ( ! [Y_4: pname] :
% 3.42/1.79 ~ ( member_pname @ Y_4 @ A_130 )
% 3.42/1.79 => ( A_130 = bot_bot_pname_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_756_equals0I,axiom,
% 3.42/1.79 ! [A_130: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ! [Y_4: hoare_1708887482_state] :
% 3.42/1.79 ~ ( member451959335_state @ Y_4 @ A_130 )
% 3.42/1.79 => ( A_130 = bot_bo19817387tate_o ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_757_MGT__alternD,axiom,
% 3.42/1.79 ! [G_7: hoare_1708887482_state > $o,C_34: com] :
% 3.42/1.79 ( hoare_1160767572gleton
% 3.42/1.79 => ( ( hoare_90032982_state @ G_7
% 3.42/1.79 @ ( insert528405184_state
% 3.42/1.79 @ ( hoare_858012674_state
% 3.42/1.79 @ ^ [Z_11: state,S0_1: state] :
% 3.42/1.79 ! [S1: state] : ( (=>) @ ( evalc @ C_34 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
% 3.42/1.79 @ C_34
% 3.42/1.79 @ fequal_state )
% 3.42/1.79 @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_758_xt1_I15_J,axiom,
% 3.42/1.79 ! [C_35: $o,F_38: $o > $o,B_83: $o,A_129: $o] :
% 3.42/1.79 ( ( A_129
% 3.42/1.79 <=> ( F_38 @ B_83 ) )
% 3.42/1.79 => ( ( ord_less_eq_o @ C_35 @ B_83 )
% 3.42/1.79 => ( ! [X_3: $o,Y_4: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ Y_4 @ X_3 )
% 3.42/1.79 => ( ord_less_eq_o @ ( F_38 @ Y_4 ) @ ( F_38 @ X_3 ) ) )
% 3.42/1.79 => ( ord_less_eq_o @ ( F_38 @ C_35 ) @ A_129 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_759_xt1_I15_J,axiom,
% 3.42/1.79 ! [C_35: pname > $o,A_129: pname > $o,F_38: ( pname > $o ) > pname > $o,B_83: pname > $o] :
% 3.42/1.79 ( ( A_129
% 3.42/1.79 = ( F_38 @ B_83 ) )
% 3.42/1.79 => ( ( ord_less_eq_pname_o @ C_35 @ B_83 )
% 3.42/1.79 => ( ! [X_3: pname > $o,Y_4: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ Y_4 @ X_3 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ ( F_38 @ Y_4 ) @ ( F_38 @ X_3 ) ) )
% 3.42/1.79 => ( ord_less_eq_pname_o @ ( F_38 @ C_35 ) @ A_129 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_760_xt1_I15_J,axiom,
% 3.42/1.79 ! [C_35: hoare_1708887482_state > $o,A_129: hoare_1708887482_state > $o,F_38: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,B_83: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( A_129
% 3.42/1.79 = ( F_38 @ B_83 ) )
% 3.42/1.79 => ( ( ord_le777019615tate_o @ C_35 @ B_83 )
% 3.42/1.79 => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ Y_4 @ X_3 )
% 3.42/1.79 => ( ord_le777019615tate_o @ ( F_38 @ Y_4 ) @ ( F_38 @ X_3 ) ) )
% 3.42/1.79 => ( ord_le777019615tate_o @ ( F_38 @ C_35 ) @ A_129 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_761_MGT__alternI,axiom,
% 3.42/1.79 ! [G_7: hoare_1708887482_state > $o,C_34: com] :
% 3.42/1.79 ( ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_7
% 3.42/1.79 @ ( insert528405184_state
% 3.42/1.79 @ ( hoare_858012674_state
% 3.42/1.79 @ ^ [Z_11: state,S0_1: state] :
% 3.42/1.79 ! [S1: state] : ( (=>) @ ( evalc @ C_34 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
% 3.42/1.79 @ C_34
% 3.42/1.79 @ fequal_state )
% 3.42/1.79 @ bot_bo19817387tate_o ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_762_MGT__def,axiom,
% 3.42/1.79 ! [C_34: com] :
% 3.42/1.79 ( ( hoare_Mirabelle_MGT @ C_34 )
% 3.42/1.79 = ( hoare_858012674_state @ fequal_state @ C_34 @ ( evalc @ C_34 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_763_evalc__elim__cases_I6_J,axiom,
% 3.42/1.79 ! [P: pname,S_4: state,S1_1: state] :
% 3.42/1.79 ( ( evalc @ ( body_1 @ P ) @ S_4 @ S1_1 )
% 3.42/1.79 => ( evalc @ ( the_com @ ( body @ P ) ) @ S_4 @ S1_1 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_764_evalc_OBody,axiom,
% 3.42/1.79 ! [Pn_1: pname,S0: state,S1_1: state] :
% 3.42/1.79 ( ( evalc @ ( the_com @ ( body @ Pn_1 ) ) @ S0 @ S1_1 )
% 3.42/1.79 => ( evalc @ ( body_1 @ Pn_1 ) @ S0 @ S1_1 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_765_evalc__elim__cases_I1_J,axiom,
% 3.42/1.79 ! [S_4: state,T: state] :
% 3.42/1.79 ( ( evalc @ skip @ S_4 @ T )
% 3.42/1.79 => ( T = S_4 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_766_evalc_OSkip,axiom,
% 3.42/1.79 ! [S_4: state] : ( evalc @ skip @ S_4 @ S_4 ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_767_evalc_OSemi,axiom,
% 3.42/1.79 ! [C1: com,S2: state,C0: com,S0: state,S1_1: state] :
% 3.42/1.79 ( ( evalc @ C0 @ S0 @ S1_1 )
% 3.42/1.79 => ( ( evalc @ C1 @ S1_1 @ S2 )
% 3.42/1.79 => ( evalc @ ( semi @ C0 @ C1 ) @ S0 @ S2 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_768_evalc_OWhileTrue,axiom,
% 3.42/1.79 ! [S2: state,C_34: com,S1_1: state,B_82: state > $o,S0: state] :
% 3.42/1.79 ( ( B_82 @ S0 )
% 3.42/1.79 => ( ( evalc @ C_34 @ S0 @ S1_1 )
% 3.42/1.79 => ( ( evalc @ ( while @ B_82 @ C_34 ) @ S1_1 @ S2 )
% 3.42/1.79 => ( evalc @ ( while @ B_82 @ C_34 ) @ S0 @ S2 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_769_evalc_OWhileFalse,axiom,
% 3.42/1.79 ! [C_34: com,B_82: state > $o,S_4: state] :
% 3.42/1.79 ( ~ ( B_82 @ S_4 )
% 3.42/1.79 => ( evalc @ ( while @ B_82 @ C_34 ) @ S_4 @ S_4 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_770_com__det,axiom,
% 3.42/1.79 ! [U: state,C_34: com,S_4: state,T: state] :
% 3.42/1.79 ( ( evalc @ C_34 @ S_4 @ T )
% 3.42/1.79 => ( ( evalc @ C_34 @ S_4 @ U )
% 3.42/1.79 => ( U = T ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_771_evalc__elim__cases_I4_J,axiom,
% 3.42/1.79 ! [C1: com,C2: com,S_4: state,T: state] :
% 3.42/1.79 ( ( evalc @ ( semi @ C1 @ C2 ) @ S_4 @ T )
% 3.42/1.79 => ~ ! [S1: state] :
% 3.42/1.79 ( ( evalc @ C1 @ S_4 @ S1 )
% 3.42/1.79 => ~ ( evalc @ C2 @ S1 @ T ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_772_evalc__WHILE__case,axiom,
% 3.42/1.79 ! [B_82: state > $o,C_34: com,S_4: state,T: state] :
% 3.42/1.79 ( ( evalc @ ( while @ B_82 @ C_34 ) @ S_4 @ T )
% 3.42/1.79 => ( ( ( T = S_4 )
% 3.42/1.79 => ( B_82 @ S_4 ) )
% 3.42/1.79 => ~ ( ( B_82 @ S_4 )
% 3.42/1.79 => ! [S1: state] :
% 3.42/1.79 ( ( evalc @ C_34 @ S_4 @ S1 )
% 3.42/1.79 => ~ ( evalc @ ( while @ B_82 @ C_34 ) @ S1 @ T ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_773_xt1_I16_J,axiom,
% 3.42/1.79 ! [C_33: $o,F_37: $o > $o,B_81: $o,A_128: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ B_81 @ A_128 )
% 3.42/1.79 => ( ( ( F_37 @ B_81 )
% 3.42/1.79 <=> C_33 )
% 3.42/1.79 => ( ! [X_3: $o,Y_4: $o] :
% 3.42/1.79 ( ( ord_less_eq_o @ Y_4 @ X_3 )
% 3.42/1.79 => ( ord_less_eq_o @ ( F_37 @ Y_4 ) @ ( F_37 @ X_3 ) ) )
% 3.42/1.79 => ( ord_less_eq_o @ C_33 @ ( F_37 @ A_128 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_774_xt1_I16_J,axiom,
% 3.42/1.79 ! [F_37: ( pname > $o ) > pname > $o,C_33: pname > $o,B_81: pname > $o,A_128: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ B_81 @ A_128 )
% 3.42/1.79 => ( ( ( F_37 @ B_81 )
% 3.42/1.79 = C_33 )
% 3.42/1.79 => ( ! [X_3: pname > $o,Y_4: pname > $o] :
% 3.42/1.79 ( ( ord_less_eq_pname_o @ Y_4 @ X_3 )
% 3.42/1.79 => ( ord_less_eq_pname_o @ ( F_37 @ Y_4 ) @ ( F_37 @ X_3 ) ) )
% 3.42/1.79 => ( ord_less_eq_pname_o @ C_33 @ ( F_37 @ A_128 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_775_xt1_I16_J,axiom,
% 3.42/1.79 ! [F_37: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,C_33: hoare_1708887482_state > $o,B_81: hoare_1708887482_state > $o,A_128: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ B_81 @ A_128 )
% 3.42/1.79 => ( ( ( F_37 @ B_81 )
% 3.42/1.79 = C_33 )
% 3.42/1.79 => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ord_le777019615tate_o @ Y_4 @ X_3 )
% 3.42/1.79 => ( ord_le777019615tate_o @ ( F_37 @ Y_4 ) @ ( F_37 @ X_3 ) ) )
% 3.42/1.79 => ( ord_le777019615tate_o @ C_33 @ ( F_37 @ A_128 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_776_folding__one_Ounion__inter,axiom,
% 3.42/1.79 ! [B_80: ( pname > $o ) > $o,A_127: ( pname > $o ) > $o,F_36: ( pname > $o ) > ( pname > $o ) > pname > $o,F_35: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.42/1.79 ( ( finite349908348name_o @ F_36 @ F_35 )
% 3.42/1.79 => ( ( finite297249702name_o @ A_127 )
% 3.42/1.79 => ( ( finite297249702name_o @ B_80 )
% 3.42/1.79 => ( ( ( semila2013987940me_o_o @ A_127 @ B_80 )
% 3.42/1.79 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ( F_36 @ ( F_35 @ ( semila181081674me_o_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila2013987940me_o_o @ A_127 @ B_80 ) ) )
% 3.42/1.79 = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_777_folding__one_Ounion__inter,axiom,
% 3.42/1.79 ! [B_80: ( hoare_1708887482_state > $o ) > $o,A_127: ( hoare_1708887482_state > $o ) > $o,F_36: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_35: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite928843026tate_o @ F_36 @ F_35 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ A_127 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ B_80 )
% 3.42/1.79 => ( ( ( semila598060698te_o_o @ A_127 @ B_80 )
% 3.42/1.79 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( F_36 @ ( F_35 @ ( semila1853742644te_o_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila598060698te_o_o @ A_127 @ B_80 ) ) )
% 3.42/1.79 = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_778_folding__one_Ounion__inter,axiom,
% 3.42/1.79 ! [B_80: pname > $o,A_127: pname > $o,F_36: pname > pname > pname,F_35: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite1282449217_pname @ F_36 @ F_35 )
% 3.42/1.79 => ( ( finite_finite_pname @ A_127 )
% 3.42/1.79 => ( ( finite_finite_pname @ B_80 )
% 3.42/1.79 => ( ( ( semila1673364395name_o @ A_127 @ B_80 )
% 3.42/1.79 != bot_bot_pname_o )
% 3.42/1.79 => ( ( F_36 @ ( F_35 @ ( semila1780557381name_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila1673364395name_o @ A_127 @ B_80 ) ) )
% 3.42/1.79 = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_779_folding__one_Ounion__inter,axiom,
% 3.42/1.79 ! [B_80: hoare_1708887482_state > $o,A_127: hoare_1708887482_state > $o,F_36: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_35: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1615457021_state @ F_36 @ F_35 )
% 3.42/1.79 => ( ( finite1625599783_state @ A_127 )
% 3.42/1.79 => ( ( finite1625599783_state @ B_80 )
% 3.42/1.79 => ( ( ( semila129691299tate_o @ A_127 @ B_80 )
% 3.42/1.79 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ( F_36 @ ( F_35 @ ( semila1122118281tate_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila129691299tate_o @ A_127 @ B_80 ) ) )
% 3.42/1.79 = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_780_folding__one_Ounion__inter,axiom,
% 3.42/1.79 ! [B_80: com > $o,A_127: com > $o,F_36: com > com > com,F_35: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite860057415ne_com @ F_36 @ F_35 )
% 3.42/1.79 => ( ( finite_finite_com @ A_127 )
% 3.42/1.79 => ( ( finite_finite_com @ B_80 )
% 3.42/1.79 => ( ( ( semila513601829_com_o @ A_127 @ B_80 )
% 3.42/1.79 != bot_bot_com_o )
% 3.42/1.79 => ( ( F_36 @ ( F_35 @ ( semila1562558655_com_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila513601829_com_o @ A_127 @ B_80 ) ) )
% 3.42/1.79 = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_781_folding__one_Ounion__disjoint,axiom,
% 3.42/1.79 ! [B_79: ( pname > $o ) > $o,A_126: ( pname > $o ) > $o,F_34: ( pname > $o ) > ( pname > $o ) > pname > $o,F_33: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.42/1.79 ( ( finite349908348name_o @ F_34 @ F_33 )
% 3.42/1.79 => ( ( finite297249702name_o @ A_126 )
% 3.42/1.79 => ( ( A_126 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ( finite297249702name_o @ B_79 )
% 3.42/1.79 => ( ( B_79 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ( ( semila2013987940me_o_o @ A_126 @ B_79 )
% 3.42/1.79 = bot_bot_pname_o_o )
% 3.42/1.79 => ( ( F_33 @ ( semila181081674me_o_o @ A_126 @ B_79 ) )
% 3.42/1.79 = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_782_folding__one_Ounion__disjoint,axiom,
% 3.42/1.79 ! [B_79: ( hoare_1708887482_state > $o ) > $o,A_126: ( hoare_1708887482_state > $o ) > $o,F_34: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_33: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite928843026tate_o @ F_34 @ F_33 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ A_126 )
% 3.42/1.79 => ( ( A_126 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( finite1329924456tate_o @ B_79 )
% 3.42/1.79 => ( ( B_79 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( ( semila598060698te_o_o @ A_126 @ B_79 )
% 3.42/1.79 = bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( F_33 @ ( semila1853742644te_o_o @ A_126 @ B_79 ) )
% 3.42/1.79 = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_783_folding__one_Ounion__disjoint,axiom,
% 3.42/1.79 ! [B_79: pname > $o,A_126: pname > $o,F_34: pname > pname > pname,F_33: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite1282449217_pname @ F_34 @ F_33 )
% 3.42/1.79 => ( ( finite_finite_pname @ A_126 )
% 3.42/1.79 => ( ( A_126 != bot_bot_pname_o )
% 3.42/1.79 => ( ( finite_finite_pname @ B_79 )
% 3.42/1.79 => ( ( B_79 != bot_bot_pname_o )
% 3.42/1.79 => ( ( ( semila1673364395name_o @ A_126 @ B_79 )
% 3.42/1.79 = bot_bot_pname_o )
% 3.42/1.79 => ( ( F_33 @ ( semila1780557381name_o @ A_126 @ B_79 ) )
% 3.42/1.79 = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_784_folding__one_Ounion__disjoint,axiom,
% 3.42/1.79 ! [B_79: hoare_1708887482_state > $o,A_126: hoare_1708887482_state > $o,F_34: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_33: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1615457021_state @ F_34 @ F_33 )
% 3.42/1.79 => ( ( finite1625599783_state @ A_126 )
% 3.42/1.79 => ( ( A_126 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ( finite1625599783_state @ B_79 )
% 3.42/1.79 => ( ( B_79 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ( ( semila129691299tate_o @ A_126 @ B_79 )
% 3.42/1.79 = bot_bo19817387tate_o )
% 3.42/1.79 => ( ( F_33 @ ( semila1122118281tate_o @ A_126 @ B_79 ) )
% 3.42/1.79 = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_785_folding__one_Ounion__disjoint,axiom,
% 3.42/1.79 ! [B_79: com > $o,A_126: com > $o,F_34: com > com > com,F_33: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite860057415ne_com @ F_34 @ F_33 )
% 3.42/1.79 => ( ( finite_finite_com @ A_126 )
% 3.42/1.79 => ( ( A_126 != bot_bot_com_o )
% 3.42/1.79 => ( ( finite_finite_com @ B_79 )
% 3.42/1.79 => ( ( B_79 != bot_bot_com_o )
% 3.42/1.79 => ( ( ( semila513601829_com_o @ A_126 @ B_79 )
% 3.42/1.79 = bot_bot_com_o )
% 3.42/1.79 => ( ( F_33 @ ( semila1562558655_com_o @ A_126 @ B_79 ) )
% 3.42/1.79 = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_786_folding__one_Oinsert__remove,axiom,
% 3.42/1.79 ! [X_47: com,A_125: com > $o,F_32: com > com > com,F_31: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite860057415ne_com @ F_32 @ F_31 )
% 3.42/1.79 => ( ( finite_finite_com @ A_125 )
% 3.42/1.79 => ( ( ( ( minus_minus_com_o @ A_125 @ ( insert_com @ X_47 @ bot_bot_com_o ) )
% 3.42/1.79 = bot_bot_com_o )
% 3.42/1.79 => ( ( F_31 @ ( insert_com @ X_47 @ A_125 ) )
% 3.42/1.79 = X_47 ) )
% 3.42/1.79 & ( ( ( minus_minus_com_o @ A_125 @ ( insert_com @ X_47 @ bot_bot_com_o ) )
% 3.42/1.79 != bot_bot_com_o )
% 3.42/1.79 => ( ( F_31 @ ( insert_com @ X_47 @ A_125 ) )
% 3.42/1.79 = ( F_32 @ X_47 @ ( F_31 @ ( minus_minus_com_o @ A_125 @ ( insert_com @ X_47 @ bot_bot_com_o ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_787_folding__one_Oinsert__remove,axiom,
% 3.42/1.79 ! [X_47: pname,A_125: pname > $o,F_32: pname > pname > pname,F_31: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite1282449217_pname @ F_32 @ F_31 )
% 3.42/1.79 => ( ( finite_finite_pname @ A_125 )
% 3.42/1.79 => ( ( ( ( minus_minus_pname_o @ A_125 @ ( insert_pname @ X_47 @ bot_bot_pname_o ) )
% 3.42/1.79 = bot_bot_pname_o )
% 3.42/1.79 => ( ( F_31 @ ( insert_pname @ X_47 @ A_125 ) )
% 3.42/1.79 = X_47 ) )
% 3.42/1.79 & ( ( ( minus_minus_pname_o @ A_125 @ ( insert_pname @ X_47 @ bot_bot_pname_o ) )
% 3.42/1.79 != bot_bot_pname_o )
% 3.42/1.79 => ( ( F_31 @ ( insert_pname @ X_47 @ A_125 ) )
% 3.42/1.79 = ( F_32 @ X_47 @ ( F_31 @ ( minus_minus_pname_o @ A_125 @ ( insert_pname @ X_47 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_788_folding__one_Oinsert__remove,axiom,
% 3.42/1.79 ! [X_47: hoare_1708887482_state,A_125: hoare_1708887482_state > $o,F_32: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_31: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1615457021_state @ F_32 @ F_31 )
% 3.42/1.79 => ( ( finite1625599783_state @ A_125 )
% 3.42/1.79 => ( ( ( ( minus_2056855718tate_o @ A_125 @ ( insert528405184_state @ X_47 @ bot_bo19817387tate_o ) )
% 3.42/1.79 = bot_bo19817387tate_o )
% 3.42/1.79 => ( ( F_31 @ ( insert528405184_state @ X_47 @ A_125 ) )
% 3.42/1.79 = X_47 ) )
% 3.42/1.79 & ( ( ( minus_2056855718tate_o @ A_125 @ ( insert528405184_state @ X_47 @ bot_bo19817387tate_o ) )
% 3.42/1.79 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ( F_31 @ ( insert528405184_state @ X_47 @ A_125 ) )
% 3.42/1.79 = ( F_32 @ X_47 @ ( F_31 @ ( minus_2056855718tate_o @ A_125 @ ( insert528405184_state @ X_47 @ bot_bo19817387tate_o ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_789_folding__one_Oinsert__remove,axiom,
% 3.42/1.79 ! [X_47: pname > $o,A_125: ( pname > $o ) > $o,F_32: ( pname > $o ) > ( pname > $o ) > pname > $o,F_31: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.42/1.79 ( ( finite349908348name_o @ F_32 @ F_31 )
% 3.42/1.79 => ( ( finite297249702name_o @ A_125 )
% 3.42/1.79 => ( ( ( ( minus_1480864103me_o_o @ A_125 @ ( insert_pname_o @ X_47 @ bot_bot_pname_o_o ) )
% 3.42/1.79 = bot_bot_pname_o_o )
% 3.42/1.79 => ( ( F_31 @ ( insert_pname_o @ X_47 @ A_125 ) )
% 3.42/1.79 = X_47 ) )
% 3.42/1.79 & ( ( ( minus_1480864103me_o_o @ A_125 @ ( insert_pname_o @ X_47 @ bot_bot_pname_o_o ) )
% 3.42/1.79 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ( F_31 @ ( insert_pname_o @ X_47 @ A_125 ) )
% 3.42/1.79 = ( F_32 @ X_47 @ ( F_31 @ ( minus_1480864103me_o_o @ A_125 @ ( insert_pname_o @ X_47 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_790_folding__one_Oinsert__remove,axiom,
% 3.42/1.79 ! [X_47: hoare_1708887482_state > $o,A_125: ( hoare_1708887482_state > $o ) > $o,F_32: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_31: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite928843026tate_o @ F_32 @ F_31 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ A_125 )
% 3.42/1.79 => ( ( ( ( minus_548038231te_o_o @ A_125 @ ( insert949073679tate_o @ X_47 @ bot_bo1678742418te_o_o ) )
% 3.42/1.79 = bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( F_31 @ ( insert949073679tate_o @ X_47 @ A_125 ) )
% 3.42/1.79 = X_47 ) )
% 3.42/1.79 & ( ( ( minus_548038231te_o_o @ A_125 @ ( insert949073679tate_o @ X_47 @ bot_bo1678742418te_o_o ) )
% 3.42/1.79 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( F_31 @ ( insert949073679tate_o @ X_47 @ A_125 ) )
% 3.42/1.79 = ( F_32 @ X_47 @ ( F_31 @ ( minus_548038231te_o_o @ A_125 @ ( insert949073679tate_o @ X_47 @ bot_bo1678742418te_o_o ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_791_folding__one_Oremove,axiom,
% 3.42/1.79 ! [X_46: com,A_124: com > $o,F_30: com > com > com,F_29: ( com > $o ) > com] :
% 3.42/1.79 ( ( finite860057415ne_com @ F_30 @ F_29 )
% 3.42/1.79 => ( ( finite_finite_com @ A_124 )
% 3.42/1.79 => ( ( member_com @ X_46 @ A_124 )
% 3.42/1.79 => ( ( ( ( minus_minus_com_o @ A_124 @ ( insert_com @ X_46 @ bot_bot_com_o ) )
% 3.42/1.79 = bot_bot_com_o )
% 3.42/1.79 => ( ( F_29 @ A_124 )
% 3.42/1.79 = X_46 ) )
% 3.42/1.79 & ( ( ( minus_minus_com_o @ A_124 @ ( insert_com @ X_46 @ bot_bot_com_o ) )
% 3.42/1.79 != bot_bot_com_o )
% 3.42/1.79 => ( ( F_29 @ A_124 )
% 3.42/1.79 = ( F_30 @ X_46 @ ( F_29 @ ( minus_minus_com_o @ A_124 @ ( insert_com @ X_46 @ bot_bot_com_o ) ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_792_folding__one_Oremove,axiom,
% 3.42/1.79 ! [X_46: pname,A_124: pname > $o,F_30: pname > pname > pname,F_29: ( pname > $o ) > pname] :
% 3.42/1.79 ( ( finite1282449217_pname @ F_30 @ F_29 )
% 3.42/1.79 => ( ( finite_finite_pname @ A_124 )
% 3.42/1.79 => ( ( member_pname @ X_46 @ A_124 )
% 3.42/1.79 => ( ( ( ( minus_minus_pname_o @ A_124 @ ( insert_pname @ X_46 @ bot_bot_pname_o ) )
% 3.42/1.79 = bot_bot_pname_o )
% 3.42/1.79 => ( ( F_29 @ A_124 )
% 3.42/1.79 = X_46 ) )
% 3.42/1.79 & ( ( ( minus_minus_pname_o @ A_124 @ ( insert_pname @ X_46 @ bot_bot_pname_o ) )
% 3.42/1.79 != bot_bot_pname_o )
% 3.42/1.79 => ( ( F_29 @ A_124 )
% 3.42/1.79 = ( F_30 @ X_46 @ ( F_29 @ ( minus_minus_pname_o @ A_124 @ ( insert_pname @ X_46 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_793_folding__one_Oremove,axiom,
% 3.42/1.79 ! [X_46: hoare_1708887482_state,A_124: hoare_1708887482_state > $o,F_30: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_29: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.42/1.79 ( ( finite1615457021_state @ F_30 @ F_29 )
% 3.42/1.79 => ( ( finite1625599783_state @ A_124 )
% 3.42/1.79 => ( ( member451959335_state @ X_46 @ A_124 )
% 3.42/1.79 => ( ( ( ( minus_2056855718tate_o @ A_124 @ ( insert528405184_state @ X_46 @ bot_bo19817387tate_o ) )
% 3.42/1.79 = bot_bo19817387tate_o )
% 3.42/1.79 => ( ( F_29 @ A_124 )
% 3.42/1.79 = X_46 ) )
% 3.42/1.79 & ( ( ( minus_2056855718tate_o @ A_124 @ ( insert528405184_state @ X_46 @ bot_bo19817387tate_o ) )
% 3.42/1.79 != bot_bo19817387tate_o )
% 3.42/1.79 => ( ( F_29 @ A_124 )
% 3.42/1.79 = ( F_30 @ X_46 @ ( F_29 @ ( minus_2056855718tate_o @ A_124 @ ( insert528405184_state @ X_46 @ bot_bo19817387tate_o ) ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_794_folding__one_Oremove,axiom,
% 3.42/1.79 ! [X_46: pname > $o,A_124: ( pname > $o ) > $o,F_30: ( pname > $o ) > ( pname > $o ) > pname > $o,F_29: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.42/1.79 ( ( finite349908348name_o @ F_30 @ F_29 )
% 3.42/1.79 => ( ( finite297249702name_o @ A_124 )
% 3.42/1.79 => ( ( member_pname_o @ X_46 @ A_124 )
% 3.42/1.79 => ( ( ( ( minus_1480864103me_o_o @ A_124 @ ( insert_pname_o @ X_46 @ bot_bot_pname_o_o ) )
% 3.42/1.79 = bot_bot_pname_o_o )
% 3.42/1.79 => ( ( F_29 @ A_124 )
% 3.42/1.79 = X_46 ) )
% 3.42/1.79 & ( ( ( minus_1480864103me_o_o @ A_124 @ ( insert_pname_o @ X_46 @ bot_bot_pname_o_o ) )
% 3.42/1.79 != bot_bot_pname_o_o )
% 3.42/1.79 => ( ( F_29 @ A_124 )
% 3.42/1.79 = ( F_30 @ X_46 @ ( F_29 @ ( minus_1480864103me_o_o @ A_124 @ ( insert_pname_o @ X_46 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_795_folding__one_Oremove,axiom,
% 3.42/1.79 ! [X_46: hoare_1708887482_state > $o,A_124: ( hoare_1708887482_state > $o ) > $o,F_30: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_29: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite928843026tate_o @ F_30 @ F_29 )
% 3.42/1.79 => ( ( finite1329924456tate_o @ A_124 )
% 3.42/1.79 => ( ( member814030440tate_o @ X_46 @ A_124 )
% 3.42/1.79 => ( ( ( ( minus_548038231te_o_o @ A_124 @ ( insert949073679tate_o @ X_46 @ bot_bo1678742418te_o_o ) )
% 3.42/1.79 = bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( F_29 @ A_124 )
% 3.42/1.79 = X_46 ) )
% 3.42/1.79 & ( ( ( minus_548038231te_o_o @ A_124 @ ( insert949073679tate_o @ X_46 @ bot_bo1678742418te_o_o ) )
% 3.42/1.79 != bot_bo1678742418te_o_o )
% 3.42/1.79 => ( ( F_29 @ A_124 )
% 3.42/1.79 = ( F_30 @ X_46 @ ( F_29 @ ( minus_548038231te_o_o @ A_124 @ ( insert949073679tate_o @ X_46 @ bot_bo1678742418te_o_o ) ) ) ) ) ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_796_is__none__code_I2_J,axiom,
% 3.42/1.79 ! [X_45: pname] :
% 3.42/1.79 ~ ( is_none_pname @ ( some_pname @ X_45 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_797_is__none__code_I2_J,axiom,
% 3.42/1.79 ! [X_45: hoare_1708887482_state] :
% 3.42/1.79 ~ ( is_non163157940_state @ ( some_H1974565227_state @ X_45 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_798_is__none__code_I2_J,axiom,
% 3.42/1.79 ! [X_45: com] :
% 3.42/1.79 ~ ( is_none_com @ ( some_com @ X_45 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_799_conseq,axiom,
% 3.42/1.79 ! [Q_2: state > state > $o,G_6: hoare_1708887482_state > $o,C_32: com,P_7: state > state > $o] :
% 3.42/1.79 ( ! [Z_11: state,S_2: state] :
% 3.42/1.79 ( ( P_7 @ Z_11 @ S_2 )
% 3.42/1.79 => ? [P_8: state > state > $o,Q_3: state > state > $o] :
% 3.42/1.79 ( ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ P_8 @ C_32 @ Q_3 ) @ bot_bo19817387tate_o ) )
% 3.42/1.79 & ! [S_3: state] :
% 3.42/1.79 ( ! [Z_12: state] :
% 3.42/1.79 ( ( P_8 @ Z_12 @ S_2 )
% 3.42/1.79 => ( Q_3 @ Z_12 @ S_3 ) )
% 3.42/1.79 => ( Q_2 @ Z_11 @ S_3 ) ) ) )
% 3.42/1.79 => ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ P_7 @ C_32 @ Q_2 ) @ bot_bo19817387tate_o ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_800_IntE,axiom,
% 3.42/1.79 ! [C_31: com,A_123: com > $o,B_78: com > $o] :
% 3.42/1.79 ( ( member_com @ C_31 @ ( semila513601829_com_o @ A_123 @ B_78 ) )
% 3.42/1.79 => ~ ( ( member_com @ C_31 @ A_123 )
% 3.42/1.79 => ~ ( member_com @ C_31 @ B_78 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_801_IntE,axiom,
% 3.42/1.79 ! [C_31: pname,A_123: pname > $o,B_78: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_31 @ ( semila1673364395name_o @ A_123 @ B_78 ) )
% 3.42/1.79 => ~ ( ( member_pname @ C_31 @ A_123 )
% 3.42/1.79 => ~ ( member_pname @ C_31 @ B_78 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_802_IntE,axiom,
% 3.42/1.79 ! [C_31: hoare_1708887482_state,A_123: hoare_1708887482_state > $o,B_78: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_31 @ ( semila129691299tate_o @ A_123 @ B_78 ) )
% 3.42/1.79 => ~ ( ( member451959335_state @ C_31 @ A_123 )
% 3.42/1.79 => ~ ( member451959335_state @ C_31 @ B_78 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_803_IntI,axiom,
% 3.42/1.79 ! [B_77: com > $o,C_30: com,A_122: com > $o] :
% 3.42/1.79 ( ( member_com @ C_30 @ A_122 )
% 3.42/1.79 => ( ( member_com @ C_30 @ B_77 )
% 3.42/1.79 => ( member_com @ C_30 @ ( semila513601829_com_o @ A_122 @ B_77 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_804_IntI,axiom,
% 3.42/1.79 ! [B_77: pname > $o,C_30: pname,A_122: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_30 @ A_122 )
% 3.42/1.79 => ( ( member_pname @ C_30 @ B_77 )
% 3.42/1.79 => ( member_pname @ C_30 @ ( semila1673364395name_o @ A_122 @ B_77 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_805_IntI,axiom,
% 3.42/1.79 ! [B_77: hoare_1708887482_state > $o,C_30: hoare_1708887482_state,A_122: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_30 @ A_122 )
% 3.42/1.79 => ( ( member451959335_state @ C_30 @ B_77 )
% 3.42/1.79 => ( member451959335_state @ C_30 @ ( semila129691299tate_o @ A_122 @ B_77 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_806_DiffE,axiom,
% 3.42/1.79 ! [C_29: com,A_121: com > $o,B_76: com > $o] :
% 3.42/1.79 ( ( member_com @ C_29 @ ( minus_minus_com_o @ A_121 @ B_76 ) )
% 3.42/1.79 => ~ ( ( member_com @ C_29 @ A_121 )
% 3.42/1.79 => ( member_com @ C_29 @ B_76 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_807_DiffE,axiom,
% 3.42/1.79 ! [C_29: pname,A_121: pname > $o,B_76: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_29 @ ( minus_minus_pname_o @ A_121 @ B_76 ) )
% 3.42/1.79 => ~ ( ( member_pname @ C_29 @ A_121 )
% 3.42/1.79 => ( member_pname @ C_29 @ B_76 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_808_DiffE,axiom,
% 3.42/1.79 ! [C_29: hoare_1708887482_state,A_121: hoare_1708887482_state > $o,B_76: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_29 @ ( minus_2056855718tate_o @ A_121 @ B_76 ) )
% 3.42/1.79 => ~ ( ( member451959335_state @ C_29 @ A_121 )
% 3.42/1.79 => ( member451959335_state @ C_29 @ B_76 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_809_DiffI,axiom,
% 3.42/1.79 ! [B_75: com > $o,C_28: com,A_120: com > $o] :
% 3.42/1.79 ( ( member_com @ C_28 @ A_120 )
% 3.42/1.79 => ( ~ ( member_com @ C_28 @ B_75 )
% 3.42/1.79 => ( member_com @ C_28 @ ( minus_minus_com_o @ A_120 @ B_75 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_810_DiffI,axiom,
% 3.42/1.79 ! [B_75: pname > $o,C_28: pname,A_120: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_28 @ A_120 )
% 3.42/1.79 => ( ~ ( member_pname @ C_28 @ B_75 )
% 3.42/1.79 => ( member_pname @ C_28 @ ( minus_minus_pname_o @ A_120 @ B_75 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_811_DiffI,axiom,
% 3.42/1.79 ! [B_75: hoare_1708887482_state > $o,C_28: hoare_1708887482_state,A_120: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_28 @ A_120 )
% 3.42/1.79 => ( ~ ( member451959335_state @ C_28 @ B_75 )
% 3.42/1.79 => ( member451959335_state @ C_28 @ ( minus_2056855718tate_o @ A_120 @ B_75 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_812_finite__Int,axiom,
% 3.42/1.79 ! [G_5: ( pname > $o ) > $o,F_28: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( ( finite297249702name_o @ F_28 )
% 3.42/1.79 | ( finite297249702name_o @ G_5 ) )
% 3.42/1.79 => ( finite297249702name_o @ ( semila2013987940me_o_o @ F_28 @ G_5 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_813_finite__Int,axiom,
% 3.42/1.79 ! [G_5: ( hoare_1708887482_state > $o ) > $o,F_28: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( ( finite1329924456tate_o @ F_28 )
% 3.42/1.79 | ( finite1329924456tate_o @ G_5 ) )
% 3.42/1.79 => ( finite1329924456tate_o @ ( semila598060698te_o_o @ F_28 @ G_5 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_814_finite__Int,axiom,
% 3.42/1.79 ! [G_5: pname > $o,F_28: pname > $o] :
% 3.42/1.79 ( ( ( finite_finite_pname @ F_28 )
% 3.42/1.79 | ( finite_finite_pname @ G_5 ) )
% 3.42/1.79 => ( finite_finite_pname @ ( semila1673364395name_o @ F_28 @ G_5 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_815_finite__Int,axiom,
% 3.42/1.79 ! [G_5: hoare_1708887482_state > $o,F_28: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ( finite1625599783_state @ F_28 )
% 3.42/1.79 | ( finite1625599783_state @ G_5 ) )
% 3.42/1.79 => ( finite1625599783_state @ ( semila129691299tate_o @ F_28 @ G_5 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_816_finite__Diff,axiom,
% 3.42/1.79 ! [B_74: ( pname > $o ) > $o,A_119: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( finite297249702name_o @ A_119 )
% 3.42/1.79 => ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_119 @ B_74 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_817_finite__Diff,axiom,
% 3.42/1.79 ! [B_74: ( hoare_1708887482_state > $o ) > $o,A_119: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( finite1329924456tate_o @ A_119 )
% 3.42/1.79 => ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_119 @ B_74 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_818_finite__Diff,axiom,
% 3.42/1.79 ! [B_74: pname > $o,A_119: pname > $o] :
% 3.42/1.79 ( ( finite_finite_pname @ A_119 )
% 3.42/1.79 => ( finite_finite_pname @ ( minus_minus_pname_o @ A_119 @ B_74 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_819_finite__Diff,axiom,
% 3.42/1.79 ! [B_74: hoare_1708887482_state > $o,A_119: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( finite1625599783_state @ A_119 )
% 3.42/1.79 => ( finite1625599783_state @ ( minus_2056855718tate_o @ A_119 @ B_74 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_820_inf__Int__eq,axiom,
% 3.42/1.79 ! [R: com > $o,S_1: com > $o,X_3: com] :
% 3.42/1.79 ( ( semila513601829_com_o
% 3.42/1.79 @ ^ [Y_4: com] : ( member_com @ Y_4 @ R )
% 3.42/1.79 @ ^ [Y_4: com] : ( member_com @ Y_4 @ S_1 )
% 3.42/1.79 @ X_3 )
% 3.42/1.79 <=> ( member_com @ X_3 @ ( semila513601829_com_o @ R @ S_1 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_821_inf__Int__eq,axiom,
% 3.42/1.79 ! [R: pname > $o,S_1: pname > $o,X_3: pname] :
% 3.42/1.79 ( ( semila1673364395name_o
% 3.42/1.79 @ ^ [Y_4: pname] : ( member_pname @ Y_4 @ R )
% 3.42/1.79 @ ^ [Y_4: pname] : ( member_pname @ Y_4 @ S_1 )
% 3.42/1.79 @ X_3 )
% 3.42/1.79 <=> ( member_pname @ X_3 @ ( semila1673364395name_o @ R @ S_1 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_822_inf__Int__eq,axiom,
% 3.42/1.79 ! [R: hoare_1708887482_state > $o,S_1: hoare_1708887482_state > $o,X_3: hoare_1708887482_state] :
% 3.42/1.79 ( ( semila129691299tate_o
% 3.42/1.79 @ ^ [Y_4: hoare_1708887482_state] : ( member451959335_state @ Y_4 @ R )
% 3.42/1.79 @ ^ [Y_4: hoare_1708887482_state] : ( member451959335_state @ Y_4 @ S_1 )
% 3.42/1.79 @ X_3 )
% 3.42/1.79 <=> ( member451959335_state @ X_3 @ ( semila129691299tate_o @ R @ S_1 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_823_Diff__disjoint,axiom,
% 3.42/1.79 ! [A_118: com > $o,B_73: com > $o] :
% 3.42/1.79 ( ( semila513601829_com_o @ A_118 @ ( minus_minus_com_o @ B_73 @ A_118 ) )
% 3.42/1.79 = bot_bot_com_o ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_824_Diff__disjoint,axiom,
% 3.42/1.79 ! [A_118: pname > $o,B_73: pname > $o] :
% 3.42/1.79 ( ( semila1673364395name_o @ A_118 @ ( minus_minus_pname_o @ B_73 @ A_118 ) )
% 3.42/1.79 = bot_bot_pname_o ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_825_Diff__disjoint,axiom,
% 3.42/1.79 ! [A_118: hoare_1708887482_state > $o,B_73: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila129691299tate_o @ A_118 @ ( minus_2056855718tate_o @ B_73 @ A_118 ) )
% 3.42/1.79 = bot_bo19817387tate_o ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_826_Diff__triv,axiom,
% 3.42/1.79 ! [A_117: com > $o,B_72: com > $o] :
% 3.42/1.79 ( ( ( semila513601829_com_o @ A_117 @ B_72 )
% 3.42/1.79 = bot_bot_com_o )
% 3.42/1.79 => ( ( minus_minus_com_o @ A_117 @ B_72 )
% 3.42/1.79 = A_117 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_827_Diff__triv,axiom,
% 3.42/1.79 ! [A_117: pname > $o,B_72: pname > $o] :
% 3.42/1.79 ( ( ( semila1673364395name_o @ A_117 @ B_72 )
% 3.42/1.79 = bot_bot_pname_o )
% 3.42/1.79 => ( ( minus_minus_pname_o @ A_117 @ B_72 )
% 3.42/1.79 = A_117 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_828_Diff__triv,axiom,
% 3.42/1.79 ! [A_117: hoare_1708887482_state > $o,B_72: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( ( semila129691299tate_o @ A_117 @ B_72 )
% 3.42/1.79 = bot_bo19817387tate_o )
% 3.42/1.79 => ( ( minus_2056855718tate_o @ A_117 @ B_72 )
% 3.42/1.79 = A_117 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_829_DiffD2,axiom,
% 3.42/1.79 ! [C_27: com,A_116: com > $o,B_71: com > $o] :
% 3.42/1.79 ( ( member_com @ C_27 @ ( minus_minus_com_o @ A_116 @ B_71 ) )
% 3.42/1.79 => ~ ( member_com @ C_27 @ B_71 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_830_DiffD2,axiom,
% 3.42/1.79 ! [C_27: pname,A_116: pname > $o,B_71: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_27 @ ( minus_minus_pname_o @ A_116 @ B_71 ) )
% 3.42/1.79 => ~ ( member_pname @ C_27 @ B_71 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_831_DiffD2,axiom,
% 3.42/1.79 ! [C_27: hoare_1708887482_state,A_116: hoare_1708887482_state > $o,B_71: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_27 @ ( minus_2056855718tate_o @ A_116 @ B_71 ) )
% 3.42/1.79 => ~ ( member451959335_state @ C_27 @ B_71 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_832_IntD2,axiom,
% 3.42/1.79 ! [C_26: com,A_115: com > $o,B_70: com > $o] :
% 3.42/1.79 ( ( member_com @ C_26 @ ( semila513601829_com_o @ A_115 @ B_70 ) )
% 3.42/1.79 => ( member_com @ C_26 @ B_70 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_833_IntD2,axiom,
% 3.42/1.79 ! [C_26: pname,A_115: pname > $o,B_70: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_26 @ ( semila1673364395name_o @ A_115 @ B_70 ) )
% 3.42/1.79 => ( member_pname @ C_26 @ B_70 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_834_IntD2,axiom,
% 3.42/1.79 ! [C_26: hoare_1708887482_state,A_115: hoare_1708887482_state > $o,B_70: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_26 @ ( semila129691299tate_o @ A_115 @ B_70 ) )
% 3.42/1.79 => ( member451959335_state @ C_26 @ B_70 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_835_IntD1,axiom,
% 3.42/1.79 ! [C_25: com,A_114: com > $o,B_69: com > $o] :
% 3.42/1.79 ( ( member_com @ C_25 @ ( semila513601829_com_o @ A_114 @ B_69 ) )
% 3.42/1.79 => ( member_com @ C_25 @ A_114 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_836_IntD1,axiom,
% 3.42/1.79 ! [C_25: pname,A_114: pname > $o,B_69: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_25 @ ( semila1673364395name_o @ A_114 @ B_69 ) )
% 3.42/1.79 => ( member_pname @ C_25 @ A_114 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_837_IntD1,axiom,
% 3.42/1.79 ! [C_25: hoare_1708887482_state,A_114: hoare_1708887482_state > $o,B_69: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_25 @ ( semila129691299tate_o @ A_114 @ B_69 ) )
% 3.42/1.79 => ( member451959335_state @ C_25 @ A_114 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_838_DiffD1,axiom,
% 3.42/1.79 ! [C_24: com,A_113: com > $o,B_68: com > $o] :
% 3.42/1.79 ( ( member_com @ C_24 @ ( minus_minus_com_o @ A_113 @ B_68 ) )
% 3.42/1.79 => ( member_com @ C_24 @ A_113 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_839_DiffD1,axiom,
% 3.42/1.79 ! [C_24: pname,A_113: pname > $o,B_68: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_24 @ ( minus_minus_pname_o @ A_113 @ B_68 ) )
% 3.42/1.79 => ( member_pname @ C_24 @ A_113 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_840_DiffD1,axiom,
% 3.42/1.79 ! [C_24: hoare_1708887482_state,A_113: hoare_1708887482_state > $o,B_68: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_24 @ ( minus_2056855718tate_o @ A_113 @ B_68 ) )
% 3.42/1.79 => ( member451959335_state @ C_24 @ A_113 ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_841_Int__iff,axiom,
% 3.42/1.79 ! [C_23: com,A_112: com > $o,B_67: com > $o] :
% 3.42/1.79 ( ( member_com @ C_23 @ ( semila513601829_com_o @ A_112 @ B_67 ) )
% 3.42/1.79 <=> ( ( member_com @ C_23 @ A_112 )
% 3.42/1.79 & ( member_com @ C_23 @ B_67 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_842_Int__iff,axiom,
% 3.42/1.79 ! [C_23: pname,A_112: pname > $o,B_67: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_23 @ ( semila1673364395name_o @ A_112 @ B_67 ) )
% 3.42/1.79 <=> ( ( member_pname @ C_23 @ A_112 )
% 3.42/1.79 & ( member_pname @ C_23 @ B_67 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_843_Int__iff,axiom,
% 3.42/1.79 ! [C_23: hoare_1708887482_state,A_112: hoare_1708887482_state > $o,B_67: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_23 @ ( semila129691299tate_o @ A_112 @ B_67 ) )
% 3.42/1.79 <=> ( ( member451959335_state @ C_23 @ A_112 )
% 3.42/1.79 & ( member451959335_state @ C_23 @ B_67 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_844_Diff__iff,axiom,
% 3.42/1.79 ! [C_22: com,A_111: com > $o,B_66: com > $o] :
% 3.42/1.79 ( ( member_com @ C_22 @ ( minus_minus_com_o @ A_111 @ B_66 ) )
% 3.42/1.79 <=> ( ( member_com @ C_22 @ A_111 )
% 3.42/1.79 & ~ ( member_com @ C_22 @ B_66 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_845_Diff__iff,axiom,
% 3.42/1.79 ! [C_22: pname,A_111: pname > $o,B_66: pname > $o] :
% 3.42/1.79 ( ( member_pname @ C_22 @ ( minus_minus_pname_o @ A_111 @ B_66 ) )
% 3.42/1.79 <=> ( ( member_pname @ C_22 @ A_111 )
% 3.42/1.79 & ~ ( member_pname @ C_22 @ B_66 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_846_Diff__iff,axiom,
% 3.42/1.79 ! [C_22: hoare_1708887482_state,A_111: hoare_1708887482_state > $o,B_66: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( member451959335_state @ C_22 @ ( minus_2056855718tate_o @ A_111 @ B_66 ) )
% 3.42/1.79 <=> ( ( member451959335_state @ C_22 @ A_111 )
% 3.42/1.79 & ~ ( member451959335_state @ C_22 @ B_66 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_847_Int__def,axiom,
% 3.42/1.79 ! [A_110: com > $o,B_65: com > $o] :
% 3.42/1.79 ( ( semila513601829_com_o @ A_110 @ B_65 )
% 3.42/1.79 = ( collect_com
% 3.42/1.79 @ ^ [X_3: com] : ( (&) @ ( member_com @ X_3 @ A_110 ) @ ( member_com @ X_3 @ B_65 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_848_Int__def,axiom,
% 3.42/1.79 ! [A_110: pname > $o,B_65: pname > $o] :
% 3.42/1.79 ( ( semila1673364395name_o @ A_110 @ B_65 )
% 3.42/1.79 = ( collect_pname
% 3.42/1.79 @ ^ [X_3: pname] : ( (&) @ ( member_pname @ X_3 @ A_110 ) @ ( member_pname @ X_3 @ B_65 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_849_Int__def,axiom,
% 3.42/1.79 ! [A_110: hoare_1708887482_state > $o,B_65: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( semila129691299tate_o @ A_110 @ B_65 )
% 3.42/1.79 = ( collec1568722789_state
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( member451959335_state @ X_3 @ A_110 ) @ ( member451959335_state @ X_3 @ B_65 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_850_Int__def,axiom,
% 3.42/1.79 ! [A_110: ( pname > $o ) > $o,B_65: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( semila2013987940me_o_o @ A_110 @ B_65 )
% 3.42/1.79 = ( collect_pname_o
% 3.42/1.79 @ ^ [X_3: pname > $o] : ( (&) @ ( member_pname_o @ X_3 @ A_110 ) @ ( member_pname_o @ X_3 @ B_65 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_851_Int__def,axiom,
% 3.42/1.79 ! [A_110: ( hoare_1708887482_state > $o ) > $o,B_65: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( semila598060698te_o_o @ A_110 @ B_65 )
% 3.42/1.79 = ( collec219771562tate_o
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( member814030440tate_o @ X_3 @ A_110 ) @ ( member814030440tate_o @ X_3 @ B_65 ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_852_set__diff__eq,axiom,
% 3.42/1.79 ! [A_109: com > $o,B_64: com > $o] :
% 3.42/1.79 ( ( minus_minus_com_o @ A_109 @ B_64 )
% 3.42/1.79 = ( collect_com
% 3.42/1.79 @ ^ [X_3: com] : ( (&) @ ( member_com @ X_3 @ A_109 ) @ ( (~) @ ( member_com @ X_3 @ B_64 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_853_set__diff__eq,axiom,
% 3.42/1.79 ! [A_109: pname > $o,B_64: pname > $o] :
% 3.42/1.79 ( ( minus_minus_pname_o @ A_109 @ B_64 )
% 3.42/1.79 = ( collect_pname
% 3.42/1.79 @ ^ [X_3: pname] : ( (&) @ ( member_pname @ X_3 @ A_109 ) @ ( (~) @ ( member_pname @ X_3 @ B_64 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_854_set__diff__eq,axiom,
% 3.42/1.79 ! [A_109: hoare_1708887482_state > $o,B_64: hoare_1708887482_state > $o] :
% 3.42/1.79 ( ( minus_2056855718tate_o @ A_109 @ B_64 )
% 3.42/1.79 = ( collec1568722789_state
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( member451959335_state @ X_3 @ A_109 ) @ ( (~) @ ( member451959335_state @ X_3 @ B_64 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_855_set__diff__eq,axiom,
% 3.42/1.79 ! [A_109: ( pname > $o ) > $o,B_64: ( pname > $o ) > $o] :
% 3.42/1.79 ( ( minus_1480864103me_o_o @ A_109 @ B_64 )
% 3.42/1.79 = ( collect_pname_o
% 3.42/1.79 @ ^ [X_3: pname > $o] : ( (&) @ ( member_pname_o @ X_3 @ A_109 ) @ ( (~) @ ( member_pname_o @ X_3 @ B_64 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_856_set__diff__eq,axiom,
% 3.42/1.79 ! [A_109: ( hoare_1708887482_state > $o ) > $o,B_64: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.79 ( ( minus_548038231te_o_o @ A_109 @ B_64 )
% 3.42/1.79 = ( collec219771562tate_o
% 3.42/1.79 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( member814030440tate_o @ X_3 @ A_109 ) @ ( (~) @ ( member814030440tate_o @ X_3 @ B_64 ) ) ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_857_Int__Collect,axiom,
% 3.42/1.79 ! [X_44: com,A_108: com > $o,P_6: com > $o] :
% 3.42/1.79 ( ( member_com @ X_44 @ ( semila513601829_com_o @ A_108 @ ( collect_com @ P_6 ) ) )
% 3.42/1.79 <=> ( ( member_com @ X_44 @ A_108 )
% 3.42/1.79 & ( P_6 @ X_44 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_858_Int__Collect,axiom,
% 3.42/1.79 ! [X_44: pname,A_108: pname > $o,P_6: pname > $o] :
% 3.42/1.79 ( ( member_pname @ X_44 @ ( semila1673364395name_o @ A_108 @ ( collect_pname @ P_6 ) ) )
% 3.42/1.79 <=> ( ( member_pname @ X_44 @ A_108 )
% 3.42/1.79 & ( P_6 @ X_44 ) ) ) ).
% 3.42/1.79
% 3.42/1.79 thf(fact_859_Int__Collect,axiom,
% 3.42/1.79 ! [X_44: hoare_1708887482_state,A_108: hoare_1708887482_state > $o,P_6: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( member451959335_state @ X_44 @ ( semila129691299tate_o @ A_108 @ ( collec1568722789_state @ P_6 ) ) )
% 3.42/1.80 <=> ( ( member451959335_state @ X_44 @ A_108 )
% 3.42/1.80 & ( P_6 @ X_44 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_860_Int__Collect,axiom,
% 3.42/1.80 ! [X_44: pname > $o,A_108: ( pname > $o ) > $o,P_6: ( pname > $o ) > $o] :
% 3.42/1.80 ( ( member_pname_o @ X_44 @ ( semila2013987940me_o_o @ A_108 @ ( collect_pname_o @ P_6 ) ) )
% 3.42/1.80 <=> ( ( member_pname_o @ X_44 @ A_108 )
% 3.42/1.80 & ( P_6 @ X_44 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_861_Int__Collect,axiom,
% 3.42/1.80 ! [X_44: hoare_1708887482_state > $o,A_108: ( hoare_1708887482_state > $o ) > $o,P_6: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.80 ( ( member814030440tate_o @ X_44 @ ( semila598060698te_o_o @ A_108 @ ( collec219771562tate_o @ P_6 ) ) )
% 3.42/1.80 <=> ( ( member814030440tate_o @ X_44 @ A_108 )
% 3.42/1.80 & ( P_6 @ X_44 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_862_Collect__conj__eq,axiom,
% 3.42/1.80 ! [P_5: hoare_1708887482_state > $o,Q_1: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( collec1568722789_state
% 3.42/1.80 @ ^ [X_3: hoare_1708887482_state] : ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
% 3.42/1.80 = ( semila129691299tate_o @ ( collec1568722789_state @ P_5 ) @ ( collec1568722789_state @ Q_1 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_863_Collect__conj__eq,axiom,
% 3.42/1.80 ! [P_5: pname > $o,Q_1: pname > $o] :
% 3.42/1.80 ( ( collect_pname
% 3.42/1.80 @ ^ [X_3: pname] : ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
% 3.42/1.80 = ( semila1673364395name_o @ ( collect_pname @ P_5 ) @ ( collect_pname @ Q_1 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_864_Collect__conj__eq,axiom,
% 3.42/1.80 ! [P_5: ( pname > $o ) > $o,Q_1: ( pname > $o ) > $o] :
% 3.42/1.80 ( ( collect_pname_o
% 3.42/1.80 @ ^ [X_3: pname > $o] : ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
% 3.42/1.80 = ( semila2013987940me_o_o @ ( collect_pname_o @ P_5 ) @ ( collect_pname_o @ Q_1 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_865_Collect__conj__eq,axiom,
% 3.42/1.80 ! [P_5: ( hoare_1708887482_state > $o ) > $o,Q_1: ( hoare_1708887482_state > $o ) > $o] :
% 3.42/1.80 ( ( collec219771562tate_o
% 3.42/1.80 @ ^ [X_3: hoare_1708887482_state > $o] : ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
% 3.42/1.80 = ( semila598060698te_o_o @ ( collec219771562tate_o @ P_5 ) @ ( collec219771562tate_o @ Q_1 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_866_Diff__Int,axiom,
% 3.42/1.80 ! [A_107: pname > $o,B_63: pname > $o,C_21: pname > $o] :
% 3.42/1.80 ( ( minus_minus_pname_o @ A_107 @ ( semila1673364395name_o @ B_63 @ C_21 ) )
% 3.42/1.80 = ( semila1780557381name_o @ ( minus_minus_pname_o @ A_107 @ B_63 ) @ ( minus_minus_pname_o @ A_107 @ C_21 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_867_Diff__Int,axiom,
% 3.42/1.80 ! [A_107: hoare_1708887482_state > $o,B_63: hoare_1708887482_state > $o,C_21: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( minus_2056855718tate_o @ A_107 @ ( semila129691299tate_o @ B_63 @ C_21 ) )
% 3.42/1.80 = ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A_107 @ B_63 ) @ ( minus_2056855718tate_o @ A_107 @ C_21 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_868_Diff__Un,axiom,
% 3.42/1.80 ! [A_106: pname > $o,B_62: pname > $o,C_20: pname > $o] :
% 3.42/1.80 ( ( minus_minus_pname_o @ A_106 @ ( semila1780557381name_o @ B_62 @ C_20 ) )
% 3.42/1.80 = ( semila1673364395name_o @ ( minus_minus_pname_o @ A_106 @ B_62 ) @ ( minus_minus_pname_o @ A_106 @ C_20 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_869_Diff__Un,axiom,
% 3.42/1.80 ! [A_106: hoare_1708887482_state > $o,B_62: hoare_1708887482_state > $o,C_20: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( minus_2056855718tate_o @ A_106 @ ( semila1122118281tate_o @ B_62 @ C_20 ) )
% 3.42/1.80 = ( semila129691299tate_o @ ( minus_2056855718tate_o @ A_106 @ B_62 ) @ ( minus_2056855718tate_o @ A_106 @ C_20 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_870_Un__Diff__Int,axiom,
% 3.42/1.80 ! [A_105: pname > $o,B_61: pname > $o] :
% 3.42/1.80 ( ( semila1780557381name_o @ ( minus_minus_pname_o @ A_105 @ B_61 ) @ ( semila1673364395name_o @ A_105 @ B_61 ) )
% 3.42/1.80 = A_105 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_871_Un__Diff__Int,axiom,
% 3.42/1.80 ! [A_105: hoare_1708887482_state > $o,B_61: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A_105 @ B_61 ) @ ( semila129691299tate_o @ A_105 @ B_61 ) )
% 3.42/1.80 = A_105 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_872_inf__sup__ord_I1_J,axiom,
% 3.42/1.80 ! [X_43: $o,Y_24: $o] : ( ord_less_eq_o @ ( semila854092349_inf_o @ X_43 @ Y_24 ) @ X_43 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_873_inf__sup__ord_I1_J,axiom,
% 3.42/1.80 ! [X_43: pname > $o,Y_24: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_43 @ Y_24 ) @ X_43 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_874_inf__sup__ord_I1_J,axiom,
% 3.42/1.80 ! [X_43: hoare_1708887482_state > $o,Y_24: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_43 @ Y_24 ) @ X_43 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_875_inf__le1,axiom,
% 3.42/1.80 ! [X_42: $o,Y_23: $o] : ( ord_less_eq_o @ ( semila854092349_inf_o @ X_42 @ Y_23 ) @ X_42 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_876_inf__le1,axiom,
% 3.42/1.80 ! [X_42: pname > $o,Y_23: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_42 @ Y_23 ) @ X_42 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_877_inf__le1,axiom,
% 3.42/1.80 ! [X_42: hoare_1708887482_state > $o,Y_23: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_42 @ Y_23 ) @ X_42 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_878_inf__sup__ord_I2_J,axiom,
% 3.42/1.80 ! [X_41: $o,Y_22: $o] : ( ord_less_eq_o @ ( semila854092349_inf_o @ X_41 @ Y_22 ) @ Y_22 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_879_inf__sup__ord_I2_J,axiom,
% 3.42/1.80 ! [X_41: pname > $o,Y_22: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_41 @ Y_22 ) @ Y_22 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_880_inf__sup__ord_I2_J,axiom,
% 3.42/1.80 ! [X_41: hoare_1708887482_state > $o,Y_22: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_41 @ Y_22 ) @ Y_22 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_881_inf__le2,axiom,
% 3.42/1.80 ! [X_40: $o,Y_21: $o] : ( ord_less_eq_o @ ( semila854092349_inf_o @ X_40 @ Y_21 ) @ Y_21 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_882_inf__le2,axiom,
% 3.42/1.80 ! [X_40: pname > $o,Y_21: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_40 @ Y_21 ) @ Y_21 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_883_inf__le2,axiom,
% 3.42/1.80 ! [X_40: hoare_1708887482_state > $o,Y_21: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_40 @ Y_21 ) @ Y_21 ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_884_le__iff__inf,axiom,
% 3.42/1.80 ! [X_39: $o,Y_20: $o] :
% 3.42/1.80 ( ( ord_less_eq_o @ X_39 @ Y_20 )
% 3.42/1.80 <=> ( ( semila854092349_inf_o @ X_39 @ Y_20 )
% 3.42/1.80 <=> X_39 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_885_le__iff__inf,axiom,
% 3.42/1.80 ! [X_39: pname > $o,Y_20: pname > $o] :
% 3.42/1.80 ( ( ord_less_eq_pname_o @ X_39 @ Y_20 )
% 3.42/1.80 <=> ( ( semila1673364395name_o @ X_39 @ Y_20 )
% 3.42/1.80 = X_39 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_886_le__iff__inf,axiom,
% 3.42/1.80 ! [X_39: hoare_1708887482_state > $o,Y_20: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( ord_le777019615tate_o @ X_39 @ Y_20 )
% 3.42/1.80 <=> ( ( semila129691299tate_o @ X_39 @ Y_20 )
% 3.42/1.80 = X_39 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_887_le__inf__iff,axiom,
% 3.42/1.80 ! [X_38: $o,Y_19: $o,Z_10: $o] :
% 3.42/1.80 ( ( ord_less_eq_o @ X_38 @ ( semila854092349_inf_o @ Y_19 @ Z_10 ) )
% 3.42/1.80 <=> ( ( ord_less_eq_o @ X_38 @ Y_19 )
% 3.42/1.80 & ( ord_less_eq_o @ X_38 @ Z_10 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_888_le__inf__iff,axiom,
% 3.42/1.80 ! [X_38: pname > $o,Y_19: pname > $o,Z_10: pname > $o] :
% 3.42/1.80 ( ( ord_less_eq_pname_o @ X_38 @ ( semila1673364395name_o @ Y_19 @ Z_10 ) )
% 3.42/1.80 <=> ( ( ord_less_eq_pname_o @ X_38 @ Y_19 )
% 3.42/1.80 & ( ord_less_eq_pname_o @ X_38 @ Z_10 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_889_le__inf__iff,axiom,
% 3.42/1.80 ! [X_38: hoare_1708887482_state > $o,Y_19: hoare_1708887482_state > $o,Z_10: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( ord_le777019615tate_o @ X_38 @ ( semila129691299tate_o @ Y_19 @ Z_10 ) )
% 3.42/1.80 <=> ( ( ord_le777019615tate_o @ X_38 @ Y_19 )
% 3.42/1.80 & ( ord_le777019615tate_o @ X_38 @ Z_10 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_890_le__infI1,axiom,
% 3.42/1.80 ! [B_60: $o,A_104: $o,X_37: $o] :
% 3.42/1.80 ( ( ord_less_eq_o @ A_104 @ X_37 )
% 3.42/1.80 => ( ord_less_eq_o @ ( semila854092349_inf_o @ A_104 @ B_60 ) @ X_37 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_891_le__infI1,axiom,
% 3.42/1.80 ! [B_60: pname > $o,A_104: pname > $o,X_37: pname > $o] :
% 3.42/1.80 ( ( ord_less_eq_pname_o @ A_104 @ X_37 )
% 3.42/1.80 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_104 @ B_60 ) @ X_37 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_892_le__infI1,axiom,
% 3.42/1.80 ! [B_60: hoare_1708887482_state > $o,A_104: hoare_1708887482_state > $o,X_37: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( ord_le777019615tate_o @ A_104 @ X_37 )
% 3.42/1.80 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_104 @ B_60 ) @ X_37 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_893_le__infI2,axiom,
% 3.42/1.80 ! [A_103: $o,B_59: $o,X_36: $o] :
% 3.42/1.80 ( ( ord_less_eq_o @ B_59 @ X_36 )
% 3.42/1.80 => ( ord_less_eq_o @ ( semila854092349_inf_o @ A_103 @ B_59 ) @ X_36 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_894_le__infI2,axiom,
% 3.42/1.80 ! [A_103: pname > $o,B_59: pname > $o,X_36: pname > $o] :
% 3.42/1.80 ( ( ord_less_eq_pname_o @ B_59 @ X_36 )
% 3.42/1.80 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_103 @ B_59 ) @ X_36 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_895_le__infI2,axiom,
% 3.42/1.80 ! [A_103: hoare_1708887482_state > $o,B_59: hoare_1708887482_state > $o,X_36: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( ord_le777019615tate_o @ B_59 @ X_36 )
% 3.42/1.80 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_103 @ B_59 ) @ X_36 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_896_inf__absorb1,axiom,
% 3.42/1.80 ! [X_35: $o,Y_18: $o] :
% 3.42/1.80 ( ( ord_less_eq_o @ X_35 @ Y_18 )
% 3.42/1.80 => ( ( semila854092349_inf_o @ X_35 @ Y_18 )
% 3.42/1.80 <=> X_35 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_897_inf__absorb1,axiom,
% 3.42/1.80 ! [X_35: pname > $o,Y_18: pname > $o] :
% 3.42/1.80 ( ( ord_less_eq_pname_o @ X_35 @ Y_18 )
% 3.42/1.80 => ( ( semila1673364395name_o @ X_35 @ Y_18 )
% 3.42/1.80 = X_35 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_898_inf__absorb1,axiom,
% 3.42/1.80 ! [X_35: hoare_1708887482_state > $o,Y_18: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( ord_le777019615tate_o @ X_35 @ Y_18 )
% 3.42/1.80 => ( ( semila129691299tate_o @ X_35 @ Y_18 )
% 3.42/1.80 = X_35 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_899_inf__absorb2,axiom,
% 3.42/1.80 ! [Y_17: $o,X_34: $o] :
% 3.42/1.80 ( ( ord_less_eq_o @ Y_17 @ X_34 )
% 3.42/1.80 => ( ( semila854092349_inf_o @ X_34 @ Y_17 )
% 3.42/1.80 <=> Y_17 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_900_inf__absorb2,axiom,
% 3.42/1.80 ! [Y_17: pname > $o,X_34: pname > $o] :
% 3.42/1.80 ( ( ord_less_eq_pname_o @ Y_17 @ X_34 )
% 3.42/1.80 => ( ( semila1673364395name_o @ X_34 @ Y_17 )
% 3.42/1.80 = Y_17 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_901_inf__absorb2,axiom,
% 3.42/1.80 ! [Y_17: hoare_1708887482_state > $o,X_34: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( ord_le777019615tate_o @ Y_17 @ X_34 )
% 3.42/1.80 => ( ( semila129691299tate_o @ X_34 @ Y_17 )
% 3.42/1.80 = Y_17 ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_902_le__infI,axiom,
% 3.42/1.80 ! [B_58: $o,X_33: $o,A_102: $o] :
% 3.42/1.80 ( ( ord_less_eq_o @ X_33 @ A_102 )
% 3.42/1.80 => ( ( ord_less_eq_o @ X_33 @ B_58 )
% 3.42/1.80 => ( ord_less_eq_o @ X_33 @ ( semila854092349_inf_o @ A_102 @ B_58 ) ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_903_le__infI,axiom,
% 3.42/1.80 ! [B_58: pname > $o,X_33: pname > $o,A_102: pname > $o] :
% 3.42/1.80 ( ( ord_less_eq_pname_o @ X_33 @ A_102 )
% 3.42/1.80 => ( ( ord_less_eq_pname_o @ X_33 @ B_58 )
% 3.42/1.80 => ( ord_less_eq_pname_o @ X_33 @ ( semila1673364395name_o @ A_102 @ B_58 ) ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_904_le__infI,axiom,
% 3.42/1.80 ! [B_58: hoare_1708887482_state > $o,X_33: hoare_1708887482_state > $o,A_102: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( ord_le777019615tate_o @ X_33 @ A_102 )
% 3.42/1.80 => ( ( ord_le777019615tate_o @ X_33 @ B_58 )
% 3.42/1.80 => ( ord_le777019615tate_o @ X_33 @ ( semila129691299tate_o @ A_102 @ B_58 ) ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_905_inf__greatest,axiom,
% 3.42/1.80 ! [Z_9: $o,X_32: $o,Y_16: $o] :
% 3.42/1.80 ( ( ord_less_eq_o @ X_32 @ Y_16 )
% 3.42/1.80 => ( ( ord_less_eq_o @ X_32 @ Z_9 )
% 3.42/1.80 => ( ord_less_eq_o @ X_32 @ ( semila854092349_inf_o @ Y_16 @ Z_9 ) ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_906_inf__greatest,axiom,
% 3.42/1.80 ! [Z_9: pname > $o,X_32: pname > $o,Y_16: pname > $o] :
% 3.42/1.80 ( ( ord_less_eq_pname_o @ X_32 @ Y_16 )
% 3.42/1.80 => ( ( ord_less_eq_pname_o @ X_32 @ Z_9 )
% 3.42/1.80 => ( ord_less_eq_pname_o @ X_32 @ ( semila1673364395name_o @ Y_16 @ Z_9 ) ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_907_inf__greatest,axiom,
% 3.42/1.80 ! [Z_9: hoare_1708887482_state > $o,X_32: hoare_1708887482_state > $o,Y_16: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( ord_le777019615tate_o @ X_32 @ Y_16 )
% 3.42/1.80 => ( ( ord_le777019615tate_o @ X_32 @ Z_9 )
% 3.42/1.80 => ( ord_le777019615tate_o @ X_32 @ ( semila129691299tate_o @ Y_16 @ Z_9 ) ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_908_inf__mono,axiom,
% 3.42/1.80 ! [B_57: $o,D_2: $o,A_101: $o,C_19: $o] :
% 3.42/1.80 ( ( ord_less_eq_o @ A_101 @ C_19 )
% 3.42/1.80 => ( ( ord_less_eq_o @ B_57 @ D_2 )
% 3.42/1.80 => ( ord_less_eq_o @ ( semila854092349_inf_o @ A_101 @ B_57 ) @ ( semila854092349_inf_o @ C_19 @ D_2 ) ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_909_inf__mono,axiom,
% 3.42/1.80 ! [B_57: pname > $o,D_2: pname > $o,A_101: pname > $o,C_19: pname > $o] :
% 3.42/1.80 ( ( ord_less_eq_pname_o @ A_101 @ C_19 )
% 3.42/1.80 => ( ( ord_less_eq_pname_o @ B_57 @ D_2 )
% 3.42/1.80 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_101 @ B_57 ) @ ( semila1673364395name_o @ C_19 @ D_2 ) ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_910_inf__mono,axiom,
% 3.42/1.80 ! [B_57: hoare_1708887482_state > $o,D_2: hoare_1708887482_state > $o,A_101: hoare_1708887482_state > $o,C_19: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( ord_le777019615tate_o @ A_101 @ C_19 )
% 3.42/1.80 => ( ( ord_le777019615tate_o @ B_57 @ D_2 )
% 3.42/1.80 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_101 @ B_57 ) @ ( semila129691299tate_o @ C_19 @ D_2 ) ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_911_le__infE,axiom,
% 3.42/1.80 ! [X_31: $o,A_100: $o,B_56: $o] :
% 3.42/1.80 ( ( ord_less_eq_o @ X_31 @ ( semila854092349_inf_o @ A_100 @ B_56 ) )
% 3.42/1.80 => ~ ( ( ord_less_eq_o @ X_31 @ A_100 )
% 3.42/1.80 => ~ ( ord_less_eq_o @ X_31 @ B_56 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_912_le__infE,axiom,
% 3.42/1.80 ! [X_31: pname > $o,A_100: pname > $o,B_56: pname > $o] :
% 3.42/1.80 ( ( ord_less_eq_pname_o @ X_31 @ ( semila1673364395name_o @ A_100 @ B_56 ) )
% 3.42/1.80 => ~ ( ( ord_less_eq_pname_o @ X_31 @ A_100 )
% 3.42/1.80 => ~ ( ord_less_eq_pname_o @ X_31 @ B_56 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_913_le__infE,axiom,
% 3.42/1.80 ! [X_31: hoare_1708887482_state > $o,A_100: hoare_1708887482_state > $o,B_56: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( ord_le777019615tate_o @ X_31 @ ( semila129691299tate_o @ A_100 @ B_56 ) )
% 3.42/1.80 => ~ ( ( ord_le777019615tate_o @ X_31 @ A_100 )
% 3.42/1.80 => ~ ( ord_le777019615tate_o @ X_31 @ B_56 ) ) ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_914_inf__bot__right,axiom,
% 3.42/1.80 ! [X_30: com > $o] :
% 3.42/1.80 ( ( semila513601829_com_o @ X_30 @ bot_bot_com_o )
% 3.42/1.80 = bot_bot_com_o ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_915_inf__bot__right,axiom,
% 3.42/1.80 ! [X_30: $o] :
% 3.42/1.80 ( ( semila854092349_inf_o @ X_30 @ bot_bot_o )
% 3.42/1.80 <=> bot_bot_o ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_916_inf__bot__right,axiom,
% 3.42/1.80 ! [X_30: pname > $o] :
% 3.42/1.80 ( ( semila1673364395name_o @ X_30 @ bot_bot_pname_o )
% 3.42/1.80 = bot_bot_pname_o ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_917_inf__bot__right,axiom,
% 3.42/1.80 ! [X_30: hoare_1708887482_state > $o] :
% 3.42/1.80 ( ( semila129691299tate_o @ X_30 @ bot_bo19817387tate_o )
% 3.42/1.80 = bot_bo19817387tate_o ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_918_inf__bot__left,axiom,
% 3.42/1.80 ! [X_29: com > $o] :
% 3.42/1.80 ( ( semila513601829_com_o @ bot_bot_com_o @ X_29 )
% 3.42/1.80 = bot_bot_com_o ) ).
% 3.42/1.80
% 3.42/1.80 thf(fact_919_inf__bot__left,axiom,
% 3.42/1.80 ! [X_29: $o] :
% 3.42/1.80 ( ( semila854092349_inf_o @ bot_bot_o @ X_29 )
% 3.54/1.80 <=> bot_bot_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_920_inf__bot__left,axiom,
% 3.54/1.80 ! [X_29: pname > $o] :
% 3.54/1.80 ( ( semila1673364395name_o @ bot_bot_pname_o @ X_29 )
% 3.54/1.80 = bot_bot_pname_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_921_inf__bot__left,axiom,
% 3.54/1.80 ! [X_29: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila129691299tate_o @ bot_bo19817387tate_o @ X_29 )
% 3.54/1.80 = bot_bo19817387tate_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_922_inf__sup__absorb,axiom,
% 3.54/1.80 ! [X_28: $o,Y_15: $o] :
% 3.54/1.80 ( ( semila854092349_inf_o @ X_28 @ ( semila10642723_sup_o @ X_28 @ Y_15 ) )
% 3.54/1.80 <=> X_28 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_923_inf__sup__absorb,axiom,
% 3.54/1.80 ! [X_28: pname > $o,Y_15: pname > $o] :
% 3.54/1.80 ( ( semila1673364395name_o @ X_28 @ ( semila1780557381name_o @ X_28 @ Y_15 ) )
% 3.54/1.80 = X_28 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_924_inf__sup__absorb,axiom,
% 3.54/1.80 ! [X_28: hoare_1708887482_state > $o,Y_15: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila129691299tate_o @ X_28 @ ( semila1122118281tate_o @ X_28 @ Y_15 ) )
% 3.54/1.80 = X_28 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_925_sup__inf__absorb,axiom,
% 3.54/1.80 ! [X_27: $o,Y_14: $o] :
% 3.54/1.80 ( ( semila10642723_sup_o @ X_27 @ ( semila854092349_inf_o @ X_27 @ Y_14 ) )
% 3.54/1.80 <=> X_27 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_926_sup__inf__absorb,axiom,
% 3.54/1.80 ! [X_27: pname > $o,Y_14: pname > $o] :
% 3.54/1.80 ( ( semila1780557381name_o @ X_27 @ ( semila1673364395name_o @ X_27 @ Y_14 ) )
% 3.54/1.80 = X_27 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_927_sup__inf__absorb,axiom,
% 3.54/1.80 ! [X_27: hoare_1708887482_state > $o,Y_14: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila1122118281tate_o @ X_27 @ ( semila129691299tate_o @ X_27 @ Y_14 ) )
% 3.54/1.80 = X_27 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_928_inf__sup__distrib1,axiom,
% 3.54/1.80 ! [X_26: $o,Y_13: $o,Z_8: $o] :
% 3.54/1.80 ( ( semila854092349_inf_o @ X_26 @ ( semila10642723_sup_o @ Y_13 @ Z_8 ) )
% 3.54/1.80 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_26 @ Y_13 ) @ ( semila854092349_inf_o @ X_26 @ Z_8 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_929_inf__sup__distrib1,axiom,
% 3.54/1.80 ! [X_26: pname > $o,Y_13: pname > $o,Z_8: pname > $o] :
% 3.54/1.80 ( ( semila1673364395name_o @ X_26 @ ( semila1780557381name_o @ Y_13 @ Z_8 ) )
% 3.54/1.80 = ( semila1780557381name_o @ ( semila1673364395name_o @ X_26 @ Y_13 ) @ ( semila1673364395name_o @ X_26 @ Z_8 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_930_inf__sup__distrib1,axiom,
% 3.54/1.80 ! [X_26: hoare_1708887482_state > $o,Y_13: hoare_1708887482_state > $o,Z_8: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila129691299tate_o @ X_26 @ ( semila1122118281tate_o @ Y_13 @ Z_8 ) )
% 3.54/1.80 = ( semila1122118281tate_o @ ( semila129691299tate_o @ X_26 @ Y_13 ) @ ( semila129691299tate_o @ X_26 @ Z_8 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_931_sup__inf__distrib1,axiom,
% 3.54/1.80 ! [X_25: $o,Y_12: $o,Z_7: $o] :
% 3.54/1.80 ( ( semila10642723_sup_o @ X_25 @ ( semila854092349_inf_o @ Y_12 @ Z_7 ) )
% 3.54/1.80 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_25 @ Y_12 ) @ ( semila10642723_sup_o @ X_25 @ Z_7 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_932_sup__inf__distrib1,axiom,
% 3.54/1.80 ! [X_25: pname > $o,Y_12: pname > $o,Z_7: pname > $o] :
% 3.54/1.80 ( ( semila1780557381name_o @ X_25 @ ( semila1673364395name_o @ Y_12 @ Z_7 ) )
% 3.54/1.80 = ( semila1673364395name_o @ ( semila1780557381name_o @ X_25 @ Y_12 ) @ ( semila1780557381name_o @ X_25 @ Z_7 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_933_sup__inf__distrib1,axiom,
% 3.54/1.80 ! [X_25: hoare_1708887482_state > $o,Y_12: hoare_1708887482_state > $o,Z_7: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila1122118281tate_o @ X_25 @ ( semila129691299tate_o @ Y_12 @ Z_7 ) )
% 3.54/1.80 = ( semila129691299tate_o @ ( semila1122118281tate_o @ X_25 @ Y_12 ) @ ( semila1122118281tate_o @ X_25 @ Z_7 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_934_inf__sup__distrib2,axiom,
% 3.54/1.80 ! [Y_11: $o,Z_6: $o,X_24: $o] :
% 3.54/1.80 ( ( semila854092349_inf_o @ ( semila10642723_sup_o @ Y_11 @ Z_6 ) @ X_24 )
% 3.54/1.80 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ Y_11 @ X_24 ) @ ( semila854092349_inf_o @ Z_6 @ X_24 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_935_inf__sup__distrib2,axiom,
% 3.54/1.80 ! [Y_11: pname > $o,Z_6: pname > $o,X_24: pname > $o] :
% 3.54/1.80 ( ( semila1673364395name_o @ ( semila1780557381name_o @ Y_11 @ Z_6 ) @ X_24 )
% 3.54/1.80 = ( semila1780557381name_o @ ( semila1673364395name_o @ Y_11 @ X_24 ) @ ( semila1673364395name_o @ Z_6 @ X_24 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_936_inf__sup__distrib2,axiom,
% 3.54/1.80 ! [Y_11: hoare_1708887482_state > $o,Z_6: hoare_1708887482_state > $o,X_24: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila129691299tate_o @ ( semila1122118281tate_o @ Y_11 @ Z_6 ) @ X_24 )
% 3.54/1.80 = ( semila1122118281tate_o @ ( semila129691299tate_o @ Y_11 @ X_24 ) @ ( semila129691299tate_o @ Z_6 @ X_24 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_937_sup__inf__distrib2,axiom,
% 3.54/1.80 ! [Y_10: $o,Z_5: $o,X_23: $o] :
% 3.54/1.80 ( ( semila10642723_sup_o @ ( semila854092349_inf_o @ Y_10 @ Z_5 ) @ X_23 )
% 3.54/1.80 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ Y_10 @ X_23 ) @ ( semila10642723_sup_o @ Z_5 @ X_23 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_938_sup__inf__distrib2,axiom,
% 3.54/1.80 ! [Y_10: pname > $o,Z_5: pname > $o,X_23: pname > $o] :
% 3.54/1.80 ( ( semila1780557381name_o @ ( semila1673364395name_o @ Y_10 @ Z_5 ) @ X_23 )
% 3.54/1.80 = ( semila1673364395name_o @ ( semila1780557381name_o @ Y_10 @ X_23 ) @ ( semila1780557381name_o @ Z_5 @ X_23 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_939_sup__inf__distrib2,axiom,
% 3.54/1.80 ! [Y_10: hoare_1708887482_state > $o,Z_5: hoare_1708887482_state > $o,X_23: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila1122118281tate_o @ ( semila129691299tate_o @ Y_10 @ Z_5 ) @ X_23 )
% 3.54/1.80 = ( semila129691299tate_o @ ( semila1122118281tate_o @ Y_10 @ X_23 ) @ ( semila1122118281tate_o @ Z_5 @ X_23 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_940_Diff__cancel,axiom,
% 3.54/1.80 ! [A_99: com > $o] :
% 3.54/1.80 ( ( minus_minus_com_o @ A_99 @ A_99 )
% 3.54/1.80 = bot_bot_com_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_941_Diff__cancel,axiom,
% 3.54/1.80 ! [A_99: pname > $o] :
% 3.54/1.80 ( ( minus_minus_pname_o @ A_99 @ A_99 )
% 3.54/1.80 = bot_bot_pname_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_942_Diff__cancel,axiom,
% 3.54/1.80 ! [A_99: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( minus_2056855718tate_o @ A_99 @ A_99 )
% 3.54/1.80 = bot_bo19817387tate_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_943_Diff__empty,axiom,
% 3.54/1.80 ! [A_98: com > $o] :
% 3.54/1.80 ( ( minus_minus_com_o @ A_98 @ bot_bot_com_o )
% 3.54/1.80 = A_98 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_944_Diff__empty,axiom,
% 3.54/1.80 ! [A_98: pname > $o] :
% 3.54/1.80 ( ( minus_minus_pname_o @ A_98 @ bot_bot_pname_o )
% 3.54/1.80 = A_98 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_945_Diff__empty,axiom,
% 3.54/1.80 ! [A_98: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( minus_2056855718tate_o @ A_98 @ bot_bo19817387tate_o )
% 3.54/1.80 = A_98 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_946_empty__Diff,axiom,
% 3.54/1.80 ! [A_97: com > $o] :
% 3.54/1.80 ( ( minus_minus_com_o @ bot_bot_com_o @ A_97 )
% 3.54/1.80 = bot_bot_com_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_947_empty__Diff,axiom,
% 3.54/1.80 ! [A_97: pname > $o] :
% 3.54/1.80 ( ( minus_minus_pname_o @ bot_bot_pname_o @ A_97 )
% 3.54/1.80 = bot_bot_pname_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_948_empty__Diff,axiom,
% 3.54/1.80 ! [A_97: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( minus_2056855718tate_o @ bot_bo19817387tate_o @ A_97 )
% 3.54/1.80 = bot_bo19817387tate_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_949_finite__Diff2,axiom,
% 3.54/1.80 ! [A_96: ( pname > $o ) > $o,B_55: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ B_55 )
% 3.54/1.80 => ( ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_96 @ B_55 ) )
% 3.54/1.80 <=> ( finite297249702name_o @ A_96 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_950_finite__Diff2,axiom,
% 3.54/1.80 ! [A_96: ( hoare_1708887482_state > $o ) > $o,B_55: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ B_55 )
% 3.54/1.80 => ( ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_96 @ B_55 ) )
% 3.54/1.80 <=> ( finite1329924456tate_o @ A_96 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_951_finite__Diff2,axiom,
% 3.54/1.80 ! [A_96: pname > $o,B_55: pname > $o] :
% 3.54/1.80 ( ( finite_finite_pname @ B_55 )
% 3.54/1.80 => ( ( finite_finite_pname @ ( minus_minus_pname_o @ A_96 @ B_55 ) )
% 3.54/1.80 <=> ( finite_finite_pname @ A_96 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_952_finite__Diff2,axiom,
% 3.54/1.80 ! [A_96: hoare_1708887482_state > $o,B_55: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( finite1625599783_state @ B_55 )
% 3.54/1.80 => ( ( finite1625599783_state @ ( minus_2056855718tate_o @ A_96 @ B_55 ) )
% 3.54/1.80 <=> ( finite1625599783_state @ A_96 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_953_insert__Diff1,axiom,
% 3.54/1.80 ! [A_95: com > $o,X_22: com,B_54: com > $o] :
% 3.54/1.80 ( ( member_com @ X_22 @ B_54 )
% 3.54/1.80 => ( ( minus_minus_com_o @ ( insert_com @ X_22 @ A_95 ) @ B_54 )
% 3.54/1.80 = ( minus_minus_com_o @ A_95 @ B_54 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_954_insert__Diff1,axiom,
% 3.54/1.80 ! [A_95: pname > $o,X_22: pname,B_54: pname > $o] :
% 3.54/1.80 ( ( member_pname @ X_22 @ B_54 )
% 3.54/1.80 => ( ( minus_minus_pname_o @ ( insert_pname @ X_22 @ A_95 ) @ B_54 )
% 3.54/1.80 = ( minus_minus_pname_o @ A_95 @ B_54 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_955_insert__Diff1,axiom,
% 3.54/1.80 ! [A_95: hoare_1708887482_state > $o,X_22: hoare_1708887482_state,B_54: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( member451959335_state @ X_22 @ B_54 )
% 3.54/1.80 => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_22 @ A_95 ) @ B_54 )
% 3.54/1.80 = ( minus_2056855718tate_o @ A_95 @ B_54 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_956_insert__Diff__if,axiom,
% 3.54/1.80 ! [A_94: com > $o,X_21: com,B_53: com > $o] :
% 3.54/1.80 ( ( ( member_com @ X_21 @ B_53 )
% 3.54/1.80 => ( ( minus_minus_com_o @ ( insert_com @ X_21 @ A_94 ) @ B_53 )
% 3.54/1.80 = ( minus_minus_com_o @ A_94 @ B_53 ) ) )
% 3.54/1.80 & ( ~ ( member_com @ X_21 @ B_53 )
% 3.54/1.80 => ( ( minus_minus_com_o @ ( insert_com @ X_21 @ A_94 ) @ B_53 )
% 3.54/1.80 = ( insert_com @ X_21 @ ( minus_minus_com_o @ A_94 @ B_53 ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_957_insert__Diff__if,axiom,
% 3.54/1.80 ! [A_94: pname > $o,X_21: pname,B_53: pname > $o] :
% 3.54/1.80 ( ( ( member_pname @ X_21 @ B_53 )
% 3.54/1.80 => ( ( minus_minus_pname_o @ ( insert_pname @ X_21 @ A_94 ) @ B_53 )
% 3.54/1.80 = ( minus_minus_pname_o @ A_94 @ B_53 ) ) )
% 3.54/1.80 & ( ~ ( member_pname @ X_21 @ B_53 )
% 3.54/1.80 => ( ( minus_minus_pname_o @ ( insert_pname @ X_21 @ A_94 ) @ B_53 )
% 3.54/1.80 = ( insert_pname @ X_21 @ ( minus_minus_pname_o @ A_94 @ B_53 ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_958_insert__Diff__if,axiom,
% 3.54/1.80 ! [A_94: hoare_1708887482_state > $o,X_21: hoare_1708887482_state,B_53: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ( member451959335_state @ X_21 @ B_53 )
% 3.54/1.80 => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_21 @ A_94 ) @ B_53 )
% 3.54/1.80 = ( minus_2056855718tate_o @ A_94 @ B_53 ) ) )
% 3.54/1.80 & ( ~ ( member451959335_state @ X_21 @ B_53 )
% 3.54/1.80 => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_21 @ A_94 ) @ B_53 )
% 3.54/1.80 = ( insert528405184_state @ X_21 @ ( minus_2056855718tate_o @ A_94 @ B_53 ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_959_disjoint__iff__not__equal,axiom,
% 3.54/1.80 ! [A_93: com > $o,B_52: com > $o] :
% 3.54/1.80 ( ( ( semila513601829_com_o @ A_93 @ B_52 )
% 3.54/1.80 = bot_bot_com_o )
% 3.54/1.80 <=> ! [X_3: com] :
% 3.54/1.80 ( ( member_com @ X_3 @ A_93 )
% 3.54/1.80 => ! [Xa: com] :
% 3.54/1.80 ( ( member_com @ Xa @ B_52 )
% 3.54/1.80 => ( X_3 != Xa ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_960_disjoint__iff__not__equal,axiom,
% 3.54/1.80 ! [A_93: pname > $o,B_52: pname > $o] :
% 3.54/1.80 ( ( ( semila1673364395name_o @ A_93 @ B_52 )
% 3.54/1.80 = bot_bot_pname_o )
% 3.54/1.80 <=> ! [X_3: pname] :
% 3.54/1.80 ( ( member_pname @ X_3 @ A_93 )
% 3.54/1.80 => ! [Xa: pname] :
% 3.54/1.80 ( ( member_pname @ Xa @ B_52 )
% 3.54/1.80 => ( X_3 != Xa ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_961_disjoint__iff__not__equal,axiom,
% 3.54/1.80 ! [A_93: hoare_1708887482_state > $o,B_52: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ( semila129691299tate_o @ A_93 @ B_52 )
% 3.54/1.80 = bot_bo19817387tate_o )
% 3.54/1.80 <=> ! [X_3: hoare_1708887482_state] :
% 3.54/1.80 ( ( member451959335_state @ X_3 @ A_93 )
% 3.54/1.80 => ! [Xa: hoare_1708887482_state] :
% 3.54/1.80 ( ( member451959335_state @ Xa @ B_52 )
% 3.54/1.80 => ( X_3 != Xa ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_962_Int__empty__right,axiom,
% 3.54/1.80 ! [A_92: com > $o] :
% 3.54/1.80 ( ( semila513601829_com_o @ A_92 @ bot_bot_com_o )
% 3.54/1.80 = bot_bot_com_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_963_Int__empty__right,axiom,
% 3.54/1.80 ! [A_92: pname > $o] :
% 3.54/1.80 ( ( semila1673364395name_o @ A_92 @ bot_bot_pname_o )
% 3.54/1.80 = bot_bot_pname_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_964_Int__empty__right,axiom,
% 3.54/1.80 ! [A_92: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila129691299tate_o @ A_92 @ bot_bo19817387tate_o )
% 3.54/1.80 = bot_bo19817387tate_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_965_Int__empty__left,axiom,
% 3.54/1.80 ! [B_51: com > $o] :
% 3.54/1.80 ( ( semila513601829_com_o @ bot_bot_com_o @ B_51 )
% 3.54/1.80 = bot_bot_com_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_966_Int__empty__left,axiom,
% 3.54/1.80 ! [B_51: pname > $o] :
% 3.54/1.80 ( ( semila1673364395name_o @ bot_bot_pname_o @ B_51 )
% 3.54/1.80 = bot_bot_pname_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_967_Int__empty__left,axiom,
% 3.54/1.80 ! [B_51: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila129691299tate_o @ bot_bo19817387tate_o @ B_51 )
% 3.54/1.80 = bot_bo19817387tate_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_968_double__diff,axiom,
% 3.54/1.80 ! [C_18: pname > $o,A_91: pname > $o,B_50: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ A_91 @ B_50 )
% 3.54/1.80 => ( ( ord_less_eq_pname_o @ B_50 @ C_18 )
% 3.54/1.80 => ( ( minus_minus_pname_o @ B_50 @ ( minus_minus_pname_o @ C_18 @ A_91 ) )
% 3.54/1.80 = A_91 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_969_double__diff,axiom,
% 3.54/1.80 ! [C_18: hoare_1708887482_state > $o,A_91: hoare_1708887482_state > $o,B_50: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ A_91 @ B_50 )
% 3.54/1.80 => ( ( ord_le777019615tate_o @ B_50 @ C_18 )
% 3.54/1.80 => ( ( minus_2056855718tate_o @ B_50 @ ( minus_2056855718tate_o @ C_18 @ A_91 ) )
% 3.54/1.80 = A_91 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_970_Diff__mono,axiom,
% 3.54/1.80 ! [D_1: pname > $o,B_49: pname > $o,A_90: pname > $o,C_17: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ A_90 @ C_17 )
% 3.54/1.80 => ( ( ord_less_eq_pname_o @ D_1 @ B_49 )
% 3.54/1.80 => ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_90 @ B_49 ) @ ( minus_minus_pname_o @ C_17 @ D_1 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_971_Diff__mono,axiom,
% 3.54/1.80 ! [D_1: hoare_1708887482_state > $o,B_49: hoare_1708887482_state > $o,A_90: hoare_1708887482_state > $o,C_17: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ A_90 @ C_17 )
% 3.54/1.80 => ( ( ord_le777019615tate_o @ D_1 @ B_49 )
% 3.54/1.80 => ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_90 @ B_49 ) @ ( minus_2056855718tate_o @ C_17 @ D_1 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_972_Diff__subset,axiom,
% 3.54/1.80 ! [A_89: pname > $o,B_48: pname > $o] : ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_89 @ B_48 ) @ A_89 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_973_Diff__subset,axiom,
% 3.54/1.80 ! [A_89: hoare_1708887482_state > $o,B_48: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_89 @ B_48 ) @ A_89 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_974_Un__Diff,axiom,
% 3.54/1.80 ! [A_88: pname > $o,B_47: pname > $o,C_16: pname > $o] :
% 3.54/1.80 ( ( minus_minus_pname_o @ ( semila1780557381name_o @ A_88 @ B_47 ) @ C_16 )
% 3.54/1.80 = ( semila1780557381name_o @ ( minus_minus_pname_o @ A_88 @ C_16 ) @ ( minus_minus_pname_o @ B_47 @ C_16 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_975_Un__Diff,axiom,
% 3.54/1.80 ! [A_88: hoare_1708887482_state > $o,B_47: hoare_1708887482_state > $o,C_16: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( minus_2056855718tate_o @ ( semila1122118281tate_o @ A_88 @ B_47 ) @ C_16 )
% 3.54/1.80 = ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A_88 @ C_16 ) @ ( minus_2056855718tate_o @ B_47 @ C_16 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_976_Un__Diff__cancel2,axiom,
% 3.54/1.80 ! [B_46: pname > $o,A_87: pname > $o] :
% 3.54/1.80 ( ( semila1780557381name_o @ ( minus_minus_pname_o @ B_46 @ A_87 ) @ A_87 )
% 3.54/1.80 = ( semila1780557381name_o @ B_46 @ A_87 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_977_Un__Diff__cancel2,axiom,
% 3.54/1.80 ! [B_46: hoare_1708887482_state > $o,A_87: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila1122118281tate_o @ ( minus_2056855718tate_o @ B_46 @ A_87 ) @ A_87 )
% 3.54/1.80 = ( semila1122118281tate_o @ B_46 @ A_87 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_978_Un__Diff__cancel,axiom,
% 3.54/1.80 ! [A_86: pname > $o,B_45: pname > $o] :
% 3.54/1.80 ( ( semila1780557381name_o @ A_86 @ ( minus_minus_pname_o @ B_45 @ A_86 ) )
% 3.54/1.80 = ( semila1780557381name_o @ A_86 @ B_45 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_979_Un__Diff__cancel,axiom,
% 3.54/1.80 ! [A_86: hoare_1708887482_state > $o,B_45: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila1122118281tate_o @ A_86 @ ( minus_2056855718tate_o @ B_45 @ A_86 ) )
% 3.54/1.80 = ( semila1122118281tate_o @ A_86 @ B_45 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_980_Int__insert__left__if1,axiom,
% 3.54/1.80 ! [B_44: com > $o,A_85: com,C_15: com > $o] :
% 3.54/1.80 ( ( member_com @ A_85 @ C_15 )
% 3.54/1.80 => ( ( semila513601829_com_o @ ( insert_com @ A_85 @ B_44 ) @ C_15 )
% 3.54/1.80 = ( insert_com @ A_85 @ ( semila513601829_com_o @ B_44 @ C_15 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_981_Int__insert__left__if1,axiom,
% 3.54/1.80 ! [B_44: pname > $o,A_85: pname,C_15: pname > $o] :
% 3.54/1.80 ( ( member_pname @ A_85 @ C_15 )
% 3.54/1.80 => ( ( semila1673364395name_o @ ( insert_pname @ A_85 @ B_44 ) @ C_15 )
% 3.54/1.80 = ( insert_pname @ A_85 @ ( semila1673364395name_o @ B_44 @ C_15 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_982_Int__insert__left__if1,axiom,
% 3.54/1.80 ! [B_44: hoare_1708887482_state > $o,A_85: hoare_1708887482_state,C_15: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( member451959335_state @ A_85 @ C_15 )
% 3.54/1.80 => ( ( semila129691299tate_o @ ( insert528405184_state @ A_85 @ B_44 ) @ C_15 )
% 3.54/1.80 = ( insert528405184_state @ A_85 @ ( semila129691299tate_o @ B_44 @ C_15 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_983_Int__insert__right__if1,axiom,
% 3.54/1.80 ! [B_43: com > $o,A_84: com,A_83: com > $o] :
% 3.54/1.80 ( ( member_com @ A_84 @ A_83 )
% 3.54/1.80 => ( ( semila513601829_com_o @ A_83 @ ( insert_com @ A_84 @ B_43 ) )
% 3.54/1.80 = ( insert_com @ A_84 @ ( semila513601829_com_o @ A_83 @ B_43 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_984_Int__insert__right__if1,axiom,
% 3.54/1.80 ! [B_43: pname > $o,A_84: pname,A_83: pname > $o] :
% 3.54/1.80 ( ( member_pname @ A_84 @ A_83 )
% 3.54/1.80 => ( ( semila1673364395name_o @ A_83 @ ( insert_pname @ A_84 @ B_43 ) )
% 3.54/1.80 = ( insert_pname @ A_84 @ ( semila1673364395name_o @ A_83 @ B_43 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_985_Int__insert__right__if1,axiom,
% 3.54/1.80 ! [B_43: hoare_1708887482_state > $o,A_84: hoare_1708887482_state,A_83: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( member451959335_state @ A_84 @ A_83 )
% 3.54/1.80 => ( ( semila129691299tate_o @ A_83 @ ( insert528405184_state @ A_84 @ B_43 ) )
% 3.54/1.80 = ( insert528405184_state @ A_84 @ ( semila129691299tate_o @ A_83 @ B_43 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_986_Int__insert__left__if0,axiom,
% 3.54/1.80 ! [B_42: com > $o,A_82: com,C_14: com > $o] :
% 3.54/1.80 ( ~ ( member_com @ A_82 @ C_14 )
% 3.54/1.80 => ( ( semila513601829_com_o @ ( insert_com @ A_82 @ B_42 ) @ C_14 )
% 3.54/1.80 = ( semila513601829_com_o @ B_42 @ C_14 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_987_Int__insert__left__if0,axiom,
% 3.54/1.80 ! [B_42: pname > $o,A_82: pname,C_14: pname > $o] :
% 3.54/1.80 ( ~ ( member_pname @ A_82 @ C_14 )
% 3.54/1.80 => ( ( semila1673364395name_o @ ( insert_pname @ A_82 @ B_42 ) @ C_14 )
% 3.54/1.80 = ( semila1673364395name_o @ B_42 @ C_14 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_988_Int__insert__left__if0,axiom,
% 3.54/1.80 ! [B_42: hoare_1708887482_state > $o,A_82: hoare_1708887482_state,C_14: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ~ ( member451959335_state @ A_82 @ C_14 )
% 3.54/1.80 => ( ( semila129691299tate_o @ ( insert528405184_state @ A_82 @ B_42 ) @ C_14 )
% 3.54/1.80 = ( semila129691299tate_o @ B_42 @ C_14 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_989_Int__insert__right__if0,axiom,
% 3.54/1.80 ! [B_41: com > $o,A_81: com,A_80: com > $o] :
% 3.54/1.80 ( ~ ( member_com @ A_81 @ A_80 )
% 3.54/1.80 => ( ( semila513601829_com_o @ A_80 @ ( insert_com @ A_81 @ B_41 ) )
% 3.54/1.80 = ( semila513601829_com_o @ A_80 @ B_41 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_990_Int__insert__right__if0,axiom,
% 3.54/1.80 ! [B_41: pname > $o,A_81: pname,A_80: pname > $o] :
% 3.54/1.80 ( ~ ( member_pname @ A_81 @ A_80 )
% 3.54/1.80 => ( ( semila1673364395name_o @ A_80 @ ( insert_pname @ A_81 @ B_41 ) )
% 3.54/1.80 = ( semila1673364395name_o @ A_80 @ B_41 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_991_Int__insert__right__if0,axiom,
% 3.54/1.80 ! [B_41: hoare_1708887482_state > $o,A_81: hoare_1708887482_state,A_80: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ~ ( member451959335_state @ A_81 @ A_80 )
% 3.54/1.80 => ( ( semila129691299tate_o @ A_80 @ ( insert528405184_state @ A_81 @ B_41 ) )
% 3.54/1.80 = ( semila129691299tate_o @ A_80 @ B_41 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_992_insert__inter__insert,axiom,
% 3.54/1.80 ! [A_79: com,A_78: com > $o,B_40: com > $o] :
% 3.54/1.80 ( ( semila513601829_com_o @ ( insert_com @ A_79 @ A_78 ) @ ( insert_com @ A_79 @ B_40 ) )
% 3.54/1.80 = ( insert_com @ A_79 @ ( semila513601829_com_o @ A_78 @ B_40 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_993_insert__inter__insert,axiom,
% 3.54/1.80 ! [A_79: pname,A_78: pname > $o,B_40: pname > $o] :
% 3.54/1.80 ( ( semila1673364395name_o @ ( insert_pname @ A_79 @ A_78 ) @ ( insert_pname @ A_79 @ B_40 ) )
% 3.54/1.80 = ( insert_pname @ A_79 @ ( semila1673364395name_o @ A_78 @ B_40 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_994_insert__inter__insert,axiom,
% 3.54/1.80 ! [A_79: hoare_1708887482_state,A_78: hoare_1708887482_state > $o,B_40: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila129691299tate_o @ ( insert528405184_state @ A_79 @ A_78 ) @ ( insert528405184_state @ A_79 @ B_40 ) )
% 3.54/1.80 = ( insert528405184_state @ A_79 @ ( semila129691299tate_o @ A_78 @ B_40 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_995_Int__insert__left,axiom,
% 3.54/1.80 ! [B_39: com > $o,A_77: com,C_13: com > $o] :
% 3.54/1.80 ( ( ( member_com @ A_77 @ C_13 )
% 3.54/1.80 => ( ( semila513601829_com_o @ ( insert_com @ A_77 @ B_39 ) @ C_13 )
% 3.54/1.80 = ( insert_com @ A_77 @ ( semila513601829_com_o @ B_39 @ C_13 ) ) ) )
% 3.54/1.80 & ( ~ ( member_com @ A_77 @ C_13 )
% 3.54/1.80 => ( ( semila513601829_com_o @ ( insert_com @ A_77 @ B_39 ) @ C_13 )
% 3.54/1.80 = ( semila513601829_com_o @ B_39 @ C_13 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_996_Int__insert__left,axiom,
% 3.54/1.80 ! [B_39: pname > $o,A_77: pname,C_13: pname > $o] :
% 3.54/1.80 ( ( ( member_pname @ A_77 @ C_13 )
% 3.54/1.80 => ( ( semila1673364395name_o @ ( insert_pname @ A_77 @ B_39 ) @ C_13 )
% 3.54/1.80 = ( insert_pname @ A_77 @ ( semila1673364395name_o @ B_39 @ C_13 ) ) ) )
% 3.54/1.80 & ( ~ ( member_pname @ A_77 @ C_13 )
% 3.54/1.80 => ( ( semila1673364395name_o @ ( insert_pname @ A_77 @ B_39 ) @ C_13 )
% 3.54/1.80 = ( semila1673364395name_o @ B_39 @ C_13 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_997_Int__insert__left,axiom,
% 3.54/1.80 ! [B_39: hoare_1708887482_state > $o,A_77: hoare_1708887482_state,C_13: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ( member451959335_state @ A_77 @ C_13 )
% 3.54/1.80 => ( ( semila129691299tate_o @ ( insert528405184_state @ A_77 @ B_39 ) @ C_13 )
% 3.54/1.80 = ( insert528405184_state @ A_77 @ ( semila129691299tate_o @ B_39 @ C_13 ) ) ) )
% 3.54/1.80 & ( ~ ( member451959335_state @ A_77 @ C_13 )
% 3.54/1.80 => ( ( semila129691299tate_o @ ( insert528405184_state @ A_77 @ B_39 ) @ C_13 )
% 3.54/1.80 = ( semila129691299tate_o @ B_39 @ C_13 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_998_Int__insert__right,axiom,
% 3.54/1.80 ! [B_38: com > $o,A_76: com,A_75: com > $o] :
% 3.54/1.80 ( ( ( member_com @ A_76 @ A_75 )
% 3.54/1.80 => ( ( semila513601829_com_o @ A_75 @ ( insert_com @ A_76 @ B_38 ) )
% 3.54/1.80 = ( insert_com @ A_76 @ ( semila513601829_com_o @ A_75 @ B_38 ) ) ) )
% 3.54/1.80 & ( ~ ( member_com @ A_76 @ A_75 )
% 3.54/1.80 => ( ( semila513601829_com_o @ A_75 @ ( insert_com @ A_76 @ B_38 ) )
% 3.54/1.80 = ( semila513601829_com_o @ A_75 @ B_38 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_999_Int__insert__right,axiom,
% 3.54/1.80 ! [B_38: pname > $o,A_76: pname,A_75: pname > $o] :
% 3.54/1.80 ( ( ( member_pname @ A_76 @ A_75 )
% 3.54/1.80 => ( ( semila1673364395name_o @ A_75 @ ( insert_pname @ A_76 @ B_38 ) )
% 3.54/1.80 = ( insert_pname @ A_76 @ ( semila1673364395name_o @ A_75 @ B_38 ) ) ) )
% 3.54/1.80 & ( ~ ( member_pname @ A_76 @ A_75 )
% 3.54/1.80 => ( ( semila1673364395name_o @ A_75 @ ( insert_pname @ A_76 @ B_38 ) )
% 3.54/1.80 = ( semila1673364395name_o @ A_75 @ B_38 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1000_Int__insert__right,axiom,
% 3.54/1.80 ! [B_38: hoare_1708887482_state > $o,A_76: hoare_1708887482_state,A_75: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ( member451959335_state @ A_76 @ A_75 )
% 3.54/1.80 => ( ( semila129691299tate_o @ A_75 @ ( insert528405184_state @ A_76 @ B_38 ) )
% 3.54/1.80 = ( insert528405184_state @ A_76 @ ( semila129691299tate_o @ A_75 @ B_38 ) ) ) )
% 3.54/1.80 & ( ~ ( member451959335_state @ A_76 @ A_75 )
% 3.54/1.80 => ( ( semila129691299tate_o @ A_75 @ ( insert528405184_state @ A_76 @ B_38 ) )
% 3.54/1.80 = ( semila129691299tate_o @ A_75 @ B_38 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1001_Int__mono,axiom,
% 3.54/1.80 ! [B_37: pname > $o,D: pname > $o,A_74: pname > $o,C_12: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ A_74 @ C_12 )
% 3.54/1.80 => ( ( ord_less_eq_pname_o @ B_37 @ D )
% 3.54/1.80 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_74 @ B_37 ) @ ( semila1673364395name_o @ C_12 @ D ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1002_Int__mono,axiom,
% 3.54/1.80 ! [B_37: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o,A_74: hoare_1708887482_state > $o,C_12: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ A_74 @ C_12 )
% 3.54/1.80 => ( ( ord_le777019615tate_o @ B_37 @ D )
% 3.54/1.80 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_74 @ B_37 ) @ ( semila129691299tate_o @ C_12 @ D ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1003_Int__greatest,axiom,
% 3.54/1.80 ! [B_36: pname > $o,C_11: pname > $o,A_73: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ C_11 @ A_73 )
% 3.54/1.80 => ( ( ord_less_eq_pname_o @ C_11 @ B_36 )
% 3.54/1.80 => ( ord_less_eq_pname_o @ C_11 @ ( semila1673364395name_o @ A_73 @ B_36 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1004_Int__greatest,axiom,
% 3.54/1.80 ! [B_36: hoare_1708887482_state > $o,C_11: hoare_1708887482_state > $o,A_73: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ C_11 @ A_73 )
% 3.54/1.80 => ( ( ord_le777019615tate_o @ C_11 @ B_36 )
% 3.54/1.80 => ( ord_le777019615tate_o @ C_11 @ ( semila129691299tate_o @ A_73 @ B_36 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1005_Int__absorb1,axiom,
% 3.54/1.80 ! [B_35: pname > $o,A_72: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ B_35 @ A_72 )
% 3.54/1.80 => ( ( semila1673364395name_o @ A_72 @ B_35 )
% 3.54/1.80 = B_35 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1006_Int__absorb1,axiom,
% 3.54/1.80 ! [B_35: hoare_1708887482_state > $o,A_72: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ B_35 @ A_72 )
% 3.54/1.80 => ( ( semila129691299tate_o @ A_72 @ B_35 )
% 3.54/1.80 = B_35 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1007_Int__absorb2,axiom,
% 3.54/1.80 ! [A_71: pname > $o,B_34: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ A_71 @ B_34 )
% 3.54/1.80 => ( ( semila1673364395name_o @ A_71 @ B_34 )
% 3.54/1.80 = A_71 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1008_Int__absorb2,axiom,
% 3.54/1.80 ! [A_71: hoare_1708887482_state > $o,B_34: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ A_71 @ B_34 )
% 3.54/1.80 => ( ( semila129691299tate_o @ A_71 @ B_34 )
% 3.54/1.80 = A_71 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1009_Int__lower2,axiom,
% 3.54/1.80 ! [A_70: pname > $o,B_33: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_70 @ B_33 ) @ B_33 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1010_Int__lower2,axiom,
% 3.54/1.80 ! [A_70: hoare_1708887482_state > $o,B_33: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_70 @ B_33 ) @ B_33 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1011_Int__lower1,axiom,
% 3.54/1.80 ! [A_69: pname > $o,B_32: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_69 @ B_32 ) @ A_69 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1012_Int__lower1,axiom,
% 3.54/1.80 ! [A_69: hoare_1708887482_state > $o,B_32: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_69 @ B_32 ) @ A_69 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1013_Un__Int__crazy,axiom,
% 3.54/1.80 ! [A_68: pname > $o,B_31: pname > $o,C_10: pname > $o] :
% 3.54/1.80 ( ( semila1780557381name_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ A_68 @ B_31 ) @ ( semila1673364395name_o @ B_31 @ C_10 ) ) @ ( semila1673364395name_o @ C_10 @ A_68 ) )
% 3.54/1.80 = ( semila1673364395name_o @ ( semila1673364395name_o @ ( semila1780557381name_o @ A_68 @ B_31 ) @ ( semila1780557381name_o @ B_31 @ C_10 ) ) @ ( semila1780557381name_o @ C_10 @ A_68 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1014_Un__Int__crazy,axiom,
% 3.54/1.80 ! [A_68: hoare_1708887482_state > $o,B_31: hoare_1708887482_state > $o,C_10: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ ( semila129691299tate_o @ A_68 @ B_31 ) @ ( semila129691299tate_o @ B_31 @ C_10 ) ) @ ( semila129691299tate_o @ C_10 @ A_68 ) )
% 3.54/1.80 = ( semila129691299tate_o @ ( semila129691299tate_o @ ( semila1122118281tate_o @ A_68 @ B_31 ) @ ( semila1122118281tate_o @ B_31 @ C_10 ) ) @ ( semila1122118281tate_o @ C_10 @ A_68 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1015_Un__Int__distrib2,axiom,
% 3.54/1.80 ! [B_30: pname > $o,C_9: pname > $o,A_67: pname > $o] :
% 3.54/1.80 ( ( semila1780557381name_o @ ( semila1673364395name_o @ B_30 @ C_9 ) @ A_67 )
% 3.54/1.80 = ( semila1673364395name_o @ ( semila1780557381name_o @ B_30 @ A_67 ) @ ( semila1780557381name_o @ C_9 @ A_67 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1016_Un__Int__distrib2,axiom,
% 3.54/1.80 ! [B_30: hoare_1708887482_state > $o,C_9: hoare_1708887482_state > $o,A_67: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila1122118281tate_o @ ( semila129691299tate_o @ B_30 @ C_9 ) @ A_67 )
% 3.54/1.80 = ( semila129691299tate_o @ ( semila1122118281tate_o @ B_30 @ A_67 ) @ ( semila1122118281tate_o @ C_9 @ A_67 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1017_Int__Un__distrib2,axiom,
% 3.54/1.80 ! [B_29: pname > $o,C_8: pname > $o,A_66: pname > $o] :
% 3.54/1.80 ( ( semila1673364395name_o @ ( semila1780557381name_o @ B_29 @ C_8 ) @ A_66 )
% 3.54/1.80 = ( semila1780557381name_o @ ( semila1673364395name_o @ B_29 @ A_66 ) @ ( semila1673364395name_o @ C_8 @ A_66 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1018_Int__Un__distrib2,axiom,
% 3.54/1.80 ! [B_29: hoare_1708887482_state > $o,C_8: hoare_1708887482_state > $o,A_66: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila129691299tate_o @ ( semila1122118281tate_o @ B_29 @ C_8 ) @ A_66 )
% 3.54/1.80 = ( semila1122118281tate_o @ ( semila129691299tate_o @ B_29 @ A_66 ) @ ( semila129691299tate_o @ C_8 @ A_66 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1019_Un__Int__distrib,axiom,
% 3.54/1.80 ! [A_65: pname > $o,B_28: pname > $o,C_7: pname > $o] :
% 3.54/1.80 ( ( semila1780557381name_o @ A_65 @ ( semila1673364395name_o @ B_28 @ C_7 ) )
% 3.54/1.80 = ( semila1673364395name_o @ ( semila1780557381name_o @ A_65 @ B_28 ) @ ( semila1780557381name_o @ A_65 @ C_7 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1020_Un__Int__distrib,axiom,
% 3.54/1.80 ! [A_65: hoare_1708887482_state > $o,B_28: hoare_1708887482_state > $o,C_7: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila1122118281tate_o @ A_65 @ ( semila129691299tate_o @ B_28 @ C_7 ) )
% 3.54/1.80 = ( semila129691299tate_o @ ( semila1122118281tate_o @ A_65 @ B_28 ) @ ( semila1122118281tate_o @ A_65 @ C_7 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1021_Int__Un__distrib,axiom,
% 3.54/1.80 ! [A_64: pname > $o,B_27: pname > $o,C_6: pname > $o] :
% 3.54/1.80 ( ( semila1673364395name_o @ A_64 @ ( semila1780557381name_o @ B_27 @ C_6 ) )
% 3.54/1.80 = ( semila1780557381name_o @ ( semila1673364395name_o @ A_64 @ B_27 ) @ ( semila1673364395name_o @ A_64 @ C_6 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1022_Int__Un__distrib,axiom,
% 3.54/1.80 ! [A_64: hoare_1708887482_state > $o,B_27: hoare_1708887482_state > $o,C_6: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila129691299tate_o @ A_64 @ ( semila1122118281tate_o @ B_27 @ C_6 ) )
% 3.54/1.80 = ( semila1122118281tate_o @ ( semila129691299tate_o @ A_64 @ B_27 ) @ ( semila129691299tate_o @ A_64 @ C_6 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1023_distrib__inf__le,axiom,
% 3.54/1.80 ! [X_20: $o,Y_9: $o,Z_4: $o] : ( ord_less_eq_o @ ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_20 @ Y_9 ) @ ( semila854092349_inf_o @ X_20 @ Z_4 ) ) @ ( semila854092349_inf_o @ X_20 @ ( semila10642723_sup_o @ Y_9 @ Z_4 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1024_distrib__inf__le,axiom,
% 3.54/1.80 ! [X_20: pname > $o,Y_9: pname > $o,Z_4: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ X_20 @ Y_9 ) @ ( semila1673364395name_o @ X_20 @ Z_4 ) ) @ ( semila1673364395name_o @ X_20 @ ( semila1780557381name_o @ Y_9 @ Z_4 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1025_distrib__inf__le,axiom,
% 3.54/1.80 ! [X_20: hoare_1708887482_state > $o,Y_9: hoare_1708887482_state > $o,Z_4: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila1122118281tate_o @ ( semila129691299tate_o @ X_20 @ Y_9 ) @ ( semila129691299tate_o @ X_20 @ Z_4 ) ) @ ( semila129691299tate_o @ X_20 @ ( semila1122118281tate_o @ Y_9 @ Z_4 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1026_distrib__sup__le,axiom,
% 3.54/1.80 ! [X_19: $o,Y_8: $o,Z_3: $o] : ( ord_less_eq_o @ ( semila10642723_sup_o @ X_19 @ ( semila854092349_inf_o @ Y_8 @ Z_3 ) ) @ ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_19 @ Y_8 ) @ ( semila10642723_sup_o @ X_19 @ Z_3 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1027_distrib__sup__le,axiom,
% 3.54/1.80 ! [X_19: pname > $o,Y_8: pname > $o,Z_3: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_19 @ ( semila1673364395name_o @ Y_8 @ Z_3 ) ) @ ( semila1673364395name_o @ ( semila1780557381name_o @ X_19 @ Y_8 ) @ ( semila1780557381name_o @ X_19 @ Z_3 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1028_distrib__sup__le,axiom,
% 3.54/1.80 ! [X_19: hoare_1708887482_state > $o,Y_8: hoare_1708887482_state > $o,Z_3: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila1122118281tate_o @ X_19 @ ( semila129691299tate_o @ Y_8 @ Z_3 ) ) @ ( semila129691299tate_o @ ( semila1122118281tate_o @ X_19 @ Y_8 ) @ ( semila1122118281tate_o @ X_19 @ Z_3 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1029_insert__Diff,axiom,
% 3.54/1.80 ! [A_63: com,A_62: com > $o] :
% 3.54/1.80 ( ( member_com @ A_63 @ A_62 )
% 3.54/1.80 => ( ( insert_com @ A_63 @ ( minus_minus_com_o @ A_62 @ ( insert_com @ A_63 @ bot_bot_com_o ) ) )
% 3.54/1.80 = A_62 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1030_insert__Diff,axiom,
% 3.54/1.80 ! [A_63: pname,A_62: pname > $o] :
% 3.54/1.80 ( ( member_pname @ A_63 @ A_62 )
% 3.54/1.80 => ( ( insert_pname @ A_63 @ ( minus_minus_pname_o @ A_62 @ ( insert_pname @ A_63 @ bot_bot_pname_o ) ) )
% 3.54/1.80 = A_62 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1031_insert__Diff,axiom,
% 3.54/1.80 ! [A_63: hoare_1708887482_state,A_62: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( member451959335_state @ A_63 @ A_62 )
% 3.54/1.80 => ( ( insert528405184_state @ A_63 @ ( minus_2056855718tate_o @ A_62 @ ( insert528405184_state @ A_63 @ bot_bo19817387tate_o ) ) )
% 3.54/1.80 = A_62 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1032_Diff__insert__absorb,axiom,
% 3.54/1.80 ! [X_18: com,A_61: com > $o] :
% 3.54/1.80 ( ~ ( member_com @ X_18 @ A_61 )
% 3.54/1.80 => ( ( minus_minus_com_o @ ( insert_com @ X_18 @ A_61 ) @ ( insert_com @ X_18 @ bot_bot_com_o ) )
% 3.54/1.80 = A_61 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1033_Diff__insert__absorb,axiom,
% 3.54/1.80 ! [X_18: pname,A_61: pname > $o] :
% 3.54/1.80 ( ~ ( member_pname @ X_18 @ A_61 )
% 3.54/1.80 => ( ( minus_minus_pname_o @ ( insert_pname @ X_18 @ A_61 ) @ ( insert_pname @ X_18 @ bot_bot_pname_o ) )
% 3.54/1.80 = A_61 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1034_Diff__insert__absorb,axiom,
% 3.54/1.80 ! [X_18: hoare_1708887482_state,A_61: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ~ ( member451959335_state @ X_18 @ A_61 )
% 3.54/1.80 => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_18 @ A_61 ) @ ( insert528405184_state @ X_18 @ bot_bo19817387tate_o ) )
% 3.54/1.80 = A_61 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1035_insert__Diff__single,axiom,
% 3.54/1.80 ! [A_60: com,A_59: com > $o] :
% 3.54/1.80 ( ( insert_com @ A_60 @ ( minus_minus_com_o @ A_59 @ ( insert_com @ A_60 @ bot_bot_com_o ) ) )
% 3.54/1.80 = ( insert_com @ A_60 @ A_59 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1036_insert__Diff__single,axiom,
% 3.54/1.80 ! [A_60: pname,A_59: pname > $o] :
% 3.54/1.80 ( ( insert_pname @ A_60 @ ( minus_minus_pname_o @ A_59 @ ( insert_pname @ A_60 @ bot_bot_pname_o ) ) )
% 3.54/1.80 = ( insert_pname @ A_60 @ A_59 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1037_insert__Diff__single,axiom,
% 3.54/1.80 ! [A_60: hoare_1708887482_state,A_59: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( insert528405184_state @ A_60 @ ( minus_2056855718tate_o @ A_59 @ ( insert528405184_state @ A_60 @ bot_bo19817387tate_o ) ) )
% 3.54/1.80 = ( insert528405184_state @ A_60 @ A_59 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1038_Diff__insert2,axiom,
% 3.54/1.80 ! [A_58: com > $o,A_57: com,B_26: com > $o] :
% 3.54/1.80 ( ( minus_minus_com_o @ A_58 @ ( insert_com @ A_57 @ B_26 ) )
% 3.54/1.80 = ( minus_minus_com_o @ ( minus_minus_com_o @ A_58 @ ( insert_com @ A_57 @ bot_bot_com_o ) ) @ B_26 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1039_Diff__insert2,axiom,
% 3.54/1.80 ! [A_58: pname > $o,A_57: pname,B_26: pname > $o] :
% 3.54/1.80 ( ( minus_minus_pname_o @ A_58 @ ( insert_pname @ A_57 @ B_26 ) )
% 3.54/1.80 = ( minus_minus_pname_o @ ( minus_minus_pname_o @ A_58 @ ( insert_pname @ A_57 @ bot_bot_pname_o ) ) @ B_26 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1040_Diff__insert2,axiom,
% 3.54/1.80 ! [A_58: hoare_1708887482_state > $o,A_57: hoare_1708887482_state,B_26: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( minus_2056855718tate_o @ A_58 @ ( insert528405184_state @ A_57 @ B_26 ) )
% 3.54/1.80 = ( minus_2056855718tate_o @ ( minus_2056855718tate_o @ A_58 @ ( insert528405184_state @ A_57 @ bot_bo19817387tate_o ) ) @ B_26 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1041_Diff__insert,axiom,
% 3.54/1.80 ! [A_56: com > $o,A_55: com,B_25: com > $o] :
% 3.54/1.80 ( ( minus_minus_com_o @ A_56 @ ( insert_com @ A_55 @ B_25 ) )
% 3.54/1.80 = ( minus_minus_com_o @ ( minus_minus_com_o @ A_56 @ B_25 ) @ ( insert_com @ A_55 @ bot_bot_com_o ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1042_Diff__insert,axiom,
% 3.54/1.80 ! [A_56: pname > $o,A_55: pname,B_25: pname > $o] :
% 3.54/1.80 ( ( minus_minus_pname_o @ A_56 @ ( insert_pname @ A_55 @ B_25 ) )
% 3.54/1.80 = ( minus_minus_pname_o @ ( minus_minus_pname_o @ A_56 @ B_25 ) @ ( insert_pname @ A_55 @ bot_bot_pname_o ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1043_Diff__insert,axiom,
% 3.54/1.80 ! [A_56: hoare_1708887482_state > $o,A_55: hoare_1708887482_state,B_25: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( minus_2056855718tate_o @ A_56 @ ( insert528405184_state @ A_55 @ B_25 ) )
% 3.54/1.80 = ( minus_2056855718tate_o @ ( minus_2056855718tate_o @ A_56 @ B_25 ) @ ( insert528405184_state @ A_55 @ bot_bo19817387tate_o ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1044_finite__Diff__insert,axiom,
% 3.54/1.80 ! [A_54: com > $o,A_53: com,B_24: com > $o] :
% 3.54/1.80 ( ( finite_finite_com @ ( minus_minus_com_o @ A_54 @ ( insert_com @ A_53 @ B_24 ) ) )
% 3.54/1.80 <=> ( finite_finite_com @ ( minus_minus_com_o @ A_54 @ B_24 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1045_finite__Diff__insert,axiom,
% 3.54/1.80 ! [A_54: pname > $o,A_53: pname,B_24: pname > $o] :
% 3.54/1.80 ( ( finite_finite_pname @ ( minus_minus_pname_o @ A_54 @ ( insert_pname @ A_53 @ B_24 ) ) )
% 3.54/1.80 <=> ( finite_finite_pname @ ( minus_minus_pname_o @ A_54 @ B_24 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1046_finite__Diff__insert,axiom,
% 3.54/1.80 ! [A_54: hoare_1708887482_state > $o,A_53: hoare_1708887482_state,B_24: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( finite1625599783_state @ ( minus_2056855718tate_o @ A_54 @ ( insert528405184_state @ A_53 @ B_24 ) ) )
% 3.54/1.80 <=> ( finite1625599783_state @ ( minus_2056855718tate_o @ A_54 @ B_24 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1047_finite__Diff__insert,axiom,
% 3.54/1.80 ! [A_54: ( pname > $o ) > $o,A_53: pname > $o,B_24: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_54 @ ( insert_pname_o @ A_53 @ B_24 ) ) )
% 3.54/1.80 <=> ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_54 @ B_24 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1048_finite__Diff__insert,axiom,
% 3.54/1.80 ! [A_54: ( hoare_1708887482_state > $o ) > $o,A_53: hoare_1708887482_state > $o,B_24: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_54 @ ( insert949073679tate_o @ A_53 @ B_24 ) ) )
% 3.54/1.80 <=> ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_54 @ B_24 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1049_image__diff__subset,axiom,
% 3.54/1.80 ! [F_27: pname > hoare_1708887482_state,A_52: pname > $o,B_23: pname > $o] : ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ ( image_1116629049_state @ F_27 @ A_52 ) @ ( image_1116629049_state @ F_27 @ B_23 ) ) @ ( image_1116629049_state @ F_27 @ ( minus_minus_pname_o @ A_52 @ B_23 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1050_Diff__partition,axiom,
% 3.54/1.80 ! [A_51: pname > $o,B_22: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ A_51 @ B_22 )
% 3.54/1.80 => ( ( semila1780557381name_o @ A_51 @ ( minus_minus_pname_o @ B_22 @ A_51 ) )
% 3.54/1.80 = B_22 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1051_Diff__partition,axiom,
% 3.54/1.80 ! [A_51: hoare_1708887482_state > $o,B_22: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ A_51 @ B_22 )
% 3.54/1.80 => ( ( semila1122118281tate_o @ A_51 @ ( minus_2056855718tate_o @ B_22 @ A_51 ) )
% 3.54/1.80 = B_22 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1052_Diff__subset__conv,axiom,
% 3.54/1.80 ! [A_50: pname > $o,B_21: pname > $o,C_5: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_50 @ B_21 ) @ C_5 )
% 3.54/1.80 <=> ( ord_less_eq_pname_o @ A_50 @ ( semila1780557381name_o @ B_21 @ C_5 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1053_Diff__subset__conv,axiom,
% 3.54/1.80 ! [A_50: hoare_1708887482_state > $o,B_21: hoare_1708887482_state > $o,C_5: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_50 @ B_21 ) @ C_5 )
% 3.54/1.80 <=> ( ord_le777019615tate_o @ A_50 @ ( semila1122118281tate_o @ B_21 @ C_5 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1054_image__Int__subset,axiom,
% 3.54/1.80 ! [F_26: pname > hoare_1708887482_state,A_49: pname > $o,B_20: pname > $o] : ( ord_le777019615tate_o @ ( image_1116629049_state @ F_26 @ ( semila1673364395name_o @ A_49 @ B_20 ) ) @ ( semila129691299tate_o @ ( image_1116629049_state @ F_26 @ A_49 ) @ ( image_1116629049_state @ F_26 @ B_20 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1055_Un__Int__assoc__eq,axiom,
% 3.54/1.80 ! [A_48: pname > $o,B_19: pname > $o,C_4: pname > $o] :
% 3.54/1.80 ( ( ( semila1780557381name_o @ ( semila1673364395name_o @ A_48 @ B_19 ) @ C_4 )
% 3.54/1.80 = ( semila1673364395name_o @ A_48 @ ( semila1780557381name_o @ B_19 @ C_4 ) ) )
% 3.54/1.80 <=> ( ord_less_eq_pname_o @ C_4 @ A_48 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1056_Un__Int__assoc__eq,axiom,
% 3.54/1.80 ! [A_48: hoare_1708887482_state > $o,B_19: hoare_1708887482_state > $o,C_4: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ( semila1122118281tate_o @ ( semila129691299tate_o @ A_48 @ B_19 ) @ C_4 )
% 3.54/1.80 = ( semila129691299tate_o @ A_48 @ ( semila1122118281tate_o @ B_19 @ C_4 ) ) )
% 3.54/1.80 <=> ( ord_le777019615tate_o @ C_4 @ A_48 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1057_if__image__distrib,axiom,
% 3.54/1.80 ! [P_4: pname > $o,F_25: pname > hoare_1708887482_state,G_4: pname > hoare_1708887482_state,S: pname > $o] :
% 3.54/1.80 ( ( image_1116629049_state
% 3.54/1.80 @ ^ [X_3: pname] : ( if_Hoa1374726218_state @ ( P_4 @ X_3 ) @ ( F_25 @ X_3 ) @ ( G_4 @ X_3 ) )
% 3.54/1.80 @ S )
% 3.54/1.80 = ( semila1122118281tate_o @ ( image_1116629049_state @ F_25 @ ( semila1673364395name_o @ S @ ( collect_pname @ P_4 ) ) )
% 3.54/1.80 @ ( image_1116629049_state @ G_4
% 3.54/1.80 @ ( semila1673364395name_o @ S
% 3.54/1.80 @ ( collect_pname
% 3.54/1.80 @ ^ [X_3: pname] : ( (~) @ ( P_4 @ X_3 ) ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1058_dom__if,axiom,
% 3.54/1.80 ! [P_3: pname > $o,F_24: pname > option_com,G_3: pname > option_com] :
% 3.54/1.80 ( ( dom_pname_com
% 3.54/1.80 @ ^ [X_3: pname] : ( if_option_com @ ( P_3 @ X_3 ) @ ( F_24 @ X_3 ) @ ( G_3 @ X_3 ) ) )
% 3.54/1.80 = ( semila1780557381name_o @ ( semila1673364395name_o @ ( dom_pname_com @ F_24 ) @ ( collect_pname @ P_3 ) )
% 3.54/1.80 @ ( semila1673364395name_o @ ( dom_pname_com @ G_3 )
% 3.54/1.80 @ ( collect_pname
% 3.54/1.80 @ ^ [X_3: pname] : ( (~) @ ( P_3 @ X_3 ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1059_diff__single__insert,axiom,
% 3.54/1.80 ! [A_47: com > $o,X_17: com,B_18: com > $o] :
% 3.54/1.80 ( ( ord_less_eq_com_o @ ( minus_minus_com_o @ A_47 @ ( insert_com @ X_17 @ bot_bot_com_o ) ) @ B_18 )
% 3.54/1.80 => ( ( member_com @ X_17 @ A_47 )
% 3.54/1.80 => ( ord_less_eq_com_o @ A_47 @ ( insert_com @ X_17 @ B_18 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1060_diff__single__insert,axiom,
% 3.54/1.80 ! [A_47: pname > $o,X_17: pname,B_18: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_47 @ ( insert_pname @ X_17 @ bot_bot_pname_o ) ) @ B_18 )
% 3.54/1.80 => ( ( member_pname @ X_17 @ A_47 )
% 3.54/1.80 => ( ord_less_eq_pname_o @ A_47 @ ( insert_pname @ X_17 @ B_18 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1061_diff__single__insert,axiom,
% 3.54/1.80 ! [A_47: hoare_1708887482_state > $o,X_17: hoare_1708887482_state,B_18: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_47 @ ( insert528405184_state @ X_17 @ bot_bo19817387tate_o ) ) @ B_18 )
% 3.54/1.80 => ( ( member451959335_state @ X_17 @ A_47 )
% 3.54/1.80 => ( ord_le777019615tate_o @ A_47 @ ( insert528405184_state @ X_17 @ B_18 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1062_subset__insert__iff,axiom,
% 3.54/1.80 ! [A_46: com > $o,X_16: com,B_17: com > $o] :
% 3.54/1.80 ( ( ord_less_eq_com_o @ A_46 @ ( insert_com @ X_16 @ B_17 ) )
% 3.54/1.80 <=> ( ( ( member_com @ X_16 @ A_46 )
% 3.54/1.80 => ( ord_less_eq_com_o @ ( minus_minus_com_o @ A_46 @ ( insert_com @ X_16 @ bot_bot_com_o ) ) @ B_17 ) )
% 3.54/1.80 & ( ~ ( member_com @ X_16 @ A_46 )
% 3.54/1.80 => ( ord_less_eq_com_o @ A_46 @ B_17 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1063_subset__insert__iff,axiom,
% 3.54/1.80 ! [A_46: pname > $o,X_16: pname,B_17: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ A_46 @ ( insert_pname @ X_16 @ B_17 ) )
% 3.54/1.80 <=> ( ( ( member_pname @ X_16 @ A_46 )
% 3.54/1.80 => ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_46 @ ( insert_pname @ X_16 @ bot_bot_pname_o ) ) @ B_17 ) )
% 3.54/1.80 & ( ~ ( member_pname @ X_16 @ A_46 )
% 3.54/1.80 => ( ord_less_eq_pname_o @ A_46 @ B_17 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1064_subset__insert__iff,axiom,
% 3.54/1.80 ! [A_46: hoare_1708887482_state > $o,X_16: hoare_1708887482_state,B_17: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ A_46 @ ( insert528405184_state @ X_16 @ B_17 ) )
% 3.54/1.80 <=> ( ( ( member451959335_state @ X_16 @ A_46 )
% 3.54/1.80 => ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_46 @ ( insert528405184_state @ X_16 @ bot_bo19817387tate_o ) ) @ B_17 ) )
% 3.54/1.80 & ( ~ ( member451959335_state @ X_16 @ A_46 )
% 3.54/1.80 => ( ord_le777019615tate_o @ A_46 @ B_17 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1065_finite__empty__induct,axiom,
% 3.54/1.80 ! [P_2: ( com > $o ) > $o,A_45: com > $o] :
% 3.54/1.80 ( ( finite_finite_com @ A_45 )
% 3.54/1.80 => ( ( P_2 @ A_45 )
% 3.54/1.80 => ( ! [A_6: com,A_39: com > $o] :
% 3.54/1.80 ( ( finite_finite_com @ A_39 )
% 3.54/1.80 => ( ( member_com @ A_6 @ A_39 )
% 3.54/1.80 => ( ( P_2 @ A_39 )
% 3.54/1.80 => ( P_2 @ ( minus_minus_com_o @ A_39 @ ( insert_com @ A_6 @ bot_bot_com_o ) ) ) ) ) )
% 3.54/1.80 => ( P_2 @ bot_bot_com_o ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1066_finite__empty__induct,axiom,
% 3.54/1.80 ! [P_2: ( pname > $o ) > $o,A_45: pname > $o] :
% 3.54/1.80 ( ( finite_finite_pname @ A_45 )
% 3.54/1.80 => ( ( P_2 @ A_45 )
% 3.54/1.80 => ( ! [A_6: pname,A_39: pname > $o] :
% 3.54/1.80 ( ( finite_finite_pname @ A_39 )
% 3.54/1.80 => ( ( member_pname @ A_6 @ A_39 )
% 3.54/1.80 => ( ( P_2 @ A_39 )
% 3.54/1.80 => ( P_2 @ ( minus_minus_pname_o @ A_39 @ ( insert_pname @ A_6 @ bot_bot_pname_o ) ) ) ) ) )
% 3.54/1.80 => ( P_2 @ bot_bot_pname_o ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1067_finite__empty__induct,axiom,
% 3.54/1.80 ! [P_2: ( hoare_1708887482_state > $o ) > $o,A_45: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( finite1625599783_state @ A_45 )
% 3.54/1.80 => ( ( P_2 @ A_45 )
% 3.54/1.80 => ( ! [A_6: hoare_1708887482_state,A_39: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( finite1625599783_state @ A_39 )
% 3.54/1.80 => ( ( member451959335_state @ A_6 @ A_39 )
% 3.54/1.80 => ( ( P_2 @ A_39 )
% 3.54/1.80 => ( P_2 @ ( minus_2056855718tate_o @ A_39 @ ( insert528405184_state @ A_6 @ bot_bo19817387tate_o ) ) ) ) ) )
% 3.54/1.80 => ( P_2 @ bot_bo19817387tate_o ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1068_finite__empty__induct,axiom,
% 3.54/1.80 ! [P_2: ( ( pname > $o ) > $o ) > $o,A_45: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_45 )
% 3.54/1.80 => ( ( P_2 @ A_45 )
% 3.54/1.80 => ( ! [A_6: pname > $o,A_39: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_39 )
% 3.54/1.80 => ( ( member_pname_o @ A_6 @ A_39 )
% 3.54/1.80 => ( ( P_2 @ A_39 )
% 3.54/1.80 => ( P_2 @ ( minus_1480864103me_o_o @ A_39 @ ( insert_pname_o @ A_6 @ bot_bot_pname_o_o ) ) ) ) ) )
% 3.54/1.80 => ( P_2 @ bot_bot_pname_o_o ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1069_finite__empty__induct,axiom,
% 3.54/1.80 ! [P_2: ( ( hoare_1708887482_state > $o ) > $o ) > $o,A_45: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_45 )
% 3.54/1.80 => ( ( P_2 @ A_45 )
% 3.54/1.80 => ( ! [A_6: hoare_1708887482_state > $o,A_39: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_39 )
% 3.54/1.80 => ( ( member814030440tate_o @ A_6 @ A_39 )
% 3.54/1.80 => ( ( P_2 @ A_39 )
% 3.54/1.80 => ( P_2 @ ( minus_548038231te_o_o @ A_39 @ ( insert949073679tate_o @ A_6 @ bot_bo1678742418te_o_o ) ) ) ) ) )
% 3.54/1.80 => ( P_2 @ bot_bo1678742418te_o_o ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1070_dom__override__on,axiom,
% 3.54/1.80 ! [F_23: pname > option_com,G_2: pname > option_com,A_44: pname > $o] :
% 3.54/1.80 ( ( dom_pname_com @ ( overri1496249029on_com @ F_23 @ G_2 @ A_44 ) )
% 3.54/1.80 = ( semila1780557381name_o
% 3.54/1.80 @ ( minus_minus_pname_o @ ( dom_pname_com @ F_23 )
% 3.54/1.80 @ ( collect_pname
% 3.54/1.80 @ ^ [A_6: pname] : ( member_pname @ A_6 @ ( minus_minus_pname_o @ A_44 @ ( dom_pname_com @ G_2 ) ) ) ) )
% 3.54/1.80 @ ( collect_pname
% 3.54/1.80 @ ^ [A_6: pname] : ( member_pname @ A_6 @ ( semila1673364395name_o @ A_44 @ ( dom_pname_com @ G_2 ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1071_Int__Collect__mono,axiom,
% 3.54/1.80 ! [Q: com > $o,P_1: com > $o,A_43: com > $o,B_16: com > $o] :
% 3.54/1.80 ( ( ord_less_eq_com_o @ A_43 @ B_16 )
% 3.54/1.80 => ( ! [X_3: com] :
% 3.54/1.80 ( ( member_com @ X_3 @ A_43 )
% 3.54/1.80 => ( ( P_1 @ X_3 )
% 3.54/1.80 => ( Q @ X_3 ) ) )
% 3.54/1.80 => ( ord_less_eq_com_o @ ( semila513601829_com_o @ A_43 @ ( collect_com @ P_1 ) ) @ ( semila513601829_com_o @ B_16 @ ( collect_com @ Q ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1072_Int__Collect__mono,axiom,
% 3.54/1.80 ! [Q: pname > $o,P_1: pname > $o,A_43: pname > $o,B_16: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ A_43 @ B_16 )
% 3.54/1.80 => ( ! [X_3: pname] :
% 3.54/1.80 ( ( member_pname @ X_3 @ A_43 )
% 3.54/1.80 => ( ( P_1 @ X_3 )
% 3.54/1.80 => ( Q @ X_3 ) ) )
% 3.54/1.80 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_43 @ ( collect_pname @ P_1 ) ) @ ( semila1673364395name_o @ B_16 @ ( collect_pname @ Q ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1073_Int__Collect__mono,axiom,
% 3.54/1.80 ! [Q: hoare_1708887482_state > $o,P_1: hoare_1708887482_state > $o,A_43: hoare_1708887482_state > $o,B_16: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ A_43 @ B_16 )
% 3.54/1.80 => ( ! [X_3: hoare_1708887482_state] :
% 3.54/1.80 ( ( member451959335_state @ X_3 @ A_43 )
% 3.54/1.80 => ( ( P_1 @ X_3 )
% 3.54/1.80 => ( Q @ X_3 ) ) )
% 3.54/1.80 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_43 @ ( collec1568722789_state @ P_1 ) ) @ ( semila129691299tate_o @ B_16 @ ( collec1568722789_state @ Q ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1074_Int__Collect__mono,axiom,
% 3.54/1.80 ! [Q: ( pname > $o ) > $o,P_1: ( pname > $o ) > $o,A_43: ( pname > $o ) > $o,B_16: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( ord_le1205211808me_o_o @ A_43 @ B_16 )
% 3.54/1.80 => ( ! [X_3: pname > $o] :
% 3.54/1.80 ( ( member_pname_o @ X_3 @ A_43 )
% 3.54/1.80 => ( ( P_1 @ X_3 )
% 3.54/1.80 => ( Q @ X_3 ) ) )
% 3.54/1.80 => ( ord_le1205211808me_o_o @ ( semila2013987940me_o_o @ A_43 @ ( collect_pname_o @ P_1 ) ) @ ( semila2013987940me_o_o @ B_16 @ ( collect_pname_o @ Q ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1075_Int__Collect__mono,axiom,
% 3.54/1.80 ! [Q: ( hoare_1708887482_state > $o ) > $o,P_1: ( hoare_1708887482_state > $o ) > $o,A_43: ( hoare_1708887482_state > $o ) > $o,B_16: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( ord_le1728773982te_o_o @ A_43 @ B_16 )
% 3.54/1.80 => ( ! [X_3: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( member814030440tate_o @ X_3 @ A_43 )
% 3.54/1.80 => ( ( P_1 @ X_3 )
% 3.54/1.80 => ( Q @ X_3 ) ) )
% 3.54/1.80 => ( ord_le1728773982te_o_o @ ( semila598060698te_o_o @ A_43 @ ( collec219771562tate_o @ P_1 ) ) @ ( semila598060698te_o_o @ B_16 @ ( collec219771562tate_o @ Q ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1076_distrib__imp2,axiom,
% 3.54/1.80 ! [X_15: $o,Y_7: $o,Z_2: $o] :
% 3.54/1.80 ( ! [X_3: $o,Y_4: $o,Z_1: $o] :
% 3.54/1.80 ( ( semila10642723_sup_o @ X_3 @ ( semila854092349_inf_o @ Y_4 @ Z_1 ) )
% 3.54/1.80 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_3 @ Y_4 ) @ ( semila10642723_sup_o @ X_3 @ Z_1 ) ) )
% 3.54/1.80 => ( ( semila854092349_inf_o @ X_15 @ ( semila10642723_sup_o @ Y_7 @ Z_2 ) )
% 3.54/1.80 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_15 @ Y_7 ) @ ( semila854092349_inf_o @ X_15 @ Z_2 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1077_distrib__imp2,axiom,
% 3.54/1.80 ! [X_15: pname > $o,Y_7: pname > $o,Z_2: pname > $o] :
% 3.54/1.80 ( ! [X_3: pname > $o,Y_4: pname > $o,Z_1: pname > $o] :
% 3.54/1.80 ( ( semila1780557381name_o @ X_3 @ ( semila1673364395name_o @ Y_4 @ Z_1 ) )
% 3.54/1.80 = ( semila1673364395name_o @ ( semila1780557381name_o @ X_3 @ Y_4 ) @ ( semila1780557381name_o @ X_3 @ Z_1 ) ) )
% 3.54/1.80 => ( ( semila1673364395name_o @ X_15 @ ( semila1780557381name_o @ Y_7 @ Z_2 ) )
% 3.54/1.80 = ( semila1780557381name_o @ ( semila1673364395name_o @ X_15 @ Y_7 ) @ ( semila1673364395name_o @ X_15 @ Z_2 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1078_distrib__imp2,axiom,
% 3.54/1.80 ! [X_15: hoare_1708887482_state > $o,Y_7: hoare_1708887482_state > $o,Z_2: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o,Z_1: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila1122118281tate_o @ X_3 @ ( semila129691299tate_o @ Y_4 @ Z_1 ) )
% 3.54/1.80 = ( semila129691299tate_o @ ( semila1122118281tate_o @ X_3 @ Y_4 ) @ ( semila1122118281tate_o @ X_3 @ Z_1 ) ) )
% 3.54/1.80 => ( ( semila129691299tate_o @ X_15 @ ( semila1122118281tate_o @ Y_7 @ Z_2 ) )
% 3.54/1.80 = ( semila1122118281tate_o @ ( semila129691299tate_o @ X_15 @ Y_7 ) @ ( semila129691299tate_o @ X_15 @ Z_2 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1079_distrib__imp1,axiom,
% 3.54/1.80 ! [X_14: $o,Y_6: $o,Z: $o] :
% 3.54/1.80 ( ! [X_3: $o,Y_4: $o,Z_1: $o] :
% 3.54/1.80 ( ( semila854092349_inf_o @ X_3 @ ( semila10642723_sup_o @ Y_4 @ Z_1 ) )
% 3.54/1.80 <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_3 @ Y_4 ) @ ( semila854092349_inf_o @ X_3 @ Z_1 ) ) )
% 3.54/1.80 => ( ( semila10642723_sup_o @ X_14 @ ( semila854092349_inf_o @ Y_6 @ Z ) )
% 3.54/1.80 <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_14 @ Y_6 ) @ ( semila10642723_sup_o @ X_14 @ Z ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1080_distrib__imp1,axiom,
% 3.54/1.80 ! [X_14: pname > $o,Y_6: pname > $o,Z: pname > $o] :
% 3.54/1.80 ( ! [X_3: pname > $o,Y_4: pname > $o,Z_1: pname > $o] :
% 3.54/1.80 ( ( semila1673364395name_o @ X_3 @ ( semila1780557381name_o @ Y_4 @ Z_1 ) )
% 3.54/1.80 = ( semila1780557381name_o @ ( semila1673364395name_o @ X_3 @ Y_4 ) @ ( semila1673364395name_o @ X_3 @ Z_1 ) ) )
% 3.54/1.80 => ( ( semila1780557381name_o @ X_14 @ ( semila1673364395name_o @ Y_6 @ Z ) )
% 3.54/1.80 = ( semila1673364395name_o @ ( semila1780557381name_o @ X_14 @ Y_6 ) @ ( semila1780557381name_o @ X_14 @ Z ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1081_distrib__imp1,axiom,
% 3.54/1.80 ! [X_14: hoare_1708887482_state > $o,Y_6: hoare_1708887482_state > $o,Z: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o,Z_1: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila129691299tate_o @ X_3 @ ( semila1122118281tate_o @ Y_4 @ Z_1 ) )
% 3.54/1.80 = ( semila1122118281tate_o @ ( semila129691299tate_o @ X_3 @ Y_4 ) @ ( semila129691299tate_o @ X_3 @ Z_1 ) ) )
% 3.54/1.80 => ( ( semila1122118281tate_o @ X_14 @ ( semila129691299tate_o @ Y_6 @ Z ) )
% 3.54/1.80 = ( semila129691299tate_o @ ( semila1122118281tate_o @ X_14 @ Y_6 ) @ ( semila1122118281tate_o @ X_14 @ Z ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1082_flat__lub__def,axiom,
% 3.54/1.80 ! [A_42: com > $o,B_15: com] :
% 3.54/1.80 ( ( ( ord_less_eq_com_o @ A_42 @ ( insert_com @ B_15 @ bot_bot_com_o ) )
% 3.54/1.80 => ( ( partial_flat_lub_com @ B_15 @ A_42 )
% 3.54/1.80 = B_15 ) )
% 3.54/1.80 & ( ~ ( ord_less_eq_com_o @ A_42 @ ( insert_com @ B_15 @ bot_bot_com_o ) )
% 3.54/1.80 => ( ( partial_flat_lub_com @ B_15 @ A_42 )
% 3.54/1.80 = ( the_com_1
% 3.54/1.80 @ ^ [X_3: com] : ( member_com @ X_3 @ ( minus_minus_com_o @ A_42 @ ( insert_com @ B_15 @ bot_bot_com_o ) ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1083_flat__lub__def,axiom,
% 3.54/1.80 ! [A_42: pname > $o,B_15: pname] :
% 3.54/1.80 ( ( ( ord_less_eq_pname_o @ A_42 @ ( insert_pname @ B_15 @ bot_bot_pname_o ) )
% 3.54/1.80 => ( ( partia752020666_pname @ B_15 @ A_42 )
% 3.54/1.80 = B_15 ) )
% 3.54/1.80 & ( ~ ( ord_less_eq_pname_o @ A_42 @ ( insert_pname @ B_15 @ bot_bot_pname_o ) )
% 3.54/1.80 => ( ( partia752020666_pname @ B_15 @ A_42 )
% 3.54/1.80 = ( the_pname
% 3.54/1.80 @ ^ [X_3: pname] : ( member_pname @ X_3 @ ( minus_minus_pname_o @ A_42 @ ( insert_pname @ B_15 @ bot_bot_pname_o ) ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1084_flat__lub__def,axiom,
% 3.54/1.80 ! [A_42: hoare_1708887482_state > $o,B_15: hoare_1708887482_state] :
% 3.54/1.80 ( ( ( ord_le777019615tate_o @ A_42 @ ( insert528405184_state @ B_15 @ bot_bo19817387tate_o ) )
% 3.54/1.80 => ( ( partia1256728516_state @ B_15 @ A_42 )
% 3.54/1.80 = B_15 ) )
% 3.54/1.80 & ( ~ ( ord_le777019615tate_o @ A_42 @ ( insert528405184_state @ B_15 @ bot_bo19817387tate_o ) )
% 3.54/1.80 => ( ( partia1256728516_state @ B_15 @ A_42 )
% 3.54/1.80 = ( the_Ho851197897_state
% 3.54/1.80 @ ^ [X_3: hoare_1708887482_state] : ( member451959335_state @ X_3 @ ( minus_2056855718tate_o @ A_42 @ ( insert528405184_state @ B_15 @ bot_bo19817387tate_o ) ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1085_comp__fun__idem__remove,axiom,
% 3.54/1.80 ( finite567462577_com_o
% 3.54/1.80 @ ^ [X_3: com,A_39: com > $o] : ( minus_minus_com_o @ A_39 @ ( insert_com @ X_3 @ bot_bot_com_o ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1086_comp__fun__idem__remove,axiom,
% 3.54/1.80 ( finite1123817265name_o
% 3.54/1.80 @ ^ [X_3: pname,A_39: pname > $o] : ( minus_minus_pname_o @ A_39 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1087_comp__fun__idem__remove,axiom,
% 3.54/1.80 ( finite662762081tate_o
% 3.54/1.80 @ ^ [X_3: hoare_1708887482_state,A_39: hoare_1708887482_state > $o] : ( minus_2056855718tate_o @ A_39 @ ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1088_fun__upd__image,axiom,
% 3.54/1.80 ! [F_22: pname > hoare_1708887482_state,Y_5: hoare_1708887482_state,X_13: pname,A_41: pname > $o] :
% 3.54/1.80 ( ( ( member_pname @ X_13 @ A_41 )
% 3.54/1.80 => ( ( image_1116629049_state @ ( fun_up1986763201_state @ F_22 @ X_13 @ Y_5 ) @ A_41 )
% 3.54/1.80 = ( insert528405184_state @ Y_5 @ ( image_1116629049_state @ F_22 @ ( minus_minus_pname_o @ A_41 @ ( insert_pname @ X_13 @ bot_bot_pname_o ) ) ) ) ) )
% 3.54/1.80 & ( ~ ( member_pname @ X_13 @ A_41 )
% 3.54/1.80 => ( ( image_1116629049_state @ ( fun_up1986763201_state @ F_22 @ X_13 @ Y_5 ) @ A_41 )
% 3.54/1.80 = ( image_1116629049_state @ F_22 @ A_41 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1089_comp__fun__idem__insert,axiom,
% 3.54/1.80 finite567462577_com_o @ insert_com ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1090_comp__fun__idem__insert,axiom,
% 3.54/1.80 finite1123817265name_o @ insert_pname ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1091_comp__fun__idem__insert,axiom,
% 3.54/1.80 finite662762081tate_o @ insert528405184_state ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1092_comp__fun__idem__sup,axiom,
% 3.54/1.80 finite2048025996em_o_o @ semila10642723_sup_o ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1093_comp__fun__idem__sup,axiom,
% 3.54/1.80 finite138924780name_o @ semila1780557381name_o ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1094_comp__fun__idem__sup,axiom,
% 3.54/1.80 finite2034616076tate_o @ semila1122118281tate_o ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1095_inj__on__Un,axiom,
% 3.54/1.80 ! [F_21: pname > hoare_1708887482_state,A_40: pname > $o,B_14: pname > $o] :
% 3.54/1.80 ( ( inj_on1553129421_state @ F_21 @ ( semila1780557381name_o @ A_40 @ B_14 ) )
% 3.54/1.80 <=> ( ( inj_on1553129421_state @ F_21 @ A_40 )
% 3.54/1.80 & ( inj_on1553129421_state @ F_21 @ B_14 )
% 3.54/1.80 & ( ( semila129691299tate_o @ ( image_1116629049_state @ F_21 @ ( minus_minus_pname_o @ A_40 @ B_14 ) ) @ ( image_1116629049_state @ F_21 @ ( minus_minus_pname_o @ B_14 @ A_40 ) ) )
% 3.54/1.80 = bot_bo19817387tate_o ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1096_dom__eq__singleton__conv,axiom,
% 3.54/1.80 ! [F_20: pname > option_com,X_12: pname] :
% 3.54/1.80 ( ( ( dom_pname_com @ F_20 )
% 3.54/1.80 = ( insert_pname @ X_12 @ bot_bot_pname_o ) )
% 3.54/1.80 <=> ? [V: com] :
% 3.54/1.80 ( F_20
% 3.54/1.80 = ( fun_up879233478on_com
% 3.54/1.80 @ ^ [X_3: pname] : none_com
% 3.54/1.80 @ X_12
% 3.54/1.80 @ ( some_com @ V ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1097_minus__fold__remove,axiom,
% 3.54/1.80 ! [B_13: com > $o,A_38: com > $o] :
% 3.54/1.80 ( ( finite_finite_com @ A_38 )
% 3.54/1.80 => ( ( minus_minus_com_o @ B_13 @ A_38 )
% 3.54/1.80 = ( finite504235573_com_o
% 3.54/1.80 @ ^ [X_3: com,A_39: com > $o] : ( minus_minus_com_o @ A_39 @ ( insert_com @ X_3 @ bot_bot_com_o ) )
% 3.54/1.80 @ B_13
% 3.54/1.80 @ A_38 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1098_minus__fold__remove,axiom,
% 3.54/1.80 ! [B_13: pname > $o,A_38: pname > $o] :
% 3.54/1.80 ( ( finite_finite_pname @ A_38 )
% 3.54/1.80 => ( ( minus_minus_pname_o @ B_13 @ A_38 )
% 3.54/1.80 = ( finite603803317name_o
% 3.54/1.80 @ ^ [X_3: pname,A_39: pname > $o] : ( minus_minus_pname_o @ A_39 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
% 3.54/1.80 @ B_13
% 3.54/1.80 @ A_38 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1099_minus__fold__remove,axiom,
% 3.54/1.80 ! [B_13: hoare_1708887482_state > $o,A_38: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( finite1625599783_state @ A_38 )
% 3.54/1.80 => ( ( minus_2056855718tate_o @ B_13 @ A_38 )
% 3.54/1.80 = ( finite96880613tate_o
% 3.54/1.80 @ ^ [X_3: hoare_1708887482_state,A_39: hoare_1708887482_state > $o] : ( minus_2056855718tate_o @ A_39 @ ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) )
% 3.54/1.80 @ B_13
% 3.54/1.80 @ A_38 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1100_minus__fold__remove,axiom,
% 3.54/1.80 ! [B_13: ( pname > $o ) > $o,A_38: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_38 )
% 3.54/1.80 => ( ( minus_1480864103me_o_o @ B_13 @ A_38 )
% 3.54/1.80 = ( finite1849951719me_o_o
% 3.54/1.80 @ ^ [X_3: pname > $o,A_39: ( pname > $o ) > $o] : ( minus_1480864103me_o_o @ A_39 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
% 3.54/1.80 @ B_13
% 3.54/1.80 @ A_38 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1101_minus__fold__remove,axiom,
% 3.54/1.80 ! [B_13: ( hoare_1708887482_state > $o ) > $o,A_38: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_38 )
% 3.54/1.80 => ( ( minus_548038231te_o_o @ B_13 @ A_38 )
% 3.54/1.80 = ( finite463603445te_o_o
% 3.54/1.80 @ ^ [X_3: hoare_1708887482_state > $o,A_39: ( hoare_1708887482_state > $o ) > $o] : ( minus_548038231te_o_o @ A_39 @ ( insert949073679tate_o @ X_3 @ bot_bo1678742418te_o_o ) )
% 3.54/1.80 @ B_13
% 3.54/1.80 @ A_38 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1102_image__eq__fold__image,axiom,
% 3.54/1.80 ! [F_19: pname > hoare_1708887482_state,A_37: pname > $o] :
% 3.54/1.80 ( ( finite_finite_pname @ A_37 )
% 3.54/1.80 => ( ( image_1116629049_state @ F_19 @ A_37 )
% 3.54/1.80 = ( finite2139561282_pname @ semila1122118281tate_o
% 3.54/1.80 @ ^ [X_3: pname] : ( insert528405184_state @ ( F_19 @ X_3 ) @ bot_bo19817387tate_o )
% 3.54/1.80 @ bot_bo19817387tate_o
% 3.54/1.80 @ A_37 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1103_inj__Some,axiom,
% 3.54/1.80 ! [A_36: pname > $o] : ( inj_on737724108_pname @ some_pname @ A_36 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1104_inj__Some,axiom,
% 3.54/1.80 ! [A_36: hoare_1708887482_state > $o] : ( inj_on945311362_state @ some_H1974565227_state @ A_36 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1105_inj__Some,axiom,
% 3.54/1.80 ! [A_36: com > $o] : ( inj_on11367768on_com @ some_com @ A_36 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1106_option_Osimps_I2_J,axiom,
% 3.54/1.80 ! [A_35: com] :
% 3.54/1.80 ( none_com
% 3.54/1.80 != ( some_com @ A_35 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1107_option_Osimps_I2_J,axiom,
% 3.54/1.80 ! [A_35: pname] :
% 3.54/1.80 ( none_pname
% 3.54/1.80 != ( some_pname @ A_35 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1108_option_Osimps_I2_J,axiom,
% 3.54/1.80 ! [A_35: hoare_1708887482_state] :
% 3.54/1.80 ( none_H1106584047_state
% 3.54/1.80 != ( some_H1974565227_state @ A_35 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1109_option_Osimps_I3_J,axiom,
% 3.54/1.80 ! [A_34: com] :
% 3.54/1.80 ( ( some_com @ A_34 )
% 3.54/1.80 != none_com ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1110_option_Osimps_I3_J,axiom,
% 3.54/1.80 ! [A_34: pname] :
% 3.54/1.80 ( ( some_pname @ A_34 )
% 3.54/1.80 != none_pname ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1111_option_Osimps_I3_J,axiom,
% 3.54/1.80 ! [A_34: hoare_1708887482_state] :
% 3.54/1.80 ( ( some_H1974565227_state @ A_34 )
% 3.54/1.80 != none_H1106584047_state ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1112_not__Some__eq,axiom,
% 3.54/1.80 ! [X_11: option_com] :
% 3.54/1.80 ( ! [Y_4: com] :
% 3.54/1.80 ( X_11
% 3.54/1.80 != ( some_com @ Y_4 ) )
% 3.54/1.80 <=> ( X_11 = none_com ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1113_not__Some__eq,axiom,
% 3.54/1.80 ! [X_11: option_pname] :
% 3.54/1.80 ( ! [Y_4: pname] :
% 3.54/1.80 ( X_11
% 3.54/1.80 != ( some_pname @ Y_4 ) )
% 3.54/1.80 <=> ( X_11 = none_pname ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1114_not__Some__eq,axiom,
% 3.54/1.80 ! [X_11: option1624383643_state] :
% 3.54/1.80 ( ! [Y_4: hoare_1708887482_state] :
% 3.54/1.80 ( X_11
% 3.54/1.80 != ( some_H1974565227_state @ Y_4 ) )
% 3.54/1.80 <=> ( X_11 = none_H1106584047_state ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1115_not__None__eq,axiom,
% 3.54/1.80 ! [X_10: option_com] :
% 3.54/1.80 ( ( X_10 != none_com )
% 3.54/1.80 <=> ? [Y_4: com] :
% 3.54/1.80 ( X_10
% 3.54/1.80 = ( some_com @ Y_4 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1116_not__None__eq,axiom,
% 3.54/1.80 ! [X_10: option_pname] :
% 3.54/1.80 ( ( X_10 != none_pname )
% 3.54/1.80 <=> ? [Y_4: pname] :
% 3.54/1.80 ( X_10
% 3.54/1.80 = ( some_pname @ Y_4 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1117_not__None__eq,axiom,
% 3.54/1.80 ! [X_10: option1624383643_state] :
% 3.54/1.80 ( ( X_10 != none_H1106584047_state )
% 3.54/1.80 <=> ? [Y_4: hoare_1708887482_state] :
% 3.54/1.80 ( X_10
% 3.54/1.80 = ( some_H1974565227_state @ Y_4 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1118_dom__def,axiom,
% 3.54/1.80 ! [M_2: pname > option_com] :
% 3.54/1.80 ( ( dom_pname_com @ M_2 )
% 3.54/1.80 = ( collect_pname
% 3.54/1.80 @ ^ [A_6: pname] :
% 3.54/1.80 ( (~)
% 3.54/1.80 @ ( ( M_2 @ A_6 )
% 3.54/1.80 = none_com ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1119_domIff,axiom,
% 3.54/1.80 ! [A_33: pname,M_1: pname > option_com] :
% 3.54/1.80 ( ( member_pname @ A_33 @ ( dom_pname_com @ M_1 ) )
% 3.54/1.80 <=> ( ( M_1 @ A_33 )
% 3.54/1.80 != none_com ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1120_finite__imageD,axiom,
% 3.54/1.80 ! [F_18: pname > hoare_1708887482_state,A_32: pname > $o] :
% 3.54/1.80 ( ( finite1625599783_state @ ( image_1116629049_state @ F_18 @ A_32 ) )
% 3.54/1.80 => ( ( inj_on1553129421_state @ F_18 @ A_32 )
% 3.54/1.80 => ( finite_finite_pname @ A_32 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1121_inj__on__Un__image__eq__iff,axiom,
% 3.54/1.80 ! [F_17: pname > hoare_1708887482_state,A_31: pname > $o,B_12: pname > $o] :
% 3.54/1.80 ( ( inj_on1553129421_state @ F_17 @ ( semila1780557381name_o @ A_31 @ B_12 ) )
% 3.54/1.80 => ( ( ( image_1116629049_state @ F_17 @ A_31 )
% 3.54/1.80 = ( image_1116629049_state @ F_17 @ B_12 ) )
% 3.54/1.80 <=> ( A_31 = B_12 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1122_is__none__def,axiom,
% 3.54/1.80 ! [X_9: option_com] :
% 3.54/1.80 ( ( is_none_com @ X_9 )
% 3.54/1.80 <=> ( X_9 = none_com ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1123_is__none__code_I1_J,axiom,
% 3.54/1.80 is_none_com @ none_com ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1124_inj__on__fun__updI,axiom,
% 3.54/1.80 ! [X_8: pname,Y_3: hoare_1708887482_state,F_16: pname > hoare_1708887482_state,A_30: pname > $o] :
% 3.54/1.80 ( ( inj_on1553129421_state @ F_16 @ A_30 )
% 3.54/1.80 => ( ~ ( member451959335_state @ Y_3 @ ( image_1116629049_state @ F_16 @ A_30 ) )
% 3.54/1.80 => ( inj_on1553129421_state @ ( fun_up1986763201_state @ F_16 @ X_8 @ Y_3 ) @ A_30 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1125_sup__le__fold__sup,axiom,
% 3.54/1.80 ! [B_11: pname > $o,A_29: pname > $o,A_28: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_28 )
% 3.54/1.80 => ( ( member_pname_o @ A_29 @ A_28 )
% 3.54/1.80 => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_29 @ B_11 ) @ ( finite472615016name_o @ semila1780557381name_o @ B_11 @ A_28 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1126_sup__le__fold__sup,axiom,
% 3.54/1.80 ! [B_11: hoare_1708887482_state > $o,A_29: hoare_1708887482_state > $o,A_28: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_28 )
% 3.54/1.80 => ( ( member814030440tate_o @ A_29 @ A_28 )
% 3.54/1.80 => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_29 @ B_11 ) @ ( finite822533768tate_o @ semila1122118281tate_o @ B_11 @ A_28 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1127_sup__le__fold__sup,axiom,
% 3.54/1.80 ! [B_11: $o,A_29: $o,A_28: $o > $o] :
% 3.54/1.80 ( ( finite_finite_o @ A_28 )
% 3.54/1.80 => ( ( member_o @ A_29 @ A_28 )
% 3.54/1.80 => ( ord_less_eq_o @ ( semila10642723_sup_o @ A_29 @ B_11 ) @ ( finite_fold_o_o @ semila10642723_sup_o @ B_11 @ A_28 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1128_fold__inf__le__inf,axiom,
% 3.54/1.80 ! [B_10: pname > $o,A_27: pname > $o,A_26: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_26 )
% 3.54/1.80 => ( ( member_pname_o @ A_27 @ A_26 )
% 3.54/1.80 => ( ord_less_eq_pname_o @ ( finite472615016name_o @ semila1673364395name_o @ B_10 @ A_26 ) @ ( semila1673364395name_o @ A_27 @ B_10 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1129_fold__inf__le__inf,axiom,
% 3.54/1.80 ! [B_10: hoare_1708887482_state > $o,A_27: hoare_1708887482_state > $o,A_26: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_26 )
% 3.54/1.80 => ( ( member814030440tate_o @ A_27 @ A_26 )
% 3.54/1.80 => ( ord_le777019615tate_o @ ( finite822533768tate_o @ semila129691299tate_o @ B_10 @ A_26 ) @ ( semila129691299tate_o @ A_27 @ B_10 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1130_fold__inf__le__inf,axiom,
% 3.54/1.80 ! [B_10: $o,A_27: $o,A_26: $o > $o] :
% 3.54/1.80 ( ( finite_finite_o @ A_26 )
% 3.54/1.80 => ( ( member_o @ A_27 @ A_26 )
% 3.54/1.80 => ( ord_less_eq_o @ ( finite_fold_o_o @ semila854092349_inf_o @ B_10 @ A_26 ) @ ( semila854092349_inf_o @ A_27 @ B_10 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1131_fold__sup__insert,axiom,
% 3.54/1.80 ! [B_9: pname > $o,A_25: pname > $o,A_24: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_24 )
% 3.54/1.80 => ( ( finite472615016name_o @ semila1780557381name_o @ B_9 @ ( insert_pname_o @ A_25 @ A_24 ) )
% 3.54/1.80 = ( semila1780557381name_o @ A_25 @ ( finite472615016name_o @ semila1780557381name_o @ B_9 @ A_24 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1132_fold__sup__insert,axiom,
% 3.54/1.80 ! [B_9: hoare_1708887482_state > $o,A_25: hoare_1708887482_state > $o,A_24: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_24 )
% 3.54/1.80 => ( ( finite822533768tate_o @ semila1122118281tate_o @ B_9 @ ( insert949073679tate_o @ A_25 @ A_24 ) )
% 3.54/1.80 = ( semila1122118281tate_o @ A_25 @ ( finite822533768tate_o @ semila1122118281tate_o @ B_9 @ A_24 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1133_fold__sup__insert,axiom,
% 3.54/1.80 ! [B_9: $o,A_25: $o,A_24: $o > $o] :
% 3.54/1.80 ( ( finite_finite_o @ A_24 )
% 3.54/1.80 => ( ( finite_fold_o_o @ semila10642723_sup_o @ B_9 @ ( insert_o @ A_25 @ A_24 ) )
% 3.54/1.80 <=> ( semila10642723_sup_o @ A_25 @ ( finite_fold_o_o @ semila10642723_sup_o @ B_9 @ A_24 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1134_fold__inf__insert,axiom,
% 3.54/1.80 ! [B_8: pname > $o,A_23: pname > $o,A_22: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_22 )
% 3.54/1.80 => ( ( finite472615016name_o @ semila1673364395name_o @ B_8 @ ( insert_pname_o @ A_23 @ A_22 ) )
% 3.54/1.80 = ( semila1673364395name_o @ A_23 @ ( finite472615016name_o @ semila1673364395name_o @ B_8 @ A_22 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1135_fold__inf__insert,axiom,
% 3.54/1.80 ! [B_8: hoare_1708887482_state > $o,A_23: hoare_1708887482_state > $o,A_22: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_22 )
% 3.54/1.80 => ( ( finite822533768tate_o @ semila129691299tate_o @ B_8 @ ( insert949073679tate_o @ A_23 @ A_22 ) )
% 3.54/1.80 = ( semila129691299tate_o @ A_23 @ ( finite822533768tate_o @ semila129691299tate_o @ B_8 @ A_22 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1136_dom__eq__empty__conv,axiom,
% 3.54/1.80 ! [F_15: pname > option_com] :
% 3.54/1.80 ( ( ( dom_pname_com @ F_15 )
% 3.54/1.80 = bot_bot_pname_o )
% 3.54/1.80 <=> ! [X_3: pname] :
% 3.54/1.80 ( ( F_15 @ X_3 )
% 3.54/1.80 = none_com ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1137_dom__empty,axiom,
% 3.54/1.80 ( ( dom_pname_com
% 3.54/1.80 @ ^ [X_3: pname] : none_com )
% 3.54/1.80 = bot_bot_pname_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1138_Option_Oset_Osimps_I1_J,axiom,
% 3.54/1.80 ( ( set_com @ none_com )
% 3.54/1.80 = bot_bot_com_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1139_Option_Oset_Osimps_I1_J,axiom,
% 3.54/1.80 ( ( set_pname @ none_pname )
% 3.54/1.80 = bot_bot_pname_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1140_Option_Oset_Osimps_I1_J,axiom,
% 3.54/1.80 ( ( set_Ho525251890_state @ none_H1106584047_state )
% 3.54/1.80 = bot_bo19817387tate_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1141_set__empty__eq,axiom,
% 3.54/1.80 ! [Xo: option_com] :
% 3.54/1.80 ( ( ( set_com @ Xo )
% 3.54/1.80 = bot_bot_com_o )
% 3.54/1.80 <=> ( Xo = none_com ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1142_set__empty__eq,axiom,
% 3.54/1.80 ! [Xo: option_pname] :
% 3.54/1.80 ( ( ( set_pname @ Xo )
% 3.54/1.80 = bot_bot_pname_o )
% 3.54/1.80 <=> ( Xo = none_pname ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1143_set__empty__eq,axiom,
% 3.54/1.80 ! [Xo: option1624383643_state] :
% 3.54/1.80 ( ( ( set_Ho525251890_state @ Xo )
% 3.54/1.80 = bot_bo19817387tate_o )
% 3.54/1.80 <=> ( Xo = none_H1106584047_state ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1144_endo__inj__surj,axiom,
% 3.54/1.80 ! [F_14: ( pname > $o ) > pname > $o,A_21: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_21 )
% 3.54/1.80 => ( ( ord_le1205211808me_o_o @ ( image_1085733413name_o @ F_14 @ A_21 ) @ A_21 )
% 3.54/1.80 => ( ( inj_on691924881name_o @ F_14 @ A_21 )
% 3.54/1.80 => ( ( image_1085733413name_o @ F_14 @ A_21 )
% 3.54/1.80 = A_21 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1145_endo__inj__surj,axiom,
% 3.54/1.80 ! [F_14: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,A_21: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_21 )
% 3.54/1.80 => ( ( ord_le1728773982te_o_o @ ( image_909543877tate_o @ F_14 @ A_21 ) @ A_21 )
% 3.54/1.80 => ( ( inj_on176908593tate_o @ F_14 @ A_21 )
% 3.54/1.80 => ( ( image_909543877tate_o @ F_14 @ A_21 )
% 3.54/1.80 = A_21 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1146_endo__inj__surj,axiom,
% 3.54/1.80 ! [F_14: pname > pname,A_21: pname > $o] :
% 3.54/1.80 ( ( finite_finite_pname @ A_21 )
% 3.54/1.80 => ( ( ord_less_eq_pname_o @ ( image_pname_pname @ F_14 @ A_21 ) @ A_21 )
% 3.54/1.80 => ( ( inj_on_pname_pname @ F_14 @ A_21 )
% 3.54/1.80 => ( ( image_pname_pname @ F_14 @ A_21 )
% 3.54/1.80 = A_21 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1147_endo__inj__surj,axiom,
% 3.54/1.80 ! [F_14: hoare_1708887482_state > hoare_1708887482_state,A_21: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( finite1625599783_state @ A_21 )
% 3.54/1.80 => ( ( ord_le777019615tate_o @ ( image_757158439_state @ F_14 @ A_21 ) @ A_21 )
% 3.54/1.80 => ( ( inj_on632008595_state @ F_14 @ A_21 )
% 3.54/1.80 => ( ( image_757158439_state @ F_14 @ A_21 )
% 3.54/1.80 = A_21 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1148_finite__surj__inj,axiom,
% 3.54/1.80 ! [F_13: ( pname > $o ) > pname > $o,A_20: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_20 )
% 3.54/1.80 => ( ( ord_le1205211808me_o_o @ A_20 @ ( image_1085733413name_o @ F_13 @ A_20 ) )
% 3.54/1.80 => ( inj_on691924881name_o @ F_13 @ A_20 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1149_finite__surj__inj,axiom,
% 3.54/1.80 ! [F_13: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,A_20: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_20 )
% 3.54/1.80 => ( ( ord_le1728773982te_o_o @ A_20 @ ( image_909543877tate_o @ F_13 @ A_20 ) )
% 3.54/1.80 => ( inj_on176908593tate_o @ F_13 @ A_20 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1150_finite__surj__inj,axiom,
% 3.54/1.80 ! [F_13: pname > pname,A_20: pname > $o] :
% 3.54/1.80 ( ( finite_finite_pname @ A_20 )
% 3.54/1.80 => ( ( ord_less_eq_pname_o @ A_20 @ ( image_pname_pname @ F_13 @ A_20 ) )
% 3.54/1.80 => ( inj_on_pname_pname @ F_13 @ A_20 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1151_finite__surj__inj,axiom,
% 3.54/1.80 ! [F_13: hoare_1708887482_state > hoare_1708887482_state,A_20: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( finite1625599783_state @ A_20 )
% 3.54/1.80 => ( ( ord_le777019615tate_o @ A_20 @ ( image_757158439_state @ F_13 @ A_20 ) )
% 3.54/1.80 => ( inj_on632008595_state @ F_13 @ A_20 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1152_inj__on__image__Int,axiom,
% 3.54/1.80 ! [B_7: pname > $o,A_19: pname > $o,F_12: pname > hoare_1708887482_state,C_3: pname > $o] :
% 3.54/1.80 ( ( inj_on1553129421_state @ F_12 @ C_3 )
% 3.54/1.80 => ( ( ord_less_eq_pname_o @ A_19 @ C_3 )
% 3.54/1.80 => ( ( ord_less_eq_pname_o @ B_7 @ C_3 )
% 3.54/1.80 => ( ( image_1116629049_state @ F_12 @ ( semila1673364395name_o @ A_19 @ B_7 ) )
% 3.54/1.80 = ( semila129691299tate_o @ ( image_1116629049_state @ F_12 @ A_19 ) @ ( image_1116629049_state @ F_12 @ B_7 ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1153_inj__on__image__set__diff,axiom,
% 3.54/1.80 ! [B_6: pname > $o,A_18: pname > $o,F_11: pname > hoare_1708887482_state,C_2: pname > $o] :
% 3.54/1.80 ( ( inj_on1553129421_state @ F_11 @ C_2 )
% 3.54/1.80 => ( ( ord_less_eq_pname_o @ A_18 @ C_2 )
% 3.54/1.80 => ( ( ord_less_eq_pname_o @ B_6 @ C_2 )
% 3.54/1.80 => ( ( image_1116629049_state @ F_11 @ ( minus_minus_pname_o @ A_18 @ B_6 ) )
% 3.54/1.80 = ( minus_2056855718tate_o @ ( image_1116629049_state @ F_11 @ A_18 ) @ ( image_1116629049_state @ F_11 @ B_6 ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1154_union__fold__insert,axiom,
% 3.54/1.80 ! [B_5: com > $o,A_17: com > $o] :
% 3.54/1.80 ( ( finite_finite_com @ A_17 )
% 3.54/1.80 => ( ( semila1562558655_com_o @ A_17 @ B_5 )
% 3.54/1.80 = ( finite504235573_com_o @ insert_com @ B_5 @ A_17 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1155_union__fold__insert,axiom,
% 3.54/1.80 ! [B_5: pname > $o,A_17: pname > $o] :
% 3.54/1.80 ( ( finite_finite_pname @ A_17 )
% 3.54/1.80 => ( ( semila1780557381name_o @ A_17 @ B_5 )
% 3.54/1.80 = ( finite603803317name_o @ insert_pname @ B_5 @ A_17 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1156_union__fold__insert,axiom,
% 3.54/1.80 ! [B_5: hoare_1708887482_state > $o,A_17: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( finite1625599783_state @ A_17 )
% 3.54/1.80 => ( ( semila1122118281tate_o @ A_17 @ B_5 )
% 3.54/1.80 = ( finite96880613tate_o @ insert528405184_state @ B_5 @ A_17 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1157_union__fold__insert,axiom,
% 3.54/1.80 ! [B_5: ( pname > $o ) > $o,A_17: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_17 )
% 3.54/1.80 => ( ( semila181081674me_o_o @ A_17 @ B_5 )
% 3.54/1.80 = ( finite1849951719me_o_o @ insert_pname_o @ B_5 @ A_17 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1158_union__fold__insert,axiom,
% 3.54/1.80 ! [B_5: ( hoare_1708887482_state > $o ) > $o,A_17: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_17 )
% 3.54/1.80 => ( ( semila1853742644te_o_o @ A_17 @ B_5 )
% 3.54/1.80 = ( finite463603445te_o_o @ insert949073679tate_o @ B_5 @ A_17 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1159_dom__minus,axiom,
% 3.54/1.80 ! [A_16: pname > $o,F_10: pname > option_com,X_7: pname] :
% 3.54/1.80 ( ( ( F_10 @ X_7 )
% 3.54/1.80 = none_com )
% 3.54/1.80 => ( ( minus_minus_pname_o @ ( dom_pname_com @ F_10 ) @ ( insert_pname @ X_7 @ A_16 ) )
% 3.54/1.80 = ( minus_minus_pname_o @ ( dom_pname_com @ F_10 ) @ A_16 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1160_Sup__fin_Oidem,axiom,
% 3.54/1.80 ! [X_6: $o] :
% 3.54/1.80 ( ( semila10642723_sup_o @ X_6 @ X_6 )
% 3.54/1.80 <=> X_6 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1161_Sup__fin_Oidem,axiom,
% 3.54/1.80 ! [X_6: pname > $o] :
% 3.54/1.80 ( ( semila1780557381name_o @ X_6 @ X_6 )
% 3.54/1.80 = X_6 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1162_Sup__fin_Oidem,axiom,
% 3.54/1.80 ! [X_6: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( semila1122118281tate_o @ X_6 @ X_6 )
% 3.54/1.80 = X_6 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1163_folding__one_Oeq__fold_H,axiom,
% 3.54/1.80 ! [X_5: com,A_15: com > $o,F_9: com > com > com,F_8: ( com > $o ) > com] :
% 3.54/1.80 ( ( finite860057415ne_com @ F_9 @ F_8 )
% 3.54/1.80 => ( ( finite_finite_com @ A_15 )
% 3.54/1.80 => ( ~ ( member_com @ X_5 @ A_15 )
% 3.54/1.80 => ( ( F_8 @ ( insert_com @ X_5 @ A_15 ) )
% 3.54/1.80 = ( finite_fold_com_com @ F_9 @ X_5 @ A_15 ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1164_folding__one_Oeq__fold_H,axiom,
% 3.54/1.80 ! [X_5: pname,A_15: pname > $o,F_9: pname > pname > pname,F_8: ( pname > $o ) > pname] :
% 3.54/1.80 ( ( finite1282449217_pname @ F_9 @ F_8 )
% 3.54/1.80 => ( ( finite_finite_pname @ A_15 )
% 3.54/1.80 => ( ~ ( member_pname @ X_5 @ A_15 )
% 3.54/1.80 => ( ( F_8 @ ( insert_pname @ X_5 @ A_15 ) )
% 3.54/1.80 = ( finite1657623752_pname @ F_9 @ X_5 @ A_15 ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1165_folding__one_Oeq__fold_H,axiom,
% 3.54/1.80 ! [X_5: hoare_1708887482_state,A_15: hoare_1708887482_state > $o,F_9: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_8: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.54/1.80 ( ( finite1615457021_state @ F_9 @ F_8 )
% 3.54/1.80 => ( ( finite1625599783_state @ A_15 )
% 3.54/1.80 => ( ~ ( member451959335_state @ X_5 @ A_15 )
% 3.54/1.80 => ( ( F_8 @ ( insert528405184_state @ X_5 @ A_15 ) )
% 3.54/1.80 = ( finite309095018_state @ F_9 @ X_5 @ A_15 ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1166_folding__one_Oeq__fold_H,axiom,
% 3.54/1.80 ! [X_5: pname > $o,A_15: ( pname > $o ) > $o,F_9: ( pname > $o ) > ( pname > $o ) > pname > $o,F_8: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.54/1.80 ( ( finite349908348name_o @ F_9 @ F_8 )
% 3.54/1.80 => ( ( finite297249702name_o @ A_15 )
% 3.54/1.80 => ( ~ ( member_pname_o @ X_5 @ A_15 )
% 3.54/1.80 => ( ( F_8 @ ( insert_pname_o @ X_5 @ A_15 ) )
% 3.54/1.80 = ( finite472615016name_o @ F_9 @ X_5 @ A_15 ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1167_folding__one_Oeq__fold_H,axiom,
% 3.54/1.80 ! [X_5: hoare_1708887482_state > $o,A_15: ( hoare_1708887482_state > $o ) > $o,F_9: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_8: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( finite928843026tate_o @ F_9 @ F_8 )
% 3.54/1.80 => ( ( finite1329924456tate_o @ A_15 )
% 3.54/1.80 => ( ~ ( member814030440tate_o @ X_5 @ A_15 )
% 3.54/1.80 => ( ( F_8 @ ( insert949073679tate_o @ X_5 @ A_15 ) )
% 3.54/1.80 = ( finite822533768tate_o @ F_9 @ X_5 @ A_15 ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1168_folding__one__idem_Oeq__fold__idem_H,axiom,
% 3.54/1.80 ! [A_14: com,A_13: com > $o,F_7: com > com > com,F_6: ( com > $o ) > com] :
% 3.54/1.80 ( ( finite666746948em_com @ F_7 @ F_6 )
% 3.54/1.80 => ( ( finite_finite_com @ A_13 )
% 3.54/1.80 => ( ( F_6 @ ( insert_com @ A_14 @ A_13 ) )
% 3.54/1.80 = ( finite_fold_com_com @ F_7 @ A_14 @ A_13 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1169_folding__one__idem_Oeq__fold__idem_H,axiom,
% 3.54/1.80 ! [A_14: pname,A_13: pname > $o,F_7: pname > pname > pname,F_6: ( pname > $o ) > pname] :
% 3.54/1.80 ( ( finite89670078_pname @ F_7 @ F_6 )
% 3.54/1.80 => ( ( finite_finite_pname @ A_13 )
% 3.54/1.80 => ( ( F_6 @ ( insert_pname @ A_14 @ A_13 ) )
% 3.54/1.80 = ( finite1657623752_pname @ F_7 @ A_14 @ A_13 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1170_folding__one__idem_Oeq__fold__idem_H,axiom,
% 3.54/1.80 ! [A_14: hoare_1708887482_state,A_13: hoare_1708887482_state > $o,F_7: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_6: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
% 3.54/1.80 ( ( finite1347568576_state @ F_7 @ F_6 )
% 3.54/1.80 => ( ( finite1625599783_state @ A_13 )
% 3.54/1.80 => ( ( F_6 @ ( insert528405184_state @ A_14 @ A_13 ) )
% 3.54/1.80 = ( finite309095018_state @ F_7 @ A_14 @ A_13 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1171_folding__one__idem_Oeq__fold__idem_H,axiom,
% 3.54/1.80 ! [A_14: pname > $o,A_13: ( pname > $o ) > $o,F_7: ( pname > $o ) > ( pname > $o ) > pname > $o,F_6: ( ( pname > $o ) > $o ) > pname > $o] :
% 3.54/1.80 ( ( finite697516351name_o @ F_7 @ F_6 )
% 3.54/1.80 => ( ( finite297249702name_o @ A_13 )
% 3.54/1.80 => ( ( F_6 @ ( insert_pname_o @ A_14 @ A_13 ) )
% 3.54/1.80 = ( finite472615016name_o @ F_7 @ A_14 @ A_13 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1172_folding__one__idem_Oeq__fold__idem_H,axiom,
% 3.54/1.80 ! [A_14: hoare_1708887482_state > $o,A_13: ( hoare_1708887482_state > $o ) > $o,F_7: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_6: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( finite621643279tate_o @ F_7 @ F_6 )
% 3.54/1.80 => ( ( finite1329924456tate_o @ A_13 )
% 3.54/1.80 => ( ( F_6 @ ( insert949073679tate_o @ A_14 @ A_13 ) )
% 3.54/1.80 = ( finite822533768tate_o @ F_7 @ A_14 @ A_13 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1173_WT_OBody,axiom,
% 3.54/1.80 ! [Pn_1: pname] :
% 3.54/1.80 ( ( ( body @ Pn_1 )
% 3.54/1.80 != none_com )
% 3.54/1.80 => ( wt @ ( body_1 @ Pn_1 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1174_inj__on__insert,axiom,
% 3.54/1.80 ! [F_5: pname > hoare_1708887482_state,A_12: pname,A_11: pname > $o] :
% 3.54/1.80 ( ( inj_on1553129421_state @ F_5 @ ( insert_pname @ A_12 @ A_11 ) )
% 3.54/1.80 <=> ( ( inj_on1553129421_state @ F_5 @ A_11 )
% 3.54/1.80 & ~ ( member451959335_state @ ( F_5 @ A_12 ) @ ( image_1116629049_state @ F_5 @ ( minus_minus_pname_o @ A_11 @ ( insert_pname @ A_12 @ bot_bot_pname_o ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1175_dom__fun__upd,axiom,
% 3.54/1.80 ! [F_4: pname > option_com,X_4: pname,Y_2: option_com] :
% 3.54/1.80 ( ( ( Y_2 = none_com )
% 3.54/1.80 => ( ( dom_pname_com @ ( fun_up879233478on_com @ F_4 @ X_4 @ Y_2 ) )
% 3.54/1.80 = ( minus_minus_pname_o @ ( dom_pname_com @ F_4 ) @ ( insert_pname @ X_4 @ bot_bot_pname_o ) ) ) )
% 3.54/1.80 & ( ( Y_2 != none_com )
% 3.54/1.80 => ( ( dom_pname_com @ ( fun_up879233478on_com @ F_4 @ X_4 @ Y_2 ) )
% 3.54/1.80 = ( insert_pname @ X_4 @ ( dom_pname_com @ F_4 ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1176_inf__le__fold__inf,axiom,
% 3.54/1.80 ! [C_1: pname > $o,B_4: pname > $o,A_10: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_10 )
% 3.54/1.80 => ( ! [X_3: pname > $o] :
% 3.54/1.80 ( ( member_pname_o @ X_3 @ A_10 )
% 3.54/1.80 => ( ord_less_eq_pname_o @ B_4 @ X_3 ) )
% 3.54/1.80 => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ B_4 @ C_1 ) @ ( finite472615016name_o @ semila1673364395name_o @ C_1 @ A_10 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1177_inf__le__fold__inf,axiom,
% 3.54/1.80 ! [C_1: hoare_1708887482_state > $o,B_4: hoare_1708887482_state > $o,A_10: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_10 )
% 3.54/1.80 => ( ! [X_3: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( member814030440tate_o @ X_3 @ A_10 )
% 3.54/1.80 => ( ord_le777019615tate_o @ B_4 @ X_3 ) )
% 3.54/1.80 => ( ord_le777019615tate_o @ ( semila129691299tate_o @ B_4 @ C_1 ) @ ( finite822533768tate_o @ semila129691299tate_o @ C_1 @ A_10 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1178_inf__le__fold__inf,axiom,
% 3.54/1.80 ! [C_1: $o,B_4: $o,A_10: $o > $o] :
% 3.54/1.80 ( ( finite_finite_o @ A_10 )
% 3.54/1.80 => ( ! [X_3: $o] :
% 3.54/1.80 ( ( member_o @ X_3 @ A_10 )
% 3.54/1.80 => ( ord_less_eq_o @ B_4 @ X_3 ) )
% 3.54/1.80 => ( ord_less_eq_o @ ( semila854092349_inf_o @ B_4 @ C_1 ) @ ( finite_fold_o_o @ semila854092349_inf_o @ C_1 @ A_10 ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1179_fold__sup__le__sup,axiom,
% 3.54/1.80 ! [C: pname > $o,B_3: pname > $o,A_9: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_9 )
% 3.54/1.80 => ( ! [X_3: pname > $o] :
% 3.54/1.80 ( ( member_pname_o @ X_3 @ A_9 )
% 3.54/1.80 => ( ord_less_eq_pname_o @ X_3 @ B_3 ) )
% 3.54/1.80 => ( ord_less_eq_pname_o @ ( finite472615016name_o @ semila1780557381name_o @ C @ A_9 ) @ ( semila1780557381name_o @ B_3 @ C ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1180_fold__sup__le__sup,axiom,
% 3.54/1.80 ! [C: hoare_1708887482_state > $o,B_3: hoare_1708887482_state > $o,A_9: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_9 )
% 3.54/1.80 => ( ! [X_3: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( member814030440tate_o @ X_3 @ A_9 )
% 3.54/1.80 => ( ord_le777019615tate_o @ X_3 @ B_3 ) )
% 3.54/1.80 => ( ord_le777019615tate_o @ ( finite822533768tate_o @ semila1122118281tate_o @ C @ A_9 ) @ ( semila1122118281tate_o @ B_3 @ C ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1181_fold__sup__le__sup,axiom,
% 3.54/1.80 ! [C: $o,B_3: $o,A_9: $o > $o] :
% 3.54/1.80 ( ( finite_finite_o @ A_9 )
% 3.54/1.80 => ( ! [X_3: $o] :
% 3.54/1.80 ( ( member_o @ X_3 @ A_9 )
% 3.54/1.80 => ( ord_less_eq_o @ X_3 @ B_3 ) )
% 3.54/1.80 => ( ord_less_eq_o @ ( finite_fold_o_o @ semila10642723_sup_o @ C @ A_9 ) @ ( semila10642723_sup_o @ B_3 @ C ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1182_inj__on__iff__surj,axiom,
% 3.54/1.80 ! [A_8: pname > $o,A_7: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( A_7 != bot_bo19817387tate_o )
% 3.54/1.80 => ( ? [F_3: hoare_1708887482_state > pname] :
% 3.54/1.80 ( ( inj_on1945914667_pname @ F_3 @ A_7 )
% 3.54/1.80 & ( ord_less_eq_pname_o @ ( image_1509414295_pname @ F_3 @ A_7 ) @ A_8 ) )
% 3.54/1.80 <=> ? [G_1: pname > hoare_1708887482_state] :
% 3.54/1.80 ( ( image_1116629049_state @ G_1 @ A_8 )
% 3.54/1.80 = A_7 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1183_inj__on__iff__surj,axiom,
% 3.54/1.80 ! [A_8: hoare_1708887482_state > $o,A_7: pname > $o] :
% 3.54/1.80 ( ( A_7 != bot_bot_pname_o )
% 3.54/1.80 => ( ? [F_3: pname > hoare_1708887482_state] :
% 3.54/1.80 ( ( inj_on1553129421_state @ F_3 @ A_7 )
% 3.54/1.80 & ( ord_le777019615tate_o @ ( image_1116629049_state @ F_3 @ A_7 ) @ A_8 ) )
% 3.54/1.80 <=> ? [G_1: hoare_1708887482_state > pname] :
% 3.54/1.80 ( ( image_1509414295_pname @ G_1 @ A_8 )
% 3.54/1.80 = A_7 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1184_option_Oexhaust,axiom,
% 3.54/1.80 ! [Y_1: option_com] :
% 3.54/1.80 ( ( Y_1 != none_com )
% 3.54/1.80 => ~ ! [A_6: com] :
% 3.54/1.80 ( Y_1
% 3.54/1.80 != ( some_com @ A_6 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1185_option_Oexhaust,axiom,
% 3.54/1.80 ! [Y_1: option_pname] :
% 3.54/1.80 ( ( Y_1 != none_pname )
% 3.54/1.80 => ~ ! [A_6: pname] :
% 3.54/1.80 ( Y_1
% 3.54/1.80 != ( some_pname @ A_6 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1186_option_Oexhaust,axiom,
% 3.54/1.80 ! [Y_1: option1624383643_state] :
% 3.54/1.80 ( ( Y_1 != none_H1106584047_state )
% 3.54/1.80 => ~ ! [A_6: hoare_1708887482_state] :
% 3.54/1.80 ( Y_1
% 3.54/1.80 != ( some_H1974565227_state @ A_6 ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1187_Cantor__Bernstein__aux,axiom,
% 3.54/1.80 ! [G: hoare_1708887482_state > pname,B_2: hoare_1708887482_state > $o,F_2: pname > hoare_1708887482_state,A_4: pname > $o] :
% 3.54/1.80 ? [A_5: pname > $o] :
% 3.54/1.80 ( ( ord_less_eq_pname_o @ A_5 @ A_4 )
% 3.54/1.80 & ! [X_3: pname] :
% 3.54/1.80 ( ( member_pname @ X_3 @ A_5 )
% 3.54/1.80 => ~ ( member_pname @ X_3 @ ( image_1509414295_pname @ G @ ( minus_2056855718tate_o @ B_2 @ ( image_1116629049_state @ F_2 @ A_5 ) ) ) ) )
% 3.54/1.80 & ? [H: pname > hoare_1708887482_state] :
% 3.54/1.80 ( ! [X_3: pname] :
% 3.54/1.80 ( ( member_pname @ X_3 @ A_5 )
% 3.54/1.80 => ( ( H @ X_3 )
% 3.54/1.80 = ( F_2 @ X_3 ) ) )
% 3.54/1.80 & ! [X_3: pname] :
% 3.54/1.80 ( ( member_pname @ X_3 @ ( minus_minus_pname_o @ A_4 @ A_5 ) )
% 3.54/1.80 => ( ( member451959335_state @ ( H @ X_3 ) @ ( minus_2056855718tate_o @ B_2 @ ( image_1116629049_state @ F_2 @ A_5 ) ) )
% 3.54/1.80 & ( X_3
% 3.54/1.80 = ( G @ ( H @ X_3 ) ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1188_Cantor__Bernstein__aux,axiom,
% 3.54/1.80 ! [G: pname > hoare_1708887482_state,B_2: pname > $o,F_2: hoare_1708887482_state > pname,A_4: hoare_1708887482_state > $o] :
% 3.54/1.80 ? [A_5: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( ord_le777019615tate_o @ A_5 @ A_4 )
% 3.54/1.80 & ! [X_3: hoare_1708887482_state] :
% 3.54/1.80 ( ( member451959335_state @ X_3 @ A_5 )
% 3.54/1.80 => ~ ( member451959335_state @ X_3 @ ( image_1116629049_state @ G @ ( minus_minus_pname_o @ B_2 @ ( image_1509414295_pname @ F_2 @ A_5 ) ) ) ) )
% 3.54/1.80 & ? [H: hoare_1708887482_state > pname] :
% 3.54/1.80 ( ! [X_3: hoare_1708887482_state] :
% 3.54/1.80 ( ( member451959335_state @ X_3 @ A_5 )
% 3.54/1.80 => ( ( H @ X_3 )
% 3.54/1.80 = ( F_2 @ X_3 ) ) )
% 3.54/1.80 & ! [X_3: hoare_1708887482_state] :
% 3.54/1.80 ( ( member451959335_state @ X_3 @ ( minus_2056855718tate_o @ A_4 @ A_5 ) )
% 3.54/1.80 => ( ( member_pname @ ( H @ X_3 ) @ ( minus_minus_pname_o @ B_2 @ ( image_1509414295_pname @ F_2 @ A_5 ) ) )
% 3.54/1.80 & ( X_3
% 3.54/1.80 = ( G @ ( H @ X_3 ) ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1189_image__vimage__subset,axiom,
% 3.54/1.80 ! [F_1: pname > hoare_1708887482_state,A_3: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( image_1116629049_state @ F_1 @ ( vimage1943311875_state @ F_1 @ A_3 ) ) @ A_3 ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1190_dom__restrict,axiom,
% 3.54/1.80 ! [M: pname > option_com,A_2: pname > $o] :
% 3.54/1.80 ( ( dom_pname_com @ ( restri1382200118me_com @ M @ A_2 ) )
% 3.54/1.80 = ( semila1673364395name_o @ ( dom_pname_com @ M ) @ A_2 ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1191_Inf__fin_Ounion__disjoint,axiom,
% 3.54/1.80 ! [B_1: ( pname > $o ) > $o,A_1: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A_1 )
% 3.54/1.80 => ( ( A_1 != bot_bot_pname_o_o )
% 3.54/1.80 => ( ( finite297249702name_o @ B_1 )
% 3.54/1.80 => ( ( B_1 != bot_bot_pname_o_o )
% 3.54/1.80 => ( ( ( semila2013987940me_o_o @ A_1 @ B_1 )
% 3.54/1.80 = bot_bot_pname_o_o )
% 3.54/1.80 => ( ( big_la1126801287name_o @ ( semila181081674me_o_o @ A_1 @ B_1 ) )
% 3.54/1.80 = ( semila1673364395name_o @ ( big_la1126801287name_o @ A_1 ) @ ( big_la1126801287name_o @ B_1 ) ) ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1192_Inf__fin_Ounion__disjoint,axiom,
% 3.54/1.80 ! [B_1: ( hoare_1708887482_state > $o ) > $o,A_1: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A_1 )
% 3.54/1.80 => ( ( A_1 != bot_bo1678742418te_o_o )
% 3.54/1.80 => ( ( finite1329924456tate_o @ B_1 )
% 3.54/1.80 => ( ( B_1 != bot_bo1678742418te_o_o )
% 3.54/1.80 => ( ( ( semila598060698te_o_o @ A_1 @ B_1 )
% 3.54/1.80 = bot_bo1678742418te_o_o )
% 3.54/1.80 => ( ( big_la781588935tate_o @ ( semila1853742644te_o_o @ A_1 @ B_1 ) )
% 3.54/1.80 = ( semila129691299tate_o @ ( big_la781588935tate_o @ A_1 ) @ ( big_la781588935tate_o @ B_1 ) ) ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1193_Inf__fin_Ounion__inter,axiom,
% 3.54/1.80 ! [B: ( pname > $o ) > $o,A: ( pname > $o ) > $o] :
% 3.54/1.80 ( ( finite297249702name_o @ A )
% 3.54/1.80 => ( ( finite297249702name_o @ B )
% 3.54/1.80 => ( ( ( semila2013987940me_o_o @ A @ B )
% 3.54/1.80 != bot_bot_pname_o_o )
% 3.54/1.80 => ( ( semila1673364395name_o @ ( big_la1126801287name_o @ ( semila181081674me_o_o @ A @ B ) ) @ ( big_la1126801287name_o @ ( semila2013987940me_o_o @ A @ B ) ) )
% 3.54/1.80 = ( semila1673364395name_o @ ( big_la1126801287name_o @ A ) @ ( big_la1126801287name_o @ B ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1194_Inf__fin_Ounion__inter,axiom,
% 3.54/1.80 ! [B: ( hoare_1708887482_state > $o ) > $o,A: ( hoare_1708887482_state > $o ) > $o] :
% 3.54/1.80 ( ( finite1329924456tate_o @ A )
% 3.54/1.80 => ( ( finite1329924456tate_o @ B )
% 3.54/1.80 => ( ( ( semila598060698te_o_o @ A @ B )
% 3.54/1.80 != bot_bo1678742418te_o_o )
% 3.54/1.80 => ( ( semila129691299tate_o @ ( big_la781588935tate_o @ ( semila1853742644te_o_o @ A @ B ) ) @ ( big_la781588935tate_o @ ( semila598060698te_o_o @ A @ B ) ) )
% 3.54/1.80 = ( semila129691299tate_o @ ( big_la781588935tate_o @ A ) @ ( big_la781588935tate_o @ B ) ) ) ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1195_UNIV__I,axiom,
% 3.54/1.80 ! [X_2: com] : ( member_com @ X_2 @ top_top_com_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1196_UNIV__I,axiom,
% 3.54/1.80 ! [X_2: pname] : ( member_pname @ X_2 @ top_top_pname_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1197_UNIV__I,axiom,
% 3.54/1.80 ! [X_2: hoare_1708887482_state] : ( member451959335_state @ X_2 @ top_to832624271tate_o ) ).
% 3.54/1.80
% 3.54/1.80 thf(fact_1198_rangeI,axiom,
% 3.54/1.80 ! [F: pname > hoare_1708887482_state,X_1: pname] : ( member451959335_state @ ( F @ X_1 ) @ ( image_1116629049_state @ F @ top_top_pname_o ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_1_1_fequal_000tc__Com__Ocom_T,axiom,
% 3.54/1.80 ! [X: com,Y: com] :
% 3.54/1.80 ( ~ ( fequal_com @ X @ Y )
% 3.54/1.80 | ( X = Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_2_1_fequal_000tc__Com__Ocom_T,axiom,
% 3.54/1.80 ! [X: com,Y: com] :
% 3.54/1.80 ( ( X != Y )
% 3.54/1.80 | ( fequal_com @ X @ Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 3.54/1.80 ! [X: pname,Y: pname] :
% 3.54/1.80 ( ~ ( fequal_pname @ X @ Y )
% 3.54/1.80 | ( X = Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 3.54/1.80 ! [X: pname,Y: pname] :
% 3.54/1.80 ( ( X != Y )
% 3.54/1.80 | ( fequal_pname @ X @ Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_1_1_fequal_000tc__Com__Ostate_T,axiom,
% 3.54/1.80 ! [X: state,Y: state] :
% 3.54/1.80 ( ~ ( fequal_state @ X @ Y )
% 3.54/1.80 | ( X = Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,
% 3.54/1.80 ! [X: state,Y: state] :
% 3.54/1.80 ( ( X != Y )
% 3.54/1.80 | ( fequal_state @ X @ Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 3.54/1.80 ! [X: pname > $o,Y: pname > $o] :
% 3.54/1.80 ( ~ ( fequal_pname_o @ X @ Y )
% 3.54/1.80 | ( X = Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 3.54/1.80 ! [X: pname > $o,Y: pname > $o] :
% 3.54/1.80 ( ( X != Y )
% 3.54/1.80 | ( fequal_pname_o @ X @ Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 3.54/1.80 ! [X: option_com,Y: option_com] :
% 3.54/1.80 ( ( if_option_com @ $true @ X @ Y )
% 3.54/1.80 = X ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 3.54/1.80 ! [X: option_com,Y: option_com] :
% 3.54/1.80 ( ( if_option_com @ $false @ X @ Y )
% 3.54/1.80 = Y ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,
% 3.54/1.80 ! [P: $o] :
% 3.54/1.80 ( ( P = $true )
% 3.54/1.80 | ( P = $false ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_If_1_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate,axiom,
% 3.54/1.80 ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
% 3.54/1.80 ( ( if_Hoa1374726218_state @ $true @ X @ Y )
% 3.54/1.80 = X ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_If_2_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate,axiom,
% 3.54/1.80 ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
% 3.54/1.80 ( ( if_Hoa1374726218_state @ $false @ X @ Y )
% 3.54/1.80 = Y ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_If_3_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate,axiom,
% 3.54/1.80 ! [P: $o] :
% 3.54/1.80 ( ( P = $true )
% 3.54/1.80 | ( P = $false ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,axiom,
% 3.54/1.80 ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
% 3.54/1.80 ( ~ ( fequal224822779_state @ X @ Y )
% 3.54/1.80 | ( X = Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,axiom,
% 3.54/1.80 ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
% 3.54/1.80 ( ( X != Y )
% 3.54/1.80 | ( fequal224822779_state @ X @ Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,axiom,
% 3.54/1.80 ! [X: hoare_1708887482_state > $o,Y: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ~ ( fequal1436017556tate_o @ X @ Y )
% 3.54/1.80 | ( X = Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,axiom,
% 3.54/1.80 ! [X: hoare_1708887482_state > $o,Y: hoare_1708887482_state > $o] :
% 3.54/1.80 ( ( X != Y )
% 3.54/1.80 | ( fequal1436017556tate_o @ X @ Y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(conj_0,hypothesis,
% 3.54/1.80 hoare_1160767572gleton ).
% 3.54/1.80
% 3.54/1.80 thf(conj_1,hypothesis,
% 3.54/1.80 wT_bodies ).
% 3.54/1.80
% 3.54/1.80 thf(conj_2,hypothesis,
% 3.54/1.80 finite1625599783_state @ fa ).
% 3.54/1.80
% 3.54/1.80 thf(conj_3,hypothesis,
% 3.54/1.80 ~ ( member451959335_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ) ).
% 3.54/1.80
% 3.54/1.80 thf(conj_4,hypothesis,
% 3.54/1.80 ( ord_le777019615tate_o @ fa
% 3.54/1.80 @ ( image_1116629049_state
% 3.54/1.80 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
% 3.54/1.80 @ ( dom_pname_com @ body ) ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(conj_5,hypothesis,
% 3.54/1.80 ( ( body @ pn )
% 3.54/1.80 = ( some_com @ y ) ) ).
% 3.54/1.80
% 3.54/1.80 thf(conj_6,hypothesis,
% 3.54/1.80 ( hoare_90032982_state
% 3.54/1.80 @ ( image_1116629049_state
% 3.54/1.80 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 3.54/1.80 @ ( dom_pname_com @ body ) )
% 3.54/1.80 @ fa ) ).
% 3.54/1.80
% 3.54/1.80 thf(conj_7,conjecture,
% 3.54/1.80 ( hoare_90032982_state
% 3.54/1.80 @ ( image_1116629049_state
% 3.54/1.80 @ ^ [Pn: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
% 3.54/1.80 @ ( dom_pname_com @ body ) )
% 3.54/1.80 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) ) ).
% 3.54/1.80 ------------------------
% 3.54/1.88 % (15823)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/183Mi)
% 3.54/1.88 % (15824)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/4Mi)
% 3.54/1.88 % (15825)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/27Mi)
% 3.54/1.88 % (15826)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/2Mi)
% 3.54/1.88 % (15827)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/2Mi)
% 3.54/1.88 % (15828)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/275Mi)
% 3.54/1.88 % (15829)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/18Mi)
% 3.54/1.88 % (15826)Instruction limit reached!
% 3.54/1.88 % (15826)------------------------------
% 3.54/1.88 % (15826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.88 % (15826)Termination reason: Unknown
% 3.54/1.88 % (15826)Termination phase: shuffling
% 3.54/1.88
% 3.54/1.88 % (15826)Memory used [KB]: 3070
% 3.54/1.88 % (15826)Time elapsed: 0.004 s
% 3.54/1.88 % (15826)Instructions burned: 2 (million)
% 3.54/1.88 % (15826)------------------------------
% 3.54/1.88 % (15826)------------------------------
% 3.54/1.88 % (15827)Instruction limit reached!
% 3.54/1.88 % (15827)------------------------------
% 3.54/1.88 % (15827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.88 % (15827)Termination reason: Unknown
% 3.54/1.88 % (15827)Termination phase: shuffling
% 3.54/1.88
% 3.54/1.88 % (15827)Memory used [KB]: 3070
% 3.54/1.88 % (15827)Time elapsed: 0.004 s
% 3.54/1.88 % (15827)Instructions burned: 2 (million)
% 3.54/1.88 % (15827)------------------------------
% 3.54/1.88 % (15827)------------------------------
% 3.54/1.88 % (15824)Instruction limit reached!
% 3.54/1.88 % (15824)------------------------------
% 3.54/1.88 % (15824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.88 % (15824)Termination reason: Unknown
% 3.54/1.88 % (15824)Termination phase: shuffling
% 3.54/1.88
% 3.54/1.88 % (15824)Memory used [KB]: 3070
% 3.54/1.88 % (15824)Time elapsed: 0.006 s
% 3.54/1.88 % (15824)Instructions burned: 4 (million)
% 3.54/1.88 % (15824)------------------------------
% 3.54/1.88 % (15824)------------------------------
% 3.54/1.89 % (15829)Instruction limit reached!
% 3.54/1.89 % (15829)------------------------------
% 3.54/1.89 % (15829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.89 % (15829)Termination reason: Unknown
% 3.54/1.89 % (15829)Termination phase: shuffling
% 3.54/1.89
% 3.54/1.89 % (15829)Memory used [KB]: 4093
% 3.54/1.89 % (15829)Time elapsed: 0.015 s
% 3.54/1.89 % (15829)Instructions burned: 18 (million)
% 3.54/1.89 % (15829)------------------------------
% 3.54/1.89 % (15829)------------------------------
% 3.54/1.90 % (15825)Instruction limit reached!
% 3.54/1.90 % (15825)------------------------------
% 3.54/1.90 % (15825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.90 % (15825)Termination reason: Unknown
% 3.54/1.90 % (15825)Termination phase: shuffling
% 3.54/1.90
% 3.54/1.90 % (15825)Memory used [KB]: 4605
% 3.54/1.90 % (15825)Time elapsed: 0.021 s
% 3.54/1.90 % (15825)Instructions burned: 27 (million)
% 3.54/1.90 % (15825)------------------------------
% 3.54/1.90 % (15825)------------------------------
% 3.54/1.90 % (15831)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/37Mi)
% 3.54/1.90 % (15830)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/3Mi)
% 3.54/1.90 % (15832)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/15Mi)
% 3.54/1.90 % (15830)Instruction limit reached!
% 3.54/1.90 % (15830)------------------------------
% 3.54/1.90 % (15830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.90 % (15830)Termination reason: Unknown
% 3.54/1.90 % (15830)Termination phase: shuffling
% 3.54/1.90
% 3.54/1.90 % (15830)Memory used [KB]: 3070
% 3.54/1.90 % (15830)Time elapsed: 0.006 s
% 3.54/1.90 % (15830)Instructions burned: 3 (million)
% 3.54/1.90 % (15830)------------------------------
% 3.54/1.90 % (15830)------------------------------
% 3.54/1.91 % (15833)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/3Mi)
% 3.54/1.91 % (15832)Instruction limit reached!
% 3.54/1.91 % (15832)------------------------------
% 3.54/1.91 % (15832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.91 % (15832)Termination reason: Unknown
% 3.54/1.91 % (15832)Termination phase: shuffling
% 3.54/1.91
% 3.54/1.91 % (15832)Memory used [KB]: 3837
% 3.54/1.91 % (15832)Time elapsed: 0.013 s
% 3.54/1.91 % (15832)Instructions burned: 15 (million)
% 3.54/1.91 % (15832)------------------------------
% 3.54/1.91 % (15832)------------------------------
% 3.54/1.91 % (15833)Instruction limit reached!
% 3.54/1.91 % (15833)------------------------------
% 3.54/1.91 % (15833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.91 % (15833)Termination reason: Unknown
% 3.54/1.91 % (15833)Termination phase: shuffling
% 3.54/1.91
% 3.54/1.91 % (15833)Memory used [KB]: 3198
% 3.54/1.91 % (15833)Time elapsed: 0.005 s
% 3.54/1.91 % (15833)Instructions burned: 4 (million)
% 3.54/1.91 % (15833)------------------------------
% 3.54/1.91 % (15833)------------------------------
% 3.54/1.91 % (15834)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/1041Mi)
% 3.54/1.92 % (15835)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15503 for (2999ds/7Mi)
% 3.54/1.92 % (15831)Instruction limit reached!
% 3.54/1.92 % (15831)------------------------------
% 3.54/1.92 % (15831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.92 % (15831)Termination reason: Unknown
% 3.54/1.92 % (15831)Termination phase: shuffling
% 3.54/1.92
% 3.54/1.92 % (15831)Memory used [KB]: 4989
% 3.54/1.92 % (15831)Time elapsed: 0.024 s
% 3.54/1.92 % (15831)Instructions burned: 38 (million)
% 3.54/1.92 % (15831)------------------------------
% 3.54/1.92 % (15831)------------------------------
% 3.54/1.92 % (15837)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/3Mi)
% 3.54/1.92 % (15835)Instruction limit reached!
% 3.54/1.92 % (15835)------------------------------
% 3.54/1.92 % (15835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.92 % (15835)Termination reason: Unknown
% 3.54/1.92 % (15835)Termination phase: shuffling
% 3.54/1.92
% 3.54/1.92 % (15835)Memory used [KB]: 3326
% 3.54/1.92 % (15835)Time elapsed: 0.007 s
% 3.54/1.92 % (15835)Instructions burned: 7 (million)
% 3.54/1.92 % (15835)------------------------------
% 3.54/1.92 % (15835)------------------------------
% 3.54/1.92 % (15837)Instruction limit reached!
% 3.54/1.92 % (15837)------------------------------
% 3.54/1.92 % (15837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.92 % (15837)Termination reason: Unknown
% 3.54/1.92 % (15837)Termination phase: shuffling
% 3.54/1.92
% 3.54/1.92 % (15837)Memory used [KB]: 3198
% 3.54/1.92 % (15837)Time elapsed: 0.003 s
% 3.54/1.92 % (15837)Instructions burned: 4 (million)
% 3.54/1.92 % (15837)------------------------------
% 3.54/1.92 % (15837)------------------------------
% 3.54/1.92 % (15836)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/16Mi)
% 3.54/1.93 % (15836)Instruction limit reached!
% 3.54/1.93 % (15836)------------------------------
% 3.54/1.93 % (15836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.93 % (15836)Termination reason: Unknown
% 3.54/1.93 % (15836)Termination phase: shuffling
% 3.54/1.93
% 3.54/1.93 % (15836)Memory used [KB]: 3965
% 3.54/1.93 % (15836)Time elapsed: 0.008 s
% 3.54/1.93 % (15836)Instructions burned: 17 (million)
% 3.54/1.93 % (15836)------------------------------
% 3.54/1.93 % (15836)------------------------------
% 3.54/1.93 % (15840)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/3Mi)
% 3.54/1.93 % (15839)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/7Mi)
% 3.54/1.93 % (15838)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/3Mi)
% 3.54/1.93 % (15840)Instruction limit reached!
% 3.54/1.93 % (15840)------------------------------
% 3.54/1.93 % (15840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.93 % (15840)Termination reason: Unknown
% 3.54/1.93 % (15840)Termination phase: shuffling
% 3.54/1.93
% 3.54/1.93 % (15840)Memory used [KB]: 3070
% 3.54/1.93 % (15840)Time elapsed: 0.003 s
% 3.54/1.93 % (15840)Instructions burned: 4 (million)
% 3.54/1.93 % (15840)------------------------------
% 3.54/1.93 % (15840)------------------------------
% 3.54/1.94 % (15838)Instruction limit reached!
% 3.54/1.94 % (15838)------------------------------
% 3.54/1.94 % (15838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.94 % (15838)Termination reason: Unknown
% 3.54/1.94 % (15838)Termination phase: shuffling
% 3.54/1.94
% 3.54/1.94 % (15838)Memory used [KB]: 3070
% 3.54/1.94 % (15838)Time elapsed: 0.003 s
% 3.54/1.94 % (15838)Instructions burned: 3 (million)
% 3.54/1.94 % (15838)------------------------------
% 3.54/1.94 % (15838)------------------------------
% 3.54/1.94 % (15839)Instruction limit reached!
% 3.54/1.94 % (15839)------------------------------
% 3.54/1.94 % (15839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.94 % (15839)Termination reason: Unknown
% 3.54/1.94 % (15839)Termination phase: shuffling
% 3.54/1.94
% 3.54/1.94 % (15839)Memory used [KB]: 3454
% 3.54/1.94 % (15839)Time elapsed: 0.005 s
% 3.54/1.94 % (15839)Instructions burned: 7 (million)
% 3.54/1.94 % (15839)------------------------------
% 3.54/1.94 % (15839)------------------------------
% 3.54/1.94 % (15841)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/4Mi)
% 3.54/1.94 % (15823)Instruction limit reached!
% 3.54/1.94 % (15823)------------------------------
% 3.54/1.94 % (15823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.94 % (15823)Termination reason: Unknown
% 3.54/1.94 % (15823)Termination phase: Preprocessing 1
% 3.54/1.94
% 3.54/1.94 % (15823)Memory used [KB]: 9210
% 3.54/1.94 % (15823)Time elapsed: 0.069 s
% 3.54/1.94 % (15823)Instructions burned: 185 (million)
% 3.54/1.94 % (15823)------------------------------
% 3.54/1.94 % (15823)------------------------------
% 3.54/1.94 % (15841)Instruction limit reached!
% 3.54/1.94 % (15841)------------------------------
% 3.54/1.94 % (15841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.94 % (15841)Termination reason: Unknown
% 3.54/1.94 % (15841)Termination phase: shuffling
% 3.54/1.94
% 3.54/1.94 % (15841)Memory used [KB]: 3198
% 3.54/1.94 % (15841)Time elapsed: 0.003 s
% 3.54/1.94 % (15841)Instructions burned: 4 (million)
% 3.54/1.94 % (15841)------------------------------
% 3.54/1.94 % (15841)------------------------------
% 3.54/1.94 % (15842)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/18Mi)
% 3.54/1.95 % (15843)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/710Mi)
% 3.54/1.95 % (15844)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/6Mi)
% 3.54/1.95 % (15844)Instruction limit reached!
% 3.54/1.95 % (15844)------------------------------
% 3.54/1.95 % (15844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.95 % (15844)Termination reason: Unknown
% 3.54/1.95 % (15844)Termination phase: shuffling
% 3.54/1.95
% 3.54/1.95 % (15844)Memory used [KB]: 3326
% 3.54/1.95 % (15844)Time elapsed: 0.005 s
% 3.54/1.95 % (15844)Instructions burned: 6 (million)
% 3.54/1.95 % (15844)------------------------------
% 3.54/1.95 % (15844)------------------------------
% 3.54/1.95 % (15842)Instruction limit reached!
% 3.54/1.95 % (15842)------------------------------
% 3.54/1.95 % (15842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.95 % (15842)Termination reason: Unknown
% 3.54/1.95 % (15842)Termination phase: shuffling
% 3.54/1.95
% 3.54/1.95 % (15842)Memory used [KB]: 4093
% 3.54/1.95 % (15842)Time elapsed: 0.008 s
% 3.54/1.95 % (15842)Instructions burned: 18 (million)
% 3.54/1.95 % (15842)------------------------------
% 3.54/1.95 % (15842)------------------------------
% 3.54/1.95 % (15846)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/21Mi)
% 3.54/1.95 % (15845)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/902Mi)
% 3.54/1.96 % (15848)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/6Mi)
% 3.54/1.96 % (15846)Instruction limit reached!
% 3.54/1.96 % (15846)------------------------------
% 3.54/1.96 % (15846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.96 % (15846)Termination reason: Unknown
% 3.54/1.96 % (15846)Termination phase: shuffling
% 3.54/1.96
% 3.54/1.96 % (15846)Memory used [KB]: 4221
% 3.54/1.96 % (15846)Time elapsed: 0.009 s
% 3.54/1.96 % (15846)Instructions burned: 21 (million)
% 3.54/1.96 % (15846)------------------------------
% 3.54/1.96 % (15846)------------------------------
% 3.54/1.96 % (15847)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/5Mi)
% 3.54/1.96 % (15848)Instruction limit reached!
% 3.54/1.96 % (15848)------------------------------
% 3.54/1.96 % (15848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.96 % (15848)Termination reason: Unknown
% 3.54/1.96 % (15848)Termination phase: shuffling
% 3.54/1.96
% 3.54/1.96 % (15848)Memory used [KB]: 3326
% 3.54/1.96 % (15848)Time elapsed: 0.004 s
% 3.54/1.96 % (15848)Instructions burned: 6 (million)
% 3.54/1.96 % (15848)------------------------------
% 3.54/1.96 % (15848)------------------------------
% 3.54/1.96 % (15847)Instruction limit reached!
% 3.54/1.96 % (15847)------------------------------
% 3.54/1.96 % (15847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.96 % (15847)Termination reason: Unknown
% 3.54/1.96 % (15847)Termination phase: shuffling
% 3.54/1.96
% 3.54/1.96 % (15847)Memory used [KB]: 3326
% 3.54/1.96 % (15847)Time elapsed: 0.004 s
% 3.54/1.96 % (15847)Instructions burned: 7 (million)
% 3.54/1.96 % (15847)------------------------------
% 3.54/1.96 % (15847)------------------------------
% 3.54/1.97 % (15849)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/377Mi)
% 3.54/1.97 % (15850)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/779Mi)
% 3.54/1.98 % (15851)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/19Mi)
% 3.54/1.98 % (15851)Instruction limit reached!
% 3.54/1.98 % (15851)------------------------------
% 3.54/1.98 % (15851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/1.98 % (15851)Termination reason: Unknown
% 3.54/1.98 % (15851)Termination phase: shuffling
% 3.54/1.98
% 3.54/1.98 % (15851)Memory used [KB]: 3965
% 3.54/1.98 % (15851)Time elapsed: 0.008 s
% 3.54/1.98 % (15851)Instructions burned: 19 (million)
% 3.54/1.98 % (15851)------------------------------
% 3.54/1.98 % (15851)------------------------------
% 3.54/1.99 % (15852)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/879Mi)
% 3.54/2.00 % (15828)Instruction limit reached!
% 3.54/2.00 % (15828)------------------------------
% 3.54/2.00 % (15828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.54/2.00 % (15828)Termination reason: Unknown
% 3.54/2.00 % (15828)Termination phase: Saturation
% 3.54/2.00
% 3.54/2.00 % (15828)Memory used [KB]: 9722
% 3.54/2.00 % (15828)Time elapsed: 0.127 s
% 3.54/2.00 % (15828)Instructions burned: 278 (million)
% 3.54/2.00 % (15828)------------------------------
% 3.54/2.00 % (15828)------------------------------
% 4.58/2.01 % (15853)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_15503 for (2998ds/17Mi)
% 4.58/2.02 % (15853)Instruction limit reached!
% 4.58/2.02 % (15853)------------------------------
% 4.58/2.02 % (15853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.58/2.02 % (15853)Termination reason: Unknown
% 4.58/2.02 % (15853)Termination phase: shuffling
% 4.58/2.02
% 4.58/2.02 % (15853)Memory used [KB]: 3965
% 4.58/2.02 % (15853)Time elapsed: 0.009 s
% 4.58/2.02 % (15853)Instructions burned: 18 (million)
% 4.58/2.02 % (15853)------------------------------
% 4.58/2.02 % (15853)------------------------------
% 4.58/2.03 % (15854)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15503 for (2997ds/3Mi)
% 4.58/2.03 % (15854)Instruction limit reached!
% 4.58/2.03 % (15854)------------------------------
% 4.58/2.03 % (15854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.58/2.03 % (15854)Termination reason: Unknown
% 4.58/2.03 % (15854)Termination phase: shuffling
% 4.58/2.03
% 4.58/2.03 % (15854)Memory used [KB]: 3198
% 4.58/2.03 % (15854)Time elapsed: 0.004 s
% 4.58/2.03 % (15854)Instructions burned: 5 (million)
% 4.58/2.03 % (15854)------------------------------
% 4.58/2.03 % (15854)------------------------------
% 4.58/2.05 % (15855)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_15503 for (2997ds/30Mi)
% 4.58/2.06 % (15855)Instruction limit reached!
% 4.58/2.06 % (15855)------------------------------
% 4.58/2.06 % (15855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.58/2.06 % (15855)Termination reason: Unknown
% 4.58/2.06 % (15855)Termination phase: shuffling
% 4.58/2.06
% 4.58/2.06 % (15855)Memory used [KB]: 4989
% 4.58/2.06 % (15855)Time elapsed: 0.014 s
% 4.58/2.06 % (15855)Instructions burned: 31 (million)
% 4.58/2.06 % (15855)------------------------------
% 4.58/2.06 % (15855)------------------------------
% 4.58/2.07 % (15856)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_15503 for (2997ds/127Mi)
% 4.58/2.08 % (15849)Instruction limit reached!
% 4.58/2.08 % (15849)------------------------------
% 4.58/2.08 % (15849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.58/2.08 % (15849)Termination reason: Unknown
% 4.58/2.08 % (15849)Termination phase: Property scanning
% 4.58/2.08
% 4.58/2.08 % (15849)Memory used [KB]: 12025
% 4.58/2.08 % (15849)Time elapsed: 0.114 s
% 4.58/2.08 % (15849)Instructions burned: 378 (million)
% 4.58/2.08 % (15849)------------------------------
% 4.58/2.08 % (15849)------------------------------
% 4.58/2.10 % (15857)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_15503 for (2997ds/100Mi)
% 5.23/2.12 % (15856)Instruction limit reached!
% 5.23/2.12 % (15856)------------------------------
% 5.23/2.12 % (15856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.23/2.12 % (15856)Termination reason: Unknown
% 5.23/2.12 % (15856)Termination phase: Property scanning
% 5.23/2.12
% 5.23/2.12 % (15856)Memory used [KB]: 8955
% 5.23/2.12 % (15856)Time elapsed: 0.049 s
% 5.23/2.12 % (15856)Instructions burned: 127 (million)
% 5.23/2.12 % (15856)------------------------------
% 5.23/2.12 % (15856)------------------------------
% 5.23/2.12 % (15857)Instruction limit reached!
% 5.23/2.12 % (15857)------------------------------
% 5.23/2.12 % (15857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.23/2.12 % (15857)Termination reason: Unknown
% 5.23/2.12 % (15857)Termination phase: shuffling
% 5.23/2.12
% 5.23/2.12 % (15857)Memory used [KB]: 8187
% 5.23/2.12 % (15857)Time elapsed: 0.031 s
% 5.23/2.12 % (15857)Instructions burned: 100 (million)
% 5.23/2.12 % (15857)------------------------------
% 5.23/2.12 % (15857)------------------------------
% 5.23/2.13 % (15858)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_15503 for (2996ds/3Mi)
% 5.23/2.13 % (15858)Instruction limit reached!
% 5.23/2.13 % (15858)------------------------------
% 5.23/2.13 % (15858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.23/2.13 % (15858)Termination reason: Unknown
% 5.23/2.13 % (15858)Termination phase: shuffling
% 5.23/2.13
% 5.23/2.13 % (15858)Memory used [KB]: 3198
% 5.23/2.13 % (15858)Time elapsed: 0.004 s
% 5.23/2.13 % (15858)Instructions burned: 5 (million)
% 5.23/2.13 % (15858)------------------------------
% 5.23/2.13 % (15858)------------------------------
% 5.23/2.13 % (15859)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_15503 for (2996ds/20Mi)
% 5.23/2.14 % (15860)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_15503 for (2996ds/86Mi)
% 5.23/2.14 % (15859)Instruction limit reached!
% 5.23/2.14 % (15859)------------------------------
% 5.23/2.14 % (15859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.23/2.14 % (15859)Termination reason: Unknown
% 5.23/2.14 % (15859)Termination phase: shuffling
% 5.23/2.14
% 5.23/2.14 % (15859)Memory used [KB]: 4221
% 5.23/2.14 % (15859)Time elapsed: 0.009 s
% 5.23/2.14 % (15859)Instructions burned: 21 (million)
% 5.23/2.14 % (15859)------------------------------
% 5.23/2.14 % (15859)------------------------------
% 5.23/2.15 % (15861)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_15503 for (2996ds/107Mi)
% 5.23/2.17 % (15860)Instruction limit reached!
% 5.23/2.17 % (15860)------------------------------
% 5.23/2.17 % (15860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.23/2.17 % (15860)Termination reason: Unknown
% 5.23/2.17 % (15860)Termination phase: shuffling
% 5.23/2.17
% 5.23/2.17 % (15860)Memory used [KB]: 7419
% 5.23/2.17 % (15860)Time elapsed: 0.035 s
% 5.23/2.17 % (15860)Instructions burned: 88 (million)
% 5.23/2.17 % (15860)------------------------------
% 5.23/2.17 % (15860)------------------------------
% 5.23/2.18 % (15850)Instruction limit reached!
% 5.23/2.18 % (15850)------------------------------
% 5.23/2.18 % (15850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.23/2.18 % (15850)Termination reason: Unknown
% 5.23/2.18 % (15850)Termination phase: Saturation
% 5.23/2.18
% 5.23/2.18 % (15850)Memory used [KB]: 18038
% 5.23/2.18 % (15850)Time elapsed: 0.210 s
% 5.23/2.18 % (15850)Instructions burned: 779 (million)
% 5.23/2.18 % (15850)------------------------------
% 5.23/2.18 % (15850)------------------------------
% 5.23/2.19 % (15862)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_15503 for (2996ds/39Mi)
% 5.23/2.19 % (15843)Instruction limit reached!
% 5.23/2.19 % (15843)------------------------------
% 5.23/2.19 % (15843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.23/2.19 % (15843)Termination reason: Unknown
% 5.23/2.19 % (15843)Termination phase: Saturation
% 5.23/2.19
% 5.23/2.19 % (15843)Memory used [KB]: 15223
% 5.23/2.19 % (15843)Time elapsed: 0.243 s
% 5.23/2.19 % (15843)Instructions burned: 712 (million)
% 5.23/2.19 % (15843)------------------------------
% 5.23/2.19 % (15843)------------------------------
% 5.23/2.19 % (15861)Instruction limit reached!
% 5.23/2.19 % (15861)------------------------------
% 5.23/2.19 % (15861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.23/2.19 % (15861)Termination reason: Unknown
% 5.23/2.19 % (15861)Termination phase: shuffling
% 5.23/2.19
% 5.23/2.19 % (15861)Memory used [KB]: 8315
% 5.23/2.19 % (15861)Time elapsed: 0.039 s
% 5.23/2.19 % (15861)Instructions burned: 109 (million)
% 5.23/2.19 % (15861)------------------------------
% 5.23/2.19 % (15861)------------------------------
% 5.23/2.19 % (15863)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_15503 for (2996ds/448Mi)
% 5.86/2.20 % (15862)Instruction limit reached!
% 5.86/2.20 % (15862)------------------------------
% 5.86/2.20 % (15862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.20 % (15862)Termination reason: Unknown
% 5.86/2.20 % (15862)Termination phase: shuffling
% 5.86/2.20
% 5.86/2.20 % (15862)Memory used [KB]: 5245
% 5.86/2.20 % (15862)Time elapsed: 0.015 s
% 5.86/2.20 % (15862)Instructions burned: 41 (million)
% 5.86/2.20 % (15862)------------------------------
% 5.86/2.20 % (15862)------------------------------
% 5.86/2.20 % (15865)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_15503 for (2996ds/98Mi)
% 5.86/2.20 % (15864)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_15503 for (2996ds/46Mi)
% 5.86/2.21 % (15834)Instruction limit reached!
% 5.86/2.21 % (15834)------------------------------
% 5.86/2.21 % (15834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.21 % (15834)Termination reason: Unknown
% 5.86/2.21 % (15834)Termination phase: Saturation
% 5.86/2.21
% 5.86/2.21 % (15834)Memory used [KB]: 18293
% 5.86/2.21 % (15834)Time elapsed: 0.296 s
% 5.86/2.21 % (15834)Instructions burned: 1042 (million)
% 5.86/2.21 % (15834)------------------------------
% 5.86/2.21 % (15834)------------------------------
% 5.86/2.21 % (15866)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_15503 for (2996ds/507Mi)
% 5.86/2.22 % (15867)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_15503 for (2995ds/149Mi)
% 5.86/2.22 % (15864)Instruction limit reached!
% 5.86/2.22 % (15864)------------------------------
% 5.86/2.22 % (15864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.22 % (15864)Termination reason: Unknown
% 5.86/2.22 % (15864)Termination phase: shuffling
% 5.86/2.22
% 5.86/2.22 % (15864)Memory used [KB]: 5756
% 5.86/2.22 % (15864)Time elapsed: 0.019 s
% 5.86/2.22 % (15864)Instructions burned: 46 (million)
% 5.86/2.22 % (15864)------------------------------
% 5.86/2.22 % (15864)------------------------------
% 5.86/2.23 % (15845)Instruction limit reached!
% 5.86/2.23 % (15845)------------------------------
% 5.86/2.23 % (15845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.23 % (15845)Termination reason: Unknown
% 5.86/2.23 % (15845)Termination phase: Saturation
% 5.86/2.23
% 5.86/2.23 % (15845)Memory used [KB]: 17654
% 5.86/2.23 % (15845)Time elapsed: 0.273 s
% 5.86/2.23 % (15845)Instructions burned: 904 (million)
% 5.86/2.23 % (15845)------------------------------
% 5.86/2.23 % (15845)------------------------------
% 5.86/2.23 % (15865)Instruction limit reached!
% 5.86/2.23 % (15865)------------------------------
% 5.86/2.23 % (15865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.23 % (15865)Termination reason: Unknown
% 5.86/2.23 % (15865)Termination phase: shuffling
% 5.86/2.23
% 5.86/2.23 % (15865)Memory used [KB]: 8059
% 5.86/2.23 % (15865)Time elapsed: 0.030 s
% 5.86/2.23 % (15865)Instructions burned: 98 (million)
% 5.86/2.23 % (15865)------------------------------
% 5.86/2.23 % (15865)------------------------------
% 5.86/2.23 % (15868)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_15503 for (2995ds/39Mi)
% 5.86/2.24 % (15869)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_15503 for (2995ds/6Mi)
% 5.86/2.24 % (15869)Instruction limit reached!
% 5.86/2.24 % (15869)------------------------------
% 5.86/2.24 % (15869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.24 % (15869)Termination reason: Unknown
% 5.86/2.24 % (15869)Termination phase: shuffling
% 5.86/2.24
% 5.86/2.24 % (15869)Memory used [KB]: 3198
% 5.86/2.24 % (15869)Time elapsed: 0.004 s
% 5.86/2.24 % (15869)Instructions burned: 6 (million)
% 5.86/2.24 % (15869)------------------------------
% 5.86/2.24 % (15869)------------------------------
% 5.86/2.24 % (15870)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_15503 for (2995ds/1087Mi)
% 5.86/2.25 % (15868)Instruction limit reached!
% 5.86/2.25 % (15868)------------------------------
% 5.86/2.25 % (15868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.25 % (15868)Termination reason: Unknown
% 5.86/2.25 % (15868)Termination phase: shuffling
% 5.86/2.25
% 5.86/2.25 % (15868)Memory used [KB]: 5373
% 5.86/2.25 % (15868)Time elapsed: 0.017 s
% 5.86/2.25 % (15868)Instructions burned: 40 (million)
% 5.86/2.25 % (15868)------------------------------
% 5.86/2.25 % (15868)------------------------------
% 5.86/2.26 % (15872)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_15503 for (2995ds/44Mi)
% 5.86/2.26 % (15871)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_15503 for (2995ds/47Mi)
% 5.86/2.27 % (15867)Instruction limit reached!
% 5.86/2.27 % (15867)------------------------------
% 5.86/2.27 % (15867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.27 % (15867)Termination reason: Unknown
% 5.86/2.27 % (15867)Termination phase: Property scanning
% 5.86/2.27
% 5.86/2.27 % (15867)Memory used [KB]: 8955
% 5.86/2.27 % (15867)Time elapsed: 0.052 s
% 5.86/2.27 % (15867)Instructions burned: 152 (million)
% 5.86/2.27 % (15867)------------------------------
% 5.86/2.27 % (15867)------------------------------
% 5.86/2.27 % (15872)Instruction limit reached!
% 5.86/2.27 % (15872)------------------------------
% 5.86/2.27 % (15872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.27 % (15872)Termination reason: Unknown
% 5.86/2.27 % (15872)Termination phase: shuffling
% 5.86/2.27
% 5.86/2.27 % (15872)Memory used [KB]: 5373
% 5.86/2.27 % (15872)Time elapsed: 0.016 s
% 5.86/2.27 % (15872)Instructions burned: 45 (million)
% 5.86/2.27 % (15872)------------------------------
% 5.86/2.27 % (15872)------------------------------
% 5.86/2.28 % (15873)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_15503 for (2995ds/432Mi)
% 5.86/2.28 % (15874)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_15503 for (2995ds/62Mi)
% 5.86/2.29 % (15871)Instruction limit reached!
% 5.86/2.29 % (15871)------------------------------
% 5.86/2.29 % (15871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.29 % (15871)Termination reason: Unknown
% 5.86/2.29 % (15871)Termination phase: shuffling
% 5.86/2.29
% 5.86/2.29 % (15871)Memory used [KB]: 5756
% 5.86/2.29 % (15871)Time elapsed: 0.034 s
% 5.86/2.29 % (15871)Instructions burned: 47 (million)
% 5.86/2.29 % (15871)------------------------------
% 5.86/2.29 % (15871)------------------------------
% 6.30/2.30 % (15874)Instruction limit reached!
% 6.30/2.30 % (15874)------------------------------
% 6.30/2.30 % (15874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.30 % (15874)Termination reason: Unknown
% 6.30/2.30 % (15874)Termination phase: shuffling
% 6.30/2.30
% 6.30/2.30 % (15874)Memory used [KB]: 6652
% 6.30/2.30 % (15874)Time elapsed: 0.020 s
% 6.30/2.30 % (15874)Instructions burned: 63 (million)
% 6.30/2.30 % (15874)------------------------------
% 6.30/2.30 % (15874)------------------------------
% 6.30/2.31 % (15875)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_15503 for (2995ds/31Mi)
% 6.30/2.31 % (15876)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_15503 for (2995ds/96Mi)
% 6.30/2.31 % (15863)Instruction limit reached!
% 6.30/2.31 % (15863)------------------------------
% 6.30/2.31 % (15863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.31 % (15863)Termination reason: Unknown
% 6.30/2.31 % (15863)Termination phase: SInE selection
% 6.30/2.31
% 6.30/2.31 % (15863)Memory used [KB]: 11513
% 6.30/2.31 % (15863)Time elapsed: 0.121 s
% 6.30/2.31 % (15863)Instructions burned: 448 (million)
% 6.30/2.31 % (15863)------------------------------
% 6.30/2.31 % (15863)------------------------------
% 6.30/2.31 % (15852)Instruction limit reached!
% 6.30/2.31 % (15852)------------------------------
% 6.30/2.31 % (15852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.31 % (15852)Termination reason: Unknown
% 6.30/2.31 % (15852)Termination phase: Saturation
% 6.30/2.31
% 6.30/2.31 % (15852)Memory used [KB]: 15607
% 6.30/2.31 % (15852)Time elapsed: 0.342 s
% 6.30/2.31 % (15852)Instructions burned: 881 (million)
% 6.30/2.31 % (15852)------------------------------
% 6.30/2.31 % (15852)------------------------------
% 6.30/2.32 % (15875)Instruction limit reached!
% 6.30/2.32 % (15875)------------------------------
% 6.30/2.32 % (15875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.32 % (15875)Termination reason: Unknown
% 6.30/2.32 % (15875)Termination phase: shuffling
% 6.30/2.32
% 6.30/2.32 % (15875)Memory used [KB]: 4733
% 6.30/2.32 % (15875)Time elapsed: 0.017 s
% 6.30/2.32 % (15875)Instructions burned: 31 (million)
% 6.30/2.32 % (15875)------------------------------
% 6.30/2.32 % (15875)------------------------------
% 6.30/2.32 % (15878)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_15503 for (2994ds/71Mi)
% 6.30/2.32 % (15877)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_15503 for (2994ds/453Mi)
% 6.30/2.33 % (15879)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_15503 for (2994ds/83Mi)
% 6.30/2.35 % (15876)Instruction limit reached!
% 6.30/2.35 % (15876)------------------------------
% 6.30/2.35 % (15876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.35 % (15876)Termination reason: Unknown
% 6.30/2.35 % (15876)Termination phase: shuffling
% 6.30/2.35
% 6.30/2.35 % (15876)Memory used [KB]: 7931
% 6.30/2.35 % (15876)Time elapsed: 0.036 s
% 6.30/2.35 % (15876)Instructions burned: 97 (million)
% 6.30/2.35 % (15876)------------------------------
% 6.30/2.35 % (15876)------------------------------
% 6.30/2.35 % (15878)Instruction limit reached!
% 6.30/2.35 % (15878)------------------------------
% 6.30/2.35 % (15878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.35 % (15878)Termination reason: Unknown
% 6.30/2.35 % (15878)Termination phase: shuffling
% 6.30/2.35
% 6.30/2.35 % (15878)Memory used [KB]: 7036
% 6.30/2.35 % (15878)Time elapsed: 0.028 s
% 6.30/2.35 % (15878)Instructions burned: 73 (million)
% 6.30/2.35 % (15878)------------------------------
% 6.30/2.35 % (15878)------------------------------
% 6.30/2.36 % (15880)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_15503 for (2994ds/11Mi)
% 6.30/2.36 % (15880)Instruction limit reached!
% 6.30/2.36 % (15880)------------------------------
% 6.30/2.36 % (15880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.36 % (15880)Termination reason: Unknown
% 6.30/2.36 % (15880)Termination phase: shuffling
% 6.30/2.36
% 6.30/2.36 % (15880)Memory used [KB]: 3582
% 6.30/2.36 % (15880)Time elapsed: 0.006 s
% 6.30/2.36 % (15880)Instructions burned: 11 (million)
% 6.30/2.36 % (15880)------------------------------
% 6.30/2.36 % (15880)------------------------------
% 6.30/2.36 % (15881)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_15503 for (2994ds/41Mi)
% 6.30/2.36 % (15879)Instruction limit reached!
% 6.30/2.36 % (15879)------------------------------
% 6.30/2.36 % (15879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.36 % (15879)Termination reason: Unknown
% 6.30/2.36 % (15879)Termination phase: shuffling
% 6.30/2.36
% 6.30/2.36 % (15879)Memory used [KB]: 7419
% 6.30/2.36 % (15879)Time elapsed: 0.033 s
% 6.30/2.36 % (15879)Instructions burned: 83 (million)
% 6.30/2.36 % (15879)------------------------------
% 6.30/2.36 % (15879)------------------------------
% 6.30/2.37 % (15882)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15503 for (2994ds/6Mi)
% 6.30/2.37 % (15866)Instruction limit reached!
% 6.30/2.37 % (15866)------------------------------
% 6.30/2.37 % (15866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.37 % (15866)Termination reason: Unknown
% 6.30/2.37 % (15866)Termination phase: Saturation
% 6.30/2.37
% 6.30/2.37 % (15866)Memory used [KB]: 13176
% 6.30/2.37 % (15866)Time elapsed: 0.163 s
% 6.30/2.37 % (15866)Instructions burned: 509 (million)
% 6.30/2.37 % (15866)------------------------------
% 6.30/2.37 % (15866)------------------------------
% 6.30/2.37 % (15882)Instruction limit reached!
% 6.30/2.37 % (15882)------------------------------
% 6.30/2.37 % (15882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.37 % (15882)Termination reason: Unknown
% 6.30/2.37 % (15882)Termination phase: shuffling
% 6.30/2.37
% 6.30/2.37 % (15882)Memory used [KB]: 3454
% 6.30/2.37 % (15882)Time elapsed: 0.005 s
% 6.30/2.37 % (15882)Instructions burned: 7 (million)
% 6.30/2.37 % (15882)------------------------------
% 6.30/2.37 % (15882)------------------------------
% 6.30/2.37 % (15881)Instruction limit reached!
% 6.30/2.37 % (15881)------------------------------
% 6.30/2.37 % (15881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.37 % (15881)Termination reason: Unknown
% 6.30/2.37 % (15881)Termination phase: shuffling
% 6.30/2.37
% 6.30/2.37 % (15881)Memory used [KB]: 5245
% 6.30/2.37 % (15881)Time elapsed: 0.015 s
% 6.30/2.37 % (15881)Instructions burned: 44 (million)
% 6.30/2.37 % (15881)------------------------------
% 6.30/2.37 % (15881)------------------------------
% 6.30/2.38 % (15883)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_15503 for (2994ds/150Mi)
% 6.30/2.38 % (15884)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_15503 for (2994ds/343Mi)
% 6.30/2.38 % (15885)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_15503 for (2994ds/109Mi)
% 6.30/2.38 % (15886)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_15503 for (2994ds/253Mi)
% 6.87/2.40 % (15873)Instruction limit reached!
% 6.87/2.40 % (15873)------------------------------
% 6.87/2.40 % (15873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.40 % (15873)Termination reason: Unknown
% 6.87/2.40 % (15873)Termination phase: Function definition elimination
% 6.87/2.40
% 6.87/2.40 % (15873)Memory used [KB]: 11513
% 6.87/2.40 % (15873)Time elapsed: 0.119 s
% 6.87/2.40 % (15873)Instructions burned: 435 (million)
% 6.87/2.40 % (15873)------------------------------
% 6.87/2.40 % (15873)------------------------------
% 6.87/2.41 % (15887)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_15503 for (2994ds/140Mi)
% 6.87/2.42 % (15885)Instruction limit reached!
% 6.87/2.42 % (15885)------------------------------
% 6.87/2.42 % (15885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.42 % (15885)Termination reason: Unknown
% 6.87/2.42 % (15885)Termination phase: shuffling
% 6.87/2.42
% 6.87/2.42 % (15885)Memory used [KB]: 8443
% 6.87/2.42 % (15885)Time elapsed: 0.040 s
% 6.87/2.42 % (15885)Instructions burned: 111 (million)
% 6.87/2.42 % (15885)------------------------------
% 6.87/2.42 % (15885)------------------------------
% 6.87/2.43 % (15883)Instruction limit reached!
% 6.87/2.43 % (15883)------------------------------
% 6.87/2.43 % (15883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.43 % (15883)Termination reason: Unknown
% 6.87/2.43 % (15883)Termination phase: Property scanning
% 6.87/2.43
% 6.87/2.43 % (15883)Memory used [KB]: 9850
% 6.87/2.43 % (15883)Time elapsed: 0.057 s
% 6.87/2.43 % (15883)Instructions burned: 150 (million)
% 6.87/2.43 % (15883)------------------------------
% 6.87/2.43 % (15883)------------------------------
% 6.87/2.43 % (15888)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_15503 for (2993ds/614Mi)
% 6.87/2.44 % (15889)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_15503 for (2993ds/202Mi)
% 6.87/2.45 % (15877)Instruction limit reached!
% 6.87/2.45 % (15877)------------------------------
% 6.87/2.45 % (15877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.45 % (15877)Termination reason: Unknown
% 6.87/2.45 % (15877)Termination phase: Property scanning
% 6.87/2.45
% 6.87/2.45 % (15877)Memory used [KB]: 11641
% 6.87/2.45 % (15877)Time elapsed: 0.124 s
% 6.87/2.45 % (15877)Instructions burned: 453 (million)
% 6.87/2.45 % (15877)------------------------------
% 6.87/2.45 % (15877)------------------------------
% 6.87/2.46 % (15887)Instruction limit reached!
% 6.87/2.46 % (15887)------------------------------
% 6.87/2.46 % (15887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.46 % (15887)Termination reason: Unknown
% 6.87/2.46 % (15887)Termination phase: shuffling
% 6.87/2.46
% 6.87/2.46 % (15887)Memory used [KB]: 9850
% 6.87/2.46 % (15887)Time elapsed: 0.050 s
% 6.87/2.46 % (15887)Instructions burned: 140 (million)
% 6.87/2.46 % (15887)------------------------------
% 6.87/2.46 % (15887)------------------------------
% 6.87/2.46 % (15890)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_15503 for (2993ds/339Mi)
% 6.87/2.46 % (15886)Instruction limit reached!
% 6.87/2.46 % (15886)------------------------------
% 6.87/2.46 % (15886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.46 % (15886)Termination reason: Unknown
% 6.87/2.46 % (15886)Termination phase: Property scanning
% 6.87/2.46
% 6.87/2.46 % (15886)Memory used [KB]: 9978
% 6.87/2.46 % (15886)Time elapsed: 0.079 s
% 6.87/2.46 % (15886)Instructions burned: 253 (million)
% 6.87/2.46 % (15886)------------------------------
% 6.87/2.46 % (15886)------------------------------
% 6.87/2.47 % (15891)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_15503 for (2993ds/283Mi)
% 6.87/2.47 % (15892)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_15503 for (2993ds/134Mi)
% 6.87/2.49 % (15884)Instruction limit reached!
% 6.87/2.49 % (15884)------------------------------
% 6.87/2.49 % (15884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.49 % (15884)Termination reason: Unknown
% 6.87/2.49 % (15884)Termination phase: Property scanning
% 6.87/2.49
% 6.87/2.49 % (15884)Memory used [KB]: 10618
% 6.87/2.49 % (15884)Time elapsed: 0.105 s
% 6.87/2.49 % (15884)Instructions burned: 345 (million)
% 6.87/2.49 % (15884)------------------------------
% 6.87/2.49 % (15884)------------------------------
% 7.51/2.50 % (15893)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_15503 for (2993ds/298Mi)
% 7.51/2.51 % (15889)Instruction limit reached!
% 7.51/2.51 % (15889)------------------------------
% 7.51/2.51 % (15889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.51 % (15889)Termination reason: Unknown
% 7.51/2.51 % (15889)Termination phase: SInE selection
% 7.51/2.51
% 7.51/2.51 % (15889)Memory used [KB]: 8827
% 7.51/2.51 % (15889)Time elapsed: 0.071 s
% 7.51/2.51 % (15889)Instructions burned: 202 (million)
% 7.51/2.51 % (15889)------------------------------
% 7.51/2.51 % (15889)------------------------------
% 7.51/2.52 % (15892)Instruction limit reached!
% 7.51/2.52 % (15892)------------------------------
% 7.51/2.52 % (15892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.52 % (15892)Termination reason: Unknown
% 7.51/2.52 % (15892)Termination phase: Property scanning
% 7.51/2.52
% 7.51/2.52 % (15892)Memory used [KB]: 8827
% 7.51/2.52 % (15892)Time elapsed: 0.048 s
% 7.51/2.52 % (15892)Instructions burned: 135 (million)
% 7.51/2.52 % (15892)------------------------------
% 7.51/2.52 % (15892)------------------------------
% 7.51/2.52 % (15894)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_15503 for (2993ds/192Mi)
% 7.51/2.53 % (15895)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_15503 for (2992ds/258Mi)
% 7.51/2.55 % (15891)Instruction limit reached!
% 7.51/2.55 % (15891)------------------------------
% 7.51/2.55 % (15891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.55 % (15891)Termination reason: Unknown
% 7.51/2.55 % (15891)Termination phase: Property scanning
% 7.51/2.55
% 7.51/2.55 % (15891)Memory used [KB]: 11257
% 7.51/2.55 % (15891)Time elapsed: 0.081 s
% 7.51/2.55 % (15891)Instructions burned: 283 (million)
% 7.51/2.55 % (15891)------------------------------
% 7.51/2.55 % (15891)------------------------------
% 7.51/2.56 % (15896)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_15503 for (2992ds/90Mi)
% 7.51/2.56 % (15890)Instruction limit reached!
% 7.51/2.56 % (15890)------------------------------
% 7.51/2.56 % (15890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.56 % (15890)Termination reason: Unknown
% 7.51/2.56 % (15890)Termination phase: Function definition elimination
% 7.51/2.56
% 7.51/2.56 % (15890)Memory used [KB]: 10746
% 7.51/2.56 % (15890)Time elapsed: 0.106 s
% 7.51/2.56 % (15890)Instructions burned: 342 (million)
% 7.51/2.56 % (15890)------------------------------
% 7.51/2.56 % (15890)------------------------------
% 7.51/2.57 % (15897)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_15503 for (2992ds/231Mi)
% 7.51/2.58 % (15893)Instruction limit reached!
% 7.51/2.58 % (15893)------------------------------
% 7.51/2.58 % (15893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.58 % (15893)Termination reason: Unknown
% 7.51/2.58 % (15893)Termination phase: Property scanning
% 7.51/2.58
% 7.51/2.58 % (15893)Memory used [KB]: 11385
% 7.51/2.58 % (15893)Time elapsed: 0.085 s
% 7.51/2.58 % (15893)Instructions burned: 299 (million)
% 7.51/2.58 % (15893)------------------------------
% 7.51/2.58 % (15893)------------------------------
% 7.51/2.59 % (15870)Instruction limit reached!
% 7.51/2.59 % (15870)------------------------------
% 7.51/2.59 % (15870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.59 % (15870)Termination reason: Unknown
% 7.51/2.59 % (15870)Termination phase: Saturation
% 7.51/2.59
% 7.51/2.59 % (15870)Memory used [KB]: 15095
% 7.51/2.59 % (15870)Time elapsed: 0.352 s
% 7.51/2.59 % (15870)Instructions burned: 1088 (million)
% 7.51/2.59 % (15870)------------------------------
% 7.51/2.59 % (15870)------------------------------
% 7.51/2.59 % (15896)Instruction limit reached!
% 7.51/2.59 % (15896)------------------------------
% 7.51/2.59 % (15896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.59 % (15896)Termination reason: Unknown
% 7.51/2.59 % (15896)Termination phase: shuffling
% 7.51/2.59
% 7.51/2.59 % (15896)Memory used [KB]: 7419
% 7.51/2.59 % (15896)Time elapsed: 0.034 s
% 7.51/2.59 % (15896)Instructions burned: 90 (million)
% 7.51/2.59 % (15896)------------------------------
% 7.51/2.59 % (15896)------------------------------
% 7.51/2.59 % (15894)Instruction limit reached!
% 7.51/2.59 % (15894)------------------------------
% 7.51/2.59 % (15894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.59 % (15894)Termination reason: Unknown
% 7.51/2.59 % (15894)Termination phase: Unused predicate definition removal
% 7.51/2.59
% 7.51/2.59 % (15894)Memory used [KB]: 9850
% 7.51/2.59 % (15894)Time elapsed: 0.069 s
% 7.51/2.59 % (15894)Instructions burned: 192 (million)
% 7.51/2.59 % (15894)------------------------------
% 7.51/2.59 % (15894)------------------------------
% 7.51/2.59 % (15898)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_15503 for (2992ds/458Mi)
% 8.44/2.60 % (15899)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_15503 for (2992ds/31Mi)
% 8.44/2.60 % (15900)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_15503 for (2992ds/297Mi)
% 8.44/2.60 % (15901)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_15503 for (2992ds/987Mi)
% 8.44/2.61 % (15895)Instruction limit reached!
% 8.44/2.61 % (15895)------------------------------
% 8.44/2.61 % (15895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.61 % (15895)Termination reason: Unknown
% 8.44/2.61 % (15895)Termination phase: Property scanning
% 8.44/2.61
% 8.44/2.61 % (15895)Memory used [KB]: 9978
% 8.44/2.61 % (15895)Time elapsed: 0.083 s
% 8.44/2.61 % (15895)Instructions burned: 260 (million)
% 8.44/2.61 % (15895)------------------------------
% 8.44/2.61 % (15895)------------------------------
% 8.44/2.61 % (15899)Instruction limit reached!
% 8.44/2.61 % (15899)------------------------------
% 8.44/2.61 % (15899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.61 % (15899)Termination reason: Unknown
% 8.44/2.61 % (15899)Termination phase: shuffling
% 8.44/2.61
% 8.44/2.61 % (15899)Memory used [KB]: 4733
% 8.44/2.61 % (15899)Time elapsed: 0.013 s
% 8.44/2.61 % (15899)Instructions burned: 31 (million)
% 8.44/2.61 % (15899)------------------------------
% 8.44/2.61 % (15899)------------------------------
% 8.44/2.62 % (15888)Instruction limit reached!
% 8.44/2.62 % (15888)------------------------------
% 8.44/2.62 % (15888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.62 % (15888)Termination reason: Unknown
% 8.44/2.62 % (15888)Termination phase: Saturation
% 8.44/2.62
% 8.44/2.62 % (15888)Memory used [KB]: 17654
% 8.44/2.62 % (15888)Time elapsed: 0.190 s
% 8.44/2.62 % (15888)Instructions burned: 614 (million)
% 8.44/2.62 % (15888)------------------------------
% 8.44/2.62 % (15888)------------------------------
% 8.44/2.62 % (15902)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_15503 for (2992ds/182Mi)
% 8.44/2.62 % (15903)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_15503 for (2992ds/182Mi)
% 8.44/2.63 % (15904)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_15503 for (2991ds/154Mi)
% 8.44/2.64 % (15897)Instruction limit reached!
% 8.44/2.64 % (15897)------------------------------
% 8.44/2.64 % (15897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.64 % (15897)Termination reason: Unknown
% 8.44/2.64 % (15897)Termination phase: Property scanning
% 8.44/2.64
% 8.44/2.64 % (15897)Memory used [KB]: 11513
% 8.44/2.64 % (15897)Time elapsed: 0.068 s
% 8.44/2.64 % (15897)Instructions burned: 232 (million)
% 8.44/2.64 % (15897)------------------------------
% 8.44/2.64 % (15897)------------------------------
% 8.44/2.65 % (15905)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_15503 for (2991ds/79Mi)
% 8.44/2.68 % (15904)Instruction limit reached!
% 8.44/2.68 % (15904)------------------------------
% 8.44/2.68 % (15904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.68 % (15904)Termination reason: Unknown
% 8.44/2.68 % (15904)Termination phase: shuffling
% 8.44/2.68
% 8.44/2.68 % (15904)Memory used [KB]: 10362
% 8.44/2.68 % (15904)Time elapsed: 0.047 s
% 8.44/2.68 % (15904)Instructions burned: 155 (million)
% 8.44/2.68 % (15904)------------------------------
% 8.44/2.68 % (15904)------------------------------
% 8.44/2.68 % (15905)Instruction limit reached!
% 8.44/2.68 % (15905)------------------------------
% 8.44/2.68 % (15905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.68 % (15905)Termination reason: Unknown
% 8.44/2.68 % (15905)Termination phase: shuffling
% 8.44/2.68
% 8.44/2.68 % (15905)Memory used [KB]: 7164
% 8.44/2.68 % (15905)Time elapsed: 0.030 s
% 8.44/2.68 % (15905)Instructions burned: 80 (million)
% 8.44/2.68 % (15905)------------------------------
% 8.44/2.68 % (15905)------------------------------
% 8.44/2.68 % (15903)Instruction limit reached!
% 8.44/2.68 % (15903)------------------------------
% 8.44/2.68 % (15903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.68 % (15903)Termination reason: Unknown
% 8.44/2.68 % (15903)Termination phase: SInE selection
% 8.44/2.68
% 8.44/2.68 % (15903)Memory used [KB]: 8827
% 8.44/2.68 % (15903)Time elapsed: 0.060 s
% 8.44/2.68 % (15903)Instructions burned: 182 (million)
% 8.44/2.68 % (15903)------------------------------
% 8.44/2.68 % (15903)------------------------------
% 8.44/2.68 % (15902)Instruction limit reached!
% 8.44/2.68 % (15902)------------------------------
% 8.44/2.68 % (15902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.68 % (15902)Termination reason: Unknown
% 8.44/2.68 % (15902)Termination phase: Preprocessing 1
% 8.44/2.68
% 8.44/2.68 % (15902)Memory used [KB]: 9210
% 8.44/2.68 % (15902)Time elapsed: 0.061 s
% 8.44/2.68 % (15902)Instructions burned: 183 (million)
% 8.44/2.68 % (15902)------------------------------
% 8.44/2.68 % (15902)------------------------------
% 8.44/2.68 % (15900)Instruction limit reached!
% 8.44/2.68 % (15900)------------------------------
% 8.44/2.68 % (15900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.44/2.68 % (15900)Termination reason: Unknown
% 8.44/2.68 % (15900)Termination phase: Property scanning
% 8.44/2.68
% 8.44/2.68 % (15900)Memory used [KB]: 11385
% 8.44/2.68 % (15900)Time elapsed: 0.084 s
% 8.44/2.68 % (15900)Instructions burned: 299 (million)
% 8.44/2.68 % (15900)------------------------------
% 8.44/2.68 % (15900)------------------------------
% 8.44/2.69 % (15907)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_15503 for (2991ds/114Mi)
% 8.44/2.69 % (15906)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_15503 for (2991ds/216Mi)
% 8.44/2.69 % (15908)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_15503 for (2991ds/922Mi)
% 8.44/2.69 % (15909)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_15503 for (2991ds/182Mi)
% 8.44/2.69 % (15910)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_15503 for (2991ds/164Mi)
% 9.15/2.73 % (15898)Instruction limit reached!
% 9.15/2.73 % (15898)------------------------------
% 9.15/2.73 % (15898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/2.73 % (15898)Termination reason: Unknown
% 9.15/2.73 % (15898)Termination phase: Saturation
% 9.15/2.73
% 9.15/2.73 % (15898)Memory used [KB]: 16247
% 9.15/2.73 % (15898)Time elapsed: 0.136 s
% 9.15/2.73 % (15898)Instructions burned: 460 (million)
% 9.15/2.73 % (15898)------------------------------
% 9.15/2.73 % (15898)------------------------------
% 9.15/2.73 % (15907)Instruction limit reached!
% 9.15/2.73 % (15907)------------------------------
% 9.15/2.73 % (15907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/2.73 % (15907)Termination reason: Unknown
% 9.15/2.73 % (15907)Termination phase: shuffling
% 9.15/2.73
% 9.15/2.73 % (15907)Memory used [KB]: 8443
% 9.15/2.73 % (15907)Time elapsed: 0.041 s
% 9.15/2.73 % (15907)Instructions burned: 114 (million)
% 9.15/2.73 % (15907)------------------------------
% 9.15/2.73 % (15907)------------------------------
% 9.15/2.74 % (15911)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_15503 for (2990ds/50Mi)
% 9.15/2.74 % (15912)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_15503 for (2990ds/368Mi)
% 9.15/2.74 % (15910)Instruction limit reached!
% 9.15/2.74 % (15910)------------------------------
% 9.15/2.74 % (15910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/2.74 % (15910)Termination reason: Unknown
% 9.15/2.74 % (15910)Termination phase: shuffling
% 9.15/2.74
% 9.15/2.74 % (15910)Memory used [KB]: 10490
% 9.15/2.74 % (15910)Time elapsed: 0.049 s
% 9.15/2.74 % (15910)Instructions burned: 166 (million)
% 9.15/2.74 % (15910)------------------------------
% 9.15/2.74 % (15910)------------------------------
% 9.15/2.74 % (15909)Instruction limit reached!
% 9.15/2.74 % (15909)------------------------------
% 9.15/2.74 % (15909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/2.74 % (15909)Termination reason: Unknown
% 9.15/2.74 % (15909)Termination phase: shuffling
% 9.15/2.74
% 9.15/2.74 % (15909)Memory used [KB]: 11129
% 9.15/2.74 % (15909)Time elapsed: 0.054 s
% 9.15/2.74 % (15909)Instructions burned: 184 (million)
% 9.15/2.74 % (15909)------------------------------
% 9.15/2.74 % (15909)------------------------------
% 9.15/2.75 % (15906)Instruction limit reached!
% 9.15/2.75 % (15906)------------------------------
% 9.15/2.75 % (15906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/2.75 % (15906)Termination reason: Unknown
% 9.15/2.75 % (15906)Termination phase: Property scanning
% 9.15/2.75
% 9.15/2.75 % (15906)Memory used [KB]: 11257
% 9.15/2.75 % (15906)Time elapsed: 0.063 s
% 9.15/2.75 % (15906)Instructions burned: 216 (million)
% 9.15/2.75 % (15906)------------------------------
% 9.15/2.75 % (15906)------------------------------
% 9.15/2.75 % (15913)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_15503 for (2990ds/1021Mi)
% 9.15/2.75 % (15911)Instruction limit reached!
% 9.15/2.75 % (15911)------------------------------
% 9.15/2.75 % (15911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/2.75 % (15911)Termination reason: Unknown
% 9.15/2.75 % (15911)Termination phase: shuffling
% 9.15/2.75
% 9.15/2.75 % (15911)Memory used [KB]: 5500
% 9.15/2.75 % (15911)Time elapsed: 0.017 s
% 9.15/2.75 % (15911)Instructions burned: 51 (million)
% 9.15/2.75 % (15911)------------------------------
% 9.15/2.75 % (15911)------------------------------
% 9.15/2.76 % (15914)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_15503 for (2990ds/267Mi)
% 9.15/2.76 % (15915)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_15503 for (2990ds/204Mi)
% 9.15/2.76 % (15916)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_15503 for (2990ds/26Mi)
% 9.15/2.77 % (15916)Instruction limit reached!
% 9.15/2.77 % (15916)------------------------------
% 9.15/2.77 % (15916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/2.77 % (15916)Termination reason: Unknown
% 9.15/2.77 % (15916)Termination phase: shuffling
% 9.15/2.77
% 9.15/2.77 % (15916)Memory used [KB]: 4221
% 9.15/2.77 % (15916)Time elapsed: 0.010 s
% 9.15/2.77 % (15916)Instructions burned: 26 (million)
% 9.15/2.77 % (15916)------------------------------
% 9.15/2.77 % (15916)------------------------------
% 9.15/2.78 % (15917)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_15503 for (2990ds/53Mi)
% 9.60/2.80 % (15917)Instruction limit reached!
% 9.60/2.80 % (15917)------------------------------
% 9.60/2.80 % (15917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.80 % (15917)Termination reason: Unknown
% 9.60/2.80 % (15917)Termination phase: shuffling
% 9.60/2.80
% 9.60/2.80 % (15917)Memory used [KB]: 5884
% 9.60/2.80 % (15917)Time elapsed: 0.018 s
% 9.60/2.80 % (15917)Instructions burned: 55 (million)
% 9.60/2.80 % (15917)------------------------------
% 9.60/2.80 % (15917)------------------------------
% 9.60/2.81 % (15918)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_15503 for (2990ds/4436Mi)
% 9.60/2.83 % (15915)Instruction limit reached!
% 9.60/2.83 % (15915)------------------------------
% 9.60/2.83 % (15915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.83 % (15915)Termination reason: Unknown
% 9.60/2.83 % (15915)Termination phase: SInE selection
% 9.60/2.83
% 9.60/2.83 % (15915)Memory used [KB]: 8699
% 9.60/2.83 % (15915)Time elapsed: 0.067 s
% 9.60/2.83 % (15915)Instructions burned: 207 (million)
% 9.60/2.83 % (15915)------------------------------
% 9.60/2.83 % (15915)------------------------------
% 9.60/2.83 % (15914)Instruction limit reached!
% 9.60/2.83 % (15914)------------------------------
% 9.60/2.83 % (15914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.83 % (15914)Termination reason: Unknown
% 9.60/2.83 % (15914)Termination phase: Property scanning
% 9.60/2.83
% 9.60/2.83 % (15914)Memory used [KB]: 11129
% 9.60/2.83 % (15914)Time elapsed: 0.076 s
% 9.60/2.83 % (15914)Instructions burned: 268 (million)
% 9.60/2.83 % (15914)------------------------------
% 9.60/2.83 % (15914)------------------------------
% 9.60/2.84 % (15919)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_15503 for (2989ds/1539Mi)
% 9.60/2.84 % (15920)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_15503 for (2989ds/408Mi)
% 9.60/2.85 % (15912)Instruction limit reached!
% 9.60/2.85 % (15912)------------------------------
% 9.60/2.85 % (15912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.85 % (15912)Termination reason: Unknown
% 9.60/2.85 % (15912)Termination phase: Property scanning
% 9.60/2.85
% 9.60/2.85 % (15912)Memory used [KB]: 11769
% 9.60/2.85 % (15912)Time elapsed: 0.111 s
% 9.60/2.85 % (15912)Instructions burned: 368 (million)
% 9.60/2.85 % (15912)------------------------------
% 9.60/2.85 % (15912)------------------------------
% 9.60/2.86 % (15921)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_15503 for (2989ds/5205Mi)
% 9.60/2.89 % (15901)Instruction limit reached!
% 9.60/2.89 % (15901)------------------------------
% 9.60/2.89 % (15901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.89 % (15901)Termination reason: Unknown
% 9.60/2.89 % (15901)Termination phase: Saturation
% 9.60/2.89
% 9.60/2.89 % (15901)Memory used [KB]: 19189
% 9.60/2.89 % (15901)Time elapsed: 0.321 s
% 9.60/2.89 % (15901)Instructions burned: 987 (million)
% 9.60/2.89 % (15901)------------------------------
% 9.60/2.89 % (15901)------------------------------
% 9.91/2.91 % (15922)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_15503 for (2989ds/1913Mi)
% 9.91/2.96 % (15920)Instruction limit reached!
% 9.91/2.96 % (15920)------------------------------
% 9.91/2.96 % (15920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.96 % (15920)Termination reason: Unknown
% 9.91/2.96 % (15920)Termination phase: Saturation
% 9.91/2.96
% 9.91/2.96 % (15920)Memory used [KB]: 12281
% 9.91/2.96 % (15920)Time elapsed: 0.123 s
% 9.91/2.96 % (15920)Instructions burned: 410 (million)
% 9.91/2.96 % (15920)------------------------------
% 9.91/2.96 % (15920)------------------------------
% 9.91/2.97 % (15923)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_15503 for (2988ds/4350Mi)
% 9.91/2.98 % (15908)Instruction limit reached!
% 9.91/2.98 % (15908)------------------------------
% 9.91/2.98 % (15908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.98 % (15908)Termination reason: Unknown
% 9.91/2.98 % (15908)Termination phase: Saturation
% 9.91/2.98
% 9.91/2.98 % (15908)Memory used [KB]: 16758
% 9.91/2.98 % (15908)Time elapsed: 0.294 s
% 9.91/2.98 % (15908)Instructions burned: 924 (million)
% 9.91/2.98 % (15908)------------------------------
% 9.91/2.98 % (15908)------------------------------
% 9.91/3.00 % (15924)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_15503 for (2988ds/68Mi)
% 11.56/3.02 % (15924)Instruction limit reached!
% 11.56/3.02 % (15924)------------------------------
% 11.56/3.02 % (15924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.56/3.02 % (15924)Termination reason: Unknown
% 11.56/3.02 % (15924)Termination phase: shuffling
% 11.56/3.02
% 11.56/3.02 % (15924)Memory used [KB]: 6652
% 11.56/3.02 % (15924)Time elapsed: 0.026 s
% 11.56/3.02 % (15924)Instructions burned: 70 (million)
% 11.56/3.02 % (15924)------------------------------
% 11.56/3.02 % (15924)------------------------------
% 11.56/3.03 % (15925)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_15503 for (2987ds/358Mi)
% 11.56/3.07 % (15913)Instruction limit reached!
% 11.56/3.07 % (15913)------------------------------
% 11.56/3.07 % (15913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.56/3.07 % (15913)Termination reason: Unknown
% 11.56/3.07 % (15913)Termination phase: Saturation
% 11.56/3.07
% 11.56/3.07 % (15913)Memory used [KB]: 17398
% 11.56/3.07 % (15913)Time elapsed: 0.319 s
% 11.56/3.07 % (15913)Instructions burned: 1023 (million)
% 11.56/3.07 % (15913)------------------------------
% 11.56/3.07 % (15913)------------------------------
% 11.56/3.08 % (15926)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_15503 for (2987ds/31Mi)
% 11.56/3.09 % (15926)Instruction limit reached!
% 11.56/3.09 % (15926)------------------------------
% 11.56/3.09 % (15926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.56/3.09 % (15926)Termination reason: Unknown
% 11.56/3.09 % (15926)Termination phase: shuffling
% 11.56/3.09
% 11.56/3.09 % (15926)Memory used [KB]: 4989
% 11.56/3.09 % (15926)Time elapsed: 0.013 s
% 11.56/3.09 % (15926)Instructions burned: 31 (million)
% 11.56/3.09 % (15926)------------------------------
% 11.56/3.09 % (15926)------------------------------
% 11.56/3.10 % (15927)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_15503 for (2987ds/279Mi)
% 12.20/3.14 % (15925)Instruction limit reached!
% 12.20/3.14 % (15925)------------------------------
% 12.20/3.14 % (15925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.20/3.14 % (15925)Termination reason: Unknown
% 12.20/3.14 % (15925)Termination phase: Function definition elimination
% 12.20/3.14
% 12.20/3.14 % (15925)Memory used [KB]: 10874
% 12.20/3.14 % (15925)Time elapsed: 0.108 s
% 12.20/3.14 % (15925)Instructions burned: 360 (million)
% 12.20/3.14 % (15925)------------------------------
% 12.20/3.14 % (15925)------------------------------
% 12.20/3.15 % (15928)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_15503 for (2986ds/258Mi)
% 12.20/3.18 % (15927)Instruction limit reached!
% 12.20/3.18 % (15927)------------------------------
% 12.20/3.18 % (15927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.20/3.18 % (15927)Termination reason: Unknown
% 12.20/3.18 % (15927)Termination phase: Property scanning
% 12.20/3.18
% 12.20/3.18 % (15927)Memory used [KB]: 11257
% 12.20/3.18 % (15927)Time elapsed: 0.079 s
% 12.20/3.18 % (15927)Instructions burned: 282 (million)
% 12.20/3.18 % (15927)------------------------------
% 12.20/3.18 % (15927)------------------------------
% 12.20/3.19 % (15929)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_15503 for (2986ds/26Mi)
% 12.84/3.20 % (15929)Instruction limit reached!
% 12.84/3.20 % (15929)------------------------------
% 12.84/3.20 % (15929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.84/3.20 % (15929)Termination reason: Unknown
% 12.84/3.20 % (15929)Termination phase: shuffling
% 12.84/3.20
% 12.84/3.20 % (15929)Memory used [KB]: 4477
% 12.84/3.20 % (15929)Time elapsed: 0.010 s
% 12.84/3.20 % (15929)Instructions burned: 27 (million)
% 12.84/3.20 % (15929)------------------------------
% 12.84/3.20 % (15929)------------------------------
% 12.84/3.21 % (15930)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_15503 for (2986ds/995Mi)
% 12.84/3.23 % (15928)Instruction limit reached!
% 12.84/3.23 % (15928)------------------------------
% 12.84/3.23 % (15928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.84/3.23 % (15928)Termination reason: Unknown
% 12.84/3.23 % (15928)Termination phase: Preprocessing 3
% 12.84/3.23
% 12.84/3.23 % (15928)Memory used [KB]: 10874
% 12.84/3.23 % (15928)Time elapsed: 0.082 s
% 12.84/3.23 % (15928)Instructions burned: 259 (million)
% 12.84/3.23 % (15928)------------------------------
% 12.84/3.23 % (15928)------------------------------
% 12.84/3.24 % (15931)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_15503 for (2985ds/373Mi)
% 13.46/3.32 % (15919)Instruction limit reached!
% 13.46/3.32 % (15919)------------------------------
% 13.46/3.32 % (15919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.46/3.32 % (15919)Termination reason: Unknown
% 13.46/3.32 % (15919)Termination phase: Saturation
% 13.46/3.32
% 13.46/3.32 % (15919)Memory used [KB]: 18677
% 13.46/3.32 % (15919)Time elapsed: 0.487 s
% 13.46/3.32 % (15919)Instructions burned: 1541 (million)
% 13.46/3.32 % (15919)------------------------------
% 13.46/3.32 % (15919)------------------------------
% 13.46/3.33 % (15932)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_15503 for (2984ds/253Mi)
% 13.46/3.35 % (15931)Instruction limit reached!
% 13.46/3.35 % (15931)------------------------------
% 13.46/3.35 % (15931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.46/3.35 % (15931)Termination reason: Unknown
% 13.46/3.35 % (15931)Termination phase: Property scanning
% 13.46/3.35
% 13.46/3.35 % (15931)Memory used [KB]: 11769
% 13.46/3.35 % (15931)Time elapsed: 0.110 s
% 13.46/3.35 % (15931)Instructions burned: 374 (million)
% 13.46/3.35 % (15931)------------------------------
% 13.46/3.35 % (15931)------------------------------
% 13.46/3.36 % (15933)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_15503 for (2984ds/832Mi)
% 14.02/3.40 % (15932)Instruction limit reached!
% 14.02/3.40 % (15932)------------------------------
% 14.02/3.40 % (15932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.02/3.40 % (15932)Termination reason: Unknown
% 14.02/3.40 % (15932)Termination phase: Property scanning
% 14.02/3.40
% 14.02/3.40 % (15932)Memory used [KB]: 11257
% 14.02/3.40 % (15932)Time elapsed: 0.072 s
% 14.02/3.40 % (15932)Instructions burned: 255 (million)
% 14.02/3.40 % (15932)------------------------------
% 14.02/3.40 % (15932)------------------------------
% 14.02/3.42 % (15934)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_15503 for (2984ds/668Mi)
% 14.02/3.49 % (15930)Instruction limit reached!
% 14.02/3.49 % (15930)------------------------------
% 14.02/3.49 % (15930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.02/3.49 % (15930)Termination reason: Unknown
% 14.02/3.49 % (15930)Termination phase: Saturation
% 14.02/3.49
% 14.02/3.49 % (15930)Memory used [KB]: 18933
% 14.02/3.49 % (15930)Time elapsed: 0.281 s
% 14.02/3.49 % (15930)Instructions burned: 997 (million)
% 14.02/3.49 % (15930)------------------------------
% 14.02/3.49 % (15930)------------------------------
% 14.79/3.50 % (15935)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_15503 for (2983ds/40Mi)
% 14.79/3.51 % (15935)Instruction limit reached!
% 14.79/3.51 % (15935)------------------------------
% 14.79/3.51 % (15935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.79/3.51 % (15935)Termination reason: Unknown
% 14.79/3.51 % (15935)Termination phase: shuffling
% 14.79/3.51
% 14.79/3.51 % (15935)Memory used [KB]: 5117
% 14.79/3.51 % (15935)Time elapsed: 0.015 s
% 14.79/3.51 % (15935)Instructions burned: 42 (million)
% 14.79/3.51 % (15935)------------------------------
% 14.79/3.51 % (15935)------------------------------
% 14.79/3.52 % (15936)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_15503 for (2982ds/294Mi)
% 14.79/3.57 % (15922)Instruction limit reached!
% 14.79/3.57 % (15922)------------------------------
% 14.79/3.57 % (15922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.79/3.57 % (15922)Termination reason: Unknown
% 14.79/3.57 % (15922)Termination phase: Saturation
% 14.79/3.57
% 14.79/3.57 % (15922)Memory used [KB]: 12409
% 14.79/3.57 % (15922)Time elapsed: 0.661 s
% 14.79/3.57 % (15922)Instructions burned: 1916 (million)
% 14.79/3.57 % (15922)------------------------------
% 14.79/3.57 % (15922)------------------------------
% 14.79/3.58 % (15937)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_15503 for (2982ds/187Mi)
% 14.79/3.59 % (15934)Instruction limit reached!
% 14.79/3.59 % (15934)------------------------------
% 14.79/3.59 % (15934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.79/3.59 % (15934)Termination reason: Unknown
% 14.79/3.59 % (15934)Termination phase: Saturation
% 14.79/3.59
% 14.79/3.59 % (15934)Memory used [KB]: 22003
% 14.79/3.59 % (15934)Time elapsed: 0.180 s
% 14.79/3.59 % (15934)Instructions burned: 670 (million)
% 14.79/3.59 % (15934)------------------------------
% 14.79/3.59 % (15934)------------------------------
% 15.40/3.60 % (15936)Instruction limit reached!
% 15.40/3.60 % (15936)------------------------------
% 15.40/3.60 % (15936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.40/3.60 % (15936)Termination reason: Unknown
% 15.40/3.60 % (15936)Termination phase: Property scanning
% 15.40/3.60
% 15.40/3.60 % (15936)Memory used [KB]: 11385
% 15.40/3.60 % (15936)Time elapsed: 0.081 s
% 15.40/3.60 % (15936)Instructions burned: 297 (million)
% 15.40/3.60 % (15936)------------------------------
% 15.40/3.60 % (15936)------------------------------
% 15.40/3.61 % (15938)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_15503 for (2982ds/371Mi)
% 15.40/3.61 % (15939)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_15503 for (2982ds/1827Mi)
% 15.40/3.62 % (15933)Instruction limit reached!
% 15.40/3.62 % (15933)------------------------------
% 15.40/3.62 % (15933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.40/3.62 % (15933)Termination reason: Unknown
% 15.40/3.62 % (15933)Termination phase: Saturation
% 15.40/3.62
% 15.40/3.62 % (15933)Memory used [KB]: 18549
% 15.40/3.62 % (15933)Time elapsed: 0.260 s
% 15.40/3.62 % (15933)Instructions burned: 832 (million)
% 15.40/3.62 % (15933)------------------------------
% 15.40/3.62 % (15933)------------------------------
% 15.40/3.63 % (15940)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_15503 for (2981ds/70Mi)
% 15.40/3.64 % (15937)Instruction limit reached!
% 15.40/3.64 % (15937)------------------------------
% 15.40/3.64 % (15937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.40/3.64 % (15937)Termination reason: Unknown
% 15.40/3.64 % (15937)Termination phase: Preprocessing 1
% 15.40/3.64
% 15.40/3.64 % (15937)Memory used [KB]: 9338
% 15.40/3.64 % (15937)Time elapsed: 0.062 s
% 15.40/3.64 % (15937)Instructions burned: 188 (million)
% 15.40/3.64 % (15937)------------------------------
% 15.40/3.64 % (15937)------------------------------
% 15.40/3.65 % (15940)Instruction limit reached!
% 15.40/3.65 % (15940)------------------------------
% 15.40/3.65 % (15940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.40/3.65 % (15940)Termination reason: Unknown
% 15.40/3.65 % (15940)Termination phase: shuffling
% 15.40/3.65
% 15.40/3.65 % (15940)Memory used [KB]: 6908
% 15.40/3.65 % (15940)Time elapsed: 0.023 s
% 15.40/3.65 % (15940)Instructions burned: 73 (million)
% 15.40/3.65 % (15940)------------------------------
% 15.40/3.65 % (15940)------------------------------
% 15.40/3.65 % (15941)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_15503 for (2981ds/316Mi)
% 15.40/3.66 % (15942)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_15503 for (2981ds/932Mi)
% 16.15/3.71 % (15938)Instruction limit reached!
% 16.15/3.71 % (15938)------------------------------
% 16.15/3.71 % (15938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.15/3.71 % (15938)Termination reason: Unknown
% 16.15/3.71 % (15938)Termination phase: Saturation
% 16.15/3.71
% 16.15/3.71 % (15938)Memory used [KB]: 15223
% 16.15/3.71 % (15938)Time elapsed: 0.111 s
% 16.15/3.71 % (15938)Instructions burned: 373 (million)
% 16.15/3.72 % (15938)------------------------------
% 16.15/3.72 % (15938)------------------------------
% 16.15/3.73 % (15943)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_15503 for (2980ds/4714Mi)
% 16.15/3.74 % (15941)Instruction limit reached!
% 16.15/3.74 % (15941)------------------------------
% 16.15/3.74 % (15941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.15/3.74 % (15941)Termination reason: Unknown
% 16.15/3.74 % (15941)Termination phase: Preprocessing 2
% 16.15/3.74
% 16.15/3.74 % (15941)Memory used [KB]: 11385
% 16.15/3.74 % (15941)Time elapsed: 0.088 s
% 16.15/3.74 % (15941)Instructions burned: 316 (million)
% 16.15/3.74 % (15941)------------------------------
% 16.15/3.74 % (15941)------------------------------
% 16.15/3.75 % (15944)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_15503 for (2980ds/8250Mi)
% 16.95/3.91 % (15942)Instruction limit reached!
% 16.95/3.91 % (15942)------------------------------
% 16.95/3.91 % (15942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.95/3.91 % (15942)Termination reason: Unknown
% 16.95/3.91 % (15942)Termination phase: Saturation
% 16.95/3.91
% 16.95/3.91 % (15942)Memory used [KB]: 17910
% 16.95/3.91 % (15942)Time elapsed: 0.250 s
% 16.95/3.91 % (15942)Instructions burned: 934 (million)
% 16.95/3.91 % (15942)------------------------------
% 16.95/3.91 % (15942)------------------------------
% 16.95/3.92 % (15945)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_15503 for (2979ds/770Mi)
% 16.95/3.95 % (15943)Refutation not found, incomplete strategy
% 16.95/3.95 % (15943)------------------------------
% 16.95/3.95 % (15943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.95/3.95 % (15943)Termination reason: Refutation not found, incomplete strategy
% 16.95/3.95
% 16.95/3.95
% 16.95/3.95 % (15943)Memory used [KB]: 18805
% 16.95/3.95 % (15943)Time elapsed: 0.225 s
% 16.95/3.95 % (15943)Instructions burned: 804 (million)
% 16.95/3.95 % (15943)------------------------------
% 16.95/3.95 % (15943)------------------------------
% 16.95/3.96 % (15946)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_15503 for (2978ds/794Mi)
% 19.39/4.16 % (15945)Instruction limit reached!
% 19.39/4.16 % (15945)------------------------------
% 19.39/4.16 % (15945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.39/4.16 % (15945)Termination reason: Unknown
% 19.39/4.16 % (15945)Termination phase: Saturation
% 19.39/4.16
% 19.39/4.16 % (15945)Memory used [KB]: 16375
% 19.39/4.16 % (15945)Time elapsed: 0.245 s
% 19.39/4.16 % (15945)Instructions burned: 770 (million)
% 19.39/4.16 % (15945)------------------------------
% 19.39/4.16 % (15945)------------------------------
% 19.39/4.17 % (15947)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_15503 for (2976ds/464Mi)
% 19.88/4.20 % (15946)Instruction limit reached!
% 19.88/4.20 % (15946)------------------------------
% 19.88/4.20 % (15946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.88/4.20 % (15946)Termination reason: Unknown
% 19.88/4.20 % (15946)Termination phase: Saturation
% 19.88/4.20
% 19.88/4.20 % (15946)Memory used [KB]: 15223
% 19.88/4.20 % (15946)Time elapsed: 0.240 s
% 19.88/4.20 % (15946)Instructions burned: 794 (million)
% 19.88/4.20 % (15946)------------------------------
% 19.88/4.20 % (15946)------------------------------
% 19.88/4.21 % (15948)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_15503 for (2975ds/1376Mi)
% 19.88/4.21 % (15939)Instruction limit reached!
% 19.88/4.21 % (15939)------------------------------
% 19.88/4.21 % (15939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.88/4.21 % (15939)Termination reason: Unknown
% 19.88/4.21 % (15939)Termination phase: Saturation
% 19.88/4.21
% 19.88/4.21 % (15939)Memory used [KB]: 18933
% 19.88/4.21 % (15939)Time elapsed: 0.599 s
% 19.88/4.21 % (15939)Instructions burned: 1829 (million)
% 19.88/4.21 % (15939)------------------------------
% 19.88/4.21 % (15939)------------------------------
% 19.88/4.22 % (15949)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_15503 for (2975ds/906Mi)
% 19.88/4.23 % (15918)Instruction limit reached!
% 19.88/4.23 % (15918)------------------------------
% 19.88/4.23 % (15918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.88/4.23 % (15918)Termination reason: Unknown
% 19.88/4.23 % (15918)Termination phase: Saturation
% 19.88/4.23
% 19.88/4.23 % (15918)Memory used [KB]: 19701
% 19.88/4.23 % (15918)Time elapsed: 1.422 s
% 19.88/4.23 % (15918)Instructions burned: 4436 (million)
% 19.88/4.23 % (15918)------------------------------
% 19.88/4.23 % (15918)------------------------------
% 19.88/4.24 % (15950)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_15503 for (2975ds/434Mi)
% 19.88/4.28 % (15923)Instruction limit reached!
% 19.88/4.28 % (15923)------------------------------
% 19.88/4.28 % (15923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.88/4.28 % (15923)Termination reason: Unknown
% 19.88/4.28 % (15923)Termination phase: Saturation
% 19.88/4.28
% 19.88/4.28 % (15923)Memory used [KB]: 18293
% 19.88/4.28 % (15923)Time elapsed: 1.304 s
% 19.88/4.28 % (15923)Instructions burned: 4352 (million)
% 19.88/4.28 % (15923)------------------------------
% 19.88/4.28 % (15923)------------------------------
% 19.88/4.29 % (15951)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_15503 for (2975ds/865Mi)
% 20.26/4.31 % (15947)Instruction limit reached!
% 20.26/4.31 % (15947)------------------------------
% 20.26/4.31 % (15947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.26/4.31 % (15947)Termination reason: Unknown
% 20.26/4.31 % (15947)Termination phase: Saturation
% 20.26/4.31
% 20.26/4.31 % (15947)Memory used [KB]: 16502
% 20.26/4.31 % (15947)Time elapsed: 0.137 s
% 20.26/4.31 % (15947)Instructions burned: 465 (million)
% 20.26/4.31 % (15947)------------------------------
% 20.26/4.31 % (15947)------------------------------
% 20.26/4.32 % (15952)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_15503 for (2974ds/593Mi)
% 20.26/4.37 % (15950)Instruction limit reached!
% 20.26/4.37 % (15950)------------------------------
% 20.26/4.37 % (15950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.26/4.37 % (15950)Termination reason: Unknown
% 20.26/4.37 % (15950)Termination phase: Saturation
% 20.26/4.37
% 20.26/4.37 % (15950)Memory used [KB]: 16247
% 20.26/4.37 % (15950)Time elapsed: 0.132 s
% 20.26/4.37 % (15950)Instructions burned: 436 (million)
% 20.26/4.37 % (15950)------------------------------
% 20.26/4.37 % (15950)------------------------------
% 20.26/4.38 % (15953)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_15503 for (2974ds/443Mi)
% 20.75/4.43 % (15921)Instruction limit reached!
% 20.75/4.43 % (15921)------------------------------
% 20.75/4.43 % (15921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.43 % (15921)Termination reason: Unknown
% 20.75/4.43 % (15921)Termination phase: Saturation
% 20.75/4.43
% 20.75/4.43 % (15921)Memory used [KB]: 24434
% 20.75/4.43 % (15921)Time elapsed: 1.576 s
% 20.75/4.43 % (15921)Instructions burned: 5206 (million)
% 20.75/4.43 % (15921)------------------------------
% 20.75/4.43 % (15921)------------------------------
% 20.75/4.45 % (15954)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_15503 for (2973ds/594Mi)
% 20.75/4.48 % (15952)Instruction limit reached!
% 20.75/4.48 % (15952)------------------------------
% 20.75/4.48 % (15952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.48 % (15952)Termination reason: Unknown
% 20.75/4.48 % (15952)Termination phase: Saturation
% 20.75/4.48
% 20.75/4.48 % (15952)Memory used [KB]: 12792
% 20.75/4.48 % (15952)Time elapsed: 0.158 s
% 20.75/4.48 % (15952)Instructions burned: 594 (million)
% 20.75/4.48 % (15952)------------------------------
% 20.75/4.48 % (15952)------------------------------
% 20.75/4.49 % (15955)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_15503 for (2973ds/327Mi)
% 21.08/4.51 % (15953)Instruction limit reached!
% 21.08/4.51 % (15953)------------------------------
% 21.08/4.51 % (15953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.51 % (15953)Termination reason: Unknown
% 21.08/4.51 % (15953)Termination phase: Saturation
% 21.08/4.51
% 21.08/4.51 % (15953)Memory used [KB]: 15479
% 21.08/4.51 % (15953)Time elapsed: 0.132 s
% 21.08/4.51 % (15953)Instructions burned: 445 (million)
% 21.08/4.51 % (15953)------------------------------
% 21.08/4.51 % (15953)------------------------------
% 21.08/4.52 % (15956)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_15503 for (2972ds/5411Mi)
% 21.08/4.53 % (15949)Instruction limit reached!
% 21.08/4.53 % (15949)------------------------------
% 21.08/4.53 % (15949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.53 % (15949)Termination reason: Unknown
% 21.08/4.53 % (15949)Termination phase: Saturation
% 21.08/4.53
% 21.08/4.53 % (15949)Memory used [KB]: 20596
% 21.08/4.53 % (15949)Time elapsed: 0.304 s
% 21.08/4.53 % (15949)Instructions burned: 906 (million)
% 21.08/4.53 % (15949)------------------------------
% 21.08/4.53 % (15949)------------------------------
% 21.08/4.53 % (15951)Instruction limit reached!
% 21.08/4.53 % (15951)------------------------------
% 21.08/4.53 % (15951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.53 % (15951)Termination reason: Unknown
% 21.08/4.53 % (15951)Termination phase: Saturation
% 21.08/4.53
% 21.08/4.53 % (15951)Memory used [KB]: 18293
% 21.08/4.53 % (15951)Time elapsed: 0.249 s
% 21.08/4.53 % (15951)Instructions burned: 867 (million)
% 21.08/4.53 % (15951)------------------------------
% 21.08/4.53 % (15951)------------------------------
% 21.08/4.54 % (15957)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_15503 for (2972ds/1762Mi)
% 21.08/4.55 % (15958)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_15503 for (2972ds/96Mi)
% 21.08/4.57 % (15958)Instruction limit reached!
% 21.08/4.57 % (15958)------------------------------
% 21.08/4.57 % (15958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.57 % (15958)Termination reason: Unknown
% 21.08/4.57 % (15958)Termination phase: shuffling
% 21.08/4.57
% 21.08/4.57 % (15958)Memory used [KB]: 8059
% 21.08/4.57 % (15958)Time elapsed: 0.030 s
% 21.08/4.57 % (15958)Instructions burned: 97 (million)
% 21.08/4.57 % (15958)------------------------------
% 21.08/4.57 % (15958)------------------------------
% 21.08/4.59 % (15959)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_15503 for (2972ds/503Mi)
% 21.08/4.59 % (15955)Instruction limit reached!
% 21.08/4.59 % (15955)------------------------------
% 21.08/4.59 % (15955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.59 % (15955)Termination reason: Unknown
% 21.08/4.59 % (15955)Termination phase: Property scanning
% 21.08/4.59
% 21.08/4.59 % (15955)Memory used [KB]: 11257
% 21.08/4.59 % (15955)Time elapsed: 0.101 s
% 21.08/4.59 % (15955)Instructions burned: 330 (million)
% 21.08/4.59 % (15955)------------------------------
% 21.08/4.59 % (15955)------------------------------
% 21.08/4.59 % (15948)Instruction limit reached!
% 21.08/4.59 % (15948)------------------------------
% 21.08/4.59 % (15948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.59 % (15948)Termination reason: Unknown
% 21.08/4.59 % (15948)Termination phase: Saturation
% 21.08/4.59
% 21.08/4.59 % (15948)Memory used [KB]: 19701
% 21.08/4.59 % (15948)Time elapsed: 0.380 s
% 21.08/4.59 % (15948)Instructions burned: 1378 (million)
% 21.08/4.59 % (15948)------------------------------
% 21.08/4.59 % (15948)------------------------------
% 22.43/4.60 % (15960)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_15503 for (2972ds/90Mi)
% 22.43/4.60 % (15961)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_15503 for (2972ds/593Mi)
% 22.43/4.63 % (15954)Instruction limit reached!
% 22.43/4.63 % (15954)------------------------------
% 22.43/4.63 % (15954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.43/4.63 % (15954)Termination reason: Unknown
% 22.43/4.63 % (15954)Termination phase: Saturation
% 22.43/4.63
% 22.43/4.63 % (15954)Memory used [KB]: 15479
% 22.43/4.63 % (15954)Time elapsed: 0.182 s
% 22.43/4.63 % (15954)Instructions burned: 594 (million)
% 22.43/4.63 % (15954)------------------------------
% 22.43/4.63 % (15954)------------------------------
% 22.43/4.63 % (15960)Instruction limit reached!
% 22.43/4.63 % (15960)------------------------------
% 22.43/4.63 % (15960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.43/4.63 % (15960)Termination reason: Unknown
% 22.43/4.63 % (15960)Termination phase: shuffling
% 22.43/4.63
% 22.43/4.63 % (15960)Memory used [KB]: 7675
% 22.43/4.63 % (15960)Time elapsed: 0.033 s
% 22.43/4.63 % (15960)Instructions burned: 91 (million)
% 22.43/4.63 % (15960)------------------------------
% 22.43/4.63 % (15960)------------------------------
% 22.43/4.64 % (15962)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_15503 for (2971ds/1512Mi)
% 22.43/4.64 % (15963)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_15503 for (2971ds/569Mi)
% 22.77/4.74 % (15956)First to succeed.
% 22.77/4.74 % (15956)Refutation found. Thanks to Tanya!
% 22.77/4.74 % SZS status Theorem for DTF2THF_15503
% 22.77/4.74 % SZS output start Proof for DTF2THF_15503
% 22.77/4.74 thf(type_def_5, type, pname: $tType).
% 22.77/4.74 thf(type_def_7, type, hoare_1708887482_state: $tType).
% 22.77/4.74 thf(type_def_8, type, com: $tType).
% 22.77/4.74 thf(type_def_9, type, option_com: $tType).
% 22.77/4.74 thf(type_def_10, type, state: $tType).
% 22.77/4.74 thf(type_def_11, type, option_pname: $tType).
% 22.77/4.74 thf(type_def_12, type, option1624383643_state: $tType).
% 22.77/4.74 thf(func_def_0, type, com: $tType).
% 22.77/4.74 thf(func_def_1, type, pname: $tType).
% 22.77/4.74 thf(func_def_2, type, state: $tType).
% 22.77/4.74 thf(func_def_3, type, hoare_1708887482_state: $tType).
% 22.77/4.74 thf(func_def_4, type, option_com: $tType).
% 22.77/4.74 thf(func_def_5, type, option_pname: $tType).
% 22.77/4.74 thf(func_def_6, type, option1624383643_state: $tType).
% 22.77/4.74 thf(func_def_7, type, big_la1126801287name_o: ((pname > $o) > $o) > pname > $o).
% 22.77/4.74 thf(func_def_8, type, big_la781588935tate_o: ((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_9, type, wt: com > $o).
% 22.77/4.74 thf(func_def_11, type, body: pname > option_com).
% 22.77/4.74 thf(func_def_12, type, body_1: pname > com).
% 22.77/4.74 thf(func_def_13, type, skip: com).
% 22.77/4.74 thf(func_def_14, type, semi: com > com > com).
% 22.77/4.74 thf(func_def_15, type, while: (state > $o) > com > com).
% 22.77/4.74 thf(func_def_16, type, finite138924780name_o: ((pname > $o) > (pname > $o) > pname > $o) > $o).
% 22.77/4.74 thf(func_def_17, type, finite2034616076tate_o: ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_18, type, finite2048025996em_o_o: ($o > $o > $o) > $o).
% 22.77/4.74 thf(func_def_19, type, finite567462577_com_o: (com > (com > $o) > com > $o) > $o).
% 22.77/4.74 thf(func_def_20, type, finite1123817265name_o: (pname > (pname > $o) > pname > $o) > $o).
% 22.77/4.74 thf(func_def_21, type, finite662762081tate_o: (hoare_1708887482_state > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_22, type, finite1066544169me_o_o: (((pname > $o) > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_23, type, finite1019950101te_o_o: (((hoare_1708887482_state > $o) > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_24, type, finite297249702name_o: ((pname > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_25, type, finite1329924456tate_o: ((hoare_1708887482_state > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_26, type, finite_finite_o: ($o > $o) > $o).
% 22.77/4.74 thf(func_def_27, type, finite_finite_com: (com > $o) > $o).
% 22.77/4.74 thf(func_def_28, type, finite_finite_pname: (pname > $o) > $o).
% 22.77/4.74 thf(func_def_29, type, finite1625599783_state: (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_30, type, finite1849951719me_o_o: ((pname > $o) > ((pname > $o) > $o) > (pname > $o) > $o) > ((pname > $o) > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_31, type, finite472615016name_o: ((pname > $o) > (pname > $o) > pname > $o) > (pname > $o) > ((pname > $o) > $o) > pname > $o).
% 22.77/4.74 thf(func_def_32, type, finite463603445te_o_o: ((hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o) > (hoare_1708887482_state > $o) > $o) > ((hoare_1708887482_state > $o) > $o) > ((hoare_1708887482_state > $o) > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_33, type, finite822533768tate_o: ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_34, type, finite_fold_o_o: ($o > $o > $o) > $o > ($o > $o) > $o).
% 22.77/4.74 thf(func_def_35, type, finite504235573_com_o: (com > (com > $o) > com > $o) > (com > $o) > (com > $o) > com > $o).
% 22.77/4.74 thf(func_def_36, type, finite_fold_com_com: (com > com > com) > com > (com > $o) > com).
% 22.77/4.74 thf(func_def_37, type, finite603803317name_o: (pname > (pname > $o) > pname > $o) > (pname > $o) > (pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_38, type, finite1657623752_pname: (pname > pname > pname) > pname > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_39, type, finite96880613tate_o: (hoare_1708887482_state > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_40, type, finite309095018_state: (hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state) > hoare_1708887482_state > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_41, type, finite2139561282_pname: ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > (pname > hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > (pname > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_42, type, finite349908348name_o: ((pname > $o) > (pname > $o) > pname > $o) > (((pname > $o) > $o) > pname > $o) > $o).
% 22.77/4.74 thf(func_def_43, type, finite928843026tate_o: ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > (((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_44, type, finite860057415ne_com: (com > com > com) > ((com > $o) > com) > $o).
% 22.77/4.74 thf(func_def_45, type, finite1282449217_pname: (pname > pname > pname) > ((pname > $o) > pname) > $o).
% 22.77/4.74 thf(func_def_46, type, finite1615457021_state: (hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state) > ((hoare_1708887482_state > $o) > hoare_1708887482_state) > $o).
% 22.77/4.74 thf(func_def_47, type, finite697516351name_o: ((pname > $o) > (pname > $o) > pname > $o) > (((pname > $o) > $o) > pname > $o) > $o).
% 22.77/4.74 thf(func_def_48, type, finite621643279tate_o: ((hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > (((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_49, type, finite666746948em_com: (com > com > com) > ((com > $o) > com) > $o).
% 22.77/4.74 thf(func_def_50, type, finite89670078_pname: (pname > pname > pname) > ((pname > $o) > pname) > $o).
% 22.77/4.74 thf(func_def_51, type, finite1347568576_state: (hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state) > ((hoare_1708887482_state > $o) > hoare_1708887482_state) > $o).
% 22.77/4.74 thf(func_def_52, type, fun_up1986763201_state: (pname > hoare_1708887482_state) > pname > hoare_1708887482_state > pname > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_53, type, fun_up879233478on_com: (pname > option_com) > pname > option_com > pname > option_com).
% 22.77/4.74 thf(func_def_54, type, inj_on691924881name_o: ((pname > $o) > pname > $o) > ((pname > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_55, type, inj_on176908593tate_o: ((hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_56, type, inj_on11367768on_com: (com > option_com) > (com > $o) > $o).
% 22.77/4.74 thf(func_def_57, type, inj_on_pname_pname: (pname > pname) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_58, type, inj_on1553129421_state: (pname > hoare_1708887482_state) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_59, type, inj_on737724108_pname: (pname > option_pname) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_60, type, inj_on1945914667_pname: (hoare_1708887482_state > pname) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_61, type, inj_on632008595_state: (hoare_1708887482_state > hoare_1708887482_state) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_62, type, inj_on945311362_state: (hoare_1708887482_state > option1624383643_state) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_63, type, overri1496249029on_com: (pname > option_com) > (pname > option_com) > (pname > $o) > pname > option_com).
% 22.77/4.74 thf(func_def_64, type, minus_1480864103me_o_o: ((pname > $o) > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_65, type, minus_548038231te_o_o: ((hoare_1708887482_state > $o) > $o) > ((hoare_1708887482_state > $o) > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_66, type, minus_minus_com_o: (com > $o) > (com > $o) > com > $o).
% 22.77/4.74 thf(func_def_67, type, minus_minus_pname_o: (pname > $o) > (pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_68, type, minus_2056855718tate_o: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_69, type, the_com_1: (com > $o) > com).
% 22.77/4.74 thf(func_def_70, type, the_pname: (pname > $o) > pname).
% 22.77/4.74 thf(func_def_71, type, the_Ho851197897_state: (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_72, type, hoare_Mirabelle_MGT: com > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_73, type, hoare_90032982_state: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_74, type, hoare_496444244_state: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_76, type, hoare_858012674_state: (state > state > $o) > com > (state > state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_77, type, if_Hoa1374726218_state: $o > hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_78, type, if_option_com: $o > option_com > option_com > option_com).
% 22.77/4.74 thf(func_def_79, type, semila2013987940me_o_o: ((pname > $o) > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_80, type, semila598060698te_o_o: ((hoare_1708887482_state > $o) > $o) > ((hoare_1708887482_state > $o) > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_81, type, semila513601829_com_o: (com > $o) > (com > $o) > com > $o).
% 22.77/4.74 thf(func_def_82, type, semila1673364395name_o: (pname > $o) > (pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_83, type, semila129691299tate_o: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_84, type, semila854092349_inf_o: $o > $o > $o).
% 22.77/4.74 thf(func_def_85, type, semila181081674me_o_o: ((pname > $o) > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_86, type, semila1853742644te_o_o: ((hoare_1708887482_state > $o) > $o) > ((hoare_1708887482_state > $o) > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_87, type, semila1562558655_com_o: (com > $o) > (com > $o) > com > $o).
% 22.77/4.74 thf(func_def_88, type, semila1780557381name_o: (pname > $o) > (pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_89, type, semila1122118281tate_o: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_90, type, semila10642723_sup_o: $o > $o > $o).
% 22.77/4.74 thf(func_def_91, type, dom_com_com: (com > option_com) > com > $o).
% 22.77/4.74 thf(func_def_92, type, dom_pname_com: (pname > option_com) > pname > $o).
% 22.77/4.74 thf(func_def_93, type, dom_pname_pname: (pname > option_pname) > pname > $o).
% 22.77/4.74 thf(func_def_94, type, dom_pn1412407212_state: (pname > option1624383643_state) > pname > $o).
% 22.77/4.74 thf(func_def_95, type, dom_Ho1805192458_pname: (hoare_1708887482_state > option_pname) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_96, type, dom_Ho1703271284_state: (hoare_1708887482_state > option1624383643_state) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_97, type, restri1382200118me_com: (pname > option_com) > (pname > $o) > pname > option_com).
% 22.77/4.74 thf(func_def_98, type, evalc: com > state > state > $o).
% 22.77/4.74 thf(func_def_99, type, is_none_com: option_com > $o).
% 22.77/4.74 thf(func_def_100, type, is_none_pname: option_pname > $o).
% 22.77/4.74 thf(func_def_101, type, is_non163157940_state: option1624383643_state > $o).
% 22.77/4.74 thf(func_def_102, type, none_com: option_com).
% 22.77/4.74 thf(func_def_103, type, none_pname: option_pname).
% 22.77/4.74 thf(func_def_104, type, none_H1106584047_state: option1624383643_state).
% 22.77/4.74 thf(func_def_105, type, some_com: com > option_com).
% 22.77/4.74 thf(func_def_106, type, some_pname: pname > option_pname).
% 22.77/4.74 thf(func_def_107, type, some_H1974565227_state: hoare_1708887482_state > option1624383643_state).
% 22.77/4.74 thf(func_def_108, type, set_com: option_com > com > $o).
% 22.77/4.74 thf(func_def_109, type, set_pname: option_pname > pname > $o).
% 22.77/4.74 thf(func_def_110, type, set_Ho525251890_state: option1624383643_state > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_111, type, the_com: option_com > com).
% 22.77/4.74 thf(func_def_112, type, the_pname_1: option_pname > pname).
% 22.77/4.74 thf(func_def_113, type, the_Ho963921505_state: option1624383643_state > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_114, type, bot_bot_pname_o_o: (pname > $o) > $o).
% 22.77/4.74 thf(func_def_115, type, bot_bo1678742418te_o_o: (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_116, type, bot_bot_com_o: com > $o).
% 22.77/4.74 thf(func_def_117, type, bot_bot_pname_o: pname > $o).
% 22.77/4.74 thf(func_def_118, type, bot_bo19817387tate_o: hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_120, type, ord_le1205211808me_o_o: ((pname > $o) > $o) > ((pname > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_121, type, ord_le1728773982te_o_o: ((hoare_1708887482_state > $o) > $o) > ((hoare_1708887482_state > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_122, type, ord_less_eq_com_o: (com > $o) > (com > $o) > $o).
% 22.77/4.74 thf(func_def_123, type, ord_less_eq_pname_o: (pname > $o) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_124, type, ord_le777019615tate_o: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_125, type, ord_less_eq_o: $o > $o > $o).
% 22.77/4.74 thf(func_def_126, type, top_top_com_o: com > $o).
% 22.77/4.74 thf(func_def_127, type, top_top_pname_o: pname > $o).
% 22.77/4.74 thf(func_def_128, type, top_to832624271tate_o: hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_129, type, partial_flat_lub_com: com > (com > $o) > com).
% 22.77/4.74 thf(func_def_130, type, partia752020666_pname: pname > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_131, type, partia1256728516_state: hoare_1708887482_state > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_132, type, collect_pname_o_o: (((pname > $o) > $o) > $o) > ((pname > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_133, type, collec58007891te_o_o: (((hoare_1708887482_state > $o) > $o) > $o) > ((hoare_1708887482_state > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_134, type, collect_pname_o: ((pname > $o) > $o) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_135, type, collec219771562tate_o: ((hoare_1708887482_state > $o) > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_136, type, collect_com: (com > $o) > com > $o).
% 22.77/4.74 thf(func_def_137, type, collect_pname: (pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_138, type, collec1568722789_state: (hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_139, type, image_1085733413name_o: ((pname > $o) > pname > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_140, type, image_pname_o_pname: ((pname > $o) > pname) > ((pname > $o) > $o) > pname > $o).
% 22.77/4.74 thf(func_def_141, type, image_1922967206_state: ((pname > $o) > hoare_1708887482_state) > ((pname > $o) > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_142, type, image_909543877tate_o: ((hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_143, type, image_2051418740_pname: ((hoare_1708887482_state > $o) > pname) > ((hoare_1708887482_state > $o) > $o) > pname > $o).
% 22.77/4.74 thf(func_def_144, type, image_27005066_state: ((hoare_1708887482_state > $o) > hoare_1708887482_state) > ((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_145, type, image_com_com: (com > com) > (com > $o) > com > $o).
% 22.77/4.74 thf(func_def_146, type, image_com_pname: (com > pname) > (com > $o) > pname > $o).
% 22.77/4.74 thf(func_def_147, type, image_934102463_state: (com > hoare_1708887482_state) > (com > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_148, type, image_pname_pname_o: (pname > pname > $o) > (pname > $o) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_149, type, image_425134806tate_o: (pname > hoare_1708887482_state > $o) > (pname > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_150, type, image_pname_com: (pname > com) > (pname > $o) > com > $o).
% 22.77/4.74 thf(func_def_151, type, image_pname_pname: (pname > pname) > (pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_152, type, image_1116629049_state: (pname > hoare_1708887482_state) > (pname > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_153, type, image_1552895654name_o: (hoare_1708887482_state > pname > $o) > (hoare_1708887482_state > $o) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_154, type, image_1551509096tate_o: (hoare_1708887482_state > hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_155, type, image_1604448413te_com: (hoare_1708887482_state > com) > (hoare_1708887482_state > $o) > com > $o).
% 22.77/4.74 thf(func_def_156, type, image_1509414295_pname: (hoare_1708887482_state > pname) > (hoare_1708887482_state > $o) > pname > $o).
% 22.77/4.74 thf(func_def_157, type, image_757158439_state: (hoare_1708887482_state > hoare_1708887482_state) > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_158, type, insert_pname_o: (pname > $o) > ((pname > $o) > $o) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_159, type, insert949073679tate_o: (hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_160, type, insert_o: $o > ($o > $o) > $o > $o).
% 22.77/4.74 thf(func_def_161, type, insert_com: com > (com > $o) > com > $o).
% 22.77/4.74 thf(func_def_162, type, insert_pname: pname > (pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_163, type, insert528405184_state: hoare_1708887482_state > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_164, type, the_elem_com: (com > $o) > com).
% 22.77/4.74 thf(func_def_165, type, the_elem_pname: (pname > $o) > pname).
% 22.77/4.74 thf(func_def_166, type, the_el864710747_state: (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_167, type, vimage1943311875_state: (pname > hoare_1708887482_state) > (hoare_1708887482_state > $o) > pname > $o).
% 22.77/4.74 thf(func_def_168, type, fequal_pname_o: (pname > $o) > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_169, type, fequal1436017556tate_o: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_170, type, fequal_com: com > com > $o).
% 22.77/4.74 thf(func_def_171, type, fequal_pname: pname > pname > $o).
% 22.77/4.74 thf(func_def_172, type, fequal_state: state > state > $o).
% 22.77/4.74 thf(func_def_173, type, fequal224822779_state: hoare_1708887482_state > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_174, type, member_pname_o: (pname > $o) > ((pname > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_175, type, member814030440tate_o: (hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o) > $o).
% 22.77/4.74 thf(func_def_176, type, member_o: $o > ($o > $o) > $o).
% 22.77/4.74 thf(func_def_177, type, member_com: com > (com > $o) > $o).
% 22.77/4.74 thf(func_def_178, type, member_pname: pname > (pname > $o) > $o).
% 22.77/4.74 thf(func_def_179, type, member451959335_state: hoare_1708887482_state > (hoare_1708887482_state > $o) > $o).
% 22.77/4.74 thf(func_def_180, type, fa: hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_181, type, pn: pname).
% 22.77/4.74 thf(func_def_182, type, y: com).
% 22.77/4.74 thf(func_def_196, type, sK0: ((hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_197, type, sK1: ((hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_198, type, sK2: (hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_199, type, sK3: (hoare_1708887482_state > $o) > ((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_200, type, sK4: hoare_1708887482_state > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_201, type, sK5: hoare_1708887482_state > (hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_202, type, sK6: (pname > $o) > pname).
% 22.77/4.74 thf(func_def_203, type, sK7: (pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_204, type, sK8: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_205, type, sK9: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_206, type, sK10: (pname > $o) > (pname > hoare_1708887482_state) > (pname > hoare_1708887482_state) > pname).
% 22.77/4.74 thf(func_def_207, type, sK11: (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_208, type, sK12: hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_209, type, sK13: hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_210, type, sK14: hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_211, type, sK15: (state > $o) > state > com > state > state).
% 22.77/4.74 thf(func_def_212, type, sK16: (state > state > $o) > (state > state > $o) > state).
% 22.77/4.74 thf(func_def_213, type, sK17: (state > state > $o) > (state > state > $o) > state).
% 22.77/4.74 thf(func_def_214, type, sK18: ((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_215, type, sK19: ((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_216, type, sK20: (state > state > $o) > (state > state > $o) > (state > state > $o) > (state > state > $o) > state).
% 22.77/4.74 thf(func_def_217, type, sK21: (state > state > $o) > (state > state > $o) > (state > state > $o) > (state > state > $o) > state).
% 22.77/4.74 thf(func_def_218, type, sK22: (state > state > $o) > (state > state > $o) > (state > state > $o) > (state > state > $o) > state).
% 22.77/4.74 thf(func_def_219, type, sK23: (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_220, type, sK24: (hoare_1708887482_state > $o) > (pname > state > state > $o) > (pname > state > state > $o) > (pname > com) > (pname > state > state > $o) > (pname > state > state > $o) > pname).
% 22.77/4.74 thf(func_def_221, type, sK25: state > state).
% 22.77/4.74 thf(func_def_222, type, sK26: (state > state > $o) > (state > state > $o) > state).
% 22.77/4.74 thf(func_def_223, type, sK27: (state > state > $o) > (state > state > $o) > state).
% 22.77/4.74 thf(func_def_224, type, sK28: ((pname > $o) > $o) > pname).
% 22.77/4.74 thf(func_def_225, type, sK29: ((pname > $o) > $o) > pname > $o).
% 22.77/4.74 thf(func_def_226, type, sK30: (pname > $o) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_227, type, sK31: (state > state > $o) > (state > state > $o) > com > (hoare_1708887482_state > $o) > state).
% 22.77/4.74 thf(func_def_228, type, sK32: (state > state > $o) > (state > state > $o) > com > (hoare_1708887482_state > $o) > state).
% 22.77/4.74 thf(func_def_229, type, sK33: ((pname > $o) > $o) > pname).
% 22.77/4.74 thf(func_def_230, type, sK34: ((pname > $o) > $o) > pname > $o).
% 22.77/4.74 thf(func_def_231, type, sK35: ((pname > $o) > $o) > pname).
% 22.77/4.74 thf(func_def_232, type, sK36: (pname > $o) > (hoare_1708887482_state > $o) > (pname > hoare_1708887482_state) > pname).
% 22.77/4.74 thf(func_def_233, type, sK37: (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_234, type, sK38: (hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_235, type, sK39: (pname > $o) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_236, type, sK40: (pname > $o) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_237, type, sK41: (pname > $o) > (pname > $o) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_238, type, sK42: (pname > $o) > pname > pname > $o).
% 22.77/4.74 thf(func_def_239, type, sK43: (pname > option_com) > pname > com).
% 22.77/4.74 thf(func_def_240, type, sK44: (pname > $o) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_241, type, sK45: (pname > $o) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_242, type, sK46: (pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_243, type, sK47: (pname > $o) > pname).
% 22.77/4.74 thf(func_def_244, type, sK48: (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_245, type, sK49: (pname > $o) > pname).
% 22.77/4.74 thf(func_def_246, type, sK50: (pname > $o) > (pname > $o) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_247, type, sK51: (pname > $o) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_248, type, sK52: (pname > $o) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_249, type, sK53: hoare_1708887482_state > state > state > $o).
% 22.77/4.74 thf(func_def_250, type, sK54: hoare_1708887482_state > state > state > $o).
% 22.77/4.74 thf(func_def_251, type, sK55: hoare_1708887482_state > com).
% 22.77/4.74 thf(func_def_252, type, sK56: (pname > $o) > pname > pname > $o).
% 22.77/4.74 thf(func_def_253, type, sK57: hoare_1708887482_state > (pname > hoare_1708887482_state) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_254, type, sK58: (hoare_1708887482_state > $o) > pname).
% 22.77/4.74 thf(func_def_255, type, sK59: ((pname > $o) > pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_256, type, sK60: ((pname > $o) > pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_257, type, sK61: (hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_258, type, sK62: (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_259, type, sK63: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_260, type, sK64: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_261, type, sK65: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_262, type, sK66: pname > $o).
% 22.77/4.74 thf(func_def_263, type, sK67: pname > $o).
% 22.77/4.74 thf(func_def_264, type, sK68: pname > $o).
% 22.77/4.74 thf(func_def_265, type, sK69: hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_266, type, sK70: hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_267, type, sK71: hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_268, type, sK72: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_269, type, sK73: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_270, type, sK74: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_271, type, sK75: pname > com).
% 22.77/4.74 thf(func_def_272, type, sK76: (pname > $o) > (pname > hoare_1708887482_state) > (hoare_1708887482_state > $o) > pname > $o).
% 22.77/4.74 thf(func_def_273, type, sK77: pname > $o).
% 22.77/4.74 thf(func_def_274, type, sK78: pname > $o).
% 22.77/4.74 thf(func_def_275, type, sK79: pname > $o).
% 22.77/4.74 thf(func_def_276, type, sK80: (pname > hoare_1708887482_state) > hoare_1708887482_state > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_277, type, sK81: ((pname > $o) > pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_278, type, sK82: ((pname > $o) > pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_279, type, sK83: (pname > hoare_1708887482_state) > (pname > $o) > (hoare_1708887482_state > $o) > pname > $o).
% 22.77/4.74 thf(func_def_280, type, sK84: state).
% 22.77/4.74 thf(func_def_281, type, sK85: state).
% 22.77/4.74 thf(func_def_282, type, sK86: (pname > $o) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_283, type, sK87: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_284, type, sK88: (pname > $o) > pname).
% 22.77/4.74 thf(func_def_285, type, sK89: ((pname > $o) > $o) > (pname > $o) > pname > $o).
% 22.77/4.74 thf(func_def_286, type, sK90: ((pname > $o) > $o) > (pname > $o) > pname).
% 22.77/4.74 thf(func_def_287, type, sK91: (hoare_1708887482_state > $o) > (hoare_1708887482_state > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_288, type, sK92: (hoare_1708887482_state > $o) > (state > state > $o) > (state > state > $o) > com > state).
% 22.77/4.74 thf(func_def_289, type, sK93: (hoare_1708887482_state > $o) > (state > state > $o) > (state > state > $o) > com > state).
% 22.77/4.74 thf(func_def_290, type, sK94: (state > state > $o) > (state > state > $o) > (hoare_1708887482_state > $o) > (state > state > $o) > (state > state > $o) > com > state).
% 22.77/4.74 thf(func_def_291, type, sK95: (pname > $o) > pname).
% 22.77/4.74 thf(func_def_292, type, sK96: ((hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_293, type, sK97: ((hoare_1708887482_state > $o) > hoare_1708887482_state > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_294, type, sK98: ((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state > $o).
% 22.77/4.74 thf(func_def_295, type, sK99: ((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_296, type, sK100: ((hoare_1708887482_state > $o) > $o) > hoare_1708887482_state).
% 22.77/4.74 thf(func_def_298, type, ph102: !>[X0: $tType]:(X0)).
% 22.77/4.74 thf(f5295,plain,(
% 22.77/4.74 $false),
% 22.77/4.74 inference(avatar_sat_refutation,[status(thm)],[f4758,f5269,f5294])).
% 22.77/4.74 thf(f5294,plain,(
% 22.77/4.74 ~spl101_1),
% 22.77/4.74 inference(avatar_contradiction_clause,[status(thm)],[f5293])).
% 22.77/4.74 thf(f5293,plain,(
% 22.77/4.74 $false | ~spl101_1),
% 22.77/4.74 inference(equality_resolution,[status(thm)],[f4753])).
% 22.77/4.74 thf(f4753,plain,(
% 22.77/4.74 ( ! [X0 : pname] : (((body @ pn) != (body @ X0))) ) | ~spl101_1),
% 22.77/4.74 inference(avatar_component_clause,[status(thm)],[f4752])).
% 22.77/4.74 thf(f4752,definition,(
% 22.77/4.74 spl101_1 <=> ! [X0 : pname] : ((body @ pn) != (body @ X0))),
% 22.77/4.74 introduced(definition,[new_symbols(naming,[spl101_1])],[avatar_definition])).
% 22.77/4.74 thf(f5269,plain,(
% 22.77/4.74 ~spl101_2),
% 22.77/4.74 inference(avatar_contradiction_clause,[status(thm)],[f5268])).
% 22.77/4.74 thf(f5268,plain,(
% 22.77/4.74 $false | ~spl101_2),
% 22.77/4.74 inference(subsumption_resolution,[status(thm)],[f5262,f4757])).
% 22.77/4.74 thf(f4757,plain,(
% 22.77/4.74 ((wt @ y) = $true) | ~spl101_2),
% 22.77/4.74 inference(avatar_component_clause,[status(thm)],[f4755])).
% 22.77/4.74 thf(f4755,definition,(
% 22.77/4.74 spl101_2 <=> ((wt @ y) = $true)),
% 22.77/4.74 introduced(definition,[new_symbols(naming,[spl101_2])],[avatar_definition])).
% 22.77/4.74 thf(f5262,plain,(
% 22.77/4.74 ((wt @ y) != $true)),
% 22.77/4.74 inference(trivial_inequality_removal,[status(thm)],[f5259])).
% 22.77/4.74 thf(f5259,plain,(
% 22.77/4.74 ($true != $true) | ((wt @ y) != $true)),
% 22.77/4.74 inference(superposition,[status(thm)],[f5178,f4739])).
% 22.77/4.74 thf(f4739,plain,(
% 22.77/4.74 ( ! [X0 : com] : (((hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo19817387tate_o)) = $true) | ((wt @ X0) != $true)) )),
% 22.77/4.74 inference(trivial_inequality_removal,[status(thm)],[f4738])).
% 22.77/4.74 thf(f4738,plain,(
% 22.77/4.74 ( ! [X0 : com] : (((wt @ X0) != $true) | ((hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo19817387tate_o)) = $true) | ($true != $true)) )),
% 22.77/4.74 inference(duplicate_literal_removal,[status(thm)],[f4628])).
% 22.77/4.74 thf(f4628,plain,(
% 22.77/4.74 ( ! [X0 : com] : (($true != $true) | ((wt @ X0) != $true) | ($true != $true) | ((hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo19817387tate_o)) = $true)) )),
% 22.77/4.74 inference(definition_unfolding,[status(thm)],[f4210,f4615,f4083])).
% 22.77/4.74 thf(f4083,plain,(
% 22.77/4.74 (hoare_1160767572gleton = $true)),
% 22.77/4.74 inference(cnf_transformation,[status(thm)],[f2897])).
% 22.77/4.74 thf(f2897,plain,(
% 22.77/4.74 (hoare_1160767572gleton = $true)),
% 22.77/4.74 inference(fool_elimination,[status(thm)],[f2896])).
% 22.77/4.74 thf(f2896,plain,(
% 22.77/4.74 hoare_1160767572gleton),
% 22.77/4.74 inference(rectify,[status(thm)],[f1218])).
% 22.77/4.74 thf(f1218,axiom,(
% 22.77/4.74 hoare_1160767572gleton),
% 22.77/4.74 file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',conj_0)).
% 22.77/4.74 thf(f4615,plain,(
% 22.77/4.74 (wT_bodies = $true)),
% 22.77/4.74 inference(cnf_transformation,[status(thm)],[f2103])).
% 22.77/4.74 thf(f2103,plain,(
% 22.77/4.74 (wT_bodies = $true)),
% 22.77/4.74 inference(fool_elimination,[status(thm)],[f2102])).
% 22.77/4.74 thf(f2102,plain,(
% 22.77/4.74 wT_bodies),
% 22.77/4.74 inference(rectify,[status(thm)],[f1219])).
% 22.77/4.74 thf(f1219,axiom,(
% 22.77/4.74 wT_bodies),
% 22.77/4.74 file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',conj_1)).
% 22.77/4.74 thf(f4210,plain,(
% 22.77/4.74 ( ! [X0 : com] : ((wT_bodies != $true) | ((wt @ X0) != $true) | (hoare_1160767572gleton != $true) | ((hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo19817387tate_o)) = $true)) )),
% 22.77/4.74 inference(cnf_transformation,[status(thm)],[f3602])).
% 22.77/4.74 thf(f3602,plain,(
% 22.77/4.74 ! [X0 : com] : ((wT_bodies != $true) | ((wt @ X0) != $true) | (hoare_1160767572gleton != $true) | ((hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo19817387tate_o)) = $true))),
% 22.77/4.74 inference(flattening,[status(thm)],[f3601])).
% 22.77/4.74 thf(f3601,plain,(
% 22.77/4.74 ! [X0 : com] : (((((hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo19817387tate_o)) = $true) | ((wt @ X0) != $true)) | (wT_bodies != $true)) | (hoare_1160767572gleton != $true))),
% 22.77/4.74 inference(ennf_transformation,[status(thm)],[f2867])).
% 22.77/4.74 thf(f2867,plain,(
% 22.77/4.74 ! [X0 : com] : ((hoare_1160767572gleton = $true) => ((wT_bodies = $true) => (((wt @ X0) = $true) => ((hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo19817387tate_o)) = $true))))),
% 22.77/4.74 inference(fool_elimination,[status(thm)],[f2866])).
% 22.77/4.74 thf(f2866,plain,(
% 22.77/4.74 ! [X0 : com] : (hoare_1160767572gleton => (wT_bodies => ((wt @ X0) => (hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ X0) @ bot_bo19817387tate_o)))))),
% 22.77/4.74 inference(rectify,[status(thm)],[f67])).
% 22.77/4.74 thf(f67,axiom,(
% 22.77/4.74 ! [X42 : com] : (hoare_1160767572gleton => (wT_bodies => ((wt @ X42) => (hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ X42) @ bot_bo19817387tate_o)))))),
% 22.77/4.74 file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',fact_66_MGF)).
% 22.77/4.74 thf(f5178,plain,(
% 22.77/4.74 ((hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o)) != $true)),
% 22.77/4.74 inference(trivial_inequality_removal,[status(thm)],[f5156])).
% 22.77/4.74 thf(f5156,plain,(
% 22.77/4.74 ($true != $true) | ((hoare_90032982_state @ bot_bo19817387tate_o @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o)) != $true)),
% 22.77/4.74 inference(superposition,[status(thm)],[f4861,f4366])).
% 22.77/4.74 thf(f4366,plain,(
% 22.77/4.74 ( ! [X0 : hoare_1708887482_state > $o] : (((ord_le777019615tate_o @ bot_bo19817387tate_o @ X0) = $true)) )),
% 22.77/4.74 inference(cnf_transformation,[status(thm)],[f1971])).
% 22.77/4.74 thf(f1971,plain,(
% 22.77/4.74 ! [X0 : hoare_1708887482_state > $o] : ((ord_le777019615tate_o @ bot_bo19817387tate_o @ X0) = $true)),
% 22.77/4.74 inference(fool_elimination,[status(thm)],[f1970])).
% 22.77/4.74 thf(f1970,plain,(
% 22.77/4.74 ! [X0 : hoare_1708887482_state > $o] : (ord_le777019615tate_o @ bot_bo19817387tate_o @ X0)),
% 22.77/4.74 inference(rectify,[status(thm)],[f515])).
% 22.77/4.74 thf(f515,axiom,(
% 22.77/4.74 ! [X366 : hoare_1708887482_state > $o] : (ord_le777019615tate_o @ bot_bo19817387tate_o @ X366)),
% 22.77/4.74 file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',fact_514_bot__least)).
% 22.77/4.74 thf(f4861,plain,(
% 22.77/4.74 ( ! [X0 : hoare_1708887482_state > $o] : (((ord_le777019615tate_o @ X0 @ (image_1116629049_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body))) != $true) | ((hoare_90032982_state @ X0 @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o)) != $true)) )),
% 22.77/4.74 inference(trivial_inequality_removal,[status(thm)],[f4858])).
% 22.77/4.74 thf(f4858,plain,(
% 22.77/4.74 ( ! [X0 : hoare_1708887482_state > $o] : (($true != $true) | ((hoare_90032982_state @ X0 @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o)) != $true) | ((ord_le777019615tate_o @ X0 @ (image_1116629049_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body))) != $true)) )),
% 22.77/4.74 inference(superposition,[status(thm)],[f4541,f4320])).
% 22.77/4.74 thf(f4320,plain,(
% 22.77/4.74 ( ! [X2 : hoare_1708887482_state > $o,X0 : hoare_1708887482_state > $o,X1 : hoare_1708887482_state > $o] : (((hoare_90032982_state @ X2 @ X0) = $true) | ((ord_le777019615tate_o @ X1 @ X2) != $true) | ((hoare_90032982_state @ X1 @ X0) != $true)) )),
% 22.77/4.74 inference(cnf_transformation,[status(thm)],[f3553])).
% 22.77/4.74 thf(f3553,plain,(
% 22.77/4.74 ! [X0 : hoare_1708887482_state > $o,X1 : hoare_1708887482_state > $o,X2 : hoare_1708887482_state > $o] : (((ord_le777019615tate_o @ X1 @ X2) != $true) | ((hoare_90032982_state @ X2 @ X0) = $true) | ((hoare_90032982_state @ X1 @ X0) != $true))),
% 22.77/4.74 inference(flattening,[status(thm)],[f3552])).
% 22.77/4.74 thf(f3552,plain,(
% 22.77/4.74 ! [X0 : hoare_1708887482_state > $o,X1 : hoare_1708887482_state > $o,X2 : hoare_1708887482_state > $o] : ((((hoare_90032982_state @ X2 @ X0) = $true) | ((ord_le777019615tate_o @ X1 @ X2) != $true)) | ((hoare_90032982_state @ X1 @ X0) != $true))),
% 22.77/4.74 inference(ennf_transformation,[status(thm)],[f1645])).
% 22.77/4.74 thf(f1645,plain,(
% 22.77/4.74 ! [X0 : hoare_1708887482_state > $o,X1 : hoare_1708887482_state > $o,X2 : hoare_1708887482_state > $o] : (((hoare_90032982_state @ X1 @ X0) = $true) => (((ord_le777019615tate_o @ X1 @ X2) = $true) => ((hoare_90032982_state @ X2 @ X0) = $true)))),
% 22.77/4.74 inference(fool_elimination,[status(thm)],[f1644])).
% 22.77/4.74 thf(f1644,plain,(
% 22.77/4.74 ! [X0 : hoare_1708887482_state > $o,X1 : hoare_1708887482_state > $o,X2 : hoare_1708887482_state > $o] : ((hoare_90032982_state @ X1 @ X0) => ((ord_le777019615tate_o @ X1 @ X2) => (hoare_90032982_state @ X2 @ X0)))),
% 22.77/4.74 inference(rectify,[status(thm)],[f4])).
% 22.77/4.74 thf(f4,axiom,(
% 22.77/4.74 ! [X8 : hoare_1708887482_state > $o,X7 : hoare_1708887482_state > $o,X6 : hoare_1708887482_state > $o] : ((hoare_90032982_state @ X7 @ X8) => ((ord_le777019615tate_o @ X7 @ X6) => (hoare_90032982_state @ X6 @ X8)))),
% 22.77/4.74 file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',fact_3_thin)).
% 22.77/4.74 thf(f4541,plain,(
% 22.77/4.74 ((hoare_90032982_state @ (image_1116629049_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o)) != $true)),
% 22.77/4.74 inference(cnf_transformation,[status(thm)],[f3181])).
% 22.77/4.74 thf(f3181,plain,(
% 22.77/4.74 ((hoare_90032982_state @ (image_1116629049_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o)) != $true)),
% 22.77/4.74 inference(flattening,[status(thm)],[f2017])).
% 22.77/4.74 thf(f2017,plain,(
% 22.77/4.74 ~((hoare_90032982_state @ (image_1116629049_state @ (^[Y0 : pname]: (hoare_Mirabelle_MGT @ (body_1 @ Y0))) @ (dom_pname_com @ body)) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o)) = $true)),
% 22.77/4.74 inference(fool_elimination,[status(thm)],[f2016])).
% 22.77/4.74 thf(f2016,plain,(
% 22.77/4.74 ~(hoare_90032982_state @ (image_1116629049_state @ (^[X0 : pname] : (hoare_Mirabelle_MGT @ (body_1 @ X0))) @ (dom_pname_com @ body)) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o))),
% 22.77/4.74 inference(rectify,[status(thm)],[f1226])).
% 22.77/4.74 thf(f1226,negated_conjecture,(
% 22.77/4.74 ~(hoare_90032982_state @ (image_1116629049_state @ (^[X217 : pname] : (hoare_Mirabelle_MGT @ (body_1 @ X217))) @ (dom_pname_com @ body)) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o))),
% 22.77/4.74 inference(negated_conjecture,[status(cth)],[f1225])).
% 22.77/4.74 thf(f1225,conjecture,(
% 22.77/4.74 (hoare_90032982_state @ (image_1116629049_state @ (^[X217 : pname] : (hoare_Mirabelle_MGT @ (body_1 @ X217))) @ (dom_pname_com @ body)) @ (insert528405184_state @ (hoare_Mirabelle_MGT @ y) @ bot_bo19817387tate_o))),
% 22.77/4.74 file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',conj_7)).
% 22.77/4.74 thf(f4758,plain,(
% 22.77/4.74 spl101_1 | spl101_2),
% 22.77/4.74 inference(avatar_split_clause,[status(thm)],[f4750,f4755,f4752])).
% 22.77/4.74 thf(f4750,plain,(
% 22.77/4.74 ( ! [X0 : pname] : (((wt @ y) = $true) | ((body @ pn) != (body @ X0))) )),
% 22.77/4.74 inference(superposition,[status(thm)],[f4734,f4200])).
% 22.77/4.74 thf(f4200,plain,(
% 22.77/4.74 ((body @ pn) = (some_com @ y))),
% 22.77/4.74 inference(cnf_transformation,[status(thm)],[f1223])).
% 22.77/4.74 thf(f1223,axiom,(
% 22.77/4.74 ((body @ pn) = (some_com @ y))),
% 22.77/4.74 file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',conj_5)).
% 22.77/4.74 thf(f4734,plain,(
% 22.77/4.74 ( ! [X0 : pname,X1 : com] : (((some_com @ X1) != (body @ X0)) | ((wt @ X1) = $true)) )),
% 22.77/4.74 inference(trivial_inequality_removal,[status(thm)],[f4631])).
% 22.77/4.74 thf(f4631,plain,(
% 22.77/4.74 ( ! [X0 : pname,X1 : com] : (($true != $true) | ((some_com @ X1) != (body @ X0)) | ((wt @ X1) = $true)) )),
% 22.77/4.74 inference(definition_unfolding,[status(thm)],[f4480,f4615])).
% 22.77/4.74 thf(f4480,plain,(
% 22.77/4.74 ( ! [X0 : pname,X1 : com] : ((wT_bodies != $true) | ((some_com @ X1) != (body @ X0)) | ((wt @ X1) = $true)) )),
% 22.77/4.74 inference(cnf_transformation,[status(thm)],[f3454])).
% 22.77/4.74 thf(f3454,plain,(
% 22.77/4.74 ! [X0 : pname,X1 : com] : ((wT_bodies != $true) | ((some_com @ X1) != (body @ X0)) | ((wt @ X1) = $true))),
% 22.77/4.74 inference(flattening,[status(thm)],[f3453])).
% 22.77/4.74 thf(f3453,plain,(
% 22.77/4.74 ! [X0 : pname,X1 : com] : ((((wt @ X1) = $true) | ((some_com @ X1) != (body @ X0))) | (wT_bodies != $true))),
% 22.77/4.74 inference(ennf_transformation,[status(thm)],[f1457])).
% 22.77/4.74 thf(f1457,plain,(
% 22.77/4.74 ! [X0 : pname,X1 : com] : ((wT_bodies = $true) => (((some_com @ X1) = (body @ X0)) => ((wt @ X1) = $true)))),
% 22.77/4.74 inference(fool_elimination,[status(thm)],[f1456])).
% 22.77/4.74 thf(f1456,plain,(
% 22.77/4.74 ! [X0 : pname,X1 : com] : (wT_bodies => (((some_com @ X1) = (body @ X0)) => (wt @ X1)))),
% 22.77/4.74 inference(rectify,[status(thm)],[f298])).
% 22.77/4.74 thf(f298,axiom,(
% 22.77/4.74 ! [X18 : pname,X192 : com] : (wT_bodies => (((body @ X18) = (some_com @ X192)) => (wt @ X192)))),
% 22.77/4.74 file('/export/starexec/sandbox/tmp/tmp.UpDNWdGJVS/DTF2THF_15503.p',fact_297_WT__bodiesD)).
% 22.77/4.74 % SZS output end Proof for DTF2THF_15503
% 22.77/4.74 % (15956)------------------------------
% 22.77/4.74 % (15956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.77/4.74 % (15956)Termination reason: Refutation
% 22.77/4.74
% 22.77/4.74 % (15956)Memory used [KB]: 15863
% 22.77/4.74 % (15956)Time elapsed: 0.214 s
% 22.77/4.74 % (15956)Instructions burned: 680 (million)
% 22.77/4.74 % (15956)------------------------------
% 22.77/4.74 % (15956)------------------------------
% 22.77/4.74 % (15822)Success in time 2.936 s
%------------------------------------------------------------------------------